Graph Indicators of Vectorial Functions and Bounds on the Algebraic Degree of Composite Functions

2020 ◽  
Vol 66 (12) ◽  
pp. 7702-7716
Author(s):  
Claude Carlet
Keyword(s):  
Algebraic Degree ◽  
Composite Functions ◽  
Vectorial Functions

The Higher Order Crack Tip Fields for Arbitrary FGM Composite Functions

2011 ◽  
Vol 19 (4-5) ◽  
pp. 401-404
Author(s):  
Dai Yao ◽  
Zhang Lei ◽  
Liu Jun-feng ◽  
Zhong Xiao
Keyword(s):  
Crack Tip ◽  
Higher Order ◽  
Composite Functions ◽  
Crack Tip Fields

scholarly journals The Algebraic Degree of Phase-Type Distributions

2010 ◽  
Vol 47 (03) ◽  
pp. 611-629
Author(s):  
Mark Fackrell ◽  
Qi-Ming He ◽  
Peter Taylor ◽  
Hanqin Zhang
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Polynomial Algorithm ◽  
Algebraic Degree ◽  
Nonnegative Matrices ◽  
Stieltjes Transform ◽  
Special Cases ◽  
Phase Type ◽  
Phase Type Distributions ◽  
The Matrix

This paper is concerned with properties of the algebraic degree of the Laplace-Stieltjes transform of phase-type (PH) distributions. The main problem of interest is: given a PH generator, how do we find the maximum and the minimum algebraic degrees of all irreducible PH representations with that PH generator? Based on the matrix exponential (ME) order of ME distributions and the spectral polynomial algorithm, a method for computing the algebraic degree of a PH distribution is developed. The maximum algebraic degree is identified explicitly. Using Perron-Frobenius theory of nonnegative matrices, a lower bound and an upper bound on the minimum algebraic degree are found, subject to some conditions. Explicit results are obtained for special cases.

Hahn-Banach-Type Theorems and Subdifferentials for Invariant and Equivariant Order Continuous Vector Lattice-Valued Operators with Applications to Optimization

2021 ◽  
Vol 78 (1) ◽  
pp. 139-156
Author(s):  
Antonio Boccuto
Keyword(s):  
Optimality Conditions ◽  
Vector Lattice ◽  
Optimization Problems ◽  
Linear Constraints ◽  
Continuous Vector ◽  
Fixed Group ◽  
Composite Functions ◽  
Order Continuous

Abstract We give some versions of Hahn-Banach, sandwich, duality, Moreau--Rockafellar-type theorems, optimality conditions and a formula for the subdifferential of composite functions for order continuous vector lattice-valued operators, invariant or equivariant with respect to a fixed group G of homomorphisms. As applications to optimization problems with both convex and linear constraints, we present some Farkas and Kuhn-Tucker-type results.

scholarly journals Injectivity of Composite Functions

1994 ◽  
Vol 17 (5) ◽  
pp. 393-408
Author(s):  
Kim S. Larsen ◽  
Michael I. Schwartzbach
Keyword(s):  
Composite Functions
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