Summation Formulas Involving Binomial Coefficients, Harmonic Numbers, and Generalized Harmonic Numbers

A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theoretical physics. Here we show how one can obtain further interesting identities about certain finite series involving binomial coefficients, harmonic numbers and generalized harmonic numbers by applying the usual differential operator to a known identity. MSC:11M06, 33B15, 33E20, 11M35, 11M41, 40C15.

The number of women physicists doing research in Armenia is far less than the number of men, because women put their family and children ahead of their careers. Only a small number of women physicists who try to combine family life and career are successful. Armenia is a small country with few research positions; in spite of this there are several women physicists in Armenia. They are working very well in various areas of physics such as theoretical physics, nuclear physics, elementary particle physics, biophysics, and solid-state physics. Due to hard and fruitful work, some women physicists occupy high positions; for example, A. Danagulyan is the Chair of Nuclear Physics of Yerevan State University. In the three years since the First IUPAP International Conference on Women in Physics, female scientists of Armenia have worked very effectively. Four defended their PhD theses (Candidate) and one defended her Doctorate thesis during this period. Many papers of female scientists were presented at international conferences and printed in refereed journals. The women scientists at Yerevan State University (Dr. Prof. A. Danagulyan, Dr. A. Balabekyan, PhD student J. Drnoyan, and young researcher G. Hovhannisyan) have participated in six international conferences devoted to the problems of nuclear physics: International Seminar on Heavy Ion Physics. Joint Institute for Nuclear Research, Dubna, 2002 25th International Colloquium on Group Theoretical Methods in Physics, Cocoyoc, Mexico 2004 52nd, 53rd, and 54th International Conference on Nuclear Spectroscopy and Nuclear Structure, Moscow 2002, St. Petersburg 2003, and Belgorod 2004 VI Conference of Young Scientists of JINR, Dubna 2002 The main results are presented in 11 scientific papers published in refereed journals such as Nuclear Physics and Physics of Atomic Nuclei. Along with their research activities, these women scientists also have wide teaching experience. They are lecturers in nuclear physics, nuclear reactions, and elementary particle physics. Gohar Haroutunyan, the Doctor of Science at the Chair of Theoretical Physics of Yerevan State University, investigates the theory of gravitation and its astrophysical application. Six of her papers were published from 2002 to 2005. She teaches theoretical mechanics, statistical physics, and Green’s functions. Dr. Prof. Yeva Dalyan is a specialist in macromolecular physics, the physics of nucleic acids, and structural biology, and works in molecular pharmacology as well. Her papers are published in Biomolecular Structure and Dynamics, Experimental and Molecular Medicine, Molecular and Cellular Proteomics, and Biophysics. Dr. Prof. Dalyan reported the results of her work at the international conference “URM-2004” in Yerevan in 2004 and at the “International Symposium on Hydration and Thermodynamics of Molecular Recognition” in Armenia in 2005. She teaches courses in molecular physics, introduction to biophysics, and the physics of proteins and nucleic acids. Two female scientists (Dr. A. Djotyan and Sh. Gasparyan) participated in the International Women’s Conference on BIEN-Technology in Daejeon, Korea, in 2003 and presented two scientific reports. The papers are included in the proceedings of the conference in a special issue of the journal Key Engineering Materials. Dr. I.G. Aznauryan (Yerevan Institute of Physics) works in the field of quantum chromodynamics (QCD), which is the fundamental theory accepted now for the description of strong interactions of elementary particles. Dr. Aznauryan works in close cooperation with experimental physicists at Jefferson Lab in the United States. Her investigation of experimental data obtained at Jefferson Lab led to the determination that up to a momentum transfer of 5 GeV, there is no indication of an approaching perturbative region of QCD. The results of her work were published in Physical Review C67 and C68 (2003) and C71 (2005).

This annual conference was established at the National Nuclear Research University – Moscow Engineering Institute in the year 2012. The scope was initially on mathematical physics and mathematical modelling, while since this year theoretical physics was also included. The Conference was organized by three leading departments of the MEPhI in the field of theoretical and mathematical physics.Each year, more than 100 participants from different countries including Belorussia, Czech Republic, France, Great Britain, Japan, Moldova, Russia, Slovakia, Spain, Sweden and the USA take part in the Conference with oral talks.The aim of this conference is to bring together researchers with interests in: Analytical Theory of Differential Equations, Interaction of Radiation With Matter and Physics of Extreme Light, Nuclear Physics and Theory of Elementary Particles, Optimization Problems, Solid Mechanics, Soft Matter and Interdisciplinary Physics, Fluid Mechanics, Mathematical Modelling, Time Series.Nikolay A. KudryashovOleg V. NagornovSergey V. Popruzhenko

Chapter 1 - Introduction

String-matching algorithm is one of the most researched algorithms in computer science which has become an important factor in many technologies. This field aims at utilizing the least time and resources to find desired sequence of character in complex data content. The most classical and famous string-search algorithms are Knuth-Morris-Pratt (KMP) algorithm and Boyer-Moore (DM) algorithm. These two algorithms provide efficient heuristic jump rules by prefix or suffix. Bitap algorithm was the first to introduce bit-parallelism into string-matching field. Backward Non-Deterministic DAWG Matching (BNDM) algorithm is a modern practical algorithm that is an outstanding combination of theoretical research and practical application. Those meaningful algorithms play a guiding role in future research in string-search algorithm to improve the average performance of the algorithm and reduce resource consumption.

A new LQR-type optimal distributed linear averaging (ODLA) problem is presented in this paper. This problem is motivated from the distributed averaging problem which arises in the context of distributed algorithms in computer science and coordination of groups of autonomous agents in engineering. The aim of the ODLA problem is to compute the average of the initial values at nodes of a graph through an LQR-type optimal distributed algorithm in which the nodes in the graph can only communicate with their neighbors. Optimality is given by a minimization problem of an LQR-type quadratic cost functional under finite horizon. We show that this problem has a very close relationship with the notion of semistability. By developing new necessary and sufficient conditions for semistability of linear discrete-time systems, we convert the original ODLA problem into two equivalent optimization problems. One of them is a convex optimization problem and can be solved by using semidefinite programming methods.

In this paper, we present a learning support system DASE-E to help students understand fundamental concepts of distributed algorithms in computer science. DASE-E is a collaborative learning system, in which the task of students is to devise a distributed algorithm. DASE-E offers a set of small wireless terminals with accelerometers. Each student plays the role of a process with a terminal, according to the algorithm that students devised. Each terminal enables a student to take physical actions that control the behavior of a process in the simulator. After the role playing simulation is finished, students discuss their activity played back on a screen. We implemented the system for learning distributed leader election algorithms, had a trial exercise in our research group, and we confirmed that it is effective to learn the critical part of distributed systems and algorithms.

In the present paper the attempt is made for the first time to formalize the modern theory of elementary particles based on the structuralist approach. To this end, the description within the scope of the so-called standard model is considered. In the physics of elementary particles the term ‘standard model’ denotes the summary of theories which describe the various elementary building blocks of matter as well as their interactions between each other. This model represents one of the most successful theories in physics, particularly because of the impressive experimental confirmation. Hence a structuralist reconstruction of it is a challenging task.

Behram N. Kursunoglu

This report discusses the following topics: Task A: theoretical elementary particle physics; Task B: experimental elementary particle physics; Task C: axion project; Task G: experimental research in collider physics; and Task S: computer acquisition. Selected papers are indexed separately for inclusion in the Energy Science and Technology Database.

Science sets itself apart from other paths to truth by recognizing that even its greate practitioners sometimes err.

INTRODUCTION Physics and metaphysics are two distinct occupations of human beings, and not long ago a lot of effort was invested into keeping them strictly apart. Nowadays, however, the situation seems to be changing. A couple of years ago, an international conference was organised at Cambridge, UK, the proceedings of which bear the title ‘Physics Meets Philosophy at the Planck Scale’. What is special about the Planck Scale that physics and philosophy (of which metaphysics is an essential part) seem to have something to tell to each other? In physicists' jargon the ‘Planck Scale’ or the ‘Planck era’ means either the most fundamental level of the physical Universe, or an edge at which our present theories of physics break down (this is why the Planck era is also called the Planck threshold). Currently, these two meanings are almost synonymous since the fundamental theory of physics lies beyond the reach of our well-founded physical theories and models. There are two directions along which we could approach the Planck era. We can either adopt the path followed by cosmologists, or that followed by elementary particle physicists. In cosmology, one tries to reconstruct the history of the Universe starting from our present era as far backward in time as possible. As one moves in this direction, the Universe contracts and becomes denser and denser, till one reaches a density of the order of 10 95 g/cm 3 , and then one finds oneself at the Planck era.

Professional journal advertisements, email newsletters, and university marketing now advertise numerous educational and research programs in computational physics, computational biology, and other fields where computation is an essential element of the discipline. These programs all have very recent origins, made possible by the exponential growth in the availability of compute power. In this presentation, I describe some milestones in my own experience as a person living through and participating in the birth of computational science - especially the contributions of computing to scientific theory and understanding. I began my history with analog computing, learned numerical methods by manual computations of derivatives and integrals, learned to program an early vacuum tube computer, and experienced challenges in finding acceptance for computer methods in traditional biomedical disciplines. Keywords—computational science, history of science, biomedicine, cardiac electrophysiology, analog computer, numerical methods. 1. Introduction : Computers are now making major contributions to all fields of science, from fundamental particle physics through chemistry, biology, and medicine, to the social sciences and cosmology. A major part of the computer contribution to these fields is related to data: acquisition, organization, presentation, sharing, and pattern recognition in data. Computers are also changing scientific theory by making it possible to explore and evaluate models that are much more realistic and complex than could be considered with only analytic and hand calculations. Computational science did not spring into existence fully developed, but experienced birth and development like a living system. In some scientific fields, the contribution of computing to theory is still in early stages. Participants needed to learn the language and techniques of computing and mathematics as well as those in their own science. In this presentation, I describe several milestones in my own personal history of development as a computational scientist. My story begins in 1956 when I entered Pacific Union College, a small private liberal arts campus in Northern California, to study physics. That year was well before personal computers existed and the few large computers that had been built were applied almost exclusively to business data. Since then, the available compute speed has increased by at least 7 to 9 orders of magnitude - a staggering increase in processing power!

M Chretien and S S Schweber (Eds) London: Gordon and Breach 1970 Vol 1 pp 448 price £14.75 cloth £6.25 paper Vol 2 pp 448 price £13.75 cloth £6.25 paper These volumes contain the lectures given at the 1967 Brandeis University summer institute in theoretical physics. The level of the lectures is introductory in the sense that they begin at a point where graduate students should be able to follow.

The present article considers Giulio Racah’s contributions to general physical theory and his establishment of theoretical physics as a discipline in Israel. Racah developed mathematical methods that are based on tensor operators and continuous groups. These methods revolutionized spectroscopy. Currently, these are essential research tools in atomic, nuclear and elementary particle physics. He himself applied them to modernizing theoretical atomic spectroscopy. Racah laid the foundations of theoretical physics in Israel. He educated several generations of Israeli physicists, and put Israel on the world map of physics.