Displaying similar documents to “On weak sharp minima for a special class of nonsmooth functions”

Specialization to the tangent cone and Whitney equisingularity

Arturo Giles Flores (2013)

Bulletin de la Société Mathématique de France

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Let ( X , 0 ) be a reduced, equidimensional germ of an analytic singularity with reduced tangent cone ( C X , 0 , 0 ) . We prove that the absence of exceptional cones is a necessary and sufficient condition for the smooth part 𝔛 0 of the specialization to the tangent cone ϕ : 𝔛 to satisfy Whitney’s conditions along the parameter axis Y . This result is a first step in generalizing to higher dimensions Lê and Teissier’s result for hypersurfaces of 3 which establishes the Whitney equisingularity of X and its tangent...

On the condition of Λ-convexity in some problems of weak continuity and weak lower semicontinuity

Agnieszka Kałamajska (2001)

Colloquium Mathematicae

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We study the functional I f ( u ) = Ω f ( u ( x ) ) d x , where u=(u₁, ..., uₘ) and each u j is constant along some subspace W j of ℝⁿ. We show that if intersections of the W j ’s satisfy a certain condition then I f is weakly lower semicontinuous if and only if f is Λ-convex (see Definition 1.1 and Theorem 1.1). We also give a necessary and sufficient condition on W j j = 1 , . . . , m to have the equivalence: I f is weakly continuous if and only if f is Λ-affine.

Generalization of the weak amenability on various Banach algebras

Madjid Eshaghi Gordji, Ali Jabbari, Abasalt Bodaghi (2019)

Mathematica Bohemica

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The generalized notion of weak amenability, namely ( ϕ , ψ ) -weak amenability, where ϕ , ψ are continuous homomorphisms on a Banach algebra 𝒜 , was introduced by Bodaghi, Eshaghi Gordji and Medghalchi (2009). In this paper, the ( ϕ , ψ ) -weak amenability on the measure algebra M ( G ) , the group algebra L 1 ( G ) and the Segal algebra S 1 ( G ) , where G is a locally compact group, are studied. As a typical example, the ( ϕ , ψ ) -weak amenability of a special semigroup algebra is shown as well.

On linear maps leaving invariant the copositive/completely positive cones

Sachindranath Jayaraman, Vatsalkumar N. Mer (2024)

Czechoslovak Mathematical Journal

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The objective of this manuscript is to investigate the structure of linear maps on the space of real symmetric matrices 𝒮 n that leave invariant the closed convex cones of copositive and completely positive matrices ( COP n and CP n ). A description of an invertible linear map on 𝒮 n such that L ( CP n ) C P n is obtained in terms of semipositive maps over the positive semidefinite cone 𝒮 + n and the cone of symmetric nonnegative matrices 𝒩 + n for n 4 , with specific calculations for n = 2 . Preserver properties of the Lyapunov...

The subspace of weak P -points of *

Salvador García-Ferreira, Y. F. Ortiz-Castillo (2015)

Commentationes Mathematicae Universitatis Carolinae

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Let W be the subspace of * consisting of all weak P -points. It is not hard to see that W is a pseudocompact space. In this paper we shall prove that this space has stronger pseudocompact properties. Indeed, it is shown that W is a p -pseudocompact space for all p * .

Relative weak derived functors

Panneerselvam Prabakaran (2020)

Commentationes Mathematicae Universitatis Carolinae

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Let R be a ring, n a fixed non-negative integer, 𝒲 the class of all left R -modules with weak injective dimension at most n , and 𝒲 the class of all right R -modules with weak flat dimension at most n . Using left (right) 𝒲 -resolutions and the left derived functors of Hom we study the weak injective dimensions of modules and rings. Also we prove that - - is right balanced on R × R by 𝒲 × 𝒲 , and investigate the global right 𝒲 -dimension of R by right derived functors of .

A uniqueness result for the continuity equation in two dimensions

Giovanni Alberti, Stefano Bianchini, Gianluca Crippa (2014)

Journal of the European Mathematical Society

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We characterize the autonomous, divergence-free vector fields b on the plane such that the Cauchy problem for the continuity equation t u + . ˙ ( b u ) = 0 admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential f associated to b . As a corollary we obtain uniqueness under the assumption that the curl of b is a measure. This result can be extended to certain non-autonomous vector fields b with...

Saddle point criteria for second order η -approximated vector optimization problems

Anurag Jayswal, Shalini Jha, Sarita Choudhury (2016)

Kybernetika

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The purpose of this paper is to apply second order η -approximation method introduced to optimization theory by Antczak [2] to obtain a new second order η -saddle point criteria for vector optimization problems involving second order invex functions. Therefore, a second order η -saddle point and the second order η -Lagrange function are defined for the second order η -approximated vector optimization problem constructed in this approach. Then, the equivalence between an (weak) efficient solution...

Weak- and strong-type inequality for the cone-like maximal operator in variable Lebesgue spaces

Kristóf Szarvas, Ferenc Weisz (2016)

Czechoslovak Mathematical Journal

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The classical Hardy-Littlewood maximal operator is bounded not only on the classical Lebesgue spaces L p ( d ) (in the case p > 1 ), but (in the case when 1 / p ( · ) is log-Hölder continuous and p - = inf { p ( x ) : x d } > 1 ) on the variable Lebesgue spaces L p ( · ) ( d ) , too. Furthermore, the classical Hardy-Littlewood maximal operator is of weak-type ( 1 , 1 ) . In the present note we generalize Besicovitch’s covering theorem for the so-called γ -rectangles. We introduce a general maximal operator M s γ , δ and with the help of generalized Φ -functions, the strong-...

Exact l 1 penalty function for nonsmooth multiobjective interval-valued problems

Julie Khatri, Ashish Kumar Prasad (2024)

Kybernetika

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Our objective in this article is to explore the idea of an unconstrained problem using the exact l 1 penalty function for the nonsmooth multiobjective interval-valued problem (MIVP) having inequality and equality constraints. First of all, we figure out the KKT-type optimality conditions for the problem (MIVP). Next, we establish the equivalence between the set of weak LU-efficient solutions to the problem (MIVP) and the penalized problem (MIVP ρ ) with the exact l 1 penalty function. The...

On a Kirchhoff-Carrier equation with nonlinear terms containing a finite number of unknown values

Nguyen Vu Dzung, Le Thi Phuong Ngoc, Nguyen Huu Nhan, Nguyen Thanh Long (2024)

Mathematica Bohemica

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We consider problem (P) of Kirchhoff-Carrier type with nonlinear terms containing a finite number of unknown values u ( η 1 , t ) , , u ( η q , t ) with 0 η 1 < η 2 < < η q < 1 . By applying the linearization method together with the Faedo-Galerkin method and the weak compact method, we first prove the existence and uniqueness of a local weak solution of problem (P). Next, we consider a specific case ( P q ) of (P) in which the nonlinear term contains the sum S q [ u 2 ] ( t ) = q - 1 i = 1 q u 2 ( ( i - 1 ) q , t ) . Under suitable conditions, we prove that the solution of ( P q ) converges to the solution...

The Ascoli property for function spaces and the weak topology of Banach and Fréchet spaces

S. Gabriyelyan, J. Kąkol, G. Plebanek (2016)

Studia Mathematica

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Following Banakh and Gabriyelyan (2016) we say that a Tychonoff space X is an Ascoli space if every compact subset of C k ( X ) is evenly continuous; this notion is closely related to the classical Ascoli theorem. Every k -space, hence any k-space, is Ascoli. Let X be a metrizable space. We prove that the space C k ( X ) is Ascoli iff C k ( X ) is a k -space iff X is locally compact. Moreover, C k ( X ) endowed with the weak topology is Ascoli iff X is countable and discrete. Using some basic concepts from probability...

Nonlinear Hyperbolic Smoothing at a Focal Point

Jean-Luc Joly, Guy Métivier, Jeffrey Rauch (1998-1999)

Séminaire Équations aux dérivées partielles

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The nonlinear dissipative wave equation u t t - Δ u + | u t | h - 1 u t = 0 in dimension d &gt; 1 has strong solutions with the following structure. In 0 t &lt; 1 the solutions have a focusing wave of singularity on the incoming light cone | x | = 1 - t . In { t 1 } that is after the focusing time, they are smoother than they were in { 0 t &lt; 1 } . The examples are radial and piecewise smooth in { 0 t &lt; 1 }