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About 10,000 papers for “Set function”

Submodularity of a Set Label Disagreement Function

Toufiq Parag · arXiv (Cornell University) · 2013

A set label disagreement function is defined over the number of variables that deviates from the dominant label. The dominant label is the value assumed by the largest number of variables within a set of binary variables. The submodularity of a certain family of set label disagreement function is discussed in this manuscript. Such disagreement function could be utilized as a cost function in combinatorial optimization approaches for problems defined over hypergraphs.

Cited by 0Open access

On Derivative Euler Phi Function Set-Graphs

Johan Kok, Eunice Gogo Mphako-Banda, Sudev Naduvath · arXiv (Cornell University) · 2019

In this paper, we study some graph theoretical properties of two derivative Euler Phi function set-graphs. For the Euler Phi function $ϕ(n)$, $n\in \mathbb{N}$, the set $S_ϕ(n) =\{i:\gcd(i,n)=1, 1\leq i \leq n\}$ and the vertex set is $\{v_i:i\in S_ϕ(n)\}$. Two graphs $G_d(S_ϕ(n))$ and $G_p(S_ϕ(n))$, defined with respect to divisibility adjacency and relatively prime adjacency conditions, are studied.

Cited by 1Open access

Combinatorial Set Theory and Cardinal Function Inequalities

R. E. Hodel · Proceedings of the American Mathematical Society · 1991

Three theorems of combinatorial set theory are proven.From the first we obtain the de Groot inequality \X\ < 2 ( , the Ginsburg-Woods inequality \X\ < 2e{x),{X), the Erds-Rado Partition Theorem for = 2, and set-theoretic versions of the Hajnal-Juhsz inequalities \X\ < 2C( '*' ' and \X\ < 2i( '*'( ' .From the second we obtain a generalization of the Arhangel'skii inequality \X\ < 2 ' '*' '.From the third we obtain the Charlesworth inequality n(X) < psw(X) ( J and a generalization of the Burke-Hodel e(X)psw{X) inequality \K(X)\ < 2

Cited by 3Open access

Set Expressions in the Function of Truisms

Galina Viktorovna Romanova · Philology Theory & Practice · 2022

The purpose of the research is to determine how the linguistic mechanism of influence is organised when set expressions are used in mass media. The research is novel in that it applies a new approach to studying set expressions, they are considered as a means of influencing the reader or listener (the function of truisms); diverse examples of transformations of set expressions in the function of truisms are collected, structured and organised into a system. The research findings have shown that set expressions in modern texts shifted the main area of their use from a usual figurative means to the function of truisms, linguistic authority; mental and behavioural attitudes are “transmitted” through them to those who perceive information and in doing so, the mechanism of influence is formed.

Cited by 0Open access

Selection function for spectroscopic surveys (main set).

Alexey Mints, S. Hekker · Zenodo (CERN European Organization for Nuclear Research) · 2018

Selection function values for large spectroscopic surveys. Supplementary material for A&amp;A paper Minst&amp;Hekker 2018 (https://ui.adsabs.harvard.edu/#abs/2018arXiv181012296M/abstract). Main set (all stars in each survey)

Cited by 0Open access

Combinatorial set theory and cardinal function inequalities

R. E. Hodel · Proceedings of the American Mathematical Society · 1991

Three theorems of combinatorial set theory are proven. From the first we obtain the de Groot inequality <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue upper X EndAbsoluteValue less-than-or-equal-to 2 Superscript h upper L left-parenthesis upper X right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>X</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mo>≤</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>h</mml:mi> <mml:mi>L</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">\left | X \right | \leq {2^{hL(X)}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the Ginsburg-Woods inequality <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue upper X EndAbsoluteValue less-than-or-equal-to 2 Superscript e left-parenthesis upper X right-parenthesis normal upper Delta left-parenthesis upper X right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>X</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mo>≤</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>e</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">\left | X \right | \leq {2^{e(X)\Delta (X)}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the Erdös-Rado Partition Theorem for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n equals 2"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">n = 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and set-theoretic versions of the Hajnal-Juhász inequalities <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue upper X EndAbsoluteValue less-than-or-equal-to 2 Superscript c left-parenthesis upper X right-parenthesis chi left-parenthesis upper X right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>X</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mo>≤</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>c</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mi>χ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">\left | X \right | \leq {2^{c(X)\chi (X)}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue upper X EndAbsoluteValue less-than-or-equal-to 2 Superscript s left-parenthesis upper X right-parenthesis psi left-parenthesis upper X right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>X</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mo>≤</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>s</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mi>ψ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">\left | X \right | \leq {2^{s(X)\psi (X)}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. From the second we obtain a generalization of the Arhangel’skiĭ inequality <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue upper X EndAbsoluteValue less-than-or-equal-to 2 Superscript upper L left-parenthesis upper X right-parenthesis chi left-parenthesis upper X right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>X</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mo>≤</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>L</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mi>χ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">\left | X \right | \leq {2^{L(X)\chi (X)}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. From the third we obtain the Charlesworth inequality <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n left-parenthesis upper X right-parenthesis less-than-or-equal-to p s w left-parenthesis upper X right-parenthesis Superscript upper L left-parenthesis upper X right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>≤</mml:mo> <mml:mi>p</mml:mi> <mml:mi>s</mml:mi> <mml:mi>w</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>L</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">n(X) \leq psw{(X)^{L(X)}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and a generalization of the Burke-Hodel inequality <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue upper K left-parenthesis upper X right-parenthesis EndAbsoluteValue less-than-or-equal-to 2 Superscript e left-parenthesis upper X right-parenthesis p s w left-parenthesis upper X right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>K</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> <mml:mo>≤</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>e</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mi>p</mml:mi> <mml:mi>s</mml:mi> <mml:mi>w</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">\left | {K(X)} \right | \leq {2^{e(X)psw(X)}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.

Cited by 33

The Pivotal Set of a Boolean Function

Raphaël Cerf · American Mathematical Monthly · 2025

<div> We define the pivotal set of a Boolean function and we prove a fundamental inequality on its expected size, when the inputs are independent random coins of parameter p. We give two complete proofs of this inequality. Along the way, we obtain the classical Margulis-Russo formula. We give a short proof of the classical Hoeffding inequality for i.i.d. Bernoulli random variables, and we use it to derive more complex deviations inequalities associated to the pivotal set. We follow finally Talagrand's footsteps and we discuss a beautiful inequality that he proved in the uniform case. </div>

Cited by 0

On Approximating a Set-Valued Function Locally.

V. F. Demyanov, Claude Lemaréchal, Jochem Zowe · Defense Technical Information Center (DTIC) · 1985

Given a multi-valued mapping F, we address the problem of finding another multi-valued mapping H that agrees locally with F in some sense. We show that, contrary to the scalar case, introducing a derivative of F is hardly convenient. For the case when F is convex-compact-valued, we give some possible approximations, and at the same time we show their limitations. The present paper is limited to Informal demonstration of concepts and mechanisms. Formal statements and proofs will be published elsewhere. Keywords: convexity, multifunctions, differentiability, Newton scheme.

Cited by 1

The Characteristic Function Of A Neutrosophic Set

A. A. Salama, Smarandache, Florentin, S. A. ALblowi · Zenodo (CERN European Organization for Nuclear Research) · 2014

The purpose of this paper is to introduce and study the characteristic function of a neutrosophic set.<br> After given the fundamental definitions of neutrosophic set operations generated by the characteristic function of a neutrosophic set ( for short), we obtain several properties, and discussed the relationship between<br> neutrosophic sets generated by Ng and others. Finally, we introduce the neutrosophic topological spaces<br> generated by . Possible application to GIS topology rules are touched upon.

Cited by 0Open access

Jensen m-Convexity on Set-Valued Function

Eko Dedi Pramana, Ratno Bagus Edy Wibowo, Mohamad Muslikh · CAUCHY Jurnal Matematika Murni dan Aplikasi · 2024

This paper discusses the class of Jensen m-convex functions and their properties, leading to enhancements of these functions and Jensen's inequalities for set-valued functions. It provides several characterizations and explores various algebraic properties. Additionally, it introduces a discrete Jensen-type inclusion.

Cited by 0Open access

The set function T and R-continuum

RCIN (Digital Repository of the Scientifics Institutes) (Institute of Archaeology and Ethnology of the Polish Academy of Sciences) · 1979

Cited by 0

Diesel Generating Set with Self-Diagnosis Function

H. Yamamura, M. Ogasawara · 1984

Diesel generating sets are widely used in telephone offices aid radio-relay stations as standby power in case of commercial power failure. However, they consist of many parts and are very complicated. Therefore, regular maintenance work and repair normally take a long time. we have been developed a new diesel generating set with self-diagnosis and test functions that make use of 8-bit microprocessors and sensors, to reduce the maintenance work. This paper outlines the diesel generating set and its self-diagnosis function.

Cited by 4

The fixed-point set and the convergence set of a continuous function

Sompong Chuysurichay, Phichet Chaoha · 2002

Let X be a Hausdorff space and f:X --&gt; X a continuous function. The fixed-point set of f, denoted by F(f), is the set of all points x E X such that f(x) = x. The convergence set of f, denoted by C(f), is the set of x E X such that the sequence (fn(x)) converges in X where fn = f o f o ... o f {n times}. We define f infinity : C(f) --&gt; F(f) by f infinity (x) = lim(n--&gt;infinity) fn(x) for all x E C(f). In this thesis, we study basic properties of F(f) and C(f) and show that f infinity is continuous if and only if f infinity is continuous at each point in F(f). Moreover, we prove that if X is a metric space and f is quasi-nonexpansive then f infinity is continuous.

Cited by 0