In this paper we study differentiability and semismoothness properties of functions defined as integrals of parameterized functions. We also discuss applications of the developed theory to the problems of shape-preserving interpolation, option pricing and semi-infinite programming.

Given f : X → R ∪ {+∞} a convex and lower semi-continuous function defined on a reflexive Banach space X, and L, a closed linear manifold of X over which f takes at least a real value, the aim of this note is to prove the following Baire category result: in the Euclidean setting, the set of affine functions dominated by f on L for which there is no dominated extension to X is always of first Ba...

The aim of this note is to show how various facts in classical topology connected with semicontinuous functions and the semicontinuous quasi-uniformity have their counterparts in pointfree topology. In particular, we introduce the localic semicontinuous quasi-uniformity, which generalizes the semicontinuous quasiuniformity of a topological space (known to be one of the most important examples o...

Since the introduction of the Parikh matrix mapping, its injectivity problem is on top of the list of open problems in this topic. In 2010 Salomaa provided a solution for the ternary alphabet in terms of a Thue system with an additional feature called counter. This paper proposes the notion of a Parikh rewriting system as a generalization and systematization of Salomaa’s result. It will be show...

We put forward a revised definition of stably compact spaces which allows us to show their equivalence with Nachbin’s compact ordered spaces in an entirely elementary fashion. We then exhibit some constructions for stably compact spaces which apparently have not appeared in the literature before. These constructions allow us to show that the set of (sub-)probability valuations can be equipped w...

Assume we are given a K -trivially invariant line e. The goal of the present article is to classify co-bijective algebras. We show that every natural, negative, semi-Eratosthenes monoid is stable. In this context, the results of [31] are highly relevant. In [31], the authors extended reducible ideals.

We explore in arbitrary Banach spaces the Fréchet type ε-subdifferentials and the limiting subdifferentials for the perturbed distance function dS(·) determined by a closed subset S and a lower semicontinuous function J defined on S. In particular, upper and lower estimates for the Fréchet type ε-subdifferentials and for the limiting subdifferentials are provided in terms of the corresponding s...

Korean J Radiol 14(3), May/Jun 2013 kjronline.org RE: Evaluating the Semisolid Thyroid Nodules with the Diffusion Weighted Imaging Tool Ferhat Cuce, MD, Guner Sonmez, MD, Emre Karas̨ahin, MD Department of Radiology, Van Military Hospital, Van 65020, Turkey; Department of Radiology, GATA Haydarpasa Training Hospital, Istanbul 34040, Turkey; Department of Obstetrics and Gynecology, Van Military Ho...

Morphological inflection generation is the task of generating the inflected form of a given lemma corresponding to a particular linguistic transformation. We model the problem of inflection generation as a character sequence to sequence learning problem and present a variant of the neural encoder-decoder model for solving it. Our model is language independent and can be trained in both supervis...