Perturbation bounds for the W-weighted core-EP inverse

2019 ◽  
Vol 19 (12) ◽  
pp. 2050232
Author(s):  
Yuefeng Gao
Keyword(s):  
Integral Representation ◽  
Rectangular Matrix ◽  
Perturbation Bounds ◽  
The Core ◽  
Special Case ◽  
Stable Matrix

In this paper, perturbation bounds are provided for the [Formula: see text]-weighted core-EP inverse of a rectangular matrix under reasonable conditions. Perturbation bounds for the core-EP inverse could be stated as a special case. Then, the continuity of the [Formula: see text]-weighted core-EP inverse is considered from the perspective of equations. Finally, we give an application to a semi-stable matrix involving an integral representation of the [Formula: see text]-weighted core-EP inverse of a perturbed matrix.

scholarly journals POPULATION DYNAMICS OF THE SEGREGATION DISTORTER POLYMORPHISM OF DROSOPHILA MELANOGASTER

Genetics ◽  
1978 ◽  
Vol 89 (1) ◽  
pp. 171-192 ◽  
Author(s):  
Brian Charlesworth ◽  
Daniel L Hartl
Keyword(s):  
Population Genetics ◽  
Population Dynamics ◽  
Drosophila Melanogaster ◽  
The Other ◽  
The Core ◽  
Segregation Distorter ◽  
Tight Linkage ◽  
Highly Oscillatory ◽  
Approximate Treatment ◽  
Special Case

ABSTRACT Two two-locus models of the population dynamics of the segregation distortion (SD) polymorphism of Drosophila melanogaster are described. One model is appropriate for understanding the population genetics of SD in nature, whereas the other is a special case appropriate for understanding an artificial population that has been extensively analysed. The models incorporate the general features of the Sd and Rsp loci which form the core of the SD system. It is shown that the SD polymorphism can be established only when there is sufficiently tight linkage between Sd and Rsp. An approximate treatment, valid for tight linkage, is given of all the equilibria of the system and their stabilities. It is shown that the observed composition of natural and artificial populations with respect to the Sd and Rsp loci is predicted well by the model, provided that restrictions are imposed on the fertilities of certain genotypes. Highly oscillatory paths towards equilibrium are usually to be expected on the basis of this model. The selection pressures on inversions introduced into this system are also investigated.

scholarly journals The Core of a Reinsurance Market

1981 ◽  
Vol 12 (1) ◽  
pp. 57-71 ◽  
Author(s):  
Bernard Baton ◽  
Jean Lemaire
Keyword(s):  
Pareto Optimality ◽  
Individual Rationality ◽  
Pareto Optimal ◽  
Collective Rationality ◽  
Important Special Case ◽  
The Core ◽  
Premium Calculation ◽  
The Individual ◽  
Special Case ◽  
Reinsurance Market

In a series of celebrated papers, K. Borch characterized the set of the Pareto-optimal risk exchange treaties in a reinsurance market. However, the Pareto-optimality and the individual rationality conditions, considered by Borch, do not preclude the possibility that a coalition of companies might be better off by seceding from the whole group. In this paper, we introduce this collective rationality condition and characterize the core of this game without transferable utilities in the important special case of exponential utilities. The mathematical conditions we obtain can be interpreted in terms of insurance premiums, calculated by means of the zero-utility premium calculation principle. We then show that the core is always non-void and conclude by an example.

scholarly journals Nearest $$\varOmega $$-stable matrix via Riemannian optimization

2021 ◽  
Author(s):  
Vanni Noferini ◽  
Federico Poloni
Keyword(s):  
Optimization Problem ◽  
Small Scale ◽  
Frobenius Norm ◽  
Unitary Matrices ◽  
Riemannian Optimization ◽  
Important Special Case ◽  
Closed Set ◽  
Standard Methods ◽  
Special Case ◽  
Stable Matrix

AbstractWe study the problem of finding the nearest $$\varOmega $$ Ω -stable matrix to a certain matrix A, i.e., the nearest matrix with all its eigenvalues in a prescribed closed set $$\varOmega $$ Ω . Distances are measured in the Frobenius norm. An important special case is finding the nearest Hurwitz or Schur stable matrix, which has applications in systems theory. We describe a reformulation of the task as an optimization problem on the Riemannian manifold of orthogonal (or unitary) matrices. The problem can then be solved using standard methods from the theory of Riemannian optimization. The resulting algorithm is remarkably fast on small-scale and medium-scale matrices, and returns directly a Schur factorization of the minimizer, sidestepping the numerical difficulties associated with eigenvalues with high multiplicity.

scholarly journals GSN: A Graph-Structured Network for Multi-Party Dialogues

2019 ◽  
Author(s):  
Wenpeng Hu ◽  
Zhangming Chan ◽  
Bing Liu ◽  
Dongyan Zhao ◽  
Jinwen Ma ◽  
...  
Keyword(s):  
Neural Network ◽  
Information Flow ◽  
Real World ◽  
Experimental Results ◽  
Neural Models ◽  
The Core ◽  
Dialogue Modeling ◽  
Special Case

Existing neural models for dialogue response generation assume that utterances are sequentially organized. However, many real-world dialogues involve multiple interlocutors (i.e., multi-party dialogues), where the assumption does not hold as utterances from different interlocutors can occur ``in parallel.'' This paper generalizes existing sequence-based models to a Graph-Structured neural Network (GSN) for dialogue modeling. The core of GSN is a graph-based encoder that can model the information flow along the graph-structured dialogues (two-party sequential dialogues are a special case). Experimental results show that GSN significantly outperforms existing sequence-based models.

Buckling of a Sandwich Cylinder Under Uniform Axial Compressive Load

1951 ◽  
Vol 18 (2) ◽  
pp. 195-202
Author(s):  
A. Cemal Eringen
Keyword(s):  
Compressive Load ◽  
Aircraft Design ◽  
Surface Forces ◽  
Core Material ◽  
Equilibrium Conditions ◽  
Thick Hollow Cylinder ◽  
The Core ◽  
Buckling Stress ◽  
Special Case ◽  
Good Agreement

Abstract A boundary-value problem of elasticity for a thick hollow circular cylinder is solved under the following boundary conditions, namely, (a) on the lateral surfaces, displacements are specified as arbitrary functions of the longitudinal co-ordinates only, and (b) at both ends, the radial displacements and the longitudinal surface forces are taken to be equal to zero. The displacements, strains, and stresses are obtained in terms of these arbitrary displacement functions. The stresses determined are used to obtain the buckling load of a sandwich cylinder, which employs the thick hollow cylinder as the core. Two simultaneous differential equations are obtained from the equilibrium conditions between the contacting lateral surfaces of the sandwich material (faces) and the core. Numerical calculations and curves are made of the buckling stress for a given core material and for two types of face materials employed in aircraft design. In a special case, when the radius approaches infinity, the result is found to be in good agreement with previously published experimental results. No test data for the general case were available to the author during the preparation of this paper.

Lateral and angular structure of electromagnetic cascades

1968 ◽  
Vol 46 (10) ◽  
pp. S278-S282
Author(s):  
R. Holynski ◽  
V. Jones ◽  
K. Pinkau
Keyword(s):  
Angular Distribution ◽  
Sandwich Structure ◽  
Angular Structure ◽  
Nuclear Emulsions ◽  
The Core ◽  
Core Approximation ◽  
Special Case ◽  
Made In

Measurements of electromagnetic cascades have been made in nuclear emulsions. Six cascades were measured in the Brawley stack (pure emulsion) and four in the SSS stack (lead–emulsion sandwich). The results show that the validity of the core approximation appears to range up to 7 × 10−2 radiation lengths, the core approximation of the angular distribution is valid to an angle of the order of 2°, and the sandwich structure of the SSS stack had no influence on the validity of the core approximation. A law for the mixed radial–angular distribution is given in one special case.

Greening Industrial Policy

2020 ◽  
pp. 265-283 ◽  
Author(s):  
John A. Mathews
Keyword(s):  
Development Strategy ◽  
Industrial Policy ◽  
Circular Economy ◽  
Fossil Fuels ◽  
First Century ◽  
Green Growth ◽  
Energy Materials ◽  
The Core ◽  
Green Industrial Policy ◽  
Special Case

The scope of industrial policy is broadened in this chapter to encompass energy, materials, and finance. Given the unprecedented scale of the industrialization of India, China, and the late latecomers in Africa, Asia, and Latin America, the traditional options of fossil fuels, linear economy, and generic finance have been found wanting, for reasons of immediate environmental spoliation but also to do with countries running up against geopolitical limits. The greening of industrial policy presents itself as a solution, involving the shift to renewables, to a circular economy, and to the greening of finance (green bonds and green loans from development banks), encompassed under the rubric of green growth. The details of these new, green options are explored, and contrasted with traditional green industrial policy. The case is made that, far from being a special case, the greening of industrial policy promises to become the core development strategy, and the general case in industrialization, as the twenty-first century unfolds.

scholarly journals Perturbation theory for core and core-EP inverses of tensor via Einstein product

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5207-5217 ◽  
Author(s):  
Hong-Mei Du ◽  
Bing-Xue Wang ◽  
Hai-Feng Ma
Keyword(s):  
Perturbation Theory ◽  
Perturbation Bounds ◽  
The Core ◽  
Core Inverse ◽  
Einstein Product

In this paper, for given tensors A,? and B = A+E, we investigate the perturbation bounds for the core inverse A# and core-EP inverse A+ under some conditions via Einstein product.

The Competitive Solution for N-Person Games Without Transferable Utility, With an Application to Committee Games

1978 ◽  
Vol 72 (2) ◽  
pp. 599-615 ◽  
Author(s):  
Richard D. McKelvey ◽  
Peter C. Ordeshook ◽  
Mark D. Winer
Keyword(s):  
Cooperative Game Theory ◽  
Solution Concept ◽  
Transferable Utility ◽  
Bargaining Set ◽  
The Core ◽  
Spatial Games ◽  
Spatial Game ◽  
Standard Solution ◽  
Special Case ◽  
Made In

This essay defines and experimentally tests a new solution concept for n-person cooperative games—the Competitive Solution. The need for a new solution concept derives from the fact that cooperative game theory focuses for the most part on the special case of games with transferable utility, even though, as we argue here, this assumption excludes the possibility of modelling most interesting political coalition processes. For the more general case, though, standard solution concepts are inadequate either because they are undefined or they fail to exist, and even if they do exist, they focus on predicting payoffs rather than the coalitions that are likely to form.The Competitive Solution seeks to avoid these problems, but it is not unrelated to existent theory in that we can establish some relationships (see Theorems 1 and 2) between its payoff predictions and those of the core, the V-solution and the bargaining set. Additionally, owing to its definition and motivation, nontrivial coalition predictions are made in conjunction with its payoff predictions.The Competitive Solution's definition is entirely general, but a special class of games—majority rule spatial games—are used for illustrations and the experimental test reported here consists of eight plays of a 5-person spatial game that does not possess a main-simple V-solution or a bargaining set. Overall, the data conform closely to the Competitive Solution's predictions.

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