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× This section is under development!

A

ssume that eigenvectors are normalized to unit $\ell_2$-norm and have a nonnegative first component. The sign convention guarantees uniqueness of the eigenvector associated with an eigenvalue with geometric multiplicity one.

# Vector norms

For $\mathrm{v} = (v_i)_{i=1}^n \in \mathbb{R}^n$.

$\norm{\mathrm{v}}_p = (\sum_{i}^n\abs{v_i}^p)^{1/p},$ hence it is a norm for $p=[1,\infty].$ $\norm{\mathrm{v}}_0 =$ # of nonzero elements. $\norm{\mathrm{v}}_\infty = \underset{1\le i \le n}{\max} \abs{v_i}$.

# Matrix norms

For $A \in \mathbb{R}^{m \times n}, r = rank(A) \le \min(m,n)$, SVs sorted $s_1 \ge s_2 \ge \ldots$.

### Operator/Spectral norm

$\norm{A} = \underset{x\in\mathbb{R}^n\backslash \{0\}}{\max} \frac{\norm{Ax}_2}{\norm{x}_2} = \underset{x\in S^{n-1}}{\max} \norm{Ax}_2 = \underset{x\in S^{n-1},\ y\in S^{m-1}}{\max} \inner{Ax,y} = s_1(A) = \norm{s}_\infty$

### Frobenius/Euclidean norm

$\norm{A}_F = \sqrt{\sum_i^m\sum_j^n \abs{A_{ij}}^2} = \sqrt{\sum_i^r s_i^2(A_{i})} = \sqrt{tr(A'A)} = \sqrt{\inner{A,A}} = \norm{s}_2$

$\norm{AA'}_F = \norm{A'A}_F \le \norm{A}_F^2$ $\norm{A+B}_F^2 = \norm{A}_F^2 + \norm{B}_F^2 + 2\inner{A+B}_F$ $\norm{A}_F \le \norm{A} _* \le \sqrt{r}\norm{A}_F$ if $A = U\Sigma V'$, then $\norm{A}_F^2 = \norm{\Sigma}_F^2$ $\norm{A}_F^2 = \sum_i^n \norm{\mathbb{a}_i}^2,$ where $\mathbb{a}_i$ are columns.

### HS norm

For $X,Y \in \mathbb{R}^{n\times n}$, the matrix inner product is $\inner{X,Y} = tr(XY')$, which induces the Hilbert-Schmidt norm $\norm{X}_{HS} = \sqrt{\inner{X,X}}$.

## Inequalities

$\norm{A} \le \norm{A}_F \le \sqrt{r} \norm{A}$. $s_i \le \frac{1}{\sqrt{i}} \norm{A}_F$. $\norm{s}_\infty \le \norm{s}_2 \le \sqrt{r} \norm{s} _\infty$.

To be added a lot more!

# Asymptotic Notation

For functions $f,g$:

• $f_n = \mathcal{O}(g_n)$ means $\exists C\in (0,\infty)$ s.t. $f_n \le Cg_n$.
• $f_n = \Omega(g_n)$ means $\exists C\in (0,\infty)$ s.t. $f_n \ge Cg_n$.
• $f_n = \Theta(g_n)$ means $f_n = \mathcal{O}(g_n)$ and $f_n = \Omega(g_n)$.
• Note: no $\cdot_p$ means $C$ is deterministic, nonrandom.

#### $\mathcal{O}_p$ and $\mathcal{o}_p$

$\boxed{X_n = \mathcal{O}_p(g_n) \Longleftrightarrow \forall \epsilon>0, \, \exists M>0 \; \text{ s.t. } \; \mathbb{P}(\abs{X_n/g_n}\ge M) < \epsilon}$ $\boxed{X_n = \mathcal{o}_p(g_n) \Longleftrightarrow \forall \epsilon>0 \quad \underset{n\to\infty}{\lim} \mathbb{P}(\abs{X_n/g_n}\ge \epsilon) = 0}$

if $X_n = \mathcal{O}_p(f_n)$ and $Y_n = \mathcal{O}_p(g_n)$:

• $X_n Y_n = \mathcal{O}_p(f_ng_n)$.
• $\abs{X_n}^s = \mathcal{O}_p(f_n^s), \quad s>0$.
• $X_n + Y_n = \max\{\mathcal{O}_p(f_n), \mathcal{O}_p(g_n)\}$.

if $X_n = \mathcal{o}_p(f_n)$ and $Y_n = \mathcal{o}_p(g_n)$:

• $X_n Y_n = \mathcal{o}_p(f_ng_n)$.
• $\abs{X_n}^s = \mathcal{o}_p(f_n^s), \quad s>0$.
• $X_n + Y_n = \max\{\mathcal{o}_p(f_n), \mathcal{o}_p(g_n)\}$.

if $X_n = \mathcal{o}_p(f_n)$ and $Y_n = \mathcal{O}_p(g_n)$:

• $X_n Y_n = \mathcal{o}_p(f_ng_n)$.
• $X_n + Y_n = \mathcal{O}_p(g_n)$.

## Continuous mapping Thm

Given $f: \mathbb{R}^k \to \mathbb{R}^m$ is “almost surely continuous”.

• $X_n \overset{d}{\to} X \Longrightarrow f(X_n) \overset{d}{\to} f(X)$.
• $X_n \overset{d}{\to} X \Longrightarrow f(X_n) \overset{p}{\to} f(X)$.
• $X_n \overset{d}{\to} X \Longrightarrow f(X_n) \overset{as}{\to} f(X)$.

## Slutsky’s Lemma

if $X_n \overset{d}{\to} X$ and $Y_n \overset{d}{\to} c$:

• $X_n + Y_n \overset{d}{\to} X + c$.
• $X_nY_n \overset{d}{\to} cX$.
• $X_n/Y_n \overset{d}{\to} X/c$.

## SVD

$\underset{n\times m}{A} = \sum_i^r s_i\mathrm{u}_i\mathrm{v}_i',$ where $r=rank(A)$.

$s_i(A) = \sqrt{\lambda_i(AA')} = \sqrt{\lambda_i(A'A)}$.

If $A$ is symmetric, then also: $s_i(A) = \abs{\lambda_i(A)}$

### Courant-Fisher min-max Thm

Courant–Fischer variational representation of max eigenvalue & eigenvector:

$\mathrm{v}_1(\widehat{\Sigma}) = \underset{\norm{z}_2 = 1}{\argmax} \; z'\widehat{\Sigma}z$

Alternative equivalent variational representation is in terms of the semidefinite program (SDP):

$Z^* = \underset{Z\in\mathbb{S}^p_+, \, tr(Z)=1}{\argmax} \, tr(\widehat{\Sigma}Z)$

### Johnson–Lindenstrauss

Given a set $Q$ of $q$ points in $\mathbb{R}^N$ with $N$ typically large, we would like to embed these points into a lower-dimensional Euclidean space $\mathbb{R}^n$ while approximately preserving the relative distances between any two of these points. The question is how small can we make $n$ (relative to $q$) and which types of embeddings work?

Given $\epsilon \in (0, 1),$ for every set $Q$ of $q$ points in $\mathbb{R}^N$, if $n$ is a positive integer such that $n>n_0 = O(\ln(q)/\epsilon^2)$, there exists a Lipschitz f’n $f: \mathbb{R}^N \to \mathbb{R}^n$ s.t.
$(1-\epsilon)\norm{u-v}^2_2 \le \norm{f(u) - f(v)}^2_2 \le (1+\epsilon)\norm{u-v}^2_2, \quad \forall \; u,v\in Q.$


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# Quark Matter 2014 - XXIV International Conference on Ultrarelativistic Nucleus-Nucleus Collisions

19-24 May 2014
Europe/Zurich timezone

## Upsilon production in U+U collisions at the STAR experiment

20 May 2014, 16:30
2h

### spectrum

Board: F-58
Poster Open Heavy Flavour and Quarkonia

### Speaker

Robert Vertesi (Nuclear Physics Institute of the Czech Academy of Sciences)

### Description

Due to color screening, the production of quarkonia in high energy heavy ion collisions is expected to be sensitive to the energy density of the medium. Sequential suppression of different quarkonium states may therefore serve as a thermometer of the medium. Although the suppression of charmonia was anticipated as a key signature of the QGP, the observed energy dependence of $J/\psi$ suppression is rather weak. This phenomenon is explained by the recombination (coalescence) of $c\bar{c}$ pairs. Bottomonia, on the other hand, are less affected by recombination and can provide a cleaner probe of the strongly interacting medium. Recent STAR results show that in $\sqrt{s_{NN}}=200$ GeV central Au+Au collisions the Upsilon 1S state is suppressed more than if only cold nuclear matter effects were present, and the excited state yields are consistent with a complete suppression. The energy density in U+U $\sqrt{s_{NN}}=193$ GeV central collisions is estimated to be about 20% higher than that of $\sqrt{s_{NN}}=200$ GeV central Au+Au. Therefore U+U collisions provide a further test of the sequential suppression hypothesis. The STAR detector collected a total of 17.2 million high-tower triggered events in $\sqrt{s_{NN}}=193$ GeV U+U collisions in the year 2012, corresponding to an integrated luminosity of 263.4 $\mu b^{-1}$. Upsilon yields at mid-rapidity, measured in central and mid-central collisions through the dielectron channel, as well as the nuclear modification factor with respect to the number of participants, will be reported in this presentation.
On behalf of collaboration: STAR

### Primary author

Robert Vertesi (Nuclear Physics Institute of the Czech Academy of Sciences)

 Poster

format: plain


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# Algebraic Expressions, Equations, and Inequalities

## Overview

### Description

Expressions, equations, and inequalities are used to describe relationships between quantities. The associative, commutative, and identity properties of addition and multiplication are used to simplify algebraic expressions. Algebraic equations and inequalities represent mathematical and practical relationships with operations, constants, and variables. A value or set of values that makes an equation or inequality true is a solution. While an equation often has a single solution, the solutions of inequalities may be represented as intervals of values. These can be represented using set-builder or interval notation. Some equations and inequalities do not have solutions.

### At A Glance

• The associative, commutative, and identity properties of addition can be used to simplify expressions with real numbers. The additive identity is zero, and the additive inverse, or opposite, of a real number $a$ is $-a$.
• The associative, commutative, and identity properties of multiplication can be used to simplify expressions with real numbers. The multiplicative identity is 1, and the multiplicative inverse, or reciprocal, of a real number $a$ is $\frac{1}{a}$.
• The distributive property of multiplication over addition can be used to simplify expressions with real numbers.
• Expressions can be simplified by combining the properties of operations with the order of operations.
• Algebraic expressions are used to represent verbal descriptions of a situation.
• To evaluate an algebraic expression, substitute the given values of the variables in the expression, and simplify.
• Algebraic equations can represent verbal statements of situations.
• Equations have many applications that aid in calculating values that are used in the real world.
• To check a solution of an equation, substitute the value of the variables in the equation and determine whether the resulting statement is true.
• Algebraic inequalities are used to represent verbal descriptions of problems.
• An inequality can have infinitely many solutions. The set of solutions of an inequality can be written using set-builder or interval notation.
• To check a solution of an inequality, substitute the value of the variables in the inequality, and determine whether the resulting statement is true.


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# Point in (skewed) circle sector

This topic is 3588 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Hi all, I have two circles - one inside the other, and I need to and I'm trying to figure out which sector (of which circle) a given point is inside. The obvious easy scenario is when one circle is perfectly centered within another; but if the inner circle isn't centered, how do I find out what I want to know? The sector edges are (2pi / #sectors) on the circumference on the outer circle. Diagram to explain: <br/> Thanks - I'd very much appreciate any tips / pointers in the right direction!

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1. Run point-in-circle tests on the given point for both circles. This will tell you if the point is outside both circles, inside the larger circle but not the smaller circle, or inside both.

2. Construct hyperplanes corresponding to each of the 'spokes' that define the sectors. These will be lines in the form ax+by+d = 0. (Post back if you're not sure how to do this.)

3. Each consecutive pair of hyperplanes forms an unbounded triangle. For each of these triangles, test the point for inclusion by performing a 'which side' test against each of the two bounding hyperplanes.

You now have enough info to determine which circle and sector (if any) the point is in (assuming I didn't mess anything up).

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You can also use the CCW function to determine on which side of a spoke you are

From http://www.macs.hw.ac.uk/~alison/ds98/node114.html :
int ccw(point p1, point p2, point p3)// Slightly deficient function to determine if the two lines p1, p2 and// p2, p3 turn in counter clockwise direction}{  int dx1, dx2, dy1, dy2;  dx1 = p2.x - p1.x; dy1 = p2.y - p1.y;  dx2 = p3.x - p2.x; dy2 = p3.y - p2.y;  if(dy1*dx2 < dy2*dx1) return 1;  else return 0;}

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Thanks for the ideas - I hadn't even thought about just performing a above/below plane test, that seems in theory to be the best way to tackle this.

Much appreciated :)

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# Changeset 3207 for Deliverables

Ignore:
Timestamp:
Apr 29, 2013, 3:31:04 PM (8 years ago)
Message:

Final version up to spellchecking.

File:
1 edited

### Legend:

Unmodified
 r3126 \begin{document} \title{??????} \author{??????} \date{dd/mm/yy} \title{Dependent labelling applied to stateful hardware components} \author{G. Pulcini$^*$, C. Sacerdoti Coen\footnote{The project CerCo acknowledges the financial support of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission, under FET-Open grant number: 243881}\\~\\ \texttt{\{pulcini,sacerdot\}@cs.unibo.it}\\~ \\Dipartimento di Informatica - Scienza ed Ingegneria\\ Universit\`a di Bologna} \date{03/04/2013} \maketitle \section{Middle and Long Term Improvements} In order to identify the middle and long term improvements, we briefly review \abstract{The Certified Complexity (CerCo) EU Project~\cite{cerco} aims at integrating and unifying the functional and non functional analyses of safety and time critical software by performing both of them together on the source code. It is based on the labelling approach~\cite{labelling} that allows to write compilers that induce on the source code a sound and precise cost model for basic blocks. The cost model is computed on object code blocks and then transferred to the source code by reversing the optimizations to the control flow~\cite{paolo}. In this technical report we address the important issue of stateful hardware whose instructions cost is a function of the internal state. Typical examples are pipelines and caches. In order to avoid loss of precision, the cost model must be parametric on the state, which has no correspondent one at the source level. We show how to enrich the source code with the minimal amount of information that allows to compute costs precisely. We also briefly argue in favour of probabilistic static time analysis and we examine how it is already supported by the labelling approach. } \section{Introduction} The labelling approach~\cite{labelling,paolo} is a new technique to implement compilers that induce on the source code a sound and precise cost model for basic blocks. The cost model is computed on object code blocks and then transferred to the source code by reversing the optimizations to the control flow~\cite{paolo}. In the rest of this technical report we assume reader's knowledge on the labelling approach. At the end of the CerCo project, we are convinced that the labelling approach can support most optimizations currently supported by real world compilers. Moreover, we have formally certified the code of a compiler that transfers cost models according to the labelling approach, greatly reducing the trusted code base of time analysis. The main issue that is left is to identify the classes of cost models that can be expressed at the source level and that we can automatically reason on. In particular, we know that cost models for modern hardware are complex objects that assign to each instruction a cost which also depends on the internal state of stateful hardware components that are designed to optimize the average case. Pipelines, caches, branch predictors are tipical examples of components that have no impact on the functional behavior of the code, but that greatly augment the code performance. Ignorance on the internal state of these components during a WCET analysis forces to assume the worst case, leading to useless time bounds. Therefore, standard WCET tools tend to statically execute code fragments as much as possible, to minimize the ignorance on the state. For loops, for example, are totally unrolled. In CerCo we could do the same, departing from the labelling approach. However, what is more natural is to stay closer to the labelling approach and avoid loosing precision by computing parametric exact costs. This is the topic of this research report. In Section~\ref{premises} we briefly review the premises and goals of the CerCo approach in order to compare the CerCo approach to the traditional WCET one, which is able to deal with modern hardware. In Section~\ref{controlflow} we compare the control flow analyses performed in CerCo and in traditional WCET, arguing that our approach is winning. In Section~\ref{static} we compare the static analyses performed in CerCo and in traditional WCET. Only the latter can deal with modern hardware. Section~\ref{static2} contains the new material. We revise our static analysis and the labelling approach in general to accomodate modern hardware. Temporary conclusions are found in Section~\ref{conclusions}. \section{\label{premises}CerCo: premises and goals} We briefly review here the premises and goals of the CerCo approach to resource analysis. \begin{itemize} choose the cost model in such a way that the cost bounds are high enough to bound the cost of every produced code. This was attempted for instance in the EmBounded project with good success. However, we believe that bounds in the EMBounded project~\cite{embounded} with good success. However, we believe that bounds obtained in this way have few possibilities of being tight. \item Therefore our approach consists in having the compiler generate the techniques need to estimate the cost of control blocks of instructions. \subsection{Control flow analysis} \section{Control flow analysis\label{controlflow}} The first main difference is in the control flow analysis. Traditional WCET techniques. \subsection{Static analysis of costs of basic blocks} \section{Static analysis of costs of basic blocks\label{static}} At the beginning of the project we have deliberately decided to focus our attention on the control flow preservation, the cost model propagation and unlikely that our methodology could contribute to the solution of the problem. \subsubsection{Static analysis of costs of basic blocks revisited} \section{Static analysis of costs of basic blocks revisited\label{static2}} We will now describe what currently seems to be the most interesting technique for the static analysis of the cost of basic blocks in presence of complex Nevertheless, operand insensitivity is an important property for the labelling approach. In~\cite{tranquilli} we introduced \emph{dependent labels} and approach. In~\cite{paolo} we introduced \emph{dependent labels} and \emph{dependent costs}, which are the possibility of assigning costs to basic blocks of instructions which are also dependent on the state of the high level independent cost functions), we need to review the behaviour of probabilistic caches as proposed by PROARTIS. The interested reader can consult~\cite{proartis2-articolo30} for further informations. consult~\cite{proartis2} for further informations. In a randomized cache, the probability of evicting a given line on every access pipelines. \paragraph{Conclusions} \section{Conclusions\label{conclusions}} At the current state of the art functional properties of programs are better proved high level languages, but the non functional ones are proved on the size of the views can be tamed in practice without ruining the whole approach. \begin{thebibliography}{} \bibitem{cerco} \textbf{Certified Complexity}, R. Amadio, A. Asperti, N. Ayache, B. Campbell, D. Mulligan, R. Pollack, Y. Regis-Gianas, C. Sacerdoti Coen, I. Stark, in Procedia Computer Science, Volume 7, 2011, Proceedings of the 2 nd European Future Technologies Conference and Exhibition 2011 (FET 11), 175-177. \bibitem{labelling} \textbf{Certifying and Reasoning on Cost Annotations in C Programs}, N.  Ayache, R.M. Amadio, Y.Régis-Gianas, in Proc. FMICS, Springer LNCS 7437: 32-46, 2012, DOI:10.1007/978-3-642-32469-7\_3. \bibitem{paolo} \textbf{Indexed Labels for Loop Iteration Dependent Costs}, P. Tranquilli, in Proceedings of the 11th International Workshop on Quantitative Aspects of Programming Languages and Systems (QAPL 2013), Rome, 23rd-24th March 2013, Electronic Proceedings in Theoretical Computer Science, to appear in 2013. \bibitem{embounded} \textbf{The EmBounded project (project paper)}, K. Hammond, R. Dyckhoff, C. Ferdinand, R. Heckmann, M. Hofmann, H. Loidl, G. Michaelson, J. Serot, A. Wallace, in Trends in Functional Programming, Volume 6, Intellect Press, 2006. \bibitem{proartis} \textbf{PROARTIS: Probabilistically Analysable Real-Time Systems}, F.J. Cazorla, E. Qui˜nones, T. Vardanega, L. Cucu, B. Triquet, G. Bernat, E. Berger, J. Abella, F. Wartel, M. Houston, et al., in ACM Transactions on Embedded Computing Systems, 2012. \bibitem{proartis2} \textbf{A Cache Design for Probabilistic Real-Time Systems}, L. Kosmidis, J. Abella, E. Quinones, and F. Cazorla, in Design, Automation, and Test in Europe (DATE), Grenoble, France, 03/2013. \end{thebibliography} \end{document}


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# Are monoids useful in optimization?

Many common operations are monoids. Haskell has leveraged this observation to make many higher-order functions more generic (Foldable being one example).

There is one obvious way in which using monoids can be used to improve performance: the programmers is asserting the operation's associativity, and so operations can be parallelized.

I'm curious if there are any other ways a compiler could optimize the code, knowing that we're dealing with a monoid.

-
Coincidentally, the author of the HLearn library has a series of posts on this now. – Xodarap Nov 25 '12 at 16:03

The compiler can optimize exponentiation with monoids. Let $\oplus$ be a binary operator calculateable in constant time such that $\oplus$ and $a_1, a_2, ... \in A$ form a monoid. Then the operation

$$\bigoplus_{[1..n]} a_k = \underbrace{a_k \oplus a_k \oplus \dots \oplus a_k}_{\text{n times}}$$

which usually takes $\cal O(n)$ time can be evaluated with the square and multiply algorithm in only $\cal O(\log n)$ time if the compiler knows that $\oplus$ obeys the monoid laws.

-
Nice observation. Maybe you should specify that you are assuming that $a_k \oplus a_k$ can be computed in $O(1)$ time. – Zach Langley Nov 24 '12 at 0:17

If you are in the constant folding/constant propagation step, whenever you come up with the identity of the monoid, you can just ignore it if it's multiplying other non-constant expressions.

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I was thinking about this - do you know if it's actually faster? – Xodarap Nov 24 '12 at 14:42
It could make a difference inside a loop, for example. – Roberto Mizzoni Nov 24 '12 at 21:25


text:
2017
Том 69
№ 9

# Volume 66, № 5, 2014

Article (English)

### On the Behavior of Algebraic Polynomial in Unbounded Regions with Piecewise Dini-Smooth Boundary

Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 579–597

Let G ⊂  be a finite region bounded by a Jordan curve L := ∂G, let $\Omega :=\mathrm{e}\mathrm{x}\mathrm{t}\overline{G}$ (with respect to $\overline{\mathbb{C}}$ ), let Δ := {w : |w| > 1}, and let w = Φ(z) be the univalent conformal mapping of Ω onto Δ normalized by Φ (∞) = ∞, Φ′(∞) > 0. Also let h(z) be a weight function and let A p (h,G), p > 0 denote a class of functions f analytic in G and satisfying the condition $${\left\Vert f\right\Vert}_{A_p\left(h,G\right)}^p:={\displaystyle \int {\displaystyle \underset{G}{\int }h(z){\left|f(z)\right|}^pd{\sigma}_z<\infty, }}$$ where σ is a two-dimensional Lebesgue measure.

Moreover, let P n (z) be an arbitrary algebraic polynomial of degree at most n ∈ ℕ. The well-known Bernstein–Walsh lemma states that * $$\begin{array}{cc}\hfill \left|{P}_n(z)\right|\le {\left|\varPhi (z)\right|}^n{\left\Vert {P}_n\right\Vert}_{C\left(\overline{G}\right)},\hfill & \hfill z\in \Omega .\hfill \end{array}$$

In this present work we continue the investigation of estimation (*) in which the norm ${\left\Vert {P}_n\right\Vert}_{C\left(\overline{G}\right)}$ is replaced by ${\left\Vert {P}_n\right\Vert}_{A_p\left(h,G\right)},p>0$ , for Jacobi-type weight function in regions with piecewise Dini-smooth boundary.

Article (English)

### Groups with the Same Prime Graph as the Simple Group $D_n (5)$

Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 598–608

Let $G$ be a finite group. The prime graph of $G$ is denoted by $Γ(G)$. Let G be a finite group such that $Γ(G) = Γ(D_n (5))$, where $n ≥ 6$. In the paper, as the main result, we show that if $n$ is odd, then $G$ is recognizable by the prime graph and if $n$ is even, then $G$ is quasirecognizable by the prime graph.

Article (English)

### Generalized Twisted Kloosterman Sum Over ℤ[i]

Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 609–618

The twisted Kloosterman sums over Z were studied by V. Bykovsky, A.Vinogradov, N. Kuznetsov, R. W. Bruggeman, R. J. Miatello, I. Pacharoni, A. Knightly, and C. Li. In our paper, we obtain similar estimates for K χ (α, β; γ; q) over [i] and improve the estimates obtained for the sums of this kind with Dirichlet character χ (mod q 1), where q 1 | q.

Article (Ukrainian)

### Multipoint (in Time) Problem for One Class of Evolutionary Pseudodifferential Equations

Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 619–633

We establish the well-posed solvability of a nonlocal multipoint (in time) problem for the evolution equations with pseudodifferential operators of infinite order.

Article (Ukrainian)

### Approximation of the Classes $H_p^{Ω}$ of Periodic Functions of Many Variables in the Space $L_p$

Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 634–644

We establish upper estimates for the approximation of the classes $H_p^{Ω}$ of periodic functions of many variables by polynomials constructed by using the system obtained as the tensor product of the systems of functions of one variable. These results are then used to establish the exact-order estimates of the orthoprojective widths for the classes $H_p^{Ω}$ in the space $L_p$ with $p ∈ \{1, ∞\}$.

Article (Russian)

### Multiperiodic Solution of a Boundary-Value Problem for one Class of Parabolic Equations with Multidimensional Time

Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 645–655

We study the existence and uniqueness of the multiperiodic solution of the first boundary-value problem for a system of parabolic equations with multidimensional time.

Article (Ukrainian)

### On the Diameters of Commuting Graphs of Permutational Wreath Products

Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 656–665

Let G be a group and let Z(G) be the center of G. The commuting graph of the group G is an undirected graph Γ(G) with the vertex set G \ Z(G) such that two vertices x, y are adjacent if and only if xy = yx. We study the commuting graphs of permutational wreath products H G, where G is a transitive permutation group acting on X (the top group of the wreath product) and (H, Y) is an Abelian permutation group acting on Y.

Article (Ukrainian)

### One Inverse Problem for the Diffusion-Wave Equation in Bounded Domain

Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 666–678

We prove the theorems on the existence and unique determination of a pair of functions: a(t) >0, t ∈ [0,T], and the solution u(x, t) of the first boundary-value problem for the equation $$\begin{array}{ll}{D}_t^{\beta }u-a(t){u}_{xx}={F}_0\left(x,t\right),\hfill & \left(x,t\right)\in \left(0,l\right)\times \left(0,T\right],\hfill \end{array}$$

with regularized derivative D t β u of the fractional order β ∈ (0, 2) under the additional condition a(t)u x (0, t) = F(t), t ∈ [0,T].

Article (English)

### Periodic and Bounded Solutions of the Coulomb Equation of Motion of Two and Three Point Charges with Equilibrium in the Line

Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 679–693

Periodic and bounded solutions of the Coulomb equation of motion in the line are obtained for two and three identical negative point charges in the fields of two and three symmetrically located fixed point charges. The systems possess equilibrium configurations. The Lyapunov, Siegel, Moser, and Weinstein theorems are applied.

Article (English)

### Second Maximal Subgroups of a Sylow p-Subgroup and the p-Nilpotency of Finite Groups

Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 694–698

A subgroup H of a group G is said to be weakly s-semipermutable in G if G has a subnormal subgroup T such that HT = G and HT ≤ ${H}_{\overline{s}G}$ , where ${H}_{\overline{s}G}$ is the subgroup of H generated by all subgroups of H that are s-semipermutable in G. The main aim of the paper is to study the p-nilpotency of a group for which every second maximal subgroup of its Sylow p-subgroups is weakly s-semipermutable. Some new results are obtained.

Brief Communications (Russian)

### On the Solvability of a Fourth-Order Operator-Differential Equation with Multiple Characteristic

Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 699–707

In the Sobolev-type space with exponential weight, we obtain sufficient conditions for the well-posed and unique solvability on the entire axis of a fourth-order operator-differential equation whose main part has a multiple characteristic. We establish estimates for the norms of the operators of intermediate derivatives related to the conditions of solvability. In addition, we deduce the relationship between the exponent of the weight and the lower bound of the spectrum of the main operator appearing in the principal part of the equation. The obtained results are illustrated by an example of a problem for partial differential equations.

Brief Communications (English)

### On the Statistical Convergence of Metric-Valued Sequences

Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 712–720

We study the conditions for the density of a subsequence of a statistically convergent sequence under which this subsequence is also statistically convergent. Some sufficient conditions of this type and almost converse necessary conditions are obtained in the setting of general metric spaces.


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## July 4, 2003

### Accessibility

I decided to see if this blog could pass some basic accessibility tests. Since 1998, Federal Agencies have been required to adhere to certain web accessibility guidelines, called Section 508. Now, I’m not a Federal employee, but I do get funding from the NSF, and so I figured I ought to at least take a stab at it.

There’s a very good tutorial on building web sites which meet the guidelines. Another invaluable resource is Mark Pilgrim’s Dive Into Accessibility site, which covers almost all of the bases for Section 508 Accessibility.

Given Mark’s fame, it’s not surprising that his recommendations (and hence most of the things required to pass the Section 508 Accessibility tests) are already incorporated into the default MT templates.

My own previous cleanup had cleared up most of the remaining things which would cause accessibility problems. I really only had three classes of problems to fix.

1. I had to ensure that all my images had real alt attributes. alt="" may pass the W3C Validator, but it still isn’t accessible.
2. MT’s default Search Template does not define s for each of the form elements. One needs to replace things like

<input type="checkbox" name="CaseSearch" /> Match case

with

<input type="checkbox" id="CaseSearch" name="CaseSearch" />
Match case

3. You must include scope attributes for table headers (that’s not the only accessible solution, but it’s the easiest). Each column header should say ...	 and each row header should say ...

Having read through the above-cited tutorials and made the requisite changes in my templates, it was time to run my pages past Bobby and Cynthia. Both require a certain amount of “manual” checking, over and above the automated tests, but in good conscience I think I can now display some new badges in my sidebar. [Well, almost good conscience. I doubt there are any screen readers out there that grock MathML. Even so, that’s still more accessible than using GIFs for equations.]

Update (8/13/2003): One point not flagged by Bobby or Cynthia was the need to explicitly indicate any use of foreign language words or phrases by using the xml:lang="" attribute. So, eg, I need to write

plus ça change

when I slip in a phrase in French. Screen readers need to know this to pronounce the text appropriately.

Update (8/19/2003): JAWS 4.51 claims to support both  and <acronym> tags. So I am now using them both. The distinction is important because a screenreader should read an acronym but spell out an abbreviation. I’ve also added an aural stylesheet, not that JAWS gives a hoot about such Standards-based niceties.

Posted by distler at July 4, 2003 1:09 AM

TrackBack URL for this Entry:   https://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/185


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# Visualizing the sentiments in U.S. Presidential Inauguration Speeches

## Tags: projects, research

« Previous post: Using tf–idf to analyse U.S. … — Next post: A technique for selection sampling … »

In previous posts, I wrote about a brief analysis of U.S. Presidential Inauguration Speeches and how to extend this analysis using tf–idf. In this post, I want to present an extended analysis based on sentiment analysis. Sentiment analysis encompasses a class of techniques for detecting whether sentences are mean either negatively, neutrally, or positively.

# Depicting sentiment over time

Since every inauguration speech has a beginning and an end, it forms a natural time-series. Hence, I first calculated the sentiment scores for every sentence in a speech and scaled an artificial time parameter over the speech between 0 and 1. This yields a nice sentiment curve plot, in which the abscissa denotes the time of the speech, and the ordinate denotes the sentiment of a given sentence—with values close to +1 meaning that the sentence is extremely positive, 0 meaning that the sentence is neutral, and -1 meaning that the sentence is extremely negative.

Here are some example visualizations of the last three inauguration speeches. Positive sentences are shown in green, while negative ones are shown in red. I am filling the distance between true neutral sentences with the colour in order to show patterns and ‘rhythm’ of different speeches. A black line indicates the mean sentiment over the speech.

It is interesting to see that Obama’s first speech appears to be more subdued and neutral than the subsequent speeches, which exhibit more peaks and thus a larger variability between extremely positive and extremely negative sentiment.

If you want to compare the different sentiment curves for your favourite presidents, you may do so—I have prepared a large visualization that combines all sentiment curves. Watching the appearance and disappearance of negative sentiments over time is quite fascinating. The 1945 speech by Roosevelt is a striking example of evoking very negative imagery for a prolonged period of time.

# Comparing mean sentiments

For comparing individual presidents, the curves are well and good, but I was also interested in the global sentiment of a speech and how it evolves over time. To this end, I calculated the mean (average) sentiment over every speech and depicted it over time. This works because sentiments are always bounded between [-1:1], making their comparison very easy. Here is the average sentiment of a speech, plotted over time:

We can see an interesting pattern: after the second World War, speeches become more positive on average. They remain that way until the first inauguration speech of Barack Obama, which, as I noted above, is somewhat subdued again. Afterwards, they pick up steam. Donald Trump’s speech evokes more positive sentiments, on average, than most of the speeches since 1945.

All in all, I think that this is a nice tool to assess patterns in speeches. If you want, go take a look at the individual sentiment curves, which are stored on GitHub. Maybe you pick up something interesting.

# Code

I used the intriguing TextBlob Python module for this analysis. All visualizations are done using gnuplot. As usual, the scripts and data files—as well as the output—is stored in the GitHub repository for the project.

Have fun!


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# characterizing commutative rings, with nilpotent nilradical , satisfying a.c.c. on radical ideals

All rings below are assumed to be commutative with unity.

It is well-known that in a Noetherian ring, the nilradical (the ideal of all nilpotent elements , or equivalently, the intersection of all prime ideals) is nilpotent (https://en.wikipedia.org/wiki/Nilpotent_ideal ) .

How much (or even at all) can we go in the converse direction ?

For a more explicit question, can we characterize those rings which satisfy a.c.c. on radical ideals and also the nilradical is nilpotent ?

(the only thing I am able to see is that in a ring satisfying a.c.c. on radical ideals, radical of every ideal is a finite intersection of prime ideals, hence the nilradical also is a finite intersection of prime ideals. )

• $R$ satisfies the acc on radical ideals iff $R/nil(R)$ does, so it's sufficient to characterize reduced rings satsifying acc on radical ideals. At this point, it becomes questionable that the nilpotency of the nilradical matters at all. – rschwieb Jan 25 '18 at 17:45
• @rschwieb $R/nil(R)$ need not be a finite product of domains. Consider $k[x,y]/(xy)$ – Lukas Heger Jan 29 '18 at 15:34
• @MatheinBoulomenos Ah, I see now another thing that the $0$ dimensionality gave you. I'll delete my comment above and continue discussing it with you on your solution. Using the line of thought I had in mind, with what you wrote in your solution, i guess we only know it is a subdirect product of domains. – rschwieb Jan 29 '18 at 15:53

Using the order-reversing correspondence between radical ideals of $R$ and closed subsets of $\operatorname{Spec}(R)$, acc on radical ideals is equivalent to dcc on closed subsets of $\operatorname{Spec}(R)$, which is by definition equivalent to $\operatorname{Spec}(R)$ being a Noetherian topological space.
Noetherian spaces have finitely many irreducible components, this translates to $R$ having only finitely many minimal prime ideals.

If we assume for a moment that $\operatorname{dim}(R) = 0$, then every prime ideal of $R$ is both maximal and minimal, so in particular, there are only finitely many and we have by the Chinese remainder theorem$$R/J(R) = R/\operatorname{nil}(R)\cong \displaystyle \prod_{\mathfrak{p} \in \operatorname{Spec}(R)}R/\mathfrak{p}$$ where each $R/\mathfrak{p}$ is a field.

This shows that $R/J(R)$ is a (commutative) semisimple ring, because it is a finite product of fields. Since we assume that $J(R)=\operatorname{nil}(R)$ is nilpotent, this means that $R$ is a semiprimary ring. (This notion is more prevalent in noncommutative algebra, it means that $J(R)$ is nilpotent and $R/J(R)$ is semisimple.)

Conversely, if we have any semiprimary commutative ring, then by the nilpotency of $J(R)$, we have $J(R)=\operatorname{nil}(R)$ (which is thus nilpotent) and $R/J(R)$ is a finite product of fields, thus $\operatorname{Spec}(R) \cong \operatorname{Spec}(R/J(R))$ (the isomorphism is as topological spaces) is finite and thus $R$ satisfies the acc on radical ideals. (And furthermore $R$ is $0$-dimensional.)

So we can say that the $0$-dimensional rings which satisfy your requirements are precisely the commutative semiprimary rings. These need not be Noetherian. A commutative counterexample is $k[x_1, x_2, \dots]/I$ where $I$ is generated by $x_ix_j$ for $i,j \in \Bbb N$ ($i=j$ is explicitly allowed) for a field $k$.
But there's an interesting theorem regarding Noetherian modules over semiprimary rings, see Hopkins-Levitzki theorem.

Edit: I'll call rings with the acc on radical ideals Spec-Noetherian for now, because that's the characterization I'll be using in the following a lot.

These are some (relatively) elementary properties of Noetherian spaces:

• Noetherian spaces have finitely many irreducible components
• Subspaces of Noetherian spaces are Noetherian
• If $X=\bigcup_{i=1}^n X_i$ is a finite union of Noetherian spaces, then $X$ is Noetherian
• $X$ is Noetherian iff every open subspace is quasi-compact

(In particular if $R=\prod_{i=1}^n R_i$ is a finite product of rings, then $R$ is Spec-Noetherian iff each $R_i$ is Spec-Noetherian.)
Using this, we can give another characterization of Spec-Noetherian rings. Open subsets of $X=\operatorname{Spec}(R)$ are of the form $X \setminus V(\mathfrak{a})$ where $\mathfrak{a}$ is a radical ideal. Since $D(f)=X\setminus V(f)$ where $f$ ranges over $R$ is a basis of $X$ consisting of compact open subspaces, the compact open subsets $U$ of $X$ are precisely the sets which may be written as a finite union $U=\bigcup_{i=1}^n D(f_i)$, where $f_i \in R$. (Cf. Atiyah-Macdonald exercise 1.7)

So $R$ is Spec-Noetherian iff for every radical ideal $\mathfrak{a} \subset R$, we can write $X \setminus V(\mathfrak{a}) = \bigcup_{i=1}^n D(f_i) = \bigcup_{i=1}^n (X \setminus V(f_i)) = X \setminus \bigcap_{i=1}^n V(f_i) = X \setminus V(f_1, \dots ,f_n)$, so $V(\mathfrak{a})=V(f_1, \dots f_n)$ which is equivalent to $\mathfrak{a}=\sqrt{(f_1, \dots, f_n)}$

So we get the following characterization of Spec-Noetherian rings, very similar to the characterizations of Noetherian rings.

Lemma A ring $R$ satisfies the acc on radical ideals iff every radical ideal is the radical of a finitely generated ideal.

For Noetherian rings, it is enough to know that every prime ideal is finitely generated. We can show the analogous result for Spec-Noetherian rings. For convenience, I'll use results about Oka families, to show this, since some part of this kind of proofs is always the same. (See here for an introduction))

Let $R$ be a commutative ring and let $\mathcal F$ be the family of ideals $I$ in $R$ such that $\sqrt{I}=\sqrt{(a_1, \dots, a_n)}$ for some $a_1, \dots, a_n \in R$. I claim that $\mathcal F$ is Oka family.
We will use the following fact: If $I,J$ are ideals and $a\in R$, then $\sqrt{IJ}=\sqrt{I} \cap \sqrt{J}$
Suppose $I$ is an ideal of $R$ such that $(I:(a)), I+(a) \in \mathcal F$.
We get $(I+(a)) \cdot (I:(a)) = I(I:(a))+(a)(I:(a)) \subset I$
Thus we get $\sqrt{(I+(a))\cdot (I:(a))} \subset \sqrt{I}$.
On the other hand $I \subset I+(a)$ and $I \subset (I:(a))$, so $I^2 \subset (I+(a))\cdot (I:(a))$, thus $\sqrt{I}=\sqrt{I^2} \subset \sqrt{(I+(a)) \cdot (I:(a))}$
So if we suppose $\sqrt{I+(a)}=\sqrt{(a_1, \dots, a_n)}$ and $\sqrt{(I:(a))}=\sqrt{(b_1, \dots, b_m)}$, we can conclude $\sqrt{I} = \sqrt{(I+(a))\cdot (I:(a)} = \sqrt{(a_1, \dots, a_n)} \cap \sqrt{(b_1, \dots, b_m)} ) = \sqrt{(a_1, \dots, a_n) \cdot (b_1, \dots, b_m)}=\sqrt{(a_1b_1, \dots , a_nb_m)}$
So $I \in \mathcal F$.
Thus $\mathcal F$ is an Oka family and we get the result.

Lemma An ideal maximal with the property that its radical is not the radical of a finitely generated ideal is prime.

Suppose that not every radical ideal of $R$ is the radical of a finitely generated ideal. Then we can use Zorn's lemma to show that the set of radicals which are not the radical ideal of a finitely generated ideal is prime. Indeed, if we have an ascending chain $I_1 \subset I_2 \subset \dots$ of radical ideals which are not the radical of a finitely generated ideal, then $I= \bigcup_{k=1}^\infty I_k$ is a radical ideal. If we had $I=\sqrt{(a_1, \dots a_n)}$, then every $a_i$ would be contained in some $I_k$, thus as we have an ascending chain, $I_k$ would contain all the $a_i$ for $k$ large enough. But then $I_k=I=\sqrt{(a_1, \dots , a_n)}$ which is impossible. Thus be conclude by Zorn's lemma. Combing this with the previous result, we get.

Lemma A ring satisfies the acc on radical ideals iff every prime ideal is the radical of a finitely generated ideal.

If we use the fact that $\operatorname{Spec}(R) = \bigcup_{\mathfrak{p} \in \operatorname{SpecMin}(R)} V(\mathfrak{p})$ is the decomposition into irreducible components, where $\operatorname{SpecMin}(R)$ is the set of minimal prime ideals, we get the following:

Lemma A ring $R$ is Spec-Noetherian, iff $R$ has finitely many minimal prime ideals and for every minimal prime ideal $\mathfrak{p}$ $R/\mathfrak{p}$ is Spec-Noetherian.

But $R/\mathfrak{p}$ is an integral domain so we have reduced the problem in some sense to integral domains.

There's a somewhat "dual" criterion that is only sufficient in general

Lemma If $R$ has only finitely many maximal ideals, then $R$ is Spec-Noetherian iff $R_{\mathfrak{m}}$ is Spec-Noetherian for each maximal ideal $\mathfrak{m}$

Proof: $\operatorname{Spec}(R) = \bigcup_{\mathfrak{m} \in \operatorname{SpecMax}(R)} \operatorname{Spec}(R_{\mathfrak{m}})$, so if this union is finite, we can apply the property of Noetherian spaces.

To see how this fails for rings with infinitely many maximal ideals, consider non-Noetherian von-Neumann-regular ring, e.g. an infinite product of fields.

For integral domains, I have no idea how to completely characterize those that are Spec-Noetherian, but here are some ideas for a special class of integral domains:

If $R$ is a valuation ring, then the ideals of $R$ are totally ordered by inclusion, so every radical ideal, being the intersection of a totally ordered chain of prime ideals is prime. Furthermore, since all the prime ideals form one chain, we get this easy lemma:

If $R$ is a valuation ring, then the following are equivalent:

• $R$ is Spec-Noetherian
• The Krull dimension of $R$ is finite
• $\operatorname{Spec}(R)$ is finite
• $\forall \mathfrak{p} \in \operatorname{Spec}(R)$ $\mathfrak{p}=\sqrt{(a)}$ for some $a \in R$

(The last point follows from the previous lemma on radical ideals, because every finitely generated ideal in a valuation ring is prinicpal.)

This makes it easy to construct examples of non-Noetherian Spec-Noetherian local integral domains of any given finite (non-zero) Krull dimension, because we can control the Krull dimension of $R$ by choosing the appropriate value group. (See for example here) And we can also construct local integral domains which are not Spec-Noetherian this way.

• Instead of adopting that $\dim(R)=\{0\}$, how far can you get with the fact that $R/nil(R)$ is isomorphic to a finite product of domains? After all, the general problem is reduced to studying $R/nil(R)$. It seems each of the domains must satisfy the ACC on radical ideals as well. So it looks like the whole problem is reduced to domains. But I know next to nothing about the spectra of domains. Perhaps the problem is still not easy even with that assumption? – rschwieb Jan 29 '18 at 14:24
• @rschwieb That might be something to try out. By Prop 2.20 in Eisenbud a Noetherian ring is a finite product of domains iff the localization at each maximal ideal is a domain, but his proof works for any ring with finitely many minimal primes. – Lukas Heger Jan 29 '18 at 15:31
• I forgot that you'd need $0$ dimensionality to say that the map was onto :) So the best we have is that $R/nil(R)$ is a subdirect product of a finite number of domains. I haven't checked to see if this implies anything about the acc on radical ideals of the domains yet, but that would be the next logical thing to do. – rschwieb Jan 29 '18 at 15:54
• @rschwieb Thanks for your suggestions. I have made some progess and reduced the problem to integral domains in another way. – Lukas Heger Jan 29 '18 at 19:44
• Glad it helped... thanks for showing me something new – rschwieb Jan 29 '18 at 20:35


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# The Case for ICT-services¶

## Energy Efficiency¶

All influential organisations consider energy efficiency (EE) the cheapest and fastest option to limit greenhouse gas (GHG) emissions and global warming. It is not only the cheapest option for society as a whole but but also for stakeholders owning, operating and using buildings.

Energy efficiency in buildings is often synonymous for low-carbon construction, insulation and installing expensive hardware. This view is naive. Modern hardware does not always run smoothly - think of your laptop getting slower with time. Causes can be faulty set-ups, systems colliding or users making mistakes. Resolving these problems without stopping you from using the laptop can only be solved with immanently available information, automation and raising the user’s understanding.

Information and Communication Technologies (ICT) are capable of collecting data from various sources and flexibly provide the necessary paths and advice for a wide range of user types in any kind of building.

Whether deploying an EE service is financially feasible predominantly depends on whether consumption and operational savings outweigh the cost. To answer this question, heating and water should be considered as much as electricity to which smart metering is often reduced to.

Final energy consumption in the EU (2012)[1]

## Buildings¶

In 2012, the 28 member states of the European Union consumed 1,103,410,100 tons of oil equivalent (TOE). Around 40% are consumed in buildings.

Note

Imagine the Niagara falls for 14 days and 3 hours, but with oil. This resembles the final energy consumption of buildings in the EU.

Investments into insulation and renovation take a long time to pay off. With ICT technology stakeholders can improve operational efficiency as much as EE today.

One immediate benefit of ICT is the detection of on-going wastage. In one example, energy services detected a heating system supplying 250 dwellings re-starting every 10 minutes. In another pilot a subcontractor had bodged the setup of a solar thermal plant reducing output by 30%. Before the projects, these instances had lead to inspections and unnecessary repairs further down the “pipe” which could have been avoided. Even if such “quick wins” are smaller in the majority of buildings, ICT can also help to increase performance at system level, reduce non-technical losses, and for remote reading and switching whilst providing a cheap platform for behavioural changes.

In order for buildings to provide their share in achieving the 20% energy efficiency target by 2020, the renovation rate of public buildings has to reach 3% every year.[2] Over the past years, this rate has not been reached and it is no wonder in times of economic crisis. ICT-enabled services allow payments by contracting future consumption savings and a the services are usually provided by SME. Surely, Energy Management Service (EMS) and Energy Decision Support Service (EDSS) will not achieve immediate savings of 40% but they break even within a few years. Moreover, once the platform has been designed other buildings can be added to the system without much ado.

The Guide will differentiate between non-residential (e.g. public) and residential (e.g. social housing) buildings. Whether the user lives in the building or merely uses it has implications on consumption patterns, user attitudes and control as well as (dis)incentives resulting from regulation / law.

## Non-residential Buildings¶

The public sector is to “lead by example” being a key element of today’s national and EU strategies for saving energy, and is mentioned explicitly in the ‘Energy Efficiency Directive’ (EED) adopted by the EU in 2012[3]. Buildings owned and/or managed by the public sector make up around 12% of overall EU building stock and spending of the public sector is 17% of EU GDP; around 40% of the construction turnover is public.[4]

Energy sources in non-residential buildings (EU)[5]

Irrespective of these figures a large share of municipalities have no sufficient policy for reducing operational cost of buildings. No doubt, the portfolio of buildings and resulting requirements are complex. At first sight, offices, schools and sports facilities do not have much in common. Yet they all have obvious usage patterns including off-times. Over the weekend or holidays, however, nobody is in the building able to detect wastage. Without smart-metering additional staff would have to be paid for to ensure optimised operation of buildings.

Another problem is responsibility. Staff does only occupy a small amount of space wishing for the best possible comfort within these boundaries. With or without rules, a compromise is found to make all staff affected as happy as possible. Does your office have a target temperature? With a target temperature there is a certain degree of accountability. Individuals cannot simply complain it to be too cold but many will - so possible - adjust temperature with thermostats, windows and other means.

Janitors and/or facility managers have no means to read the varying temperatures in a building and approaching individuals is a rather unrewarding task. Individuals can be motivated to recognise responsibility for their own space but they cannot foresee possible inefficiencies across the building unless it is explained in simple and graphical form ideally linking cause and effect. Achieving this requires a measurable goal all staff can work towards to at building level and sophisticated services might even allow management for :term:zones.

If you consider implementing the service in a museum do not only look at the references provided to museums. The consumption patterns of a school and a museum obviously differ. However, being in one country they both share regulation, climate and user attitudes. Consider any kind of car in comparison: You can reduce fuel consumption by not breaking at the very last moment possible but lifting your foot sooner. Whether to turn off your engine at a red light, however, depends more on the age of the car than on driving a 4x4 or a sports car. After all, a museum can also be a “modernised glass box” or an Georgian Palace.

## Residential Buildings¶

As car drivers, we are very sensitive to costs; we react to the smallest of changes in prices at the pump. Likewise, we make much fuss about changes to public transport ticket prices. Once at home, we seem to take little notice of the cost of energy: Hardly anybody knows how much they pay for heating their homes and how large their electricity bill is.

What is more, there is very little awareness about how changes in day-to-day behaviour affect actual costs. Despite of EU regulation[6], individual metering is not yet the standard for multi-apartment buildings and without transparency most residential users consider the size of their monthly bill for electricity and heating to be outside of their control.

Use of energy tends to be physically “invisible” to consumers. Only the status and comfort of using energy will be visible to residents. Some might consider a reduction of energy consumption as a threat to comfort or status. Such uncertainty about the impact of own behaviour can only be approached with access to information in combination with raising awareness.

Energy sources in residential buildings (EU)[7]

In 2012, around 80% of all energy consumed in households was used for heating (68%) and water heating (12%). The exact distribution of cost, however, depends on the quality of the build as much as the energy source and own behaviour. Various European projects successfully deployed web-portals informing residents in social housing upon water, heating and electricity consumption. These citizens are faced with rising prices and an increased risk of what is now being called “fuel poverty”.[8] An increasing share of the population is affected, for instance, in Germany annual rates of disconnection of households from the electricity grid recently reached nearly 600,000.[9]

Not only families are affected. For instance, public bodies pay for energy consumption in some countries as part of social security. Since implementation cost are low and can be deployed quickly, ICT solutions are of high importance for European councils’ in dire need to reduce their spending.

Hint

The BECA project designed, developed and piloted new solutions to enable sustained reductions in energy consumption across European social housing. This was accomplished by providing usable ICT-based services for Energy Management (EMS) and Energy Decision Support Service (EDSS) directly to tenants as well as to social housing staff.

The project achieved 15% savings for heating, 11% for cold water and 17% for hot water. Savings amount to 570MWh which equals 177 tons of CO2 per year. Financial pay-off is achieved by most stakeholders during the first 3 years. The socio-economic net benefit for the BECA project, extrapolated for ten years, amounts to €1.7Million in pilot buildings alone.

BECA was deployed in seven pilots in seven countries across Europe, Eastern Europe in particular. More than 5,000 social housing tenants were given access to ICT services. 19 organisations participated including relevant government authorities and social housing providers, and coordinated by empirica. The project was supported financially by the European Commission under the ICT Policy Support Programme.

## The more insulation you have...¶

An often used argument against ICT is that insulation and good construction will solve the problem as it diminishes any saving potentials by other means. This, however, is only true for the best case scenario (as well as super-modern self-regulating eco-houses).

The best-case scenario assumes that the theoretical value is met at all times and nothing goes wrong or users do not make mistakes. Imagine you recently insulated your home reducing cost dramatically but someone leaves the window open without you noticing: What does this to your bill in per cent? It soon increases it multi-fold as the heating / cooling system is not prepared for such demand. You have already paid for all the insulation but it can only deliver its worth within certain limits. Costs can also come from faulty set-up / operation of heating and solar thermal systems as described in section Buildings above (more will follow...) which combined diminish the theoretical performance.

Warning

Any form of energy wastage in a super efficient building is more expensive than in an old building. A lot of heat/cold can escape through a single open window.

As for self-regulating eco-houses: The authors love innovation and if time and money allows we do recommend constructing these smart buildings with potential to be CO2-negative. However, such concepts often only work in new buildings. Retro-fitting can “only” reach the insulation part but cannot handle regulate themselves. If inhabitants make mistakes the buildings will waste electricity, water and heat unless a smart system can reduce the likelihood, detect and act upon random occurrences.

The more insulation you have...the more information you need.

## Barriers and obstacles¶

The 2014 IPCC report on ‘Mitigation of Climate Change’ describes strong barriers, “such as split incentives (e.g., tenants and builders), fragmented markets and inadequate access to information and financing, hinder the market‐based uptake of cost‐effective opportunities.”[10] Many of these barriers apply to a full deployment of ICT-enabled energy services in Europe. The ‘Guide for Replication’ provides the European community with a wide range of recommendations for more than one scenario due to its composition: The reader will be enabled to derive “policy interventions addressing all stages of the building and appliance lifecycles” from stakeholder specific lessons learnt and the step-by-step checklists based on a wide range of pilots.

## In-built upgrade potentials¶

Technologies are becoming more integrated and dependent in information. With ICT it will be easier to deploy and ensure efficiency of renewables, the untapped potentials of combined heating-power (CHP) plants_ [#] and local energy storage using mostly existing infrastructure. Using the same systems, partners of the consortia described in this Guide are soon to implement, for instance, a social housing estate almost independent from the gird utilising CHP, batteries and water tanks to store heat; a local distributing heating systems capable of exchanging heat/cold between housing estates, shops and office blocks using only renewables; and extension cards for smart-meters empowering home-owners to demand response (e.g. heat pumps) hereby optimising own production / consumption and energy bills.

This “technology ladder” starts with Energy Management and Decision Support services described in this ‘Guide for Replication’. The information services collect and provide will help to make good decisions about future investments, digital or analog.

—— Footnotes

 [1] Own compilation, Source: eurostat
 [2] See, among others, Energy Performance of Buildings Directive (EPBD) and Concerted Action deviced to support countries in their goal for renovation.
 [3] Sources for figures: Ecorys, Ecofys and BioIntelligence (2010): Study to Support the Impact Assessment for the EU Energy Saving Action Plan. The estimate is based on the assumption of 5 m² of public buildings per citizen, translating into a total floor area of public buildings (excluding social housing) in the EU of 2.5 billion m². The total floor area is 21 billion m²; COM(2011) 15: Green Paper on the modernization of EU public procurement policy: Towards a more efficient European procurement market; ICT for a Low Carbon Economy Smart Buildings, July 2009, Findings by the High-Level Advisory Group, the REEB Consortium ‘On the Building and Construction sector’.
 [4] Energy Efficiency Directive (2012/27/EU), amending Directives 2009/125/EC and 2010/30/EU and repealing Directives 2004/8/EC and 2006/32/EC
 [5] ©empirica 2014, Sources: Odyssee-Project, eurostat
 [6] See in particular, Article 9-11 of Energy Efficiency Directive (2012/27/EU)
 [7] ©empirica 2014, Sources: Odyssee-Project, eurostat
 [8] Brunner, Spitzer, et al. (2011). Experiencing fuel poverty. Coping strategies of low-income households in Vienna/Austria. Energy Policy.
 [9] Die Welt (29.04.2012). Strom ist für viele Deutsche unbezahlbar geworden.
 [10] IPCC (2014), Mitigation of Climate Change – Summary for Policy Makers, p. 26.
 [11] The IEA considers CHP capacity could double in most Western countries by 2030: IEA (2011) Co-generation and Renewables: Solutions for a low-carbon energy future


text:
# How Sui Differs from Other Blockchains

This page summarizes how Sui compares with existing blockchains and is intended for potential adopters of Sui to decide whether it fits their use cases. See How Sui Works for an introduction to the Sui architecture.

Here are Sui's key features:

Traditional blockchain validators collectively build a shared accumulator: a representation of the state of the blockchain, a chain to which they add increments over time, called blocks. In blockchains that offer deterministic finality, every time validators want to make an incremental addition to the blockchain, i.e., a block proposal, they sequence the proposal. This protocol lets them form an agreement over the current state of the chain, whether the proposed increment is valid, and what the state of the chain will be after the new addition.

This method of maintaining common state over time has known practical success over the last 14 years or so, using a wealth of theory from the last 50 years of research in the field of Byzantine Fault Tolerant distributed systems.

Yet it is inherently sequential: increments to the chain are added one at a time, like pearls on a string. In practice, this approach pauses the influx of transactions (often stored in a "mempool"), while the current block is under consideration.

## Sui's approach to validating new transactions

A lot of transactions do not have complex interdependencies with other, arbitrary parts of the state of the blockchain. Often financial users just want to send an asset to a recipient, and the only data required to gauge whether this simple transaction is admissible is a fresh view of the sender's address. Hence Sui takes the approach of only taking a lock - or "stopping the world" - for the relevant piece of data rather than the whole chain -- in this case, the address of the sender, which can only send one transaction at a time.

Sui further expands this approach to more involved transactions that may explicitly depend on multiple elements under their sender's control, using an object model and leveraging Move's strong ownership model. By requiring that dependencies be explicit, Sui applies a "multi-lane" approach to transaction validation, making sure those independent transaction flows can progress without impediment from the others.

This doesn't mean that Sui as a platform never orders transactions with respect to each other, or that it allows owners to affect only their owned microcosm of objects. Sui also processes transactions that have an effect on some shared state in a rigorous, consensus-ordered manner. They're just not the default use case. See the State-of-the-art consensus section for details on the Narwhal and Bullshark consensus engine.

## A collaborative approach to transaction submission

Sui validates transactions individually, rather than batching them in the traditional blocks. The key advantage of this approach is low latency; each successful transaction quickly obtains a certificate of finality that proves to anyone that the transaction will be processed by the Sui network.

But the process of submitting a transaction is a bit more involved. That little more work occurs on the network. (With bandwidth getting cheaper, this is less of a concern.) Whereas a usual blockchain can accept a bunch of transactions from the same author in a fire-and-forget mode, Sui transaction submission follows these steps:

1. Sender broadcasts a transaction to all Sui validators.
2. Sui validators send individual votes on this transaction to the sender.
3. Each vote has a certain weight since each validator has weight based upon the rules of Proof of Stake.
4. Sender collects a Byzantine-resistant-majority of these votes into a certificate and broadcasts it to all Sui validators, thereby ensuring finality, or assurance the transaction will not be dropped (revoked).
5. Optionally, the sender collects a certificate detailing the effects of the transaction.

While those steps demand more of the sender, performing them efficiently can still yield a cryptographic proof of finality with minimum latency. Aside from crafting the original transaction itself, the session management for a transaction does not require access to any private keys and can be delegated to a third party.

## A different approach to state

Because Sui focuses on managing specific objects rather than a single aggregate of state, it also reports on them in a unique way:

• Every object in Sui has a unique version number.
• Every new version is created from a transaction that may involve several dependencies, themselves versioned objects.

As a consequence, a Sui validator -- or any other validator with a copy of the state -- can exhibit a causal history of an object, showing its history since genesis. Sui explicitly makes the bet that in many cases, the ordering of that causal history with the causal history of another object is irrelevant; and in the few cases where this information is relevant, Sui makes this relationship explicit in the data.

## Causal order vs. total order

Unlike most existing blockchain systems (and as the reader may have guessed from the description of write requests above), Sui does not always impose a total order on the transactions submitted by clients, with shared objects being the exception. Instead, many transactions are causally ordered--if a transaction T1 produces output objects O1 that are used as input objects in a transaction T2, a validator must execute T1 before it executes T2. Note that T2 need not use these objects directly for a causal relationship to exist--e.g., T1 might produce output objects which are then used by T3, and T2 might use T3's output objects. However, transactions with no causal relationship can be processed by Sui validators in any order.

## State-of-the-art consensus

Narwhal and Bullshark represent the latest variant of decades of work on multi-proposer, high-throughput consensus algorithms that reaches throughputs more than 130,000 transactions per second on a WAN, with production cryptography, permanent storage, and a scaled-out primary-worker architecture.

The Narwhal mempool offers a high-throughput data availability engine and a scaled architecture, splitting the disk I/O and networking requirements across several workers. And Bullshark is a zero-message overhead consensus algorithm, leveraging graph traversals.

## Where Sui excels

This section summarizes the main advantages of Sui with respect to traditional blockchains.

### High performance

Sui’s main selling point is its unprecedented performance. The following bullet points summarize the main performance benefits of Sui with respect to traditional blockchains:

• Sui forgoes consensus for many transactions while other blockchains always totally order them. Causally ordering transactions allows Sui to massively parallelize the execution of many transactions; this reduces latency and allows validators to take advantage of all their CPU cores.
• Sui pushes the complexity at the edges: the client is involved in a number of protocol steps. This minimizes the interactions between validators and keeps their code simpler and more efficient. Sui always gives the possibility to offload most of the client’s workload to a Sui Gateway service for better user experience. In contrast, traditional blockchains follow a fire-and-forget model where clients monitor the blockchain state to assess the success of their transaction submission.
• Sui operates at network speed without waiting for system timeouts between protocol steps. This significantly reduces latency when the network is good and not under attack. In contrast, the security of a number of traditional blockchains (including most proof-of-work based blockchains) need to wait for predefined timeouts before committing transactions.
• Sui can take advantage of more machines per validator to increase its performance. Traditional blockchains are often designed to run on a single machine per validator (or even on a single CPU).

### Performance under faults

Sui runs a leaderless protocol to process simple transactions (i.e. containing only owned objects). As a result, faulty validators do not impact performance in any significant way. For transactions involving shared objects, Sui employs a state-of-the-art consensus protocol requiring no view-change sub-protocol and thus experiences only slight performance degradations. In contrast, most leader-based blockchains experiencing even a single validator’s crash see their throughput fall and their latency increase (often by more than one order of magnitude).

### Security assumptions

Contrary to many traditional blockchains, Sui does not make strong synchrony assumptions on the network. This means that Sui maintains its security properties under bad network conditions (even excessively bad), network splits/partitions, or even powerful DoS attacks targeted on the validators. Sustained network attacks on synchronous blockchains (i.e., most proof-of-work based blockchains) can lead to double-spend of resources and deadlocks.

The reading process of Sui enormously differs from other blockchains. Users interested in only a handful of objects and their history perform authenticated reads at a low granularity and low latency. Sui creates a narrow family tree of objects starting from the genesis allowing it to read only objects tied to the sender of the transaction. Users requiring a global view of the system (e.g., to audit the system) can take advantage of checkpoints to improve performance.

In traditional blockchains, families are ordered with respect to each other to totally order transactions. This then requires querying a massive blob for the precise information needed. Disk I/O thus becomes a performance bottleneck, and some blockchains now require SSD drives on their validators as a result.

### Easier developer experience

Sui provides these benefits to developers:

• Move and object-centric data model (enables composable objects/NFTs)
• Asset-centric programming model
• Easier developer experience

This section presents the main disadvantages of Sui with respect to traditional blockchains.

### Design complexity

While traditional blockchains require implementing only a single consensus protocol, Sui requires two protocols: (i) a protocol based on Byzantine Consistent Broadcast to handle simple transactions, and (ii) a consensus protocol to handle transactions with shared objects. This means the Sui team needs to maintain a much larger codebase.

Transactions involving shared objects require a little overhead (adding two extra round trips - 200ms for well-connected clients using a Sui Gateway service) before submitting it to the consensus protocol. This overhead is required to securely compose the two protocols described above. Other blockchains can instead directly submit the transaction to the consensus protocol. Note the finality for shared object transactions is still in the 2-3 second range even with this overhead.

Building an efficient synchronizer is harder in Sui than in traditional blockchains. The synchronizer sub-protocol allows validators to update each other by sharing data, and it allows slow validators to catch up. Building an efficient synchronizer for traditional blockchains is no easy task, but still simpler than in Sui.

### Sequential writes in the simple case

Traditional blockchains totally order all client transactions with respect to each other. This design requires reaching consensus across validators, which is effective but slow.

As mentioned in previous sections, Sui forgoes consensus for many transactions to reduce their latency. In this manner, Sui enables multi-lane processing and eliminates head-of-line blocking. All other transactions no longer need to wait for the completion of the first transaction’s increment in a single lane. Sui provides a lane of the appropriate breadth for each transaction. Simple transactions require viewing only the sender address, which greatly improves the system’s capacity.

The downside of allowing head-of-line blocking on the sender for these simple transactions is that the sender can send only one transaction at a time. As a result, it is imperative the transactions finalize quickly.

### Complex total queries

Sui can make total queries more difficult than in traditional blockchains since it does not always impose total order of transactions. Total queries are fairly rare with respect to local reads (see above) but useful in some scenarios. For example, a new validator joins the network and needs to download the total state to disk, or an auditor wishes to audit the entire blockchain.

Sui mitigates this with checkpoints. A checkpoint is established every time an increment is added to a blockchain resulting from a certified transaction. Checkpoints work much like a write ahead log that stores state prior to full execution of a program. The calls in that program represent a smart contract in a blockchain. A checkpoint contains not only the transactions but also commitments to the state of the blockchain before and after the transactions.

Sui uses the state commitment that arrives upon epoch change. Sui requires a single answer from the multiple validators and leverages an accessory protocol to derive the hash representing the state of the blockchain. This protocol consumes little bandwidth and does not impede the ingestion of transactions. Validators produce checkpoints at every epoch change. Sui requires the validators to also produce checkpoints even more frequently. So users may use these checkpoints to audit the blockchain with some effort.

## Conclusion

In summary, Sui offers many performance and usability gains at the cost of some complexity in less simple use cases. Direct sender transactions excel in Sui. And complex smart contracts may benefit from shared objects where more than one user can mutate those objects (following smart contract specific rules). In this case, Sui totally orders all transactions involving shared objects using a consensus protocol.

Sui uses a novel peer-reviewed consensus protocol based on Narwhal and Bullshark, which provides a DAG-based mempool and efficient Byzantine Fault Tolerant (BFT) consensus. This is state-of-the-art in terms of both performance and robustness.

Last update 8/30/2022, 5:26:32 PM


text:
Algorithm for computing basis of zero dimensional ring? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T02:23:09Z http://mathoverflow.net/feeds/question/123696 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/123696/algorithm-for-computing-basis-of-zero-dimensional-ring Algorithm for computing basis of zero dimensional ring? minimax 2013-03-06T02:49:05Z 2013-03-06T06:40:16Z
If given a zero dimensional ring over a field, for example, a polynomial ring \$A=k[x_1,\ldots,x_n]/(f_1,\ldots,f_n)\$ such that \$A\$ is 0-dimensional, is there an algorithm to compute a monomial basis for this ring?


text:
## Manipulating Polynomials

You may be required to manipulate polynomials including expanding brackets, simplifying expressions, factorising and polynomial division possibly with the use of remainder and factor theorem.

### Expand and Simplify

Expand and simpify $(2x-3)\left(3x^2-4x+1\right)$ – this works in the same way as expanding double brackets but you should end up with 6 terms before simplification. $(2x-3)\left(3x^2-4x+1\right)=6x^3-8x^2+2x-9x^2+12x-3=6x^3-17x^2+14x-3$

### Factor Theorem

Factor theorem states that if a polynomial is divisible by $x+a$ then $f(-a)=0$ and vice versa.

Example – show that $f(x)=x^5-3x^3-8$ is divisible by x-2. The easiest way to do this is to use factor theorem which states that f(x) is divisible by x-2 if f(2)=0. $f(2)=2^5-3(2)^3-8=32-24-8=0$, hence x-2 is a factor of f(x) and f(x) is divisible by x-2.

### Remainder Theorem

Remainder theorem states that if a polynomial is not divisible by $x+a$ then dividing by $x+a$ will result in a remainder $b$ in which case $f(-a)=b$.
Example – find the remainder when $f(x)=x^5-3x^3-8$ is divided by x+1. The simplest way to do this is to use remainder theorem which states that the remainder when f(x) is divided by x+1 is f(-1). $f(-1)=(-1)^5-3(-1)^3-8=-1+3-8=-6$ and so the remainder when f(x) is divided by x+1 is -6.


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# How to use the ConditionFormatOperator CONTAINS? [SOVLED]

I'm trying to write a spreadsheet macro that conditionally formats rows of a range I've named. LibreOffice allows an operator of Contains to be used and I am trying to write a macro that automates this. The following code does NOT work. What am I missing?

sub formatTeamTable
breaks = ThisComponent.sheets.getByName("Tiebreakers")
table = breaks.getCellRangeByName("TeamTable")
tableColumns = table.Rows.Count-1
dim condition(2) as new com.sun.star.beans.PropertyValue
for r = 0 to tableColumns
condition(0).Name = "Operator"
condition(0).Value = com.sun.star.sheet.ConditionFormatOperator.CONTAINS
condition(1).Name = "Formula1"
condition(1).Value = """Tied"""
condition(2).Name = "StyleName"
condition(2).Value = "Tied"
row = table.getCellRangeByPosition(0,r,tableColumns,r)
cf = row.ConditionalFormat : cf.addNew(condition) : row.ConditionalFormat = cf
next

end sub

edit retag close merge delete

Sort by » oldest newest most voted

Hi

Ok, you can not do that (expected: "com.sun.star.sheet.ConditionOperator") but it seems I found a workaround:

• create the conditional formating with an accepted operator (e.g. EQUAL), then...
• "go up" to the sheet level to browse the defined formats and...
• modify the one for the range we are interested in.

In my example the TeamTable name refers to this cell range: $Tiebreakers.$A$1:$A$11 (adapt to your case). I do not have much time so this name written "hard". One could of course improve e.g. by retrieving these references from the name. sub formatTeamTable2 breaks = ThisComponent.sheets.getByName("Tiebreakers") table = breaks.getCellRangeByName("TeamTable") cf = table.getPropertyValue("ConditionalFormat") cf.Clear() dim condition(3) as new com.sun.star.beans.PropertyValue condition(0).Name = "Operator" condition(0).Value = com.sun.star.sheet.ConditionOperator.EQUAL condition(1).Name = "Formula1" condition(1).Value = """Tied""" condition(2).Name = "StyleName" condition(2).Value = "Tied" cf.addNew(condition) table.setPropertyValue("ConditionalFormat", cf) oCFS = breaks.ConditionalFormats() odummy = oCFS.getConditionalFormats() for i = 0 to oCFS.length -1 oneCF = oDummy(i) if oneCF.range.absolutename = "$Tiebreakers.$A$1:$A$11" then
oMyCF = oneCF.getByIndex(0) 'just created so only one condition'
oMyCF.setPropertyValue("Operator",  com.sun.star.sheet.ConditionFormatOperator.CONTAINS)
exit for
end if
next i

end sub

Regards

more

Good job -- how did you figure this out? I tried XrayTool and searching for documentation but neither helped. Note: To get this to work, define the range as $A$1:$A$11 and put the "Tied" values in that column.

( 2017-10-07 17:33:44 +0200 )edit

Thank you @Jim K

how did you figure this out?

Some time ago, as an exercise for courses, I asked the trainees to write a "detective" function (list of formula, formats ...). I had already dug the API on these issues.

To get this to work, define the range as...

This was explained in my answer, was not it?

Regards

( 2017-10-08 06:48:28 +0200 )edit

Conditional formatting is described at https://wiki.openoffice.org/wiki/Docu... The operator must be of type com.sun.star.sheet.ConditionOperator, not com.sun.star.sheet.ConditionFormatOperator like in your attempt.

Here is working code using EQUAL.

sub formatTeamTable
breaks = ThisComponent.sheets.getByName("Tiebreakers")
table = breaks.getCellRangeByName("TeamTable")
cf = table.getPropertyValue("ConditionalFormat")
cf.Clear()
dim condition(3) as new com.sun.star.beans.PropertyValue
condition(0).Name = "Operator"
condition(0).Value = com.sun.star.sheet.ConditionOperator.EQUAL
condition(1).Name = "Formula1"
condition(1).Value = """Tied"""
condition(2).Name = "StyleName"
condition(2).Value = "Tied"
table.setPropertyValue("ConditionalFormat", cf)
end sub

more

Thanks for your response. I know how to use EQUAL and the ConditionalOperators, I'm asking how to use the ConditionFormatOperators. Calc uses them.

( 2017-10-06 05:33:53 +0200 )edit

A search for "ConditionFormatOperators" reveals nothing about where these are used in the API, so it may not be possible. Yes, Calc uses them, but that does not mean the functionality is exposed through the API.

( 2017-10-06 19:13:37 +0200 )edit

Thanks again. I can see them used in the ConditionalFormat, but my knowledge of the API is meager.

( 2017-10-07 00:08:03 +0200 )edit

Come back after working on another project and interesting things have happened. First of all I want to thank everyone who participated in answering this question, especially pierre-yves samyn who's answer I went with. This was my first time posting a question to a forum, I'm normally able to find answers to whatever questions I have by googling, thanks again for your patience with me. What follows is just a bit of code to setup an example table, skip below it to find my take on pierre's answer.

sub createTable
sheet = thiscomponent.sheets(0)

data = array(array("Team","BOS","CHI","HOU","KC"),array("Boston","","CHI","HOU(1)","KC"),_
array("Chicago","CHI","","CHI","Tied"),array("Houston","HOU(1)","CHI","","Tied(1)"),_
array("Kansas City","KC","Tied","Tied(1)",""))
sheet.getCellRangeByName("A1:E5").DataArray = data

'make some ranges
if sheet.NamedRanges.hasByName("TeamTable") then sheet.NamedRanges.removeByName("TeamTable")
if sheet.NamedRanges.hasByName("Teams") then sheet.NamedRanges.removeByName("Teams")

border = createUnoStruct("com.sun.star.table.BorderLine")
border.Color = RGB(0,0,128)     'blue
border.OuterLineWidth = 26      '26=.75pt, 35=1.00pt
table = sheet.getCellRangeByName("TeamTable")
for pos = 0 to table.Rows.Count-1
cell = table.getCellByPosition(pos, pos)
cell.DiagonalTLBR = border : cell.DiagonalBLTR = border
next

'prettify stuff
table.HoriJustify = com.sun.star.table.CellHoriJustify.CENTER
sheet.getCellRangeByName("Teams").HoriJustify = com.sun.star.table.CellHoriJustify.CENTER
sheet.getCellRangeByName("A1:E1").CharWeight = com.sun.star.awt.FontWeight.BOLD

'make some styles
cellStyles = thiscomponent.StyleFamilies.getByName("CellStyles")
styles = array(array("Positive", RGB(0,153,0)), array("Tied", RGB(128,0,128)),_
array("Negative", RGB(255,0,0)))
for each style in styles
if cellStyles.hasByName(style(0)) then cellStyles.removeByName(style(0))
cs = thiscomponent.createInstance("com.sun.star.style.CellStyle")
cellStyles.insertByName(style(0), cs) : cellStyle = cellStyles.getByName(style(0))
cellStyle.ParentStyle = "Default" : cellStyle.CharColor = style(1)
next
end sub

What follows is, largely, the code I implemented. This code creates mutliple conditions on a range.

sub formatTable
sheet = ThisComponent.Sheets(0)
table = sheet.getCellRangeByName("TeamTable") : teams = sheet.getCellRangeByName("Teams")
tableColumns = table.Columns.Count-1    'columns rows doesn't matter, table is square

dim empty() as new com.sun.star.beans.PropertyValue 'create an empty property
for r = 0 to tableColumns
row = table.getCellRangeByPosition(0,r,tableColumns,r)  'get row of table

'creates a conditional range format and an empty entry format for the row range,
'clear is optional, it's just there so that this sub can run multiple times
cf = row.ConditionalFormat : cf.clear : cf.addNew(empty) : row.ConditionalFormat = cf

'get sheet conditional range format you just made, formats are added to a list,
'most recent format is at the bottom of the list. if you're adding a condition entry
'to an ...
more


text:
# Math Help - Algebra after using l'Hopital's Rule

1. ## Algebra after using l'Hopital's Rule

I would like to ask another question.
I had to calculate a limit using l'Hospital's rule.
I know that I got the correct numerical answer but unfortunately my answer has a different form from that of the professor.

Professor's answer: $\frac{3^\frac{5}{3}}{2^\frac{3}{2}}$

$\frac{\frac{-1}{2}*2^\frac{-1}{2}}{\frac{-1}{3}*3^\frac{-2}{3}}$

How can I change my form in the better one which he uses?

2. Originally Posted by Sebastian de Vries
I would like to ask another question.
I had to calculate a limit using l'Hospital's rule.
I know that I got the correct numerical answer but unfortunately my answer has a different form from that of the professor.

Professor's answer: $\frac{3^\frac{5}{3}}{2^\frac{3}{2}}$

$\frac{\frac{-1}{2}*2^\frac{-1}{2}}{\frac{-1}{3}*3^\frac{-2}{3}}$

How can I change my form in the better one which he uses?
Multiply top and bottom by -1 to get rid of the minus signs, so now you have:

$\frac{\frac{1}{2}\times 2^\frac{-1}{2}}{\frac{1}{3}\times 3^\frac{-2}{3}}$

Then observe that $1/2=2^{-1}$ and $1/3=3^{-1}$ to get:

$\frac{2^{-1}\times 2^\frac{-1}{2}}{3^{-1}\times 3^\frac{-2}{3}}$

Now laws of indices give:

$\frac{ 2^\frac{-1-1}{2}}{ 3^\frac{-1-2}{3}} =\frac{ 2^\frac{-3}{2}}{ 3^\frac{-5}{3}}$

Now flip the whole thing upside down to get rid of the negative powers to get the Prof's answer.

.

3. $\lim_{ x\to1}\frac{(x+1)^\frac{1}{2}-(2x)^\frac{1}{2}}{(x+2)^\frac{1}{3}-(2x+1)^\frac{1}{3}}$

I attempted to type the asked limit but as you can see the software can't execute the code (my mistake of course).

Mr F edit: You would see that I had fixed the latex if you stopped re-editing and hence undoing my editing!
Sebastian: sorry.

4. Originally Posted by Sebastian de Vries
$\lim_{ x\to1}\frac{(x+1)^\frac{1}{2}-(2x)^\frac{1}{2}}{(x+2)^\frac{1}{3}-(2x+1)^\frac{1}{3}}$

I attempted to type the asked limit but as you can see the software can't execute the code (my mistake of course).

If x approaches 1 your quotient will become $\dfrac00$. Therefore you should use de l'Hopitals rule:
$\lim_{ x\to1}\dfrac{(x+1)^\frac{1}{2}-(2x)^\frac{1}{2}}{(x+2)^\frac{1}{3}-(2x+1)^\frac{1}{3}} = \lim_{x\to1}\dfrac{\dfrac{\sqrt{x}-\sqrt{2} \sqrt{x+1}}{2\sqrt{x}\sqrt{x+1}}}{\dfrac{(2x+1)^{\ frac23} - 2(x+2)^{\frac23}}{3(x+2)^{\frac23}(2x+1)^{\frac23} }}$
$\lim_{ x\to1}\dfrac{(x+1)^\frac{1}{2}-(2x)^\frac{1}{2}}{(x+2)^\frac{1}{3}-(2x+1)^\frac{1}{3}} = \dfrac34 \cdot \sqrt{2} \cdot \sqrt[3]{9}\approx 2.206$


text:
# Integration Mania

Calculus Level 4

$\displaystyle \int_{\frac{\pi}{4}}^{\frac{\pi}{3}} e^x \left ( \frac{2+\sin(2x)}{1 + \cos(2x)} \right) \, dx$

If the integral above can be expressed as $$\large e^{\frac{\pi}{a}} ( be^{\frac{\pi}{c}} - d)$$, evaluate $$\dfrac{ b^2 c}{ad^{10} }$$.

×


text:
# Pang Yan Han's blog

## How to disable Control Q on Firefox 57

20 Feb 2018, by Pang Yan Han

NOTE: This applies to Firefox 57 on Linux.

1. Open a new tab and type about:config in the address bar and press enter

You will see a warning. Click on the I accept the risk button.

1. Search for the string showquit. You should see a browser.showQuitWarning. Double click so its value is toggled to True.

When you press Control Q, there will be a prompt asking you if you actually want to quit Firefox.


text:
You are currently browsing the tag archive for the ‘fractals’ tag.

In the last post we looked at the Mandelbrot set, a beautiful 2d fractal with infinite complexity along its boundary. The challenge is to find a three dimensional version of the set, the Mandelbulb, which we can then lovingly render with dynamic lighting and shadows.

The three-dimensional Mandelbulb

Mathematicians were doing work related to the Mandelbrot set in the very early 20th century. However, it wasn’t until the 1980s that computers were powerful enough to draw high quality pictures of it. The Mandelbulb is even more complicated, and requires even more computational power (once you’ve located the object, you then need to render it — this is where the computer spends most of its time). This is why we’ve not been able to see pictures of the Mandelbulb until very recently.

The first problem is determining the rule which will generate the Mandelbulb. For technical reasons there is no such thing as a 3d analogue of the complex numbers (the quaternions are the closest 4d analogue) and thus coming up with the ‘correct’ map is tricky. The key is to re-use the ideas of multiplying the radius, rotating the angles and then translating. Mathematicians use a set of coordinates for 3d space called spherical polar coordinates, which tell you location of a point in terms of the distance from the origin, $r$, and two other angles, $\theta$ and $\phi$.

For those with the appropriate background, the map which takes you from one point to the next is given by composing a stretching and rotation:

$(r,\theta,\phi) \to (r^n,n\theta,n\phi)$

with a constant translation:

$(x,y,z) \to (x+a,y+b,z+c)$

A zoom of the Mandelbulb

We use spherical coordinates to do the first transformation, and cartesian coordinates to do the second. If the sequence of iterates remains bounded when using the parameters a, b and c then the point with coordinates (a,b,c) is part of the Mandelbulb. If the sequence diverges, then it is not.

We’ve introduced a parameter n into the map — this tells you how much to rotate the angles. If n is 2, that means we double the angles. If n is 3 we triple them, and so forth (in the 2d Mandelbrot set we only looked at n = 2). In three dimensions, the low values of n don’t give us a very interesting object. As we increase n the object gets progressively more complex. It turns out that n = 8 gives a nice balance between beauty and novelty.

Another zoom of the Mandelbulb

Now that we have the ingredients, all we need to do is complete the renders. This is a very computationally intensive process, but the results are worth it! By playing around with the color of lighting and the depth of shadows, we can create some truly stunning images — certainly the most striking examples of fractal beauty that I’ve ever seen.

All of the information in this post is sourced from the Mandelbulb page at Skytopia, which is well worth a visit!

It sounds like a poorly thought through Pokémon name from 1995. But in fact the Mandelbulb is a beautiful three-dimensional mathematical object that generalises the two-dimensional Mandelbrot set, which has become well known as an example of a fractal.

The Mandelbrot set (black) with additional coloring (blue to white).

The Mandelbrot set is generated by a very simple idea: we take a point in the 2d plane, and use that as the input to a rule which generates a new point. We then use the new point as the input to the same rule, to generate a third point, then a fourth point, and so on. If we start with the point $z_0 = 0$ (the origin) we generate the sequence $z_1, z_2, z_3,\dots$ from it. This simple but powerful idea, iteration, is at the heart of chaos theory and fractal images.

The rule that generates the Mandolbrot set is given by the following formula, where $c$, $z_n$ and $z_{n+1}$ are complex numbers:

$z_{n+1} = z_n^2 + c$

If we think of a point in the plane defined by its magnitude (or distance from the origin) and the angle it makes with the horizontal, then this rule simply says: “to get the next point in the sequence you square the magnitude, double the angle, and then shift the point by a constant amount $c$.”

There are two possibilities when we start iterating points in this way: for some values of $c$ the points get further and further away from where they started, and head off to infinity (we say that the sequence diverges) but for other values of $c$ they never stray further away than some limit (in which case we say that the sequence is bounded.) To make the Mandelbrot set we color a point $c$ black if the sequence for that value of $c$ is bounded, and leave it white if the sequence diverges.

The boundary of the Mandelbrot set is infinitely complicated: no matter how far you zoom into it, you never stop seeing more and more detail. This never-ending detail qualifies it to be a fractal. We can make prettier pictures by coloring the points that diverge according to how long they take to diverge: in the image above the points that diverge quickly are shown in blue, whereas points that diverge only after many iterations (i.e. they’re nearly in the Mandelbrot set) are shown in white.

The challenge of the Mandelbulb is to extend this concept into three dimensions, to allow fully 3d renders that incorporate dramatic lighting and shadows. As we’ll see this isn’t as easy as it sounds at first.


text:
# Write an equation that defines the exponential function with base = a, (a > 0).

Wouldn't it just be $y = a^{x}$, with $a>0$?


text:
# The temperature 2

The temperature of Siberia fell13 degrees below 2/3 degrees centigrad. What is the temperature there now?

Result

t =  -12.333 °C

#### Solution:

$t=2/3 - 13=- \dfrac{ 37 }{ 3 } \doteq -12.3333 \doteq -12.333 ^\circ \text{C}$

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