The Interval [0,1] Admits no Functorial Embedding into a Finite-Dimensional or Metrizable Topological Group

An embedding X ⊂ G of a topological space X into a topological group G is called functorial if every homeomorphism of X extends to a continuous group homomorphism of G. It is shown that the interval [0, 1] admits no functorial embedding into a finite-dimensional or metrizable topological group.

Searching for Nearest Strings with Neural-Like String Embedding

We analyze an approach to a similarity preserving coding of symbol sequences based on neural distributed representations and show that it can be viewed as a metric embedding process.

Systemological Knowledge-based Technology for Solving Complete Ill-structured Problems

Original method and technology of systemological «Unit-Function-Object» analysis for solving complete ill-structured problems is proposed. The given visual grapho-analytical UFO technology for the fist time combines capabilities and advantages of the system and object approaches and can be used for business reengineering and for information systems design. UFO- technology procedures are formalized by pattern-theory methods and developed by embedding systemological conceptual classification models into the system-object analysis and software tools. Technology is based on natural classification and helps to investigate deep semantic regularities of subject domain and to take proper account of system-classes essential properties the most objectively. Systemological knowledge models are based on method which for the first time synthesizes system and classification analysis. It allows creating CASE-toolkit of a new generation for organizational modelling for companies’ sustainable development and competitive advantages providing.

Equivariant Embeddings of Differentiable Spaces

Given a differentiable action of a compact Lie group G on a compact smooth manifold V , there exists [3] a closed embedding of V into a finite-dimensional real vector space E so that the action of G on V may be extended to a differentiable linear action (a linear representation) of G on E. We prove an analogous equivariant embedding theorem for compact differentiable spaces (∞-standard in the sense of [6, 7, 8]).

File Format for Storage of Multimedia Information

AMS Subj. Classification: 68U05, 68P30

Quaternion Extensions of Order 16

2000 Mathematics Subject Classification: 12F12

Developing Students’ Mathematical Thinking and Algorithmic Culture in IT Classes

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2012

Demo: Shield UI JavaScript Chart - A Flexible HTML5 Data Visualization Component

Shield UI’s advanced framework for creating rich charts and graphs is the first of a line of data visualization components, giving web developers the power for embedding rich graphics in their web projects with minimum effort. Built with HTML, CSS3 and packaged as a jQuery plugin, the library has full support for legacy and modern desktop web browsers, as well as the latest mobile devices.

On the Algebraic Properties of Convex Bodies

AMS subject classification: 52A01, 13C99.

Modular Digital Watermarking for Image Verification and Secure Data Storage in Web Applications

Our modular approach to data hiding is an innovative concept in the data hiding research field. It enables the creation of modular digital watermarking methods that have extendable features and are designed for use in web applications. The methods consist of two types of modules – a basic module and an application-specific module. The basic module mainly provides features which are connected with the specific image format. As JPEG is a preferred image format on the Internet, we have put a focus on the achievement of a robust and error-free embedding and retrieval of the embedded data in JPEG images. The application-specific modules are adaptable to user requirements in the concrete web application. The experimental results of the modular data watermarking are very promising. They indicate excellent image quality, satisfactory size of the embedded data and perfect robustness against JPEG transformations with prespecified compression ratios. ACM Computing Classification System (1998): C.2.0.

Groups of Order 32 as Galois Groups

2000 Mathematics Subject Classification: 12F12.

Denoising Manifolds for Dimension

2000 Mathematics Subject Classification: 68T01, 62H30, 32C09.

On realizability of p-groups as Galois groups

2000 Mathematics Subject Classification: 12F12, 15A66.