text:
Who's up with nmap, revisited

I am, sad to say, the de facto network administrator for my small company. Today, one of my partners was having a connectivity problem, and while I was solving that problem (some cabling got disconnected), I learned that my little network probing script, whosup, needed to be updated.

Originally, whosup was a one-line shell script that ran nmap with certain parameters,

nmap -sP 192.168.1.*

which told nmap to do a “ping scan” of my local network and report the hosts that respond. The reason I made a script out of such a simple command is that I didn’t use nmap very often and couldn’t remember the options from one use to the next.

Two things have changed since the last time I used whosup:

1. We now have a few Vista machines at work, and they don’t respond to the ping scan unless I run it as the superuser.
2. Nmap has been upgraded, and the current version is more verbose in its output and is in the process of changing its ping scan option.

To account for these changes and to do a little future-proofing, I changed whosup from a shell script to Perl:

1:  #!/usr/bin/perl
2:
3:  @nmap = sudo nmap -sn 192.168.1.0/24 2>&1;
4:  for (@nmap) {
5:    print "\$1\n" if /^Nmap scan.+?(\d+\.\d+\.\d+\.\d+).*/;
6:  }

Line 3 runs nmap as the superuser (prompting me for my administrative password) and puts the output lines into the @nmap list.

• The -sn option is the “no port scan” option used for host discovery. The older -sP option, which -sn replaces, still works in Version 5.21 but is being phased out.
• The 192.168.1.0/24 tells nmap to look at all the IPs whose first three bytes are 192, 168, and 1. Three bytes is 24 bits, which is where the /24 comes from.
• Finally, the 2>&1 is the standard bash redirection operator which merges standard error into standard output. I did this because nmap often writes messages to standard error, and I wanted the rest of the program to filter them out.

Lines 4-6 then filter the nmap output lines. The nmap output from Line 3 looks something like this,

Starting Nmap 5.21 ( http://nmap.org ) at 2010-08-19 22:16 CDT
Nmap scan report for 192.168.1.1
Host is up (0.0053s latency).
Nmap scan report for 192.168.1.10
Host is up (0.0038s latency).
Nmap scan report for 192.168.1.100
Host is up (0.034s latency).
Nmap scan report for 192.168.1.101
Host is up (0.035s latency).
Nmap scan report for 192.168.1.103
Host is up (0.27s latency).
Nmap scan report for 192.168.1.107
Host is up (0.27s latency).
Nmap scan report for 192.168.1.109
Host is up.
Nmap scan report for 192.168.1.110
Host is up (0.16s latency).
MAC Address: 00:11:22:33:44:55 (Sony Computer Entertainment)
Nmap done: 256 IP addresses (8 hosts up) scanned in 10.23 seconds

which has way too much information.1 I just want the IP numbers of the hosts that respond. Line 5 plucks out the IP numbers and prints them, one per line. The final whosup output looks like this:

192.168.1.1
192.168.1.10
192.168.1.100
192.168.1.101
192.168.1.105
192.168.1.109
192.168.1.110

A simple list of the hosts connected to the network. When I ran it at work today, I found a host I didn’t know about. Turns out one of my other partners has an old router in his office acting as hub.

1. The MAC addresses in the output above have been changed to protect the innocent (how many of you are old enough to get that reference?), but the rest of the output is real.


text:
Volume 405 - 7th Symposium on Prospects in the Physics of Discrete Symmetries, DISCRETE 2020-2021 (DISCRETE2020-2021) - Parallel sessions Monday
Belle II experiment: status and prospects
E. Waheed
Full text: pdf
Pre-published on: May 19, 2022
Published on:
Abstract
The Belle~II experiment at the SuperKEKB $e^{+}e^{-}$ collider is the successor to the Belle experiment. The instantaneous luminosity is designed to reach $6.5\times 10^{35}~\rm cm^{-2}s^{-1}$ and it aims to record target integrated luminosity of $50~\rm ab^{-1}$ which is 50 times more than that of Belle. The current integrated luminosity has so far reached $213~\rm fb^{-1}$ by summer 2021. Belle~II aims to measure the matrix elements of Cabibbo-Kobayashi- Maskawa (CKM) matrix and their phases with unprecedented precision. With $50~\rm ab^{-1}$ of data, Belle~II will be able to discover New Physics beyond the Standard Model. The initial physics results have already confirmed the performance of the detector. We briefly report the status and prospects of the Belle~II experiment.
DOI: https://doi.org/10.22323/1.405.0031
How to cite

Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.

Open Access

format: plain


text:
# what's the formula?

• March 22nd 2009, 07:23 PM
faolan
what's the formula?
What is the formula for this?

If the line passing through (7,y) and (1,0) is parallel to the line joining 4,4 and -2,1, find y.

How do I solve for y?
• March 22nd 2009, 07:29 PM
Reckoner
Quote:

Originally Posted by faolan
If the line passing through (7,y) and (1,0) is parallel to the line joining 4,4 and -2,1, find y.

Find the slope of the second line. Find the slope of the first line (in terms of $y$). What must be true about the slopes of two parallel lines? This fact will give you your equation, which you can then solve for $y.$


text:
# Math Help - First Order Differential Equation

1. ## First Order Differential Equation

find the general solution of the first order differential equation, t2 y’ – 2 ty = 3

2. Originally Posted by winsome
find the general solution of the first order differential equation, t2 y’ – 2 ty = 3
I'm assuming you mean $t^2y^{\prime}-2ty=3$.

First note that this is the same thing as saying $y^{\prime}-\frac{2}{t}y=\frac{3}{t^2}$.

Now this is a first order linear DE. Do you know how to proceed using the integrating factor method?

3. i got integrating factor of this equaiton is t^-2
is that is right ?
if yes then i m unable to get its final answer

4. Yes it's right.

So multiply both sides by the integrating factor to get

$\displaystyle t^{-2}\frac{dy}{dt} - 2t^{-3}\,y = 3t^{-4}$

$\displaystyle \frac{d}{dt}(t^{-2}y) = 3t^{-4}$.

You should be able to go from here.

5. thanks

6. Originally Posted by Prove It
Yes it's right.

So multiply both sides by the integrating factor to get

$\displaystyle t^{-2}\frac{dy}{dt} - 2t^{-3}\,y = 3t^{-4}$

$\displaystyle \frac{d}{dt}(t^{-2}y) = 3t^{-4}$.

You should be able to go from here.

thanks for providing solution


text:
Difference between revisions of "expert"

Template programming (%if; ... %end;)

The template mechanism provides a very powerful mechanism to construct HTML (or other) pages according to the content of a GeneWeb base. This section is not intending to give an exhaustive description of the corresponding language. Through some examples extracted from gw/etc/perso.txt, it provides a glimpse of the possibility. The last two examples are extracted from a template that generates LaTeX rather than HTML.

For further analysis, explore the various other template files, and on last resort, explore the Ocaml source files!!

Programming constructs:

 %define; ... %end;
%if; [%elseif;] [%else;] %end;
%let;xxx;zzz%in;
%foreach; ... %end;
%apply; ... [%with;... [%and;] ...%end;]
%nl; %nn; %sp;

 <title>%nn;
%if;has_public_name;
%if;has_qualifiers;%public_name; %qualifier;
%else;%public_name; %surname;%end;
%else;
%if;has_qualifiers;%first_name; %qualifier;
%else;%first_name; %surname;%end;
%end;
</title>

%define;married_to(sexx, date_place)
%if;(sexx = 0 or sexx = 2)
%if;are_married;[*married%t to:::date_place]0%nn;
%elseif;are_not_married;[*relationship%t to:::date_place]0%nn;
%elseif;are_engaged;[*engaged%t to:::date_place]0%nn;
%elseif;is_no_sexes_check;[*relationship%t to:::date_place]0%nn;
%elseif;is_no_mention;date_place [*with]%nn;
%end;
%else;
%if;are_married;[*married%t to:::date_place]1%nn;
%elseif;are_not_married;[*relationship%t to:::date_place]1%nn;
%elseif;are_engaged;[*engaged%t to:::date_place]1%nn;
%elseif;is_no_sexes_check;[*relationship%t to:::date_place]1%nn;
%elseif;is_no_mention;date_place [*with]%nn;
%end;
%end;
%end;

%if;(bvar.can_send_image != "no" and image = "" and first_name != "?" and surname != "?")

%end;

%define;hgindex(alxx, snxx, fnxx, occxx)
%if;(alxx = "0")
%if;(occxx = "0")
\index{snxx, fnxx}
%else;
\index{snxx, fnxx (occxx)}
%end;
%else;
%if;(occxx = "0")
\index{alxx, voir snxx, fnxx}
%else;
\index{alxx, voir snxx, fnxx (occxx)}
%end;
%end;
%end

%foreach;alias;
{\it {\bf %alias;}}%apply;hgindex(alias, surname, first_name, occ)\\%nl;
%end;

This list does not claim to be exhaustive (but pretty close!!).

"access_by_key"
"access"
"age"
"alias"
"anc_sosa"
"ancestor_level"
"ancestor_level2"
"ancestor_surname"
"ancestor_tree_line"
"ancestor"
"are_divorced"
"are_engaged"
"are_married"
"are_not_married"
"are_separated"
"auto_image_file_name"
"baptism_date"
"baptism_note"
"baptism_place"
"baptism_witness"
"base"
"birth_date"
"birth_note"
"birth_place"
"birth_witness"
"birth_witness"
"birthday"
"browsing_with_sosa_ref"
"burial_date"
"burial_note"
"burial_place"
"burial_witness"
"bvar"
"canton"
"cell"
"child_cnt"
"child_name"
"child"
"colspan"
"comment"
"compilation_time"
"computable_age"
"computable_death_age"
"computable_marriage_age"
"consanguinity"
"count"
"country"
"county"
"cousin_level"
"cremated_date"
"cremation_place"
"cremation_witness"
"date_begin"
"date_end"
"date"
"dates"
"day"
"death_age"
"death_date"
"death_note"
"death_place"
"death_witness"
"desc_level"
"descendant_level"
"died"
"district"
"divorce_date"
"empty_sorted_list"
"enclosing"
"evar"
"event_witness_kind"
"event_witness_relation_kind"
"event_witness_relation"
"event_witness"
"event"
"fam_access"
"family_cnt"
"family"
"father_age_at_birth"
"father_sosa"
"father"
"first_name_alias"
"first_name_key_strip"
"first_name_key_val"
"first_name_key"
"first_name"
"fwitness"
"has_aliases"
"has_baptism_date"
"has_baptism_note"
"has_baptism_place"
"has_baptism_witnesses"
"has_birth_date"
"has_birth_note"
"has_birth_place"
"has_birth_witnesses"
"has_burial_date"
"has_burial_note"
"has_burial_place"
"has_burial_witnesses"
"has_children"
"has_comment"
"has_consanguinity"
"has_cremation_date"
"has_cremation_place"
"has_cremation_witnesses"
"has_date"
"has_death_date"
"has_death_note"
"has_death_place"
"has_death_witnesses"
"has_event"
"has_families"
"has_first_names_aliases"
"has_fsources"
"has_fwitness"
"has_history"
"has_image"
"has_marriage_note"
"has_nephews_or_nieces"
"has_nobility_titles"
"has_note"
"has_notes"
"has_occupation"
"has_parents"
"has_place"
"has_possible_duplications"
"has_psources"
"has_public_name"
"has_qualifiers"
"has_relation_her"
"has_relation_him"
"has_relations"
"has_siblings"
"has_sosa"
"has_sources"
"has_spouse"
"has_src"
"has_surnames_aliases"
"has_witnesses"
"hexa"
"history_file"
"ident_key"
"image_html_url"
"image_medium_size"
"image_size"
"image_small_size"
"image_url"
"image"
"incr_count"
"ind_access"
"index"
"interval"
"is_buried"
"is_center"
"is_cremated"
"is_descendant"
"is_empty"
"is_female"
"is_first"
"is_invisible"
"is_last"
"is_left"
"is_male"
"is_no_mention"
"is_no_sexes_check"
"is_private"
"is_public"
"is_restricted"
"is_right"
"is_self"
"is_sibling_after"
"is_sibling_before"
"is_top"
"item"
"lazy_force"
"lazy_printed"
"level"
"mark_descendants"
"marriage_age"
"marriage_date"
"marriage_note"
"marriage_place"
"max_anc_level"
"max_cous_level"
"max_desc_level"
"misc_names"
"month"
"mother_age_at_birth"
"mother_sosa"
"mother"
"name"
"nb_children"
"nb_events"
"nb_families"
"nb_ind"
"nb_times"
"next_item"
"nobility_title"
"note"
"notes"
"number_of_ancestors"
"number_of_descendants"
"number_of_subitems"
"occ"
"occupation"
"octal"
"on_baptism_date"
"on_birth_date"
"on_burial_date"
"on_cremation_date"
"on_date"
"on_death_date"
"on_marriage_date"
"origin_file"
"other"
"parent"
"place_key"
"place"
"prec"
"prev_fam_father"
"prev_fam_index"
"prev_fam_mother"
"prev_family"
"prev_item"
"public_name"
"pvar"
"qualifier"
"region"
"related_type"
"related"
"relation_her"
"relation_him"
"relation_type"
"relation"
"reset_count"
"reset_desc_level"
"same"
"self"
"set_infinite_desc_level"
"sex"
"slash_baptism_date"
"slash_birth_date"
"slash_burial_date"
"slash_cremation_date"
"slash_death_date"
"slash_divorce_date"
"slash_marriage_date"
"sorted_list_item"
"sosa_access"
"sosa_in_list"
"sosa_ref"
"sosa"
"source_type"
"source"
"spouse"
"src"
"surname_alias"
"surname_begin"
"surname_end"
"surname_key_strip"
"surname_key_val"
"surname_key"
"surname"
"title"
"town"
"township"
"v"
"var"
"version"
"wedding_birthday"
"witness_relation"
"witness"
"year"

Note for has_event (v7)

Note that the has_event function does not consider birth, baptism, death and burial as "events" per se. If you want those events to be taken into account in this function, then you have to add display_timeline=yes in your .gwf parameter file.

Macros (%x)

See Macros for a description of their use.

Below is the result of calling all 26 lower case possible macros: This table is automatically generated by inserting a bit of HTML/GeneWeb code into the notes of one person in your base. The corresponding code is here

Commands (m=XXX)

List of the commands appearing in URL with the form:

%sm=COMMAND;p=param1;n=param2;

This list does not claim to be exhaustive, and does not "explain" what each command does!

"A"
"ANM"
"AN"
"AM"
"AS_OK"
"B"
"C"
"CAL"
"CHG_CHN"
"CHG_CHN_OK"
"CHG_FAM_ORD"
"CHG_FAM_ORD_OK"
"CONN_WIZ" *
"D"
"DAG" *
"DEL_FAM"
"DEL_FAM_OK"
"DEL_IMAGE"
"DEL_IMAGE_OK"
"DEL_IND"
"DEL_IND_OK"
"DOC" (* obsolete *)
"FORUM"
"FORUM_DEL"
"FORUM_P_P"
"FORUM_SEARCH"
"FORUM_VAL"
"FORUM_VIEW"
"H"
"HIST"
"HIST_CLEAN"
"HIST_CLEAN_OK"
"HIST_DIFF"
"HIST_SEARCH"
"IM" *
"IMH" *
"INV_FAM"
"INV_FAM_OK"
"KILL_ANC"
"LB"
"LD"
"LL"
"LM"
"LEX"
"MISC_NOTES"
"MISC_NOTES_SEARCH"
"MOD_DATA"
"MOD_DATA_OK"
"MOD_FAM"
"MOD_FAM_OK"
"MOD_IND"
"MOD_IND_OK"
"MOD_NOTES"
"MOD_NOTES_OK"
"MOD_WDOC"  (* obsolete *)
"MOD_WDOC_OK"  (* obsolete *)
"MOD_WIZNOTES" *
"MOD_WIZNOTES_OK" *
"MRG"
"MRG_DUP"
"MRG_DUP_IND_Y_N"
"MRG_DUP_FAM_Y_N"
"MRG_FAM"
"MRG_FAM_OK"
"MRG_MOD_FAM_OK"
"MRG_IND"
"MRG_IND_OK"
"MRG_MOD_IND_OK"
"N"
"NG"
"NOTES"
"OA"
"OE"
"P"
"POP_PYR"
"PS" P
"R"
"REQUEST"
"RL"
"RLM" *
"S"
"SND_IMAGE"
"SND_IMAGE_OK"
"SRC" *
"STAT" B
"CHANGE_WIZ_VIS" *
"TT"
"U"
"VIEW_WIZNOTES"
"WDOC" (* obsolete *)
"WIZNOTES" *
"WIZNOTES_SEARCH" *

Commands marked with a * are documented below:

Variables (evar and bvar)

GeneWeb proposed a general purpose mechanism allowing the user/programmer to extend at will the notion of variable described here.

If a new variable is defined in the .gwf configuration file, then it will be possible to test for the value of this variable in the context of a template file. For instance, if we have added

new_var=some-text

in .gwf, then the following code in the template will be able to perform some specific action:

%if; (bvar.new_var = "sometext" )
... perform some specific action ...
%end;

Similarly, if we have added a new variable in the URL of the query to GeneWeb (localhost:2317/base?p=first-name;n=last-name;lang=fr;tree=3, then it is possible to test for this variable with code such as:

%if; (evar.tree = 3 )
... display 3 generation tree ...
%end;

The value itself of such variables can be inserted in the body of a template by typing %evar.tree;, for instance:

<title>Tree with %evar.tree; generations</title>

The special variable var is treated in the following fashion within notes, sources and comments: If you define in the .gwf file a variable {{{1}}}, then invoquing the macro %vtext; in a note or a template will produce the text some_text as in the following example:

var_who=Bond, James Bond

"My name is %vwho;." in a note will be transformed into "My name is Bond, James Bond.".

This feature is used by some to facilitate signature of sources. The .gwf file contains a list of var_nickname definitions whose value is a full name and possibly a pointer to a page containing more detailed information:

var_henri=First_name Lastname

(no %x or %macro; in the value of the parameter!!).

Building trees through direct url construction

See trees or trees/fr

GeneWeb Manual

Use and manage genealogical databases

Technical annex


text:
# Which statistical method should I use for comparing machine run-time of two algorithms?

I am comparing the run-time of two algorithm by solving different instance of the problems. Sample of my data:

problem_id  |  algo_original_time  |  algo_improved_time
---------------------------------------------------------
prob_01     |  0.56                |  0.036
prob_02     |  0.26                |  0.005
prob_03     |  0.75                |  0.055
....

Note that, all of the problem instances are distinct and they do not have any correlation.

I have already used cross-validation plot to represent the data. Is there any better way/ statistical method to compare the run-time of this two algorithms.

• At the level of measurement, it's seldom the case that run-time measurements are this precisely repeatable- if you ran the same problems again would you get exactly the same times? If not, then you need to quantify the variation in running times and most likely repeat runs to average out the variation. – Brian Borchers Sep 12 '19 at 14:23
• Are you trying to determine how much faster the one code is than the other (e.g. A is 10.6 times faster than B)? In that case it might be appropriate to use the geometric mean of the run times. – Brian Borchers Sep 12 '19 at 14:24

This is a typical use case for a paired t-test. The idea is to consider only the runtime difference $$\Delta t$$ for each problem and test for the null hypothesis $$E(\Delta t)=0$$. For a step-by-step explanation, see e.g. (the article refers to segmentation evaluation, but on an abstract level the problem is identiclal to yours):

Mao, Kanungo: "Empirical performance evaluation methodology and its application to page segmentation algorithms". IEEE Transactions on Pattern Analysis and Machine Intelligence 23 (3), pp. 242-256 (2001)


text:
# Easy Probability

• Sep 10th 2010, 10:25 AM
Mr Rayon
Easy Probability
If Pr(A) = 4 Pr(B), $Pr(A\cup B) =0.8$ and $Pr(A\cap B) = 0.2$, find:
a) Pr(B)
b) Pr(A)

The bit that confuses me most was probably "Pr(A) = 4 Pr(B)" in the question above. Is this a typo? I've tried figuring this out for few times but I keep getting negative numbers.

Any help would be appreciated.
• Sep 10th 2010, 10:28 AM
Plato
Recall that $P(A\cup B)=P(A)+P(B)-P(A\cap B)$
• Sep 10th 2010, 10:32 AM
Mr Rayon
Yeah, I used that formula, just rearranged but kept getting negative numbers, ignoring Pr(B) in the question and assuming it was a typo.
• Sep 10th 2010, 10:42 AM
Plato
$0.8 = 5P(B) - 0.2\, \Rightarrow \,5P(B) = 1$

Where is there a negative?
• Sep 10th 2010, 05:55 PM
Soroban
Hello, Mr Rayon!

Quote:

$\text{If }\text{Pr}(A) = 4\!\cdot\!\text{Pr}(B),\;\;\text{Pr}(A\cup B) = 0.8,\;\;\text{Pr}(A\cap B) = 0.2$

$\text{Find: }\,\text{Pr}(A)\,\text{ and }\,\text{Pr}(B)$

That first equation says: . $\text{Pr}(A)$ is four times $\text{Pr}(B).$

Formula: . $\text{Pr}(A \cup B) \;=\;\text{Pr}(A) + \text{Pr}(B) - \text{Pr}(A \cap B)$

Substitute: . . . $0.8 \quad\;= \;4\!\cdot\!\text{Pr}(B) + \text{Pr}(B) \;\;- \;\; 0.2$

So we have: . $1.0 \;=\;5\!\cdot\!\text{Pr}(B) \quad\Rightarrow\quad \boxed{\text{Pr}(B) \,=\,0.2}$

Then: . $\text{Pr}(A) \:=\:4\!\cdot\!\text{Pr}(B) \;=\;4(0.2) \quad\Rightarrow\quad \boxed{\text{Pr}(A)\;=\;0.8}$


text:
# NDK_AIRLINE_FITTED

 int __stdcall NDK_AIRLINE_FITTED ( double * pData, size_t nSize, double mean, double sigma, WORD S, double theta, double theta2, FIT_RETVAL_FUNC retType )

Returns an array of cells for the fitted values (i.e. mean, volatility and residuals)

Returns
status code of the operation
Return values
 NDK_SUCCESS Operation successful NDK_FAILED Operation unsuccessful. See Macros for full list.
Parameters
[in] pData is the univariate time series data (a one dimensional array).
[in] nSize is the number of observations in pData.
[in] mean is the model mean (i.e. mu).
[in] sigma is the standard deviation of the model's residuals/innovations.
[in] S is the length of seasonality (expressed in terms of lags, where s > 1).
[in] theta is the coefficient of first-lagged innovation (see model description).
[in] theta2 is the coefficient of s-lagged innovation (see model description).
[in] retType is a switch to select a output type
Order   Description
1 Fitted mean (default)
2 Fitted standard deviation or volatility
3 Raw (non-standardized) residuals
4 Standardized residuals
Remarks
1. The underlying model is described here.
2. The time series is homogeneous or equally spaced
3. The time series may include missing values (e.g. NaN) at either end.
4. The long-run mean argument (mean) can take any value or be omitted, in which case a zero value is assumed.
5. The value of the residuals/innovations standard deviation (sigma) must be positive.
6. The season length must be greater than one.
7. The input argument for the non-seasonal MA parameter - theta - is optional and can be omitted, in which case no non-seasonal MA component is included.
8. The input argument for the seasonal MA parameter - theta2 - is optional and can be omitted, in which case no seasonal MA component is included.
Requirements
Header SFSDK.H SFSDK.LIB SFSDK.DLL
Examples

 Namespace: NumXLAPI Class: SFSDK Scope: Public Lifetime: Static
 NDK_AIRLINE_FITTED ( double[] pData, UIntPtr nSize, double mean, double sigma, short dSeason, double theta, double theta2, FIT_RETVAL_FUNC retType )

Returns an array of cells for the fitted values (i.e. mean, volatility and residuals)

Return Value

a value from NDK_RETCODE enumeration for the status of the call.

 NDK_SUCCESS operation successful Error Error Code
Parameters
[in] pData is the univariate time series data (a one dimensional array).
[in] nSize is the number of observations in pData.
[in] mean is the model mean (i.e. mu).
[in] sigma is the standard deviation of the model's residuals/innovations.
[in] dSeason is the length of seasonality (expressed in terms of lags, where s > 1).
[in] theta is the coefficient of first-lagged innovation (see model description).
[in] theta2 is the coefficient of s-lagged innovation (see model description).
[in] retType is a switch to select a output type
Order   Description
1 Fitted mean (default)
2 Fitted standard deviation or volatility
3 Raw (non-standardized) residuals
4 Standardized residuals
Remarks
1. The underlying model is described here.
2. The time series is homogeneous or equally spaced
3. The time series may include missing values (e.g. NaN) at either end.
4. The long-run mean argument (mean) can take any value or be omitted, in which case a zero value is assumed.
5. The value of the residuals/innovations standard deviation (sigma) must be positive.
6. The season length must be greater than one.
7. The input argument for the non-seasonal MA parameter - theta - is optional and can be omitted, in which case no non-seasonal MA component is included.
8. The input argument for the seasonal MA parameter - theta2 - is optional and can be omitted, in which case no seasonal MA component is included.
Exceptions
Exception Type Condition
None N/A
Requirements
Namespace NumXLAPI SFSDK Public Static NumXLAPI.DLL
Examples

References
* Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
* Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740
* D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
* Box, Jenkins and Reisel; Time Series Analysis: Forecasting and Control; John Wiley & SONS.; 4th edition(Jun 30, 2008), ISBN: 470272848


text:
By Math Original No comments

### Definition

Geometric Progression is the sequence of numbers such that the next term of the sequence comes by multiplying or dividing the preceding number with the constant (non-zero) number. And the constant number is called the Common Ratio. It is also known as the Geometric Sequence.

a, ar, ar2, ar3,……..,arn

The first term of the sequence is called the Initial Term or the scale factor which is denoted as ‘a’.

The ratio of a term to its next term of the sequence is called the Common ratio which is denoted by ‘r’.

The general term that is the nth term of the geometric progression with the initial term ‘a’ and the common ratio ‘r’ is $\displaystyle {{a}_{n}}=a\cdot {{r}^{{n-1}}}$.

Example 1: Find the nth term of 3, 6, 12, 24, 48,……….aif the number of terms are 10?

Solution: Given the progression  3, 6, 12, 24, 48,……….aand n=10.
By the general formula of the geometric progression $\displaystyle {{a}_{n}}=a\cdot {{r}^{{n-1}}}$

The first term a=3
Common ratio is r=6/3=2
Therefore $\displaystyle {{a}_{n}}=3\cdot {{2}^{{10-1}}}=3\cdot {{2}^{9}}=3\cdot 512=1536$

### Finite and Infinite Geometric Progression

The Geometric Progression with a limited number of terms is called Finite Sequence. It has a last term.

### Example: 1, 3, 9, 27,…..729

This is a finite sequence with a=1 and r=3

The Geometric Progression with unlimited number of terms is called Infinite Sequence. It does not have a last term.

Example: 1, 5, 25, 125,……..
This is an infinite sequence with a=1 and r=5

### How to find the common ratio?

The common ratio is the ratio of the term of the geometric sequence to its previous term.And is denoted by “r”.
To find the common ratio we need to take the ratio of the terms with their preceding term.
$\displaystyle \frac{{{{a}_{2}}}}{{{{a}_{1}}}}=\frac{{{{a}_{3}}}}{{{{a}_{2}}}}=………..\frac{{{{a}_{n}}}}{{{{a}_{{n-1}}}}}$

Example 2: What is the common ratio of the sequence 1, 2, 4, 8,……..?

Solution: We have
a1=1,  a2=2,  a3=4,  a4=8

$\displaystyle r=\frac{{{{a}_{2}}}}{{{{a}_{1}}}}=\frac{{{{a}_{3}}}}{{{{a}_{2}}}}=\frac{{{{a}_{4}}}}{{{{a}_{3}}}}$

$\displaystyle r=\frac{2}{1}=\frac{4}{2}=\frac{8}{4}=2$

Therefore the common ratio is 2.

Tip! When we want to check if the sequence is Geometric or not we can use the formula of common ratio.

Example 3: Check whether the sequence$\displaystyle \frac{1}{3},\frac{1}{6},\frac{1}{{12}},\frac{1}{{24}},……..$ is geometric progression or not?

Solution: We have:

$\displaystyle {{a}_{1}}=\frac{1}{3}$

$\displaystyle {{a}_{2}}=\frac{1}{6}$

$\displaystyle {{a}_{3}}=\frac{1}{{12}}$

$\displaystyle {{a}_{4}}=\frac{1}{{24}}$

Let’s find the common ratio of our sequence.

$\displaystyle r=\frac{{{{a}_{2}}}}{{{{a}_{1}}}}=\frac{1}{6}\div \frac{1}{3}=\frac{1}{2}$

$\displaystyle r=\frac{{{{a}_{3}}}}{{{{a}_{2}}}}=\frac{1}{{12}}\div \frac{1}{6}=\frac{1}{2}$

$\displaystyle r=\frac{{{{a}_{4}}}}{{{{a}_{3}}}}=\frac{1}{{24}}\div \frac{1}{{12}}=\frac{1}{2}$

Since the ratio of all the terms with their preceding terms is constant $\displaystyle \frac{1}{2}$ then this is a Geometric Progression.

### Formula of the nth term

If a is the first term, r is the common ratio and n is the total number of the terms, then the formula for the nth term is $\displaystyle {{a}_{n}}=a\cdot {{r}^{{n-1}}}$

### Example 4: Find the 7th term of the geometric progression 2,4,8,16…

Solution: We have a=2 and r=2
All we have to do is substitute the values in the formula of the nth term.
$\displaystyle {{a}_{n}}=a\cdot {{r}^{{n-1}}}$
$\displaystyle {{a}_{7}}=2{{\left( 2 \right)}^{{7-1}}}=2\cdot {{2}^{6}}=2\cdot 64=128$
So the 7th term of the geometric progression is 128.

### Sum of a Finite Geometric Progression

IF “a” is the first term and “r”  is the common ratio of the sequence with “n” number of terms where r≠1 than the sum of the sequence is   a + ar + ar+ ar+…………+ arn

The formula of the sum: $\displaystyle {{s}_{n}}=\frac{{{{a}_{1}}(1-{{r}^{n}})}}{{1-r}}$

Example 5: Find the sum of the given geometric progression 1, 2, 4, 8, 16, 32 ?

Solution: We have 6 number of terms in total so n=6
The first term is a1=1 and the common ratio is r=2
All we have to do is substitute the values in the formula
$\displaystyle {{s}_{n}}=\frac{{{{a}_{1}}(1-{{r}^{n}})}}{{1-r}}$
$\displaystyle {{s}_{n}}=\frac{{1(1-{{2}^{6}})}}{{1-2}}$
$\displaystyle {{s}_{n}}=\frac{{1-64}}{{-1}}$
$\displaystyle {{s}_{n}}=\frac{{-63}}{{-1}}$
$\displaystyle {{s}_{n}}=63$
So the sum is 63.

Tip! If r=1 then the sequence will be in the form a, a, a, a, a,…..a and the formula of the sum will be Sn=a × n

### Sum of an Infinite Geometric Progression

If we have to find the sum of the infinite geometric progression then we have a different formula.
When -1<r<1 and n is infinite that is ∞ then rn will tend to zero
So our formula transforms to $\displaystyle {{s}_{\infty }}=\frac{{{{a}_{1}}}}{{1-r}}$

Example 6: Find the sum of the geometric progression  $\displaystyle 1,\frac{1}{2},\frac{1}{4},\frac{1}{8}………….$ ?

Solution: We have $\displaystyle {{a}_{1}}=1$ and  $\displaystyle r=\frac{1}{2}$
Since -1<r<1 then we use the formula $\displaystyle {{s}_{\infty }}=\frac{{{{a}_{1}}}}{{1-r}}$
All we have to do is substitute the values in the formula
$\displaystyle {{s}_{\infty }}=\frac{1}{{1-\frac{1}{2}}}=\frac{1}{{\frac{1}{2}}}=2$
So the sum is 2.


text:
# Are there half-transitive convex polytopes?

I only consider convex polytopes, i.e. convex hulls of finitely many points. The (edge-)graph of a polytope $$P\subseteq\Bbb R^d$$ is the graph consisting of the polytope's vertices, two are adjacent if they lie on a common edge in $$P$$.

The orthogonal symmetry group of $$P$$ induces a permutation symmetry group on its graph. We say that a polytope is vertex-, edge-, arc- and/or half-transitive if the symmetry group induced on its graph acts in the respective way.

Question: Are there half-transitive polytopes, i.e. polytopes which are vertex- and edge-transitive, but not arc-transitive?

I looked a bit into chiral polytopes (i.e. two flag orbits), but I read somewhere that these only exist for abstract polytopes, and not for convex ones. However, I think that chirality is a much stronger requirement for a polytope than half-transitivity (as the latter only speaks about vertices and edges instead of flags).

• I don't see why the graph needs to be half-transitive. The symmetry group of the polytope might not induce the full group of the graph. Graphs with a half-transitive subgroup are much more common. (Cycles, for example.) – verret Jan 4 at 18:23
• @verret You are absolutely right. I edited that part out. – M. Winter Jan 4 at 18:38


text:
# Recent developments in the theory of electromagnetic probes in relativistic heavy-ion collisions

@article{Shen2015RecentDI,
title={Recent developments in the theory of electromagnetic probes in relativistic heavy-ion collisions},
author={Chun Shen},
journal={arXiv: Nuclear Theory},
year={2015}
}
• C. Shen
• Published 24 November 2015
• Physics
• arXiv: Nuclear Theory
10 Citations

## Figures from this paper

### Overview of electromagnetic probe production in ultra-relativistic heavy ion collisions

An introductory overview of electromagnetic probe production in ultra-relativistic heavy ion collisions is provided. Experimental evidence supporting the production of thermal photons and dileptons

### Exploring theoretical uncertainties in the hydrodynamic description of relativistic heavy-ion collisions

• Physics
• 2021
We explore theoretical uncertainties in the hydrodynamic description of relativistic heavy-ion collisions by examining the full non-linear causality conditions and quantifying the second-order

### Thermal photons as a sensitive probe of $$\alpha$$-cluster in C + Au collisions at the BNL Relativistic Heavy Ion Collider

• Physics
• 2020
Different orientations of $\alpha$-clustered carbon nuclei colliding with heavy ions can result in a large variation in the value of anisotropic flow. Thus, photon flow observables from clustered

### Holographic photon production in heavy ion collisions

• Physics
• 2016
A bstractThe thermal-photon emission from strongly coupled gauge theories at finite temperature is calculated using holographic models for QCD in the Veneziano limit (V-QCD). The emission rates are

## References

SHOWING 1-10 OF 53 REFERENCES

### Viscous photons in relativistic heavy ion collisions

• Physics
• 2011
Theoretical studies of the production of real thermal photons in relativistic heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) are performed. The space-time evolution of the

### Production of photons in relativistic heavy-ion collisions

• Physics
• 2016
In this work it is shown that the use of a hydrodynamical model of heavy-ion collisions which incorporates recent developments, together with updated photon emission rates, greatly improves agreement

### The standard model for relativistic heavy-ion collisions and electromagnetic tomography

This thesis focuses on developing a standard theoretical framework to study the bulk dynamics and electromagnetic probes of ultra-relativistic heavy-ion collisions, which are presently studied

### Thermal Photon Radiation in High Multiplicity p+Pb Collisions at the Large Hadron Collider.

• Physics
Physical review letters
• 2016
This work presents the first calculation, in the hydrodynamic framework, of thermal photon radiation from such small collision systems, which can serve as a signature of the existence of a hot quark-gluon plasma during the evolution of these small collision Systems, as well as validate hydrod dynamic behavior in small systems.

### Importance of the Bulk Viscosity of QCD in Ultrarelativistic Heavy-Ion Collisions.

• Physics
Physical review letters
• 2015
We investigate the consequences of a nonzero bulk viscosity coefficient on the transverse momentum spectra, azimuthal momentum anisotropy, and multiplicity of charged hadrons produced in heavy ion

### Jet energy loss, photon production, and photon-hadron correlations at RHIC

• Physics
• 2009
Jet energy loss, photon production and photon-hadron correlations are studied together at high transverse momentum in relativistic heavy-ion collisions at RHIC energies. The modification of hard jets

### Dilepton Production in Heavy-Ion Collisions

The properties of electromagnetic radiation from hot fireballs as created in ultra-relativistic heavy-ion collisions are reviewed. We first outline how the medium effects in the electromagnetic

### Jet energy loss, photon production, and photon-hadron correlations at energies available at the BNL Relativistic Heavy Ion Collider (RHIC)

• Physics
• 2009
Jet energy loss, photon production, and photon-hadron correlations are studied together at high transverse momentum in relativistic heavy-ion collisions at Relativistic Heavy Ion Collider (RHIC)

### Thermal photon v 2 with slow quark chemical equilibration

Elliptic flow of direct photons in high-energy heavy ion collisions has been a topic of great interest as it is experimentally found larger than most hydrodynamic expectations. I discuss the


text:
# Part 2 - Developing a PySpark Application

This is the 2nd part of a series of posts to show how you can develop PySpark applications for Databricks with Databricks-Connect and Azure DevOps. All source code can be found here.

Now that we have a working local application we should add some tests. As with any data based project testing can be very difficult. Strictly speaking all tests should setup the data they need and be fully independent. This is actually a good case to use normal PySpark locally rather than Databricks-Connect as that forces you to use small local files which you could add to a repo. Databricks-Connect executes on the cluster and therefore you need to store your test data somewhere accessible to the cluster, sandboxing requires extra effort. I’ll hopefully do another post on this in the future.

In this case I’m going to keep things very simple.

The first test for config management just tests a method returns true as it always should when running through Databricks-Connect.

The second test is for the amazon pipeline and contains this code:

    def mock_extract():
data = [("A1","B1"), ("A2","B2")]
return spark.createDataFrame(data, ["col1", "col2"])

def test_transform_Amazon_newColumn(self):
df = Test_amazon.mock_extract()
df = amazon.transform_Amazon(df)
assert "meta_timestamp" in df.columns

Ideally your testing can work like this for your pipelines. When we look at E, T & L - it’s generally the T that is complex part, E & L are quite basic operations, and whilst they deserve testing as well, I focus the bulk of effort on the T as that is where we are likely to see bugs.

In PySpark the common method of transforming data is to chain together transformation functions that accept a dataframe as an input and return the dataframe transformed. Rather than just “listing” all the transformations in a single function as this is hard to test.

So in the above example we can create a dummy dataframe with some values and pass that into our function and inspect the output.

The test simply validate that the column has been added as expected.

The context.py file in this folder is a helper to add the pipelines folder to PATH on our system. Python does not allow navigating backwards hence this requirement.

## Executing Tests

The test can be executed from Anaconda prompt and executing “pytest” from the root folder:

You can also pass a single filename if you would like, such as:

pytest .\tests\amazon_test.py

That’s it we now have a testing method for our pipelines.

## Next

Package in a Wheel

Back to the Series Intro


text:
# Kamehamaha

I just had the weirdest idea for a comic. Normally I don’t even like this kind of humor but this idea just cracked me up:

So I actually made this one last week, but I thought it would not be appropriate to post on my website. Then I realized how dumb that thought was, Judge for yourself:

I don’t think most people cares about some innocent toilet humor on somebodies website.

So before putting it on here I tried posting it on Instagram, but that is surprisingly difficult since it assumes you’ll be doing everything on your phone. This is the first time since long that I felt really incompetent with a service (and I use gentoo/linux…). I guess I’m not really their target audience (to old perhaps).


text:
Psalm 103 Meaning, Box Blight Treatment Amazon, What Do Political Scientists Do, Tender Of Electrical Work, Country Brook Apartments Rochester, Nh, " /> Psalm 103 Meaning, Box Blight Treatment Amazon, What Do Political Scientists Do, Tender Of Electrical Work, Country Brook Apartments Rochester, Nh, " />

# sampling theorem definition

The central limit theorem also states that the sampling distribution will have the following properties: 1. Nyquist’s theorem deals with the maximum signalling rate over a channel of given bandwidth. Sampling Theorem and Pulse Amplitude Modulation (PAM) Reference – Stremler, Communication Systems, Chapter 3.15, 7.1 I.2 Sampling Theorem Signals bearing information are either in analog form, discrete form or digital form. As an example of the Nyquist interval, in past telephone practice the bandwidth, commonly fixed at 3,000 hertz, was sampled at least… This theorem was the key to d igitizing the analog signal. Related to sampling: random sampling, sampling distribution, probability sampling, sampling theorem sample (sale by, implied term) a contract of sale is a sale by sample where there is an express or implied term to that effect in the contract. n. 1. The central limit theorem states that the sampling distribution of a sample mean is approximately normal if the sample size is large enough, even if the population distribution is not normal. Sampling Rate and Bit Depth Explained (Mangold Project) Sampling Rate, Nyquist Frequency, and Aliasing (data acquisition effects) (Billiards, Colorado State) Interpolation, Sampler Channels & Aliasing (FL Studio Guru) Reference Material. Its named for Harry Nyquist, whose work on telegraph technology was instrumental in the later work by Claude Shannon in 1949. A sampler is a subsystem or operation that extracts samples from a continuous signal. Nyquist{Shannon sampling theorem Emiel Por, Maaike van Kooten & Vanja Sarkovic May 2019 1 Theory 1.1 The Nyquist-Shannon sampling theorem The Nyquist theorem describes how to sample a signal or waveform in such a way as to not lose information. Suppose that we have a bandlimited signal X(t). A little later, in 1939, a German, contains a wealth of imaginative geometric ideas Raabe9 published a paper on the Sampling Theorem in applied to signals of finite time duration T. As has been communication. Glossary definition of Nyquist-Shannon Sampling Theorem. • Presented by., • S.Shanmathee Sampling Theorem 2. See: sampling. It was derived by Shannon. For our simulink con guration, we set the sinusoidal signal frequency as 500Hz and we give three sampling frequencies, 500Hz , 1kHz and 10kHz. 2. i.e., F s 2F. Theorem $$\PageIndex{1}$$ central limit theorem. Sampling theorem 1. Definition $$\PageIndex{2}$$: Sampling Distribution. For analog-to-digital conversion to result in a faithful reproduction of the signal, slices, called samples, of the analog waveform must be taken frequently.The number of samples per second is called the sampling rate or sampling frequency. Using this, it was possible to turn the human voice into a series of ones and zeroes. See analog and Nyquist theorem. 2. a. Sampling Rate - When to Measure ... (8 kHz), twice the 4 kHz required for the full spectrum of the human voice. The sampling rate must be equal to, or greater than, twice the highest frequency component in the analog signal. Nyquist-Shannon Sampling Theorem … Sampling Theorem In order for a band-limited (i.e., one with a zero power spectrum for frequencies ) baseband ( ) signal to be reconstructed fully, it must be sampled at a rate . If you can exactly reconstruct the analog signal from the samples, you must have done the sampling properly. The Nyquist–Shannon sampling theorem, after Harry Nyquist and Claude Shannon, is a fundamental result in the field of information theory, in particular telecommunications and signal processing. ... sampling - items selected at random from a population and used to test hypotheses about the population. The sampling theorem is not by Nyquist. Sampling performed by an auditor is referred to as "audit sampling." The following theorem tells you the requirement to have $$\overline{x}$$ normally distributed. Europe and the former USSR, the Sampling Theorem is As well as the Sampling Theorem, the paper2 named after him. • To process the analog signal by digital means, it is essential to convert them to discrete-time signal , and then convert them to a sequence of numbers. The sampling theorem, which is also called as Nyquist theorem, delivers the theory of sufficient sample rate in terms of bandwidth for the class of functions that are bandlimited. To approach it from formulaic way, looking back to the definition of the Central Limit Theorem, the standard deviation of the sampling distribution, also called standard error, is equal to σ/ √n. A signal sampled at is said to be Nyquist sampled , and is called the Nyquist frequency. The Nyquist Theorem, also known as the sampling theorem, is a principle that engineers follow in the digitization of analog signals. Sampling. Sampling Distribution: how a sample statistic is distributed when repeated trials of size n are taken. ADC • Generally signals are analog in nature (eg:speech,weather signals). The definition of proper sampling is quite simple. Suppose you sample a continuous signal in some manner. Nyquist's Law: Nyquist’s law is a formula which states that to accurately represent an analog signal in a digital format, two samples per cycle are sufficient. In telecommunication: Sampling …commonly referred to as the sampling theorem, and the sampling interval (1/2B seconds) is referred to as the Nyquist interval (after the Swedish-born American electrical engineer Harry Nyquist). In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal.A common example is the conversion of a sound wave (a continuous signal) to a sequence of samples (a discrete-time signal).. A sample is a value or set of values at a point in time and/or space. From sampling theorem, sampling rate F s should be equal or larger than twice frequency of sinusoidal signal F. Sampling Theorem. Sampling theorem determines the necessary conditions which allow us to change an analog signal to a discrete one, This should hopefully leave the reader with a comfortable understanding of the sampling theorem. Sampling is the process of converting a signal (for example, a function of continuous time or space) into a numeric sequence (a function of discrete time or space). The Nyquist Sampling Theorem states that: A bandlimited continuous-time signal can be sampled and perfectly reconstructed from its samples if the waveform is sampled over twice as fast as it's highest frequency component. Signal & System: Sampling Theorem in Signal and System Topics discussed: 1. So, as the sample size increases the denominator also increases, and makes the overall standard value smaller. To explain Nyquist's theorem a bit more: in its most basic form, Nyquist’s work states that an analog signal waveform can be converted into digital by sampling the analog signal at equal time intervals. 2/6/2015 3. Synonym sampling theorem. The act, process, or technique of selecting an appropriate sample. It means that a continuous time signal is converted into a discrete time signal. For Nyquist theorem, if the sampling rate is smaller, it will result in aliasing. Sampling Theorem. The variance of the sampling distribution of the mean is computed as follows: $\sigma_M^2 = \dfrac{\sigma^2}{N}$ That is, the variance of the sampling distribution of the mean is the population variance divided by $$N$$, the sample size (the number of scores used to compute a mean). sampling the selection of part of a total population of consumers or products whose behaviour or performance can be analysed, in order to make inferences about the behaviour or performance of the total population, without the difficulty and expense of undertaking a … The Sampling Theorem (Nyquist); The definition of proper sampling is quite simple. Nyquist Theorem synonyms, Nyquist Theorem pronunciation, Nyquist Theorem translation, English dictionary definition of Nyquist Theorem. Nyquist's theorem: A theorem, developed by H. Nyquist, which states that an analog signal waveform may be uniquely reconstructed, without error, from samples taken at equal time intervals. The mean of the sampling distribution will be equal to the mean of population distribution: sampling the selection of part of a total population of consumers or products whose behaviour or performance can be analysed, in order to make inferences about the behaviour or performance of the total population, without the difficulty and expense of undertaking a … 3 The Sampling Theorem To solidify some of the intuitive thoughts presented in the previous section, the sampling theorem will be presented applying the rigor of mathematics supported by an illustrative proof. Nyquist Sampling Theorem •Special case of sinusoidal signals •Aliasing (and folding) ambiguities •Shannon/Nyquist sampling theorem •Ideal reconstruction of a cts time signal Prof Alfred Hero EECS206 F02 Lect 20 Alfred Hero University of Michigan 2 Sampling and Reconstruction • Consider time sampling/reconstruction without quantization: Statistics See sample. If you can exactly reconstruct the analog signal from the samples, you must have done the sampling properly.Even if the sampled data appears confusing or incomplete, the key information has been captured if you can reverse the process. Suppose you sample a continuous signal in some manner. Sampling is defined as the process in which an analog signals are converted into digital signals. Psychology Definition of SAMPLING THEORY: Guidelines for taking samples which will correctly characterize the populace from which they are drawn. Nyquist Sampling Theorem. b. Over sampling and under sampling are techniques used in data mining and data analytics to modify unequal data classes to create balanced data sets.Over sampling and under sampling are also known as resampling. Sampling Variance. It is necessary to perform audit sampling when the population, in this case account transaction information, is large. THIS DEFINITION IS FOR PERSONAL USE ONLY. Even if the sampled data appears confusing or incomplete, the key information has been captured if you can reverse the process. The Nyquist-Shannon Sampling Theorem is the basis for all digital sampling of analog signals. The central limit theorem states that the distribution of sample means approximates a normal ... A sampling distribution describes the data chosen for a sample ... Null Hypothesis Definition.


text:
## Real Analysis Exchange

#### Abstract

It is proved that $g(C\times C)$ contains an interval if $g:\mathbb{R}\times\mathbb{R}\to\mathbb{R}$ satisfies appropriate conditions and $C$ is the Cantor set.

#### Article information

Source
Real Anal. Exchange, Volume 22, Number 1 (1996), 213-224.

Dates
First available in Project Euclid: 1 June 2012

https://projecteuclid.org/euclid.rae/1338515216

Mathematical Reviews number (MathSciNet)
MR1433609

Zentralblatt MATH identifier
0879.26048

#### Citation

Crnjac, Miljenko; Guljaš, Boris; Miller, Harry I. A positive answer to a question about the Cantor set. Real Anal. Exchange 22 (1996), no. 1, 213--224. https://projecteuclid.org/euclid.rae/1338515216

#### References

• P. Erdős and J. C. Oxtoby, Partitions of the plane into sets having positive measures in every non-null product set, Trans. Amer. Math. Soc., 79 (1955), 91–102.
• Z. Kominek, Some generalization of the theorem of S. Piccard, Prace Nauk. Univ. \' Sląski Katowice, Prace Mat., 4 (1973), 31–33.
• M. E. Kuczma and M. Kuczma, An elementary proof and an extension of a theorem of Steinhaus, Glas. Mat. Ser. III, 6(26) (1971), 11–18.
• H. I. Miller, Generalization of a classical theorem of measure theory, Radovi Akad. Nauka i Umjetnosti B i H, 45 (1973), 45–48.
• H. I. Miller, Relationships between various gauges of the size of sets of real numbers, Glas. Mat. Ser. III, 9(29) (1974), 59–64.
• H. I. Miller, Relationships between various gauges of the size of sets of real numbers II, Radovi Akad. Nauka i Umjetnosti B i H, 59 (1976), 37–48.
• H. I. Miller, A universal null set whose Steinhaus distance set is $[0,\i)$, Radovi Akad. Nauka i Umjetnosti B i H, 61 (1978), 37–40.
• J. C. Oxtoby, Measure and Category, Springer-Verlag, New York, 1970.
• W. R. Utz, The distance set of the Cantor discontinuum, Amer. Math. Monthly, June (1951), 407–408.


text:
# \hfill in math mode

Is there any easy way of declaring a new command which emulates \hfill in math mode. I don't want flalign or something similar. I want to use the command in the same way (and with the same freedom) I use \hfill.

Is that possible?

i.e. this is an example:

\begin{align*}
a + b + c &= a + b + c + d + e + f + g + h + i \\
& \mathhfill \text{(foo)}
\end{align*}

where I want (foo) to be right aligned (under + h + i and here

\begin{align*}
a + b + c + d + e + f + g + h + i &= a + b + c \\
\text{(foo)} \mathhfill &
\end{align*}

I want the text aligned on the left (just under the a + b +. But I don't want flalign or other solutions. Because there are lots of situations (this is a minimal example). And I would like to see a solution which work just as \hfill.

EDIT: well, as Carlisle said, it works in $a \hfill b$, but I would like to see it working in align, i.e.

EDIT2: The answers solved my needs. But it would be great if somebody would give a command which works exactly like \hfill or i.e. \dotfill in align.

-
Would you please make an example of what you'd like to achieve? –  egreg Nov 20 '12 at 13:07
Is it possible that you are trying to tag the equation and the tag doesn't fit on one line so you are doing it manually? –  percusse Nov 20 '12 at 13:23
No, I'm not tagging. It's just some text which I would like to watch right aligned (and other situations, but at this moment it's just this). But everything would be more flexible if \hfill worked. –  Manuel Nov 20 '12 at 13:28
Based on personal experience with this kind of situation, I believe this may be a XY Problem. When I started using LaTeX last year, I spent quite a bit of time with exactly the same issue with align -- only later did I learn that I did not properly understand how to fully use align and the related alignat (and even tabular/array). So, if you show (in perhaps a different question) exactly what you want to achieve (as opposed to how you want to achieve it) you may get better answers. If I am mistaken, please ignore this comment. –  Peter Grill Nov 20 '12 at 18:57
No, you are right. And I haven't write a good explanation because I don't have it. I just needed that at this moment (and may be won't need it again, that's why my intention is not to solve my problem, but discovering \mathhfill). But I thought What if we could simply, without head ache, use hfill,dotfill, etc. in align exactly as we use in text mode? At this moment the @egreg answer fits me, but my real objective is to have a command \mathhfill and \mathdotfill which work exactly like the normal ones, but in align. –  Manuel Nov 20 '12 at 19:24

You can do it, but not with \hfill, because of how align works. Here's a way:

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\newcommand{\pushright}[1]{\ifmeasuring@#1\else\omit\hfill$\displaystyle#1$\fi\ignorespaces}
\newcommand{\pushleft}[1]{\ifmeasuring@#1\else\omit$\displaystyle#1$\hfill\fi\ignorespaces}
\makeatother

\begin{document}
\begin{align*}
a + b + c &= a + b + c + d + e + f + g + h + i \\
& \pushright{\text{(foo)}}
\end{align*}

\begin{align*}
a + b + c + d + e + f + g + h + i &= a + b + c \\
\pushleft{\text{(foo)}} &
\end{align*}

\end{document}

A slightly different implementation allows you to use \hfill where you want:

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\newcommand{\specialcell}[1]{\ifmeasuring@#1\else\omit$\displaystyle#1$\ignorespaces\fi}
\makeatother

\begin{document}
\begin{align*}
a + b + c &= a + b + c + d + e + f + g + h + i \\
& \specialcell{\hfill\text{(foo)}}
\end{align*}

\begin{align*}
a + b + c + d + e + f + g + h + i &= a + b + c \\
\specialcell{\text{(foo)}\hfill} \\
\specialcell{\hfill\text{(foo)}\hfill}
\end{align*}

\end{document}

I'd recommend against using the simple \omit.

-
Cool. Well, that works, but I will wait some time just to see if anybody shows a command more like \hfill. i.e. if you write (foo1) \mathhfill (foo2) it will align (foo1) to the left and (foo2) to the right. If not, I'll accept your answer. May be you could addapt \dotfill to work in align, and then use \phantom{\dotfill} –  Manuel Nov 20 '12 at 13:45
Great!. That's much better. –  Manuel Nov 20 '12 at 19:17
Does this work in align environment instead of align*? In align the compilation fails with Misplaced \omit. –  devil Dec 13 '12 at 5:51
@devil If I run both examples with align instead of align* I get no error. –  egreg Dec 13 '12 at 7:39

The most obvious answer is \hfill as demonstrated by this plain TeX file

$a\hfill b$

\bye

-
Well, I didn't tried that, and it works in , but this is not what I want. I would like this to work in align, gather and similar environments. –  Manuel Nov 20 '12 at 13:22

In align you can use \omit at the start of cells:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
a + b + c &= a + b + c + d + e + f + g + h + i \\
&\omit\hfill foo\\
a&=b\\
\omit text & =c \\
\omit\hfill text&=d
\end{align*}
\end{document}

-
That's also great. But it don't work in every case: i.e. (foo1) \omit\hfill (foo2). Anyway, where can I find info about the \omit command? –  Manuel Nov 20 '12 at 13:58
The \omit must be at the begin of the cell (it tells the underlying \halign that in this cell the template should be ignored and is described e.g. in the texbook). Btw: Enrico's solution uses \omit too, it is only a bit more hidden. –  Ulrike Fischer Nov 20 '12 at 14:09
Note that it's only the \omit that has to be first, the hfill can be anywhere  &\omit$a \hfill b$ for example –  David Carlisle Nov 20 '12 at 14:32
@David Carlisle and egreg Okey. I'm pleased enough. I like this mode of working. I thank you all, because the solution is a mix of all the answer. –  Manuel Nov 20 '12 at 15:27
Note that to be really safe you should only do the omit on aligns second pass not on its first so have a macro \@ifmeasuring\else\omit\fi as in @egreg's solution otherwise you omit this cell on the internal measuring phase (which is safe enough unless the cell ends up being the widest in this column in which case that will not be recorded if you omit it) –  David Carlisle Nov 20 '12 at 15:49


text:
# Find the point on the line -5x + 6y + 6 = 0 which is closest to the point (-1,3) .

## Question:

Find the point on the line {eq}-5x + 6y + 6 = 0 {/eq} which is closest to the point {eq}(-1,3) {/eq}.

## Distance Between a Point and a Line:

When we know the equation of a line {eq}L:\,\,ax + by + c = 0 {/eq} and a point {eq}P\left( {{x_0},{y_0}} \right) {/eq} outside the line we are able to apply the corresponding formula to derive the distance between the point {eq}P\left( {{x_0},{y_0}} \right) {/eq} and the line {eq}L {/eq}: {eq}d\left( {P,L} \right) = \frac{{\left| {a{x_0} + b{y_0} + c} \right|}}{{\sqrt {{a^2} + {b^2}} }} {/eq}.

## Answer and Explanation:

{eq}\eqalign{ & {\text{If we have that the equation of the line }}\,L{\text{ is }}\,ax + by + c = 0{\text{ and a point }}\,{P_0}\left( {{x_0},{y_0}} \right){\text{ }} \cr & {\text{outside the line}}{\text{, then}}{\text{, the shortest distance from the point }}\,{P_0}{\text{ to the line }}L{\text{ is given by: }} \cr & \,\,\,\,d\left( {P,L} \right) = \frac{{\left| {a{x_0} + b{y_0} + c} \right|}}{{\sqrt {{a^2} + {b^2}} }} \cr & {\text{Now}}{\text{, in this particular case we have the point }}P\left( {{x_0},{y_0}} \right) = \left( { - 1,3} \right){\text{ and the line}} \cr & - 5x + 6y + 6 = 0.{\text{ So}}{\text{, by replacing:}} \cr & \,\,\,\,d\left( {P,L} \right) = \frac{{\left| { - 5 \cdot \left( { - 1} \right) + 6 \cdot 3 + 6} \right|}}{{\sqrt {{{\left( { - 5} \right)}^2} + {6^2}} }} \cr & \,\,\,\,d\left( {P,L} \right) = \frac{{\left| {5 + 18 + 6} \right|}}{{\sqrt {25 + 36} }} = \frac{{29}}{{\sqrt {61} }} = \boxed{3.713} \cr & {\text{Therefore}}{\text{, the closest distance from the point }}\,{P}{\text{ to the line }}L{\text{ is }}\,\boxed{d\left( {P,L} \right) = 3.713} \cr} {/eq}


text:
Compton and X Ray

1. Oct 28, 2008

getcarter

3) X-rays of wavelentgh 0.010nm are directed onto a target containing loosely bound electrons. For Compton scattering from one of those electrons, at an angle of 180 degrees, what are

a) the Compton shift,

b) the corresponding change in photon energy,

c) the kinetic energy of the recoiling electron, and

d) the electron's direction of motion?

2. Relevant equations

Lamda'-Lamda = [h/mc] (1-cos@)
\frac{h}{m_e c} = 2.43 \times 10^{-12}\,m

3. The attempt at a solution
p_{e'}^2c^2 = (hf + mc^2-hf')^2-m^2c^4

2. Oct 28, 2008

olgranpappy

in your equation, for scattering at 180 degrees, what is "cos@" equal to?

3. Oct 29, 2008

getcarter

relevants are above, i did not understand that you ask cos@,
sorry i don't understand the main idea of the question
and i need help.

4. Oct 29, 2008

olgranpappy

I am asking you this to determine whether or not you understand what the symbols in the equation are.
You wrote down something that says "cos@". Do you know what the symbol @ stands for?

5. Oct 30, 2008

getcarter

i tried to show tetha, [degree of cos.]
sorry.

6. Oct 30, 2008

olgranpappy

Yes. And in the statement of the problem, what number is theta equal to?


text:
# Math Help - differentiable function of 3 variables

1. ## differentiable function of 3 variables

If someone can help, please do help me for this question. I got stuck with it since yesterdays.

Prove that if f is a differentiable function of 3 variables and g(x,y,z) = f(x-y, y-z, z-x), then gsubx(x,y,z) + gsuby(x,y,z) +gsubz(x,y,z)=0.

Hint Let u =x-y, v=y-z, w=z-x, and write g(x,y,z)=f(u(x,y,z), v(x,y,z), w(x,y,z))

Thank you very much.

2. Originally Posted by littlemu
If someone can help, please do help me for this question. I got stuck with it since yesterdays.

Prove that if f is a differentiable function of 3 variables and g(x,y,z) = f(x-y, y-z, z-x), then gsubx(x,y,z) + gsuby(x,y,z) +gsubz(x,y,z)=0.

Hint Let u =x-y, v=y-z, w=z-x, and write g(x,y,z)=f(u(x,y,z), v(x,y,z), w(x,y,z))

Thank you very much.
You have,
g(u,v,w) with u=x-y and v=y-z and w=z-x

Now you can use the Chain Rule.


text:
# Linear Function Calculator Table

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This is especially true if I'm using a graphing calculator to fill in my T-chart, because graphing calculators can only handle line equations when they're in the form "y =". Preferred is perhaps too weak a word here. Press S and scroll right to the TESTS menu. （input by clicking each white cell in the table below）. Linear function: If each term is either a constant or It is the product of a constant and also (the first power of) a single variable, then it is called as an algebraic equation. The x-intercept is the point at which the graph of a linear function crosses the x-axis. A logarithm function is defined with respect to a “base”, which is a positive number: if b denotes the base number, then the base-b logarithm of X is, by definition, the number Y such that b Y = X. However, as the rest of this article will show, this "reality" is an illusion. Answer by KMST(5211) (Show Source): You can put this solution on YOUR website! When the input is , the output is. The function notation for sequences is used in the study and application of z-transforms. In Mathematica, the Fit function takes a list of points, a list of expressions, and a list of independent variables, and determines which linear combination of the given expressions produces the best fit to the data. Positive Linear Function Machine is one of the Interactivate assessment explorers. For example, use the following commands to find out what’s available on anova and linear models. We can write the sample as a sequence using the notation. Linear Parent Function Characteristics. Pre-Algebra. To be proficient in answering questions about linear functions, it helps to be skillful in translating given information from one form into another. Also, as well as the expansion ratio, porosity fraction of snacks decreased with added Yellow mealworm. Linear Regression. In other words, a table of values is simply some of the points that are on the line. insidemathematics. Linear algebra gives you mini-spreadsheets for your math equations. Vector Calculator - (High School/College) Graphically add two vectors together. For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. Also covers function tables, equations, graphs and mapping of functions. A linear regression model that contains more than one predictor variable is called a multiple linear regression model. com, a math practice program for schools and individual families. We say that y is a function of x because if you choose any value for x, this formula will give you a unique value of y. Table of Contents. It calls Mathematica's Integrate function, which represents a huge amount of mathematical and computational research. A 2nd-degree polynomial function is called a quadratic function. With negative slope the line moves down when going from left to right. Performing a Linear Regression on the TI-83+ or TI-84+. More Examples Here are more examples of how to graph equations in Algebra Calculator. The function below determines how many people have swine where t = time in days and S = the number of people in thousands. Ideally, it will capture the trend in the data and allow us to make predictions of how the data series will behave in the future. Write a linear function that represents the cost y of x pounds of seeds. Linear Programming: Slope of the Objective Function. Download Now (. Select angle type of degrees (°) or radians (rad) in the combo box. One method is to observe the shape of the graph. Although it is temperature dependent, it can be used at a given temperature to calculate the resistance of a wire of given geometry. , going up by 3 each time or down by 5). ! y = 2x2 – x + 6 ! The x-values are consistently increasing by one, the first differences are not the same, there this relation is not linear, the second difference are equal, therefore this relation represents a quadratic function. （input by clicking each white cell in the table below）. 6 Graph an equation in y=mx+c form. Select Scientific. All mass pro. R is similar to the award-winning 1 S system, which was developed at Bell Laboratories by John Chambers et al. a table chart, the regression must be calculated. You can click-and-drag to move the graph around. Because each car depreciates by4000 per year,the slope of the linear function is The linear function that represents the value of. Consider an equation such as. Using Linear Equations. Build a set of equations from the table such that. • The orange more information box has useful information about the arguments of the function (for Sin it notes that the argument is to be in radians). Figure 1: Black line: Linear response function (y = 3 2x). How many of each calculator was sold if a simple calculator costs $5 and scientific calculator costs$16 and the store sold 35 calculators for total amount of $340? Is this a linear equation #xy=6#? Is this a linear equation #y^2- 4x=6#?. Abstract: In this paper, we will report the result of the study on the effectiveness of using scientific calculator in solving non-linear equation by Newton- Raphson method from the aspect of students’ marks and duration taken in solving question. MathGrapher: Graphing Calculator-Function Grapher. The new differential equation satisfied by z is. Earlier, we discussed the average rate of change for linear functions; in this section, I will be discussing the average rate of change for non-linear functions. y = 2(3) – 1. function table, data editor, and the %h menu), the TI-30XS MultiView™ calculator may display E instead of Ã10n. if michael switches to the smaller scoops, by how much will his profit per container go up or down?. Calculates the table of the specified function with a variable specified as variable data table. In the previous lesson on functions you learned how to find the slope and write an equation when given a function. Math 093 and Math 117A – Linear Functions. Math Highlights. Using the calculator. This page will show you how to solve a relationship involving an inequality. The objective function is linear, and the domain, or feasible set, is de ned by linear constraints. Using Excel to solve linear programming problems Technology can be used to solve a system of equations once the constraints and objective function have been defined. In the process of solving a word problem it is often useful to make a chart of a few specific instances of the independent and dependent variables. Complete The Function Table Ilfattooggi Info. Ls 1 Solving Systems Of Linear Equations By Graphing Mathops. Linear regression is a model of the relationship between a dependent variable y and independent variables x by linear prediction function$\hat {y}=a+bx\$. Feel free to try them now. (These points are often referred to as the x-intercept and the y-intercept. Do not use the back button. We will find that the graph of each degree leaves its characteristic signature on the x- y-plane. Linear interpolant is the straight line between the two known co-ordinate points (x0, y0) and (x1, y1). ) How do changes in the slope and intercept affect (move) the regression line?. When you enter a function, the calculator will begin by expanding (simplifying) it. This is a VERY COMPLEX calculator. High school geometry lays the foundation for all higher math, and these thought-provoking worksheets cover everything from the basics through coordinate geometry and trigonometry, in addition to logic problems, so students will be fully prepared for whatever higher math they pursue!. Line AB contains points A(4, 5) and B(9, 7). Ready-to-use mathematics resources for Key Stage 3, Key Stage 4 and GCSE maths classes. When this occurs, there are two simple solutions: chaining; linear probe (aka linear open addressing). To the left zooms in, to the right zooms out. In order to calculate a straight line, you need a linear equation i. We call the term containing the highest power of x (i. The critical assumption of the model is that the conditional mean function is linear: E(Y|X) = α +βX. A value of x which makes a function f(x) equal 0. The simplest functions, from the perspective of formulas, are linear functions. Creating Number Table from Function Initializing Calculator Settings calculate the linear. Most applications of regression aim to identify what variables are associated with Y, to postulate what causes Y, to predict future observations of Y, or to assess control over a process or system (quality control). 4 Find a missing coordinate using gradient. Linear regression calculator Two-dimensional linear regression of statistical data is done by the method of least squares. International Debt Statistics (IDS)—formerly known as Global Development Finance (GDF)—provides external debt and financial flows statistics for countries that report public and publicly-guaranteed debt under the World Bank's Debtor Reporting System (DRS). Problem 1 : The table shows the temperature of a fish tank during an experiment. Resistance: Temperature Coefficient. Imagine the individual pieces lined up end-to-end and determine the length from one end to the other. GraphyCalc is a 3d graphing calculator, allowing you to interactively explore 3d functions. Byju's Linear Function Calculator is a tool which makes calculations very simple and interesting. This page will show you how to solve a relationship involving an inequality. 45 respectively for i0, i10 and i20, indicating a negative linear relationship with the level of mealworm enrichment (r 2 0. These tutorials introduce you to linear relationships, their graphs, and functions. Loss of Lkb1 impairs Treg function and stability to aggravate graft-versus-host disease after bone marrow transplantation Skip to main content Thank you for visiting nature. 1 The z-transform. Various forms of the equations of linear functions are named and tested for their efficiency for different mathematical purposes. On the graphics calculator, set a standard window (ZOOM 6). The Linear Function Calculator an online tool which shows Linear Function for the given input. Free math problem solver answers your algebra homework questions with step-by-step explanations. We can do more than giving an example of a linear equation: we can give the expression of every possible linear function.