27,221 results
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2. Remarks on a paper by El-Guindy and Papanikolas
- Author
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Takehiro Hasegawa
- Subjects
Pure mathematics ,Algebra and Number Theory ,010102 general mathematics ,0102 computer and information sciences ,01 natural sciences ,Continuation ,symbols.namesake ,Number theory ,010201 computation theory & mathematics ,Fourier analysis ,symbols ,0101 mathematics ,Abelian group ,Mathematics - Abstract
There are similarities between Drinfeld modules and abelian varieties. The purpose of this paper is to investigate these similarities in terms of supersingularity. More specifically, we provide explicit formulas of Hasse invariants (or, equivalently, of supersingular polynomials) for Drinfeld modules, which is a continuation of the 2013 paper by Ahmad El-Guindy and Matthew A. Papanikolas. We present several supersingular Drinfeld modules as an application.
- Published
- 2020
3. Properties of a novel stochastic rock–paper–scissors dynamics
- Author
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Hailing Wang, Zuxiong Li, Zhusong Chu, and Jun Cheng
- Subjects
Lyapunov function ,education.field_of_study ,Stochastic modelling ,Applied Mathematics ,Dynamics (mechanics) ,Population ,01 natural sciences ,010305 fluids & plasmas ,Computational Mathematics ,symbols.namesake ,Bounded function ,0103 physical sciences ,Theory of computation ,symbols ,Applied mathematics ,010306 general physics ,education ,Mathematics - Abstract
This paper is concerned with some stochastic properties of a novel rock–paper–scissors model. Firstly, the global existence of an unique positive solution of the stochastic model is obtained. Then we demonstrate the positive solution of the model is stochastically bounded. Besides, some sufficient conditions for population to be stochastically permanent and extinct are derived with the use of some appropriate Lyapunov functions. At last, some numerical simulations are carried out to illustrate our theoretical analysis results.
- Published
- 2020
4. Folding a Paper Strip to Minimize Thickness
- Author
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Hiro Ito, Erik D. Demaine, Anna Lubiw, David Eppstein, Ryuhei Uehara, Yushi Uno, Adam Hesterberg, Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science, and Massachusetts Institute of Technology. Department of Mathematics
- Subjects
Computational Geometry (cs.CG) ,FOS: Computer and information sciences ,paper folding ,0102 computer and information sciences ,02 engineering and technology ,Topology ,01 natural sciences ,Theoretical Computer Science ,NP completeness ,symbols.namesake ,Exponential growth ,crease width ,Computer Science - Data Structures and Algorithms ,0202 electrical engineering, electronic engineering, information engineering ,Discrete Mathematics and Combinatorics ,Data Structures and Algorithms (cs.DS) ,Mathematics ,NP-complete ,computational origami ,Planar graph ,rigid origami ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,symbols ,Computer Science - Computational Geometry ,020201 artificial intelligence & image processing ,linkage ,optimization problem - Abstract
In this paper, we study how to fold a specified origami crease pattern in order to minimize the impact of paper thickness. Specifically, origami designs are often expressed by a mountain-valley pattern (plane graph of creases with relative fold orientations), but in general this specification is consistent with exponentially many possible folded states. We analyze the complexity of finding the best consistent folded state according to twometrics:minimizing the total number of layers in the folded state (so that a “flat folding” is indeed close toflat), andminimizing the total amount of paper required to execute the folding (where “thicker” creases consume more paper). We prove both problems strongly NP-complete even for 1D folding. On the other hand, we prove the first problem fixed-parameter tractable in 1D with respect to the number of layers., National Science Foundation (U.S.). Origami Design for Integration of Self-assembling Systems for Engineering Innovation (grant EFRI- 124038), National Science Foundation (U.S.). Expedition grant (CCF-1138967), United States. Department of Defense. National Defense Science and Engineering Graduate (NDSEG) Fellowship (32 CFR 168a)
- Published
- 2015
5. On the paper 'On an identity for the zeros of Bessel functions' by Baricz et al
- Author
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N. Anghel
- Subjects
Pure mathematics ,Applied Mathematics ,Entire function ,010102 general mathematics ,Order (ring theory) ,Riemann–Stieltjes integral ,Type (model theory) ,01 natural sciences ,symbols.namesake ,Identity (mathematics) ,0103 physical sciences ,symbols ,0101 mathematics ,010306 general physics ,Analysis ,Bessel function ,Mathematics - Abstract
In this note we offer some criticism on the paper “On an identity for zeros of Bessel functions” by Baricz et al. [3] . The paper gives identities of type Stieltjes–Calogero for the sums of reciprocals of differences of fourth powers of zeros of Bessel functions. Although interesting in principle, by containing one too many sums of similar complexity the identities fail to convey the true spirit of the work of Stieltjes and Calogero. We rectify this by providing what we think is the correct type of identity for the above-said sums, in the general setup of entire functions of order
- Published
- 2018
6. Time‐varying model for the effective diagnosis of oil‐paper insulation used in power transformers
- Author
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Chandra Madhab Banerjee, Arijit Baral, Saurabh Dutta, and Sivaji Chakravorti
- Subjects
010302 applied physics ,Transformer oil ,020209 energy ,Energy Engineering and Power Technology ,02 engineering and technology ,Function (mathematics) ,01 natural sciences ,Dielectric response ,symbols.namesake ,Control and Systems Engineering ,Control theory ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Curve fitting ,Dielectric function ,Electrical and Electronic Engineering ,Debye model ,Mathematics ,Electronic circuit - Abstract
The analysis of dielectric response function obtained from the power transformer is a well-accepted technique in insulation diagnosis. A convenient way of analysing time-domain dielectric response φ(t) is the formulation of simple resistance−capacitance-based circuits like the conventional Debye model (CDM) or the modified Debye model (MDM) that are capable of modelling φ(t). However, available techniques do not guarantee unique branch parameters of such circuits for a given φ(t). In fact, the branch parameters are known to depend on the curve-fitting procedure opted during model formulation. This makes accuracy of CDM and MDM parameter-based diagnosis techniques less reliable. Furthermore, it seems logical to analyse the time-domain dielectric response of oil-paper insulation using a model containing time-varying parameters. In this study, a methodology is proposed using which such an insulation model (containing time-varying parameters) is formulated using time-domain insulation response. Related analysis presented suggests that the proposed model is immune to problems associated with available insulation models (containing time-invariant parameters). The performance of the proposed model in indicating insulation condition is tested on data obtained from several real-life power transformers.
- Published
- 2019
7. Bifurcation analysis of the rock–paper–scissors game with discrete-time logit dynamics
- Author
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Yosuke Umezuki
- Subjects
Computer Science::Computer Science and Game Theory ,Sociology and Political Science ,05 social sciences ,General Social Sciences ,01 natural sciences ,010305 fluids & plasmas ,symbols.namesake ,Bifurcation theory ,Discrete time and continuous time ,Nash equilibrium ,Best response ,0502 economics and business ,0103 physical sciences ,Attractor ,symbols ,Applied mathematics ,050207 economics ,Statistics, Probability and Uncertainty ,Invariant (mathematics) ,General Psychology ,Bifurcation ,Saddle ,Mathematics - Abstract
In this study, we investigate a discrete-time version of logit dynamics, as applied to the rock–paper–scissors (RPS) game. First, we show that around the Nash equilibrium point, an attracting closed invariant curve appears due to the Neimark–Sacker bifurcation. Next, near the resonance point, we find a period-three attracting cycle, which can be thought of as a counterpart to the cyclically stable set in the RPS game with best response dynamics. Moreover, we show that the cycle can coexist with an attracting closed invariant curve, a period-three saddle cycle, and the attracting or repelling Nash equilibrium point. Finally, we use the codimension-two bifurcation theory to specify the set of heteroclinic bifurcations that destroy the coexistence of the attractors.
- Published
- 2018
8. A Simple Paper Model Illustrates How To Cyclize Monosaccharides from Fischer Projections to Haworth
- Author
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Chi H. Mak
- Subjects
chemistry.chemical_classification ,010405 organic chemistry ,05 social sciences ,050301 education ,General Chemistry ,01 natural sciences ,0104 chemical sciences ,Education ,Algebra ,symbols.namesake ,chemistry ,Simple (abstract algebra) ,symbols ,Monosaccharide ,0503 education ,Fischer projection ,Mathematics - Abstract
Turning a linear sugar into its cyclized form is an essential skill in biochemistry. A simple paper model is described that can be used by any student to transform a carbohydrate in its Fischer projection and correctly cyclize it into its Haworth form. The model can also be used to illustrate several key aspects of the Fischer projection of which many students are typically unaware.
- Published
- 2018
9. Comment on the paper 'On conservation laws by Lie symmetry analysis for (2+1)-dimensional Bogoyavlensky–Konopelchenko equation in wave propagation' by S. Saha Ray
- Author
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Muhammad Alim Abdulwahhab
- Subjects
Conservation law ,Wave propagation ,010102 general mathematics ,One-dimensional space ,010103 numerical & computational mathematics ,System of linear equations ,01 natural sciences ,Symmetry (physics) ,Computational Mathematics ,symbols.namesake ,Computational Theory and Mathematics ,Modeling and Simulation ,symbols ,0101 mathematics ,Noether's theorem ,Mathematics ,Mathematical physics - Abstract
In a recent paper referred to in the title, the author used the concept of quasi self-adjointness to obtain conservation laws for a system of the ( 2 + 1 ) -dimensional Bogoyavlensky–Konopelchenko equation. Apart from the adjoint system of equations, all the results on the quasi self-adjointness and the subsequent conservation laws obtained are inaccurate. In this comment, we clarify these inaccuracies and also generate conservation laws for a potential form of the underlying equation through Noether theorem.
- Published
- 2018
10. Universal scaling law of an origami paper spring
- Author
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Bohua Sun
- Subjects
Environmental Engineering ,Biomedical Engineering ,Computational Mechanics ,Aerospace Engineering ,FOS: Physical sciences ,Ocean Engineering ,Poisson distribution ,01 natural sciences ,Square (algebra) ,010305 fluids & plasmas ,symbols.namesake ,Physics - General Physics ,0103 physical sciences ,010306 general physics ,Civil and Structural Engineering ,Mathematics ,Mechanical Engineering ,Mathematical analysis ,Extension (predicate logic) ,Poisson's ratio ,Power (physics) ,Nonlinear system ,General Physics (physics.gen-ph) ,Mechanics of Materials ,Spring (device) ,lcsh:TA1-2040 ,symbols ,Curve fitting ,lcsh:Engineering (General). Civil engineering (General) - Abstract
This letter solves an open question of origami paper spring risen by Yoneda et al.(Phys. Rev. E 2019). By using both dimensional analysis and data fitting, a universal scaling law of a paper spring is formulated. The scaling law shows that origami spring force obeys power square law of spring extension, however strong nonlinear to the total twist angle. The study has also successfully generalized the scaling law from the Poisson ratio 0.3 to an arbitrary Poisson's ratio with the help of dimensional analysis., Comment: 3 pages, 3 figues and 1 table
- Published
- 2020
- Full Text
- View/download PDF
11. ‘The life of man, solitary, poore, nasty, brutish, and short’: Discussion of the paper by Rootzén and Zholud
- Author
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Anthony C. Davison
- Subjects
Statistics and Probability ,05 social sciences ,Economics, Econometrics and Finance (miscellaneous) ,Poisson process ,01 natural sciences ,010104 statistics & probability ,symbols.namesake ,Non stationarity ,0502 economics and business ,symbols ,050207 economics ,0101 mathematics ,Engineering (miscellaneous) ,Mathematical economics ,Mathematics - Published
- 2018
12. An unpublished paper ‘Über einige durch unendliche Reihen definirte Functionen eines complexen Argumentes’ by Adolf Hurwitz
- Author
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Nicola Oswald
- Subjects
History ,Pure mathematics ,General Mathematics ,010102 general mathematics ,01 natural sciences ,Algebra ,symbols.namesake ,Continuation ,0103 physical sciences ,Functional equation ,symbols ,010307 mathematical physics ,0101 mathematics ,Dirichlet series ,Meromorphic function ,Mathematics - Abstract
In 1903, Epstein published his proof of meromorphic continuation and a functional equation for Dirichlet series associated with quadratic forms, now called Epstein zeta-functions. However, already in 1889 (or even earlier) Hurwitz was aware of these results as his mathematical diaries and some unpublished notes (in an almost final form) found in his estate at the ETH Zurich show. In this article we present and analyze Hurwitz's notes and compare his reasoning with Epstein's paper in detail.
- Published
- 2017
13. A Remark on the Paper 'Properties of Intersecting Families of Ordered Sets' by O. Einstein
- Author
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Sounggun Wee and Sang-il Oum
- Subjects
010102 general mathematics ,Mistake ,0102 computer and information sciences ,01 natural sciences ,Linear subspace ,Combinatorics ,Computational Mathematics ,symbols.namesake ,010201 computation theory & mathematics ,Ordered set ,FOS: Mathematics ,symbols ,Mathematics - Combinatorics ,Discrete Mathematics and Combinatorics ,Combinatorics (math.CO) ,0101 mathematics ,Einstein ,05C35 ,Finite set ,Mathematics - Abstract
O. Einstein (2008) proved Bollob\'as-type theorems on intersecting families of ordered sets of finite sets and subspaces. Unfortunately, we report that the proof of a theorem on ordered sets of subspaces had a mistake. We prove two weaker variants., Comment: 6 pages. Improved bound for Theorem 4
- Published
- 2018
14. Refined exponential stability analysis of a coupled system * *The paper was partially supported by the ANR projects LimICoS and SCIDIS. Corresponding author. Fax +33-561336411
- Author
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Alexandre Seuret, Mohammed Safi, and Lucie Baudouin
- Subjects
Lyapunov function ,Lyapunov stability ,0209 industrial biotechnology ,Mathematical analysis ,02 engineering and technology ,Lyapunov exponent ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,020901 industrial engineering & automation ,Exponential stability ,Control and Systems Engineering ,Stability theory ,Ordinary differential equation ,symbols ,Lyapunov equation ,0101 mathematics ,Lyapunov redesign ,Mathematics - Abstract
The objective of this contribution is to improve recent stability results for a system coupling ordinary differential equations to a vectorial transport partial differential equation by proposing a new structure of Lyapunov functional. Following the same process of most of the investigations in literature, that are based on an a priori selection of Lyapunov functionals and use the usual integral inequalities (Jensen, Wirtinger, Bessel...), we will present an efficient method to estimate the exponential decay rate of this coupled system leading to a tractable test expressed in terms of linear matrix inequalities. These LMI conditions stem from the new design of a candidate Lyapunov functional, but also the inherent properties of the Legendre polynomials, that are used to build a projection of the infinite dimensional part of the state of the system. Based on these polynomials and using the appropriate Bessel-Legendre inequality, we will prove an exponential stability result and in the end, we will show the efficiency of our approach on academic example.
- Published
- 2017
15. A trio of heteroclinic bifurcations arising from a model of spatially-extended Rock-Paper-Scissors
- Author
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Claire M. Postlethwaite and Alastair M. Rucklidge
- Subjects
Population ,General Physics and Astronomy ,FOS: Physical sciences ,Pattern Formation and Solitons (nlin.PS) ,01 natural sciences ,symbols.namesake ,0101 mathematics ,education ,Quantitative Biology - Populations and Evolution ,Mathematical Physics ,Saddle ,Mathematics ,Hopf bifurcation ,Equilibrium point ,education.field_of_study ,Partial differential equation ,37G15, 34C37, 37C29, 91A22 ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Ode ,Populations and Evolution (q-bio.PE) ,Heteroclinic cycle ,Statistical and Nonlinear Physics ,Nonlinear Sciences - Pattern Formation and Solitons ,010101 applied mathematics ,Ordinary differential equation ,FOS: Biological sciences ,symbols - Abstract
One of the simplest examples of a robust heteroclinic cycle involves three saddle equilibria: each one is unstable to the next in turn, and connections from one to the next occur within invariant subspaces. Such a situation can be described by a third-order ordinary differential equation (ODE), and typical trajectories approach each equilibrium point in turn, spending progressively longer to cycle around the three points but never stopping. This cycle has been invoked as a model of cyclic competition between populations adopting three strategies, characterised as Rock, Paper and Scissors. When spatial distribution and mobility of the populations is taken into account, waves of Rock can invade regions of Scissors, only to be invaded by Paper in turn. The dynamics is described by a set of partial differential equations (PDEs) that has travelling wave (in one dimension) and spiral (in two dimensions) solutions. In this paper, we explore how the robust heteroclinic cycle in the ODE manifests itself in the PDEs. Taking the wavespeed as a parameter, and moving into a travelling frame, the PDEs reduce to a sixth-order set of ODEs, in which travelling waves are created in a Hopf bifurcation and are destroyed in three different heteroclinic bifurcations, depending on parameters, as the travelling wave approaches the heteroclinic cycle. We explore the three different heteroclinic bifurcations, none of which have been observed in the context of robust heteroclinic cycles previously. These results are an important step towards a full understanding of the spiral patterns found in two dimensions, with possible application to travelling waves and spirals in other population dynamics models., Comment: 36 pages, 8 figures
- Published
- 2019
- Full Text
- View/download PDF
16. Multiple limit cycles for the continuous model of the rock–scissors–paper game between bacteriocin producing bacteria
- Author
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Ping Yan and Zhang Dao-xiang
- Subjects
Hopf bifurcation ,Continuous modelling ,Applied Mathematics ,010102 general mathematics ,Heteroclinic cycle ,16. Peace & justice ,01 natural sciences ,010101 applied mathematics ,Computational Mathematics ,symbols.namesake ,symbols ,Applied mathematics ,Limit (mathematics) ,0101 mathematics ,Mathematical economics ,Mathematics - Abstract
Two limit cycles for the continuous model of the rockscissorspaper (RSP) game is constructed.The Hopf bifurcation method is used for the construction of limit cycles.The results give a partial answer to an open question posed by Neumann and Schuster. In this paper we construct two limit cycles with a heteroclinic polycycle for the three-dimensional continuous model of the rockscissorspaper (RSP) game between bacteriocin producing bacteria. Our construction gives a partial answer to an open question posed by Neumann and Schuster (2007) concerning how many limit cycles can coexist for the RSP game.
- Published
- 2017
17. Einstein’s Approach to Statistical Mechanics: The 1902–04 Papers
- Author
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Raúl Rechtman and Luca Peliti
- Subjects
Thermal equilibrium ,Basis (linear algebra) ,Physics - History and Philosophy of Physics ,Equations of motion ,Statistical and Nonlinear Physics ,Statistical mechanics ,01 natural sciences ,Sketch ,010305 fluids & plasmas ,Theoretical physics ,symbols.namesake ,0103 physical sciences ,symbols ,Einstein ,010306 general physics ,Focus (optics) ,Mathematical Physics ,Mathematics - Abstract
We summarize the papers published by Einstein in the Annalen der Physik in the years 1902-04 on the derivation of the properties of thermal equilibrium on the basis of the mechanical equations of motion and of the calculus of probabilities. We point out the line of thought that led Einstein to an especially economical foundation of the discipline, and to focus on fluctuations of the energy as a possible tool for establishing the validity of this foundation. We also sketch a comparison of Einstein's approach with that of Gibbs, suggesting that although they obtained similar results, they had different motivations and interpreted them in very different ways., Comment: 22 pages, submitted to JSP
- Published
- 2016
18. A Note on a Paper by Nieminen
- Author
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Marcel Roman and Adrian Sandovici
- Subjects
Pure mathematics ,Mathematics::Operator Algebras ,Applied Mathematics ,010102 general mathematics ,Linear operators ,Hilbert space ,Mathematics::Spectral Theory ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,Mathematics (miscellaneous) ,symbols ,0101 mathematics ,Mathematics - Abstract
A criteria due to Toivo Nieminen concerning selfadjoint linear operators in complex Hilbert spaces is extended to the case of linear relations.
- Published
- 2019
19. Remarks on a paper by Gavrilov: Grad-Shafranov equations, steady solutions of the three dimensional incompressible Euler equations with compactly supported velocities, and applications
- Author
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Peter Constantin, Vlad Vicol, and Joonhyun La
- Subjects
010102 general mathematics ,Mathematical analysis ,Euler flow ,01 natural sciences ,Euler equations ,010101 applied mathematics ,symbols.namesake ,Mathematics - Analysis of PDEs ,Physics::Plasma Physics ,Physics::Space Physics ,symbols ,FOS: Mathematics ,Incompressible euler equations ,Geometry and Topology ,0101 mathematics ,GEOM ,35Q30, 35Q35, 35Q92 ,Analysis ,Mathematics ,Analysis of PDEs (math.AP) - Abstract
We describe a method to construct smooth and compactly supported solutions of 3D incompressible Euler equations and related models. The method is based on localizable Grad–Shafranov equations and is inspired by the recent result (Gavrilov in A steady Euler flow with compact support. Geom Funct Anal 29(1):90–197, [Gav19]).
- Published
- 2019
- Full Text
- View/download PDF
20. An Upper Bound on the Capacity of Vector Dirty Paper with Unknown Spin and Stretch
- Author
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David T. H. Kao and Ashutosh Sabharwal
- Subjects
010302 applied physics ,FOS: Computer and information sciences ,business.industry ,Gaussian ,Computer Science - Information Theory ,Information Theory (cs.IT) ,Scalar (mathematics) ,Significant difference ,Transmitter ,020206 networking & telecommunications ,02 engineering and technology ,Topology ,01 natural sciences ,Upper and lower bounds ,Dirty paper ,Channel capacity ,symbols.namesake ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Zero-forcing precoding ,Telecommunications ,business ,Mathematics ,Computer Science::Information Theory - Abstract
Dirty paper codes are a powerful tool for combating known interference. However, there is a significant difference between knowing the transmitted interference sequence and knowing the received interference sequence, especially when the channel modifying the interference is uncertain. We present an upper bound on the capacity of a compound vector dirty paper channel where although an additive Gaussian sequence is known to the transmitter, the channel matrix between the interferer and receiver is uncertain but known to lie within a bounded set. Our bound is tighter than previous bounds in the low-SIR regime for the scalar version of the compound dirty paper channel and employs a construction that focuses on the relationship between the dimension of the message-bearing signal and the dimension of the additive state sequence. Additionally, a bound on the high-SNR behavior of the system is established., Comment: to be presented at ISIT 2013
- Published
- 2013
- Full Text
- View/download PDF
21. A note on O. Frolkina’s paper 'pairwise disjoint moebius bands in space'
- Author
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Sergey A. Melikhov
- Subjects
Algebra and Number Theory ,010102 general mathematics ,Disjoint sets ,Space (mathematics) ,01 natural sciences ,Combinatorics ,symbols.namesake ,Simple (abstract algebra) ,0103 physical sciences ,symbols ,010307 mathematical physics ,Möbius strip ,0101 mathematics ,Algebraic number ,Mathematics - Abstract
We note a simple algebraic proof of Frolkina’s result that [Formula: see text] does not contain uncountably many pairwise disjoint copies of the Möbius band, and of a similar result in higher dimensions.
- Published
- 2019
22. Hopf Bifurcations in Delayed Rock–Paper–Scissors Replicator Dynamics
- Author
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Richard H. Rand and Elizabeth Wesson
- Subjects
Statistics and Probability ,Economics and Econometrics ,Population ,Interval (mathematics) ,01 natural sciences ,010305 fluids & plasmas ,symbols.namesake ,Control theory ,Limit cycle ,0103 physical sciences ,Replicator equation ,Applied mathematics ,Limit (mathematics) ,010306 general physics ,education ,Bifurcation ,Mathematics ,Hopf bifurcation ,education.field_of_study ,Applied Mathematics ,Function (mathematics) ,Computer Graphics and Computer-Aided Design ,Computer Science Applications ,Nonlinear Sciences::Chaotic Dynamics ,Computational Mathematics ,Computational Theory and Mathematics ,symbols - Abstract
We investigate the dynamics of three-strategy (rock–paper–scissors) replicator equations in which the fitness of each strategy is a function of the population frequencies delayed by a time interval $$T$$ . Taking $$T$$ as a bifurcation parameter, we demonstrate the existence of (non-degenerate) Hopf bifurcations in these systems and present an analysis of the resulting limit cycles using Lindstedt’s method.
- Published
- 2015
23. On the Capacity of the Carbon Copy onto Dirty Paper Channel
- Author
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Shlomo Shamai Shitz and Stefano Rini
- Subjects
Independent and identically distributed random variables ,FOS: Computer and information sciences ,Computer Science - Information Theory ,02 engineering and technology ,Library and Information Sciences ,01 natural sciences ,Precoding ,010305 fluids & plasmas ,Channel capacity ,symbols.namesake ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,Fading ,Mathematics ,Channel use ,Computer Science::Information Theory ,business.industry ,Information Theory (cs.IT) ,020206 networking & telecommunications ,Computer Science Applications ,Additive white Gaussian noise ,Gaussian noise ,symbols ,Telecommunications ,business ,Algorithm ,Information Systems ,Communication channel - Abstract
The "Carbon Copy onto Dirty Paper" (CCDP) channel is the compound "writing on dirty paper" channel in which the channel output is obtained as the sum of the channel input, white Gaussian noise and a Gaussian state sequence randomly selected among a set possible realizations. The transmitter has non-causal knowledge of the set of possible state sequences but does not know which sequence is selected to produce the channel output. We study the capacity of the CCDP channel for two scenarios: (i) the state sequences are independent and identically distributed, and (ii) the state sequences are scaled versions of the same sequence. In the first scenario, we show that a combination of superposition coding, time-sharing and Gel'fand-Pinsker binning is sufficient to approach the capacity to within three bits per channel use for any number of possible state realizations. In the second scenario, we derive capacity to within four bits-per-channel-use for the case of two possible state sequences. This result is extended to the CCDP channel with any number of possible state sequences under certain conditions on the scaling parameters which we denote as "strong fading" regime. We conclude by providing some remarks on the capacity of the CCDP channel in which the state sequences have any jointly Gaussian distribution.
- Published
- 2017
- Full Text
- View/download PDF
24. Note on A. Barbour’s paper on Stein’s method for diffusion approximations
- Author
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Andrew B. Duncan, Mikołaj Kasprzak, and Sebastian J. Vollmer
- Subjects
Statistics and Probability ,Pure mathematics ,60B10 ,Statistics & Probability ,Gaussian ,Banach space ,Stein’s method ,01 natural sciences ,010104 statistics & probability ,symbols.namesake ,FOS: Mathematics ,60J65 ,60E05 ,0101 mathematics ,QA ,60J60 ,Mathematics ,Semigroup ,0104 Statistics ,010102 general mathematics ,Probability (math.PR) ,Stein's method ,Heavy traffic approximation ,60F17 ,Primary: 60B10, 60F17, Secondary: 60J60, 60J65, 60E05 ,Norm (mathematics) ,symbols ,Stein equation ,Mathematics [G03] [Physical, chemical, mathematical & earth Sciences] ,Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre] ,Statistics, Probability and Uncertainty ,Donsker’s theorem ,Mathematics - Probability ,diffusion approximations - Abstract
In (Barbour, 1990) foundations for diffusion approximation via Stein's method are laid. This paper has been cited more than 130 times and is a cornerstone in the area of Stein's method. A semigroup argument is used therein to solve a Stein equation for Gaussian diffusion approximation. We prove that, contrary to the claim in (Barbour, 1990), the semigroup considered therein is not strongly continuous on the Banach space of continuous, real-valued functions on D[0,1] growing slower than a cubic, equipped with an appropriate norm. We also provide a proof of the exact formulation of the solution to the Stein equation of interest, which does not require the aforementioned strong continuity. This shows that the main results of (Barbour, 1990) hold true., Comment: 8 pages
- Published
- 2017
25. Physics in Riemann’s Mathematical Papers
- Author
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Athanase Papadopoulos
- Subjects
Physics ,Physical reasoning ,Mathematics::Complex Variables ,Riemann surface ,Mathematics::History and Overview ,010102 general mathematics ,Face (sociological concept) ,06 humanities and the arts ,Riemannian geometry ,Space (mathematics) ,01 natural sciences ,Physics::History of Physics ,symbols.namesake ,Riemann hypothesis ,060105 history of science, technology & medicine ,symbols ,Calculus ,0601 history and archaeology ,0101 mathematics ,Relation (history of concept) ,Mathematics - Abstract
Riemann’s mathematical papers contain many ideas that arise in physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann’s ideas in mathematics from there in physics. Furthermore, Riemann’s philosophical ideas are often in the background of his work on science. The aim of this chapter is to give an overview of Riemann’s mathematical results based on physical reasoning or motivated by physics. We also elaborate on the relation with philosophy. While we discuss some of Riemann’s philosophical points of view, we review some ideas on the same subjects emitted by Riemann’s predecessors, and in particular Greek philosophers, mainly the pre-socratics and Aristotle.
- Published
- 2017
26. Lp-solution for BSDEs with jumps in the case p<2 : Corrections to the paper ‘BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration’
- Author
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Alexandre Popier and Thomas Kruse
- Subjects
Statistics and Probability ,Generator (computer programming) ,010102 general mathematics ,Monotonic function ,Poisson distribution ,01 natural sciences ,010104 statistics & probability ,symbols.namesake ,Stochastic differential equation ,Monotone polygon ,Modeling and Simulation ,Mathematik ,symbols ,Filtration (mathematics) ,Applied mathematics ,Uniqueness ,0101 mathematics ,Brownian motion ,Mathematics - Abstract
In T. Kruse and A. Popier, we established existence and uniqueness of solutions of backward stochastic differential equations in under a monotonicity condition on the generator and in a general filtration. There was a mistake in the case . Here we give a corrected proof. Moreover the quasi-left continuity condition on the filtration is removed.
- Published
- 2017
27. A commentary on Teichmüller’s paper Extremale quasikonforme Abbildungen und quadratische Differentiale
- Author
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Athanase Papadopoulos, Weixu Su, and Vincent Alberge
- Subjects
Teichmüller space ,Fuchsian group ,Quasiconformal mapping ,Riemann surface ,010102 general mathematics ,06 humanities and the arts ,01 natural sciences ,Beltrami equation ,Moduli ,Algebra ,symbols.namesake ,060105 history of science, technology & medicine ,symbols ,0601 history and archaeology ,0101 mathematics ,Uniformization (set theory) ,Mathematics - Abstract
We provide a commentary on Teichmuller's paper "Extremale quasikonforme Abbildungen und quadratische Differentiale" (Extremal quasiconformal mappings of closed oriented Riemann surfaces), Abh. Preuss. Akad. Wiss., Math.-Naturw. Kl. 1940, No.22, 1-197 (1940). The paper is quoted in several works, although it was read by very few people. Some of the results it contains were rediscovered later on and published without any reference to Teichmuller. In this commentary, we highlight the main results and the main ideas contained in that paper and we describe some of the important developments they gave rise to.
- Published
- 2016
28. A commentary on Teichmüller’s paper Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Flächen
- Author
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Athanase Papadopoulos, Annette A'Campo-Neuen, Norbert A'Campo, and Vincent Alberge
- Subjects
Fuchsian group ,Teichmüller space ,Quasiconformal mapping ,Pure mathematics ,Euclidean space ,Riemann surface ,010102 general mathematics ,Surface (topology) ,Mathematics::Geometric Topology ,01 natural sciences ,Algebra ,symbols.namesake ,Invariance of domain ,0103 physical sciences ,Uniformization theorem ,symbols ,010307 mathematical physics ,0101 mathematics ,Mathematics - Abstract
This is a mathematical commentary on Teichmuller's paper ``Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Flachen" (Determination of extremal quasiconformal maps of closed oriented Riemann surfaces). This paper is among the last (and may be the last one) that Teichmuller wrote on the theory of moduli. It contains the proof of the so-called Teichmuller existence theorem for a closed surface of genus at least 2. For this proof, the author defines a mapping between a space of equivalence classes of marked Riemann surfaces (the Teichmuller space) and a space of equivalence classes of certain Fuchsian groups (the so-called Fricke space). After that, he defines a map between the latter and the Euclidean space of dimension 6g-6 Using Brouwer's theorem of invariance of domain, he shows that this map is a homeomorphism. This involves in particular a careful definition of the topologies of Fricke space, the computation of its dimension, and comparison results between hyperbolic distance and quasiconformal dilatation. The use of the invariance of domain theorem is in the spirit of Poincare and Klein's use of the so-called ``continuity principle" in their attempts to prove the uniformization theorem.
- Published
- 2016
29. Folding a Paper Strip to Minimize Thickness
- Author
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David Eppstein, Yushi Uno, Anna Lubiw, Erik D. Demaine, Ryuhei Uehara, Hiro Ito, and Adam Hesterberg
- Subjects
0209 industrial biotechnology ,symbols.namesake ,020901 industrial engineering & automation ,010201 computation theory & mathematics ,symbols ,Vertical segment ,Geometry ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Mathematics ,Planar graph - Abstract
In this paper, we study how to fold a specified origami crease pattern in order to minimize the impact of paper thickness. Specifically, origami designs are often expressed by a mountain-valley pattern (plane graph of creases with relative fold orientations), but in general this specification is consistent with exponentially many possible folded states. We analyze the complexity of finding the best consistent folded state according to two metrics: minimizing the total number of layers in the folded state (so that a “flat folding” is indeed close to flat), and minimizing the total amount of paper required to execute the folding (where “thicker” creases consume more paper). We prove both problems strongly NP-complete even for 1D folding. On the other hand, we prove the first problem fixed-parameter tractable in 1D with respect to the number of layers.
- Published
- 2015
30. The Asymptotic Expansion of Kummer Functions for Large Values of the a-Parameter, and Remarks on a Paper by Olver
- Author
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Hans Volkmer
- Subjects
Pure mathematics ,Logarithm ,media_common.quotation_subject ,Riemann surface ,010102 general mathematics ,Mathematical analysis ,010103 numerical & computational mathematics ,Infinity ,01 natural sciences ,Kummer's function ,symbols.namesake ,Mathematics - Classical Analysis and ODEs ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,symbols ,Geometry and Topology ,0101 mathematics ,Asymptotic expansion ,Mathematical Physics ,Analysis ,media_common ,Mathematics - Abstract
It is shown that a known asymptotic expansion of the Kummer function $U(a,b,z)$ as $a$ tends to infinity is valid for $z$ on the full Riemann surface of the logarithm. A corresponding result is also proved in a more general setting considered by Olver (1956).
- Published
- 2016
31. Corrigendum to our paper ‘The Markov–Stieltjes transform on Hardy and Lebesgue spaces’
- Author
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A. R. Mirotin and I. S. Kovalyova
- Subjects
Pure mathematics ,Markov chain ,Applied Mathematics ,010102 general mathematics ,Lebesgue's number lemma ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,symbols ,0101 mathematics ,Lp space ,Analysis ,Stieltjes transform ,Mathematics - Published
- 2017
32. The non validity of the gaussian approximation for multi-user interference in ultra wide band impulse radio: from an inconvenience to an advantage - transactions papers
- Author
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Daniele Domenicali, Jocelyn Fiorina, SUPELEC-Campus Gif, Ecole Supérieure d'Electricité - SUPELEC (FRANCE), and Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome]
- Subjects
Ultra-wideband ,02 engineering and technology ,Impulse (physics) ,01 natural sciences ,[SPI]Engineering Sciences [physics] ,010104 statistics & probability ,symbols.namesake ,Non-Gaussianity ,0202 electrical engineering, electronic engineering, information engineering ,0101 mathematics ,Electrical and Electronic Engineering ,Gaussian process ,Computer Science::Information Theory ,Mathematics ,business.industry ,Applied Mathematics ,020206 networking & telecommunications ,Computer Science Applications ,Gaussian approximation ,Multi user interference ,Additive white Gaussian noise ,Gaussian noise ,symbols ,Telecommunications ,business ,[SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing ,Algorithm - Abstract
International audience; The huge potential of ultra wide band impulse radio (UWB IR) with multiple access was initially evaluated using the standard Gaussian approximation which assumed that multi user interference could be approximated as classical Gaussian noise. Later the standard Gaussian approximation has been proved to be invalid in several cases. Thus the performance of the classical UWB IR correlation receiver dramatically reduces. We show in this paper how the non Gaussianity of the multi user interference can be exploited, turning the non Gaussianity into an advantage, increasing the performance with respect to the Gaussian interference case which was supposed to be too optimistic until now.
- Published
- 2009
33. Notes on Perelman’s papers
- Author
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Bruce Kleiner and John Lott
- Subjects
Mathematics - Differential Geometry ,three-manifold ,geometrization theorem ,53C21 ,Mathematical proof ,57M40 ,53C44 ,01 natural sciences ,Physics::Fluid Dynamics ,Perelman ,symbols.namesake ,Ricci flow ,0103 physical sciences ,FOS: Mathematics ,Mathematics::Metric Geometry ,0101 mathematics ,Mathematics::Symplectic Geometry ,Mathematics ,Poincaré Conjecture ,Discrete mathematics ,Ricci flow with surgery ,Conjecture ,010102 general mathematics ,Hyperbolization theorem ,Mathematics::Geometric Topology ,57M50 ,Manifold ,long-term behaviour ,Differential Geometry (math.DG) ,Cover (topology) ,Poincaré conjecture ,symbols ,Mathematics::Differential Geometry ,010307 mathematical physics ,Geometry and Topology ,Geometrization conjecture ,entropy formula - Abstract
These are detailed notes on Perelman's papers "The entropy formula for the Ricci flow and its geometric applications" and "Ricci flow with surgery on three-manifolds"., 216 pages, minor corrections made
- Published
- 2008
34. Some Remarks on a Paper of V. A. Liskovets
- Author
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László Tóth
- Subjects
Pure mathematics ,Mathematics - Number Theory ,Mathematics::Number Theory ,010102 general mathematics ,Multiplicative function ,0102 computer and information sciences ,Function (mathematics) ,Type (model theory) ,Congruence relation ,16. Peace & justice ,Mathematical proof ,01 natural sciences ,Ramanujan's sum ,Connection (mathematics) ,symbols.namesake ,010201 computation theory & mathematics ,Simple (abstract algebra) ,symbols ,Mathematics - Combinatorics ,0101 mathematics ,Mathematics - Abstract
We deduce new properties of the orbicyclic function $E$ of several variables investigated in a recent paper by V. A. Liskovets. We point out that the function $E$ and its connection to the number of solutions of certain linear congruences occur in the literature in a slightly different form. We investigate another similar function considered by Deitmar, Koyama and Kurokawa by studying analytic properties of some zeta functions of Igusa type. Simple number theoretic proofs for some known properties are also given., Comment: 10 pages
- Published
- 2012
35. Recurrent critical points and typical limit sets for conformal measures☆☆Portions of the paper were presented at the AMS Special Session on Low-Dimensional Dynamics in Milwaukee, Wisconsin, October 1997
- Author
-
Lex Oversteegen, Alexander Blokh, and John C. Mayer
- Subjects
Discrete mathematics ,010102 general mathematics ,Julia set ,Conformal map ,Density theorem ,Lebesgue integration ,Postcritical set ,01 natural sciences ,Measure (mathematics) ,symbols.namesake ,0103 physical sciences ,symbols ,Complex dynamics ,Ergodic theory ,ω-limit set ,Point (geometry) ,010307 mathematical physics ,Geometry and Topology ,Limit (mathematics) ,0101 mathematics ,Conformal measure ,Mathematics - Abstract
For a rational f : C → C with a conformal measure μ we show that if there is a subset of the Julia set J(f) of positive μ -measure whose points are not eventual preimages of critical or parabolic points and have limit sets not contained in the union of the limit sets of recurrent critical points, then μ is non-atomic, μ(J(f))=1 , ω(x)=J(f) for μ -a.e. point x∈J(f) and f is conservative, ergodic and exact. The proof uses a version of the Lebesgue Density Theorem valid for Borel measures and conformal balls.
- Published
- 2000
36. Remarks on a Paper by Giordano, Laforgia, and Pečarić
- Author
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Mourad E. H. Ismail
- Subjects
symbols.namesake ,Applied Mathematics ,010102 general mathematics ,symbols ,Calculus ,Point (geometry) ,010103 numerical & computational mathematics ,0101 mathematics ,01 natural sciences ,Bessel function ,Analysis ,Mathematics - Abstract
We point out errors and oversights in a paper by Giordano, Laforgia, and Pecaric [3] on inequalities involving Bessel functions.
- Published
- 1997
- Full Text
- View/download PDF
37. Oscillatory dynamics in rock–paper–scissors games with mutations
- Author
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Mauro Mobilia
- Subjects
Mutation rate ,Population Dynamics ,Fixed point ,Parameter space ,01 natural sciences ,010305 fluids & plasmas ,Quantitative Biology::Populations and Evolution ,Statistical physics ,Limit (mathematics) ,Mathematics ,Reproduction ,Applied Mathematics ,Biodiversity ,General Medicine ,Biological Evolution ,Nonlinear Sciences - Adaptation and Self-Organizing Systems ,Markov Chains ,Amplitude ,Modeling and Simulation ,symbols ,General Agricultural and Biological Sciences ,Adaptation and Self-Organizing Systems (nlin.AO) ,Algorithms ,Statistics and Probability ,Physics - Physics and Society ,FOS: Physical sciences ,Physics and Society (physics.soc-ph) ,Models, Biological ,General Biochemistry, Genetics and Molecular Biology ,symbols.namesake ,Game Theory ,Control theory ,Limit cycle ,0103 physical sciences ,Computer Simulation ,Selection, Genetic ,Quantitative Biology - Populations and Evolution ,010306 general physics ,Condensed Matter - Statistical Mechanics ,Ecosystem ,Hopf bifurcation ,Stochastic Processes ,General Immunology and Microbiology ,Statistical Mechanics (cond-mat.stat-mech) ,Stochastic process ,Populations and Evolution (q-bio.PE) ,Kinetics ,Nonlinear Dynamics ,FOS: Biological sciences ,Mutation ,Linear Models - Abstract
We study the oscillatory dynamics in the generic three-species rock-paper-scissors games with mutations. In the mean-field limit, different behaviors are found: (a) for high mutation rate, there is a stable interior fixed point with coexistence of all species; (b) for low mutation rates, there is a region of the parameter space characterized by a limit cycle resulting from a Hopf bifurcation; (c) in the absence of mutations, there is a region where heteroclinic cycles yield oscillations of large amplitude (not robust against noise). After a discussion on the main properties of the mean-field dynamics, we investigate the stochastic version of the model within an individual-based formulation. Demographic fluctuations are therefore naturally accounted and their effects are studied using a diffusion theory complemented by numerical simulations. It is thus shown that persistent erratic oscillations (quasi-cycles) of large amplitude emerge from a noise-induced resonance phenomenon. We also analytically and numerically compute the average escape time necessary to reach a (quasi-)cycle on which the system oscillates at a given amplitude., Comment: 25 pages, 9 figures. To appear in the Journal of Theoretical Biology
- Published
- 2010
38. Rebuttal of Donnelly's paper on the spectral gap
- Author
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Antoine Henrot, Mark S. Ashbaugh, Richard S. Laugesen, Department of Mathematics, University of Missouri Columbia, University of Missouri [Columbia] (Mizzou), University of Missouri System-University of Missouri System, Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Department of Mathematics [Urbana], University of Illinois at Urbana-Champaign [Urbana], University of Illinois System-University of Illinois System, CORIDA, and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est
- Subjects
Discrete mathematics ,Sequence ,Conjecture ,General Mathematics ,010102 general mathematics ,Mathematics::History and Overview ,Mathematics::Spectral Theory ,01 natural sciences ,Domain (mathematical analysis) ,Computer Science::Computers and Society ,010101 applied mathematics ,symbols.namesake ,Physics::Popular Physics ,Dirichlet boundary condition ,Euclidean geometry ,symbols ,Calculus ,Convex body ,Quantitative Biology::Populations and Evolution ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Spectral gap ,0101 mathematics ,Mathematics ,Unit interval - Abstract
The spectral gap conjecture of M. van den Berg [2, formula (65)] asserts that λ2 − λ1 ≥ 3π for all convex euclidean domains of diameter 1, where λ1 and λ2 denote the first two eigenvalues of the Dirichlet Laplacian. Notice that equality holds for the 1-dimensional unit interval, which can be regarded also as a degenerate n-dimensional rectangular box. The gap estimate is conjectured to hold more generally for Schrodinger operators with convex potentials, under Dirichlet boundary conditions; see the work of S.-T. Yau and collaborators [9, 11]. This Schrodinger gap conjecture was proved some time ago in 1 dimension by R. Lavine [8], and more recently in all dimensions by B. Andrews and J. Clutterbuck [1]. The proof in this journal by H. Donnelly [3] of the original gap conjecture in 2 dimensions (for the Dirichlet Laplacian with zero potential) is not correct. The Editors of Mathematische Zeitschrift have asked us to describe the flaws in the proof, in order to clarify the state of the literature. Donnelly’s approach to the problem is a natural one: first perform a shape optimization to rule out a non-degenerate minimizing domain, and then analyze the spectral gap for a sequence of domains degenerating to an interval, with the help of results by D. Jerison [5]. (For some history on this approach, and on the gap conjecture more generally, see the report on the AIM meeting “Low Eigenvalues of Laplace and Schrodinger Operators” [10], especially page 12 of the open problems list.) The error lies in the proof of the shape optimization step, as we now explain. Donnelly wishes to prove that no minimizing domain can exist for
- Published
- 2011
39. Note on a paper by A. Granville and K. Soundararajan
- Author
-
Jie Wu, Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), and Wu, Jie
- Subjects
Discrete mathematics ,Algebra and Number Theory ,Distribution (number theory) ,010102 general mathematics ,Equal probability ,01 natural sciences ,[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] ,Combinatorics ,symbols.namesake ,Results on L(1,χ) ,\chi)$ ,0103 physical sciences ,symbols ,Results on $L(1 ,010307 mathematical physics ,11M20 ,0101 mathematics ,Random variable ,Euler product ,[MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT] ,Mathematics - Abstract
In this note, we improve some results of Granville and Soundararajan on the distribution of values of the truncated random Euler product L ( 1 , X ; y ) : = ∏ p ⩽ y ( 1 − X ( p ) / p ) −1 , where the X ( p ) are independent random variables, taking the values ±1 with equal probability p / 2 ( p + 1 ) and 0 with probability 1 / ( p + 1 ) .
- Published
- 2007
40. Review papers : Variance components for statistical genetics: applications in medical research to characteristics related to human diseases and health
- Author
-
John L. Hopper
- Subjects
Statistics and Probability ,Multivariate statistics ,Epidemiology ,Health Status ,Structure (category theory) ,Multivariate normal distribution ,Social Environment ,01 natural sciences ,010104 statistics & probability ,symbols.namesake ,0504 sociology ,Health Information Management ,Statistics ,Econometrics ,Humans ,0101 mathematics ,Mathematics ,Models, Statistical ,Models, Genetic ,05 social sciences ,Genetic Diseases, Inborn ,Genetic Variation ,050401 social sciences methods ,History, 20th Century ,Covariance ,Pedigree ,Darwin (ADL) ,Multivariate Analysis ,Mendelian inheritance ,symbols ,Identifiability ,Analysis of variance - Abstract
RA Fisher introduced variance components in 1918. He synthesized Mendelian inheritance with Darwin's theory of evolution by showing that the genetic variance of a continuous trait could be decomposed into additive and non-additive components. The model can be extended to include environmental factors, interactions, covariation, and non-random mating. Identifiability depends critically on design. Methods of analysis include modelling the mean squares from a fixed effects analysis of variance, and covariance structure modelling, which can be extended to multivariate traits and has been used to study ordinal traits by reference to postulated, unmeasured, latent 'liabilities'. These methods operate on dependent observa tions within independent groups of the same size and structure, and therefore require balanced designs ('regular' pedigrees). A multivariate normal model handles data in its generic form, utilizes data efficiently from all members of pedigrees of unequal size or varying structure, accommodates individuals missing at random, and allows flexible modelling with tests of distributional assumptions and fit. Most analytical methods use least squares or maximum likelihood under normal theory. Robust methods, scale transforma tion, ascertainment, path diagrams and correlational path models (popular in behavioural genetics through addressing nonrandom mating and social interactions), 'heritability', and the contribution and limitations of statistical modelling to the 'nature-nurture' debate, are discussed.
- Published
- 1993
41. Co-actions, Isometries and isomorphism classes of Hilbert modules
- Author
-
Dan Z. Kučerovský
- Subjects
Pure mathematics ,0211 other engineering and technologies ,02 engineering and technology ,Hilbert modules ,01 natural sciences ,Unitary state ,C*-algebraic quantum group ,symbols.namesake ,16T05 ,FOS: Mathematics ,0101 mathematics ,Operator Algebras (math.OA) ,47L80 ,16T20 ,Mathematics ,Original Paper ,021103 operations research ,Algebra and Number Theory ,Functor ,Semigroup ,Mathematics::Operator Algebras ,Computer Science::Information Retrieval ,Operator (physics) ,010102 general mathematics ,Multiplicative function ,Hilbert space ,Mathematics - Operator Algebras ,Operator theory ,Multiplicative unitaries ,Cuntz semigroups ,symbols ,Isomorphism ,Analysis ,47L50 - Abstract
We show that a A-linear map of Hilbert A-modules is induced by a unitary Hilbert module operator if and only if it extends to an ordinary unitary on appropriately defined enveloping Hilbert spaces. Applications to the theory of multiplicative unitaries let us to compute the equivalence classes of Hilbert modules over a class of C*-algebraic quantum groups. We, thus, develop a theory that, for example, could be used to show non-existence of certain co-actions. In particular, we show that the Cuntz semigroup functor takes a co-action to a multiplicative action.
- Published
- 2023
42. A topological proof of the modified Euler characteristic based on the orbifold concept
- Author
-
Bartosz Naskręcki, Mariusz Jaskolski, and Zbigniew Dauter
- Subjects
asymmetric units ,02 engineering and technology ,Topological space ,010403 inorganic & nuclear chemistry ,Topology ,01 natural sciences ,Biochemistry ,space-filling polyhedra ,Inorganic Chemistry ,Polyhedron ,symbols.namesake ,Structural Biology ,Euler characteristic ,General Materials Science ,Physical and Theoretical Chemistry ,Orbifold ,Mathematics ,Tessellation ,space groups ,Group (mathematics) ,Coxeter group ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,Research Papers ,0104 chemical sciences ,Euler equations ,symbols ,orbifolds ,0210 nano-technology - Abstract
The vanishing of the modified Euler characteristic for symmetrically arranged space-filling polytopes is given a general proof based on the topological concept of orbifolds. The modified Euler characteristic is applicable to such important crystallographic objects as asymmetric units and Dirichlet domains., The notion of the Euler characteristic of a polyhedron or tessellation has been the subject of in-depth investigations by many authors. Two previous papers worked to explain the phenomenon of the vanishing (or zeroing) of the modified Euler characteristic of a polyhedron that underlies a periodic tessellation of a space under a crystallographic space group. The present paper formally expresses this phenomenon as a theorem about the vanishing of the Euler characteristic of certain topological spaces called topological orbifolds. In this new approach, it is explained that the theorem in question follows from the fundamental properties of the orbifold Euler characteristic. As a side effect of these considerations, a theorem due to Coxeter about the vanishing Euler characteristic of a honeycomb tessellation is re-proved in a context which frees the calculations from the assumptions made by Coxeter in his proof. The abstract mathematical concepts are visualized with down-to-earth examples motivated by concrete situations illustrating wallpaper and 3D crystallographic space groups. In a way analogous to the application of the classic Euler equation to completely bounded solids, the formula proven in this paper is applicable to such important crystallographic objects as asymmetric units and Dirichlet domains.
- Published
- 2021
43. On a Method of Solution of Systems of Fractional Pseudo-Differential Equations
- Author
-
YangQuan Chen, Ravshan Ashurov, and Sabir Umarov
- Subjects
matrix symbol ,Differential equation ,Primary 35E15 ,33E12 ,01 natural sciences ,symbols.namesake ,solution operator ,Completeness (order theory) ,Mittag-Leffler function ,fractional order differential equation ,Applied mathematics ,fractional system of differential equations ,Uniqueness ,0101 mathematics ,Differential (infinitesimal) ,Secondary 35S10 ,Mathematics ,Applied Mathematics ,010102 general mathematics ,Linear system ,system of differential equations ,pseudo-differential operator ,Pseudo-differential operator ,010101 applied mathematics ,Sobolev space ,35R11 ,symbols ,Analysis ,Research Paper - Abstract
This paper is devoted to the general theory of linear systems of fractional order pseudo-differential equations. Single fractional order differential and pseudo-differential equations are studied by many authors and several monographs and handbooks have been published devoted to its theory and applications. However, the state of systems of fractional order ordinary and partial or pseudo-differential equations is still far from completeness, even in the linear case. In this paper we develop a new method of solution of general systems of fractional order linear pseudo-differential equations and prove existence and uniqueness theorems in the special classes of distributions, as well as in the Sobolev spaces.
- Published
- 2021
44. Stationary distribution and density function expression for a stochastic SIQRS epidemic model with temporary immunity
- Author
-
Baoquan Zhou, Yucong Dai, Daqing Jiang, and Tasawar Hayat
- Subjects
Lyapunov function ,Aerospace Engineering ,Temporary immunity ,Ocean Engineering ,Probability density function ,01 natural sciences ,symbols.namesake ,0103 physical sciences ,Applied mathematics ,Ergodic theory ,Density function ,Ergodic stationary distribution ,Electrical and Electronic Engineering ,Logistic function ,010301 acoustics ,Mathematics ,Original Paper ,Stationary distribution ,Applied Mathematics ,Mechanical Engineering ,Stochastic SIQRS epidemic model ,Control and Systems Engineering ,Fokker–Planck equation ,symbols ,Epidemic model ,Deterministic system - Abstract
Recently, considering the temporary immunity of individuals who have recovered from certain infectious diseases, Liu et al. (Phys A Stat Mech Appl 551:124152, 2020) proposed and studied a stochastic susceptible-infected-recovered-susceptible model with logistic growth. For a more realistic situation, the effects of quarantine strategies and stochasticity should be taken into account. Hence, our paper focuses on a stochastic susceptible-infected-quarantined-recovered-susceptible epidemic model with temporary immunity. First, by means of the Khas’minskii theory and Lyapunov function approach, we construct a critical value \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr {R}}_0^S$$\end{document}R0S corresponding to the basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr {R}}_0$$\end{document}R0 of the deterministic system. Moreover, we prove that there is a unique ergodic stationary distribution if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr {R}}_0^S>1$$\end{document}R0S>1. Focusing on the results of Zhou et al. (Chaos Soliton Fractals 137:109865, 2020), we develop some suitable solving theories for the general four-dimensional Fokker–Planck equation. The key aim of the present study is to obtain the explicit density function expression of the stationary distribution under \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr {R}}_0^S>1$$\end{document}R0S>1. It should be noted that the existence of an ergodic stationary distribution together with the unique exact probability density function can reveal all the dynamical properties of disease persistence in both epidemiological and statistical aspects. Next, some numerical simulations together with parameter analyses are shown to support our theoretical results. Last, through comparison with other articles, results are discussed and the main conclusions are highlighted.
- Published
- 2021
45. Dynamical Study of an Eco-Epidemiological Delay Model for Plankton System with Toxicity
- Author
-
Archana Ojha, Nilesh Kumar Thakur, and Smriti Chandra Srivastava
- Subjects
General Mathematics ,Population ,Chaotic ,General Physics and Astronomy ,01 natural sciences ,Stability (probability) ,Zooplankton ,010305 fluids & plasmas ,symbols.namesake ,0103 physical sciences ,Carrying capacity ,Quantitative Biology::Populations and Evolution ,education ,010301 acoustics ,Mathematics ,Equilibrium point ,Hopf bifurcation ,education.field_of_study ,Toxicity ,fungi ,General Chemistry ,Plankton ,System dynamics ,Local stability ,Hopf-bifurcation ,symbols ,General Earth and Planetary Sciences ,Chaos ,General Agricultural and Biological Sciences ,Biological system ,Time delay ,Research Paper - Abstract
In this paper, we analyze the complexity of an eco-epidemiological model for phytoplankton–zooplankton system in presence of toxicity and time delay. Holling type II function response is incorporated to address the predation rate as well as toxic substance distribution in zooplankton. It is also presumed that infected phytoplankton does recover from the viral infection. In the absence of time delay, stability and Hopf-bifurcation conditions are investigated to explore the system dynamics around all the possible equilibrium points. Further, in the presence of time delay, conditions for local stability are derived around the interior equilibria and the properties of the periodic solution are obtained by applying normal form theory and central manifold arguments. Computational simulation is performed to illustrate our theoretical findings. It is explored that system dynamics is very sensitive corresponding to carrying capacity and toxin liberation rate and able to generate chaos. Further, it is observed that time delay in the viral infection process can destabilize the phytoplankton density whereas zooplankton density remains in its old state. Incorporation of time delay also gives the scenario of double Hopf-bifurcation. Some control parameters are discussed to stabilize system dynamics. The effect of time delay on (i) growth rate of susceptible phytoplankton shows the extinction and double Hopf-bifurcation in the zooplankton population, (ii) a sufficiently large value of carrying capacity stabilizes the chaotic dynamics or makes the whole system chaotic with further increment.
- Published
- 2021
46. The effect of transformer parameters on reliability assessment with the help of health index
- Author
-
Suraj B. Singh and Neelam Chantola
- Subjects
010302 applied physics ,Mean time between failures ,Laplace transform ,Transformer oil ,Strategy and Management ,0211 other engineering and technologies ,Electrical insulation paper ,Markov process ,02 engineering and technology ,01 natural sciences ,General Business, Management and Accounting ,law.invention ,Reliability engineering ,symbols.namesake ,law ,0103 physical sciences ,symbols ,Dissipation factor ,Breakdown voltage ,021108 energy ,Transformer ,Mathematics - Abstract
Purpose The purpose of this paper is to study various reliability measures like reliability, mean time to failure (MTTF) and sensitivity of transformer including different parameters of insulating oil/paper as health index. Design/methodology/approach The reliability characteristics of transformer incorporating different parameters of insulating oil as well as paper have been evaluated using Markov process incorporating Gumbel–Hougaard copula, Laplace transforms and supplementary variable technique. The parameters taken into consideration are breakdown voltage (BDV) and moisture content (MC) of both insulating oil and paper, and other parameters considered are interfacial tension (IFT), dissipation factor (DF), degree of polymerization (DOP) and furanic content (FC) for insulating oil and paper, respectively. By probability consideration and continuity influence, difference-differential equations have been obtained for the considered model. Findings Transition state probabilities, reliability, MTTF and sensitivity of the transformer corresponding to different parameters of insulating oil and paper have been evaluated with the help of aforementioned technique. Variations of reliability with respect to time along with the variations of MTTF and sensitivity have also been examined. Remarkable points during the study have also been pointed out. Originality/value Reliability characteristics of the transformer have been evaluated including two parameters: insulating oil and paper with the help of supplementary variable technique, considering two different types of repairs incorporating Gumbel–Hougaard family of copula unlike done earlier. Reliability, MTTF and sensitivity of transformer have been analyzed considering the parameters: BDV, MC, IFT and FC of insulating oil, and BDV, MC, DOP, DF of insulating paper.
- Published
- 2019
47. Stability analysis of the coexistence equilibrium of a balanced metapopulation model
- Author
-
Nathan Muyinda, Bernard De Baets, and Shodhan Rao
- Subjects
0106 biological sciences ,Lyapunov function ,DYNAMICS ,PROMOTES ,Science ,GAME ,Metapopulation ,010603 evolutionary biology ,01 natural sciences ,Stability (probability) ,Article ,03 medical and health sciences ,symbols.namesake ,DISPERSAL ,Stability theory ,COMPETITIVE NETWORK ,Statistical physics ,SCISSORS ,030304 developmental biology ,Mathematics ,Ecological modelling ,Equilibrium point ,0303 health sciences ,Multidisciplinary ,COMPLEX ,CONSEQUENCES ,Invariance principle ,Ode ,INTRANSITIVITY ,Applied mathematics ,Mathematics and Statistics ,Ordinary differential equation ,symbols ,PAPER ,Medicine ,Theoretical ecology - Abstract
We analyze the stability of a unique coexistence equilibrium point of a system of ordinary differential equations (ODE system) modelling the dynamics of a metapopulation, more specifically, a set of local populations inhabiting discrete habitat patches that are connected to one another through dispersal or migration. We assume that the inter-patch migrations are detailed balanced and that the patches are identical with intra-patch dynamics governed by a mean-field ODE system with a coexistence equilibrium. By making use of an appropriate Lyapunov function coupled with LaSalle’s invariance principle, we are able to show that the coexistence equilibrium point within each patch is locally asymptotically stable if the inter-patch dispersal network is heterogeneous, whereas it is neutrally stable in the case of a homogeneous network. These results provide a mathematical proof confirming the existing numerical simulations and broaden the range of networks for which they are valid.
- Published
- 2021
48. Biased Adjusted Poisson Ridge Estimators-Method and Application
- Author
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Pär Sjölander, Muhammad Qasim, Muhammad Amin, B. M. Golam Kibria, and Kristofer Månsson
- Subjects
Mean squared error ,General Mathematics ,Maximum likelihood ,General Physics and Astronomy ,Regression estimator ,Poisson distribution ,Modified almost unbiased ridge estimators ,01 natural sciences ,symbols.namesake ,0103 physical sciences ,Statistics ,Poisson regression ,0101 mathematics ,Mathematics ,010308 nuclear & particles physics ,010102 general mathematics ,Estimator ,Mean square error ,General Chemistry ,Ridge (differential geometry) ,Poisson ridge regression ,Multicollinearity ,Maximum likelihood estimator ,symbols ,General Earth and Planetary Sciences ,General Agricultural and Biological Sciences ,Research Paper - Abstract
Månsson and Shukur (Econ Model 28:1475–1481, 2011) proposed a Poisson ridge regression estimator (PRRE) to reduce the negative effects of multicollinearity. However, a weakness of the PRRE is its relatively large bias. Therefore, as a remedy, Türkan and Özel (J Appl Stat 43:1892–1905, 2016) examined the performance of almost unbiased ridge estimators for the Poisson regression model. These estimators will not only reduce the consequences of multicollinearity but also decrease the bias of PRRE and thus perform more efficiently. The aim of this paper is twofold. Firstly, to derive the mean square error properties of the Modified Almost Unbiased PRRE (MAUPRRE) and Almost Unbiased PRRE (AUPRRE) and then propose new ridge estimators for MAUPRRE and AUPRRE. Secondly, to compare the performance of the MAUPRRE with the AUPRRE, PRRE and maximum likelihood estimator. Using both simulation study and real-world dataset from the Swedish football league, it is evidenced that one of the proposed, MAUPRRE ($$ \hat{k}_{q4} $$ k ^ q 4 ) performed better than the rest in the presence of high to strong (0.80–0.99) multicollinearity situation.
- Published
- 2020
49. Direct statistical inference for finite Markov jump processes via the matrix exponential
- Author
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Sherlock, Chris
- Subjects
FOS: Computer and information sciences ,Statistics and Probability ,Bayesian inference ,Population ,01 natural sciences ,Methodology (stat.ME) ,010104 statistics & probability ,03 medical and health sciences ,Matrix (mathematics) ,symbols.namesake ,62M05 ,Statistical inference ,Applied mathematics ,0101 mathematics ,education ,Markov jump process ,Statistics - Methodology ,030304 developmental biology ,Mathematics ,Original Paper ,0303 health sciences ,education.field_of_study ,Markov chain ,Stochastic matrix ,Markov chain Monte Carlo ,Matrix exponential ,Likelihood inference ,Computational Mathematics ,symbols ,Statistics, Probability and Uncertainty - Abstract
Given noisy, partial observations of a time-homogeneous, finite-statespace Markov chain, conceptually simple, direct statistical inference is available, in theory, via its rate matrix, or infinitesimal generator, $\mathsf{Q}$, since $\exp (\mathsf{Q}t)$ is the transition matrix over time $t$. However, perhaps because of inadequate tools for matrix exponentiation in programming languages commonly used amongst statisticians or a belief that the necessary calculations are prohibitively expensive, statistical inference for continuous-time Markov chains with a large but finite state space is typically conducted via particle MCMC or other relatively complex inference schemes. When, as in many applications $\mathsf{Q}$ arises from a reaction network, it is usually sparse. We describe variations on known algorithms which allow fast, robust and accurate evaluation of the product of a non-negative vector with the exponential of a large, sparse rate matrix. Our implementation uses relatively recently developed, efficient, linear algebra tools that take advantage of such sparsity. We demonstrate the straightforward statistical application of the key algorithm on a model for the mixing of two alleles in a population and on the Susceptible-Infectious-Removed epidemic model., Focus much more on statistical inference, filtering and prediction
- Published
- 2021
50. Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions
- Author
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Feng Qi and Chuan-Jun Huang
- Subjects
Pure mathematics ,Binomial (polynomial) ,Determinant ,33B15 ,11A25 ,01 natural sciences ,Inversion (discrete mathematics) ,11B65 ,symbols.namesake ,Beta function ,Identity ,Gauss hypergeometric function ,Differentiable function ,0101 mathematics ,Hypergeometric function ,Secondary 05A10 ,Mathematics ,Original Paper ,Algebra and Number Theory ,Applied Mathematics ,010102 general mathematics ,Gauss ,Sum ,Primary 33C05 ,Binomial inversion formula ,Polygamma function ,010101 applied mathematics ,Derivative formula for a ratio of two differential functions ,Computational Mathematics ,symbols ,Partial derivative ,Geometry and Topology ,Analysis - Abstract
In the paper, by virtue of the binomial inversion formula, a general formula of higher order derivatives for a ratio of two differentiable function, and other techniques, the authors compute several sums in terms of the beta function and its partial derivatives, polygamma functions, the Gauss hypergeometric function, and a determinant. These results generalize known ones in combinatorics. This preprint has been formally published as "Feng Qi and Chuan-Jun Huang, Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales Serie A Matematicas, Vol. 114, Paper No. 191, 9 pages (2020); available online at https://doi.org/10.1007/s13398-020-00927-y."
- Published
- 2020
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