A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory

The first motivation for this note is to obtain a general version of the following result: let E be a Banach space and f : E → R be a differentiable function, bounded below and satisfying the Palais-Smale condition; then, f is coercive, i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references therein. A general result of this type was given in [3, Theorem 5.1] for a lower semicontinuous function defined on a Banach space, through an approach based on an abstract notion of subdifferential operator, and taking into account the “smoothness” of the Banach space. Here, we give (Theorem 1) an extension in a metric setting, based on the notion of slope from [11] and coercivity is considered in a generalized sense, inspired by [9]; our result allows to recover, for example, the coercivity result of [19], where a weakened version of the Palais-Smale condition is used. Our main tool (Proposition 1) is a consequence of Ekeland’s variational principle extending [12, Corollary 3.4], and deals with a function f which is, in some sense, the “uniform” Γ-limit of a sequence of functions.

Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings

The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gˆateaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key element of the unified approach to obtaining various calculus rules for various types of derivatives presented in the paper are simple formulas for subdifferentials of marginal, or performance functions.

On Root Arrangements of Polynomial-Like Functions and their Derivatives

2000 Mathematics Subject Classification: 12D10.

l-stable Functions and Constrained Optimization

Иван Гинчев - Класът на ℓ-устойчивите в точка функции, дефиниран в [2] и разширяващ класа на C1,1 функциите, се обобщава от скаларни за векторни функции. Доказани са някои свойства на ℓ-устойчивите векторни функции. Показано е, че векторни оптимизационни задачи с ограничения допускат условия от втори ред изразени чрез посочни производни, което обобщава резултати от [2] и [5].

On some Properties of Boolean Functions and Their Binary Decision Diagrams

Иво Й. Дамянов - Манипулирането на булеви функции е основнo за теоретичната информатика, в това число логическата оптимизация, валидирането и синтеза на схеми. В тази статия се разглеждат някои първоначални резултати относно връзката между граф-базираното представяне на булевите функции и свойствата на техните променливи.

Exact Solutions of Nonlocal Boundary Value Problems for One- and Two-Dimensional Heat Equation

Иван Хр. Димовски, Юлиан Ц. Цанков - Предложен е метод за намиране на явни решения на клас двумерни уравнения на топлопроводността с нелокални условия по пространствените променливи. Методът е основан на директно тримерно операционно смятане. Класическата дюамелова конволюция е комбинирана с две некласически конволюции за операторите ∂xx и ∂yy в една тримерна конволюция. Съответното операционно смятане използва мултипликаторни частни. Мултипликаторните частни позволяват да се продължи принципът на Дюамел за пространствените променливи и да се намерят явни решения на разглежданите гранични задачи. Общите разглеждания са приложени в случая на гранични условия от типа на Йонкин. Намерени са експлицитни решения в затворен вид.

On Connection between Characterestic Functions and the Caratheodori Class Functions

2000 Mathematics Subject Classification: 47A65, 45S78.

Speciális kockázatok és kockázatkezelés a kockázatitőke-finanszírozásban (The special risks and risk management of venture capital)

A tanulmányban a szerzők arra a kérdésre keresik a választ, hogy az aszimmetrikus információk hatására a vállalkozók és a befektetők között kialakuló megbízó-ügynök viszonynak melyek a speciális vetületei a kockázatitőke-finanszírozás vonatkozásában. A szerzők arra a következtetésre jutottak, hogy a hiányos információk, a megbízó-ügynök viszony, illetve az ügyletek speciális jellege miatt fokozottan jelentkező ügynökprobléma kezelésére a kockázatitőke-finanszírozás szereplői speciális kockázatkezelési technikákat alkalmaznak. Ilyenek a magas elvárt hozamok, a szigorú kiválasztási kritériumok, a speciális befektetési vagy szindikátusi szerződések, a befektetést követő monitoring tevékenység, a több lépcsőben történő finanszírozás és a portfólióvállalatok hálózatba szervezése. A speciális kockázati megközelítés következtében a befektetéseket opciós szemlélet is áthatja. _____ This paper focuses on the special aspects of imperfect information in case of venture capital financing including principal-agent relationship between entrepreneurs and investors as well as adverse selection that evolves as a result of information asymmetries. The authors’ finding is that venture capital is able to manage the problems caused by imperfect information via applying divers risk management techniques such as high profit expectations, scrutiny of portfolio-companies, the use of special contracting stipulations and syndicate agreements, the monitoring of investments, multi-staged financing of companies and the integration of portfolio-companies into networks. In addition to the risk management techniques the authors also give the interpretation of the unique attitude of venture capital toward uncertainty and its special real option-like risk valuation approach that makes venture capitalists capable of handling high uncertainty under imperfect information.

Calibrated embeddings in the special Lagrangian and coassociative cases

Every closed, oriented, real analytic Riemannian 3-manifold can be isometrically embedded as a special Lagrangian submanifold of a Calabi-Yau 3-fold, even as the real locus of an antiholomorphic, isometric involution. Every closed, oriented, real analytic Riemannian 4-manifold whose bundle of self-dual 2-forms is trivial can be isometrically embedded as a coassociative submanifold in a G_2-manifold, even as the fixed locus of an anti-G_2 involution. These results, when coupled with McLean's analysis of the moduli spaces of such calibrated submanifolds, yield a plentiful supply of examples of compact calibrated submanifolds with nontrivial deformation spaces.

Network analysis approach to find new candidate genes and pathways involved in the pathophysiology of familial hypercholesterolemia

Still a big gap exists between clinical and genetic diagnosis of dyslipidemic disorders. Almost the 60% of the patients with a clinical diagnosis of Familial hypercholesterolemia (FH) still lack of a genetic diagnosis. Here we present the preliminary results of an integrative approach intended to identify new candidate genes and to dissect pathways that can be dysregulated in the disease. Interesting hits will be subsequently knocked down in vitro in order to evaluate their functional role in the uptake of fluorescently-labeled LDL and free cell cholesterol using automated microscopy.

An examination of Special Forces and their transfer of skillsets under crisis management settings in Singapore

The thesis focuses on military crisis management and strategy.