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Or rather, what can the shapes of proofs tell us about them?

 April CACM source

Juris Hartmanis did much to lay the landscape of computational complexity beginning in the 1960s. His seminal paper with Richard Stearns, “On the Computational Complexity of Algorithms,” was published 50 years ago this month, as observed by Lance Fortnow in his blog with Bill Gasarch. It is a great achievement to open a new world, but all the more mysterious that after 50 years so much of its landscape remains unknown.

Today we ask what might determine the unseen topography and how much some recent large-data discoveries may help to map it.

The idea for this post arose from a possibly phantom memory that Juris (co-)wrote a short draft survey on “Shapes of Computations” sometime in 1986–1989 when I was at Cornell. I recall the specific phrase “long and skinny” to describe space-bounded computations. An ${\ell = O(\log n)}$ space-bounded computation can explore all of a polynomial ${p(n)}$-sized undirected graph by saving just the current node and some ${O(\log n)}$ auxiliary information by which to choose a neighbor for the next step. The trace of this computation becomes an ${\exp(\ell)}$-length sequence of ${\ell}$-bit strings. A polynomial-space computation doing an exponential search of a game tree has the same long-and-skinny “shape” even though the scale is greater with regard to the input length ${n}$. Polynomial time-bounded computations, however, can use polynomial space, whereupon they become “short and fat.” Breadth-first search of a graph is a canonical algorithm that hogs space for its relatively short duration.

Which computations fall between these “Laurel and Hardy” extremes? For SAT and the other ${\mathsf{NP}}$-complete problems, this is the great question. The surest way to separate ${\mathsf{NP}}$ from ${\mathsf{P}}$ and from ${\mathsf{PSPACE}}$ would be to characterize these problems by a third distinct shape of computation. But we have not even separated ${\mathsf{P}}$ from ${\mathsf{PSPACE}}$, nor logspace from ${\mathsf{NP}}$, so what can we pretend to know?

## Shapes of Proofs

My memory has probably been transferred from a column Juris wrote with his students Richard Chang, Desh Ranjan, and Pankaj Rohatgi for the May 1990 issue of the Bulletin of the EATCS. It has this nice diagram:

The analogy between computations and proofs has been instrumental since the early days of Kurt Gödel and Alonzo Church and Alan Turing. Proofs do, however, give nondeterminism “for free”; ${\mathsf{NP}}$ is treated the same as ${\mathsf{P}}$ in their diagram, ${\mathsf{NEXP}}$ same as ${\mathsf{EXP}}$, while “nondeterministic polynomial space” equals ${\mathsf{PSPACE}}$. Hence I’ve regarded “proofs” as secondary to “computations” as objects for complexity. However:

• We have a lot more examples of proofs, going back before Euclid;

• The search for a proof is computational;

• Interactive proofs reflect a two-player game setting where the emphasis is more on solving; and

• We now have examples of large computer-generated proofs to analyze.

The EATCS column defines a notion of width of a proof, characterizes ${\mathsf{PSPACE}}$ via polynomial width proofs, and marvels at how the classic interactive protocol for ${\mathsf{IP = PSPACE}}$ retains the “skinny” shape with less length. Indeed, in cases where the verifier is able directly to check evaluations of the unique multilinear extension ${\hat{f}}$ of the arithmetization ${f}$ of a quantified Boolean formula, every proof step involves just two terms ${a_i x_i + b_i}$ for the rounds ${i = 1}$ to ${n}$. A related form of skinniness had been brought out by Jin-Yi Cai and Merrick Furst in their 1987 paper, “${\mathsf{PSPACE}}$ Survives Three-Bit Bottlenecks.” The column goes on to emphasize that the ${\mathsf{IP}}$ form of the proof lends itself to quicker probabilistic verification. This aspect was shortly codified in the definition of probabilistically checkable proof, which lends itself most readily to characterize ${\mathsf{NP}}$ and ${\mathsf{NEXP}}$.

## Three Kinds of Proofs

Amid all this development on “long and skinny” proofs, what can we say about “short and fat” ones? Intuitively, such proofs have lots of cases, but that is not their full story. The network of logical dependence matters too. Hence we think there are most helpfully three kinds of proofs in regard to shape:

1. Proofs with close to one single path to the conclusion;

2. Proofs with many cases, but the cases have a simple hierarchical tree pattern and can mostly be checked sequentially;

3. Proofs with a more web-like pattern of logical dependence between parts.

Direct evaluations of quantified Boolean formulas in ${\mathsf{PSPACE}}$ have type 2, while the interactive proof with polynomials gives the “feel” of type 1 to both the prover and the recipient of the proof.

Chess problems prefer types 1 or a limited form of 2 for esthetics. The website ChessBase.com recently republished the longest branching-free “Mate-In-N” problem ever created, by Walther Jörgenson in 1976. It is mate-in-203 with no alternative move allowed to the winner, and virtually no case analysis of alternate defensive tries by the loser either.

However, a chess search often has type 3. Often there will be different starting sequences of moves that come to the same position ${P}$. The value of ${P}$ that was computed the first time is stored in a hash table so that the later sequences are immediately shown that value, cutting off their need for any further work. This resembles breadth-first search insofar as marked nodes may be touched later along other paths. The dependencies of values become web-like. Injured values from hash collisions can cause huge ripple effects, as I covered in a post three years ago.

The stored-hash tactic is much the same as a lemma in a proof that is used multiple times. We suspect that last year’s 6-gigabyte computer-generated proof of discrepancy > 2 in the Erdős Discrepancy Conjecture has many such lemmas, and hence is more type 3 than 2. The provers Boris Konev and Alexei Lisitsa have an updated page with further computations. They do not link the whole impossibility proof of a length 1,161-or-more sequence of discrepancy 2, but do give some of the “DRUP” certificates of unsatisfiability. DRUP stands for reverse-unit propagation with clause deletion, and that propagation strikes us as largely composed of cases and lemmas. The subcases might be codable at high level via predicates ${P(m,\cdots)}$ for m < 1,161 expressing the unavailability of length-${m}$ subsequences fulfilling some extra conditions ${(\cdots)}$, with such predicates being copiously re-used.

One finds an explosion of stored sub-cases in chess endgame tables. However, in many positions a vast majority of them are to prove wins that a chess master would see as “trivially true” in a few seconds. In other cases an alternative by the loser might simply jump to a later stage of the main trunk line, thus merely accelerating the same loss rather than posing a new case. (Similarly, an alternative by the winner might merely allow the defender to wind back to an initial stage, without much need for separate verification.) We wonder how far this pertains to the longest endgame win discovered in the new 7-piece endgame tables–mate in 545 moves. That is, how large is the part of the proof tree that needs to be specified, so that a chess program given values for positions in the tree could verify the rest via its local search?

## Computations Short-Cutting Proofs?

This last eventuality prompts our new speculation: Perhaps we can rigorously develop a science of when large sections of proofs can be effectively handwaved. This would appeal to the computational style most often postulated for our human brains: shallow but broad and with great power of heuristic association, analogous to the complexity class ${\mathsf{TC^0}}$ of poly-size constant-depth threshold circuits. Even when yoked with computers the added-value of our grey matter is not to be discounted, as attested in my joint paper last summer—in section 6 showing how human-computer tandems performed better at chess in 2005–08 than computers alone.

We have recently twice covered a conjecture by Freeman Dyson that one feels should lend itself to this kind of treatment. Many other open conjectures in number theory are felt to be “probably” true, where “probably” has a technical sense that might be developed further into some kind of dependent structure: if that handwave is valid then all-the-more certainly so is this one. The idea could be helped by enumeration of exceptions that, once handled, enable the rest of the proof to be executed with a broad brush. As linked from an essay post by Scott Aaronson, Tim Gowers relates a relevant opinion by Don Zagier in a MathOverflow comment. We morph this opinion to say that mathematicians may need a “handwave heuristic” simply because many “obviously true” statements don’t connect to anything substantial that would give a reason for their truth.

This could push many proofs of type 3 toward types 2 or 1. Note that in the way interaction and randomness combine to move type 2 toward type 1, we are already agreeing to tolerate a chance of error. It is the nature of the kind of error involved in converting instances of type 3 into type 2 that needs further consideration. We wonder whether current developments such as homotopy type theory are embracing not just exact patterns but also heuristics for when a search is overwhelmingly likely to succeed—or to fail.

This still leaves our original question of shapes of computations. In the past both Dick and I have undertaken some exploration of conditions under which computations might be similarly “self-improved.” That idea will have to be for another time.

## Open Problems

Can we assign particular “shapes” of computations canonically to specific computational problems? Can this help guide concrete attacks, or is it no more than tantamount to solving the big open questions to begin with?

Again we congratulate Juris and Richard on this 50th anniversary of their achievement. We also tip our hat to a comment by John Sidles in our “Case Against Cases” post which partly prompted this further essay.

[word changes to second paragraph of “short-cutting” section, ending, and caption]

The polynomial hierarchy is infinite for a random oracle

Benjamin Rossman, Rocco Servedio, and Li-Yang Tan have made a breakthrough in proving lower bounds on constant-depth circuits. It came from a bi-coastal collaboration of Rossman visiting the Berkeley Simons Institute from Japan and Tan visiting from Berkeley to Servedio at Columbia University in New York. Their new paper solves several 20- and 30-year old open problems.

Today we congratulate them on their achievement and describe part of how their new result works.

Problems beyond brute force search

 Cropped from Wikipedia source

Hans-Joachim Bremermann was a mathematician and biophysicist. He is famous for a limit on computation, Bremermann’s limit, which is the maximum computational speed of a self-contained system in the material universe.

Today Ken and I wish to talk about the limit and why it is not a limit.

 “Dr. Kibzwang” source

Colin Potts is Vice Provost for Undergraduate Education at Georgia Tech. His job includes being a member of the President’s Cabinet—our president, not the real one—and he is charged with academic policies and changes to such policies. He is also a College of Computing colleague and fellow chess fan.

Today I want to state a conjecture about the behavior of faculty that arose when Tech tried to change a policy.

How to avoid too many cases at least some of the time

Theon of Alexandria was history’s main editor of Euclid’s Elements.

Today I want to talk about case analysis proofs.

Congratulations to John Nash and Louis Nirenberg on the 2015 Abel Prize

 Combined from src1, src2.

John Nash and Louis Nirenberg have jointly won the 2015 Abel Prize for their work on partial differential equations (PDEs). They did not write any joint papers, but Nirenberg evidently got Nash excited about David Hilbert’s 19th problem during Nash’s frequent visits to New York University’s Courant Institute in the mid-1950s. Nash in return stimulated Nirenberg by his verbal approach of barraging a problem with off-kilter ideas. The Norwegian Academy of Sciences and Letters recognized their ‘great influence on each other’ in its prize announcement.

Today we congratulate both men on their joint achievement.

More mileage than expected from a little example

 Cropped from World Science Festival source

Sean Carroll is a cosmologist in the Department of Physics at Caltech. He also maintains a blog, “Preposterous Universe,” and writes books promoting the public understanding of science. I have recently been enjoying his 2010 book From Eternity to Here: The Quest for the Ultimate Theory of Time.

Today—yes, Carroll would agree that there is a today—I would like to share an interpretation of a little quantum computing example that occurred to me while reading his book.


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# Question

a. The mean of a sample of 25 was calculated as x̄ = 500. The sample was randomly drawn from a population with a standard deviation of 15. Estimate the population mean with 99% confidence.
b. Repeat part (a) changing the population standard deviation to 30.
c. Repeat part (a) changing the population standard deviation to 60.
d. Describe what happens to the confidence interval estimate when the standard deviation is increased.

Sales1
Views26

format: plain


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## Cryptology ePrint Archive: Report 2022/008

Beating Classical Impossibility of Position Verification

Jiahui Liu and Qipeng Liu and Luowen Qian

Abstract: Chandran et al. (SIAM J. Comput.'14) formally introduced the cryptographic task of position verification, where they also showed that it cannot be achieved by classical protocols. In this work, we initiate the study of position verification protocols with classical verifiers. We identify that proofs of quantumness (and thus computational assumptions) are necessary for such position verification protocols. For the other direction, we adapt the proof of quantumness protocol by Brakerski et al. (FOCS'18) to instantiate such a position verification protocol. As a result, we achieve classically verifiable position verification assuming the quantum hardness of Learning with Errors.

Along the way, we develop the notion of 1-of-2 non-local soundness for a natural non-local game for 1-of-2 puzzles, first introduced by Radian and Sattath (AFT'19), which can be viewed as a computational unclonability property. We show that 1-of-2 non-local soundness follows from the standard 2-of-2 soundness (and therefore the adaptive hardcore bit property), which could be of independent interest.

Category / Keywords: cryptographic protocols / cryptographic protocol, position verification, quantum cryptography, proof of quantumness, non-locality

Original Publication (in the same form): ITCS 2022


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# Homework Help: Net Potential Energy between two Adjacent Ions

1. Jan 13, 2009

1. The problem statement, all variables and given/known data

The net energy is given by:

$$E_N=-\frac{A}{r}+\frac{B}{r^n}$$

where A, B , and n are constants and r is the interionic separation. Calculate E0 in terms of A, B, and n by the following procedure:

1. find dEN/dr
2. set this expression equal to zero and solve for r=ro
3. substitute ro back into the original equation

3. The attempt at a solution

Okay, this is more or less an algebra problem that I am stuck on:

$$E_N=-\frac{A}{r}+\frac{B}{r^n}$$

$$=-Ar^{-1}+Br^{-n}$$

$$\Rightarrow \frac{dE_N}{dr}=Ar^{-2}-nBr^{-n-1}$$

$$0=Ar^{-2}-nBr^{-n-1}$$

$$\Rightarrow 0=\frac{A}{r^2}-\frac{nB}{r^{n+1}}$$

$$\Rightarrow 0=\frac{Ar^{n+1}-nBr^2}{r^2*r^{n+1}}$$

$$\Rightarrow 0=Ar^{n+1}-nBr^2$$

Here is where my brain melted. Any blatant errors and/or hints?

Hmmm delicious hints

2. Jan 13, 2009

### Thaakisfox

factor it out:

$$0=r^2(Ar^{n-1}-nB)$$

r_0=0 is nonsense, so we have:

$$r_0^{n-1}=\frac{nB}{A}$$

Now plug this back, and you are done.. :D

3. Jan 13, 2009

Egads man! That was easy. Nice catch Thaakisfox

Except that $r_0^{n-1}=\frac{nB}{A}$ is not what I plug back in; I still have to solve explicitly for r which means I need to take the (n-1)th root of nB/A
right?

4. Jan 13, 2009

What am I still missing here?

If:
$$r=(\frac{nB}{A})^{\frac{1}{n-1}}$$

then:

$$E_0=-\frac{A}{(\frac{nB}{A})^{\frac{1}{n-1}}}+\frac{B}{(\frac{nB}{A})^{\frac{n}{n-1}}}$$

which is just silly.

Last edited: Jan 14, 2009
5. Jan 14, 2009


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# APPLIED DYNAMICS

Here is a sample of my papers dealing with different problems from the same general area.

My main result  of recent few years on this topic is based on the observation that  a class of  van der Pol--type relaxation oscillators resembling an original forced van der Pol equation exhibit chaotic behavior with zero probability: Lebesque almost all initial conditions give riseto simple periodic behavior, while only exceptional (physically unobservable) solutions are chaotic".

The note [39] describes a previously unnoticed  basic stretching mechanism in the phase space of forced relaxation oscillators. This stretching takes place for most initial conditions (in the sense of Lebesgue measure), and it is somewhat surprising that this simple basic mechanismhas been overlooked in the half century  since the original work by  Cartwright and Littlewood.

The rigorous result of [] disproved an experiment reported in a physics journal. More generally, I showed that the Josephson equation of the form $\beta\ddot\phi+\dot\phi +\sin\phi = p(t)$ (here $p(t)$ is  any periodic function) exhibits only periodic or quasiperiodic behavior, but no chaos, as long as        $\beta <{1\over 4}$. The interesting point about this result is that it specifies the numerical range of the parameter, rather than asking for $\beta$ to be sufficiently small".  This result has answered some specific questions that   some experimentalists in Josephson thermometry were interested in.

The paper [22] explains geometrically an interesting period--adding phenomenon in a nonlinear circuit which was observed experimentally in 1927 by  van der Pol. The paper explained also some  experimental findings whose mechanism was not known: for instance, why the frequency lock--in plateaus overlap in one parameter range and why they are separated by chaotic'' gaps in another.

In [59]  it is shown that for a certain class of relaxation oscillations there is a hidden linearity when the relaxation parameter becomes small.  Specifically, it is well known that the Poincar\'e map of a periodically forced van der Pol type oscillator is well approximated by a circle map. All the work on the subject starting with that of Cartwright, Littlewood and Levinson   amounts to understanding this map.

Now the gist of [59] is the  proof of the fact that  this circle map is in fact close to piecewise linear (when the relaxation parameter is small)  for a certain class of oscillators.  This shows that the system is as simple as it can possibly be, contrary to what may have been expected on the basis of the work of the past 50 years.

My thesis [6] is a study of the van der Pol-type relaxation oscillators with periodic forcing. The main result of this paper is a  geometric description of the  Poincar\'e map (this geometry was not known from the earlier papers) and the qualitative analysis using symbolic dynamics and other methods.


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# Which of the following binary solutions of volatile liquids have negative deviation?

## A) chloroform and acetone B) chlorobenzene and bromobenzene C) benzene and toluene D) hexane and heptane

May 15, 2017

The mixture is A), and has negative deviation, as indicated by ${P}_{A B}^{\text{re" < P_(AB)^"id}}$. This is because chloroform hydrogen-bonds with acetone, but before mixing, they had dipole-dipole interactions within themselves.

Since the two liquids are volatile (i.e. they vaporize easily), we're going to have to find an expression for the total vapor pressure of the ideal binary mixture, ${P}_{A B}^{\text{id}}$. This will be compared with the real total vapor pressure, ${P}_{A B}^{\text{re}}$.

DETERMINING THE TOTAL VAPOR PRESSURE

We assume the vapor above the solution is ideal so that we can utilize Dalton's law of partial pressures:

${P}_{A B}^{\text{id}} = {P}_{A} + {P}_{B}$

where $A$ is the solvent and $B$ is the solute. $\text{^"id}$ indicates an ideal solution.

In an ideal solution, the solvent always follows Raoult's law, so we can write:

${P}_{A} = {\chi}_{A} {P}_{A}^{\circ}$

where the $\circ$ indicates the pure component, and $\chi$ is the mol fraction of the component.

We assume the solution is also not dilute, since ${\chi}_{A} = 0.4$ is not a small mole fraction. Hence, the solute $B$ also follows Raoult's law (rather than Henry's law), and we can write:

${P}_{B} = {\chi}_{B} {P}_{B}^{\circ}$

That means the vapor pressure of the mixture of volatile liquids is:

${P}_{A B}^{\text{id}} = {\chi}_{A} {P}_{A}^{\circ} + {\chi}_{B} {P}_{B}^{\circ}$

But since this is a binary mixture, i.e. two components, we know that the mol fractions add up to $1$, meaning ${\chi}_{A} + {\chi}_{B} = 1$, and thus:

$\boldsymbol{{P}_{A B}^{\text{id}}} = {\chi}_{A} {P}_{A}^{\circ} + \left(1 - {\chi}_{A}\right) {P}_{B}^{\circ}$

$= \boldsymbol{{\chi}_{A} \left({P}_{A}^{\circ} - {P}_{B}^{\circ}\right) + {P}_{B}^{\circ}}$

The total vapor pressure assuming ideality is therefore:

color(blue)(P_(AB)^"id") = 0.4("300 torr" - "800 torr") + "800 torr"

$=$ $\textcolor{b l u e}{\text{600 torr}}$

CLASSIFYING THE SOLUTION'S DEVIATION FROM IDEALITY

We're not done yet though. The real vapor pressure you've given us is ${P}_{A B}^{\text{re" = "580 torr}}$, which is less than what is predicted by Raoult's law.

That is indicative of negative deviation, which is depicted by this diagram:

(The dashed diagonal lines and the horizontal line at the top are from Raoult's law, and the solid lines are the real vapor pressures.)

Negative deviation is when the average distance between solvent and solute particles is closer than in an ideal solution. This is when the energy of solute-solvent interaction ($A B$) is lower than the energy of solute-solute (BB) or solvent-solvent ($A A$) interaction.

This means that the intermolecular forces formed between solute and solvent are stronger than those that were present previously amongst the solute and solvent within themselves.

Recall the most important ones:

$\text{H"-"bonding" > "dipole-dipole" > "dispersion}$

CONSIDERING THE BINARY MIXTURE OPTIONS

We now examine the mixture choices.

A) chloroform with acetone

This is a tricky example, but chloroform has dipole-dipole interactions with itself, and acetone also has dipole-dipole interactions with itself... however, acetone hydrogen-bonds with chloroform!!

The three chlorine atoms are electron-withdrawing groups, which make the hydrogen very electropositive.

This is enough for the carbonyl oxygen on acetone to become a hydrogen-bond acceptor, polarizing the hydrogen atom and forming a hydrogen-bonding interaction.

Since hydrogen-bonding is stronger than dipole-dipole interactions on average, this mixture will have negative deviation, which agrees with how we got ${P}_{A B}^{\text{re" < P_(AB)^"id}}$. That is, the mixture is $A$.

B) chlorobenzene and bromobenzene

This mixture has two substances that only have dipole-dipole forces to exchange, and they therefore form essentially ideal solutions.

C) benzene with toluene

D) hexane with heptane

Both of these primarily have dispersion forces (toluene, ${\text{C"_6"H"_5"CH}}_{3}$, is mostly nonpolar), and it is not expected that any exchange of intermolecular forces leads to any more stabilizing or less stabilizing interactions. That is, these will be essentially ideal solutions.


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# Sum of infinite series - Catalan constant

Why is this identity true? $$\sum_{k=1}^{\infty} \frac{\sin(k\pi/2)}{k^2} = G$$ where $$G$$ is Catalan's constant.

• Hint: What is the definition of the Catalan constant, and what does the sequence of numbers $\sin(k\pi / 2)$ look like? – John Barber Dec 29 '15 at 20:49

The series sums to $$\frac{1}{1^2}-\frac{1}{3^2}+\frac{1}{5^2}-\cdots$$ which is just the definition of Catalan's constant.


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I noticed people were trying to find a generator like fancy letters, but were ending up on actual font sites rather than generators of copy-paste text like this one. Output 3D formats. Today, we will demonstrate the steps we outlined with a 3D generator model example, comparing our results with an analogous 2D model. Kate Compton. label the vertices $1,2,3,4$. We show that all these symmetry-protected topological states can be adiabatically deformed into a special class of states we call topological crystals. Keywords: flip mirror image rotate. Aim the block then press M to cycle symmetry mode. Fermilab and the LHC. Annoyed GIF - Find & Share on GIPHY. Cyclic Groups. Start by clicking on the cube along the left side; then, place cubes on the grid where. Multiply this value by six. 46,408 downloads. When I think an oval face I automatically imagine Drew Barr. If you select Random symmetry, guess what it is! You can show the symmetry line, and then hide it again if you wish. Other Resources: My Worksheet Maker My Word Search The Lesson Builder Common Core Scholarship National Education Association American Federation of Teachers Understanding By Design Universal Design for Learning Gamification of the Classroom Gifts Further Information: Crossword Hobbyist is a site centered around its crossword puzzle maker, also known as a crossword puzzle creator, crossword. You can export these shapes in forms appropriate for 3D printing by shapeways. I dunno about others but I usually place my cursor over the point which I wanna move when I don't wanna loose track of it, so gesturing is actually detrimental in this case. #N#GeoGebra Classic. Delta Connection (Δ): 3 Phase Power, Voltage & Current Values Difference Between Star (Y) and Delta (Δ) Connections If a balance symmetrical load is connected across three phase voltage system in parallel, then the three currents will flow in neutral wire which quantities would be same, but they would be differ by 120° (out of phase), hence. Explore more Type settings. So currently this is basically a duplicate of the above, but I think I'll try to collect a few more "cool" text fonts, like the old enlgish one, and. Do not draw hard lines between each tooth. The box is square based, and the height is variable. Reptiles are air-breathing vertebrates covered in special skin made up of scales, bony plates, or a combination of both. The eyes may be considered windows into the soul, but according to some researchers, the rest of your facial features say something about you, too. These guidelines show the following rules of facial symmetry: 1) Eyes are positioned at the vertical center line of the head. 1984-01-01 00:00:00 Abstract Canonical generator states provide an overcomplete, nonorthonormal basis for the irreducible representation spaces of the unitary group. The hexagon is the highest regular polygon which allows a regular tesselation (tiling). 4 List of Angels. OCP Junior Executive Kenny is killed after holding a gun in a meeting. Analyze your face in 3 minutes. This is the main page for the subtraction worksheets. Shaft misalignment is responsible for as much as 50 percent of all costs related to rotating machinery breakdowns. Iterates N times. 7 × 10−7 C/m 3. The ambigram generator allows you to type in any two names, words or phrases and create your own unique, personalized ambigrams which can be read upright or upside-down. Spotting the plane or axis of symmetry is tricky but I think there is always one. Everyone wants a happy, healthy baby; however, babies often experience discomfort from diaper rash – a condition that causes skin underneath the diaper to become red and tender. You can follow the question or vote as helpful, but you cannot reply to this thread. Personal-use only Download Add to Favorites. Icosahedral symmetry is equivalently the projective special linear group PSL(2,5), and is the symmetry group of the modular curve X(5), and more generally PSL(2,p) is the symmetry group of the modular curve X(p). I'm an artist, animator, social media personality, author, and television presenter. Your face has good horizontal symmetry. A chain of tori produced by the symmetry generator. Take a glimpse of the activity for the day to check out if there's anything you didn't do. The Path Tool (replacing the old Bezier Selection tool) can be used in many creative ways. Adults find average and symmetric faces attractive. Physical attraction depends on ratio, and in particular symmetry. For this purpose, a new space with three basis vectors b 1, b 2, b 3, is created, which is orthogonal to real space. Automatically retouches the photo with customizable presets. A line is defined as a line of points that extends infinitely in two directions. Rate my face 1-100. SKETCHBOOK GOES FREE! At Autodesk, we believe creativity starts with an idea. Unfortunately there aren't mirrored characters for every letter and number, but there are some vauguely similar ones which are used to fill the gaps. The trick in graphing the Greatest Integer Function is to first understand that it looks like steps or a staircase, and that we are actually rounding down to the integer less than or equal to the value we plug in. Cyan, a blend of green and blue, is a secondary color that’s commonly used to achieve an aquatic look. I am the face, as well as the creative mind behind the popular art YouTube channel ‘Draw With Jazza’, which is filled with entertaining art challenges, tutorials and competitions. It is also a perfect way to start off the summer, nice and cool. Created with the generator script at Seventh Sanctum , one of the best time-wasters on the Internet. Find out how attractive your body is. Geometry of Crystals Crystal is a solid composed of atoms, ions or molecules that demonstrate long range periodic order in three dimensions. Suitable for Key Stage 2, Early and 1st Level and. PHYSICAL EXAM TEMPLATE FORMAT # 1: PHYSICAL EXAMINATION: GENERAL APPEARANCE: The patient is alert, oriented and has a bandage over his left eye. Paint had this ability in. See below for details. Your face has good horizontal symmetry. Select your Photo to Retouch; Pricing. The Department of Chemistry offers undergraduate major and minor programs in chemistry along with graduate training (M. 95] helo=metall-rras) by ietf-mx. Get ready to see how RoboCop is an almost perfectly symmetrical film. The mean symmetry of all faces was 0 (SD = 0. Enter the rep count. 45) and the overall symmetry of the most symmetrical face in our set was −0. For example, if you have an oval face, then you can wear one piercing in each nostril because symmetry doesn't make your face look wider. Electric Utility Data is also often provided in terms of Per Unit and Symmetrical Components. How to Treat a Dorsal Hump. I came up with the original methods in these 3 tutorials by measuring over a dozen adult faces, so each tut. The term vaporwave developed as a music term that essentially talked about a general vibe or aesthetic generator that was far from the ordinary and one that defies the likes of consumerism and capitalism. , the chimeras may have width. In DM, click Tools, Symmetry then select the Plane. Does each artifact have a distinct personality? That may be too much to ask, and too many for any user to remember distinctly. Why? Because the body and. Symmetry is everywhere in art, nature and geometry! Learn about periodic and nonperiodic tilings. Cool Text Fonts. E-stim therapy is commonly used to help treat pain, but is also useful has the ability to: Electrodes are attached to patient's skin and when used, e-stim causes specific muscles. Symmetry manipulation for facial images with natural skin textures. How do you find the area of a hexagon? There are several ways to find the area of a hexagon. * Add asymmetry to the hull: Pick random faces and extrude them out in a similar manner, reducing in scale each time. Get stunning snowflake images for free from our handpicked collection HD to 4K quality Free for commercial use Download for free!. Symmetry-IT utilizes services than are cloud based and reside in data centers across Australia. To make it easy to digest, I split the tutorial up into 3 parts: How to draw a face from the front, side and 3/4 view. For this technique I implemented my own pseudo random number generator using a linear feedback shift register technique. A stationary point is reached when the generator produces faces that have high quality as well as preserve identity. Instead of pulling problems out of a database, Wolfram Problem Generator makes them on the fly, so you can have new practice problems and worksheets each time. Female only. The website, thispersondoesnotexist. Visual Polyhedra. Miller Indices for Directions •A vector r passing from the origin to a lattice point can be written as: r = r 1 a + r 2 b + r 3 c where, a, b, c → basic vectors and miller indices → (r. 36,000+ Vectors, Stock Photos & PSD files. Each of the 3 arms branches into 3 more arms, becoming 9-fold symmetry. Permission You may use/modify and distribute this mod anyway you want as long as attribute the. Bunker, Per Jensen ©Encyclopedia of Life Support Systems (EOLSS) triangular prism. Generate random words and images then use them in a variety of activities to help your creativity flow. Generator look updated, HTTPS added, redirect to new location added. Jan 28, 2017 - Explore pstohrhu's board "Symmetry", followed by 6480 people on Pinterest. Similarly, fixing vertex 1, and rotating the opposite face will create the permutation $$(2\,3\,4)$$. Any use of information and images is prohibited unless prior express consent is given by The Perfect Face LLC. The polyhedra in this series have the symmetry of a flat triangle whose top and bottom faces are different (so turning it over is not a symmetry). Then a symmetry is known when you know how it permutes the. To craft, place 1 cactus green and 1 lapis lazuli anywhere in the grid to yield two cyan dyes. Raphtalia (Personal Use Only) by Nurf Designs. Ma, Joshua Correll, and Bernd Wittenbrink. Create your ideal female body by interactively altering corpulence, pelvic width, waist width, bust size and leg length:. Practice materials for the phonics screening check, key stage 1 and key stage 2 national curriculum tests, including past test papers. There’s the odd shot that has a symmetrical object in the centre of the frame, but almost all of the time this is framed by asymmetry. Flattens faces. Active 2 years, 1 month ago. These 14 Bravais Lattices provide no additional rotational symmetry, but may give additional translational symmetry to the unit cell. 3D shapes for kids are not always easy to teach. Go to the 'Force' tool. Right-click and open it with IDLE. Triangle area calculator by points. Each of these twelve edge-located sites is shared with four adjacent cells, and thus contributes (12 × ¼) = 3 atoms to the cell. May give more pleasing symmetry, but can be unstable for certain shapes. Follow the links for Spaceship Math Subtraction worksheets, timed subtraction tests, multiple digit subtraction worksheets, simple borrowing and regrouping worksheets, and math worksheets with mixed addition and subtraction problems. Buy Inspiring Symmetry by alkis on AudioJungle. Most faces of human beings have approximate bilateral symmetry. Group coordinates Symmetry generators A Lie group is a space, so we generally want to introduce some coordinates. Each block has 6 connectors, one for each face. Séquin CS Division, University of California, Berkeley E-mail: [email protected] Note: If you can do over 10 reps, start doing weighted chin-ups for the most accurate results. It's both easy and difficult to create alien names, as they can be anything in any language. Unlike asymmetrical distribution. Researchers have discovered that the human perception of physical beauty is closely related with Golden ratio. Symmetry CompleteView Video Management System is a leading edge approach to video surveillance offering users unlimited scalability and flexibility. Dead as a doornail. Note which is the largest, and use the information below to determine your face shape. Synonyms for symmetry in Free Thesaurus. Thus, any symmetry element is connected with one ore more symmetry operations that yield an image identical to the original molecule. Why am I ugly? or not pretty enough? Online test for face beauty analysis. A stationary point is reached when the generator produces faces that have high quality as well as preserve identity. ZoneFoker New iPad 7th Generation Tablet Leather Case (10. Use the drawing canvas below to create your own snowflake. Knowing the properties of of 2D shapes is basic but important skill. Biometrics is nowadays widely being used in several daily applications ranging from smart device user authentication to border crossing. The development of this web resource was supported by a grant from The Higher Education Academy. Golden beauty ratio is approximately 1. Headshot, the AI-powered Character Creator plugin generates 3D realtime digital humans from one photo. These Platform Sandals Are The Perfect Way to Elevate Your Summer. Write down these four measurements. In this case a (high-energy) atom or ion penetrates the crystal. Symmetry definition, the correspondence in size, form, and arrangement of parts on opposite sides of a plane, line, or point; regularity of form or arrangement in terms of like, reciprocal, or corresponding parts. Arched windows and bronze house numbers add an elegant touch. When one side of your face is considerably smaller than the other, you may find that the muscles of your face are weaker on that side. If the face is a quad, and the edges are neighbors, we have three possible behaviors, depending on the setting of Corner Cut Type (the select menu next to the Subdivide button, in Mesh Tools panel). Interactive Fractal Tree The fractal explorer shows how a simple pattern, when repeated can produce an incredible range of images. In this case, then the Model Type is Partial Model. He is in no acute distress. You just have to choose the photo of yourself that you wish to upload to the Facial Attractiveness Test, which will then scan the photo to determine the person’s facial features based on a number of. These may be used to check homework answers, practice or explore with various values for deep understanding. The seven faces of Donald Trump – a psychologist’s view From the chin-jut to the zipped smile, we examine the president-elect’s signature facial expressions and what they tell us about him. If you select Random symmetry, guess what it is! You can show the symmetry line, and then hide it again if you wish. Instead of pulling problems out of a database, Wolfram Problem Generator makes them on the fly, so you can have new practice problems and worksheets each time. appearance synonyms, appearance pronunciation, appearance translation, English dictionary definition of appearance. In the "Sketch" layer, using the Blob Brush Tool (Shift + B), we draw our sketch using the photo as a guide. Before we start, you should know that almost all human faces follow a few basic rules of symmetry. Active 2 years, 1 month ago. Viralemon must receive the following info:. Start by clicking on the cube along the left side; then, place cubes on the grid where. Symmetrical designs are comforting for our brains because they feel familiar. [1] It uses a grid with diagonal lines to help the student break up a multiplication. In a portrait or artwork of people, faces would be the main focal point, so each stroke has a significant effect on what mood is. If a system-source fault occurs, the short-circuit current is established at high magnitudes and the breaker is located close to the generator. Try rotational symmetry yourself with Symmetry Artist !. Find out more in this blog post. Enter the rep count. SACRED-GEOMETRY. Your skin also dries out and loses the underlying layer of fat so that your face no longer has a. When pressed It will appear in layers. Iron is an essential heavy metal that is included in many over-the-counter multivitamin and mineral supplements and is used therapeutically in higher doses to treat or prevent iron deficiency anemia. com was launched in May 2009 by the St. For example, a face with a dark spot on the left cheek combined with its mirror image would generate a face with two slightly paler symmetric spots on the left and right cheeks. There are several photo ethnicity analyzers available, but ultimately the best app for telling you what race you look like is Kairos. Please do not take this test if you have low self-esteem or confidence issues. The rule of thumb to determine the handedness is: If an x- or s-face is present at the left side of an r-face, the quartz is called left-handed (or left quartz, for short). In the most general context, if you have a metric space $(X,d)$, then the group is given by the group of bijections \phi:X\to X. Design and analysis software for Windows and Mac, inspired by Phi, the Golden Ratio. Psychologists use this test in an attempt to examine the personality characteristics and emotional functioning of their patients. 1984-01-01 00:00:00 Abstract Canonical generator states provide an overcomplete, nonorthonormal basis for the irreducible representation spaces of the unitary group. We are proud to have created ageing and lifestyle software for award winning campaigns and we are always open to new ideas and projects. A blaze is much wider than the strip. In Transmitter Crystals, the center face is a perfect triangle, and located at each side of this center triangle is a seven sided face. Golden beauty ratio is approximately 1. Face perception: social, neuropsychological and comparative perspectives, the special issue of Philosophical Transactions of the Royal Society B guest edited by Anthony Little, Benedict Jones and Lisa DeBruine. faces as an indexed list, count, list of adjacent face indices, rule list of edge count tallies, polygons, graphic, graphics complex, or image "Net" polyhedron net as a graphic, graphics compex, image, list of vertex coordinates, count, list of face indices, or graph "Skeleton". First of all, I’ll write out the chiasmus in the film’s sequence of events: A. As you zoom in to a Sim's face using the fine detail mode, hovering over just about anything will cause it to light up, showing every area you can. Find descriptive alternatives for symmetrical. OCP Junior Executive Kenny is killed after holding a gun in a meeting. symmetry property possessed in varying degrees (Type face that creates, mirror similarities) A way to rise above the meaning, not to exist just for yourself Clockwork Freestyle (feat. 5M - 1994, Geometric Dimensioning and Tolerancing (GD&T). Overlay any image on your screen. Once you have rotated the figure 360 degrees, you are back to the original figure. As a part of the vaporwave, famous musical pieces were taken and distorted in different ways. Follow the links for Spaceship Math Subtraction worksheets, timed subtraction tests, multiple digit subtraction worksheets, simple borrowing and regrouping worksheets, and math worksheets with mixed addition and subtraction problems. The connector has a number. Photography. VESTA is a 3D visualization program for structural models, volumetric data such as electron/nuclear densities, and crystal morphologies. Synonyms for symmetrical at Thesaurus. Villeroy Calls for ECB Symmetrical Inflation Target in Review By. This then trifurcates into 27 arms, 81, 243, etc. Beauty is in the balance of these face analysis features. Emojis have become essential for communication and also for expressing emotions through text messages or emails. To craft, place 1 cactus green and 1 lapis lazuli anywhere in the grid to yield two cyan dyes. The Evolutionary Advantage theory proposed that symmetrical faces are perceived as more attractive because the symmetry indicates good health in an individual. Example B. They used symmetric bifurcation theory to predict the existence of four primary gaits and seven secondary. Symmetric Embedding of Locally Regular Hyperbolic Tilings Carlo H. Overlay any image on your screen. The App detects the face and creates a facial pattern and your celebrity twin, celebrity look like and famous gradient System facial point detection can locate the key components of faces, including eyebrows, eyes, nose, mouth, and position. Added possibility to have an optional central room in all mazes (not optional in the. Here are home facade ideas we've pinched from houses for sale. The overall goal of creating mutual understanding between parties also is much more palatable for audiences, because in human nature, no one desires to be controlled. Interactive Fractal Tree The fractal explorer shows how a simple pattern, when repeated can produce an incredible range of images. Start by clicking on the cube along the left side; then, place cubes on the grid where you would like them. Who will be number 2,000? We have been on a fast journey. In the wall-drawing (shown above) we find translational operations (the motif is repeated by translation). Symmetry is the correspondence in size, shape, and position of parts on opposite sides of a dividing line or medium plane or about a center or axis. For example, a face with a dark spot on the left cheek combined with its mirror image would generate a face with two slightly paler symmetric spots on the left and right cheeks. In DM, click Tools, Symmetry then select the Plane. ∗ The method of symmetrical components is a general one, applicable to any polyphase system. With a bit of practice you will be able to create many interesting fractal forms, from organic looking trees to symmetrical structures like snow flakes. Maybe the best thing in it is the smooth, beautiful curves it produces. In the case of the rhombic pyramid, these would be 4 identical faces, labeled p, in the diagram. 913-926 2000 36 Acta Inf. Abstract logos with symmetrical patterns — Abstract symmetrical patterns are centered by nature, which makes them well-suited for businesses that help people become centered or balanced, too. N disables the whole mode. Biometrics is a scientific technology to recognize a person using their physical, behavior or chemical attributes. 3*=Void Center Between 3 Lattice Voids: This origin is designated "3 star". Watch RoboCop: The Chiasmus. Cyan, a blend of green and blue, is a secondary color that’s commonly used to achieve an aquatic look. Table of Content. Find the best digital activities for your math class — or build your own. Schmid says the length of an ear is equal to the length the nose, and the width of an eye is equal to the distance between the eyes. 0_jx, revision: 20191031195744. When you take a familiar landscape or your own face, you can take pictures that are totally different from ordinary cameras. Nobody has a perfectly symmetrical head, but if the features on each respective side of your head and face — ears, cheek bones, brows, etc. 0 and Beauty. These cat emoticons look like they belong in an anime. Kaleidosketch is a kaleidoscope-inspired symmetry drawing program. It uses a set of meshing algorithms and their corresponding conditions (hypotheses) to compute meshes. Posted by 11 years ago. 2D Space MA2-1WM Uses appropriate terminology to describe, and symbols to represent, mathematical ideas MA2-3WM Checks the accuracy of a statement and explains the reasoning used MA2-15MG Manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features. two sides or events being identical. Aging changes in the face. This is in contrast to the values of the short-circuit current under conditions according IEC 62271-100, which is 25 % of the rated short circuit current. Take a look at the beautiful use of symmetry as part or all of their design for some reflective inspiration. If you select Random symmetry, guess what it is! You can show the symmetry line, and then hide it again if you wish. When something is symmetrical, it is exactly the same on both sides. There are several photo ethnicity analyzers available, but ultimately the best app for telling you what race you look like is Kairos. That phase difference, P, is simply one full cycle expressed as an angle, 360 degrees or radians, divided by the number of phases. A generative adversarial network (GAN) is a class of machine learning frameworks invented by Ian Goodfellow and his colleagues in 2014. The centres are marked by A. Make games, stories and interactive art with Scratch. There are no simple formulas for calculating the magnetic flux density of the various magnetic shapes. For example, if you use reflection symmetry in your logo, you really only have to worry about designing one half of your logo—and then create a mirror image of that side for the rest of your design. \textures\actors\character\femalebrows - thin eyebrows. Dozens of applications. Geometry: Nets of Solids - cubes, cuboids, rectangular solids, prisms, cylinders, spheres, cones, pyramids, net of solids, What is meant by the net of a solid, net of cylinder, Examples, activities and demonstrations, How to use nets to find surface area and volumes, Interactive animations for nets of solids, examples with step by step solutions. Dark matter and dark energy. Deal with multiple structural models, volumetric data, and crystal morphologies in the same window. Schmid says the length of an ear is equal to the length the nose, and the width of an eye is equal to the distance between the eyes. These faces belong to forms {100}, {110}, and {111}. You never know when a great idea will strike, so access to fast and powerful creative sketching tools is an invaluable part of any creative process. In the sample image, we'll exaggerate this man's surprised expression by adjusting his eyes, mouth, and other facial features. 3D Bravais Lattices Bravais lattice is a lattice with translation symmetry which consists of equivalent nodes. Headshot, the AI-powered Character Creator plugin generates 3D realtime digital humans from one photo. Prescribing a singularity. This name generator will give you 10 random names for alien species. ) Generate and this is the result. The cube, with two more faces and twice as many vertices and edges as the tetrahedron, has a more complex symmetry, but describing it can be tackled in roughly the same way. 43) id 1HMfXt-0002Bw-1z for calsch-archive. The text needs to be reversed as if. There are three unique rotational symmetry axes of the cube, and three associated types of rotation (see Figure 3): r, a rotation of ˇ. Ansys software can uniquely simulate electromagnetic performance across component, circuit and system design, and can evaluate temperature, vibration and other critical mechanical effects. Psychologists use this test in an attempt to examine the personality characteristics and emotional functioning of their patients. Free vector icon. The first condition results from the symmetry of the situation. Right-click and open it with IDLE. symmetry property possessed in varying degrees (Type face that creates, mirror similarities) A way to rise above the meaning, not to exist just for yourself Clockwork Freestyle (feat. com with free online thesaurus, antonyms, and definitions. Radial Symmetry. These geometry worksheets are free and easily printable. This is a free geometry lesson on line symmetry for grades 3-4. maybe because averaging faces adds some symmetry or something. ai offers anybody the ability to have their photo scanned by facial recognition software and compared against a database of other photos. Formulae: Mandelbrot set, Julia sets, Multibrot sets and multijulia sets for any power of z, Newtonian fractals for any polynomial, Phoenix fractal, rational maps, Burning Ship fractal and Julia sets. These cat emoticons look like they belong in an anime. Sound familiar? But if you take a look around, you’ll notice slight variations. Main title B. In lower dimensions, the higher spin symmetry appears less restrictive, so one would need a more sophisticated analysis than the one presented in this paper. You can shift, rotate, color, decompose, and view in 2‑D or 3‑D. Wolfram Problem Generator offers beginner, intermediate, and advanced difficulty levels for a number of topics. Symmetry and Groups, and Crystal Structures 2. htm db/conf/b/b1998. A dice challenge from S. Facial symmetry, where each side of the face is the exact mirror image of the other, is definitely one of these aspects. Accelerator complex. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k). Symmetry Financial Group is based just outside of Asheville in Swannanoa, NC. Geogebra is the best online geometry software for creating different geometric figures - points, lines, angles, triangles, polygons, circles, elipses, 3D planes, pyramids, cones, spheres Please wait while loading (approx. Group coordinates Symmetry generators A Lie group is a space, so we generally want to introduce some coordinates. Enter the rep count. Menachof, MD, FACS has performed thousands of facial plastic surgery procedures in over 20 years of experience. Price High To Low. 7-cm radius sphere. Download : Download full-size image; Figure 1. Find & Download Free Graphic Resources for Triangle. Here the laws of physics are symmetric but the state of the. Point group symmetry is an important property of molecules widely used in some branches of chemistry: spectroscopy, quantum chemistry and crystallography. Since it’s a curved space, the choice of coordinates generally varies according to application. OCP Junior Executive Kenny is killed after holding a gun in a meeting. In fact, in our first example below, we create a concentric circle. a previous version. You can change the symmetry count with left-click, right-click, X, and Shift-X; and you can change the symmetry mode with middle-click or R. page: 2 Next define symmetry planes by selecting 'Symmetry Plane' in the fixed constraint to the two bottom mounting faces on the part. ) The spacing dimension is commonly referred to as the "O. If the atoms of the crystal have a low density in the direction of. Compared to your eye wideth, your innerocular distance is nearly ideal. Each of these twelve edge-located sites is shared with four adjacent cells, and thus contributes (12 × ¼) = 3 atoms to the cell. “Symmetry is the perfect collision of science and art. refine_face: add an additional network to refine the face region. We use and thanks for these great tools: This website uses cookies to ensure you get the best experience here. The Online Fractal Generator is a web application for generating fractals using JavaScript, canvas and web workers. Disentangled Representation Learning GAN for Pose-Invariant Face Recognition Luan Tran, Xi Yin, Xiaoming Liu Department of Computer Science and Engineering Michigan State University, East Lansing MI 48824 {tranluan, yinxi1, liuxm}@msu. Attach comments to models or even individual vertices. A more profound way of hiding symmetry is the phenomenon of spontaneous symmetry breaking. Level up your Desmos skills with videos, challenges, and more. Vertex of a Parabola. Locates features, skin, hair and background areas. Click on the left to colour in a square. Design and analysis software for Windows and Mac, inspired by Phi, the Golden Ratio. The ratio of secodary to primary line voltage is √3 times the transformation. In some people, sagging jowls may create the look of a double chin. Female only. Draw figures using edges, faces, or cubes. This is in contrast to the values of the short-circuit current under conditions according IEC 62271-100, which is 25 % of the rated short circuit current. Use our online logo creator in order to create hundreds of unique logos instantly - no technical skills are required!. This article is about the possible link between facial symmetry and the attractiveness of a human face. 4 List of Angels. in order to print this on a t-shirt. 3D Solid State Crystal models WebGL models To see these models you need a modern graphical card and a browser with WebGL support (see get. It's a camera application that can take symmetrically as if mirrored. The hexagon is the highest regular polygon which allows a regular tesselation (tiling). A typical N is 200 or 300. Even if you can't draw a straight line, it allows you to generate professional looking illustrations of your science fiction, fantasy, or super-hero characters. But the names have to sound like a good fit for the species you've invented, so I've tried to make sure many different types of names can be generated, but they generally fit in 3. Symmetric Embedding of Locally Regular Hyperbolic Tilings Carlo H. Facial symmetry is the degree to which the features on each side of the human face line up and match in both size and orientation. Perhaps you would prefer our time worksheets, or learning about line or block symmetry?. Louis-based consulting service company Atama Group. 1 - Visiting the Mineralogical Museum No Slides Transcript of the Unit 2. Golden beauty ratio is approximately 1. Use the grid method and a mechanical pencil to create a line drawing of a mouth and teeth. The seven faces of Donald Trump – a psychologist’s view From the chin-jut to the zipped smile, we examine the president-elect’s signature facial expressions and what they tell us about him. Example: He has his head in the clouds if he thinks he can pass his test without studying. Want more? It is the difference between being an actor being a face in a crowd scene and a character that is memorable. We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. To work out the area of a face of a 3D shape, you use square units such as cm 2 as the face of a 3D shape is a 2D shape in its own right (a pyramid’s face will form a triangle, or its base a. Hours: 8:30AM - 5:00PM CST. A generative adversarial network (GAN) is a class of machine learning frameworks invented by Ian Goodfellow and his colleagues in 2014. While there are several art blogs out there that have lovely photos of student work using the same process I'm not finding a tutorial with photos of how to lead your. E-stim therapy is commonly used to help treat pain, but is also useful has the ability to: Electrodes are attached to patient’s skin and when used, e-stim causes specific muscles. Open in full-screen mode. Shop for symmetrical art from the world's greatest living artists. Round: Cheekbones and face length have a similar measurement. Take a look at the beautiful use of symmetry as part or all of their design for some reflective inspiration. It's both easy and difficult to create alien names, as they can be anything in any language. For accuracy, draw the shapes of the gum line and the edges of the teeth. Click on the pattern on the left to start designing the picture. These can blow up the geometry of the weirder polyhedra, which can be interesting too! 3D Printing. It can scan uploaded image files or image URLs, find faces and analyze them. 3D shapes for kids are not always easy to teach. “This is bad news for earthquake early warning. Find the best digital activities for your math class — or build your own. * Sometimes apply horizontal symmetry. OCP Junior Executive Kenny is killed after holding a gun in a meeting. @MrMcDonoughMath Used #Desmos online calculator today for scatter plots. Head in the clouds. We’re going to define a function that either draws a line with a kink in it, or draws a straight line the same length. Photography. The primary and secondary of the transformer can be independently connected either in star or delta. Learn from step-by-step solutions for over 34,000 ISBNs in Math, Science, Engineering, Business and more. There are two ways to adjust the behavior of symmetry. just above the Trash Can icon a little to the right. Build a standard grayscale snowflake, or have fun with the color options!. Answers in a pinch from experts and subject enthusiasts all semester long. The first polyhedron (Seq=1) is the same tetrahedron that's generated by origin 4, except it's shifted off-center. Wondering what race you really look like? Today, a photo ethnicity analyzer can use AI to analyze a photo of your face and guess your ethnic heritage. 3 Motivations & Psychology. One C 4 rotation axis, one C 2 rotation axis (equivalent to C 4 2), Four C 2 axes perpendicular to the C 4 axis. Here are home facade ideas we've pinched from houses for sale. At the intersection of the radius and the angle on the polar coordinate plane, plot a dot and call it a day! This figure shows point E on the plane. Perfect for infographics, voice overs, documentaries, film. 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# Math Help - Reduction of order

1. ## Reduction of order

(t)d^2y/dt^2 - (t+1)dy/dy + y = t^2
y1(t) = e^t y2(t) = t + 1

I have to do this is 2 different methods the first method was using variation of parameters which I could do but then when it came to using reduction of order I kept getting stuck half way.

The first thing i did was let y = ue^t then i differentiated and subbed back intothe equation then it was u absent which let me use p = du/dt and dp/dt = d^2u/dt^2 then i got P = tc/(e^t -t) where c is a constant then i couldnt integrate that to find u.

Rewrite your equation in this form $\displaystyle{\frac{t(y''-y')-(y'-y)}{t^2}=1}$
Then $\displaystyle{\left(\frac{y'-y}{t}\right)'=(t+C)'~\Rightarrow~\frac{y'-y}{t}=t+C~\Rightarrow~y'-y=t^2+Ct}$


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# Classical transport example: using the isotropic diffusion stabilization

### Purpose

This example tests the simplest stabilization scheme, i.e. that with the isotropic diffusion balance approach. In OGS, the type name of that stabilization scheme is IsotropicDiffusion.

### Theory

Stabilization is the numerical approach to eliminate the spatial oscillations produced by the Galerkin finite element method for the advection diffusion transport equation.

The advection diffusion transport equation takes the form $$\frac{\partial u}{\partial t} - \nabla(\mathbf{K}\nabla u) + {\mathbf v}\cdot \nabla u = Q$$ with $u$ the primary variable, $\mathbf v$ the fluid velocity, $\mathbf{K}$ the diffusion coefficient.

The stabilization scheme adds an artificial isotropic balancing dissipation to the diffusion coefficient to force the Péclet number to be smaller than 1. The isotropic balancing dissipation is defined as $$\mathbf{K}_{\delta} = \frac{1}{2}\alpha ||\mathbf v||h \mathbf I$$ with $\alpha \in [0,1]$ the tuning parameter, $h$ the element size (e.g. the maximum edge length of element), and $\mathbf I$ the identity matrix.

### Example description

The example defines the mass transport in liquid flow with a constant liquid velocity in 1D domain.

The domain size is 0.8 m. The initial value of the primary variable is 0. The Dirichlet boundary conditions are applied on the left and right boundaries with respective values 1.0 and 0.0. The constant velocity is 1.e-4 m/s. The diffusion coefficient is $10^{-9}$ m/s. The analysis duration is 7200 s.

Derived by Ogata, A. and Banks [1], the analytical solution of the example is $$c(x, t)=\frac{1}{2}\left(\mathrm{erfc}\left(\frac{x-v t}{2\sqrt{K t}}\right) +\mathrm{exp}(vx/K) \mathrm{erfc}\left(\frac{x+v t}{2\sqrt{K t}}\right) \right)$$ where $v$ and $K$ are the scalar values of $\mathbf v$ and $\mathbf K$, respectively. Since the given diffusion coefficient is too small, the term with $\mathrm {exp}$ function is dropped due to overflow. This leads to $$c(x, t) \approx \frac{1}{2} \mathrm{erfc}\left(\frac{x-v t}{2\sqrt{K t}}\right)$$

The example is for mass transport process. To tailor it for running with HT process in OGS, the input material data are defined such as

• for liquid phase, the density, the viscosity and the specific heat capacity are set to 1 and the thermal conductivity is $10^{-9}$.
• for solid phase all input data are zero,
• The porosity is set to 1.

The tuning parameter for IsotropicDiffusion takes small value 0.15, while the cutoff velocity is 0.

Note: With the same material data, the example is also tested with ThermoHydroMechanics process by fixing displacement to zero at all mesh nodes.

### Result

With the Galerkin finite element method, fine spatial and temporal discretizations give more accurate results, however, it can lead to spatial oscillation when Péclet number is large.

To investigate such phenomenon, different spatial and temporal discretizations are considered for the example.

The following figures show the benchmark results with two different spatial and temporal discretization sets. Both results show that the stabilization of IsotropicDiffusion eliminates the spatial oscillation.

The following figure compares the simulation results obtained with $\alpha=0.15$ and its maximum value 1, respectively:

### Reference

[1] Ogata, A. and Banks, R.B., 1961. A solution of the differential equation of longitudinal dispersion in porous media: fluid movement in earth materials. US Government Printing Office.

This article was written by Wenqing Wang. If you are missing something or you find an error please let us know. Generated with Hugo 0.96.0. Last revision: July 26, 2022
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## Useful UNIX API:s

Had an interesting conversation with a buddy last night. It started out as a shift-reduce problem with Bison and ended up a ping-pong of useful UNIX API:s. We concluded that despite having worked professionally with UNIX for over a decade, it is still very satisfying finding gems like these.

Most people are completely unaware they exist and end up rolling their own (buggy) implementations. For instance, string manipulation and various forms of linked lists. Which is why I many years ago extracted the frog DNA from Finit to a separate library called libite, or -lite for short. It imports the OpenBSD strlcpy() family of API:s, up-to-date queue.h with the _SAFE iterators, and more. Some people like libbsd for this, but I’ve found many of the ports incomplete and unsafe and prefer to stay closer to the upstream *BSD versions.

Update: This post was originally written Nov 14, 2015. It was a Saturday and I remember being extremely inspired when I wrote it. I’ve continued adding to it over the years, and still do. So, as of Jul 2, 2017 I’m bumping the modification date each time I add something new :-)

## GIT, Autoconf and Automake in OpenBSD

Reminder to self:

echo "https://ftp.eu.openbsd.org/pub/OpenBSD/" >/etc/installurl

Select the latest versions, then add the following to ~/.profile:

AUTOCONF_VERSION=2.69
AUTOMAKE_VERSION=1.15
export AUTOCONF_VERSION AUTOMAKE_VERSION

With your selected versions, of course.

## HTTPS proxy for Merecat httpd

This is a HTTPS proxy HowTo for Merecat httpd using pound and OpenSSL. Pound is a reverse proxy, load balancer, and HTTPS front-end for Web servers. It is available in Debian/Ubuntu and is very simple to set up: First install the package, including OpenSSL, or LibreSSL: sudo apt install pound openssl Use OpenSSL to create a self-signed certificate: mkdir ~/certs cd ~/certs openssl req -x509 -newkey rsa:4096 -keyout key.pem -out cert. [Read More]

## Running ikiwiki in Merecat httpd

This is a HowTo for setting up ikiwiki with Merecat httpd. First install ikiwiki $sudo apt install ikiwiki libcgi-session-perl libcgi-formbuilder-perl Follow the steps to setup a new Wiki or Blog. In this example we set up a wiki in our ~/public_html:$ ikiwiki --setup /etc/ikiwiki/auto.setup ... Successfully set up wiki: url: http://localhost/~jocke/wiki srcdir: ~/wiki destdir: ~/public_html/wiki repository: ~/wiki.git To modify settings, edit ~/home.setup and then run: \$ ikiwiki --setup ~/home. [Read More]

## Emulate an actual MTD device in Qemu

Having worked with Linux for the last 20 years, and embedded for more than ten of them, I’ve become quite a fan of virtualization in general and Qemu in particular.

Qemu is a fantastic little tool, created by the Open Source superhero Fabrice Bellard. It can be used to verify an embedded system without having to deal with the problems of actual HW until you really have to. Don’t get me wrong, HW excites me like any other nerd, but if the HW is new and shaky it can be quite a pain to develop higher level functions.

My holy grail is to have a 100% complete and accurate virtualization target per architecture to test my various software projects on. That’s why I created TroglOS.


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# Can someone help Scott Manley explain this Snoopy-capturing maneuver?

In his recent video Apollo 10's Lunar Module Snoopy Is Lost In Space - Could We Bring it Home? Scott Manley uses some fancy supplemental techniques in KSP to simulate and explain a possible mission to capture Snoopy (Apollo 10 Lunar Module) "...and returning him safely to the Earth."

But at about 09:38 Manley surprisingly finds himself at a bit of a loss for words. This explanation says little more than "it takes less Delta V because you square it and so it takes less Delta V":

Now when you’re doing capture from deep space, you want to get down close to the Earth, because that way you’re actually using Earth’s gravity to reduce the amount of Delta V you need to perform the capture.

If Earth wasn’t there, you’d actually need more Delta V to match the orbit, because you fall down into it you get this square law where you’re adding your velocity squared, and… listen, it’s just a simple thing to do. You drop down into the gravity well and then you perform your burn there and then it becomes… it means you need less Delta V to perform this.

Question: Can someone help Scott Manley out and explain more clearly what it is that he's trying to explain?

cued at 09:38

• Scott Manley studied Astrophysics. He definitely knows what he is talking about, he just doesn’t want to give a lengthy explanation that most people would not understand and make them just annoyed. – Hans May 31 '19 at 8:10
• Possible duplicate of Oberth effect for Earth vehicles – Hans May 31 '19 at 8:19
• I do not mean to be overly defensive here, but according to His bio on the B612 foundation homepage ”Scott spent a decade in academia studying astrophysics and computational physics at the University of Glasgow and Armagh Observatory where he focused on small bodies in the solar system and specifically the probabilities of collision.”, so he most definitely knows what he is talking about. – Hans May 31 '19 at 8:24
• I'm pretty sure he's talking about the Oberth effect - I've heard him describe it similarly before in previous videos with a few "squarings then addings" and "bangs for bucks" – Jack May 31 '19 at 10:54
• @uhoh yeah I agree, I don't think that answers your question - I was just confirming that, in my experience, Manley often talks in a - shall we say - inexact way about somewhat complex concepts ;) – Jack May 31 '19 at 11:44

Despite watching a few times it looks like I linked the use of the term "capture" at this point in the video with the use of the term "capture" at 08:20 in the video. But that's about the mechanical capture of Snoopy during a docking maneuver and this is about the gravitational capture of the combined pair in the Earth's gravitational field.

What Manley is trying to say is that:

If you want to transition from a gravitationally unbound to gravitationally bound status in the Earth's field, this is a manipulation of the energy of the spacecraft's orbit, which depends on position and $$v^2$$, and a $$\Delta v$$ impulse can have the largest effect on $$v^2$$ when

1. the $$\Delta \mathbf{v}$$ vector is parallel or antiparallel with $$\mathbf{v}$$, and
2. the speed $$v$$ is maximum.

And for some further mathematical insight into why this is true, and some intriguing graphical illustrations of this as well, one can read the several excellent answers to Oberth effect for Earth vehicles.

• I think this answer is spot-on. – uhoh Jun 1 '19 at 1:45
• So I've accepted it for now. I'm happy to consider a different answer though – uhoh Jun 2 '19 at 14:59


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# Eigenvalues and eigenvectors

1. May 28, 2009

### Jennifer1990

1. The problem statement, all variables and given/known data
Let A and B be similar matrices
a)Prove that A and B have the same eigenvalues

2. Relevant equations
None

3. The attempt at a solution
Firstly, i dont see how this can even be possible unless the matrices are exactly the same :S

2. May 28, 2009

### matt grime

So you think that eigenvalues uniquely characterize a matrix? What about

10
01

and

11
01

for example?

You've put 'none' for relevant equations. That isn't true - there's a definition of 'similar' and many for 'eigenvalue'. Try it. HINT: polynomials.

3. May 28, 2009

### Random Variable

EDIT: Changed "equation" to "polynomial"

You have to show that A and B=P^-1AP (for some invertible matrix P) have the same characteristic polynomial.

Last edited: May 28, 2009
4. May 28, 2009

### HallsofIvy

Staff Emeritus
Oh, I think that way is much too complicated!

Do it directly from the equation:
If $Av= \lambda v$ then, for any invertible P, $P^{-1}Av= \lambda P^{-1}v$. Now define $u= P^{-1}v$.

5. May 28, 2009

### Random Variable

6. May 28, 2009

### Random Variable

or let $$Av = \lambda v$$

then $$AP^{-1}Pv = \lambda v$$ and go from there

7. May 28, 2009

### Jennifer1990

what do u mean by the same characteristic equation?

8. May 28, 2009

### Random Variable

EDIT: changed "equation" to "polynomial"

The the characteristic polynomial of matrix A is $$det(A- \lambda I).$$

The characterisitc polynomial of matrix B is $$det(B - \lambda I) = det(PAP^{-1} - \lambda I)$$

so show that $$det(A- \lambda I) = det(PAP^{-1} - \lambda I)$$

But there are easier ways as HallsofIvy noted.

Start with $$Av = \lambda v$$ where v is a nonzero vector

then $$AP^{-1}Pv = \lambda v$$ since $$P^{-1}P = I$$

Do you know what to do next?

Last edited: May 28, 2009
9. May 28, 2009

### jbunniii

A and B are similar if and only if they both represent the same linear map, with respect to two possibly different bases. Eigenvalues are defined independently of what basis, if any, you choose. QED.

10. May 28, 2009

### Staff: Mentor

Make that "The characteristic equation of matrix A is $$det(A- \lambda I) = 0.$$"
For it to be an equation, it at least has to have an equals sign.

11. May 28, 2009

### Random Variable

Sorry. What I should have said is that they have the same characteristic POLYNOMIAL.

12. May 28, 2009

### Jennifer1990

Av = lambda v
(AP^-1 P)v = lambda v
Bv = lambda v

i think?

13. May 28, 2009

### Jennifer1990

oh wait....B = P^-1 AP .....so what i said is wrong...

how can i manipulate A P^-1 P to look like P^-1 AP?

14. May 29, 2009

### Jennifer1990

ohhh i see...

since they can have the same eigenvalues, does this mean that the matrices can also have the same eigenvectors?

15. May 29, 2009

### Random Variable

They can, but it's not likely.

16. May 29, 2009

### Jennifer1990

I just tried several similar matrices but they all share the same eigenvector
Can i get an example where two similar matrices have different eigenvectors?

17. May 29, 2009

### HallsofIvy

Staff Emeritus
I'm surprised you were able to find similar matrices that had the same eigenvectors!

$$A= \begin{bmatrix}2 & 0 \\ 0 & 3\end{bmatrix}$$
has, obviously, 2 and 3 as eigenvalues with corresponding eigenvectors <1 0> and <0 1>.

$$B= \begin{bmatrix}1 & -1 \\ 2 & 4\end{bmatrix}$$
has the same eigenvalues with corresponding eigenvectors <1, -1> and <1, -2>.

All I did was start with the obvious diagonal matrix, A, choose a simple invertible P:
$$P= \begin{bmatrix}2 & 1 \\ 1 & 1\end{bmatrix}$$
and calculate $B= P^{-1}AP$.


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