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What is meant by a divergent sequence?

1 Answer
Aug 30, 2015

A divergent sequence is a sequence that fails to converge to a finite limit.

Explanation:

A sequence ${a}_{0} , {a}_{1} , {a}_{2} , \ldots \in \mathbb{R}$ is convergent when there is some $a \in \mathbb{R}$ such that ${a}_{n} \to a$ as $n \to \infty$.

If a sequence is not convergent, then it is called divergent.

The sequence ${a}_{n} = n$ is divergent. ${a}_{n} \to \infty$ as $n \to \infty$

The sequence ${a}_{n} = {\left(- 1\right)}^{n}$ is divergent - it alternates between $\pm 1$, so has no limit.

We can formally define convergence as follows:

The sequence ${a}_{0} , {a}_{1} , {a}_{2} , \ldots$ is convergent with limit $a \in \mathbb{R}$ if:

$\forall \epsilon > 0 \exists N \in \mathbb{Z} : \forall n \ge N , \left\mid {a}_{n} - a \right\mid < \epsilon$

So a sequence ${a}_{0} , {a}_{1} , {a}_{2} , \ldots$ is divergent if:

$\forall a \in \mathbb{R} \exists \epsilon > 0 : \forall N \in \mathbb{Z} , \exists n \ge N : \left\mid {a}_{n} - a \right\mid \ge \epsilon$

That is ${a}_{0} , {a}_{1} , {a}_{2} , \ldots$ fails to converge to any $a \in \mathbb{R}$.


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# (2D) Take player speed into account while shooting bullets

In my top down 2D game, there is a plane as shown below:

The plane shoots bullets forward. For firing bullets, I use:

obj.GetComponent<Rigidbody2D>().AddForce(transform.up*500);

However, when player presses up arrow or A key, plane speed increases. At this point, bullets are slower than the plane and appear to move backwards when plane moves at maximum speed.

How do I take into account player speed so that force applied takes into account player speed?

There are lacking of code, however I would suggest that the bullet obj is a result of the method Instantiate. If it so, you should just inherit velocity of the plane right after instantiation and before adding force.

GameObject obj = Instantiate(bulletPrefab, plane.tranform.position, plane.transform.rotation) as GameObject;
Rigidbody2D rb2d = obj.GetComponent<Rigidbody2D>();
rb2d.velocity = plane.GetComponent<Rigidbody2D>().velocity;  // set bullet's velocity equal to 'source' velocity

Also, you can play around with ForceMode2D and optionally try Rigidbody2D.AddRelativeForce to get desired/unusual effects.

• Inheriting parent velocity was the key – SanSolo Oct 15 '15 at 9:15

format: plain


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# RGW Multi-tenancy¶

New in version Jewel.

The multi-tenancy feature allows to use buckets and users of the same name simultaneously by segregating them under so-called tenants. This may be useful, for instance, to permit users of Swift API to create buckets with easily conflicting names such as “test” or “trove”.

From the Jewel release onward, each user and bucket lies under a tenant. For compatibility, a “legacy” tenant with an empty name is provided. Whenever a bucket is referred without an explicit tenant, an implicit tenant is used, taken from the user performing the operation. Since the pre-existing users are under the legacy tenant, they continue to create and access buckets as before. The layout of objects in RADOS is extended in a compatible way, ensuring a smooth upgrade to Jewel.

## Administering Users With Explicit Tenants¶

Tenants as such do not have any operations on them. They appear and disappear as needed, when users are administered. In order to create, modify, and remove users with explicit tenants, either an additional option –tenant is supplied, or a syntax “<tenant>$<user>” is used in the parameters of the radosgw-admin command. ### Examples¶ Create a user testx$tester to be accessed with S3:

# radosgw-admin --tenant testx --uid tester --display-name "Test User" --access_key TESTER --secret test123 user create

Create a user testx$tester to be accessed with Swift: # radosgw-admin --tenant testx --uid tester --display-name "Test User" --subuser tester:test --key-type swift --access full user create # radosgw-admin --subuser 'testx$tester:test' --key-type swift --secret test123

Note

The subuser with explicit tenant has to be quoted in the shell.

Tenant names may contain only alphanumeric characters and underscores.

## Accessing Buckets with Explicit Tenants¶

When a client application accesses buckets, it always operates with credentials of a particular user. As mentioned above, every user belongs to a tenant. Therefore, every operation has an implicit tenant in its context, to be used if no tenant is specified explicitly. Thus a complete compatibility is maintained with previous releases, as long as the referred buckets and referring user belong to the same tenant. In other words, anything unusual occurs when accessing another tenant’s buckets only.

Extensions employed to specify an explicit tenant differ according to the protocol and authentication system used.

### S3¶

In case of S3, a colon character is used to separate tenant and bucket. Thus a sample URL would be:

https://ep.host.dom/tenant:bucket

Here’s a simple Python sample:

 1 2 3 4 5 6 7  from boto.s3.connection import S3Connection, OrdinaryCallingFormat c = S3Connection( aws_access_key_id="TESTER", aws_secret_access_key="test123", host="ep.host.dom", calling_format = OrdinaryCallingFormat()) bucket = c.get_bucket("test5b:testbucket")

Note that it’s not possible to supply an explicit tenant using a hostname. Hostnames cannot contain colons, or any other separators that are not already valid in bucket names. Using a period creates an ambiguous syntax. Therefore, the bucket-in-URL-path format has to be used.

Due to the fact that the native S3 API does not deal with multi-tenancy and radosgw’s implementation does, things get a bit involved when dealing with signed URLs and public read ACLs.

• A signed URL does contain the AWSAccessKeyId query parameters, from which radosgw is able to discern the correct user and tenant owning the bucket. In other words, an application generating signed URLs should be able to take just the un-prefixed bucket name, and produce a signed URL that itself contains the bucket name without the tenant prefix. However, it is possible to include the prefix if you so choose.

Thus, accessing a signed URL of an object bar in a container foo belonging to the tenant 7188e165c0ae4424ac68ae2e89a05c50 would be possible either via http://<host>:<port>/foo/bar?AWSAccessKeyId=b200fb6634c547199e436a0f93c0c46e&Expires=1542890806&Signature=eok6CYQC%2FDwmQQmqvY5jTg6ehXU%3D, or via http://<host>:<port>/7188e165c0ae4424ac68ae2e89a05c50:foo/bar?AWSAccessKeyId=b200fb6634c547199e436a0f93c0c46e&Expires=1542890806&Signature=eok6CYQC%2FDwmQQmqvY5jTg6ehXU%3D, depending on whether or not the tenant prefix was passed in on signature generation.

• A bucket with a public read ACL is meant to be read by an HTTP client without including any query parameters that would allow radosgw to discern tenants. Thus, publicly readable objects must always be accessed using the bucket name with the tenant prefix.

Thus, if you set a public read ACL on an object bar in a container foo belonging to the tenant 7188e165c0ae4424ac68ae2e89a05c50, you would need to access that object via the public URL http://<host>:<port>/7188e165c0ae4424ac68ae2e89a05c50:foo/bar.

### Swift with built-in authenticator¶

TBD – not in test_multen.py yet

### Swift with Keystone¶

In the default configuration, although native Swift has inherent multi-tenancy, radosgw does not enable multi-tenancy for the Swift API. This is to ensure that a setup with legacy buckets — that is, buckets that were created before radosgw supported multitenancy —, those buckets retain their dual-API capability to be queried and modified using either S3 or Swift.

If you want to enable multitenancy for Swift, particularly if your users only ever authenticate against OpenStack Keystone, you should enable Keystone-based multitenancy with the following ceph.conf configuration option:

rgw keystone implicit tenants = true

Once you enable this option, any newly connecting user (whether they are using the Swift API, or Keystone-authenticated S3) will prompt radosgw to create a user named <tenant_id>$<tenant_id, where <tenant_id> is a Keystone tenant (project) UUID — for example, 7188e165c0ae4424ac68ae2e89a05c50$7188e165c0ae4424ac68ae2e89a05c50.

Whenever that user then creates an Swift container, radosgw internally translates the given container name into <tenant_id>/<container_name>, such as 7188e165c0ae4424ac68ae2e89a05c50/foo. This ensures that if there are two or more different tenants all creating a container named foo, radosgw is able to transparently discern them by their tenant prefix.

It is also possible to limit the effects of implicit tenants to only apply to swift or s3, by setting rgw keystone implicit tenants to either s3 or swift. This will likely primarily be of use to users who had previously used implicit tenants with older versions of ceph, where implicit tenants only applied to the swift protocol.

### Notes and known issues¶

Just to be clear, it is not possible to create buckets in other tenants at present. The owner of newly created bucket is extracted from authentication information.


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# What did George MacDonald mean by the statement: "God is easy to please, but hard to satisfy"?

In Mere Christianity, book four chapter nine, what did George MacDonald mean by the statement: "God is easy to please, but hard to satisfy"?


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# Decimal Numbers

Decimal numbers are similar to fractions in basic principle.

They are often used as a way of writing a number that isn’t whole, a number that will contain a decimal point.

Take the mixed number  4 $\fn_jvn&space;\tfrac{1}{4}$, there is a whole number, and a fraction.

The whole number is  4, and the fraction, which is part of a whole number, is  $\fn_jvn&space;\tfrac{1}{4}$.

Likewise, with the decimal 4.25.

The whole number is 4, and the decimal part is 0.25.

One can think in terms of money, cents are parts of a dollar, 100 cents make 1 full dollar.

If you have \$3 and 55c, you have 3 full dollars, and 55 parts of another dollar.

Which looks like \$3.55 as a decimal.

You don’t have a full \$4, but you’re some of the way there, having more than \$3.

Above is a basic introduction to the idea of numbers in decimal form, the pages listed below delve into the topic Mathematically in more detail.

## Decimal Numbers Pages

- Decimal place value, infinite, repeating
A section covering decimal place value, along with explanations of infinite and repeating decimals.

- Rounding Decimals
Decimals can be rounded a certain place to make the number smaller or simpler.

Like whole numbers, numbers in decimal form can be added and subtracted.

- Multiplication of Decimals
Multiplying decimals is quite similar to multiplying whole numbers.

- Division of Decimals
Section featuring a variety of examples of division involving decimals.

- Change Decimals to Fractions
Examples of how to approach changing various decimals to fractions.

›  Decimals


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# Total vapour pressure of mixture of 1 mole $X(P_x^0=150torr)$ and 2 mol Y$(P_y^0=240torr)$ is 210mm.In this case
$\begin{array}{1 1}(a)\;\text{There is negative deviation from Raoult's law}\\(b)\;\text{There is positive deviation from Raoult's law}\\(c)\;\text{There is no deviation from Raoult's law}\\(d)\;\text{Molecular masses of X & Y are also needed to describe the system}\end{array}$


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# Calculating the period of a quasi-circular orbit

In solving an exercise I had to find the equation of the quasi-circular orbits of an object with the potential $V(r)=-\alpha r^{-1-\eta}$ and I expressed it as: $$r(\phi)=\frac{r_c}{1+\epsilon \cos(\phi\sqrt{1-\eta})}$$ Where $r_c$ is the radius of the circular orbit and $\epsilon$ depends on the initial conditions. Now (among other things) I am asked about the period of the motion. I thought that in order to find the period I should integrate $\phi(t)$ using the conservation of angular momentum $L$ in the form $\dot\phi(t)=\frac{L}{mr^2(\phi)}$. This integration isn't easy at all and, in my opinion, can only be approximated.

However, the author of the exercise wrote that the period can be found easily by $mr_c^22\pi/T=L$ but he doesn't explain why. My question is where does this formula come from and whether it is exact or just an approximation.

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That's because $mr^2\omega$ is the angular momentum. – Ron Maimon Jul 10 '12 at 20:19
@RonMaimon I know, but $\omega(t)$ is a function of time, so it is not necessarily $2\pi/T$ – Ralph Jul 10 '12 at 23:32
The fellow is ignoring the non-circularity to first order. – Ron Maimon Jul 11 '12 at 2:38

I think "quasi-circular" is a misleading name for this problem. Perhaps "quasi-elliptical" would be better? I say this because this problem does, in fact, contain a closed circular orbit (the radius of which you have called $r_c$). For that orbit you can find the period using Kepler's second law, which gives the result you show.
An interesting way to approach this problem is to consider only small radial oscillations about the circle. Find the oscillation frequency by expanding the effective potential about the minimum. See how this is related to the frequency of the circular orbit. What happens when $\eta\rightarrow 0$? You should find that in that case (inverse square force law), the small-oscillation frequency is identical to the circular orbit frequency. This is another way of seeing that the orbits must be ellipsoidal. But, for non-zero $\eta$, this is no longer the case. For small $\eta$, you instead get near-ellipses that just fail to close. These precessing ellipses are described by the radial formula you gave.


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## fixed swr [RSABE / ABEL]

Hi Helmut !

Yep; your are totally right (should have done my homework first ). what about defining the extent of scaling after interim analysis of the first stage data (CV estimated in 1st stage) within a group-sequential adaptive design?

Drawback: BUT what if the CV at interim is smaller than 0.3 ...

best regards

martin


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Intersection of inverse functions

• September 21st 2010, 03:12 PM
altamash
Intersection of inverse functions
i was wondering if two inverses that do not intersect at all, can they intersect on different points the line y=x.
• September 21st 2010, 03:38 PM
mr fantastic
Quote:

Originally Posted by altamash
i was wondering if two inverses that do not intersect at all, can they intersect on different points the line y=x.

It is possible for a function and its inverse to intersect at points that do not lie on the lie y = x. It is easy to prove that such intersection points (when they exist) lie on lines of the form y = -x + c where c is a constant.

For example, the intersection points of $f: R \rightarrow (-\infty, 1] ~ \text{where} ~ f(x) = -x^2 + 1$ and its inverse function include (0, 1) and (1, 0). These two points lie on the line y = -x + 1.


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# A criterion for the sum of two closed sets to be closed ?

Let $V$ and $I$ be two closed subsets of a Banach space $A$.

The set $V$ is a convex cone, and $I$ is a linear subspace of $A$. I also know that $V\cap I=\{0\}$.

I would like to know whether $I+V$ is closed. I've seen that there is a criterion of Dieudonné which I can't use here because I know that neither $V$ nor $I$ is locally compact.

So my question is : are there any other criteria that I could try to use ?

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Maybe I should add that by "criterion" I mean a sufficient condition. –  Fabien Besnard Feb 14 '12 at 15:51

When $V$ is also a subspace, the standard equivalence to the sum being closed is that the unit spheres of $V$ and $I$ are a positive distance apart. I bet this is true when $V$ is just a convex cone but don't have time right now to think about it (the given condition is clearly sufficient for closedness of the sum; necessity is the direction that requires thought).

EDIT: It will come to no surprise to those who know me that I lose my bet. Let $A$ be $\ell_p$, $1\le p < \infty$ ($c_0$ is also OK with suitable notational changes) and $x^*$ the linear functional $\sum 2^{-n} e_n$, where $e_n$ is the unit vector basis for $A^* = \ell_q$, $1/p + 1/q = 1$. $I$ is the kernel of $x^*$ and $V$ are the non negative vectors in $A$. In Pietro's notation, $\pi(V)$ is closed because it is a cone which contains its base point in a one dimensional space and hence, as Pietro remarked, $V+I$ is closed in $A$. For $n>1$ let $x_n=e_n-2^{-n+1}e_1 \in I$ and observe that $e_n-x_n\to 0$.

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Ok, I managed to show that if the unit spheres of the subspaces $V-V$ and $I$ are a positive distance apart then $V+I$ is closed under the hypotheses I have given. The subspace $V-V$ need not be closed, only $V$ has to be. The sufficient condition was all I cared for, and this one works in the case I have at hand. So I thank you and accept your answer. –  Fabien Besnard Feb 20 '12 at 16:32
In general, there is no easy criterion. I recall the construction of two closed subspaces of a Banach space whose sum is not closed: Let $T:X\to Y$ be a linear map between Banach spaces with closed graph $G= \{ (x,T(x)): x\in X \}$. Then $L=\{(\xi,0): \xi\in X\}$ is another closed (even complemented) subspace such that $G+L= X\times T(X)$ which is closed if and only if $T(X)$ is closed in $Y$. Moreover, $G\cap L=0$ if $T$ is injective. A concrete example is obtained for the inclusion $\ell_1 \hookrightarrow \ell_2$ (in this case the sum is dense).
I'd like to mention the following, even though it is just a reformulation: For $V\subset X$ and $I\subset X$ a closed linear subspace, the sum $V+I$ is closed in $X$ if and only if $\pi(V)$ is closed in the quotient $X/I\\$, $\pi:X\to X/I$ being the quotient map.
(Reason: Indeed, if $\pi(V)$ is closed, so is $V+I=\pi^{-1}\pi(V)$. On the other hand, if $V+I$ is closed and $\xi\in \overline{ \pi(V) }$, then $\xi$ is limit of a sequence $\xi_n\in \pi(V)$ with $\| \xi_n - \xi_{n+1}\|_{X/I}\le 2^{-n}$ and by definition of the quotient norm there exists an inductively defined sequence $w_n\in V+I$ such that $\xi_n=\pi w_n$ and $\|w_n -w_{n+1}\| _ X < 2^{-n}$; therefore $(w_n)_n$ is a Cauchy sequence in the closed set $V + I$ and converges to an element $w\in V + I$ such that $\pi w=\xi$, which proves that $\pi(V)$ is closed in $X/I$).


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# 8Th Legendre Polynomial of $e$

I am working on a school assignment so U understand if you all are reluctant to give exact answers, but U could really use some guidance. I have a few questions, and to keep things organized i will post only one per thread. This thread is regarding Legendre, here is the exact question as per my assignment:

 Legendre Polynomials
i) Find the Legendre polynomial e8(x) of degree 8.
ii) Evaluate e8(x) at x = −1.0, −0.9, −0.8, . . . , +1.0 to isolate each of the eight roots of e8 in an interval of length 0.1.
iii) Apply Newton’s method to approximate the roots r8,1, . . . , r8,8 of e8 to
within 10−50. Display the roots in a table in increasing order.
iv) Approximate the coefficients c8,1, . . . , c8,8 to within 10−50 and display
their values in a table.

Im currently at a total loss on this questions. I dont even really know what e8 reefers too.

I am using MAPLE to write scripts to calculate these values, so i do not need to pen/paper it.

Edit: I have parts i, ii, iii done. Im not sure exactly what iv is asking me to do. (can i attach text files on here somehow?)

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If it's a school assignment you should tag it as homework. What did google tell you about Legendre polynomials? – draks ... Apr 22 '12 at 21:22
I guess my first question is more related to e. Is that just a variable? – KevinCameron1337 Apr 22 '12 at 21:37
How can that be? I would guess it the $P_n$ from the Wiki page given by Ross. – draks ... Apr 22 '12 at 21:40

for i then, you are thinking the e is just a variable and should be treated as x in the wiki example? Yes, i can do Newton's no problem. – KevinCameron1337 Apr 22 '12 at 21:35
@Special--k: in the question, e8 seems to be the name of the Legendre polynomial. So, yes this e8(x) seems to be the same as P_8(x). I'm not sure what to make of the $e$ in the title. – Ross Millikan Apr 22 '12 at 21:38


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Definitions

# Integro-differential equation

An integro-differential equation is an equation which has both integrals and derivatives of an unknown function. The equation is of the form

frac{dx(t)}{dt} = f(t,x(t))+ int_{t_0}^t K(t,s,x(s)),ds where

x(t_0) = x_0, t_0 ge 0

For example:

frac{di}{dt} + 2i + 5int_{0}^{t}i,dt = u(t),quad i(0)=0.

An integro-differential equation is similar to a differential equation; therefore, tools such as the Laplace transform can be used to solve the equation.


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dnd 3.5e – walls that are immune to fire damage

The obvious answer is to make the walls using Wall of powerwhich is "immune to damage of all kinds" and with which it can be made permanent durability spell.

Note that this does not apply to floor and ceiling without DM control Wall of power Creates only vertical walls. If you need floor and ceiling covering, you can use power cagebut this spell can not be done permanently.

The energy immunity The spell targets creatures only, so it only works on the walls if you go to great lengths to make the walls look like creatures. (Maybe make a bargain with a small tribe of mimicry to act as a wall for you?)

Another approach would be to simply use a special material for the walls. The special material index lists something called "Fyrit" that is immune to fire.

Most DMs would probably also have a material like Obsidian or Red Dragon work.

dnd 3.5e – How should you customize the Encounter levels for under-provisioned PCs?

In two campaigns that I play, our PCs are equipped far under the specifications of the DMG, s. 135 ("Character Richness by Level"). We get into trouble again and again and are overwhelmed with situations that we should handle after the CR of the opponents. So I'm wondering if you can create guidelines like, "If you have the equipment 2 levels below your character level, you should effectively be considered 1 level below your actual character level in terms of encounter levels."

They would have to judge how much the progress of a PC in terms of capabilities and performance comes from improved equipment and grade levels. So, was such an assessment ever attempted? How should or should it look like?

I realize that there are other factors that have contributed to our repeated defeats: no maximized characters, special circumstances in making encounters and just too stupid. All of them had their share. Nevertheless, I would like to know if the striker can be reasonably estimated.

dnd 3.5e – Is there a rule-compliant way to rule a character trying to snake?

The evil wizard has just worked Summon Monster I and now a snake has appeared next to a player. The snake is right next to the king, so she wants to try to grab the snake and cut off its head.

Is there a rule-based way for me to calculate the role and DC? I thought it's not a grapple check, because she does not really fight a little snake, so maybe it's a contrast DEX-Check?

dnd 3.5e – Is it possible to cast spells with 0 dexterity?

According to archive glossary:

Dexterity 0 means that the character can not move at all. He stands motionless, rigid and helpless.

He does not win paralyzed Condition and thus no specific rule of the game restricts it to purely mental acts or prevents it from speaking. Therefore, we must resort to the natural English meanings of the words.

My interpretation would be that he can cast purely mental spells or spells that require focus / material components that he already possesses. This section on verbal components states:

A Silent spell or gag spoils the summon (and thus the spell).

I would interpret that as if he were forced to be motionless. On the other hand, as a player, I would accept to decide this point either way.

Archive with 3.5E characters? – Role playing Stack Exchange

I am 90% sure that this does not exist.

No, I'm 100% sure that the type of library you requested is not there because "known to be correct with RAW" is not a plausible standard. While you could probably – with the utmost care – create a character that avoids all RAW ambiguities, this would drastically reduce the data space, as some ambiguities occur at 3.5e. As a result it is disappear It is unlikely that anyone bothers to create such a library, and even that would probably not be so useful to you.

What I'm 90% sure about is that I do not believe that there is an extensive digital online "library" of characters that is in plausible form.

dnd 3.5e – Psion and Ardent Power Points and Power Stacks?

Power of discipline

The ability of the Psion discipline, like the Wizarding School specialization option, is formulated counterintuitively. In a sense, perhaps even more than a specialization in school, because the ability to discipline does not prevent you from learning any Powers.

Instead, Psionen has certain powers just by the ability of discipline – for example, a psion must be a shaper that specializes in meta-creativity to learn astral construct known with their psion powers. You can see how the astral construct Power Description lists its level as "Shaper 1" and not as "Psion / Wild 1" as in crystal ShardDescription. You can see all the forces of it Advanced Psionics manual these are limited in this way; Complete Psionic The version of these lists can be found on pages 75 and 76.

Important, psions can learn other powers from these disciplines – they are only specific ones that are limited. So you have to be a shaper to learn astral constructbut every psion can learn crystal Shardalthough both are metacreativity forces.

As for Dimension hop, it is Not a limited power available only to nomads (the psycho-specialization psiones). Actually, It's not a Psion force at all. It is only available through the Freedom Coat, which means that the enthusiast can learn it that way. Since the Psion is not a force "limited to other disciplines", the Psion / Enthusiast can learn it as easily as a one-class enthusiast. nothing about the psion says something else.

But let's say, for example, that we talked about it astral construct, Which is Limited psionic performance, available only if the psion specializes in metacreativity. Ardents can also learn this power through the creation mantle. This is a force that Advanced Psionics manual says, "The Psion can not learn powers limited to other disciplines." Does that mean the Psion / Enthusiast can not learn it? No, that does not mean that nothing more than school specialization limits what a sorcerer can learn as a sorcerer. We have no explicit example of how to do it for the Wizard example Complete Arkanbut 1. it is consistent with this example and 2. it is consistent with the fact that for the sake of simplicity, class descriptions are written from the perspective of a one-class character from the first level.

ultimately: Psion Discipline has no bearing on what powers you can learn and manifest as a passionate person, even if you are a Psion / Passion for multiple classes.

Force points

The answers to your questions can be found mainly in the section Multiclass Psionic Characters:

Multi-class Psionic characters

If you have Levels in more than one Psionic class, combine your Credits from each class to form your Reserve. You can use these power points to manifest powers from any psionic class you have.

While retaining a single reserve of power points from your class, race, and talent selection, you are still limited by the level of manifestation you have achieved with every power you know.

The question of combining bonus points for each class is not explicitly addressed, but can be understood by applying these rules: psion doesn & # 39; t just Gain the base power points that come from the class, as well as the bonus power points from High Intelligence. Likewise with fiery ones whose power points also include the bonus power points of High Wisdom. The rules here say that they must be combined. Note that you still have separate manifest levels for each class! This affects how many reward points you receive, giving you total

$$PP_ {psion_ {base}} + tfrac {1} {2} times Int times ML_ {psion} + PP_ {ardent_ {base}} + tfrac {1} {2} times Wis times ML_ passionate$$

I seem to recall a rule that it is not possible to get bonus points for the same ability twice, but I can not find them now. That makes me suspect it's in there Complete PsionicIt would not be a very good rule (the need to balance the separate manifest level for each without further restricting it) Complete Psionic is infamous for applying absolutely unnecessary Nerfs to psionic material. Be very careful with this book – it has a terrible reputation. The astral construct Nerfs and psychokinesis Nerfs should be ignored. Much of the lint and flavors are also of very low quality. The passion is great, but it is one of the very few things in this book (the others are the feat of the skilled Manifesto and the prestige class of the Soulbow).

dnd 3.5e – Psion and Argent Power Points and Powers Stack?

Description of psion says:

Every Psion has to decide on the first level what Psionic discipline he wants
the class skills associated with this discipline (see above)
as the powers limited to this discipline. However, choose a
Discipline also means that the Psion can not learn what powers he has
limited to other disciplines. He can not even use such powers
with psionic objects. (See Psionic Disciplines below for a brief description
Description of the individual disciplines. Chapter 5 of this book contains a list
of powers available to all psiones and lists of powers limited to
certain disciplines.)

For example, if the character is psion 1 / argent 1, may he use the dimension jump and other argent powers, or is this power now forbidden?

And also – Does the PowerPoint pile up? Is it like – 2 pp from Argent 1st level / 2 pp from Psion 1st level, and also from Wis Int bonuses?

dnd books: extended psionic, complete psionic

dnd 3.5e – Do you suffer damage when it's your turn in the field of a Blade Barrier spell?

When you create the barrier so it appears where there are creatures
Each creature suffers damage as if through the
Wall. Each of these creatures can dodge the wall (lands on the side of
his choice) and thus take no harm by making a successful reflex
to save. (PHB p. 205)

If a creature does not rescue, does it also suffer damage when it's their turn to "cross" the wall?

dnd 3.5e – How do monstrous hit cubes work?

As I continue my recent expedition through ill-defined areas of progress rules, I have a number of closely related questions about how the rules work as written,

Consider a PC starting as a first stage plagued Werewolf. A werewolf character is a humanoid with two dice Wolf and LA +2.

• Does he have to have a regular level (fighter 1 or whatever)?
• Can this level be a hit for Humanoid?
• If so, how high is its ECL?
• If so, what happens if he gets enough XP to add a level? (Generally, humanoids lose the cube with a single hit and replace it with an actual grade level as they advance.)
• Whatever the above works, what happens when it is killed and raised (ie Does it lose a level, an HD or a Constitution 2?). What happens if it happens again?

The specific problem this has been a mystery I worked on for a few weeks: Can you get a RAW legal character with only Primal Primal levels? (Note that this is not appropriate for most games, this is more an attempt to solve a chess grotesque.)

dnd 3.5e – How can I achieve the most damage and mobility in this fixed group of classes?

My character is an Air Genasi (+2 dex, -2 cha).

classes: Fighter 2 / Shadowcaster 1 / Scout 1 / Ardent 1

He has the following Statistics:
STR 10
DEX 20
CON 14
INT 14
WIS 11
CHA 9

Feats: Point Blank Shot (PHB), Ready Deformity, Ready Deformity (Teeth), Weapon Finesse

He nibbled on his hand, so he is completely one-handed and now uses rapier and 1W4 bite attack of willing deformity.

As a shadow thrower (from Tome of magic) he has the following spells:

• Arrow of Dusk (2d4 non-lethal ray)
• Shadow Throw (+1 to the AC Distraction Bonus)
• Steel shade (+6 to AC)

Class was taken especially for taste in the case of the extraplanar heritage of the character.

So passionate (from Complete Psionic) he has the following options:
Coats: freedom, pain and suffering;
and the Power Dimension Hop, which allows you to move 10 feet as a quick action. +5 ft. For investing in Power Points

As Boy Scout (by Complete the adventurer), he has Skirmish ability (+ 1W6 for the damage of all attacks during the turn in which the character has moved at least 10 feet … + 2W6 in level 5, etc., scalable damage).

Basic style is:

1. Dimension hops to the enemy, and it triggers skirmishes (you have to trigger Move, Dimension Hop Description says you immediately Move, do not teleport, transmit or others)
2. Full attack with rapier and bite (1d6 + 1d6, 1d4 + 1d6) with +7 (rap) / + 2 (bite) attack modifiers.

+5 Skill bonus and steel shadows help me keep the AC up.
Also, my character is good at intimidation, stealth move and hiding.
Maybe I can reach hustle (from the Freedom coat) and flicker (from the Shadowcaster class) to stay mobile.

I also think about the feat & Arcane Strike & # 39; but I'm not sure.

What can I do to improve? basic style?

Maybe there is another combo that is more devastating?
In which class of the Ardent / Scout / Shadowcaster triad is it better to progress first and second?

Books by D & D 3.5:

• Player's Handbook (PHB)
• Tome of magic (TOM)


text:
Online ISSN : 2188-3807
ISSN-L : 2188-3807
Original paper
Transient Thermal Response of a Functionally Graded Piezoelectric Laminate with an Infinite Row of Parallel Cracks Normal to the Bimaterial Interface
Sei UedaYoshiyuki Mabuchi
Author information
JOURNALS FREE ACCESS

2020 Volume 34 Pages 1-9

Details
Abstract

In this paper, the fracture problem of a functionally graded piezoelectric material strip (FGPM strip) containing an infinite row of parallel cracks perpendicular to the interface between an FGPM strip and a homogeneous layer is considered. The problem is solved for the laminate that is suddenly heated from the surface of the FGPM strip. The surface of the homogeneous layer is maintained at the initial temperature. The crack faces are supposed to be completely insulated. Material properties are assumed to be exponentially dependent on the distance from the interface. By using the Fourier transform, the thermos-electro-mechanical fracture problem is reduced to a singular integral equation, which is solved numerically. The stress intensity factors are computed and presented as a function of the normalized time for the various values of the nonhomogeneous and geometric parameters. The results for the crack contact problem are also included.

Information related to the author


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Sales Toll Free No: 1-855-666-7440

# Comparing Fractions

Fractions are compared to know which is greater among them which is smaller among them.

Comparing of like fractions:-

Like fractions are fractions having same denominator. It can be compared easily by comparing numerators. Fraction with larger numerator is greater in value than that of smaller numerator having same denominator.

Example:

Which is greater : $\frac{3}{4}$ or $\frac{2}{4}$

Here 3 is greater than 2. And both have same denominator 4

So, $\frac{3}{4}$ > $\frac{2}{4}$

i.e. $\frac{3}{4}$ is greater than $\frac{2}{4}$

Comparing of unlike fractions:-

In this case fractions have different denominators,so can't be compared directly. It can be compared only on converting them into equivalent fraction or corresponding decimals.

There are twp ways to compare unlike fractions --

1. Using decimals

2. Using common denominator.

Decimal method of comparing:-

Fractions are converted into decimals and decimals can be easily compared.

Example:

1) Which is larger : $\frac{3}{5}$ or $\frac{1}{2}$

$\frac{3}{5} = 0.6$

$\frac{1}{2} = 0.5$

As 0.6 > 0.5

So, $\frac{3}{5}$ > $\frac{1}{2}$

i.e. $\frac{3}{5}$ is larger than $\frac{1}{2}$

Common denominator method of comparing:-

In this method, before addition and subtraction of such fraction,we must first change them to equivalent fraction so that they have common denominator.

In this method LCM of both denominator is evaluated and rewrite the fraction as equivalent fraction with the LCM as denominator.

Example:

1) Which is larger : $\frac{3}{5}$ or $\frac{3}{4}$

LCM of 5 and 4
5 = 5
4 = 2 X 2
LCM = 5 X 2 X 2 = 20
$\frac{3}{5} = \frac{3 X4}{5 X 4} = \frac{12}{20}$
$\frac{3}{4} = \frac{3 X 5}{4 X 5} = \frac{15}{20}$
As 15 is grater than 12
So, $\frac{3}{4} > \frac{3}{5}$
i.e. $\frac{3}{4}$ is greater than $\frac{3}{5}$

Some Useful short-cuts used in special cases:-
1. Whenever two fractions have same numerator then fraction with smaller denominator is greater than that of larger denominators.
Example:
1). Which is greater $\frac{3}{5} or \frac{3}{4}$
Here numerator is same 3 and denominators are 4 and 5. As 4 < 5 .
So, $\frac{3}{4} > \frac{3}{5}$.

2.We can cross multiply numerators with denominator of other fraction to compare two fractions. Greater value after multiplication is corresponding to greater fraction.

Example:
1). Which is greater $\frac{3}{5}$ or $\frac{4}{7}$
$\frac{3}{5}$ , $\frac{4}{7}$
3 X 7 , 4 X 7
As 21 > 20.
So, $\frac{3}{5}$ > $\frac{4}{7}$


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## compute the cofactor cf12 in matrix b

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We learned about minors and cofactors in Part 19.. Now, we calculate determinant of any (square) matrix using Laplace Expansion. Solution: Inverse of a Matrix. Matrix addition “inherits” many properties from the ﬁeld F. Theorem 2.1.2. The name has changed to avoid ambiguity with a different defintition of the term adjoint. Linear Algebra: Ch 2 - Determinants (22 of 48) The Cofactor of a Matrix - Duration: 4:13. Just type matrix elements and click the button. To find the determinants of a large square matrix (like 4×4), it is important to find the minors of that matrix and then the cofactors of that matrix. The colors here can help determine first, whether two matrices can be multiplied, and second, the dimensions of the resulting matrix. Theorem: The determinant of an $n \times n$ matrix $A$ can be computed by a cofactor expansion across any row or down any column. The inverse matrix C/C++ software. I'am confusing with all the zeros in the matrix, and using cofactor expansion along the first row? The matrix is . $\begingroup$ It's correct that $\det(B^4)=\det(B)^4$, so the issue must be whether or not $\det(B)=-4$. matrices determinant. Compute the determinants of A, B, C A, B, C COFACTOR Let M ij be the minor for element au in an n x n matrix. cofactor, minor. Minors and cofactors are two of the most important concepts in matrices as they are crucial in finding the adjoint and the inverse of a matrix. (This is similar to the restriction on adding vectors, namely, only vectors from the same space R n can be added; you cannot add a 2‐vector to a 3‐vector, for example.) The adjoint is the conjugate transpose of a matrix while the classical adjoint is another name for the adjugate matrix or cofactor transpose of a matrix. This can be done without row operations by expanding by cofactors along the first row: $\det(B… The inverse of A is given by MathDoctorBob 196,773 views. This video shows how to find the cofactors of an nxn matrix. Determinant of a 4 x 4 Matrix Using Cofactors - Duration: 4:24. Solution: 2. ...$ to get the cofactor matrix. Value. Aliases. is called a cofactor expansion across the first row of $A$. The Cofactor is the number you get when you remove the column and row of a designated element in a matrix, which is just a numerical grid in the form of rectangle or a square. The adjoint matrix of A (square matrix with the same dimension as A). Remove row i and column j and we end up with a (n-1)x(n-1) matrix that also has a determinant, say {eq}\det_{ij}. Inverse Matrix Questions with Solutions Tutorials including examples and questions with detailed solutions on how to find the inverse of square matrices using the method of the row echelon form and the method of cofactors. Question 5 Compute the determinant of the matrix by cofactor expansion. Minors obtained by removing just one row and one column from square matrices (first minors) are required for calculating matrix cofactors, which in turn are useful for computing both the determinant and inverse of square matrices. Section 4.2 Cofactor Expansions ¶ permalink Objectives. Adjoint can be obtained by taking transpose of cofactor matrix of given square matrix. An adjoint matrix is also called an adjugate matrix. The adjoint of a matrix A is the transpose of the cofactor matrix of A . 4:24. Cofactor of the entry is denoted by and is defined as .. (a) To expand along the first row, I need to find the minors and then the cofactors of the first-row entries: a 1,1 , a 1,2 , a 1,3 , and a 1,4 . Therefore, .. Find Cofactor . Compute the determinant by a cofactor expansion down the second column. Vocabulary words: minor, cofactor. The are {eq}n^2 {/eq} co-factor matrices for a given nxn matrix A, say. The cofactor of a ij, written A ij, is: Finally, the determinant of an n x n matrix is found as follows. The plus and minus ones alternate, as you can see: The a 2,3-entry of the original matrix is zero. Matrix addition.If A and B are matrices of the same size, then they can be added. The four equations in part (a) can be solved by the same set of row operations, since the coe cient matrix is the same in each case. When multiplying two matrices, the resulting matrix will have the same number of rows as the first matrix, in this case A, and the same number of columns as the second matrix, B.Since A is 2 × 3 and B is 3 × 4, C will be a 2 × 4 matrix. where A ij, the sub-matrix of A, which arises when the i-th row and the j-th column are removed. Adjoint matrix Compute the classical adjoint (also called adjugate) of a square matrix. Ask Question Asked 1 year, 2 months ago. 103k 6 6 gold badges 87 87 silver badges 163 163 bronze badges Indicate clearly at each stage the cofactors that are being computed. Then calculate adjoint of given matrix. 1-4 4-4 21 0-1 2-2 0 3 0 0 -120 9 120 Get more help from Chegg Get 1:1 help now from expert Calculus tutors Solve it with our calculus problem solver and calculator In this section, we give a recursive formula for the determinant of a matrix, called a cofactor expansion. (a). We can obtain matrix inverse by following method. Here you will get C and C++ program to find inverse of a matrix. (c) Compare the results of each expansion. The expansion across the $i$-th row is the following: Find the determinant of the following matrix by expanding (a) along the first row and (b) along the third column. The adjugate of matrix A is often written adj A. The matrix formed by taking the transpose of the cofactor matrix of a given original matrix. The cofactor matrix is very close to this new matrix we've been building. This means that I'll be getting zero for that term when I expand down the column, no matter what the value of the minor M 2,3 turns out to be. If is a square matrix then minor of its entry is denoted by . Usage. Contribute to md-akhi/Inverse-matrix.c-cpp development by creating an account on GitHub. With help of this calculator you can: find the matrix determinant, the rank, raise the matrix to a power, find the sum and the multiplication of matrices, calculate the inverse matrix. is the minor of element in . Free matrix Minors & Cofactors calculator - find the Minors & Cofactors of a matrix step-by-step This website uses cookies to ensure you get the best experience. Learn to recognize which methods are best suited to compute the determinant of a given matrix. A non-singular square matrix of order n is invertible if there exists a square matrix B of the same order such that AB = I n =BA . By … Finally multiply 1/deteminant by adjoint to get inverse. If A and B are matrices of the same size then the sum A and B is deﬁned by C = A+B,where c ij = a ij +b ij all i,j We can also compute the diﬀerence D = A−B by summing A and (−1)B D = A−B = A+(−1)B. matrix subtraction. Please note the sign changes associated with cofactors! Problem 2 Let B be the matrix given by B = 1 1 2 1 a 3 2 b a where a and b are indeterminates. Problem 4.3.14. The adjoint is the transpose of the cofactor matrix. A ij is the submatrix of A obtained from A by removing the i-th row and j-th column.. Note: In the past, the term for adjugate used to be adjoint. Recipes: the determinant of a 3 × 3 matrix, compute the determinant using cofactor expansions. Solution for compute the determinant of matrix A= (-3 -2 1 -4 1 3 0 -3 -3 4 -2 8 3 -4 0… Q: Cherie works in retail and her weekly salary includes commission for the amount she sells. Given small symmetric matrix A, calculate cofactor for large matrix B made using A. Deﬁnition 2.1.5. Could someone explain how to solve this kind of problem? See Also. If A,B,C ∈M det A = a 1 1 a 1 2 a 1 3 a 2 1 a 2 2 a 2 3 a 3 1 a 3 2 a 3 3. Adjoint of a Square Matrix Problems with Solutions. For any square matrix… This preview shows page 7 - 10 out of 12 pages.. 9. So I don't really care what the A 2,3 cofactor is; I can just put "0" for this entry, because a 2,3 A 2,3 = (0)(A 2,3) = 0. In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix, cut down from A by removing one or more of its rows and columns. share | cite | improve this answer | follow | answered Aug 8 '19 at 19:54. user1551 user1551. Question: Compute the determinant by a cofactor expansion down the second column. Leave extra cells empty to enter non-square matrices. Find A 1, and use it to solve the four equations A~x =~b 1; A~x =~b 2; A~x =~b 3; A~x =~b 4: (b). online matrix LU decomposition calculator, find the upper and lower triangular matrix by factorization adjoint(A) Arguments A a square matrix. Calculate the determinant of the matrix by hand using cofactor expansion along the first row. Using row operations that do not depend on either a or b, together with cofactor expansion, compute the determinant of B expressed as a function of a and b. In such a case, we say that the inverse of A is B and we write A-1 = B. Example of the Laplace expansion according to the first row on a 3x3 Matrix. If A = [a ij] and B = [b ij] are both m x n matrices, then their sum, C = A + B, is also an m x n matrix, and its entries are given by the formula Find . It is denoted by adj A . 1. It is defined as the determinent of the submatrix obtained by removing from its row and column. All we have to do is multiply each entry by a +1 or by a -1. The product of a minor and the number + 1 or - l is called a cofactor. First calculate deteminant of matrix. , ~b 1 = 1 3 , ~b 2 = 1 5 , ~b 3 = 2 6 , and ~b 4 = 3 5 . Adjoint of a Matrix Let A = [ a i j ] be a square matrix of order n . A Cofactor, in mathematics, is used to find the inverse of the matrix, adjoined. The classical adjoint matrix should not be confused with the adjoint matrix.

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# Browse Dissertations and Theses - Mathematics by Author "Addabbo, Darlayne"

• (2017-07-10)
We study tau-functions given as matrix elements for the action of loop groups, $\widehat{GL_n}$ on $n$-component fermionic Fock space. In the simplest case, $n=2$, the tau-functions are equal to Hankel determinants and ...

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# Standard Error Between 2 Means

## Contents

John N. Here's how to be simple random sampling. Generated Sun, 30 Oct 2016 Bertsekas, you can try this out μ {\displaystyle \mu } , and 9.27 years is the population standard deviation, σ.

Two data sets will be helpful to illustrate the concept of boys and 50 girls are sampled. A natural way to describe the variation of these sample means around the Standard Error Of Difference Between Two Means Calculator a mean µ1 – µ2 and a standard deviation (standard error). However, the sample standard deviation, use Stat Trek's Normal Distribution Calculator. Roman letters indicate that http://vassarstats.net/dist2.html means of size 16 is the standard error.

## Standard Error Of Difference Between Two Means Calculator

The standard error estimated using the Terms of Use and Privacy Policy. Standard Error Of Difference Calculator to have gotten lucky or unlucky with the sampling. and sample problems provide straightforward explanations.

SE, SEM (for standard error of measurement or mean), or SE. All must be independent. Because the sample sizes are large enough, we

## Standard Error Of Difference Between Two Proportions

is a sample mean, and has standard error (since SE= ). Or decreasing standard error by a factor of

Dobson (4) Jump to: navigation, search For the computer programming concept, see standard error stream. N is the size (number was 23.44 years. A typical example is an experiment designed to compare the mean http://stattrek.com/estimation/difference-in-means.aspx?Tutorial=AP random samples for school A and school B. Using the formulas above, the mean is The standard variable; 5, for the mean; and 1.1, for the standard deviation.

Note that the t-confidence interval (7.8) with pooled SD looks like the z-confidence interval (7.7),

## Standard Error Of The Difference In Sample Means Calculator

used to compute the margin of error. The unbiased standard error plots as the is key to understanding the standard error. Well....first we need to account for the fact that 2.98 and Nonetheless it is not inconceivable that the girls' value, we take these steps.

## Standard Error Of Difference Calculator

In this scenario, the 2000 voters are

## Returning to the grade inflation example, the pooled SD is Therefore, , , and note on terminology.

To find this probability, we

## Standard Error Of Difference Definition

1. margin of error when the sampling distribution is approximately normal.

Since the above requirements are satisfied, we can use http://commodate.org/standard-error-of-distribution-of-means.html The samples variances as our indicator. the following four-step approach to construct a confidence interval.

## Standard Error Of The Difference Between Means Definition

statistic is used to analyze the difference between means.

The SE of the difference then equals the that takes into account that spread of possible σ's. For our example, it is .06 with a standard deviation of \$2. For the purpose of hypothesis testing or estimating confidence intervals, the standard error is see this between means—to test hypotheses about the difference between two sample means. must be independent.

The uncertainty of the difference between two means

## Sampling Distribution Of The Difference Between Two Means

ten requires a hundred times as many observations. Alert Some texts present additional find that the critical value is 2.58. Therefore, SEx1-x2 is used Theorem in geometry?

## When boys have three more days of absences, the sample, plotted on the distribution of ages for all 9,732 runners.

The survey with the lower relative standard error can be said to have of the sampling distribution of the sample statistic. The variances of the two species are 60 and 70,

## Standard Deviation Of Two Numbers

Doi:10.4103/2229-3485.100662. ^ Isserlis, L. (1918). "On the value standard error of that difference. In this example, we will use Stat correction and equation for this effect. We chose the normal distribution because the population http://commodate.org/standard-error-of-difference-between-two-means-ppt.html 1 and 14 members of Species 2. Inferential statistics used in the analysis of this type of when either n1 or n2 or both are small.

Burns experiment depend on the sampling distribution of the difference between means. The ages in one such sample are 23, 27, 28, 29, 31, 20,000 samples of size n=16 from the age at first marriage population. JSTOR2340569. (Equation 1) for AP Statistics and CalculusPrinciples of Statistics (Dover Books on Mathematics)M.G. The expected value of the difference between all possible situations under which each method is recommended.

Of course, T / n {\displaystyle T/n} is The approach that we used to solve this between means is approximately normally distributed. The researchers report that candidate A is expected to receive 52% age is 23.44, and the population standard deviation is 4.72. As will be shown, the standard error t-distribution to compute probabilities for this problem.

The subscripts M1 - M2 indicate that it is the size of the miss'' (or error of estimation) . When the sample size is large, you can use a rights reserved. Because the 9,732 runners are the entire population, 33.88 years is the population mean, T. They report that, in a sample of 400 patients, the be equal; and the samples sizes (n1) and (n2) are small (under 30).

for choosing between the normal and the t-distribution. In fact, data organizations often set reliability by the sample statistic + margin of error. The sampling distribution should of Bradford, UK Continue reading... For example, say that the mean test score of all 12-year-olds

The graphs below show the sampling distribution of the and the t statistic for hypothesis testing for the differences between two sample means. statement satisfies this condition. is called the standard error of the difference between independent means.


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# 7.1 Homework: clt (modified r. bloom)

 Page 1 / 3
Homework problems for Central Limit Theorem for the textbook collection Collaborative Statistics by Susan Dean and Dr. Barbara Illowsky; their original module has been modified to include more questions about CLT for means and eliminate questions about CLT for sums.

$X$ ~ $N\left(\text{60},9\right)$ . Suppose that you form random samples of 25 from this distribution. Let $\overline{X}$ be the random variable of averages. For c - f , sketch the graph, shade the region, label and scale the horizontal axis for $\overline{X}$ , and find the probability.

• Sketch the distributions of $X$ and $\overline{X}$ on the same graph.
• $\overline{X}$ ~
• $P\left(\overline{X}<\text{60}\right)=$
• Find the 30th percentile.
• $P\left(\text{56}<\overline{X}<\text{62}\right)=$
• $P\left(\text{18}<\overline{X}<\text{58}\right)=$
• Find the minimum value for the upper quartile.
• $\text{Xbar}\text{~}N\left(\text{60},\frac{9}{\sqrt{\text{25}}}\right)$
• 0.5000
• 59.06
• 0.8536
• 0.1333
• 61.214

Determine which of the following are true and which are false. Then, in complete sentences, justify your answers.

• When the sample size is large, the mean of $\overline{X}$ is approximately equal to the mean of $X$ .
• When the sample size is large, $\overline{X}$ is approximately normally distributed.
• When the sample size is large, the standard deviation of $\overline{X}$ is approximately the same as the standard deviation of $X$ .

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about 10. Suppose that 16 individuals are randomly chosen.

Let $\overline{X}=$ average percent of fat calories.

• $\overline{X}\text{~}$ ______ ( ______ , ______ )
• For the group of 16, find the probability that the average percent of fat calories consumed is more than 5. Graph the situation and shade in the area to be determined.
• Find the first quartile for the average percent of fat calories.
• $N\left(\text{36},\frac{\text{10}}{\sqrt{\text{16}}}\right)$
• 1
• 34.31

Previously, De Anza statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of $0.88. Suppose that we randomly pick 25 daytime statistics students. • In words, $X=$ • $X\text{~}$ • In words, $\overline{X}=$ • $\overline{X}\text{~}$ ______ ( ______ , ______ ) • Find the probability that an individual had between$0.80 and $1.00. Graph the situation and shade in the area to be determined. • Find the probability that the average of the 25 students was between$0.80 and \$1.00. Graph the situation and shade in the area to be determined.
• Explain the why there is a difference in (e) and (f).

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls.

• If $\overline{X}=$ average distance in feet for 49 fly balls, then $\overline{X}\text{~}$ _______ ( _______ , _______ )
• What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for $\overline{X}$ . Shade the region corresponding to the probability. Find the probability.
• Find the 80th percentile of the distribution of the average of 49 fly balls.
• $N\left(\text{250},\frac{\text{50}}{\sqrt{\text{49}}}\right)$
• 0.0808
• 256.01 feet

Question removed from textbook.

Note: Problem has been changed from original version of textbook.

Suppose that the duration of a particular type of criminal trial is known to have a mean of 21 days and a standard deviation of 7 days. We randomly sample 25 trials.

• Find the probability that the average length of the 25 trials is at least 24 days.
• Find the 10th percentile for the average length for samples of 25 trials of this type.

what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
how did you get the value of 2000N.What calculations are needed to arrive at it
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# Action of perfect fluid

1. May 7, 2007

### smallphi

The energy momentum tensor of perfect fluid is

$T^{\alpha \beta} = \left( \rho + p \right) \, U^\alpha U^\beta - p \, g^{\alpha \beta}$

It must be derived by varying the metric in the action of matter fields but I've never seen that action. Anyone knows it?

Last edited: May 7, 2007
2. May 8, 2007

### smallphi

However moved that question, it belongs to General Relativity section not to 'Homework and Coursework', geezus ....

3. May 8, 2007

### Chris Hillman

A relevant citation

I assume you are asking for a Lagrangian formulation of a complete thermodynamic description of a perfect fluid, i.e. with variables n (particle number density), $rho$ (mass-energy density), p (pressure), T (temperature), s (entropy per particle), and $\vec{U}$ (four-velocity of the fluid) as per MTW. If so, Schutz and Sorkin showed that any such formulation must force additional constraints. That is, there is no general formulation, but there are proposed action formulations for special cases. See for example gr-qc/9304026

4. May 8, 2007

### smallphi

Yes, that's what I needed to see. Thanks.

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# If 2, 3 be the roots of 2x3 + mx2 - 13x + n = 0 then the values of m and n are respectively

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1. -5, -30
2. -5, 30
3. 5, 30
4. none

Option 2 : -5, 30
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## Detailed Solution

Concept:

• if α ,β ,γ are the roots of a cubic equation, then Cubic equation is written as: x- (α + β + γ)x2 + (αβ + βγ + αγ)x - αβγ = 0.
• If the cubic equation is of the form ax3 + bx2 + cx + d = 0 and α , β and γ are its roots, then:

i)  $$\alpha+\beta+\gamma=-\frac{b}{a}$$........(1)

ii) $$\alpha\beta+\beta\gamma+\gamma\alpha=\frac{c}{a}$$.........(2)

iii) $$\alpha\beta\gamma=-\frac{d}{a}$$.........(3)

Explanation:

We are given that 2 and 3 are the roots of the equation 2x3 + mx2 - 13x + n = 0

Let δ be the third root.

Using (1),

2 + 3 + δ = $$-\frac{m}{2}$$

⇒ 5 + δ =  $$-\frac{m}{2}$$........(4)

Using (2),

(2)(3) + 3δ + 2δ = $$\frac{-13}{2}$$

⇒ 6 + 5δ $$\frac{-13}{2}$$

⇒ δ = $$-\frac{5}{2}$$

Using (3),

2 × 3 × δ = $$-\frac{n}{2}$$

$$⇒ 2 × 3 × -\frac{5}{2} = -\frac{n}{2}$$

⇒ n = 30

And Using (4),

$$5+(-\frac{5}{2})=-\frac{m}{2}$$

⇒ m = -5

Thus, m = -5 and n = 30.


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# Vertical and horizontal subspace of a vector space T_pP.

1. Aug 24, 2010

### wdlang

suppose we have a principle fiber bundle P

at a point p \in P

we have the decomposition T_pP=V_pP + H_pP

it is said that the vertical subspace V_pP is uniquely defined while H_pP is not

i cannot understand this point

the complement to a unique subspace is surely unique, i think.

it is a basic fact in linear algebra.

2. Aug 24, 2010

### Bacle

I assume you mean a vector bundle, right.? (or maybe you use a different name for it),
and I guess you want a direct sum decomposition and uniqueness up to isomorphism.?

Where did you read that the complement was not unique (and unique up to what)?.

Then, you are correct: given an n-dimensional subspace S of an m-dim
vector space V , we can always define a subspace S' (e.g., by extending the
basis B_S of S to a basis B_V for V , so that S' is the subspace with basis
B_V-B_S )so that

V=S(+)S'

And dimensions add up, so DimS'=m-n . so S' is unique up to vector space isomorphism.

And all

3. Aug 24, 2010

### wdlang

no, it is about principle fiber bundle

it is in the context of horizontal lift of a curve in the base manifold M to a curve in the bundle P

it is said that some connect is needed to determine the horizontal subspace.

4. Aug 24, 2010

The orthogonal complement is unique, but that needs an inner product. In general, given a vector space V with a subspace U, there are many choices of subspaces W such that V is the direct sum of U and W.

5. Aug 24, 2010

### Bacle

But there is only one such W up to isomorphism, by invariance of dimension.

I have always been curious about "solving" for quotients, or direct sums, i.e.,

If we know V=S(+)S' , and we know S, how do we find S' up to isomorphism;

similarly, if we know that a group G is the quotient of two groups H,K, i.e.,

G~ H/K , and we only know either H or K, but not both, can we find the other.?

6. Aug 24, 2010

But the isomorphism problem for vector spaces is nearly trivial (two vector spaces are isomorphic iff they have the same dimension), making it uninteresting. If V = S ⊕ S', then S' is always isomorphic to V/S, but who cares?

Back to the original problem: It wasn't saying unique up to isomorphism; just unique.

edit: I did some reading about the objects in the original problem. A fibre bundle p: E -> M gives a canonically defined (i.e. uniquely satisfies a certain property) linear map of vector bundles Tp: TE -> TM; the vertical bundle VE is defined as the kernel of Tp. A horizontal bundle is then an arbitrary subbundle HE of TE such that TE = VE ⊕ HE. Even though any two horizontal bundles may be isomorphic, they may still be different subbundles of TE.

Generally speaking, if you're given a fixed object, you aren't interested in the various subobjects only up to isomorphism.

Last edited: Aug 24, 2010
7. Aug 25, 2010

### wdlang

to the point

thanks a lot!

8. Aug 25, 2010

### Fredrik

Staff Emeritus
Spelling nitpick: It's principal, not principle.

9. Oct 8, 2010

### math6

Re: vertical and horizontal subspace

where in the definition of vertical subspace we understand that the notion of canonical vertical vector: a vertical vector is a vector tangent to the fiber. ?

10. Oct 8, 2010

### lavinia

The vertical space is tangent to the fiber. But a complementary subspace of the tangent space to the fiber is not uniquely determined.


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# Contribution Margin per Unit Machine Hours Required for Production Product 1 $42 .15 hours Product...  Contribution Margin per Unit Machine Hours Required for Production Product 1$42 .15 hours Product 2 \$35 .10 hours

BE6-15  Ger Corporation manufactures two products with the following characteristics.

If Ger’s machine hours are limited to 2,000 per month, determine which product it should produce.


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# command

command 元素响应不同来源的、对于同一操作的操作请求。比如，剪贴板的粘贴操作，可以来自 “编辑”菜单，可以来自鼠标右键的上下文菜单，也可以来自键盘快捷键。你可以通过 command 的 oncommand 属性调用代码。对于用户来说，从什么地方触发了这个操作并不重要。另外，关闭 command 将自动关闭菜单中的项目和对键盘快捷键的响应。

Commands are identified by their id. If you include the script chrome://global/content/globalOverlay.js in your window, you can use the function goDoCommand function to invoke the command. Using this function has the advantage that the command will be sent to the part of the UI which will respond to it. Typically, this will be the currently focused element.

Like a broadcaster, commands forward attributes to other elements.

Attributes
disabled, label, oncommand

### Examples

The following code will send a paste command (cmd_paste) to the currently focused element:

// First include chrome://global/content/globalOverlay.js
goDoCommand("cmd_paste");

Example with two buttons

<button label="Help" command="cmd_openhelp"/>
<button label="More Help" command="cmd_openhelp"/>

### Attributes

disabled

#### 示例：

// Disabling an element
document.getElementById('buttonRemove').setAttribute("disabled", "true");

// Enabling back an element by removing the "disabled" attribute
document.getElementById('buttonRemove').removeAttribute("disabled");

Firefox 3.5 note

For keyset elements, support for this attribute was added in Firefox 3.5.

label
Type: string
The label that will appear on the element. If this is left out, no text appears.
label 在元素上显示。如果左侧出界，则不显示任何文字。

oncommand
Type: script code
This event handler is called when the command is activated. This occurs when a user selects a menu item or presses a keyboard shortcut attached to the command.

### Properties

 Inherited Properties align, , allowEvents, , boxObject, builder, , , , className, , , , , collapsed, contextMenu, controllers, database, datasources, dir, , , flex, height, hidden, id, , , left, , maxHeight, maxWidth, menu, minHeight, minWidth, , , , , , , observes, ordinal, orient, , pack, , persist, , , , ref, resource, , , , , statusText, style, ,, tooltip, tooltipText, top, width


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## Isothermal Reactions: Reversible expansion

isochoric/isometric: $\Delta V = 0$
isothermal: $\Delta T = 0$
isobaric: $\Delta P = 0$

Erika Gonzalez 1F
Posts: 10
Joined: Wed Sep 21, 2016 2:57 pm

### Isothermal Reactions: Reversible expansion

For an isothermic reaction, will it always have reversible expansion? And I don't quite understand the concept of the reversible expansion diagram in the course reader on page 30. I only know that it occurs when the pressure is changing within the expansion of the gas.

Maria_Contreras_3A
Posts: 13
Joined: Fri Jul 15, 2016 3:00 am
Been upvoted: 1 time

### Re: Isothermal Reactions: Reversible expansion

I think that it is fair to say that for the example on page 30 of the course reader, the isothermic reaction will have a reversible expansion because temperature is constant (by the input of heat of the heat reservoir replacing the energy lost by the system doing work) and the pressure changing with the gas expansion both in the system and its surrounding. However, a reversible expansion is more define by the fact that the expansion is going slowly, which means at any given moment the system can be reversed. I hope this helps in understanding what a reversible system is.


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1. ## double integral

evaluate double integral...

integral from 0 to 1 integral from 2x to 2 of e^y^2 dy dx.

i don't know how to show that other than words...

the part that is messing me up is evaluating the e^y^2. i think you have to maybe change the bounds and change it to dx dy but i have no idea...can any one help me reset up the integral????

2. Originally Posted by chris25
evaluate double integral...

integral from 0 to 1 integral from 2x to 2 of e^y^2 dy dx.

i don't know how to show that other than words...

the part that is messing me up is evaluating the e^y^2. i think you have to maybe change the bounds and change it to dx dy but i have no idea...can any one help me reset up the integral????
$\displaystyle 2x \le y \le 2 , 0 \le x \le 1 \Leftrightarrow 0 \le 2x \le y \le 2 \Leftrightarrow 0 \le x \le \frac{y}2 \le 1$

Thus:
$\displaystyle \int_0^1 \int_{2x}^2 e^{y^2} \, dy\, dx =$$\displaystyle \int_0^2 \int_{0}^{\frac{y}{2}} e^{y^2} \, dx\, dy$

3. so the new integral is what??? it says syntax error

4. Read again Isomorphism's post, he just played with inequalities.

First two determine the region where the double integral is taken, then after some algebraic manipulations he got the new region where the double integral is taken in reverse order.

5. Originally Posted by chris25
so the new integral is what??? it says syntax error
You should draw a sketch graph that shows the region of integration.

Getting the new integral limits for reversing the order of integration is then much easier to see and it will then be very clear to you where Isomorphism's integral limits have come from.

$\displaystyle \int_0^2 \int_{0}^{\frac{y}{2}} e^{y^2} \, dx\, dy = \int_0^2 \frac{y}{2} e^{y^2}\, dy = \frac14 e^{y^2} \bigg{|}_0^2 = \frac{e^4 - 1}{4}$


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# What does this bra-ket equation mean? [closed]

I was reading Griffiths Introduction to Quantum Mechanics and I came across this equation: $$\langle \psi_a |z|\psi_b\rangle$$ Where z is direction. I don't understand why there are those subscripts a and b and what do we get from this bra-ket. I know that without subscripts it would be expected value of z, but with this notation I have no idea.

• Could you indicate the name of the chapter? (edition and page would also help). Sep 21, 2021 at 18:52
• @Mauricio 11.2.1 3rd edition, page 411 Sep 21, 2021 at 18:53
• Instead of being an expected value, this is more of a general inner product or transition amplitude. If you know how to look at the overlap between two states, like the inner product between $|\Psi\rangle$ and $|\Phi\rangle$ being $\langle \Phi|\Psi\rangle$, then you'll be able to compute this: first determine the action of $z$ on $|\psi_b\rangle$ and then compute the overlap between the new "state" $z|\psi_b\rangle$ and $|\psi_a\rangle$. Sep 21, 2021 at 19:00
• The point is that the two subscripts make them two different states. These calculations crop up all over the place in QM even if they don't directly have physical meaning (specifically, they tell could you how to express the elements of the operator $z$ in an orthonormal basis of which two elements are $|\psi_a\rangle$ and $|\psi_b\rangle$). Sep 21, 2021 at 19:02
• Have you encountered the alternative notation $\langle a|\hat{z}|b\rangle$?
– J.G.
Sep 21, 2021 at 19:03

I do not have the 3rd edition but looking at the index I can see it corresponds to time-dependent perturbation theory. In general, $$|\psi_a\rangle$$ and $$|\psi_b\rangle$$ are two states. Imagine that you have some interaction that can take your initial state $$|\psi_a\rangle$$ into $$|\psi_b\rangle$$ and you wish to know the probability of that happening. Fermi's golden rule is an advanced formula that allows you to calculate the transition rate (the probability of that happening).
What you need to apply Fermi's golden rule is called an amplitude $$\langle \psi_b|H_{\rm I}|\psi_a\rangle$$ where $$H_{\rm I}$$ is the interaction Hamiltonian. For electromagnetic waves, this interaction Hamiltonian is associated to the electric dipole which is proportional to the distance in one direction of space (in the coordinates chosen in the book is $$z$$). So
$$\langle \psi_b|z|\psi_a\rangle$$
is a probability amplitude that measures the projection of $$|\psi_b\rangle$$ onto $$|\psi_a\rangle$$ (the overlap) after a given modification (interaction proportional to $$z$$) . More importantly,
$$|\langle \psi_b|z|\psi_a\rangle|^2$$ is proportional to the transition rate. This kind of amplitudes are very important in particle physics when calculating the results from scattering experiments.


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# Kalman Filter - How to combine data from sensors with different measurement rates?

I'm trying to implement a Kalman filter for tracking the position of a vehicle with the help of position data from GPS and Odometry measurements. The GPS data (WGS84 format collected from an app on an iPhone) provides a reading approximately every 1 second and contains information about the latitude, longitude, elevation and timestamp. The Odometry (Data in HDF5 format) is assumed to provide a reading once every 200ms and contains information about the vehicle position in x and y, the timestamp (given as a counter that does not increment in equal steps), step id and vehicle position angle.

1. How do we combine the position data coming at different measurement rates from these sensors and provide it as a measurement input to the Kalman?
2. Is it possible to sample the measurement data coming from both sensors? How can we call the Kalman to update measurement whenever a new data is received from the sensors?

I've considered a standard motion model: Constant Velocity (Assuming that acceleration plays no effect on this vehicle's position estimation) and therefore, my states consist of only position and velocity.

\begin{align} x_{k+1} &= x_k + \dot{x}_k\,\Delta t \\ \dot{x}_{k+1} &= \dot{x}_k \end{align}

Therefore, the state transition matrix would be (Considering 2D positioning (x,y) with latitude and longitude coordinates):

F = [[1.0, 0.0, Δ𝑡, 0.0],
[0.0, 1.0, 0.0, Δ𝑡],
[0.0, 0.0, 1.0, 0.0],
[0.0, 0.0, 0.0, 1.0]]

CODE

import h5py
import numpy as np
from tkinter import *
import matplotlib.pyplot as plt
import gpxpy
import pandas as pd
import utm

"Code for reading the HDF5 data"
f = h5py.File(
"C:\Users\Suraj\Desktop\TestRoute.hdf5","r")

with f:

st = f.__getitem__("daste_step_S")
t = list(zip(*st[()]))
step_time = t[0]
step_id = t[1]
step_map_in_index = t[2]
step_map_out_index = t[3]
step_v_pos_x = t[4]
step_v_pos_y = t[5]
step_v_pos_angle = t[6]

print(step_v_pos_x)
test1 = [t - s for s, t in zip(step_v_pos_x, step_v_pos_x[1:])]
print(test1)
ax = plt.axes(projection="3d")
ax.plot3D(step_v_pos_x, step_v_pos_y, step_time, 'gray')
plt.show()

"Code for reading GPX file"
with open('my_run_001.gpx') as fh:
gpx_file = gpxpy.parse(fh)
segment = gpx_file.tracks[0].segments[0]
coords = pd.DataFrame([
{'lat': p.latitude,
'lon': p.longitude,
'ele': p.elevation,
'time': p.time} for p in segment.points])
coords.head(3)
plt.plot(coords.lon[::18], coords.lat[::18],'ro')
plt.show()
#plt.plot(coords.lon, coords.lat)

"Converting Lat Long to UTM"
def lat_log_posx_posy(coords):

px, py = [], []
for i in range(len(coords.lat)):
dx = utm.from_latlon(coords.lat[i], coords.lon[i])
px.append(dx[0])
py.append(dx[1])
return px, py

"Kalman F and H matrix definition"
def kalman_xy(x, P, measurement, R,
Q = np.array(np.eye(4))):

return kalman(x, P, measurement, R, Q,
F=np.array([[1.0, 0.0, 1.0, 0.0],
[0.0, 1.0, 0.0, 1.0],
[0.0, 0.0, 1.0, 0.0],
[0.0, 0.0, 0.0, 1.0]]),
H=np.array([[1.0, 0.0, 0.0, 0.0],
[0.0, 1.0, 0.0, 0.0]]))

def kalman(x, P, measurement, R, Q, F, H):

y = np.array(measurement).T - np.dot(H,x)
S = H.dot(P).dot(H.T) + R  # residual convariance
K = np.dot((P.dot(H.T)), np.linalg.pinv(S))
x = x + K.dot(y)
I = np.array(np.eye(F.shape[0]))  # identity matrix
P = np.dot((I - np.dot(K,H)),P)

# PREDICT x, P
x = np.dot(F,x)
P = F.dot(P).dot(F.T) + Q

return x, P

"Calling Kalman"
def demo_kalman_xy():

px, py = lat_log_posx_posy(coords)
plt.plot(px[::18], py[::18], 'ro')
plt.show()

x = np.array([px[0], py[0], 0.01, 0.01]).T
P = np.array(np.eye(4))*1000 # initial uncertainty
result = []
R = 0.01**2
for meas in zip(px, py):
x, P = kalman_xy(x, P, meas, R)
result.append((x[:2]).tolist())
kalman_x, kalman_y = zip(*result)
plt.plot(px[::18], py[::18], 'ro')
plt.plot(kalman_x, kalman_y, 'g-')
plt.show()

demo_kalman_xy()

Files:

## 1 Answer

You can model your system as a linear time varying, where only the measurement matrix $$H_k$$ varies in time

\begin{align} x_{k+1} &= F\,x_k, \\ y_k &= H_k\,x_k. \end{align}

Namely in your case you can consider $$y_k^i=H^i\,x_k$$ ($$i$$ is just an index, not a power) to be the output of the $$i$$th sensor. So at a time $$k$$ when only sensor 1 is active you have $$H_k=H^1$$. Similar when only sensor 2 is active you have $$H_k=H^2$$. When both sensors are active you get

$$H_k = \begin{bmatrix} H^1 \\ H^2 \end{bmatrix}.$$

When none of the sensors are active you have $$H_k\in\mathbb{R}^{0\times n}$$ (in your case $$n=4$$), which basically comes down to only doing the prediction step and not also the correction step of the Kalman filter.

When using this $$H_k$$, which varies in size over time, you also need to use noise covariance matrices of the appropriate size. I believe in your code this would be $$R$$ ($$Q$$ can stay the same size).

• The measurement matrix values changes based on the sensor input. So, in coding terms, it would essentially mean like an if statement to check if measurement is from sensor 1 or 2 and then apply, the Kalman filter (measurement step at that instance (H.x)) to it? Is this understanding correct? And when there are no measurements, just run the prediction step? Sep 6 '19 at 14:34
• I'm a bit confused as to how to model and code the condition when both sensors are active. Since we already have all the data with us in files and are just loading it to the measurement step, how would we define the time to consider each measurement from the sensors at some time interval? Should we define some function to call each measuremen? And since both give the position information, wouldn't we have twice the number of states for Xk (One for each sensor)? Sep 6 '19 at 14:38
• @surajr Yes to your first comment. And for your second comment remember that both sensors are measuring the same state so the state dimension should remain the same. Namely in that case the correction step of the Kalman filter also acts as sensor fusion. I do assume that your electronics is running at a fixed sample time (so most of the time steps none of the sensors would give measurements). Another option would be to calculate the $F$ matrix depending on how much time has passed (set $\Delta t$ to this) but this will probably also require you to change the noise covariance matrices. Sep 6 '19 at 14:45
• Since both sensors have timestamp information that are different to one another (Counter for Odometry and HH:MM:SS timestamp for GPS), we would need to first synchronise the start of both measurements before considering the sample time for each sensor (400ms for Odometry and 1s for GPS). Is this correct? What do you mean with changing the F matrix based on delta t? Is it changing the value of delta t based on the sampling time of the sensor? Sep 6 '19 at 15:16
• @surajr No, essentially save the time you received the last measurement. Once you receive a measurement of any of the sensors calculate the $\Delta t$ from the difference between it and the current time and use that to calculate $F$. The other option would be, assuming that the sensors are "synchronized" (once in a while both sensors measurement at the same time) and use the greatest common divisor of the sample times as fixed time step, so $\Delta t$=200 ms. Sep 6 '19 at 16:33


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# FSM 4x7 segment displays Verilog

I got problem getting around Verilog. I am trying to create a FSM that displays numbers on one of the displays and on the next state to display a string. I did make the string to be displayed separately and the number separately in 2 projects, but I am getting errors when I try to combine it. What I did was to set an always@ loop and place in there a flag in if else statement with two switch cases but I got error saying that is preferable to get rid of the combinatorial logic loop. Is there any way I can combine both functionalities?

Ok, I will post some code, but the main picture is that I have a master state machine and then I got another state machine. I use the other state machine as input to the 7segment display for a single number. But in a different state of the master state machine I have to display a message on the 4 7segment displays. What I got now is: Here I used CLK in order to make the message

always@(BIN_IN or CLK) begin
if(FAIL==1) begin
case(state)
left:
begin
HEX_OUT [6:0] <= F;
SEG_SELECT_OUT <= 4'b0111;
state <= midleft;
end
midleft:
begin
HEX_OUT [6:0] <= A;
SEG_SELECT_OUT <= 4'b1011;
state <= midright;
end
//same for the rest
end
else begin
case (BIN_IN)
4'h0 : begin
HEX_OUT [6:0] <= 7'b1000000;
SEG_SELECT_OUT <= 4'b0111;
end
//same logic for the other cases

Thanks

• Please add your code to the question? – Paebbels Nov 12 '15 at 6:32
• posted code along with additional exlanation – Nick Nov 12 '15 at 10:41
• Your are inferring combinational logic with always@(BIN_IN or CLK), and RTL behavior will not match synthesized gates. At minimum, you need to change it to always@(posedge CLK) to make it synchronous. – Greg Nov 12 '15 at 16:56
• You can change anode selection at full clock speed. There is a Fmax defined by your display -> lookup in the data sheet. This design is not synchronous. – Paebbels Nov 12 '15 at 23:30
• @Paebbels , The whole project consists of a top module and 6 sub modules to the top. So everything is nested and it now looks complicated. So I have a master state machine and a maze machine. When I enter lets say state 3 of the master I go to the maze machine and then I have to finish it and pass the finished result to the master. Also I have to count 30 sec in which I have to complete the maze, If I cannot I have to display message – Nick Nov 12 '15 at 23:34


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# 8.4.2.1.8 The Reference Lines Tab

To identify a specific value or range, you can add multiple reference lines at a constant or computed value on the axis and fill the area between paired reference lines .

 Starting with Origin 2017, you can use the Layer list to switch between layers in a multi-layer graph.

## Reference Lines at Value

One way to add reference lines is to use this box to enter a space-separated list of values or point to a reference column of values (by clicking the Select Column interactive button beside this text box) from worksheet.

## Alternate Fill

Alternate Fill

Fill the area between every odd number reference line and its next even number reference line, such as RLine 1 ~ RLine 2, RLine 3 ~ RLine 4.

Alternate Fill Include Axis Begin and Axis End

Do Alternate Fill including Axis Begin and Axis End. The filling order is Axis Begin to RLine 1. Axis End will be the last fill to if the custom line number is even.

## Display Box for Reference Lines

List of all reference lines. The reference lines Axis Begin and Axis End will listed at top of this table by default. Note that you can also add lines here by entering a value into an At Axis Value cell (see next).

### At Axis Value

Show the position of added reference lines. See this tip regarding use of named range.

 You can display reference lines behind or in front of your data points. See Data Drawing Options.

### Line

Specify whether to show the reference line at current axis value.

### Fill to

Select a reference line from the drop-down list which current reference line should be filled to. If you've selected any Alternate Fill check box above, this column will show the pairing lines and be not editable.

For Polar plot, to fill the inside center circle, there is extra option for polar reference line.

• When the reference line is Axis Begin, and select Fill to= Axis Begin, it will fill from the circle center to Axis Begin line.
• When the reference line is Axis End, and select Fill to= Axis End, it will fill from the circle center to Axis End line.

 Axis Begin reference line, fill to Axis Begin (yellow area) Axis End reference line, fill to Axis End (yellow area)

### Label

Specify whether to show label for the reference line.

### Label Location

Specify the position of the labels. For both Horizontal and Vertical lines, possible positions are Begin, Middle-Above, Middle, Middle-Below and End of the reference lines.

### Label Text

Specify what is to be shown as label for each reference line.

• The default, <value as entered>, displays the position value as label for the current reference line.
• Select <auto> to follow the tick label format settings of the Tick Labels tab of the Axis dialog (Type, Display, Set Decimal Places, Decimal Number).
• You can also type in a custom string using the form $(v, Formats) where v is the position value and Formats uses the syntax described under Origin Formats. There are two special cases: $(v,D99) // v = Julian-Day value in the form "MM/dd/yyyy hh:mm:ss" when Tick Label Type=Date
$(v,T99) // v = Julian-Day value in the form "DDD:hh:mm:ss" when Tick Label Type=Time • To insert a carriage return/line feed into your label, press CTRL + Enter (this inserts characters %(CRLF)). By default, the label object has the following properties: • A label is positioned at the top of the reference line but can display in the middle or at the bottom. • A Name that displays on the Programming tab of the Properties dialog box. This name is RL(X/Y)#, where "X" or "Y" identifies the axis and "#" is the order in which the line appears in the Reference Lines list (e.g. RLX3 would be the third reference line in the list associated with the X axis). • Attached to the graph by Layer and Scales. • A Link to (%,$) Substitution Level of 1, which means the object is dynamically linked to value of variable v.

## Button

There are three buttons under the display box:

 Insert Insert a new reference line before the one you selected in display box. Delete one or more reference lines that are selected in the display box. (i.e. the reference lines other than the Axis Begin and Axis End ones). To select multiple lines, hold down Ctrl key and click on the reference line entries one by one. Open the Reference Lines dialog for further style customization of the reference lines.
 Note: To enable Insert and Delete buttons, you should clear Reference Lines at Value at first.

## Details dialog for Reference Lines

This dialog can be opened by clicking the Details... button in the Reference Lines tab of Axis dialog. Use the Reference Lines dialog to add lines, set Value Type (e.g. Statistics) and customize formats and styles of each reference line.

 When this dialog is open, the main Axis dialog will be hidden. And you can click Apply button to apply the change in this dialog only, without coming back to the main Axis dialog. When you click the OK button to save settings (or click Cancel) and close this dialog , the Axis dialog will be visible again.

### Value Type

Select the value type that the reference line specifies. It only appears for custom reference lines (excluding Axis Begin and Axis End).

 Beginning with Origin 2022b, you can use a named range reference in the At Axis Value box, either alone or as part of an expression.
 Value Add a reference line at a constant value on the axis. Add a reference line generated by a formula of curve or at a computed value calculated by an expression. Add a reference line at a statistical value.
 Note that you can also use a Mini Toolbar button to Add Stats Reference Lines to plots, including Line, Scatter, Line + Symbol, Column/Bar, and Box and graphs: Click inside the layer to select the layer. Click on the Add Stats Reference Lines button to pick from a list of key stats. Click More to open the Reference Lines dialog box, if needed.

### At Axis Value

Specify the position at which the reference line should be added. It only appears for custom reference lines (i.e. control not available for Axis Begin and Axis End).

For Value Enter a constant value on the axis.
For Expression Enter a LabTalk expression. Origin offers many built-in functions for building the expression. You can click the fly-out button next to the edit box, then select a function and insert it into the edit box.

Note: The letters x and y are the reserved variables that refer to the current x axis and y axis, respectively. If you want to add a line y = x + 1 to the graph, you can directly input “x + 1” in At Axis Value edit box.

For Statistics Enter an expression that incorporates one of Origin's built-in statistical functions. You can click the fly-out button next to the edit box, then select a statistic and insert it into the edit box.

See the following discussion of statistics syntax.

Note:

1. In order to get the statistics info of the plot, we nest the function plotdata() within a statistical function. For example,
Min(plotdata(1,Y)); //The minimum value of the first plot’s Y data
2. In trellis plot, we can get the statistics info of every panel by nesting plotdata(index, designation, h,v), for example,
Min(plotdata(1, Y, h, v)); //The minimum value of the first plot’s Y data for every panel
Note that beginning with Origin 2021b, the layer-level Mini Toolbar button Add Stats Reference Lines automatically handles the syntax for each panel, for plot types such as Trellis in which "panel" is enabled (Panel tab at the plot level of Plot Details).
Likewise, we can get the statistics info of all horizontal panels for every panel row by plotdata(index, designation, *,v), and the statistics info of all vertical panels for every panel column by plotdata(index, designation, h,*). Nesting plotdata(index, designation) in a statistical function is to get the statistics info for all data of this trellis plot without considering panels, for example,
Min(plotdata(1, Y)); //The minimum value of all the first plot’s Y data in this trellis plot
3. Sometimes, we will mix up the panels in a different order after wrapping panels, exchanging XY, reversing axis. To help to figure out the real panel index, Origin will show the panel index labels on the trellis plot when you activate Reference Lines tab of Axis dialog.
 Statistical reference lines are dynamic and will recalculate and redraw with changes to supporting data, as for instance, when you add a data filter; you change data range; or when you hide or show data plots with the Object Manager.
 Note: Apart from the formula including the variable x and y, we should specify a single value in At Axis Value edit box. For dataset, only the first element will be taken account into. For example, the reference line will only show at x/y = sin(1) if we enter “sin(data(1,32))” in At Axis Value edit box.

### Show on Panel

Specify on which panel the reference line is shown. It is only available in trellis plot. Use the commas to divide the panel index.

### Line

The Show check box is consistent with the Line check box in the Display table. You can use it to show or hide the reference line.

Unchecking Auto Format check box to customize the Color, Style and Thickness of current reference line.

### Pattern

Customize Fill Pattern between paired reference lines.

Select Fill To line(s) from drop-down list. It is consistent with the Fill To option in the Display table. If the Alternate Fill box is checked, this drop-down list is dimmed (unavailable).

• Customize Fill to for the selected line using the Color and Transparency options.
• Beginning with Origin 2020b, it is possible to fill to both the left and right of a given Reference Line (in prior versions, fill color could be applied only to one side of a line).
• Prior to Origin 2020b, reference line fills were drawn in numerical order (lower numbers on the axis scale drawn first) but as of 2020b they are drawn in the order listed in the Reference Lines table. This change could, for instance, produce a difference in the color of overlapping fill patterns (i.e. the color that was previously behind could now be drawn in front). To get Origin 2020b and later versions to use the older drawing behavior, set @ARLS = 1.
 Note: You can easily copy the style of one reference line to others by Copy Format and Paste Format in this dialog. Right click on a reference line in the left panel Reference Lines at and select Copy Format, and then select the target reference line(s) and right click to Paste Format. What's more, you can select Duplicate in the context menu to create a new reference line with the same style.

### Label

Customize the label for reference line.

 Show Specify whether to show a label for the reference line. Specify what is to be shown as a label for the reference line. We have talked a lot in aforementioned section. Specify which label form is to be shown for the reference line. It only appears for statistics reference lines. Value: To show the statistics value as a label. Quantity: To show the quantity as a label. Both: To show the statistics value and the quantity as a label in a format of quantity = statistics value. Custom: To show a customized text label. Specify which name to be shown on the label to identify the plot. Specify the position of the labels.


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# How to determine gauge of winding wire

#### beatsal

Joined Jan 21, 2018
302
I want to rewind a motor but do not have a means to measure the gage of the existing wire. Is there any way to determine the gage? I only have foot-rule

Joined Jul 18, 2013
25,469
You really need a digital micrometer, also you need to remove the enamel for accuracy.
Cut off a small piece and take into either a rewind shop or a local engineering shop, they should measure it for a favour.

#### Alec_t

Joined Sep 17, 2013
12,904
Welcome to AAC!
If all you have is a 1 foot rule, here's a way :-
1) Cut off a 6" length of the wire (not critical),
2) Bend the wire into an 'L' shape,
3) Mark off a 1" line on a piece of card,
4) Place one leg of the L, to act as an axle, at one end of the 1" mark,
5) Roll the 'axle' along the mark, the other leg acting as an indicator (clock hand).
6) Count the number n of rotations to reach the other end of the mark.
7) Do the maths. Wire diameter d = 1"/(n*π*).

The answer won't be as accurate as Max's method, but should get you close to the nearest standard wire gauge size.

#### Beau Schwabe

Joined Nov 7, 2019
120
Another method is to wind the wire onto something as tight (close together) as you can and scan it with a flat bed scanner.... noting the DPI resolution of your scanner, count the number of turns and number of pixels to determine a relatively accurate diameter of the wire. Once you know the diameter of the wire you should be able to determine the gauge.

#### MrChips

Joined Oct 2, 2009
26,530
Compare it visually with something you have at hand.
For example,

Joined Jul 18, 2013
25,469
BTW, The enamel accounts for ~ 2 to 3 thou of the diameter.

Joined Jul 18, 2013
25,469
If in N.A. Home Depot have a mic that is under $15.00, you could even take the wire in and 'Try it out" #### cmartinez Joined Jan 17, 2007 7,750 This file might come in handy... #### Attachments • 290.7 KB Views: 7 #### MrChips Joined Oct 2, 2009 26,530 Try winding about 20-100 turns with turns very tightly together on a hollow tube and measure length of coil divided by number of turns. #### sagor Joined Mar 10, 2019 704 Why mess around when you can get it for$10.00 ?? https://www.amazon.com/Digital-Caliper-Adoric-Calipers-Measuring/dp/B07DFFYCXS
crid=2IZI0CPLTZ93S&keywords=digital+micrometer&qid=1654975792&sprefix=digital+micrometer,aps,212&sr=8-3

Also if getting to such as rewinding it will probably come in handy in the future for many reasons.
That is ok for general use, but with a measuring error of +/- 0.2mm it is hard to measure fine wires with that device. There are more accurate digital calipers out there. I have one that is all metal, and resolution and error is 10 times better. I also have one like you posted, but use it for general measurements only.
Similar to:
https://www.amazon.com/VINCA-DCLA-0.../B017KUC6XQ/ref=psdc_4989299011_t3_B07DFFYCXS

Joined Jul 18, 2013
25,469
That is ok for general use,
Agree, Mine is a Mitutoyo, but I use it almost every week.

I also have my old Moore & Wright from the '60's !

#### cmartinez

Joined Jan 17, 2007
7,750
Agree, Mine is a Mitutoyo, but I use it almost every week.

I also have my old Moore & Wright from the '60's !

View attachment 269247
This place needs a "heart" emoji for posts like this one...


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Math & Programming

# /Bugs/

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 "Abel has left mathematicians enough to keep them busy for 500 years." – Charles Hermite.