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# Which of the following when expressed as a decimal has a finite number

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Which of the following when expressed as a decimal has a finite number [#permalink]

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Which of the following when expressed as a decimal has a finite number of non-zero digits to the right of the decimal?

A. $$\frac{0.27^3}{0.09^4}$$

B. $$\frac{0.27^2}{0.09^8}$$

C. $$\frac{27^3}{0.09^6}$$

D. $$\frac{0.27^3}{0.09^5}$$

E. $$\frac{0.27^3}{0.09^9}$$
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Which of the following when expressed as a decimal has a finite number [#permalink]

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14 Jan 2018, 05:45
Bunuel wrote:
Which of the following when expressed as a decimal has a finite number of non-zero digits to the right of the decimal?

A. $$\frac{0.27^3}{0.09^4}$$

B. $$\frac{0.27^2}{0.09^8}$$

C. $$\frac{27^3}{0.09^6}$$

D. $$\frac{0.27^3}{0.09^5}$$

E. $$\frac{0.27^3}{0.09^9}$$

RULE: A number will always be NON-TERMINATING if the denominator of fraction in least form has any prime factor other than 2 and 5

i.e. RULE: A number will always be TERMINATING if the denominator of fraction in least form has NO prime factor other than 2 and 5

A. $$\frac{0.27^3}{0.09^4} = 27^3/9^4 = 3^9/3^8 = 3$$ CORRECT ANSWER

B. $$\frac{0.27^2}{0.09^8} = 27^2/9^8 = 3^6/3^16 = 1/3^10$$

C. $$\frac{27^3}{0.09^6} = 27^3/9^6 = 3^9/3^12 = 1/3^3$$

D. $$\frac{0.27^3}{0.09^5} = 27^3/9^4 = 3^9/3^10 = 1/3$$

E. $$\frac{0.27^3}{0.09^9} = 27^3/9^9 = 3^9/3^18 = 1/3^9$$

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Re: Which of the following when expressed as a decimal has a finite number [#permalink]

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23 Jan 2018, 01:57
GMATinsight wrote:
Bunuel wrote:
Which of the following when expressed as a decimal has a finite number of non-zero digits to the right of the decimal?

A. $$\frac{0.27^3}{0.09^4}$$

B. $$\frac{0.27^2}{0.09^8}$$

C. $$\frac{27^3}{0.09^6}$$

D. $$\frac{0.27^3}{0.09^5}$$

E. $$\frac{0.27^3}{0.09^9}$$

RULE: A number will always be NON-TERMINATING if the denominator of fraction in least form has any prime factor other than 2 and 5

i.e. RULE: A number will always be TERMINATING if the denominator of fraction in least form has NO prime factor other than 2 and 5

A. $$\frac{0.27^3}{0.09^4} = 27^3/9^4 = 3^9/3^8 = 3$$ CORRECT ANSWER

B. $$\frac{0.27^2}{0.09^8} = 27^2/9^8 = 3^6/3^16 = 1/3^10$$

C. $$\frac{27^3}{0.09^6} = 27^3/9^6 = 3^9/3^12 = 1/3^3$$

D. $$\frac{0.27^3}{0.09^5} = 27^3/9^4 = 3^9/3^10 = 1/3$$

E. $$\frac{0.27^3}{0.09^9} = 27^3/9^9 = 3^9/3^18 = 1/3^9$$

Dear GMATINSIGHTS,
Can you please explain to me in detail how you eliminate the 10^-2? Thanks a LOT!
Re: Which of the following when expressed as a decimal has a finite number   [#permalink] 23 Jan 2018, 01:57
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# Which of the following when expressed as a decimal has a finite number

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[U] User's Guide - Stata

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STATA USER’S GUIDERELEASE 16 A Stata Press PublicationStataCorp LLCCollege Station, Texas

ContentsStata basics1Read this—it will help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22A brief description of Stata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .93Resources for learning and using Stata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .134Stata’s help and search facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .245Flavors of Stata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .316Managing memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .347–more– conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .368Error messages and return codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .379The Break key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4010Keyboard use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42Elements of Stata11Language syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4912Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8413Functions and expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12314Matrix expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14415Saving and printing output—log files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15916Do-files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16517Ado-files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17818Programming Stata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18319Immediate commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23720Estimation and postestimation commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24121Creating reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .304Advice22Entering and importing data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30823Combining datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .317i

iiContents24Working with strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31925Working with dates and times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32326Working with categorical data and factor variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33227Overview of Stata estimation commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35028Commands everyone should know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38329Using the Internet to keep up to date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .385Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .392Subject and author index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .397

Stata basics1Read this—it will help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22A brief description of Stata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .93Resources for learning and using Stata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .134Stata’s help and search facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .245Flavors of Stata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .316Managing memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .347–more– conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .368Error messages and return codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .379The Break key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4010Keyboard use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .421

1Read this—it will helpContents1.11.21.31.4Getting Started with Stata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The User’s Guide and the Reference manuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.1PDF manuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.1.1Video example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.2Example datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.2.1Video example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.3Cross-referencing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.4The index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.5The subject table of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.6Typography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.7Vignette . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .What’s new . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24445566667788

[ U ] 1 Read this—it will helpThe Stata Documentation consists of the following [PSS][P][RPT][SP][SEM][SVY][ST][TS][TE][I]Getting Started with Stata for MacGetting Started with Stata for UnixGetting Started with Stata for WindowsStata User’s GuideStata Base Reference ManualStata Bayesian Analysis Reference ManualStata Choice Models Reference ManualStata Data Management Reference ManualStata Dynamic Stochastic General Equilibrium Models Reference ManualStata Extended Regression Models Reference ManualStata Finite Mixture Models Reference ManualStata Functions Reference ManualStata Graphics Reference ManualStata Item Response Theory Reference ManualStata Lasso Reference ManualStata Longitudinal-Data/Panel-Data Reference ManualStata Meta-Analysis Reference ManualStata Multilevel Mixed-Effects Reference ManualStata Multiple-Imputation Reference ManualStata Multivariate Statistics Reference ManualStata Power, Precision, and Sample-Size Reference ManualStata Programming Reference ManualStata Reporting Reference ManualStata Spatial Autoregressive Models Reference ManualStata Structural Equation Modeling Reference ManualStata Survey Data Reference ManualStata Survival Analysis Reference ManualStata Time-Series Reference ManualStata Treatment-Effects Reference Manual:Potential Outcomes/Counterfactual OutcomesStata Glossary and Index[M]Mata Reference ManualIn addition, installation instructions may be found in the Installation Guide.3

[ U ] 1 Read this—it will help1.2.1.15Video examplePDF documentation in Stata1.2.2Example datasetsVarious examples in this manual use what is referred to as the automobile dataset, auto.dta. Wehave created a dataset on the prices, mileages, weights, and other characteristics of 74 automobilesand have saved it in a file called auto.dta. (These data originally came from the April 1979 issueof Consumer Reports and from the United States Government EPA statistics on fuel consumption;they were compiled and published by Chambers et al. [1983].)In our examples, you will often see us type. use https://www.stata-press.com/data/r16/autoWe include the auto.dta file with Stata. If you want to use it from your own computer rather thanvia the Internet, you can type. sysuse autoSee [D] sysuse.You can also access auto.dta by selecting File Example datasets., clicking on Exampledatasets installed with Stata, and clicking on use beside the auto.dta filename.There are many other example datasets that ship with Stata or are available over the web. Here isa partial list of the example datasets included with eexp.dtauslifeexp2.dtavoter.dtaxtline1.dta1978 Automobile Data1978 Automobile DataSubset of 1978 Automobile Datafictional blood pressure datafictional blood pressure dataPatient Survival in Drug Trial1980 Census data by stateCity Temperature DataCity Temperature DataEducation and GDPU.S. GNP, 1967–2002Life expectancy, 1998fictional network diagram datafictional network diagram dataU.S. National Longitudinal Study of Young Women (NLSW, 1988 extract)U.S. National Longitudinal Study of Young Women (NLSW, 1988 extract)U.S. Census, 2000, extractSubsea elevation of Lamont sandstone in an area of OhioS&P 500NOAA Sea Surface Temperaturesimulated time-series datafictional data on calories consumedU.S. life expectancy, 1900–1999U.S. life expectancy, 1900–19401992 presidential voter datafictional data on calories consumed

[ U ] 1 Read this—it will help1.2.67TypographyWe mix the ordinary typeface that you are reading now with a typewriter-style typeface that lookslike this. When something is printed in the typewriter-style typeface, it means that something is acommand or an option — it is something that Stata understands and something that you might actuallytype into your computer. Differences in typeface are important. If a sentence reads, “You could listthe result . . . ”, it is just an English sentence — you could list the result, but the sentence providesno clue as to how you might actually do that. On the other hand, if the sentence reads, “You couldlist the result . . . ”, it is telling you much more — you could list the result, and you could do thatby using the list command.We will occasionally lapse into periods of inordinate cuteness and write, “We described the dataand then listed the data.” You get the idea. describe and list are Stata commands. We purposelybegan the previous sentence with a lowercase letter. Because describe is a Stata command, it mustbe typed in lowercase letters. The ordinary rules of capitalization are temporarily suspended in favorof preciseness.We also mix in words printed in italic type, such as “To perform the rank-sum test, type ranksumvarname, by(groupvar)”. Italicized words are not supposed to be typed; instead, you are to substituteanother word for them.We would also like users to note our rule for punctuation of quotes. We follow a rule that is oftenused in mathematics books and British literature. The punctuation mark at the end of the quote isincluded in the quote only if it is a part of the quote. For instance, the pleased Stata user said shethought that Stata was a “very powerful program”. Another user simply said, “I love Stata.”In this manual, however, there is little dialogue,

The Getting Started manual, the User’s Guide, and the Reference manuals cross-reference each other. [R] regress [D] reshape [XT] xtreg The ﬁrst is a reference to the regressentry in the Base Reference Manual, the second is a reference to the reshapeentry in the Data Management Reference Manual, and the third is a reference to the

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A monomial is an algebraic expression with only one term. Monomial expressions involve the multiplication or division of numbers and variables in some valid combination. $\begin{array}{c|c} z^5 & {\color{#009600}{\Large{\checkmark}}} \\ \hline\\[-1em] 2x & {\color{#009600}{\Large{\checkmark}}} \\ \hline\\[-1em] \dfrac{\text{-} 7yz^4}{2} & {\color{#009600}{\Large{\checkmark}}} \end{array}$ Note, the exponents of the variables in a monomial are whole numbers and a monomial cannot have variables in its denominator. $\begin{array}{c|c} m^{\frac{4}{7}} & {\color{#FF0000}{\Large{\mathbf{\times}}}} \\ \hline\\[-1em] g^{\text{-} 3} & {\color{#FF0000}{\Large{\mathbf{\times}}}} \\ \hline\\[-1em] \dfrac{1}{x} & {\color{#FF0000}{\Large{\mathbf{\times}}}} \end{array}$ When multiple monomials are put together, separated by $+$ or $-$ signs, they are the terms that form polynomials.


text:
Expected distance between leaf nodes in a binary tree

Let T be a full binary tree with $$8$$ leaves. (A full binary tree has every level full). Suppose that two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e number of edges in the unique path between a and b) is ?

My Attempt:

This question is really simple. The only thing I want to confirm is whether the answer to this question will be $$4.86$$ or $$4.25$$ ? As per me the answer should be $$4.86$$. I solved it this way: sum of distances from a particular leaf to the remaining $$7$$ leaves is $$34$$. The sum would remain the same for each leaf node. Therefore total sum of distance of all the leaf nodes $$= 34\times8$$. So, expectation $$= (34 \times 8)/(8 \times 7) = 4.86$$.

Am I correct with the answer?

• Your are unfair in calculating total path length (i.e. 34*8, means you assumed that all 8 leaf nodes has distance), then why are not counting as total number of ways (i.e., 8*8 instead of 8*7)? So, $$\frac{(34 \times 8)}{(8 \times 8)} = 4.25$$ Feb 19, 2019 at 8:18

Your answer assumes that once $$a$$ is chosen, there are $$7$$ possibilities for the $$b$$, at an average distance of $$34/7$$ (and this value doesn't depend on $$a$$). But this ignores the possibility that $$a$$ and $$b$$ are equal (distance $$0$$); since they are chosen independently this can happen, and so in fact there are $$8$$ possibilities for $$b$$ at an average distance of $$34/8$$.
Hint: Two leaf nodes can be selected in $$8\times8 = 64$$ ways.


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# American Institute of Mathematical Sciences

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June  2002, 1(2): 191-219. doi: 10.3934/cpaa.2002.1.191

## Existence of a weak solution for a quasilinear wave equation with boundary condition

 1 Department of Mathematics, University of Corsica, UMR CNRS 6134 S.P.E., BP 52, 20250 Corte, France, France

Received  July 2001 Revised  November 2001 Published  March 2002

In this paper we get by the Glimm scheme the existence of a weak solution to the quasilinear wave equation $w_{t t}=( \sigma_n(w_x))_x$ where $\sigma_n(x)=ax+\gamma x^{2n+1}$, $\alpha$, $\gamma>0$ and $n$ is an integer $n\ge 1$ with $w_x(0,t)=0$ for initial data not necessarily small.
Citation: Alain Hertzog, Antoine Mondoloni. Existence of a weak solution for a quasilinear wave equation with boundary condition. Communications on Pure & Applied Analysis, 2002, 1 (2) : 191-219. doi: 10.3934/cpaa.2002.1.191
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Closed Set Measurable in Borel Sigma-Algebra

Theorem

Let $\left({S, \tau}\right)$ be a topological space, and let $\mathcal B \left({\tau}\right)$ be the associated Borel $\sigma$-algebra.

Let $C$ be a closed set in $S$.

Then $C$ is $\mathcal B \left({\tau}\right)$-measurable.

Proof

Since $C$ is closed, $S \setminus C$ is open.

By definition of Borel $\sigma$-algebra, $S \setminus C \in \mathcal B \left({\tau}\right)$.

By axiom $(2)$ for $\sigma$-algebras:

$S \setminus \left({S \setminus C}\right) \in \mathcal B \left({\tau}\right)$

and this set equals $C$ by Set Difference with Set Difference since $C \subseteq S$.

The result follows by definition of measurable set.

$\blacksquare$


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# How many atoms in a 10*mol quantity of CaCl_2?

Jul 18, 2017

How many?

#### Explanation:

If I have 12 dozen eggses, how many dozens do I have? Do you agree that it is one dozen? Well then how many eggs in 12 dozen?

Now we gots a $10 \cdot m o l$ quantity of $C a C {l}_{2}$, i.e. there are $10 \cdot m o l \times {N}_{A}$ individual formula units of $C a C {l}_{2}$, where ${N}_{A} \equiv \text{Avocado number} \equiv 6.022 \times {10}^{23} \cdot m o {l}^{-} 1$. And I am perfectly at liberty to use the symbol ${N}_{A}$ to represent that number.

And so we got $10 \times {N}_{A} = 6.022 \times {10}^{24}$ individual calcium ions.

And we also gots $2 \times 10 \times {N}_{A} = 12.044 \times {10}^{24}$ individual chloride ions.

Can you tell me what mass of $C a C {l}_{2}$ we got?


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Definition of a Transcendental Function

1. Jun 19, 2010

psholtz

I had grown up thinking that the transcendental functions (to wit, e(x), sin(x), cos(x), etc) were (somewhat) arbitrary functions, "defined" simply by the fact that they could not be expressed as polynomials (or some such loose definition).

Indeed, from Wikipedia, we read that:
But now I'm reading from Ince's classic treatise on ODEs, and on page 23, he gets into a brief footnote about the nature of transcendental functions. Specifically, he writes:
This is a rather different definition than that given by Wikipedia.

Indeed, Ince goes on to define the logarithm function as:

$$\ln(x) = \int_1^x t^{-1}dt$$
and then defines the exponential function as the inverse of the logarithm, and then tersely states that the remaining elementary transcendentals, like the sine, cosine, and their hyperbolic equivalents, can be defined in terms of the exponential.

Now, it's obvious to me how to define hyperbolic sine and cosine in terms of exponentials. That follows directly from their definition.

For the "regular" sine and cosine, he must have in mind Euler's formula, no?

$$e^{ix} = \cos x + i \sin x$$

I'm asking, just b/c I'm not sure how else to define sine and cosine in terms of an exponential..

At any rate, this was a little surprising to me, and I thought I would bring it up for discussion.

Is there a reference where I can read more about transcendental functions, and how they are defined? (i.e., defined in terms of integrating algebraic functions?)

Moreover, the imagination can easily conjure up a wide array of "transcendental" functions, to wit:

$$f(x) = x^\pi$$
$$g(x) = x^ {1/x}$$

and so on..

How might these functions be defined in terms of integration from algebraic functions?

2. Jun 19, 2010

Office_Shredder

Staff Emeritus
I'm not familiar with the text you're citing, but I think the key here is "elementary transcendental functions". Not all transcendental functions can be defined by integration (any function defined by integration has to be continuous, and obviously there are transcendental functions that are not continuous).

As for defining sine and cosine, it does use Euler's formula

$$cos(x)=\frac{e^{ix}+e^{-ix}}{2}$$

$$sin(x)=\frac{e^{ix}-e^{-ix}}{2}$$

You can check by Euler's formula being plugged into the right hand side of each equation

3. Jun 19, 2010

Hurkyl

Staff Emeritus
You know Euler's identity for eix. What about for e-ix? Now solve for the two unknowns. (the unknowns being cos(x) and sin(x))

4. Jun 23, 2010

nekronaut

Almost right

$$\sin(x)=\frac{e^{ix}-e^{-ix}}{2i}$$


text:
# Chapter 8 - Section 8.2 - Estimation of a Population Mean: σ Known - Exercises - Page 322: 8.7

The confidence level is denoted by (1-α)100%, and it is associated with a confidence interval to state how much confidence we have that this interval contains the true population parameter. Confidence interval is constructed with regard to a given confidence level and is given as Point estimate ± Margin of error.

#### Work Step by Step

--

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


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# Example of a linear operator whose graph is not closed but it takes a closed set to a closed set

I want an example of a linear operator $T:X\to Y$, where $X$ and $Y$ are normed linear spaces, such that graph of $T$ is not closed but $T$ maps closed sets of $X$ to closed sets in $Y$.

For functions other than linear operators it is not that difficult. If we consider $f:\mathbb R\to \mathbb R$ by $f(0)=0$ and $f(x)=1$ for all $x\in \mathbb R\setminus \{0\}$, then $f$ maps every subset of $\mathbb R$ to a closed set in $\mathbb R$ but grapf of $f$ is not closed.

Any help will be appreciated.

We know that there always exists a discontinuous linear functional $f:X\to \mathbb R$, where $X$ is an infinite dimensional normed linear space. If $f:c_0\to \mathbb R$ is a discontinuous linear functional then for every $n>0$, there exists $x^{(n)}\in c_0$ such that $|f(x^{(n)})|>n\|x^{(n)}\|_{\infty}$. Now we define $T:c_0\to c_0$ by $T(x)=(f(x),x_1,x_2,\ldots)$ for all $x\in c_0$. Then $\|T(x^{(n)})\|_{\infty}=\sup\{|f(x^{(n)})|,|x_1|,|x_2|,\ldots\}>n\|x^{(n)}\|_{\infty}$. Thus $T$ is a discontinuous linear operator. Since $c_0$ is a Banach space, therefore graph of $T$ is not closed. Is the function $T$ maps every closed set in $c_0$ to a closed subset of $c_0$?

• Start by looking for one example of a linear operator whose graph is not closed. – uniquesolution Mar 27 '17 at 9:53
• I am not getting a suitable example – Anupam Mar 27 '17 at 10:12
• so how do you imagine you will solve the problem? It seems to me that if you are looking for an object of type X with property Y, you certainly need to find first an object of type X. – uniquesolution Mar 27 '17 at 10:27
• Yes. I want an operator that is not closed. If I consider Banach spaces, then unbounded operator will do. But I am not finding such an operator – Anupam Mar 27 '17 at 10:37
• I have found such an example. But I could not establish that my function is closed. Any suggestion will be appreciated. – Anupam Mar 28 '17 at 14:15

Indeed, suppose the graph of $T$ is not closed. Then there exists a sequence $(x_n)$ that converges to $0$ in $X$ and such that $Tx_n\to y\ne 0$ in $Y$. Furthermore, we can arrange that $Tx_n\ne y$ for all $n$. Indeed, if $Tx_n$ happens to be equal to $y$, replace $x_n$ with $(1+1/n)x_n$ which does not change the limit of the sequence $(Tx_n)$.
Let $A= \{x_n:n\in\mathbb N\} \cup \{0\}$; this is a closed subset of $X$. Its image $T(A)$ has $y$ as its limit point, but does not contain $y$. Thus, $T(A)$ is not closed.


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# Stability analysis of algorithms for solving confluent Vandermonde-like systems

Higham, Nicholas J. (1990) Stability analysis of algorithms for solving confluent Vandermonde-like systems. SIAM Journal On Matrix Analysis And Applications, 11 (1). pp. 23-41. ISSN 1095-7162

 PDF 0611002.pdf Download (1MB)

## Abstract

A confluent Vandermonde-like matrix $P(\alpha _0 ,\alpha _1 , \cdots ,\alpha _n )$ is a generalisation of the confluent Vandermonde matrix in which the monomials are replaced by arbitrary polynomials. For the case where the polynomials satisfy a three-term recurrence relation algorithms for solving the systems $Px = b$ and $P^T a = f$ in $O(n^2 )$ operations are derived. Forward and backward error analyses that provide bounds for the relative error and the residual of the computed solution are given. The bounds reveal a rich variety of problem-dependent phenomena, including both good and bad stability properties and the possibility of Xextremely accurate solutions. To combat potential instability, a method is derived for computing a “stable” ordering of the points $\alpha _i$; it mimics the interchanges performed by Gaussian elimination with partial pivoting, using only $O(n^2)$ operations. The results of extensive numerical tests are summarised, and recommendations are given for how to use the fast algorithms to solve Vandermonde-like systems in a stable manner.

Item Type: Article Vandermonde matrix, orthogonal polynomials, Hermite interpolation, Clenshaw recurrence, forward error analysis, backward error analysis, stability, iterative refinement MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theoryMSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis Ms Lucy van Russelt 04 Jul 2006 20 Oct 2017 14:12 http://eprints.maths.manchester.ac.uk/id/eprint/355

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# Bepo - levi implies monotonone convergence theorem??

For Lebesgue measurable functions, Is is true that Beppo-Levi theorem implies the monotone convergence theorem?

Beppo-Levi: Suppose $\sum_{k=1}^{\infty} \int |f_k |\, dm$ is finite. Then the series $\sum f_k(x)$ converges for almost all $x$, its sum is integrable and $$\int \sum f_k \,dm = \sum \int f_k\, dm$$

Monotone convergence theorem: if $\{ f_n \}$ is a sequence of non-negative measurable functions and $\{ f_n(x) : n \geq 1 \}$ increases monotonically to $f(x)$ for each $x$ $( f_n \to_{pointwise} f$), then $$\lim \int\limits_E f_n\, dm = \int\limits_E f\, dm$$

• Levi's theorem is usually used to prove Lebesgue's theorem, along with Fatou's lemma. – Pedro Tamaroff May 4 '14 at 22:25

The monotone convergence theorem handles infinities gracefully, which can only be done for functions that are positive (or otherwise reasonably controlled from below). In particular, nowhere does it assume that $f_n$, $f$, or the integrals, are finite. This seems to be beyond the scope of Beppo Levi, so I'm not sure that fixing this issue alone is considerably easier than proving everything from scratch. But let me try.

Depending on your version of definitions, it may or may not be trivial that for a positive function $f$ the following special case of monotone convergence holds:

$$\intop_E f dm = \lim_{C \to +\infty, E_n \uparrow E} \intop_{E_n} \min(f, C) dm$$

where $E_n$ are sets of finite measure that approximate $E$ (I assume $\sigma$-finiteness; if it fails then we should restrict to $\{f > 0\}$; if it fails even there then monotone convergence holds almost trivially with both sides infinite).

Now in order to make use of Beppo Levi we should make the limit finite. I would do that by replacing $f_n$ by $f_{n,C,k} := (f_n \wedge C) \mathsf{1}[E_k]$ and $f$ by $f_{C,k} := (f \wedge C) \mathsf{1}[E_k]$ for some fixed $k$. Now we can safely apply Beppo Levi to the successive differences $f_{n+1,C,k} - f_{n,C,k}$ to obtain

$$\intop f_{C,k} dm = \lim_{n \to \infty} \intop f_{n,C,k} dm$$

Now take $C$ and $k$ to $\infty$ and interchange the limits. You can always do this with monotonely increasing limits (this is equivalent to rearrangement of terms in positive series, or Fubini on $\mathbb{N} \times \mathbb{N}$, or whatever you prefer). On the other hand, monotone convergence itself is about rearrangement or Fubini on $E \times \mathbb{N}$, so I'm not even sure you would view the things that I rely on as more basic than those that you prove...

The hypothesis for Beppo-Levi can be changed as $f_k$ being non-negative. It is equivalent of Tonelli theorem. Now,

let $g_k(x) = f_{k+1}(x)- f_k(x)$ and $f_0(x) = 0$. Then

$$f_n(x) = \sum_{k=0}^{k=n-1}g_k(x)$$ and each $g_k(x) \geq 0$ because of monotonicity of $f_k$. So applying Beppo Levi on $g_k$ we have that

$$\int \sum_{k=1}^\infty g_k dm = \sum_{k=1}^\infty \int g_k dm$$

$$\sum_{k=1}^\infty g_k = \lim_{n \to \infty}\sum_{k=1}^n g_k = \lim_{n \to \infty} f_{n+1} = \lim_{n \to \infty} f_{n}$$ and

$$\sum_{k=1}^\infty \int g_k dm = \lim_{n \to \infty}\sum_{k=1}^n \int g_k dm = \lim_{n \to \infty} \int f_{n+1} dm = \lim_{n \to \infty} \int f_{n} dm$$ and hence we have monotone convergence theorem.


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# How will Occam's Razor principle work in Machine learning

The following question displayed in the image was asked during one of the exams recently. I am not sure if I have correctly understood the Occam's Razor principle or not. According to the distributions and decision boundaries given in the question and following the Occam's Razor the decision boundary B in both the cases should be the answer. Because as per Occam's Razor, choose the simpler classifier which does a decent job rather than the complex one.

Can someone please testify if my understanding is correct and the answer chosen is appropriate or not? Please help as I am just a beginner in machine learning

• 3.328 "If a sign is not necessary then it is meaningless. That is the meaning of Occam's Razor." From the Tractatus Logico-Philosophicus by Wittgenstein – Jorge Barrios Mar 7 at 11:25

Occam’s razor principle:

Having two hypotheses (here, decision boundaries) that has the same empirical risk (here, training error), a short explanation (here, a boundary with fewer parameters) tends to be more valid than a long explanation.

In your example, both A and B have zero training error, thus B (shorter explanation) is preferred.

What if training error is not the same?

If boundary A had a smaller training error than B, selecting becomes tricky. We need to quantify "explanation size" the same as "empirical risk" and combine the two in one scoring function, then proceed to compare A and B. An example would be Akaike Information Criterion (AIC) that combines empirical risk (measured with negative log-likelihood) and explanation size (measured with the number of parameters) in one score.

As a side note, AIC cannot be used for all models, there are many alternatives to AIC too.

Relation to validation set

In many practical cases, when model progresses toward more complexity (larger explanation) to reach a lower training error, AIC and the like can be replaced with a validation set (a set on which the model is not trained). We stop the progress when validation error (error of model on validation set) starts to increase. This way, we strike a balance between low training error and short explanation.

Occam Razor is just a synonym to Parsimony principal. (KISS, Keep it simple and stupid.) Most algos work in this principal.

In above question one has to think in designing the simple separable boundaries,

like in first picture D1 answer is B. As it define the best line separating 2 samples, as a is polynomial and may end up in over-fitting. (if I would have used SVM that line would have come)

similarly in figure 2 D2 answer is B.

Occam’s razor in data-fitting tasks :

1. First try linear equation
2. If (1) don't helps much - choose a non-linear one with less terms and/or smaller degrees of variables.

## D2

B clearly wins, because it's linear boundary which nicely separates data. (What is "nicely" I can't currently define. You have to develop this feeling with experience). A boundary is highly non-linear which seems like a jittered sine wave.

## D1

However I am not sure about this one. A boundary is like a circle and B is strictly linear. IMHO, for me - boundary line is neither circle segment nor a line segment,- it's parabola-like curve :

So I opt for a C :-)

• I'm still unsure of why you want an in-between line for D1. Occam's Razor says to use the simple solution that works. Absent more data, B is a perfectly valid division that fits the data. If we received more data that suggests more of a curve to B's data set then I could see your argument, but requesting C goes against your point (1), since it's a linear boundary that works. – Delioth Mar 7 at 20:36
• Because there is a lot of empty space from B line towards the left circular cluster of points. This means that any new random point arriving has a very high chance being assigned to circular cluster on the left and a very small chance for being assigned to the cluster in the right. Thus, B line is not an optimal boundary in case of new random points on plane. And you can't ignore randomness of data, because usually there is always a random displacement of points – Agnius Vasiliauskas Mar 8 at 9:39

I am not sure if I have correctly understood the Occam's Razor principle or not.


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# Tag Info

7

I don't think you can do it with join alone. You could do: join -t, -a1 -a2 -o0,1.2,1.3,1.4,1.5,2.2,2.3,2.4,2.5 -e MISSING 1.txt 2.txt | perl -F, -lape '@F[1..2]=@F[5..6] if $F[1] eq "MISSING";$_=join",",@F[0..4],@F[7..8]' -p: use a line by line reading loop like in sed/awk -a, -F,: like awk, split the lines into fields (into the @F ...

5

You can use bash scripting, but for compression etc. it relies on other programs. You might be better of with Python, or any other scripting language which can generate CSV files for you (although CSV syntax is not necessarily difficult to generate), and that can do the concatenation and compression. Given this directory of files (all different length, but ...

5

I'll assume that extra field from the n lines of file2 should be appended to the last n lines of file1: awk -F, -v OFS=, 'FNR==NR {a[FNR]=$3; next} {print$0, a[FNR]}' <(tac file2) <(tac file1) | tac paste -d, <(tac file1) <(cut -d, -f3- <(tac file2)) | tac These solution add a trailing comma to the first line. You can remove it by ...

5

This is definitely feasible. Many of us were running mixed, load-balanced broadband configs for corporate years ago and they worked really well. Many probably still do! You can do it in a number of ways, including using iptables rules and/or iproute2 (ip(8) command) to setup policy routing. The load balancing is not done at the packet level, but at the ...

5

awk ' NR==FNR {vals[$1] =$2 " " $3 " "$4; next} !($1 in vals) {vals[$1] = "0 0 0"} {$(NF+1) = vals[$1]; print} ' file2 file1 TABLES REF-IO HEAD-IO DIFF-IO REF-SELECT HEAD-SELECT DIFF-SELECT test 200 500 -300 5 7 -2 exam 2 3 -1 0 7 -7 final 2 1 1 12 6 6 mail 4 2 2 0 0 0 TOTAL 208 506 -298 20 23 -3

4

What implementation of join are you using? With join (GNU coreutils) 5.97, I can use [0 1021] ~/temp/jointest % join -a1 -a2 jointest1.txt jointest2.txt a 1 10 b 2 11 c 12 d 4 13 e 5 and the "plain" join works, too (but omits c and e). There is an -e option which supposedly lets you choose the marker for empty fields, but it appears to be broken in my ...

4

Use vimdiff if you like vim. Otherwise, diffuse works great as well.

4

You can use rsync to do this: $rsync -abviuzP src/ dest/ -a archive mode; equals -rlptgoD (no -H,-A,-X) -i turns on the itemized format, which shows more information than the default format -b makes rsync backup files that exist in both folders, appending ~ to the old file. You can control this suffix with --suffix .suf -u makes rsync transfer skip ... 4 If you don't mind the order of output:$ awk -F',' 'NF>1{a[$1] = a[$1]","$2}END{for(i in a){print i""a[i]}}' file jkl, words and numbers, words and numbers, words and numbers, words and numbers abc, 12345, 56345, 15475, 123345 ghi, something else, something else, something else, something else def, text and nos, text and nos, text and nos, text and nos ... 3 The PyPdf library makes this sort of things easy if you're willing to write a bit of Python. Save the code below in a script called pdf-cat-even (or whatever you like), make it executable (chmod +x pdf-cat-even), and run it as a filter (./pdf-cat-even a.pdf b.pdf >concatenated.pdf). You need pyPdf ≥1.13 for the addBlankPage method. #!/usr/bin/env python ... 3 Yes - bash scripting will be able to meet the requirements. But you should use whatever scripting language you are comfortable with. python, perl are other possibilities. 3 This is a useful1 use of cat:$ cat File1 File2 > CombinedFile Footnotes: 1. As opposed to the useless use of cat

3

The first step is to produce a pdf file with an empty page. You can do this easily with a lot of programs (LibreOffice/OpenOffice, inkscape, (La)TeX, scribus, etc.) Then just include this empty page where needed: pdftk A.pdf empty_page.pdf B.pdf output result.pdf If you want to do this automatically with a script, you can use e.g. pdftk file.pdf ...

3

You don't need patch for this; it's for extracting changes and sending them on without the unchanged part of the file. The tool for merging two versions of a file is merge, but as @vonbrand wrote, you need the "base" file from which your two versions diverged. To do a merge without it, use diff like this: diff -DVERSION1 file1.xml file2.xml > merged.xml ...

3

As far as I know, there isn't any universal way; it depends on which version control system you are using, e.g.: Mercurial uses a setting in .hgrc. git uses merge.tool configuration, as told in a comment. for svn, you specify in /etc/subversion/config.

3

I usually use paste from coreutils for this sort of thing: paste -d'\n' file1 file2 file3

3

using just awk: awk -F, -v OFS=, ' BEGIN {m = " MISSING"} # process file1 NR == FNR {lines[$1] =$0; next} # process file2 { added[$1] =$4 OFS $5 if (!($1 in lines)) { $4 = m$5 = m lines[$1] =$0 } } # print the combined output END { for (id in lines) ...

3

The 'x' file: FNR==1 { ++FILENO } { T[$1]++ X[$1,FILENO]=$2 } END { print "type\tvalue1\tvalue2\tdifference" for(t in T) print t"\t"X[t,1]+0"\t"X[t,2]+0"\t"0+X[t,1]-X[t,2] } The run:$ awk -f x file1 file2 type value1 value2 difference viewer 23 2990 -2967 remark 2 240 -238 test 27 0 27 ...

3

Another awk solution: $awk ' FNR==NR { a[$1] = $2; c[$1] = $1; next; } { b[$1] = $2; c[$1] = $1; } END { printf "type\tvalue1\tvalue2\tdifference\n"; for(i in c) printf "%s\t%d\t%d\t%d\n", i, a[i], b[i], a[i]-b[i] }' file1 file2 type value1 value2 difference remark 2 240 -238 test 27 0 27 ... 3 Assuming you're talking about merging 3 partitions into 1 with all the original data intact I do not believe you'll be able to merge these partitions, as they are. There is not enough unused space on any of the partitions that can contain the other partitions' used space. You could shuffle them around and maximize the free space so that it's on 1 of the 3 ... 2 i wrote a little perl script, that do this #!/usr/bin/perl do { open($fh[$_], "<$ARGV[$_]") or die("'$ARGV[$_]' does not exist") } for(0..$#ARGV); for($i=0;;$i++) { $j=$#ARGV+1; $fh =$fh[$i%$j]; if ( $_ = <$fh> ) { print $_; } else {$end |= 2**($i%$j); } if($end == (2**($j))-1) { last; } } ...

2

Another Python version that does not need to read all files into memory at once: paddy$more f[123].tmp :::::::::::::: f1.tmp :::::::::::::: line1 file1 line2 file1 line3 file1 :::::::::::::: f2.tmp :::::::::::::: line1 file2 line2 file2 line3 file2 line4 file2 :::::::::::::: f3.tmp :::::::::::::: line1 file3 line2 file3 line3 file3 line4 file3 line5 file3 ... 2 join -j2 <(sort -k2 file1) <(sort -k2 file2) -o 1.1,1.2,2.1,2.3 | column -t outputs 873 1.1.1.1 test7 p10 1108 78.2.204.174 test8 p4 1257 78.2.8.181 test1 p6 1033 99.99.99.10 test2 p9 2 You can use join for this. First we have to sort both files using the 2nd column as key:$ sort -t' ' -k 2,2 a > as $sort -t' ' -k 2,2 b > bs Resulting in:$ cat as 873 1.1.1.1 1108 78.2.204.174 1257 78.2.8.181 1033 99.99.99.10 $cat bs test7 1.1.1.1 p10 test8 78.2.204.174 p4 test1 78.2.8.181 p6 test2 99.99.99.10 p9 Then the actual join:$ ...

2

merge(1) is probably nearer to what you want, but that requires a common ancestor to your two files. A (dirty!) way of doing it is: Get rid of the first and last lines, use grep(1) to exclude them Smash the results together sort -u leaves a sorted list, eliminates duplicates Replace first/last line Humm... something along the lines: echo ...

2

You can use cp -r name_of_the_folder/* name_of_the_destination_folder where the asterisk(*) stands for all files and -r for recursive copy. You can use also the -i option which will ask you if you want to overwrite the contents.

2

If I understand your question correctly you have the following: $echo -e "line1\nline2\nline3\n" line1 line2 line3$ And you want this: line1line2line3 So you should only need to remove the blank lines. A command like this should do it: \$ echo -e "line1\nline2\nline3\n" | paste -s -d '' line1line2line3 I'm not sure where your output is being kept, ...

1

You could also use LaTeX to do this (though I'm aware it's probably not what you want). Something like the following should work: \documentclass{book} \usepackage{pdfpages} \begin{document} \includepdf[pages=-]{A} \cleardoublepage % Make sure we clear to an odd page \includepdf[pages=-]{B} % This inserts all pages. Or you can specify specific pages, a ...

1

Gilles' answer worked for me, but since i have to merge many files it's more convenient if i can read their names from a text file. I've slightly modified Gilles' code to do just that, maybe it would help someone else: #!/usr/bin/env python # requires PyPdf library, version 1.13 or above - # its homepage is http://pybrary.net/pyPdf/ # running: ...

1

Create a file mylist.txt with all the files you want to have concatenated in the following form: # this is a comment file '/path/to/file1' file '/path/to/file2' file '/path/to/file3' Then you can encode your files with: ffmpeg -f concat -i mylist.txt -c copy output Edit: You may need to compile ffmpeg from source to get a recent ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
# Build AirSim on Linux & MacOS#

The current recommended and tested environment is Ubuntu 18.04 LTS. Theoretically, you can build on other distros as well, but we haven't tested it.

Only macOS Catalina (10.15) is supported.

We've two options - you can either build inside docker containers or your host machine.

## Host machine#

### Pre-build Setup#

#### Linux - Build Unreal Engine#

• Make sure you are registered with Epic Games. This is required to get source code access for Unreal Engine.

• Clone Unreal in your favorite folder and build it (this may take a while!). Note: We only support Unreal >= 4.24 at present. We recommend using 4.25.

# go to the folder where you clone GitHub projects
git clone -b 4.25 https://github.com/EpicGames/UnrealEngine.git
cd UnrealEngine
./Setup.sh
./GenerateProjectFiles.sh
make

2. Run the Epic Games Launcher, open the Library tab on the left pane. Click on the Add Versions which should show the option to download Unreal 4.25 as shown below. If you have multiple versions of Unreal installed then make sure 4.25 is set to current by clicking down arrow next to the Launch button for the version.

Note: AirSim also works with UE >= 4.24, however, we recommend 4.25. Note: If you have UE 4.16 or older projects, please see the upgrade guide to upgrade your projects.

### Build AirSim#

• Clone AirSim and build it:
# go to the folder where you clone GitHub projects
git clone https://github.com/Microsoft/AirSim.git
cd AirSim

By default AirSim uses clang 8 to build for compatibility with UE 4.25. The setup script will install the right version of cmake, llvm, and eigen.

./setup.sh
./build.sh
# use ./build.sh --debug to build in debug mode

### Build Unreal Environment#

Finally, you will need an Unreal project that hosts the environment for your vehicles. AirSim comes with a built-in "Blocks Environment" which you can use, or you can create your own. Please see setting up Unreal Environment if you'd like to setup your own environment.

## How to Use AirSim#

### Linux#

Once AirSim is setup:

• Go to UnrealEngine installation folder and start Unreal by running ./Engine/Binaries/Linux/UE4Editor.
• When Unreal Engine prompts for opening or creating project, select Browse and choose AirSim/Unreal/Environments/Blocks (or your custom Unreal project).
• Alternatively, the project file can be passed as a commandline argument. For Blocks: ./Engine/Binaries/Linux/UE4Editor <AirSim_path>/Unreal/Environments/Blocks/Blocks.uproject
• If you get prompts to convert project, look for More Options or Convert-In-Place option. If you get prompted to build, choose Yes. If you get prompted to disable AirSim plugin, choose No.
• After Unreal Editor loads, press Play button.

### Mac#

• Browse to AirSim/Unreal/Environments/Blocks.
• Run ./GenerateProjectFiles.sh <UE_PATH> from the terminal, where UE_PATH is the path to the Unreal installation folder. (By default, this is /Users/Shared/Epic\ Games/UE_4.25/) The script creates an XCode workspace by the name Blocks.xcworkspace.
• Open the XCode workspace, and press the Build and run button in the top left.
• After Unreal Editor loads, press Play button.

See Using APIs and settings.json for various options available for AirSim usage.

Tip

Go to 'Edit->Editor Preferences', in the 'Search' box type 'CPU' and ensure that the 'Use Less CPU when in Background' is unchecked.

### [Optional] Setup Remote Control (Multirotor Only)#

A remote control is required if you want to fly manually. See the remote control setup for more details.

Alternatively, you can use APIs for programmatic control or use the so-called Computer Vision mode to move around using the keyboard.

## FAQs#

• I'm getting error <MyProject> could not be compiled. Try rebuilding from source manually.
• This could either happen because of compile error or the fact that your gch files are outdated. Look in to your console window. Do you see something like below?

fatal error: file '/usr/include/linux/version.h''/usr/include/linux/version.h' has been modified since the precompiled header

• If this is the case then look for *.gch file(s) that follows after that message, delete them and try again. Here's relevant thread on Unreal Engine forums.

• If you see other compile errors in console then open up those source files and see if it is due to changes you made. If not, then report it as issue on GitHub.

• Unreal crashed! How do I know what went wrong?

• Go to the MyUnrealProject/Saved/Crashes folder and search for the file MyProject.log within its subdirectories. At the end of this file you will see the stack trace and messages. You can also take a look at the Diagnostics.txt file.
• How do I use an IDE on Linux?

• You can use Qt Creator or CodeLite. Instructions for Qt Creator are available here.
• Can I cross compile for Linux from a Windows machine?

• Yes, you can, but we haven't tested it. You can find the instructions here.
• What compiler and stdlib does AirSim use?

• We use the same compiler that Unreal Engine uses, Clang 8, and stdlib, libc++. AirSim's setup.sh will automatically download them.
• What version of CMake does the AirSim build use?

• 3.10.0 or higher. This is not the default in Ubuntu 16.04 so setup.sh installs it for you. You can check your CMake version using cmake --version. If you have an older version, follow these instructions or see the CMake website.
• Can I compile AirSim in BashOnWindows?

• Yes, however, you can't run Unreal from BashOnWindows. So this is kind of useful to check a Linux compile, but not for an end-to-end run. See the BashOnWindows install guide. Make sure to have the latest version (Windows 10 Creators Edition) as previous versions had various issues. Also, don't invoke bash from Visual Studio Command Prompt, otherwise CMake might find VC++ and try and use that!
• Where can I find more info on running Unreal on Linux?


text:
Lemma 35.3.5. Suppose that $R \to A$ has a section. Then for any $R$-module $M$ the extended cochain complex (35.3.4.1) is exact.

Proof. By Simplicial, Lemma 14.28.5 the map $R \to (A/R)_\bullet$ is a homotopy equivalence of cosimplicial $R$-algebras (here $R$ denotes the constant cosimplicial $R$-algebra). Hence $M \to (A/R)_\bullet \otimes _ R M$ is a homotopy equivalence in the category of cosimplicial $R$-modules, because $\otimes _ R M$ is a functor from the category of $R$-algebras to the category of $R$-modules, see Simplicial, Lemma 14.28.4. This implies that the induced map of associated complexes is a homotopy equivalence, see Simplicial, Lemma 14.28.6. Since the complex associated to the constant cosimplicial $R$-module $M$ is the complex

$\xymatrix{ M \ar[r]^0 & M \ar[r]^1 & M \ar[r]^0 & M \ar[r]^1 & M \ldots }$

we win (since the extended version simply puts an extra $M$ at the beginning). $\square$

There are also:

• 3 comment(s) on Section 35.3: Descent for modules

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).


text:
# The Unapologetic Mathematician

## Lie Algebras

One more little side trip before we proceed with the differential geometry: Lie algebras. These are like “regular” associative algebras in that we take a module (often a vector space) and define a bilinear operation on it. This much is covered at the top of the post on algebras.

The difference is that instead of insisting that the operation be associative, we impose different conditions. Also, instead of writing our operation like a multiplication (and using the word “multiplication”), we will write it as $[A,B]$ and call it the “bracket” of $A$ and $B$. Now, our first condition is that the bracket be antisymmetric:

$\displaystyle[A,B]=-[B,A]$

Secondly, and more importantly, we demand that the bracket should satisfy the “Jacobi identity”:

$\displaystyle[A,[B,C]]=[[A,B],C]+[B,[A,C]]$

What this means is that the operation of “bracketing with $A$” acts like a derivation on the Lie algebra; we can apply $[A,\underline{\hphantom{X}}]$ to the bracket $[B,C]$ by first applying it to $B$ and bracketing the result with $C$, then bracketing $B$ with the result of applying the operation to $C$, and adding the two together.

This condition is often stated in the equivalent form

$\displaystyle[A,[B,C]]+[C,[A,B]]+[B,[C,A]]=0$

It’s a nice exercise to show that (assuming antisymmetry) these two equations are indeed equivalent. This form of the Jacobi identity is neat in the way it shows a rotational symmetry among the three algebra elements, but I feel that it misses the deep algebraic point about why the Jacobi identity is so important: it makes for an algebra that acts on itself by derivations of its own structure.

It turns out that we already know of an example of a Lie algebra: the cross product of vectors in $\mathbb{R}^3$. Indeed, take three vectors $u$, $v$, and $w$ and try multiplying them out in all three orders:

\displaystyle\begin{aligned}u\times&(v\times w)\\w\times&(u\times v)\\v\times&(w\times u)\end{aligned}

and add the results together to see that you always get zero, thus satisfying the Jacobi identity.

May 17, 2011 - Posted by | Algebra, Lie Algebras

## 4 Comments »

1. […] Algebras from Associative Algebras There is a great source for generating many Lie algebras: associative algebras. Specifically, if we have an associative algebra we can build a lie algebra […]

Pingback by Lie Algebras from Associative Algebras « The Unapologetic Mathematician | May 18, 2011 | Reply

2. […] John Armstrong: Another Existence Proof (of the convergence of the Picard iteration), Gronwall’s Inequality, Lie Algebras […]

Pingback by Sixth Linkfest | May 25, 2011 | Reply

3. […] a Lie group is a smooth manifold we know that the collection of vector fields form a Lie algebra. But this is a big, messy object because smoothness isn’t a very stringent requirement on a […]

Pingback by The Lie Algebra of a Lie Group « The Unapologetic Mathematician | June 8, 2011 | Reply

4. […] I was all set to start with Lie algebras today, only to find that I’ve already defined them over a year ago. So let’s pick up with a recap: a Lie algebra is a module — usually a vector space over […]

Pingback by Lie Algebras Revisited « The Unapologetic Mathematician | August 6, 2012 | Reply


text:
Question

# If the $$n^{th}$$ term of an arithmetic progression is $$15n + 10$$ then its fifth term is _______.

A
25
B
75
C
55
D
85

Solution

## The correct option is D $$85$$$$n^{th}$$ term of Arithmetic Progressive$$T_{n} = 15n + 10$$To find the fifth term of A.P.,take $$n = 5$$$$T_{5} = 15(5) + 10$$$$= 75 + 10$$$$= 85$$$$5^{th}$$ term of A.P. is $$85$$.Mathematics

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text:
# Cannot install MiKTeX 2.9 after a new Windows installation [closed]

I used to have MiKTeX working well. I then recently had to reinstall Windows, hence I have to reinstall MiKTeX. It always stops during the installation and here is the log file:

starting package maintenance...

installation directory: "C:\Program Files (x86)\MiKTeX 2.9"
package repository: "C:\Users\mef7si\Desktop\MikTeX 2.9.4279"
visiting repository "C:\Users\mef7si\Desktop\MikTeX 2.9.4279"...
repository type: local package repository
lightweight database digest: 849a1791c324b8bb1c740173c680412b
going to install 75476 file(s) (2191 package(s))
problem: C:\Program Files (x86)\MiKTeX 2.9\miktex/bin\MiKTeX209-core-PS.dll does not exist
problem: C:\Program Files (x86)\MiKTeX 2.9\miktex/bin\MiKTeX209-core.dll does not exist
problem: C:\Program Files (x86)\MiKTeX 2.9\miktex/bin\MiKTeX209-packagemanager-PS.dll does not exist
problem: C:\Program Files (x86)\MiKTeX 2.9\miktex/bin\MiKTeX209-packagemanager.dll does not exist
extracting files from [...]
[...]
extracting files from [...]

Error: Permission denied: C:\Program Files (x86)\MiKTeX 2.9\source\cdpbundl-src.cab

PS: it doesn't always give the same src name, however, it is always an error due to the Permission Denied.

I tried everything with the Firewall (solution from internet), but nothing succesful until now. Does anyone have an idea?

-

## closed as off-topic by Speravir, Peter Jansson, Sean Allred, Guido, moeweFeb 25 '14 at 20:34

• This question does not fall within the scope of TeX, LaTeX or related typesetting systems as defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

IT is not necesary to copy the whole log file, and also I formatted it, that is shown as block quote of code, cf. my edit. Deactivate also the Antivirus software. –  Speravir Feb 25 '14 at 18:32
A suggestion: Do us a favour and change your username to something more telling than "user1234". –  Speravir Feb 25 '14 at 19:37
This question appears to be off-topic because it is either not TeX related or could only valuably answered by the MiKTeX developer. –  Speravir Feb 25 '14 at 19:38
@Speravir Eh, while I agree that TeX.SX can't be very helpful here, I would encourage migration to SU. –  Sean Allred Feb 25 '14 at 20:05
@SeanAllred: I am quite sure they also could not give a definitive answer. –  Speravir Feb 25 '14 at 20:25

Sorry, but this kind of questions is not answerable on a valuable level. The issue is in most cases not related to MiKTeX installer itself, not speaking of TeX in general.

Possible reasons for problems are:

• a problem of user rights (writing access forbidden for simple users). A solution can consist in installing not in C:\Program Files (or the (x86) companion), because then the UAC (user access control) will not be involved. A simple user can always install in his %UserProfile% (the problem could then be an institutional size limit).
• a Firewall. Solution: deactivate firewall or better, when possible, set a temporary exception.
• an Antivirus program. Solution again: deactivate program or better, when possible, set a temporary exception.
• a temporary problem of the MiKTeX.org (at least one subdomain is called on every installation or update when “the nearest” repository, i.e. a random one, is selected, cf. Can I avoid connecting to MiKTeX update server?). Then you only could wait and try again after some time.
• a corrupt installation file. This could be caused by
• the installer itself (back in past sometimes the installer had a flaw). Then only an installer update would help.
• the MiKTeX download mirror, that could host corrupt files for unknown reasons. Choose a different one.
• the downloading to your computer, which can be responsible for breaking files especially when Proxies are involved. Try to download without Proxies or at least check settings of your installer (cf. update 2 in this question: MiKTeX: connect failed in tcp_connect).

In praxis a combination of these is probable.

-


text:
# Talk:HIDE

## 1 A proposition for hIDE (to make it a unique editor for Haskell)

WARNING! This proposal is not well thought and promotes 'artistic' (as opposed to 'pragmatic') views and may have several design limitations. Feel free to contribute as long as you allow yourself to dream.

### 1.1 The idea

Proxima is more like an idea of a very general IDE that has different layers for presenting, editing, and storing documents. hIDE can be a Haskell specific implementation of it. To be precise, hIDE should store Haskell in a tree structure (preferably XML) but provide enough functionality to let the programmer completely forget about this inner representation. Of course, transformers to and fro (literate) Haskell is a must.

### 1.2 The approach

Proxima does not advocate a top-down editor. Haskell source code do not have deep tree structure so this is desirable.

Proxima identifies the different levels of an editor as document level (my translation: raw ASCII code), enriched document level (function and type declaration boundaries), presentation level (syntax highlight), layout level (collapsing, for example), arrangement level (word wrap, margins), and finally, rendering level.

### 1.3 Separating presentation from representation

What if we have for all, exists, and logical implication symbols displayed, instead of their ASCII equivalents? may be Greek letters for type variables?

$\mbox{sequence :: Monad }m\mbox{ }\implies\mbox{ }\forall \alpha.\mbox{ }[m\mbox{ }\alpha] \rightarrow m\mbox{ }[\alpha]$

This is just a funny way of displaying the original text

sequence :: Monad m => [m a] -> m [a]

The programmer can click on the displayed image to edit the underlying text.

What if we do not display the
--
or
{- -}

Haskell source gets a WYSIWYG editor (almost like modern HTML editors).

The C-style directives can have a different color and folding.

### 1.4 Pros

• Compact presentation of code
• Faster navigation (based on the structure of the source code)
• The document has to be parsed anyway if we want refactoring, so why not?

### 1.5 Cons

• Too much work
• The presentation must be "broken down" in order to edit it

--Pirated Dreams 17:19, 1 May 2006 (UTC)

## 2 Lemmih's comment on the previous (written with a flu) proposition

So you want a full Proxima style IDE?

Lemmih 16:23, 6 May 2006 (UTC)

hell yeah, man, thanks for the link. I'm checking it out. why don't you build it on top of Proxima, should be easy enough. --Pirated Dreams 12:00, 7 May 2006 (UTC)

The guy wrote a 200 page long PhD thesis on the topic, and even then, didn't solve all the problems. In my opinion, writing a great IDE isn't trivial. If you disagree, feel free to take the first step.

Lemmih 18:47, 7 May 2006 (UTC)

:) Who wants to write a great IDE? there are too many of those already! --Pirated Dreams 08:41, 6 December 2006 (UTC)


text:
Home » Physics » Mass Vs. Weight

# Difference Between Mass and Weight

## Mass Vs. Weight Comparing and Understanding differences

Mass and weight, most of the time both physical quantities are used interchangeably in our day-to-day life. People mix them up most of the time, but both these quantities are not the same.

The basic difference between weight and mass is that mass is the amount of matter that an object possesses whereas the weight ($W=m\times g$) of an object is force acted upon that object due to gravity

So, here in this article, we shall look at the difference between mass and weight, and as a physics students, we must pledge together not to make this sloppy mistake again at least not while solving physics problems. We will compare both these physical quantities and understand the difference between them. When studying physics, we must be aware of the clear distinction between these two quantities.

## Why we get confused?

There is a reason why people so often get confused between mass and weight. You might have observed people saying

“My weight is 70 Kg”

But this statement is not technically correct because weight is the force of gravity on any person’s mass. Here we are using a unit of mass with weight in the above statement. Here 70 Kg is the mass that you have in your body.

So, if a person of 70Kg wants to know his weight then he would have to calculate it using equation $W=mg$. So,

Weight $W=mg=70Kg \times 9.8 m/s^2 = 686 Kg m/s^2=686N$

$Kg m/s^2$ is also written as $N$.

So, in saying 70 Kg weight, the term weight we so casually use is not our weight, but mass contained in our body.  Here you can see that mass and weight are confused because the measure of the quantity of matter in things (mass) is done by their gravitational attraction to earth (weight).

## Difference between mass and weight

• The term mass is used for how much matter an object under consideration has. Mass is the measure of the inertia of an object. Weight is the most familiar force acting on an object that is the force of gravitation acting on objects by Earth.
• The mass contained in a body is denoted by letter $M$ or $m$ whereas the weight of a body is denoted by letter $W$ and can be calculated by relation $W=mg$ where $m$ is mass of the body and $g=9.8m/s^2$ is the acceleration due to the gravity of Earth.
• The weight of a body can be zero at places where there is no gravity. The mass of an object can never be zero.
• Mass of a body always remains the same, but we cannot say the same thing about the weight of a body. The weight of the body also changes with a change in location. For example, acceleration due to gravity on the Moon’s surface is less than the acceleration due to gravity on the surface of Earth. So, the weight of an object on the surface of the moon would be less than the weight of the same object on the surface of Earth.
• Mass is a scalar quantity as it has magnitude only but no direction. Weight on the other hand is a vector quantity and it has both magnitude and direction. The weight of anybody on Earth’s surface is directed towards the center of the Earth.
• The mass may be measured using an ordinary balance, but weight is measured using a spring balance.
• Mass is a fundamental quantity whereas weight is a derived quantity because it depends on other physical quantities for defining it,
• Mass is measured in grams or kilograms whereas weight is measured in Newton (N) which is a unit of force.

## Mass Vs. Weight in tabular form

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text:
# Weird GRE mistake [duplicate]

According to the answer key, the correct answer is (a).... This is obviously a mistake, right? If a square matrix is invertible, then it has full rank.

• Well B, C, D and E are all equivalent, and B implies A, but not vice versa. Jul 23, 2017 at 14:40
• But is a saying it has full rank?
– user223391
Jul 23, 2017 at 14:41
• Nope, it is not. :) Jul 23, 2017 at 14:43
• @SihOASHoihd This might help math.stackexchange.com/questions/6734/… Jul 23, 2017 at 14:43

$$\begin{bmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{bmatrix}$$


text:
# Require help understanding small angle approximation

1. Sep 3, 2012

### Kaldanis

1. The problem statement, all variables and given/known data
I was recently given this question and very little explanation of the concept. I've struggled with this for a week and read absolutely everything I can find and I'm still not any closer to understanding it. Can anyone please point me in the right direction or explain how to do question 1) and 2)? There are many more questions, but if I can get 1) and 2) down then I should be able to answer the rest by myself. I appreciate any help.

2. Relevant equations
Unsure

3. The attempt at a solution
Unsure

2. Sep 3, 2012

### Nessdude14

The equation at the end explains that |sinθ-θ|/|sinθ| gives the error in approximating sinθ by θ. In other words, it gives the percentage which theta differs from sinθ.

The first question asks: For what values of theta does theta differ from sinθ by less than 5%? in other words:
$\displaystyle \frac{|sinθ-θ|}{|sinθ|}≤.05$

3. Sep 3, 2012

### Kaldanis

Thank you, I had been using the equation incorrectly without realising. I have the correct answers now.


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Expressing a fraction as the sum of its partial fractions. A fraction is a symbol indicating the division of integers. This method in which the integrand is expressed as the sum of simpler rational functions is known as decomposition into partial fractions. Partial fractions fraction mathematics algebra free. Fractions in which the denominator has a quadratic term 6 6. Each of the two fractions on the right is called a partial fraction. The whole idea is to take rational functions and a rational function is just a function or. Partial fractions and inverse laplace transform unit iii. Fraction decimal mix fraction singapore math precent to fraction grade 5 partial fraction decomposition pdf.

In this section we will take a look at the process of partial fractions and finding the partial fraction decomposition of a rational expression. This is not so informative so lets break it down a bit. Partial fraction decomposition free math lessons chilimath. We will start by trying to determine the partial fraction decomposition of, \\fracp\left x \rightq\left x \right\. In other words, if i am given a single complicated fraction, my goal is to break it down into a series of smaller components or parts. Fractiondecimal mix partial fraction decomposition pdf precent to fraction grade 5 usp 23 plasma protein fraction fraction. Fractions where the denominator has a repeated factor. Previously on addingsubtracting rational expressions, we want to combine two or more rational expressions into a. By using this website, you agree to our cookie policy. Integration by partial fractions we now turn to the problem of integrating rational functions, i. In this case, the denominator has three nonrepeated linear factors so the unknowns will be a, b, and c. Remark functions with same derivatives dif fer by a constant. Download englishus transcript pdf the following content is provided under a creative commons license. The section also places the scope of studies in apm346 within the vast universe of mathematics.

This mode keeps numbers in their exact symbolic form. Partial fraction decomposition matlab partfrac mathworks. Find the partial fraction decomposition of this expression using the full factorization mode. The sum of these fractions is called the partial fraction decompositionof the rational expression on the lefthand side. To make a donation or to view additional materials from hundreds of mit courses, visit mit opencourseware at ocw. In this mode, partfrac factors the denominator into linear expressions, reducing quadratic polynomials to linear expressions with complex coefficients. Partial fractions application to integration on brilliant, the largest community of math and science problem solvers. For the following problems, just nd the partial fraction decomposition no need to integrate.

We will focus on rational functions px qx such that the degree of the numerator px is strictly less than the degree of qx. Enter a rational function and click the partial fractions button. The whole idea is to take rational functions and a. Well, that was a pretty tiring problem, and you can see, the partial fraction decomposition becomes a lot more complicated when you have a higher degree denominators, but hopefully you found that a little bit useful. Partial fraction decomposition is an important skill that makes differentiation and integration much easier. Partial fractions calculator find the partial fractions of a fractions stepbystep this website uses cookies to ensure you get the best experience. Among others, partial fractions are used in engineering for finding inverse. Your support will help mit opencourseware continue to offer high quality educational resources for free. Integral ch 7 national council of educational research and. This section provides materials for a session on how to compute the inverse laplace transform. Partial fraction decomposition notes page 4 of 10 example 3 find the partial fraction decomposition of 2 32 0 x.

The problem is that we have no technique for evaluating the integral on the left side. Partial fractions jeremy orlo much of this note is freely borrowed from an mit 18. The method for computing partial fraction decompositions applies to all rational functions with one qualification. Partial fractions free download as powerpoint presentation. Here the list of partial fractions formulas are given. Here is a set of practice problems to accompany the partial fractions section of the polynomial functions chapter of the notes for paul dawkins algebra course at lamar university.

The dividend upper number is called the numerator nx and. This textbook is free and open which means that anyone can use it without any permission or fees. It is often helpful to break down a complicated algebraic fraction into a sum of simpler fractions. Partial fractions is the name given to a technique of integration that may be used to integrate any ratio of polynomials. However you can print every page to pdf to keep on you computer or download pdf copy of the whole textbook. Expressing a fraction as the sum of its partial fractions 3 4. Integration by partial fractions stepbystep math problem. This document contains examples and explanations covering all 4 decomposition cases, plus 20 practice problems with an answer key. Theres one more case of partial fraction expansion or decomposition problems that you might see, so i thought i would cover it. In particular, so, when integrating rational functions it would be helpful if we could undo the simpli. Lets see if we can learn a thing or two about partial fraction expansion, or sometimes its called partial fraction decomposition. The method we use, partial fraction decomposition, is also very important for solving differential equations with.

Partial fractions application to integration practice. Year 6 fraction year 6 fraction worksheets fraction 2. Learn about the different types of partial fraction decomposition in this free math video tutorial by marios math tutoring. Partial fractions examples partial fractions is the name given to a technique of integration that may be used to integrate any ratio of polynomials. Partial fractions big example download from itunes u mp4 1mb download from internet archive mp4 1mb download englishus transcript pdf download englishus caption srt. Materials include course notes, a lecture video clip, practice problems with solutions, a problem solving video, and a problem set with solutions. Precalculus 7 3 partial fractions worksheet answers.

The aim of this is to introduce and motivate partial di erential equations pde. Intro to partial fraction expansion video khan academy. A ratio of polynomials is called a rational function. Partial fraction decomposition this method is used to decompose a given rational expression into simpler fractions. Pdf in this article a different approach to find a partial fraction is discussed. Fractiondecimal mix fraction singapore math precent to fraction grade 5 partial fraction decomposition pdf. After splitting the integrand into partial fractions, it is integrated accordingly with the help of traditional integrating techniques. So the partial fraction decomposition of this, were now done, is 7 over x minus 2 plus 3x plus 4, over x squared plus 2x plus 4. The process can be a little long and on occasion messy, but it is actually fairly simple. Fractions where the denominator has a repeated factor 5 5. The process of doing this is called partial fractions and the result is often called the partial fraction decomposition. In algebra, the partial fraction decomposition or partial fraction expansion of a rational function that is, a fraction such that the numerator and the denominator are both polynomials is an operation that consists of expressing the fraction as a sum of a polynomial possibly zero and one or several fractions with a simpler denominator. Well, that was a pretty tiring problem, and you can see, the partial fraction decomposition. Partial fractions combining fractions over a common denominator is a familiar operation from algebra.

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News

# AMD Releases Study Detailing Datacenter Energy Use In Five Regions Across Globe

December 16, 2007 by Jeff Shepard

Advanced Micro Devices (AMD) released a study revealing shifting patterns in worldwide datacenter energy use at regional levels. The study, which was conducted by Jonathan Koomey, Ph.D. (project scientist at the Lawrence Berkeley National Laboratory and a consulting professor at Stanford University), documents energy use across five regions: the United States, Western Europe, Japan, Asia/Pacific (excluding Japan) and the rest of the world. The new study forecasts datacenter energy consumption, estimating that by 2010 U.S. consumption will decline relative to consumption worldwide.

The study forecasts that, based on current growth trends, the U.S. share of total world server electricity use from datacenters will likely decline from 40% in 2000 to about one-third by 2010, while the Asia/Pacific region (excluding Japan) will increase its share from 10 to about 16% over that period. The absolute electricity consumption for servers in the Asia/Pacific region under this scenario would more than double from 2005 to 2010, requiring electricity capacity equal to output from two new 1000MW power plants. For the entire world, server consumption from 2005 to 2010 would require additional capacity equal to more than 10 additional 1000MW power plants.

"Our hope is that this research helps bridge the gap between knowledge and action by furthering worldwide understanding of the economic and environmental costs associated with escalating datacenter energy consumption," said Bruce Shaw, Director, Server and Workstation Marketing, AMD. "According to a recent U.S. EPA Report, datacenter energy consumption in the United States five years from now could be cut by as much as 20% with relatively minor efforts by datacenter managers, including turning on available power management features, enabling higher rates of resource consolidation, shutting off unused servers and improving infrastructure operations."

Dr. Koomey’s report shows that electricity used by servers in the United States and Europe currently comprise about two thirds of the world’s total, with Japan, Asia/Pacific and the rest of the world each falling at between 10 and 15% of the total. Examining electricity use by region from 2000 to 2005, the study found that server electricity use in the Asia/Pacific region (excluding Japan) grew at a 23% annual rate, compared to a world average of 16% a year, making this region the only one with server electricity use growing at a rate significantly greater than the world average. The Western European growth rate of 17% was slightly above the world average, while growth rates in the other regions were lower than the world average.

Datacenters throughout the world are designed and operated in similar ways to those in the United States. Accordingly, if the 20% savings estimated in the EPA report are applied to Dr. Koomey’s projections for global datacenter electricity use in 2010, total savings would equal approximately five 1000 MW power plants. In other words, relatively modest changes in the way datacenters are designed and operated could offset approximately half the expected growth in global datacenter electricity use in 2010.

"With the findings released today we can begin to take next steps, including examining how we can power datacenters around the world while addressing impacts on global climate," said Larry Vertal, Senior Strategist for AMD Green. "For example, coal currently provides 25% of global primary energy needs and generates 40% of the world’s electricity. Clearly, we must work harder than ever to not only deliver more efficient server and cooling technology, but also just as importantly, to work with our industry and government partners to develop environmentally sustainable solutions in areas where we see the most dramatic increases in energy use."

This new research adds detail to an AMD-sponsored study published in February that identified the worldwide costs associated with datacenter energy use, finding that in 2005 total datacenter electricity consumption in the United States (including servers, cooling and auxiliary equipment) was approximately 45 billion kWh, resulting in total utility bills amounting to $2.7 billion. That study estimated total datacenter power and electricity consumption for the world to cost$7.2 billion annually. Both of Dr. Koomey’s studies were subject to peer review by IT industry, government and energy efficiency policy professionals.


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Results of December 2018 Observing Trip

Dr. Richard Russel put together this slide set about the latest results from this month’s observing.  Contents:

• Galactic Rotation Rate Results
• Earth’s Position in Solar System
• Complete HI spectrum Measurements from all observing trips

Dr. Russel is now utilizing Doppler shift measurements, and hence velocity, to also estimate the Earth’s position in the Solar System.

DSES Observation Trip December 2018 [Click to open the pptx slide show file.]


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# how to set up Archimedean property for numbers on the number axis?

I think the prerequisite of this question relies on assuming that we haven't give irrational numbers a rigorous definition .

Rational numbers and the points of a horizontal straight line becomes a real correspondence when we select upon the straight line a definite origin or zero-point and a definite unit of length for the measurement of segments. Of the greatest importance, however, is the fact that in the straight line there are infinitely many points which correspond to no rational number. If we name these points non-rational points, and say every of these points corresponds to one and only one non-rational number. Similarly , we define the point corresponding to a rational number a rational point.

If a non-rational point lies to the right(or left) of a rational point, we say the non-rational number corresponding to the non-rational point greater( or less) than the rational number corresponding to the rational point. If we denote the union of all these non-rational numbers and all rational numbers $K$, can we show that between two different numbers $a_1$ and $a_2$ ($a_1<a_2$) in $K$ such that there is a rational number $a\in K$ satisfying $a_1<a<a_2$?

I've read a proof on this result within real numbers , the proof relies on the Archimedean property for real numbers , so I think my question may lead to set up the Archimedean property for $K$, so how to set up Archimedean property for $K$?

• Using geometric intuition to define real numbers is fine, but not in the way you indicate. We have to take clues from the geometric intuition rather than base our definitions on them. There is no other way to prove your point apart from mentioning that the straight line also possesses Archimedean property. – Paramanand Singh Oct 28 '17 at 15:32
• Thus Hardy mentions in his A Course of Pure Mathematics that if $BC$ is a line segment then it is evident that there is a positive integer $k$ such that $k\cdot BC>1$ and then remarks that the assumption that this is possible is equivalent to the assumption of what is known as the axiom of Archimedes. – Paramanand Singh Oct 28 '17 at 15:42
• @ParamanandSingh Thanks, nice to see you again! (1) Why "We have to take clues from the geometric intuition rather than base our definitions on them"? why we have to divorce the concept of the real numbers from its geometric origins? (2) I think it is possible to prove the conclusion provided treating the least upper bound property to be an axiom. – iMath Oct 28 '17 at 16:08
• @ParamanandSingh As Dedekind observed ,“If all points of the straight line fall into two classes such that every point of the first class lies to the left of every point of the second class, then there exists one and only one point which produces this division of all points into two classes, this severing of the straight line into two portions.” – iMath Oct 28 '17 at 16:09
• @ParamanandSingh Utilizing an analogy, one could figure out that the number continuum should have the property that "If the system R of all numbers breaks up into two classes A1 , A2 such that every number α1 of the class A1 is less than every number α2 of the class A2 then there exists one and only one number α by which this separation is produced." This indicate that every bounded A1 must have a least upper bound , I treat it as an axiom, with the least upper bound axiom, the Archimedean property is not hard to prove . – iMath Oct 28 '17 at 16:09


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Requests for technical support from the VASP group should be posted in the VASP-forum.

# ML RDES SPARSDES

(Redirected from ML FF RDES SPARSDES MB)

ML_RDES_SPARSDES = [real]
Default: ML_RDES_SPARSDES = 0.5

Description: This tag sets ratio of the selected descriptors to the total number of descriptors within the sparsification of the angular descriptors is done within machine learning force fields.

For details on the theory of angular descriptor sparsification see here.

For details on how to use the sparsification see the tag ML_LSPARSDES.

The values for ML_RDES_SPARSDES should be chosen between ${\displaystyle 0.