scholarly journals Kurdyka–Łojasiewicz Property of Zero-Norm Composite Functions

2020 ◽  
Author(s):  
Yuqia Wu ◽  
Shaohua Pan ◽  
Shujun Bi
Keyword(s):  
Composite Functions ◽  
Zero Norm

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

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.

Stable Lattices

1954 ◽  
Vol 6 ◽  
pp. 265-273 ◽  
Author(s):  
Harvey Cohn
Keyword(s):  
Local Maximum ◽  
Absolute Maximum ◽  
Square Root ◽  
Stable Norm ◽  
Algebraic Modules ◽  
Zero Norm

The most interesting cases of stable lattices, introduced in an earlier volume of this journal (12), were the (algebraic) modules of stable norm, or modules whose ratio of minimum absolute non-zero norm to lattice determinant (i.e., to the square root of module-discriminant) is a local maximum for small variations of the basis. We soon found that these modules were perhaps more numerous than we should have desired if we were interested only in finding an absolute maximum.

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

scholarly journals Integrability Formulas. Part II

2010 ◽  
Vol 18 (2) ◽  
pp. 129-141
Author(s):  
Bo Li ◽  
Na Ma ◽  
Xiquan Liang
Keyword(s):  
Polynomial Function ◽  
Trigonometric Function ◽  
Composite Functions

Integrability Formulas. Part II In this article, we give several differentiation and integrability formulas of special and composite functions including trigonometric function, and polynomial function.

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