scholarly journals Linear functional inequalities–-a general theory and new special cases

2006 ◽  
Vol 438 ◽  
pp. 1-62 ◽  
Author(s):  
Marek Pycia
Keyword(s):  
General Theory ◽  
Linear Functional ◽  
Functional Inequalities ◽  
Special Cases

scholarly journals A pair of linear functional inequalities and a characterization of Lp-norm

2005 ◽  
Vol 85 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Dorota Krassowska ◽  
Janusz Matkowski
Keyword(s):  
Linear Functional ◽  
Functional Inequalities ◽  
Lp Norm

scholarly journals Inbreeding parents should invest more resources in fewer offspring

2016 ◽  
Author(s):  
A. Bradley Duthie ◽  
Aline M. Lee ◽  
Jane M. Reid
Keyword(s):  
General Theory ◽  
Evolutionary Dynamics ◽  
Inbreeding Avoidance ◽  
The Other ◽  
Trade Off ◽  
Offspring Number ◽  
Focal Female ◽  
Special Cases ◽  
Selection For ◽  
Joint Consideration

AbstractInbreeding increases parent-offspring relatedness and commonly reduces offspring viability, shaping selection on reproductive interactions involving relatives and associated parental investment (PI). Nevertheless, theories predicting selection for inbreeding versus inbreeding avoidance and selection for optimal PI have only been considered separately, precluding prediction of optimal PI and associated reproductive strategy given inbreeding. We unify inbreeding and PI theory, demonstrating that optimal PI increases when a female's inbreeding decreases the viability of her offspring. Inbreeding females should therefore produce fewer offspring due to the fundamental trade-off between offspring number and PI. Accordingly, selection for inbreeding versus inbreeding avoidance changes when females can adjust PI with the degree that they inbreed. In contrast, optimal PI does not depend on whether a focal female is herself inbred. However, inbreeding causes optimal PI to increase given strict monogamy and associated biparental investment compared to female-only investment. Our model implies that understanding evolutionary dynamics of inbreeding strategy, inbreeding depression, and PI requires joint consideration of the expression of each in relation to the other. Overall, we demonstrate that existing PI and inbreeding theories represent special cases of a more general theory, implying that intrinsic links between inbreeding and PI affect evolution of behaviour and intra-familial conflict.

scholarly journals LIFTING THEOREMS FOR TENSOR FUNCTORS ON MODULE CATEGORIES

2011 ◽  
Vol 10 (01) ◽  
pp. 129-155 ◽  
Author(s):  
ROBERT WISBAUER
Keyword(s):  
General Theory ◽  
Tensor Product ◽  
Category Theory ◽  
Systematic Approach ◽  
Wreath Products ◽  
Baxter Equation ◽  
General Category ◽  
Module Theory ◽  
Elementary Module ◽  
Special Cases

Any (co)ring R is an endofunctor with (co)multiplication on the category of abelian groups. These notions were generalized to monads and comonads on arbitrary categories. Starting around 1970 with papers by Beck, Barr and others a rich theory of the interplay between such endofunctors was elaborated based on distributive laws between them and Applegate's lifting theorem of functors between categories to related (co)module categories. Curiously enough some of these results were not noticed by researchers in module theory and thus notions like entwining structures and smash products between algebras and coalgebras were introduced (in the nineties) without being aware that these are special cases of the more general theory. The purpose of this survey is to explain several of these notions and recent results from general category theory in the language of elementary module theory focusing on functors between module categories given by tensoring with a bimodule. This provides a simple and systematic approach to smash products, wreath products, corings and rings over corings (C-rings). We also highlight the relevance of the Yang–Baxter equation for the structures on the threefold tensor product of algebras or coalgebras (see 3.6).

A General Theory for Analysis of Catch and Effort Data

1985 ◽  
Vol 42 (3) ◽  
pp. 414-429 ◽  
Author(s):  
Jon Schnute
Keyword(s):  
General Theory ◽  
Model Identification ◽  
Identification Problem ◽  
Mathematical Proofs ◽  
Structured Population ◽  
Analysis Technique ◽  
Special Cases ◽  
Age Structured ◽  
Almost All ◽  
Special Case

This paper presents a general theory for analysis of catch and effort data from a fishery. Almost all previous methods are shown to be special cases, including those of Schaefer, Pella and Tomlinson, Schnute, and Deriso, as well as the stock reduction analysis technique of Kimura and Tagart and Kimura, Balsiger, and Ito. Like that of Deriso, the theory here is based on natural equations for an age structured population. However, instead of a fixed single model, this paper gives a general model that can be tailored to any particular fishery. The problem of determining the appropriate special case is conceptually identical to the model identification problem described by Box and Jenkins in the context of time series analysis, Identification necessarily begins with a suitable class of models. This paper defines such a class, unique to fisheries, complete with mathematical proofs and biological explanations of all important equations.

Voronoi Domains and Dual Cells in the Generalized Kaleidoscope with Applications to Root and Weight Lattices

1995 ◽  
Vol 47 (3) ◽  
pp. 573-605 ◽  
Author(s):  
R. V. Moody ◽  
J. Patera
Keyword(s):  
General Theory ◽  
Lie Algebra ◽  
Reflection Groups ◽  
Semisimple Lie Algebra ◽  
Voronoi Cells ◽  
Special Cases

AbstractWe give a uniform description, in terms of Coxeter diagrams, of the Voronoi domains of the root and weight lattices of any semisimple Lie algebra. This description provides a classification not only of all the facets of these Voronoi domains but simultaneously a classification of their dual or Delaunay cells and their facets. It is based on a much more general theory that we develop here providing the same sort of information in the setting of chamber geometries defined by arbitrary reflection groups. These generalized kaleidoscopes include the classical spherical, Euclidean, and hyperbolic kaleidoscopes as special cases. We prove that under certain conditions the Delaunay cells are Voronoi cells for the vertices of the Voronoi complex. This leads to the description in terms of Wythoff polytopes of the Voronoi cells of the weight lattices.

Refined General Theory of Stress Analysis for Tubesheet

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Hongsong Zhu
Keyword(s):  
General Theory ◽  
Stress Analysis ◽  
Heat Exchangers ◽  
Numerical Comparison ◽  
Refined Theory ◽  
Element Analysis ◽  
Comparison Results ◽  
Special Cases ◽  
Edge Conditions ◽  
Plate On Elastic Foundation

The stress analysis method for fixed tubesheet (TS) heat exchangers (HEX) in pressure vessel codes such as ASME VIII-1, EN13445, and GB151 is based on the classical theory of thin plate on elastic foundation. In addition, these codes all assume a geometric and loading plane of symmetry at the midway between the two TSs so that only half of the unit or one TS is needed to be considered. In this study, a refined general theory of stress analysis for TS is presented which also considers unequal thickness for two TSs, different edge conditions, pressure drop and deadweight on two TSs, the anisotropic behavior of the TS in thickness direction, and transverse shear deformation in TS. Analysis shows floating and U-tube heat exchangers are the two special cases of the refined theory. Theoretical comparison shows that ASME method can be obtained from the special case of the simplified mechanical model of the refined theory. Numerical comparison results indicate that predictions given by the refined theory agree well with finite element analysis (FEA) for both thin and thick TS heat exchangers, while ASME results are not accurate or not correct. Therefore, it is concluded that the presented refined general theory provides a single unified method, dealing with both thin and thick TSs for different type (U type, floating, and fixed) HEXs in equal detail, with confidence to predict design stresses.

scholarly journals On the cohomology of local groups

1971 ◽  
Vol 12 (2) ◽  
pp. 249-255 ◽  
Author(s):  
S. Świerczkowski
Keyword(s):  
General Theory ◽  
Local Group ◽  
Group Cohomology ◽  
Derived Functor ◽  
Special Cases

Most known homology theories (e.g. the homology of modules, rings, groups, sheaves, …) have been found to be special cases of a general theory proposed by M. Barr and J. Beck [1], [2]. The aim of this paper is to show that the cohomology of a local group, as defined by W. T. van Est [4], also fits the scheme of Barr and Beck. At the same time it will be shown that local group cohomology is a relative derived functor in the sense of S. Eilenberg and J. C. Moore [3].

scholarly journals A Markovian growth-collapse model

2006 ◽  
Vol 38 (1) ◽  
pp. 221-243 ◽  
Author(s):  
Onno Boxma ◽  
David Perry ◽  
Wolfgang Stadje ◽  
Shelemyahu Zacks
Keyword(s):  
General Theory ◽  
Rate Function ◽  
Current Level ◽  
Hitting Times ◽  
Dependent Rate ◽  
State Dependent ◽  
Long Run ◽  
Special Cases ◽  
Collapse Model ◽  
Markov Modulated

We consider growth-collapse processes (GCPs) that grow linearly between random partial collapse times, at which they jump down according to some distribution depending on their current level. The jump occurrences are governed by a state-dependent rate function r(x). We deal with the stationary distribution of such a GCP, (Xt)t≥0, and the distributions of the hitting times Ta = inf{t ≥ 0 : Xt = a}, a > 0. After presenting the general theory of these GCPs, several important special cases are studied. We also take a brief look at the Markov-modulated case. In particular, we present a method of computing the distribution of min[Ta, σ] in this case (where σ is the time of the first jump), and apply it to determine the long-run average cost of running a certain Markov-modulated disaster-ridden system.

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