q-analogues of Ehrhart polynomials

AbstractWe consider weighted sums over points of lattice polytopes, where the weight of a point v is the monomial qλ(v) for some linear form λ. We propose a q-analogue of the classical theory of Ehrhart series and Ehrhart polynomials, including Ehrhart reciprocity and involving evaluation at the q-integers. The main novelty is the proposal to consider q-Ehrhart polynomials. This general theory is then applied to the special case of order polytopes associated with partially ordered sets. Some more specific properties are described in the case of empty polytopes.

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Best proximity point theorems for G-proximal weak contractions in complete metric spaces endowed with graphs

Carpathian Journal of Mathematics ◽

10.37193/cjm.2018.01.07 ◽

2018 ◽

Vol 34 (1) ◽

pp. 65-75

Author(s):

CHALONGCHAI KLANARONG ◽

◽

SUTHEP SUANTAI ◽

Keyword(s):

Directed Graph ◽

Metric Space ◽

Metric Spaces ◽

Best Proximity Point ◽

Complete Metric Space ◽

Partially Ordered Sets ◽

Ordered Sets ◽

Complete Metric Spaces ◽

Partially Ordered ◽

Special Case

In this paper, the existence of best proximity point theorems for two new types of nonlinear non-self mappings in a complete metric space endowed with a directed graph are established. Our main results extend and generalize many known results in the literatures. As a special case of the main results, the best proximity point theorems on partially ordered sets are obtained.

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KEYNES’ CRITIQUE OF THE CLASSICAL AND NEOCLASSICAL THEORIES OF THE RATE OF INTEREST

Análise Econômica ◽

10.22456/2176-5456.73001 ◽

2019 ◽

Vol 37 (72) ◽

Author(s):

André Cutrim Carvalho ◽

David Ferreira Carvalho

Keyword(s):

General Theory ◽

Interest Rates ◽

Economic System ◽

Classical Theory ◽

Critical Analysis ◽

Full Employment ◽

John Maynard Keynes ◽

Independent Variables ◽

Special Case

The classical theory of the rate of interest is the theory that mainstream economists inherited chiefly from Marshall, Ricardo and Wicksell, and is also this same theory that John Maynard Keynes criticizes in his General Theory for presenting an explanation centered solely on the special case of full employment. Despite the difficulties, Keynes offered a scathing critique of the theory of the rate of interest from both classical and neoclassical economists. This was only made possible because the traditional rationale of these economists remained imprisoned by the trap set by Say's Law. Therefore, within this context, the main objective of this paper is to undertake a critical analysis of Keynes regarding the classical general theory of the rate of interest, through which we may then demonstrate the points on which he was in disagreement with the neoclassical school. The main conclusion is that Keynes considered that traditional analysis is defective because it was unable to identify the independent variables of the system. Indeed, savings and investment are determined variables and not the determinants of the dynamics of the capitalist economic system. Such determined variables are the twin product of the true determinants, i.e., from the propensity to consume, from the scale of the marginal efficiency of capital and from the interest rates, and this is why the flow of investments tends to expand until the marginal efficiency of capital remains at the rate of interest.

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On the Livingstone-Wagner Theorem

The Electronic Journal of Combinatorics ◽

10.37236/1782 ◽

2004 ◽

Vol 11 (1) ◽

Author(s):

V. B. Mnukhin ◽

I. J. Siemons

Keyword(s):

Permutation Group ◽

Partially Ordered Sets ◽

Simplicial Complexes ◽

Ordered Sets ◽

Partially Ordered ◽

Special Case

Let $G$ be a permutation group on the set $\Omega$ and let ${\cal S}$ be a collection of subsets of $\Omega,$ all of size $\geq m$ for some integer $m$. For $s\leq m$ let $n_{s}(G,\,{\cal S})$ be the number of $G$-orbits on the subsets of $\Omega$ which have a representative $y\subseteq x$ with $|y|=s$ and $y\subseteq x$ for some $x\in {\cal S}$. We prove that if $s < t$ with $s+t\leq m$ then $n_{s}(G,\,{\cal S})\leq n_{t}(G,\,{\cal S})$. A special case of this theorem is the Livingstone-Wagner Theorem when ${\cal S}=\{\Omega\}$. We show how the result can be applied to estimate orbit numbers for simplicial complexes, sequences, graphs and amalgamation classes. It is also shown how this theorem can be extended to orbit theorems on more general partially ordered sets.

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Cross-connections of the singular transformation semigroup

Journal of Algebra and Its Applications ◽

10.1142/s0219498818500470 ◽

2018 ◽

Vol 17 (03) ◽

pp. 1850047 ◽

Cited By ~ 2

Author(s):

P. A. Azeef Muhammed ◽

A. R. Rajan

Keyword(s):

General Theory ◽

Transformation Semigroup ◽

Partially Ordered Sets ◽

Ordered Sets ◽

Regular Semigroups ◽

Partially Ordered ◽

Singular Transformation ◽

The Cross ◽

The Right ◽

Cross Connection

Cross-connection is a construction of regular semigroups using certain categories called normal categories which are abstractions of the partially ordered sets of principal left (right) ideals of a semigroup. We describe the cross-connections in the semigroup [Formula: see text] of all non-invertible transformations on a set [Formula: see text]. The categories involved are characterized as the powerset category [Formula: see text] and the category of partitions [Formula: see text]. We describe these categories and show how a permutation on [Formula: see text] gives rise to a cross-connection. Further, we prove that every cross-connection between them is induced by a permutation and construct the regular semigroups that arise from the cross-connections. We show that each of the cross-connection semigroups arising this way is isomorphic to [Formula: see text]. We also describe the right reductive subsemigroups of [Formula: see text] with the category of principal left ideals isomorphic to [Formula: see text]. This study sheds light into the more general theory of cross-connections and also provides an alternate way of studying the structure of [Formula: see text].

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Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

Behavioral and Brain Sciences ◽

10.1017/s0140525x18001620 ◽

2018 ◽

Vol 41 ◽

Cited By ~ 2

Author(s):

Daniel Crimston ◽

Matthew J. Hornsey

Keyword(s):

General Theory ◽

Biological Markers ◽

Natural Environment ◽

Relevant Dimension ◽

Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

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To the spectral theory of partially ordered sets

Sibirskii matematicheskii zhurnal ◽

10.33048/smzh.2019.60.308 ◽

2018 ◽

Vol 60 (3) ◽

pp. 578-598

Author(s):

Yu. L. Ershov ◽

M. V. Schwidefsky

Keyword(s):

Spectral Theory ◽

Partially Ordered Sets ◽

Ordered Sets ◽

Partially Ordered

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Modelling Nondeterministic Concurrent Processes with Event Structures

Fundamenta Informaticae ◽

10.3233/fi-1991-14103 ◽

1991 ◽

Vol 14 (1) ◽

pp. 39-73

Author(s):

Rita Loogen ◽

Ursula Goltz

Keyword(s):

Dynamic Behaviour ◽

Partially Ordered Sets ◽

Parallel Composition ◽

Ordered Sets ◽

Communicating Sequential Processes ◽

Partially Ordered ◽

Event Structures ◽

Transition Relation ◽

Concurrent Processes ◽

Sequential Processes

We present a non-interleaving model for non deterministic concurrent processes that is based on labelled event structures. We define operators on labelled event structures like parallel composition, nondeterministic combination, choice, prefixing and hiding. These operators correspond to the operations of the “Theory of Communicating Sequential Processes” (TCSP). Infinite processes are defined using the metric approach. The dynamic behaviour of event structures is defined by a transition relation which describes the execution of partially ordered sets of actions, abstracting from internal events.

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Estimating the area under a receiver operating characteristic curve using partially ordered sets

The International Journal of Biostatistics ◽

10.1515/ijb-2019-0127 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Ehsan Zamanzade ◽

Xinlei Wang

Keyword(s):

Roc Curve ◽

Characteristic Curve ◽

Partially Ordered Sets ◽

Sampling Technique ◽

Real Data ◽

Cost Effective ◽

Ordered Sets ◽

Operating Characteristics ◽

Partially Ordered ◽

Receiver Operating

AbstractRanked set sampling (RSS), known as a cost-effective sampling technique, requires that the ranker gives a complete ranking of the units in each set. Frey (2012) proposed a modification of RSS based on partially ordered sets, referred to as RSS-t in this paper, to allow the ranker to declare ties as much as he/she wishes. We consider the problem of estimating the area under a receiver operating characteristics (ROC) curve using RSS-t samples. The area under the ROC curve (AUC) is commonly used as a measure for the effectiveness of diagnostic markers. We develop six nonparametric estimators of the AUC with/without utilizing tie information based on different approaches. We then compare the estimators using a Monte Carlo simulation and an empirical study with real data from the National Health and Nutrition Examination Survey. The results show that utilizing tie information increases the efficiency of estimating the AUC. Suggestions about when to choose which estimator are also made available to practitioners.

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