Operations for D-algebraic Functions

A function is differentially algebraic (or simply D-algebraic) if there is a polynomial relationship between some of its derivatives and the indeterminate variable. Many functions in the sciences, such as Mathieu functions, the Weierstrass elliptic functions, and holonomic or D-finite functions are D-algebraic. These functions form a field, and are closed under composition, taking functional inverse, and derivation. We present implementation for each underlying operation. We also give a systematic way for computing an algebraic differential equation from a linear differential equation with D-finite function coefficients. Each command is a feature of our Maple package $NLDE$ available at https://mathrepo.mis.mpg.de/OperationsForDAlgebraicFunctions.Comment: 4 pages + 1 (10 references). Mathematical software pape

Rapid Industrial Prototyping and SoC Design of 3G/4G Wireless Systems Using an HLS Methodology

Many very-high-complexity signal processing algorithms are required in future wireless systems, giving tremendous challenges to real-time implementations. In this paper, we present our industrial rapid prototyping experiences on 3G/4G wireless systems using advanced signal processing algorithms in MIMO-CDMA and MIMO-OFDM systems. Core system design issues are studied and advanced receiver algorithms suitable for implementation are proposed for synchronization, MIMO equalization, and detection. We then present VLSI-oriented complexity reduction schemes and demonstrate how to interact these high-complexity algorithms with an HLS-based methodology for extensive design space exploration. This is achieved by abstracting the main effort from hardware iterations to the algorithmic C/C++ fixed-point design. We also analyze the advantages and limitations of the methodology. Our industrial design experience demonstrates that it is possible to enable an extensive architectural analysis in a short-time frame using HLS methodology, which significantly shortens the time to market for wireless systems.National Science Foundatio

Collapsing D-Branes in Calabi-Yau Moduli Space: I

We study the quantum volume of D-branes wrapped around various cycles in Calabi-Yau manifolds, as the manifold's moduli are varied. In particular, we focus on the behaviour of these D-branes near phase transitions between distinct low energy physical descriptions of the resulting string theory. Whereas previous studies have solely considered quantum volumes in the context of two-cycles in perturbative string theory or D-branes in the specific example of the quintic hypersurface, we work more generally and find qualitatively new features. On the mathematical side, as we briefly note, our work has some interesting implications for certain issues in arithmetics.Comment: 77 pages, 15 figure

Учебный русско-английский математический словарь

Настоящий словарь содержит терминологические единицы по разделам курса математики, которые включены в программу довузовской подготовки для иностранных граждан. Основные математические термины проиллюстрированы примерами употребления и рисунками. Учебный словарь предназначен как для студентов-иностранцев, изучающих математику на русском (английском) языках по программе довузовской подготовки, так и для тех, кто проходит обучение математическим дисциплинам на основных факультетах вузов. Словарь также может быть полезен математикам-методистам, исследователям и переводчикам

TetGen, towards a quality tetrahedral mesh generator

TetGen is a C++ program for generating quality tetrahedral meshes aimed to support numerical methods and scientific computing. It is also a research project for studying the underlying mathematical problems and evaluating algorithms. This paper presents the essential meshing components developed in TetGen for robust and efficient software implementation. And it highlights the state-of-the-art algorithms and technologies currently implemented and developed in TetGen for automatic quality tetrahedral mesh generation