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Application of Some Methods of Mathematical and Functional Analysis Part 2 of this two-part book covers the fundamentals of vector analysis, the calculus of variations, and the elements of functional analysis as applied to solving Fredholm's equation. It also introduces basic numerical methods. This book is specifically written for engineering students. This is the sequel to Mathematical Analysis (Advanced Topics) Part 1. General Functional Series and Their A pplica- tion. It is a treatment of some of the most widespread meth- ods of mathematical and functional analysis. The feature of this study aid is that it contains methods of functional analysis not included in textbooks for engineering students. This enables the authors to set forth approximate calcula- tions using the methods of functional analysis and to present modern mathematical methods for solving applied problems. The book gives an application of vector analysis to the study of various vector fields. Certain elements of functional analysis are applied to the methods of a fixed point and also to the solution of Fredholm’s equations. In approximate computations, the student’s attention is drawn to numerical methods of mathematical analysis which can be realized on a computer. Professor Aleksandr V. Efimov, D.Sc., leads the Department of Higher Mathematics at the Moscow Institute of Electronic Technology. He has dedicated over thirty years to teaching, beginning his lecturing career in 1952. Efimov's research primarily focuses on the approximation properties of general orthogonal systems. He's a prolific author, with numerous scientific papers, monographs, and textbooks to his name, some of which have been translated into English. Notable examples include Problem Book of Mathematics for Engineering Students, Part 1. Linear Algebra and Fundamentals of Mathematical Analysis and Part 2. Advanced Topics of Mathematical Analysis (Mir Publishers, Moscow, 1984). Part 3. Special Courses is currently in preparation. Professor Yuri G. Zolotarev, D.Sc., is also a lecturer in the Department of Higher Mathematics at the Moscow Institute of Electronic Technology, where he has taught for thirty years. He earned his Candidate of Science degree in 1954 and his Doctor of Physical and Mathematical Sciences degree in 1974. With over fifty publications, his main scientific interests lie in technical cybernetics, information theory, and applied mathematics. His other scientific works include "Holomorphic Functions with an Even Number of Arguments and Their Applications to Differential Equations" and "Functional Systems in Residual Classes and Their Use in Computational Systems." Valentina M. Terpigoreva, Cand.Sc., is an assistant professor in the Department of Higher Mathematics at the Moscow Institute of Electronic Technology. She began her teaching career in 1951. In 1967, she defended her thesis, "Extremal Problems for Certain Classes of Analytic Functions," which earned her a Candidate's degree in physical and mathematical sciences. She has over thirty publications, with "Extremal Problems in H p   Classes" being her most significant work. Translated from the Russian by Leonid Levant All credits to IA user  Quantum AI CONTENTS Preface Chapter 1. Elements of Vector Analysis Sec. 1.1. Some Concepts of Vector Analysis Sec. 1.2. Scalar Field Sec. 1.3. Work Done by a Vector Field Sec. 1.4. Flux of a Vector Field Sec. 1.5. Divergence Sec. 1.6. The Curl of a Vector Field Chapter 2. Special Kinds of Vector Fields Sec. 2.1. Potential Vector Field Sec. 2.2. Solenoidal Vector Field Sec. 2.3. Laplace’s Vector Field Sec. 2.4. Dirichlet Problem and Neumann Problem Sec. 2.5. Deriving Certain Equations of Mathematical Physics Chapter 3. Certain Concepts of Functional Analysis Sec. 3.1. Statement of Problems. Hölder’s and Minkowski's Inequalities Sec. 3.2. Metric Spaces Sec. 3.3. Completeness of Metric Spaces Sec. 3.4. Contraction Mapping Principle and Its Application Sec. 3.5. Compact Sets Chapter 4. Completely Continuous Operators in Normed Linear Spaces Sec. 4.1. Normed Linear Spaces Sec. 4.2. Continuous and Completely Continuous Operators Sec. 4.3. Schauder’s Theorem and Its Application Sec. 4.4. Iteration Method for Solving Fredholm’s Equation Chapter 5. Self-adjoint Operators in a Hilbert Space Sec. 5.1. Basic Concepts of a Hilbert Space Sec. 5.2. Self-adjoint Operators and Their Properties Sec. 5.3. Hilbert-Schmidt Theorem and Its Application Chapter 6. Fundamentals of the Calculus of Variations Sec. 6.1. Basic Notions Sec. 6.2. Extremum of a Functional Sec. 6.3. Variation Problems with Fixed Boundaries Sec. 6.4. Variation Problems Involving a Conditional Extremum Chapter 7. Certain Methods of Solving Variation Problems Sec. 7.1. Variation Problems with Moving Boundaries Sec. 7.2. Variation Problems Involving Functions of Several Variables Sec. 7.3. Connection of Variation Problems with Differential Equations Sec. 7.4. Direct Methods in the Calculus of Variations Chapter 8. Problems of Computation and Uniform Approximation of Functions Sec. 8.1. Errors Due to Approximate Calculations Sec. 8.2. Fundamentals of the Theory of Function Approximation Sec. 8.3. Polynomials of Best Approximation in Space a, b of rT Chapter 9. Interpolation and Its Application to Problems of Numerical Differentiation and Integration Sec. 9.1. Interpolation Sec. 9.2. Formulas for Numerical Differentiation and Integration. Error Estimates Sec. 9.3. Optimization Methods. Cubature Formulas Chapter 10. Numerical Methods of Solving Algebraic and Differential Equations Sec. 10.1. Systems of Linear Algebraic Equations Sec. 10.2. Solving Nonlinear Equations Sec. 10.3. Numerical Methods of Solving Differential Equations Sec. 10.4. Net-point Method

This article is from PLoS ONE , volume 9 . Abstract The metagenomic method directly sequences and analyses genome information from microbial communities. The main computational tasks for metagenomic analyses include taxonomical and functional structure analysis for all genomes in a microbial community (also referred to as a metagenomic sample). With the advancement of Next Generation Sequencing (NGS) techniques, the number of metagenomic samples and the data size for each sample are increasing rapidly. Current metagenomic analysis is both data- and computation- intensive, especially when there are many species in a metagenomic sample, and each has a large number of sequences. As such, metagenomic analyses require extensive computational power. The increasing analytical requirements further augment the challenges for computation analysis. In this work, we have proposed Parallel-META 2.0, a metagenomic analysis software package, to cope with such needs for efficient and fast analyses of taxonomical and functional structures for microbial communities. Parallel-META 2.0 is an extended and improved version of Parallel-META 1.0, which enhances the taxonomical analysis using multiple databases, improves computation efficiency by optimized parallel computing, and supports interactive visualization of results in multiple views. Furthermore, it enables functional analysis for metagenomic samples including short-reads assembly, gene prediction and functional annotation. Therefore, it could provide accurate taxonomical and functional analyses of the metagenomic samples in high-throughput manner and on large scale.

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The Advanced Instructional Design Advisor (AIDA) is an R and D project being conducted by the Armstrong Laboratory Human Resources Directorate and is aimed at producing automated instructional design for developers of computer-based instructional materials. The process of producing effective computer-based instructional materials is complex and time-consuming. Few experts exist to ensure the effectiveness of the process. The content of this paper addresses the major implications for instruction based on cognitive and educational research. Principles such as the ones contained in this paper would comprise a substantial pan of the knowledge base for the AIDA.

The world's demand for energy is increasing dramatically, but the best energy conversion systems operate at approximately 30% efficiency. One way to decrease energy loss is in the recovery of waste heat using thermoelectric (TE) generators. A TE generator is device that generates electricity by exploiting heat flow across a thermal gradient. The efficiency of a TE material for power generation and cooling is determined by the dimensionless Figure of Merit (ZT): ZT = S(exp. 2)sigmaT/?: where S is the Seebeck coefficient, sigma is the electrical conductivity, T is the absolute temperature, and ? is the thermal conductivity. The parameters are not physically independent, but intrinsically coupled since they are a function of the transport properties of electrons. Traditional research on TE materials has focused on synthesizing bulk semiconductor-type materials that have low thermal conductivity and high electrical conductivity affording ZT values of 1. The optimization of the s/? ratio is difficult to achieve using current material formats, as these material constants are complementary. Recent areas of research are focusing on using nanostructural artifacts that introduce specific dislocations and boundary conditions that scatter the phonons. This disrupts the physical link between thermal (phonon) and electrical (electron) transport. The result is that ? is decreased without decreasing s. These material formats give ZT values of up to 2 which represent approximately 18% energy gain from waste heat recovery. The next challenge in developing the next generation of TE materials with superior performance is to tailor the interconnected thermoelectric physical parameters of the material system. In order to approach this problem, the fundamental physics of each parameter S, sigma, and ? need to be physically understood in their context of electron/phonon interaction for the construction of new high ZT thermoelectric devices. Is it possible to overcome the physical limit imposed by of the effect of phonon lattice oscillation and energetic electrons towards thermal conductivity? Is the Seebeck coefficient, based on the difference in voltage over temperature gradient ( deltaV/deltaT), an intrinsic parameter of each material? All these parameters were manipulated using nano-bridge and twin-lattice structural concepts at the NASA Langley Research Center. This talk will review the current trend of TE research to optimize the ZT and discuss about new approaches on increasing ZT within functional limits of each parameter.

This article is from GMS Zeitschrift für Medizinische Ausbildung , volume 31 . Abstract Introduction: The decision to consolidate European higher education was reached by the Bologna Conference. Based on the Anglo-American system, a two-cycle degree program (Bachelor and Master) has been introduced. Subjects culminating in a state examination, such as Medicine and Dentistry, were excluded from this reform. Since the state examination is already comparable in its caliber to a Master’s degree in Medicine or Dentistry, only advanced Master’s degree programs with post-graduate specializations come into consideration for these subjects. In the field of dentistry numerous post-graduate study programs are increasingly coming into existence. Many different models and approaches are being pursued.Method: Since the 2004-2005 winter semester, the University of Greifswald has offered the Master’s degree program in Dental Functional Analysis and Therapy. Two and a half years in duration, this program is structured to allow program participation while working and targets licensed dentists who wish to attain certified skills for the future in state-of-the-art functional analysis and therapy.Aim: The design of this post-graduate program and the initial results of the evaluation by alumni are presented here.Conclusion: Our experiences show that the conceptual idea of an advanced Master’s program has proved successful. The program covers a specialty which leads to increased confidence in handling challenging patient cases. The sharing of experiences among colleagues was evaluated as being especially important.

This article is from GMS Zeitschrift für Medizinische Ausbildung , volume 31 . Abstract Introduction: The decision to consolidate European higher education was reached by the Bologna Conference. Based on the Anglo-American system, a two-cycle degree program (Bachelor and Master) has been introduced. Subjects culminating in a state examination, such as Medicine and Dentistry, were excluded from this reform. Since the state examination is already comparable in its caliber to a Master’s degree in Medicine or Dentistry, only advanced Master’s degree programs with post-graduate specializations come into consideration for these subjects. In the field of dentistry numerous post-graduate study programs are increasingly coming into existence. Many different models and approaches are being pursued.Method: Since the 2004-2005 winter semester, the University of Greifswald has offered the Master’s degree program in Dental Functional Analysis and Therapy. Two and a half years in duration, this program is structured to allow program participation while working and targets licensed dentists who wish to attain certified skills for the future in state-of-the-art functional analysis and therapy.Aim: The design of this post-graduate program and the initial results of the evaluation by alumni are presented here.Conclusion: Our experiences show that the conceptual idea of an advanced Master’s program has proved successful. The program covers a specialty which leads to increased confidence in handling challenging patient cases. The sharing of experiences among colleagues was evaluated as being especially important.

This is the sequel to Mathematical Analysis (Advanced Topics) Part I. General Functional Series and Their Application. It is a treatment of some of the most widespread methods of mathematical and functional analysis. The feature of this study aid is that it contains methods of functional analysis not included in textbooks for engineering students.  This enables the authors to set forth approximate calculations using the methods of functional analysis and to present modern mathematical methods for solving applied problems.  The book gives an application of vector analysis to the study of various vector fields. Certain elements of functional analysis are applied to the methods of a fixed point and also to the solution of Fredholm’s equations. In approximate computations, the student’s attention is drawn to numerical methods of mathematical analysis which can be realized on  a computer. The material contained in Chapters 3, 4, 5, 8, and 9 may be used for lectures for individual specialities. Chapters 1, 2, 6, and 7 were written by V. M. Terpigoreva, Chapters 3, 4, and 5 by A. V. Efimov, and Chapters 8, 9, and 10 by Yu. G. Zolotarev.  Using the same layout as in Part 1, each section has its own enumeration of the theorems and formulas. When referring to a formula (theorem) in the same section, only the formula (theorem) number is given, for instance, (5). When referring to something in the same chapter, the number of the formula (theorem) is preceded by the chapter number, e.g.  (2.5), and when referring to a formula (theorem) from another chapter, three numbers are given: the chapter number, the section number, and the formula (theorem) number, for example, (3, 2, 5).  The authors are grateful to the staff of the Department of Higher Mathematics at the Moscow Institute of Electronic Technology for their useful discussions that helped to improve the manuscript.  Special thanks are due to Professors V. A. Trenogin and S. I. Pokhozhaev, and Associate Professors M. L. Krasnov, A.I. Kiselev, A.L. Pavlov, and A. M. Sedletsky for the valuable suggestions and remarks they made when reviewing the manuscript.  Invaluable assistance in editing and preparing the manuscript was rendered by A. I. Seliverstova, L. V. Lapenko, and S. A. Fomina.