The role of the Rogers–Shephard inequality in the characterization of the difference body

2017 ◽  
Vol 29 (6) ◽  
Author(s):  
Judit Abardia-Evéquoz ◽  
Eugenia Saorín Gómez
Keyword(s):  
Lower Bounds ◽  
The Body ◽  
Upper And Lower Bounds ◽  
Difference Body ◽  
The Difference

AbstractThe Rogers–Shephard and Brunn–Minkowski inequalities provide upper and lower bounds for the volume of the difference body in terms of the volume of the body itself. In this work it is shown that the difference body operator is the only continuous and

Stochastic inequalities for an overflow model

1987 ◽  
Vol 24 (3) ◽  
pp. 696-708 ◽  
Author(s):  
Arie Hordijk ◽  
Ad Ridder
Keyword(s):  
Failure Rate ◽  
Lower Bounds ◽  
Approximation Method ◽  
Queueing Networks ◽  
Upper And Lower Bounds ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Decreasing Failure Rate ◽  
General Method

A general method to obtain insensitive upper and lower bounds for the stationary distribution of queueing networks is sketched. It is applied to an overflow model. The bounds are shown to be valid for service distributions with decreasing failure rate. A characterization of phase-type distributions with decreasing failure rate is given. An approximation method is proposed. The methods are illustrated with numerical results.

scholarly journals From Affect to Action: Choices in Attending to Disconcertment in Interdisciplinary Collaborations

2020 ◽  
pp. 016224392097408
Author(s):  
Mareike Smolka ◽  
Erik Fisher ◽  
Alexandra Hausstein
Keyword(s):  
Science And Technology Studies ◽  
Interdisciplinary Collaboration ◽  
The Body ◽  
Affective Labor ◽  
Methodological Choices ◽  
The Social ◽  
Interdisciplinary Collaborations ◽  
Social Shaping ◽  
The Difference

Reports from integrative researchers who have followed calls for sociotechnical integration emphasize that the potential of interdisciplinary collaboration to inflect the social shaping of technoscience is often constrained by their liminal position. Integrative researchers tend to be positioned as either adversarial outsiders or co-opted insiders. In an attempt to navigate these dynamics, we show that attending to affective disturbances can open up possibilities for productive engagements across disciplinary divides. Drawing on the work of Helen Verran, we analyze “disconcertment” in three sociotechnical integration research studies. We develop a heuristic that weaves together disconcertment, affective labor, and responsivity to analyze the role of the body in interdisciplinary collaborations. We draw out how bodies do affective labor when generating responsivity between collaborators in moments of disconcertment. Responsive bodies can function as sensors, sources, and processors of disconcerting experiences of difference. We further show how attending to disconcertment can stimulate methodological choices to recognize, amplify, or minimize the difference between collaborators. Although these choices are context-dependent, each one examined generates responsivity that supports collaborators to readjust the technical in terms of the social. This analysis contributes to science and technology studies scholarship on the role of affect in successes and failures of interdisciplinary collaboration.

scholarly journals Spectral Properties with the Difference between Topological Indices in Graphs

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Akbar Jahanbani ◽  
Roslan Hasni ◽  
Zhibin Du ◽  
Seyed Mahmoud Sheikholeslami
Keyword(s):  
Characteristic Polynomial ◽  
Lower Bounds ◽  
Adjacency Matrix ◽  
Spectral Properties ◽  
Main Tool ◽  
Topological Indices ◽  
Upper And Lower Bounds ◽  
New Energy ◽  
Energy Of Graph ◽  
The Difference

Let G be a graph of order n with vertices labeled as v1,v2,…,vn. Let di be the degree of the vertex vi, for i=1,2,…,n. The difference adjacency matrix of G is the square matrix of order n whose i,j entry is equal to di+dj−2−1/didj if the vertices vi and vj of G are adjacent or vivj∈EG and zero otherwise. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix, that is, a modification of the classical adjacency matrix involving the degrees of the vertices. In this paper, some properties of its characteristic polynomial are studied. We also investigate the difference energy of a graph. In addition, we establish some upper and lower bounds for this new energy of graph.

ON THE DIFFERENCE OF COEFFICIENTS OF OZAKI CLOSE-TO-CONVEX FUNCTIONS

2020 ◽  
pp. 1-8
Author(s):  
YOUNG JAE SIM ◽  
DEREK K. THOMAS
Keyword(s):  
Unit Disk ◽  
Lower Bounds ◽  
Convex Functions ◽  
Univalent Functions ◽  
Upper And Lower Bounds ◽  
The Difference

Let $f$ be analytic in the unit disk $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$ and ${\mathcal{S}}$ be the subclass of normalised univalent functions given by $f(z)=z+\sum _{n=2}^{\infty }a_{n}z^{n}$ for $z\in \mathbb{D}$ . We give sharp upper and lower bounds for $|a_{3}|-|a_{2}|$ and other related functionals for the subclass ${\mathcal{F}}_{O}(\unicode[STIX]{x1D706})$ of Ozaki close-to-convex functions.

Көркөм тексттеги диалогдун табияты

2019 ◽  
pp. 51-54
Author(s):  
А.М. Токтосунова
Keyword(s):  
Literary Text ◽  
Conversational Speech ◽  
The World ◽  
The Difference

Аннотация. Макалада көркөм тексттеги диалогдун табияты жана аткарган кызматы жөнүндө сөз болот. Мисалдагы диалогдор Ч.Айтматовдун, Т.Касымбековдун чыгармаларынан алынып, талдоо жүргүзүлдү. Диалогдук кептин көркөм чыгармадагы орду жана оозеки кептеги диалогдон айырмачылыгы жөнүндө маалымат берилди. Диалог каармандардын деңгэлин, социалдык, моралдык, психологиялык, интеллектуалдык өзгөчөлүктөрүн, коомдогу социалдык-психологиялык кырдаалды ар тараптуу туюндурушу тууралуу сөз козголот. Ошону менен бирге диалогдун автордук идеяга, анын тажрыйбасына, чеберчилигине, дүйнө таанымына, чыгармачылык деңгээлине байланыштуу макалада белгиленди. Диалог аркылуу образ түзүү, дүйнөнү образдуу чагылдырылып берилери мисалдар менен бекемделди. Б.Усубалиевдин, Т.С.Маразыковдун пикирлери жетекчиликке алынды. Түйүндүү сөздөр: диалог, коммуникация, коннотация, стиль, семантика, функционалдык стиль, эстетика, прагматика, образ, подтексттик информация. Аннотация. В этой статье рассматриваются природа диалога и его роли в художественном тексте. Анализ приведен на примерах произведений Ч. Айтматова и Т. Касымбекова. Дана информация места диалога в художественных произведениях и устной речи, и различия от устной речи. В статье речь идёт о роли диалога в социально-психологической, моральной, интеллектуальной характеристике героев в различных социально-психологических ситуациях. В статье отмечается, что диалог связан с идеями, опытом, мировоззрением, уровнем творческого мастерства автора. Приведены примеры того, что через диалог создаются образы, даётся образная картина мира в различных условиях и ситуациях в художественной литературе. Взяты за руководство мнения Б.Усубалиева и Т. Маразыкова. Ключевые слова: диалог, коммуникация, коннотация, стиль, семантика, функциональный стиль, эстетика, прагматика, образ, подтекстная информация. Annotation. In the article the speech is going about the nature of dialogue and the literary text. The dialogues on examples are from Ch. Aitmatov᾿s and T. Kasymbekov᾿s works and they were analysed. It has been informed about the difference the role of dialogue in creative works and conversational speech. The article deals with the role of dialogue in the socio-psychological, moral, intellectual characterization of the characters in various socio-psychological situations. The article notes that the dialogue is connected with the ideas, experience, worldview, level of the creative skill of the author. Examples are given that images are created through dialogue, an imaginative picture of the world is given in various conditions and situations in fiction.The article has been guided by the opinions of T. Marazykov and B. Usubaliev. Keyword: dialogue, communication, connotation, style, semantics, functional style, aesthetics, pragmatics, image, subtext information.

scholarly journals How do difference bodies in complex vector spaces look like? A geometrical approach

2015 ◽  
Vol 17 (04) ◽  
pp. 1450023 ◽  
Author(s):  
Judit Abardia ◽  
Eugenia Saorín Gómez
Keyword(s):  
Complex Structure ◽  
Classical Case ◽  
The Body ◽  
Geometrical Approach ◽  
Complex Vector ◽  
Geometrical Properties ◽  
Complex Difference ◽  
Difference Body ◽  
The Difference ◽  
Two Bodies

We investigate geometrical properties and inequalities satisfied by the complex difference body, in the sense of studying which of the classical ones for the difference body have an analog in the complex framework. Among others we give an equivalent expression for the support function of the complex difference body and prove that, unlike the classical case, the dimension of the complex difference body depends on the position of the body with respect to the complex structure of the vector space. We use spherical harmonics to characterize the bodies for which the complex difference body is a ball, we prove that it is a polytope if and only if the two bodies involved in the construction are polytopes and provide several inequalities for classical magnitudes of the complex difference body, as volume, quermassintegrals and diameter, in terms of the corresponding ones for the involved bodies.

scholarly journals EXACT UPPER AND LOWER BOUNDS ON THE DIFFERENCE BETWEEN THE ARITHMETIC AND GEOMETRIC MEANS

2015 ◽  
Vol 92 (1) ◽  
pp. 149-158 ◽  
Author(s):  
IOSIF PINELIS
Keyword(s):  
Convex Function ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Jensen Inequality ◽  
Geometric Means ◽  
The Difference

Exact upper and lower bounds on the difference between the arithmetic and geometric means are obtained. The inequalities providing these bounds may be viewed, respectively, as a reverse Jensen inequality and an improvement of the direct Jensen inequality, in the case when the convex function is the exponential.

scholarly journals Locating Chromatic Number of Powers of Paths and Cycles

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 389
Author(s):  
Manal Ghanem ◽  
Hasan Al-Ezeh ◽  
Ala’a Dabbour
Keyword(s):  
Chromatic Number ◽  
Lower Bounds ◽  
Minimum Distance ◽  
Upper And Lower Bounds ◽  
Color Code ◽  
Partition Class ◽  
Distinct Color

Let c be a proper k-coloring of a graph G. Let π = { R 1 , R 2 , … , R k } be the partition of V ( G ) induced by c, where R i is the partition class receiving color i. The color code c π ( v ) of a vertex v of G is the ordered k-tuple ( d ( v , R 1 ) , d ( v , R 2 ) , … , d ( v , R k ) ) , where d ( v , R i ) is the minimum distance from v to each other vertex u ∈ R i for 1 ≤ i ≤ k . If all vertices of G have distinct color codes, then c is called a locating k-coloring of G. The locating-chromatic number of G, denoted by χ L ( G ) , is the smallest k such that G admits a locating coloring with k colors. In this paper, we give a characterization of the locating chromatic number of powers of paths. In addition, we find sharp upper and lower bounds for the locating chromatic number of powers of cycles.

scholarly journals Dimer–monomer model on the Towers of Hanoi graphs

2015 ◽  
Vol 29 (23) ◽  
pp. 1550173 ◽  
Author(s):  
Hanlin Chen ◽  
Renfang Wu ◽  
Guihua Huang ◽  
Hanyuan Deng
Keyword(s):  
Asymptotic Behavior ◽  
Lower Bounds ◽  
Statistical Physics ◽  
Upper And Lower Bounds ◽  
Recursion Relations ◽  
Sierpiński Graphs ◽  
Towers Of Hanoi ◽  
The Difference ◽  
Significant Figures

The number of dimer–monomers (matchings) of a graph [Formula: see text] is an important graph parameter in statistical physics. Following recent research, we study the asymptotic behavior of the number of dimer–monomers [Formula: see text] on the Towers of Hanoi graphs and another variation of the Sierpiński graphs which is similar to the Towers of Hanoi graphs, and derive the recursion relations for the numbers of dimer–monomers. Upper and lower bounds for the entropy per site, defined as [Formula: see text], where [Formula: see text] is the number of vertices in a graph [Formula: see text], on these Sierpiński graphs are derived in terms of the numbers at a certain stage. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of the entropy can be evaluated with more than a hundred significant figures accuracy.

scholarly journals TOTAL CURVATURES OF HOLONOMIC LINKS

2000 ◽  
Vol 09 (07) ◽  
pp. 893-906 ◽  
Author(s):  
TOBIAS EKHOLM ◽  
OLA WEISTRAND
Keyword(s):  
Lower Bounds ◽  
Total Curvature ◽  
Geometric Characterization ◽  
Upper And Lower Bounds ◽  
Braid Index

A differential geometric characterization of the braid-index of a link is found. After multiplication by 2π, it equals the infimum of the sum of total curvature and total absolute torsion over holonomic representatives of the link. Upper and lower bounds for the infimum of the total curvature over holonomic representatives of a link are given in terms of its braid- and bridge-index. Examples showing that these bounds are sharp are constructed.

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