295 research outputs found

    "Rotterdam econometrics": publications of the econometric institute 1956-2005

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    This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005

    On Some Quadratic Algebras I 12\frac{1}{2}: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials

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    We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang-Baxter equations. One can find more details about the content of present paper in Extended Abstract.Comment: Dedicated to the memory of Alain Lascoux (1944-2013). Preprint RIMS-1817, 172 page

    International Symposium on Mathematics, Quantum Theory, and Cryptography

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    This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography

    International Symposium on Mathematics, Quantum Theory, and Cryptography

    Get PDF
    This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography

    The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals

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    Dimensionally-regulated Feynman integrals are a cornerstone of all perturbative computations in quantum field theory. They are known to exhibit a rich mathematical structure, which has led to the development of powerful new techniques for their computation. We review some of the most recent advances in our understanding of the analytic structure of multiloop Feynman integrals in dimensional regularisation. In particular, we give an overview of modern approaches to computing Feynman integrals using differential equations, and we discuss some of the properties of the functions that appear in the solutions. We then review how dimensional regularisation has a natural mathematical interpretation in terms of the theory of twisted cohomology groups, and how many of the well-known ideas about Feynman integrals arise naturally in this context. This is Chapter 3 of a series of review articles on scattering amplitudes, of which Chapter 0 [arXiv:2203.13011] presents an overview and Chapter 4 [arXiv:2203.13015] contains closely related topics.Comment: 62 pages, see also the overview article arXiv:2203.13011. v3: journal versio

    µ-Hyperholomorphic Function Theory in R³: Geometric Mapping Properties and Applications

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    This thesis applies the theory of \psi-hyperholomorphic functions dened in R^3 with values in the set of paravectors, which is identified with the Eucledian space R^3, to tackle some problems in theory and practice: geometric mapping properties, additive decompositions of harmonic functions and applications in the theory of linear elasticity

    Preconditioned fast solvers for large linear systems with specific sparse and/or Toeplitz-like structures and applications

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    In this thesis, the design of the preconditioners we propose starts from applications instead of treating the problem in a completely general way. The reason is that not all types of linear systems can be addressed with the same tools. In this sense, the techniques for designing efficient iterative solvers depends mostly on properties inherited from the continuous problem, that has originated the discretized sequence of matrices. Classical examples are locality, isotropy in the PDE context, whose discrete counterparts are sparsity and matrices constant along the diagonals, respectively. Therefore, it is often important to take into account the properties of the originating continuous model for obtaining better performances and for providing an accurate convergence analysis. We consider linear systems that arise in the solution of both linear and nonlinear partial differential equation of both integer and fractional type. For the latter case, an introduction to both the theory and the numerical treatment is given. All the algorithms and the strategies presented in this thesis are developed having in mind their parallel implementation. In particular, we consider the processor-co-processor framework, in which the main part of the computation is performed on a Graphics Processing Unit (GPU) accelerator. In Part I we introduce our proposal for sparse approximate inverse preconditioners for either the solution of time-dependent Partial Differential Equations (PDEs), Chapter 3, and Fractional Differential Equations (FDEs), containing both classical and fractional terms, Chapter 5. More precisely, we propose a new technique for updating preconditioners for dealing with sequences of linear systems for PDEs and FDEs, that can be used also to compute matrix functions of large matrices via quadrature formula in Chapter 4 and for optimal control of FDEs in Chapter 6. At last, in Part II, we consider structured preconditioners for quasi-Toeplitz systems. The focus is towards the numerical treatment of discretized convection-diffusion equations in Chapter 7 and on the solution of FDEs with linear multistep formula in boundary value form in Chapter 8

    Annales Mathematicae et Informaticae (55.)

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    High-precision scattering amplitudes for LHC phenomenology

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    In this work, we consider scattering amplitudes relevant for high-precision Large Hadron Collider (LHC) phenomenology. We analyse the general structure of amplitudes, and we review state-of-the-art methods for computing them. We discuss advantages and shortcomings of these methods, and we point out the bottlenecks in modern amplitude computations. As a practical illustration, we present frontier applications relevant for multi-loop multi-scale processes. We compute the helicity amplitudes for diphoton production in gluon fusion and photon+jet production in proton scattering in three-loop massless Quantum Chromodynamics (QCD). We have adopted a new projector-based prescription to compute helicity amplitudes in the 't Hooft-Veltman scheme. We also rederived the minimal set of independent Feynman integrals for this problem using the differential equations method, and we confirmed their intricate analytic properties. By employing modern methods for integral reduction, we provide the final results in a compact form, which is appropriate for efficient numerical evaluation. Beyond QCD, we have computed the two-loop mixed QCD-electroweak amplitudes for Z+jet production in proton scattering in light-quark-initiated channels, without closed fermion loops. This process provides important insight into the high-precision studies of the Standard Model, as well as into Dark Matter searches at the LHC. We have employed a numerical approach based on high-precision evaluation of Feynman integrals with the modern Auxiliary Mass Flow method. The obtained numerical results in all relevant partonic channels are evaluated on a two-dimensional grid appropriate for further phenomenological applications.Comment: DPhil thesis, University of Oxford: 158 pages, 52 figures, 4 tables, based on arXiv:2211.13595, arXiv:2212.06287, and arXiv:2212.1406

    Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 04. bis 06.07. 2012, Bauhaus-Universität Weimar

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    The 19th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 4th till 6th July 2012. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference
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