Well-Behavior, Well-Posedness and Nonsmooth Analysis

AMS subject classification: 90C30, 90C33.

On The Cauchy Problem for Non Effectively Hyperbolic Operators, The Ivrii-Petkov-Hörmander Condition and the Gevrey Well Posedness

2000 Mathematics Subject Classification: 35L15, Secondary 35L30.

Well-Posedness and Conditioning of Optimization Problems

AMS subject classification: 49K40, 90C31.

Well-Posedness, Conditioning and Regularization of Minimization, Inclusion and Fixed-Point Problems

AMS subject classification: 65K10, 49M07, 90C25, 90C48.

Accent Recognition for Noisy Audio Signals

It is well established that accent recognition can be as accurate as up to 95% when the signals are noise-free, using feature extraction techniques such as mel-frequency cepstral coefficients and binary classifiers such as discriminant analysis, support vector machine and k-nearest neighbors. In this paper, we demonstrate that the predictive performance can be reduced by as much as 15% when the signals are noisy. Specifically, in this paper we perturb the signals with different levels of white noise, and as the noise become stronger, the out-of-sample predictive performance deteriorates from 95% to 80%, although the in-sample prediction gives overly-optimistic results. ACM Computing Classification System (1998): C.3, C.5.1, H.1.2, H.2.4., G.3.

Porosity and Variational Principles

We prove that in some classes of optimization problems, like lower semicontinuous functions which are bounded from below, lower semi-continuous or continuous functions which are bounded below by a coercive function and quasi-convex continuous functions with the topology of the uniform convergence, the complement of the set of well-posed problems is σ-porous. These results are obtained as realization of a theorem extending a variational principle of Ioffe-Zaslavski.

A Note About the Nowicki Conjecture on Weitzenböck Derivations

2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.

Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations

Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12

Well-Posedness of Diffusion-Wave Problem with Arbitrary Finite Number of Time Fractional Derivatives in Sobolev Spaces H^s

Mathematics Subject Classification 2010: 26A33, 33E12, 35S10, 45K05.

The Darboux Problem for a Class of 3-D Weakly Hyperbolic Equations

Недю Попиванов, Цветан Христов - Изследвани са някои тримерни аналози на задачата на Дарбу в равнината. През 1952 М. Протер формулира нови тримерни гранични задачи както за клас слабо хиперболични уравнения, така и за някои хиперболично-елиптични уравнения. За разлика от коректността на двумерната задача на Дарбу, новите задачи са некоректни. За слабо хиперболични уравнения, съдържащи младши членове, ние намираме достатъчни условия както за съществуване и единственост на обобщени решения с изолирана степенна особеност, така и за единственост на квази-регулярни решения на задачата на Протер.

Applying Genetic Algorithm In Query Improvement Problem

This paper presents an adaptive method using genetic algorithm to modify user’s queries, based on relevance judgments. This algorithm was adapted for the three well-known documents collections (CISI, NLP and CACM). The method is shown to be applicable to large text collections, where more relevant documents are presented to users in the genetic modification. The algorithm shows the effects of applying GA to improve the effectiveness of queries in IR systems. Further studies are planned to adjust the system parameters to improve its effectiveness. The goal is to retrieve most relevant documents with less number of non-relevant documents with respect to user's query in information retrieval system using genetic algorithm.

Expert System for Decision-Making Problem in Economics

An expert system (ES) is a class of computer programs developed by researchers in artificial intelligence. In essence, they are programs made up of a set of rules that analyze information about a specific class of problems, as well as provide analysis of the problems, and, depending upon their design, recommend a course of user action in order to implement corrections. ES are computerized tools designed to enhance the quality and availability of knowledge required by decision makers in a wide range of industries. Decision-making is important for the financial institutions involved due to the high level of risk associated with wrong decisions. The process of making decision is complex and unstructured. The existing models for decision-making do not capture the learned knowledge well enough. In this study, we analyze the beneficial aspects of using ES for decision- making process.

An Effective Method for Constructing Data Structures Solving an Array Maintenance Problem

In this paper a constructive method of data structures solving an array maintenance problem is offered. These data structures are defined in terms of a family of digraphs which have previously been defined, representing solutions for this problem. We present as well a prototype of the method in Haskell.

Symbolic Dynamics in the Free-Fall Equal-Mass Three-Body Problem

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem

This paper is a survey of our recent results on the bispectral problem. We describe a new method for constructing bispectral algebras of any rank and illustrate the method by a series of new examples as well as by all previously known ones. Next we exhibit a close connection of the bispectral problem to the representation theory of W1+∞–algerba. This connection allows us to explain and generalise to any rank the result of Magri and Zubelli on the symmetries of the manifold of the bispectral operators of rank and order two.