Dunkl-Schrödinger Equations with and without Quadratic Potentials

2000 Mathematics Subject Classification: Primary 42A38. Secondary 42B10.

Global Results for Solution to the Mass-Critical Schrödinger Equation with Convolution Nonlinearity in R^n

Георги Венков, Христо Генев - Разглеждаме един клас от L^2 - критични нелинейни уравнения на Шрьодингер в R^(1+n) с конволюционна нелинейност от тип Хартри. Целта ни е да установим локалното и глобално съществуване на решенията, както и коректност на задачата на Коши в достатъчно малка околност на нулата в пространството L^2 (R^n). Като естествено следствие на глобалните резултати ние доказваме съществуване на оператор на разсейване за малки начални условия.

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

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

Well-Behavior, Well-Posedness and Nonsmooth Analysis

AMS subject classification: 90C30, 90C33.

Well-Posedness and Conditioning of Optimization Problems

AMS subject classification: 49K40, 90C31.

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 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.

Tutorial on Computing: Technological Advances, Social Implications, Ethical and Legal Issues

Computing and information technology have made significant advances. The use of computing and technology is a major aspect of our lives, and this use will only continue to increase in our lifetime. Electronic digital computers and high performance communication networks are central to contemporary information technology. The computing applications in a wide range of areas including business, communications, medical research, transportation, entertainments, and education are transforming local and global societies around the globe. The rapid changes in the fields of computing and information technology also make the study of ethics exciting and challenging, as nearly every day, the media report on a new invention, controversy, or court ruling. This tutorial will explore a broad overview on the scientific foundations, technological advances, social implications, and ethical and legal issues related to computing. It will provide the milestones in computing and in networking, social context of computing, professional and ethical responsibilities, philosophical frameworks, and social, ethical, historical, and political implications of computer and information technology. It will outline the impact of the tremendous growth of computer and information technology on people, ethics and law. Political and legal implications will become clear when we analyze how technology has outpaced the legal and political arenas.

Automatic Discovery of Word Semantic Relations

In this paper, we propose an unsupervised methodology to automatically discover pairs of semantically related words by highlighting their local environment and evaluating their semantic similarity in local and global semantic spaces. This proposal di®ers from previous research as it tries to take the best of two different methodologies i.e. semantic space models and information extraction models. It can be applied to extract close semantic relations, it limits the search space and it is unsupervised.