# PDF Number Theoretic Methods: Future Trends (Developments in Mathematics)

## Proof Theory on the eve of Year 2000

Procedures for the approval of a proposal for a Session-Workshop or Minisymposium. The organizer must provide: 1. A proposal for the organization of a Session-Workshop or Minisymposium. A short CV. Information about the procedures which will be followed for the promotion of that Session-Workshop or Minisymposium the organizer is responsible for the promotion. Attention Note: The maximum number of papers per author is four 4 After the approval, the organizer will be the person responsible for the selection of the papers. If a Symposium consists of at least 10 registrations, the organizer will be granted free registration and have a part of the accomodation expenses covered.

If a participant wants to send a paper to a Symposium mentioned below, please use the e-mail address es of the organizer s. It represents one of the largest and most successful activities of ICNAAM with a strong commitment to research and development within the academic community. Since its start, the focus of the symposium is numerical mathematics for fluid flow problems and related topics.

This Symposium on Advanced Computation and Information in Natural and Applied Sciences focusses on architectures and methods for high end computational and numerical applications. Up to date computing and information systems software engineering, communication, and architectures are an undispensable tool for progress in various scientific fields.

We invite scientists and engineers from academia and industry using and implementing computation and information systems, High Performance Computing, Cloud Computing, and Distributed Computing for scientific research, engineering, education, and future internet applications. Authors are invited to submit original unpublished results which are not under review in any other conference or journal, to the peer review for publication and presentation, in the following, but not limited to, the following topic areas of this symposium.

Deadline for submitting your fully formatted 4 page paper for peer review: May 6, final date. Deadline for improved paper and sources: June 20, final date. Other deadlines and relevant information, e. Difference Equation or discrete dynamical system is a very interesting subject because they are central to the analysis of many models of dynamic programming and we can derive many complex behavior based on simple formulation. The aim of this symposium is to discuss the new developments in the field of difference equations, and their applications.

Topics of interest include but not limited to:.

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Martin Kotyrba — Chairman 1Assoc. Eva Volna — Vice-Chairman.

Luigi Brugnano, Dipartimento di Matematica "U. Ewa B. Alexander N. Marina A. Martin Krejsa, Ph. Petr S. Elena N. Fernanda A. Ferreira and Prof. Sancho I, , Vila do Conde, Portugal. Professor Dr. Computational Mathematics is a hybrid topic that sits at the intersection of applied mathematics and computer science.

It puts on show the power of computers for solving industrial-size mathematical problems. The authors are invited to submit original research articles to stimulate the continuing efforts in numerical approximation of mathematical problems and related theories. Rua Sergio Buarque de Holanda, CEP Muhammed I. The goal of the Symposium is to bring together all the researchers working in various fields of Mathematics, Mathematical Physics-Engineering and related areas such as Analysis, Non-linear Analysis, Integral transforms, Number Theory, p-adic Analysis and Applied Algebra, Special Functions, q-analysis and Discrete Mathematics, Probability and Statistics, Mathematical Physics, Mathematical modeling and their applications.

Our main aim is also to bring together theoretical, numerical and apply analyst, number theorists, quantum physicist working in the areas of generating functions of the special numbers and polynomials and their applications. All of the participants will likely lead to significant uncover new connections on these fields which are special numbers and polynomials, and also the family of zeta functions and L-functions.

Organizers: Prof. Calogero Orlando, Dr. Antonio Esposito, Dr. E-mail: calogero. MPAS Symposium focuses on new results of aerospace science researches carried out by using mathematical techniques. The aim of the Session is to collect relevant papers dealing with important approaches of applied mathematics, which have relevance to the engineering in the field of Aerodynamics and Fluid dynamics, Propulsion, Materials and Structures, Aerospace Systems, Flight Mechanics and Control, Space Systems and Missions in order to create new collaborations between mathematicians and aerospace engineers.

Papers must be characterized by innovative models, methods and approaches that can found practical application to the engineering field or by new useful application of existing models to solve engineering problems. Alexander P. Krishchenko and Prof. Georgy N. Krishchenko ; fn2 bmstu. Kuvyrkin link sends e-mail. Fabio Russo and Prof. Francesco Napolitano and Dr.

Mihai Viteazu, no. Starting from the reality that there is always more to discover about nonlinear dynamical systems, this mini-symposium aims to bring together researchers concerned with applying the Optimal Homotopy Asymptotic Approach to nonlinear and strongly nonlinear dynamical systems from various fields of engineering. It is expected to be emphasized new developments and improvements of this approach with applications in classical mechanics, fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and other engineering branches where nonlinear dynamical systems are involved.

Various emerging topics in Statistics and Statistical Modelling will be addressed. This Symposium is dedicated to the geomatics approaches used for surveying, monitoring and modeling the territory, both with classical techniques and innovative technologies. Particular attention will be given to the use of free and open source information technologies GIS software, DBMS, photogrammetry, etc. This session will allow attendees to review and share knowledge and experience about environmental monitoring and modelling, reinforcing the cooperation between applied mathematics, engineering, environmental science, and remote sensing.

Take Ionescu, Romania and Dr. Popov, St. Petersburg, , Russia. Development of nano-science resulted in creation and using of many new objects and structures: grapheme, nanotubes, fullerene, quantum dots, quantum wires, etc. To study the properties of such structures, processes of its constructions, one should develop new mathematical methods or modify the existing approaches.

New effective mathematical models are of special interest. The goal of the mini-symposium is to bring together mathematicians and theoretical physicists working in the field. Papers related to mathematical methods and models for description of mechanical, electronic, magnetic or optical properties quantum or classical of nanosystems are welcome. China, Prof. China, Dr. The focus of the symposium is on the theory of multi-armed bandits, neural networks, deep learning, and reinforcement learning in addition to their applications in engineering, including but not limited to representation models, computational biology, automatic speech recognition, image recognition, visual art processing, drug discovery and toxicology, customer relationship management, recommendation systems, medical Image Analysis, mobile advertising, image restoration, financial fraud detection, bioinformatics, molecular dynamics, coarse-graining, natural language processing, etc.

Although the main focus of this special issue is on neural network, deep learning, and reinforcement learning, it also includes other machine learning topics including but not limited to decision trees, support vector machines, Bayesian models, Genetic algorithms and their applications in supervised and semi-supervised learning, unsupervised learning, feature learning, anomaly detection, sparse dictionary learning, association rules, fairness in learning, prediction models, regression, online algorithms, ranking algorithms, recommendation systems, Bayesian inference, Bayesian prediction, hypothesis learning, risk minimization, regularization and stability, multi-class clustering, Bayesian SVM, evolutionary algorithms, and stochastic optimization.

All researchers in the fields of electrical and computer engineering, computer science, mathematics, physics, civil engineering, biotechnology, mechanical engineering, chemistry, biology, medical, humanities, agriculture, horticulture, forestry, animation and multimedia are encouraged to submit their work at this symposium as long as they take advantage of multi-armed bandits, neural networks, deep learning, reinforcement learning, and any other machine learning tools in their work. COM ; QQ. COM link sends e-mail. Skip to main content. Procedures for the approval of a proposal for a Session-Workshop or Minisymposium The organizer must provide: 1.

Such processes are of great interest for the fields such as plasma physics, aerospace engineering, astrophysics, chemical engineering, etc. The basic objects of study are "Elliptic Curves" and "Modular Forms". The faculty group is involved in the development, analysis and application of efficient and robust algorithms for solving challenging problems arising in several applied areas.

This encompasses a very high level of computation that requires software skills of the highest order and parallel computing as well. Dutt, B. Finding combinatorially interesting bases for certain invariant theoretic spaces associated to classical algebraic groups. Such bases lead to various modular representation theoretic consequences as well. Classification of nilpotent and unipotent orbits of semisimple algebraic groups and its consequences.

Faculty : S. Category theory and logic, especially model theory, provide languages to talk about almost all areas of pure mathematics and to study their interconnections. For example, a model of the theory of groups in the category of topological spaces is a topological group. My main research interest in this area lies in the category-theoretic syntax-semantics dualities.

On the model theory side, computation and study of algebraic invariants, namely the the K-groups, associated with structures that classify the collections of sets definable in the structure is also my area of interest. Faculty : Amit Kuber. In everyday discourse, we place a grid over reality, the grid being typically induced by attributes.

Then pieces of data having the same values for a set of attributes, cannot be distinguished. As a result, our concepts, generally, are not definable in terms of the grid. RST prescribes approximations to describe such concepts, and there may be several concepts with the same approximations describing them. RST thus serves as a means for reasoning with objects and concepts that are rendered indiscernible, due to incomplete information about the domain of discourse.

A major concern here is to look for appropriate formal logical frameworks to represent reasoning in RST. Inherent modalities point to the domain of modal logics.

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It is thus that we have some modal systems capturing 'rough truth', and different versions of 'rough modus ponens'. Modal logics also come in while studying dynamic aspects of RST. Data is presented in RST with the help of an information system, which may be complete, incomplete or non-deterministic. One then investigates sequences of information systems that evolve with time, or which arise from multiple sources agents , and notions of information updates in the context.

New temporal and quantified modal logics, and logics for information systems along with their 'dynamic' versions, have surfaced during this study. Algebraic studies of structures that have arisen in the course of RST investigations constitute an important part of the research. Of special interest is a category-theoretic study of rough sets, and in fact, of concepts in a general framework of 'granulations'.

Other applications of RST are also being studied, e. Techniques for computation of 'minimal' sets of attributes required for classification reducts of objects also hold interest. On another side, there is interest in the use of modal systems for reasoning with beliefs revealed by agents. The primary interest is in studying equivariant algebraic topology and homotopy theory with emphasis on unstable homotopy. Faculty : Debasis Sen,.

The interest is in studying Abelian Polyhedral Maps and Polyhedral Manifolds, in particular the aim is to minimize the total number of faces and flag numbers in all polyhedral manifolds of the same p. Faculty : N. The main interest is in Knot Theory and its Applications. This includes the study of amphicheirality, the study of closed braids, and the knot polynomials, specially the Jones polynomial. Work in this area involves relatively hyperbolic groups and Cannon-Thurston maps between relatively hyperbolic boundaries.

Mapping Class Groups are also explored. Faculty : Abhijit Pal. We are interested in the construction of new examples of non-Kahler complex manifolds. We aim also at answering the question of existence of almost-complex structures on certain even dimension real manifolds. Characteristic classes of vector bundles over certain spaces are also studied.

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Faculty : Ajay Singh Thakur. The central question we study here to find combinatorial descriptions of moduli spaces of closed and oriented hyperbolic surfaces. Also, we study isometric embedding of metric graphs on surfaces of following types: a quasi-essential on closed and oriented hyperbolic surfaces b non-compact surfaces, where complementary regions are punctured discs, c on half-translation surfaces etc.

Faculty : Bidyut Sanki. We are interested to study the configuration of systolic geodesics i. Also, we are interested in studying the maximal surfaces and deformations on hyperbolic surfaces of finite type to increase systolic lengths. We study configuration of graphs, curves, arcs on surfaces, fillings, action of mapping class groups on graphs on surfaces, minimal graphs of higher genera. Detection of different features in terms of shape of non-parametric regression functions are studied; asymptotic distributions of the proposed estimators along with their robustness properties of the shape-restricted regression function are also investigated.

Apart from this, work on the test of independence for more than two random variables is pursued.

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The manner in which a component or system improves or deteriorates with time can be described by concepts of aging. Various aging notions have been proposed in the literature. Similarly lifetimes of two different systems can be compared using the concepts of stochastic orders between the probability distributions of corresponding random lifetimes. Various stochastic orders between probability distributions have been defined in the literature. We study the concepts of aging and stochastic orders for various coherent systems.

In many situations, the performance of a system can be improved by introducing some kind of redundancy into the system. The problem of allocating redundant components to the components of a coherent system, in order to optimize its reliability or some other system performance characteristic, is of considerable interest in reliability engineering. These problems often lead to interesting theoretical results in Probability Theory. We study the problem of optimally allocating spares to the components of various coherent systems, in order to optimize their reliability or some other system performance characteristic.

Performances of systems arising out of different allocations are studied using concepts of aging and stochastic orders. Estimation of entropies of molecules is an important problem in molecular sciences. A commonly used method by molecular scientist is based on the assumption of a multivariate normal distribution for the internal molecular coordinates.

For the multivariate normal distribution, we have proposed various estimators of entropy and established their optimum properties. The assumption of a multivariate normal distribution for the internal coordinates of molecules is adequate when the temperature at which the molecule is studied is low, and thus the fluctuations in internal coordinates are small. However, at higher temperatures, the multivariate normal distribution is inadequate as the dihedral angles at higher temperatures exhibit multimodes and skewness in their distribution. Moreover the internal coordinates of molecules are circular variables and thus the assumption of multivariate normality is inappropriate.

Therefore a nonparametric and circular statistic approach to the problem of estimation of entropy is desirable. We have adopted a circular nonparametric approach for estimating entropy of a molecule. This approach is getting a lot of attention among molecular scientists.

About fifty years ago statistical inference problems were first formulated in the now-familiar "Ranking and Selection" framework. Ranking and selection problems broadly deal with the goal of ordering of different populations in terms of unknown parameters associated with them. We deal with the following aspects of Ranking and Selection Problems Obtaining optimal ranking and selection procedures using decision theoretic approach;2.

Obtaining optimal ranking and selection procedures under heteroscedasticity;3. Estimation of ranked parameters when the ranking between parameters is not known apriori;5. Estimation of random parameters of the populations selected using a given decision rule for ranking and selection problems. Neeraj Mishra. In many practical situations, it is natural to restrict the parameter space. This additional information of restricted parameter space can be intelligently used to derive estimators that improve upon the standard natural estimators, meant for the case of unrestricted parameter space.

We deal with the problems of estimation parameters of one or more populations when it is known apriori that some or all of them satisfy certain restrictions, leading to the consideration of restricted parameter space. The goal is to find estimators that improve upon the standard natural estimators, meant for the case of unrestricted parameter space.

We also deal with the decision theoretic aspects of this problem. The outcome of any experiment depends on several variables and such dependence involves some randomness which can be characterized by a statistical model. The statistical tools in regression analysis help in determining such relationships based on the sample experimental data. This helps further in describing the behaviour of the process involved in experiment. The tools in regression analysis can be applied in social sciences, basic sciences, engineering sciences, medical sciences etc.

The unknown and unspecified form of relationship among the variables can be linear as well as nonlinear which is to be determined on the basis of a sample of experimental data only.

## Read PDF Number Theoretic Methods: Future Trends (Developments in Mathematics)

The tools in regression analysis help in the determination of such relationships under some standard statistical assumptions. Both teams did this by exploiting recent results — different ones in each case — about patterns in the spacing of prime numbers. The new work has no immediate applications, although understanding large prime gaps could ultimately have implications for cryptography algorithms. Tao has a more personal motivation for studying prime gaps.

Tao is toying with the idea of creating a new prize for anyone who makes a big enough improvement on the latest result, he said. The recent progress in understanding both small and large prime gaps has spawned a generation of number theorists who feel that anything is possible, Granville said. Original story reprinted with permission from Quanta Magazine , an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.

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