DISTRIBUTIVE IDEMPOTENT UNINORMS

2003 ◽  
Vol 11 (04) ◽  
pp. 413-428 ◽  
Author(s):  
D. RUIZ ◽  
J. TORRENS
Keyword(s):  
Distributive Property ◽  
Special Cases

A characterization of all idempotent uninorms satisfying the distributive property is given. The special cases of left-continuous and right-continuous idempotent uninorms are presented separately and it is also proved that all idempotent uninorms are autodistributive. Moreover, all distributive pairs of idempotent uninorms (pairs U1, U2 such that Ul is distributive over U2 and U2 is distributive over U1) are also characterized.

Exceptional solutions to the Painlevé VI equation associated with the generalized Jacobi weight

2017 ◽  
Vol 06 (01) ◽  
pp. 1750003
Author(s):  
Shulin Lyu ◽  
Yang Chen
Keyword(s):  
Asymptotic Expansions ◽  
Hankel Determinant ◽  
Generalized Jacobi Weight ◽  
Jacobi Weight ◽  
Special Cases ◽  
Painlevé Vi Equation

We consider the generalized Jacobi weight [Formula: see text], [Formula: see text]. As is shown in [D. Dai and L. Zhang, Painlevé VI and Henkel determinants for the generalized Jocobi weight, J. Phys. A: Math. Theor. 43 (2010), Article ID:055207, 14pp.], the corresponding Hankel determinant is the [Formula: see text]-function of a particular Painlevé VI. We present all the possible asymptotic expansions of the solution of the Painlevé VI equation near [Formula: see text] and [Formula: see text] for generic [Formula: see text]. For four special cases of [Formula: see text] which are related to the dimension of the Hankel determinant, we can find the exceptional solutions of the Painlevé VI equation according to the results of [A. Eremenko, A. Gabrielov and A. Hinkkanen, Exceptional solutions to the Painlevé VI equation, preprint (2016), arXiv:1602.04694 ], and thus give another characterization of the Hankel determinant.

On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

2005 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Closed Curves ◽  
Special Cases ◽  
Dynamic Performances ◽  
Definition Of ◽  
Geometric Locus

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

scholarly journals Harmonic univalent functions defined by post quantum calculus operators

2019 ◽  
Vol 11 (1) ◽  
pp. 5-17 ◽  
Author(s):  
Om P. Ahuja ◽  
Asena Çetinkaya ◽  
V. Ravichandran
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disc ◽  
Quantum Calculus ◽  
Special Cases ◽  
The Family ◽  
Covering Theorems

Abstract We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion and covering theorems were also obtained. The extreme points of the family and a radius result were also obtained. The results obtained include several known results as special cases.

scholarly journals Theoretical framework for higher-order quantum theory

2019 ◽  
Vol 475 (2225) ◽  
pp. 20180706 ◽  
Author(s):  
Alessandro Bisio ◽  
Paolo Perinotti
Keyword(s):  
Quantum Theory ◽  
Convex Sets ◽  
Mathematical Structure ◽  
Higher Order ◽  
Equivalence Relations ◽  
Full Generality ◽  
Special Cases ◽  
Different Types ◽  
Causal Structures

Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes recursively, with the construction of a full hierarchy of maps of increasingly higher order. The analysis of special cases already showed that higher-order quantum functions exhibit features that cannot be tracked down to the usual circuits, such as indefinite causal structures, providing provable advantages over circuital maps. The present treatment provides a general framework where this kind of analysis can be carried out in full generality. The hierarchy of higher-order quantum maps is introduced axiomatically with a formulation based on the language of types of transformations. Complete positivity of higher-order maps is derived from the general admissibility conditions instead of being postulated as in previous approaches. The recursive characterization of convex sets of maps of a given type is used to prove equivalence relations between different types. The axioms of the framework do not refer to the specific mathematical structure of quantum theory, and can therefore be exported in the context of any operational probabilistic theory.

scholarly journals Conjectures and results about parabolic induction of representations of $${\text {GL}}_n(F)$$

2020 ◽  
Vol 222 (3) ◽  
pp. 695-747
Author(s):  
Erez Lapid ◽  
Alberto Mínguez
Keyword(s):  
Linear Group ◽  
Local Field ◽  
General Linear Group ◽  
Irreducible Representations ◽  
General Linear ◽  
Parabolic Induction ◽  
Geometric Conditions ◽  
Irreducible Components ◽  
Special Cases

Abstract In 1980 Zelevinsky introduced certain commuting varieties whose irreducible components classify complex, irreducible representations of the general linear group over a non-archimedean local field with a given supercuspidal support. We formulate geometric conditions for certain triples of such components and conjecture that these conditions are related to irreducibility of parabolic induction. The conditions are in the spirit of the Geiss–Leclerc–Schröer condition that occurs in the conjectural characterization of $$\square $$ □ -irreducible representations. We verify some special cases of the new conjecture and check that the geometric and representation-theoretic conditions are compatible in various ways.

R&D projects analyzed by semimartingale methods

1985 ◽  
Vol 22 (02) ◽  
pp. 288-299 ◽  
Author(s):  
Knut K. Aase
Keyword(s):  
Brownian Motion ◽  
Stochastic Equation ◽  
Compound Poisson Process ◽  
General Nature ◽  
Decision Variable ◽  
Non Linear Equation ◽  
Special Cases ◽  
Dynamic Stochastic ◽  
Present Setting

In this article we examine R&D projects where the project status changes according to a general dynamic stochastic equation. This allows for both continuous and jump behavior of the project status. The time parameter is continuous. The decision variable includes a non-stationary resource expenditure strategy and a stopping policy which determines when the project should be terminated. Characterization of stationary policies becomes straightforward in the present setting. A non-linear equation is determined for the expected discounted return from the project. This equation, which is of a very general nature, has been considered in certain special cases, where it becomes manageable. The examples include situations where the project status changes according to a compound Poisson process, a geometric Brownian motion, and a Brownian motion with drift. In those cases we demonstrate how the exact solution can be obtained and the optimal policy found.

Recent results on characterization of probability distributions: a unified approach through extensions of Deny&s theorem

1986 ◽  
Vol 18 (03) ◽  
pp. 660-678 ◽  
Author(s):  
C. Radhakrishna Rao ◽  
D. N. Shanbhag
Keyword(s):  
Negative Binomial ◽  
Short Proof ◽  
Probability Distributions ◽  
Direct Link ◽  
Unified Approach ◽  
Binomial Distributions ◽  
Characterization Of Probability Distributions ◽  
Special Cases ◽  
Convolution Equations

The problem of identifying solutions of general convolution equations relative to a group has been studied in two classical papers by Choquet and Deny (1960) and Deny (1961). Recently, Lau and Rao (1982) have considered the analogous problem relative to a certain semigroup of the real line, which extends the results of Marsaglia and Tubilla (1975) and a lemma of Shanbhag (1977). The extended versions of Deny&s theorem contained in the papers by Lau and Rao, and Shanbhag (which we refer to as LRS theorems) yield as special cases improved versions of several characterizations of exponential, Weibull, stable, Pareto, geometric, Poisson and negative binomial distributions obtained by various authors during the last few years. In this paper we review some of the recent contributions to characterization of probability distributions (whose authors do not seem to be aware of LRS theorems or special cases existing earlier) and show how improved versions of these results follow as immediate corollaries to LRS theorems. We also give a short proof of Lau–Rao theorem based on Deny&s theorem and thus establish a direct link between the results of Deny (1961) and those of Lau and Rao (1982). A variant of Lau–Rao theorem is proved and applied to some characterization problems.

Functional Characterization of Compliant Building Blocks Utilizing Eigentwists and Eigenwrenches

2008 ◽  
Author(s):  
Charles J. Kim
Keyword(s):  
Building Block ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Deformable Body ◽  
Functional Characterization ◽  
Building Blocks ◽  
Future Research ◽  
Special Cases ◽  
Block Approach

Compliant mechanisms are devices which utilize the flexibility of their constituent members to transmit motion and forces. Unlike their rigid body counterparts, compliant mechanisms typically contain no traditional joints. The focus of this research is the development of a building block approach for the synthesis of compliant mechanisms. Building block methods better facilitate the augmentation of designer intuition while offering a systematic approach to open-ended problems. In this paper, we investigate the use of the eigentwists and eigenwrenches of a deformable body to characterize basic kinematic function. The eigentwists and eigenwrenches are shown to demonstrate parametric behavior when applied to the compliant dyad building block, and in special cases may be compared to compliance ellipsoids. The paper concludes by articulating future research in a building block approach to compliant mechanism synthesis.

scholarly journals ON SOME GENERALIZATION OF SMOOTHING PROBLEMS

2015 ◽  
Vol 20 (3) ◽  
pp. 311-328 ◽  
Author(s):  
Svetlana Asmuss ◽  
Natalja Budkina
Keyword(s):  
Hilbert Spaces ◽  
Convex Sets ◽  
Special Cases

The paper deals with the generalized smoothing problem in abstract Hilbert spaces. This generalized problem involves particular cases such as the interpolating problem, the smoothing problem with weights, the smoothing problem with obstacles, the problem on splines in convex sets and others. The theorem on the existence and characterization of a solution of the generalized problem is proved. It is shown how the theorem gives already known theorems in special cases as well as some new results.

Turing machines and the spectra of first-order formulas

1974 ◽  
Vol 39 (1) ◽  
pp. 139-150 ◽  
Author(s):  
Neil D. Jones ◽  
Alan L. Selman
Keyword(s):  
Order Logic ◽  
Automata Theory ◽  
Turing Machines ◽  
First Order ◽  
Context Sensitive ◽  
Open Questions ◽  
Special Cases ◽  
Computational Aspects ◽  
The Difference

H. Scholz [11] defined the spectrum of a formula φ of first-order logic with equality to be the set of all natural numbers n for which φ has a model of cardinality n. He then asked for a characterization of spectra. Only partial progress has been made. Computational aspects of this problem have been worked on by Gunter Asser [1], A. Mostowski [9], and J. H. Bennett [2]. It is known that spectra include the Grzegorczyk class and are properly included in . However, no progress has been made toward establishing whether spectra properly include , or whether spectra are closed under complementation.A possible connection with automata theory arises from the fact that contains just those sets which are accepted by deterministic linear-bounded Turing machines (Ritchie [10]). Another resemblance lies in the fact that the same two problems (closure under complement, and proper inclusion of ) have remained open for the class of context sensitive languages for several years.In this paper we show that these similarities are not accidental—that spectra and context sensitive languages are closely related, and that their open questions are merely special cases of a family of open questions which relate to the difference (if any) between deterministic and nondeterministic time or space bounded Turing machines.In particular we show that spectra are just those sets which are acceptable by nondeterministic Turing machines in time 2cx, where c is constant and x is the length of the input. Combining this result with results of Bennett [2], Ritchie [10], Kuroda [7], and Cook [3], we obtain the “hierarchy” of classes of sets shown in Figure 1. It is of interest to note that in all of these cases the amount of unrestricted read/write memory appears to be too small to allow diagonalization within the larger classes.

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