Schauder a priori estimates and regularity of solutions to boundary-degenerate elliptic linear second-order partial differential equations

We establish Schauder a priori estimates and regularity for solutions to a class of boundary-degenerate elliptic linear second-order partial differential equations. Furthermore, given a smooth source function, we prove regularity of solutions up to the portion of the boundary where the operator is degenerate. Degenerate-elliptic operators of the kind described in our article appear in a diverse range of applications, including as generators of affine diffusion processes employed in stochastic volatility models in mathematical finance, generators of diffusion processes arising in mathematical biology, and the study of porous media.Comment: 58 pages, 1 figure. To appear in the Journal of Differential Equations. Incorporates final galley proof corrections corresponding to published versio

SOFTWARE PIRACY AND HOW IT IS INFLUENCED BY THE CORRUPTION LEVEL FOR ANY GIVEN COUNTRY. OPEN SOURCE AND FREE SOFTWARE AS SOLUTIONS TO THE PROBLEM.

Today’s IT world is slowly driving towards open source and open software trends. Even Microsoft is taking such approach with some of its software products (the MSDNAA program is the best example). Although everyone is happy that software is becoming cheaper or even open source, we must ask ourselves what led to this trend. Why are software companies giving out software products for free when just a few years ago they were charging us big money for it? The answer is, of course, marketing issues. But another big factor is the piracy factor.software piracy, corruption, open source, free software, statistic, test

DESIGNING AN OBJECT RELATION MAPPING SYSTEM IN PHP

Object Relational Mapping is a programming technique used by software developers to convert data between incompatible systems. This technique is used in object-oriented programming languages, hence the “Object” in Object Relational Mapping. Often times we see ORM systems being used by developers when interacting with relational database management systems. ORM is about creating classes that mimic the tables in the database but in a more business oriented manner rather than the normalized form used by the RDBMS.ORM, object, relational, mapping, class, business model, normalization, primary key, foreign key, methods, properties

DESIGNING HTML HELPERS TO OPTIMIZE WEB APPLICATION DEVELOPMENT

Building a web application or a website can become difficult, just because so many technologies are involved. Generally companies tend to people that work in teams to develop web applications. These teams are made up of professionals that focus on different technologies, such as CGI, HTML, JavaScript, CSS and databases. When the work of many people gathers to make up a single document there is often a mismatch between parts of code written by different team members. This article focuses on improving this matter by bringing consistency in code through the use of HTML helpers in server-side scripting languages. The examples in this article use PHP as the server-side language, but the model can be applied in any other language a developer works with.HTML, CGI, Helper, OOP, code generation

INTRODUCTION TO ZEND FRAMEWORK

A software framework provides the skeleton of an application that can be customized by an application developer. Like software libraries, software frameworks aid the software developer by containing source code that solves problems for a given domain and provides a simple API. However, while a code library acts like a servant to other programs, software frameworks reverse the master/servant relationship. This reversal, called inversion of control, expresses the essence of software frameworks. A web application framework is a software framework that is designed to support the development of dynamic websites, Web applications and Web services. The framework aims to alleviate the overhead associated with common activities used in Web development. For example, many frameworks provide libraries for database access, templating frameworks and session management, and often promote code reuse.Zend Framework

INTRODUCING MICROSOFT SILVERLIGHT

Despite all the wonderful things you can say about HTML, CSS, and JavaScript, they form a pretty poor environment for developing modern sites and applications. If you care about your content working on most web browsers (or even just Internet Explorer and Firefox), accommodating their differences can be maddening. Many techniques and JavaScript libraries have been developed and shared over the years that can reduce this frustration, but none of them are silver bullets. In addition to browser differences, the graphical capabilities of HTML are too limiting for many user experiences that people want to create. Drawing a simple line, incorporating video, and a number of other things are extremely difficult or impossible with HTML alone. It’s not that these technologies were poorly designed, but simply that they were designed for hyperlinked documents rather than the extremely rich presentations that most people want to create on the Web these days.Silverlight, Microsoft

Quality-Of-Control-Aware Scheduling of Communication in TSN-Based Fog Computing Platforms Using Constraint Programming

In this paper we are interested in real-time control applications that are implemented using Fog Computing Platforms consisting of interconnected heterogeneous Fog Nodes (FNs). Similar to previous research and ongoing standardization efforts, we assume that the communication between FNs is achieved via IEEE 802.1 Time Sensitive Networking (TSN). We model the control applications as a set of real-time streams, and we assume that the messages are transmitted using time-sensitive traffic that is scheduled using the Gate Control Lists (GCLs) in TSN. Given a network topology and a set of control applications, we are interested to synthesize the GCLs for messages such that the quality-of-control of applications is maximized and the deadlines of real-time messages are satisfied. We have proposed a Constraint Programming-based solution to this problem, and evaluated it on several test cases

Stochastic representation of solutions to degenerate elliptic and parabolic boundary value and obstacle problems with Dirichlet boundary conditions

We prove existence and uniqueness of stochastic representations for solutions to elliptic and parabolic boundary value and obstacle problems associated with a degenerate Markov diffusion process. In particular, our article focuses on the Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance and a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate, elliptic partial differential operator whose coefficients have linear growth in the spatial variables and where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. In mathematical finance, solutions to terminal/boundary value or obstacle problems for the parabolic Heston operator correspond to value functions for American-style options on the underlying asset.Comment: 47 pages; to appear in Transactions of the American Mathematical Societ

THE EUROPEAN EMERGENCY NUMBER 112

The working of the 112 Emergency Call System is a natural need in a civilized country that has as a main objective to protect its citizens. The single European emergency number 112 was introduced to enable citizens to call the emergency services (such as police, ambulance and fire brigade) by using the same number anywhere in the European Union (EU). This is especially important as European citizens increasingly travel to other EU countries for work, study or leisure. According to EU legislation, Member States must ensure that users of any type of telephone, fixed or mobile are able to call the emergency services free of charge by using the European emergency number 112. This number is now available in all Member States.112, emergency call, European Union