23,002 results
Search Results
2. On Variability and Interdependence of Local Porosity and Local Tortuosity in Porous Materials: a Case Study for Sack Paper
- Author
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Matthias Neumann, Eduardo Machado Charry, Volker Schmidt, and Karin Zojer
- Subjects
Statistics and Probability ,Geodesic ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Copula (linguistics) ,Sinuosity ,01 natural sciences ,Tortuosity ,010104 statistics & probability ,Goodness of fit ,Gumbel distribution ,Joint probability distribution ,0101 mathematics ,Porosity ,Mathematics - Abstract
The variability and interdependence of local porosity and local mean geodesic tortuosity, which is a measure for the sinuosity of shortest transportation paths, is investigated at the example of the microstructure in sack paper. By means of statistical image analysis, these two morphological characteristics are computed for several cutouts of 3D image data obtained by X-ray microcomputed tomography. Considering cutouts of different sizes allows us to study the influence of the sample size on the local variability of the considered characteristics. Moreover, the interdependence between local porosity and local mean geodesic tortuosity is quantified by modeling their joint distribution parametrically using Archimedean copulas. It turns out that the family of Gumbel copulas is an appropriate model type, which is formally validated by a goodness of fit test. Besides mean geodesic tortuosity, we consider further related morphological characteristics, describing the sinuosity of those shortest transportation paths, whose minimum diameter exceeds a predefined threshold. Moreover, we show that the copula approach investigated in this paper can also be used to quantify the negative correlation between local porosity and these modified versions of local mean geodesic tortuosity. Our results elucidate the impact of local porosity on various kinds of morphological characteristics, which are not experimentally accessible and which are important for local air permeance – a key property of sack paper.
- Published
- 2020
3. Note on a paper by Bordellès, Dai, Heyman, Pan and Shparlinski
- Author
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Jie Wu
- Subjects
Combinatorics ,General Mathematics ,010102 general mathematics ,0211 other engineering and technologies ,021107 urban & regional planning ,02 engineering and technology ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
Very recently Bordelles, Dai, Heyman, Pan and Shparlinski studied asymptotic behaviour of the quantity $$\begin{aligned} S_f(x) := \sum _{n\leqslant x} f\left( \left[ \frac{x}{n}\right] \right) , \end{aligned}$$and established some asymptotic formulas for $$S_f(x)$$ under three different types of assumptions on f. In this short note we improve some of their results.
- Published
- 2019
4. An example regarding Kalton's paper 'Isomorphisms between spaces of vector-valued continuous functions'
- Author
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Félix Cabello Sánchez
- Subjects
Pure mathematics ,Mathematics::Functional Analysis ,General Mathematics ,010102 general mathematics ,General Topology (math.GN) ,01 natural sciences ,Functional Analysis (math.FA) ,010101 applied mathematics ,Mathematics - Functional Analysis ,Dimension (vector space) ,46A16, 46E10 ,Metric (mathematics) ,FOS: Mathematics ,0101 mathematics ,Mathematics ,Mathematics - General Topology - Abstract
The paper alluded to in the title contains the following striking result: Let $I$ be the unit interval and $\Delta$ the Cantor set. If $X$ is a quasi Banach space containing no copy of $c_0$ which is isomorphic to a closed subspace of a space with a basis and $C(I, X)$ is linearly homeomorphic to $C(\Delta, X)$, then $X$ is locally convex, i.e., a Banach space. It is shown that Kalton result is sharp by exhibiting non locally convex quasi Banach spaces X with a basis for which $C(I, X)$ and $C(\Delta, X)$ are isomorphic. Our examples are rather specific and actually in all cases X is isomorphic to $C(\Delta, X)$ if $K$ is a metric compactum of finite covering dimension., Comment: 4 pages
- Published
- 2021
- Full Text
- View/download PDF
5. What Have We (Not) Learnt from Millions of Scientific Papers with P Values?
- Author
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John P. A. Ioannidis
- Subjects
Statistics and Probability ,Empirical data ,General Mathematics ,05 social sciences ,01 natural sciences ,050105 experimental psychology ,010104 statistics & probability ,Statistical significance ,Statistics ,Statistical inference ,0501 psychology and cognitive sciences ,p-value ,0101 mathematics ,Statistics, Probability and Uncertainty ,Mathematics ,Statistical hypothesis testing - Abstract
P values linked to null hypothesis significance testing (NHST) is the most widely (mis)used method of statistical inference. Empirical data suggest that across the biomedical literature (1990–2015)...
- Published
- 2019
6. On a paper of Erdös and Szekeres
- Author
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Mei-Chu Chang and Jean Bourgain
- Subjects
010101 applied mathematics ,Discrete mathematics ,Set (abstract data type) ,Partial differential equation ,Functional analysis ,General Mathematics ,010102 general mathematics ,0101 mathematics ,01 natural sciences ,Analysis ,Mathematics - Abstract
Propositions 1.1–1.3 stated below contribute to results and certain problems considered in [E-S], on the behavior of products $$\Pi^n_1(1-z^{a_j}),1\leq{a_1}...\leq{a_n}$$ integers. In the discussion below, {a1,..., an} will be either a proportional subset of {1,..., n} or a set of large arithmetic diameter.
- Published
- 2018
7. Notes on the paper 'A note on pronormal p-subgroups of finite groups'
- Author
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Haoran Yu and Suli Liu
- Subjects
Discrete mathematics ,Lemma (mathematics) ,010505 oceanography ,General Mathematics ,010102 general mathematics ,0101 mathematics ,01 natural sciences ,0105 earth and related environmental sciences ,Mathematics - Abstract
In this short note, we show that Theorem 4.3 of Liu and Yu (Monatshefte Math 195:173–176, 2021) is a consequence of Lemma 2 of Ballester-Bolinches and Esteban-Romero (J Aust Math Soc 75:181–191, 2003).
- Published
- 2021
8. A Look at Robustness and Stability of $\ell_{1}$-versus $\ell_{0}$-Regularization: Discussion of Papers by Bertsimas et al. and Hastie et al
- Author
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Peter Bühlmann, Armeen Taeb, and Yuansi Chen
- Subjects
Statistics and Probability ,latent variables ,low-rank estimation ,General Mathematics ,Linear model ,020206 networking & telecommunications ,Feature selection ,02 engineering and technology ,Latent variable ,01 natural sciences ,Regularization (mathematics) ,010104 statistics & probability ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,Distributional robustness ,0101 mathematics ,Statistics, Probability and Uncertainty ,high-dimensional estimation ,Mathematics ,variable selection - Abstract
We congratulate the authors Bertsimas, Pauphilet and van Parys (hereafter BPvP) and Hastie, Tibshirani and Tibshirani (hereafter HTT) for providing fresh and insightful views on the problem of variable selection and prediction in linear models. Their contributions at the fundamental level provide guidance for more complex models and procedures.
- Published
- 2020
- Full Text
- View/download PDF
9. Scientific heritage of L.D. Faddeev. Survey of papers
- Author
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M. A. Semenov-Tian-Shansky, I. Ya. Aref'eva, Evgeny Sklyanin, A. Yu. Alekseev, Samson L. Shatashvili, F. A. Smirnov, Leon A. Takhtajan, Euler International Mathematical Institute [St. Petersburg], Stony Brook University [SUNY] (SBU), State University of New York (SUNY), University of Geneva [Switzerland], Steklov Mathematical Institute [Moscow] (SMI), Russian Academy of Sciences [Moscow] (RAS), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), University of York [York, UK], Université Pierre et Marie Curie - Paris 6 (UPMC), Institut des Hautes Etudes Scientifiques (IHES), IHES, Trinity College Dublin, Institute for Information Transmission Problems, The work of Semenov-Tian-Shansky was supported by the Presidium of the Russian Academy of Sciences programme no. 02 'Non-linear dynamics: fundamental problems and applications' (grant no. PRAS-18-02). Sklyanin worked as a Royal Society Leverhulme Trust Senior Research Fellow. The work of Shatashvili was supported by the Simons Foundation under the programme 'Targeted Grants to Institutes' (The Hamilton Mathematics Institute)., Université de Genève = University of Geneva (UNIGE), Université de Bourgogne (UB)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), and Institut des Hautes Études Scientifiques (IHES)
- Subjects
Inverse scattering problem ,Scattering theory ,General Mathematics ,Yang-Baxter equation ,Inverse scattering method ,Quantum groups ,01 natural sciences ,AMS 2010 Mathematics Subject Classification. Primary 01A70, 16T25, 17B37, 35J10, 35P25,35Q53, 35Q55, 37K15, 58B32, 58J52, 70S15, 81-03, 81R50, 81S40, 81T10, 81T13, 81T50, 81T70,81U40, 82B23, 82C23 ,Eigenfunction expansion ,[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] ,Quantization of gauge fields ,Korteweg-de Vries equation ,0103 physical sciences ,Schrodinger operator ,0101 mathematics ,Korteweg–de Vries equation ,Mathematics ,Mathematical physics ,Quantum anomalies ,010308 nuclear & particles physics ,Yang–Baxter equation ,Faddeev-Popov ghosts ,010102 general mathematics ,Algebraic Bethe ansatz ,Quantum dilogarithm ,Complete integrability ,Quantum inverse problem method - Abstract
International audience; This survey was written by students of L. D. Faddeev under the editorship of L. A. Takhtajan. Sections 1.1, 1.2, 2–4, and 6 were written by Takhtajan, §§1.3 and 1.4 by F. A. Smirnov, §§5.1 and 5.2 by E. K. Sklyanin, §§5.3–5.6 by Sklyanin, Smirnov, and Takhtajan, §7.1 by M. A. Semenov- Tian-Shansky, §§7.2–7.6 by Takhtajan and S. L. Shatashvili, §7.7 by A. Yu. Alekseev and Shatashvili, and §8 by I. Ya. Aref'eva.
- Published
- 2017
10. On A.Ya. Khinchin's paper ‘Ideas of intuitionism and the struggle for a subject matter in contemporary mathematics’ (1926): A translation with introduction and commentary
- Author
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Lukas M. Verburgt and Olga Hoppe-Kondrikova
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History ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,Victory ,Ignorance ,06 humanities and the arts ,0603 philosophy, ethics and religion ,01 natural sciences ,Epistemology ,Subject matter ,Formalism (philosophy of mathematics) ,Intuitionism ,060302 philosophy ,Calculus ,Ideology ,0101 mathematics ,Communism ,media_common ,Mathematics - Abstract
The translation into English of Aleksandr Yakovlevich Khinchin's (1894–1959) 1926 paper entitled ‘Ideas of intuitionism and the struggle for a subject matter in contemporary mathematics’ is made available for the first time. Here, Khinchin presented the famous foundational debate between L.E.J. Brouwer and David Hilbert of the 1920s in terms of a search for a mathematics with content. His main aim seems to have been to make intuitionism ideologically acceptable to his audience at the Communist Academy by means of the claim that insofar as Brouwer's intuitionism had a clear ‘subject matter’ and Hilbert's new program was a concession to intuitionism, the alleged victory of intuitionism not only implied the defeat of ‘empty’ formalism, but also showed the compatibility and affinity of Marxism with the newest developments in modern mathematics. This introduction provides a tentative exploration of the issue of what was tactical (or due to ideological pressure) and what was real scientific interest (or due to ignorance) (or what was both) in Khinchin's 1926 paper in the form of a detailed commentary, especially, on the tactical side of his presentation of the positions of Brouwer and Hilbert.
- Published
- 2016
11. 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
12. From coin tossing to rock-paper-scissors and beyond: a log-exp gap theorem for selecting a leader
- Author
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Hsien-Kuei Hwang, Yoshiaki Itoh, and Michael Fuchs
- Subjects
Statistics and Probability ,Discrete mathematics ,Class (set theory) ,Coin flipping ,Group (mathematics) ,General Mathematics ,Variance (accounting) ,01 natural sciences ,Exponential function ,010104 statistics & probability ,Logarithmic mean ,Bounded function ,0103 physical sciences ,Gap theorem ,0101 mathematics ,Statistics, Probability and Uncertainty ,010306 general physics ,Mathematics - Abstract
A class of games for finding a leader among a group of candidates is studied in detail. This class covers games based on coin tossing and rock-paper-scissors as special cases and its complexity exhibits similar stochastic behaviors: either of logarithmic mean and bounded variance or of exponential mean and exponential variance. Many applications are also discussed.
- Published
- 2017
13. Notes on the Paper 'On SS-Quasinormal and S-Quasinormally Embedded Subgroups of Finite Groups' of Shen et al
- Author
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Yuemei Mao, Xiaolan Yi, and Changwen Li
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Discrete mathematics ,General Mathematics ,010102 general mathematics ,0103 physical sciences ,Zhàng ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,010307 mathematical physics ,0101 mathematics ,01 natural sciences ,GeneralLiterature_MISCELLANEOUS ,Mathematics - Abstract
We correct an error in the paper of Z. Shen, S. Li, and J. Zhang published in [4]. In addition, we give an answer to a question posed by the authors.
- Published
- 2018
14. Corrections and complements to my paper 'On a class of operator monotone functions of several variables'
- Author
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A. R. Mirotin
- Subjects
Discrete mathematics ,General Mathematics ,010102 general mathematics ,0211 other engineering and technologies ,021107 urban & regional planning ,02 engineering and technology ,Finite-rank operator ,Compact operator ,Strongly monotone ,Shift operator ,01 natural sciences ,Semi-elliptic operator ,Algebra ,Pseudo-monotone operator ,Monotone polygon ,Multiplication operator ,0101 mathematics ,Mathematics - Published
- 2017
15. Using A4-sized paper to illustrate that is irrational
- Author
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Nick Lord
- Subjects
General Mathematics ,Irrational number ,010102 general mathematics ,0101 mathematics ,01 natural sciences ,Mathematical economics ,Mathematics - Published
- 2017
16. Remark on the paper 'On products of Fourier coefficients of cusp forms'
- Author
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Yuk-Kam Lau, Deyu Zhang, and Yingnan Wang
- Subjects
Cusp (singularity) ,Discrete group ,Mathematics::Number Theory ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Holomorphic function ,02 engineering and technology ,01 natural sciences ,Cusp form ,Combinatorics ,Integer ,Product (mathematics) ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,0101 mathematics ,Fourier series ,Mathematics - Abstract
Let a(n) be the Fourier coefficient of a holomorphic cusp form on some discrete subgroup of \(SL_2({\mathbb R})\). This note is to refine a recent result of Hofmann and Kohnen on the non-positive (resp. non-negative) product of \(a(n)a(n+r)\) for a fixed positive integer r.
- Published
- 2016
17. On Nash’s unique contribution to analysis in just three of his papers
- Author
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Sergiu Klainerman
- Subjects
Applied Mathematics ,General Mathematics ,010102 general mathematics ,0103 physical sciences ,010307 mathematical physics ,0101 mathematics ,01 natural sciences ,Mathematics - Published
- 2016
18. Addendum to the paper 'Linearly topologized modules over a discrete valuation ring'
- Author
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Patricia Couto G. Mauro and Dinamérico P. Pombo
- Subjects
Discrete mathematics ,General Mathematics ,010102 general mathematics ,Addendum ,0101 mathematics ,01 natural sciences ,Discrete valuation ring ,Linear equation ,Mathematics - Abstract
For any discrete valuation ring R, any R-linear mapping u from an R-module E into an R-module F and any \(y_0\in F\), a necessary and sufficient condition for the solvability of the equation \(u(x)=y_0\) is established, and an application of this result is presented.
- Published
- 2016
19. Derived length of zero entropy groups acting on projective varieties in arbitrary characteristic — A remark to a paper of Dinh-Oguiso-Zhang
- Author
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Sichen Li
- Subjects
Automorphism group ,Pure mathematics ,Computer Science::Information Retrieval ,General Mathematics ,010102 general mathematics ,Zhàng ,Astrophysics::Instrumentation and Methods for Astrophysics ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,01 natural sciences ,0103 physical sciences ,Computer Science::General Literature ,Entropy (information theory) ,010307 mathematical physics ,0101 mathematics ,Algebraically closed field ,Projective test ,Projective variety ,Mathematics - Abstract
Let [Formula: see text] be a projective variety of dimension [Formula: see text] over an algebraically closed field of arbitrary characteristic. We prove a Fujiki–Lieberman type theorem on the structure of the automorphism group of [Formula: see text]. Let [Formula: see text] be a group of zero entropy automorphisms of [Formula: see text] and [Formula: see text] the set of elements in [Formula: see text] which are isotopic to the identity. We show that after replacing [Formula: see text] by a suitable finite-index subgroup, [Formula: see text] is a unipotent group of the derived length at most [Formula: see text]. This result was first proved by Dinh et al. for compact Kähler manifolds.
- Published
- 2020
20. NOTES ON THE PAPER 'A CRITERION FOR BOUNDED FUNCTIONS' [BULL. KOREAN MATH. SOC. 53 (2016), NO. 1, 215-225]
- Author
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Jin-Lin Liu and Yi-Ling Cang
- Subjects
Algebra ,General Mathematics ,Bounded function ,010102 general mathematics ,0101 mathematics ,Arithmetic ,01 natural sciences ,Mathematics - Published
- 2016
21. Entropy criteria and stability of extreme shocks: a remark on a paper of Leger and Vasseur
- Author
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Kevin Zumbrun and Benjamin Texier
- Subjects
Conservation law ,Kullback–Leibler divergence ,Standard molar entropy ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Mathematics::Analysis of PDEs ,Regular polygon ,Min entropy ,Shock strength ,01 natural sciences ,010101 applied mathematics ,Mathematics - Analysis of PDEs ,FOS: Mathematics ,Uniqueness ,0101 mathematics ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
We show that a relative entropy condition recently shown by Leger and Vasseur to imply uniqueness and stable $L^2$ dependence on initial data of Lax 1- or $n$-shock solutions of an $n\times n$ system of hyperbolic conservation laws with convex entropy implies Lopatinski stability in the sense of Majda. This means in particular that Leger and Vasseur's relative entropy condition represents a considerable improvement over the standard entropy condition of decreasing shock strength and increasing entropy along forward Hugoniot curves, which, in a recent example exhibited by Barker, Freist\"uhler and Zumbrun, was shown to fail to imply Lopatinski stability, even for systems with convex entropy. This observation bears also on the parallel question of existence, at least for small $BV$ or $H^s$ perturbations, Comment: to appear in Proceedings of the AMS
- Published
- 2014
22. On D.Y. Gao and X. Lu paper 'On the extrema of a nonconvex functional with double-well potential in 1D'
- Author
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Constantin Zălinescu
- Subjects
021103 operations research ,Applied Mathematics ,General Mathematics ,0211 other engineering and technologies ,General Physics and Astronomy ,Double-well potential ,02 engineering and technology ,Space (mathematics) ,01 natural sciences ,010101 applied mathematics ,Combinatorics ,Maxima and minima ,35J20, 35J60, 74G65, 74S30 ,Optimization and Control (math.OC) ,FOS: Mathematics ,Preprint ,0101 mathematics ,Constant (mathematics) ,Mathematics - Optimization and Control ,Subspace topology ,Mathematics - Abstract
The aim of this paper is to discuss the main result in the paper by D.Y. Gao and X. Lu [On the extrema of a nonconvex functional with double-well potential in 1D, Z. Angew. Math. Phys. (2016) 67:62]. More precisely we provide a detailed study of the problem considered in that paper, pointing out the importance of the norm on the space $C^{1}[a,b]$; because no norm (topology) is mentioned on $C^{1}[a,b]$ we look at it as being a subspace of $W^{1,p}(a,b)$ for $p\in [1,\infty]$ endowed with its usual norm. We show that the objective function has not local extrema with the mentioned constraints for $p\in [1,4)$, and has (up to an additive constant) only a local maximizer for $p=\infty$, unlike the conclusion of the main result of the discussed paper where it is mentioned that there are (up to additive constants) two local minimizers and a local maximizer. We also show that the same conclusions are valid for the similar problem treated in the preprint by X. Lu and D.Y. Gao [On the extrema of a nonconvex functional with double-well potential in higher dimensions, arXiv:1607.03995]., 12 pages; in this version we added the forgotten condition $F(x) \ne 0$ for $x\in (a,b)$ on page 3
- Published
- 2017
23. Some comments on the paper of Khuangsatung and Kangtunyakarn
- Author
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Kanokwan Wongchan
- Subjects
010101 applied mathematics ,Nonlinear system ,Fixed point problem ,General Mathematics ,010102 general mathematics ,Convergence (routing) ,Applied mathematics ,0101 mathematics ,Fixed point ,01 natural sciences ,Mathematics - Abstract
In this paper, we discuss the validity of the result of Khuangsatung and Kangtunyakarn [Existence and convergence theorem for fixed point problem of various nonlinear mappings and variational inequality problems without some assumptions, Filomat 32(1) (2018) 305–309].
- Published
- 2018
24. 'Graph Paper' Trace Characterizations of Functions of Finite Energy
- Author
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Robert S. Strichartz
- Subjects
Discrete mathematics ,Plane (geometry) ,General Mathematics ,010102 general mathematics ,Voltage graph ,Mathematics::General Topology ,Graph paper ,01 natural sciences ,Sierpinski triangle ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,Sobolev space ,Coxeter graph ,Sierpinski carpet ,0103 physical sciences ,String graph ,FOS: Mathematics ,010307 mathematical physics ,0101 mathematics ,Analysis ,Mathematics - Abstract
We characterize functions of finite energy in the plane in terms of their traces on the lines that make up "graph paper" with squares of side length $mn$ for all $n$, and certain $\12-$order Sobolev norms on the graph paper lines. We also obtain analogous results for functions of finite energy on two classical fractals: the Sierpinski gasket and the Sierpinski carpet.
- Published
- 2013
- Full Text
- View/download PDF
25. Appearance of Temporal and Spatial Chaos in an Ecological System: A Mathematical Modeling Study
- Author
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S. N. Raw, B P Sarangi, P. Mishra, and B. Tiwari
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Patter formulation ,Computer science ,General Mathematics ,General Physics and Astronomy ,Lyapunov exponent ,01 natural sciences ,Stability (probability) ,symbols.namesake ,Quantitative Biology::Populations and Evolution ,Statistical physics ,0101 mathematics ,Bifurcation ,Hopf bifurcation ,Computer simulation ,Phase portrait ,Turing instability ,010102 general mathematics ,Time evolution ,General Chemistry ,Function (mathematics) ,010101 applied mathematics ,symbols ,Chaos ,Mutual interference ,General Earth and Planetary Sciences ,General Agricultural and Biological Sciences ,Research Paper - Abstract
The ecological theory of species interactions rests largely on the competition, interference, and predator–prey models. In this paper, we propose and investigate a three-species predator–prey model to inspect the mutual interference between predators. We analyze boundedness and Kolmogorov conditions for the non-spatial model. The dynamical behavior of the system is analyzed by stability and Hopf bifurcation analysis. The Turing instability criteria for the Spatio-temporal system is estimated. In the numerical simulation, phase portrait with time evolution diagrams shows periodic and chaotic oscillations. Bifurcation diagrams show the very rich and complex dynamical behavior of the non-spatial model. We calculate the Lyapunov exponent to justify the dynamics of the non-spatial model. A variety of patterns like interference, spot, and stripe are observed with special emphasis on Beddington–DeAngelis function response. These complex patterns explore the beauty of the spatio-temporal model and it can be easily related to real-world biological systems.
- Published
- 2021
26. A Note on a Paper by Wong and Heyde
- Author
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Mikhail Urusov and Aleksandar Mijatović
- Subjects
Statistics and Probability ,Statistics::Theory ,Pure mathematics ,60G44, 60G48, 60H10, 60J60 ,General Mathematics ,Applied probability ,01 natural sciences ,FOS: Economics and business ,010104 statistics & probability ,60G48 ,FOS: Mathematics ,60G44 ,0101 mathematics ,60J60 ,Mathematics ,Local martingales versus true martingales ,010102 general mathematics ,Probability (math.PR) ,stochastic exponential ,Exponential function ,Mathematik ,60H10 ,Statistics, Probability and Uncertainty ,Martingale (probability theory) ,Quantitative Finance - General Finance ,General Finance (q-fin.GN) ,Mathematics - Probability ,Counterexample - Abstract
In this note we re-examine the analysis of the paper "On the martingale property of stochastic exponentials" by B. Wong and C.C. Heyde, Journal of Applied Probability, 41(3):654-664, 2004. Some counterexamples are presented and alternative formulations are discussed., Comment: To appear in Journal of Applied Probability, 11 pages
- Published
- 2011
27. Some comments on the paper: Controllability of fractional neutral stochastic functional differential systems, Z. Angew. Math. Phys. 65 (2014), no. 5, 941–959
- Author
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Michelle Pierri and Donal O'Regan
- Subjects
Discrete mathematics ,Class (set theory) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,General Physics and Astronomy ,Differential systems ,01 natural sciences ,010101 applied mathematics ,Controllability ,Algebra ,0101 mathematics ,Differential (mathematics) ,Mathematics - Abstract
The abstract results and applications presented in “Controllability of fractional neutral stochastic functional differential systems, Z. Angew. Math. Phys. 65 (2014), no. 5, 941–959, are not correct. Moreover, the class of differential control problems studied in [1] is not H-controllable.
- Published
- 2016
28. A study on fractional COVID‐19 disease model by using Hermite wavelets
- Author
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Shaher Momani, Ranbir Kumar, Samir Hadid, and Sunil Kumar
- Subjects
General Mathematics ,coronavirus ,Value (computer science) ,Derivative ,34a34 ,01 natural sciences ,Caputo derivative ,convergence analysis ,Wavelet ,Special Issue Paper ,operational matrix ,Applied mathematics ,0101 mathematics ,26a33 ,Hermite wavelets ,Mathematics ,Hermite polynomials ,Collocation ,Special Issue Papers ,Basis (linear algebra) ,010102 general mathematics ,General Engineering ,34a08 ,010101 applied mathematics ,Algebraic equation ,Scheme (mathematics) ,60g22 ,mathematical model - Abstract
The preeminent target of present study is to reveal the speed characteristic of ongoing outbreak COVID-19 due to novel coronavirus. On January 2020, the novel coronavirus infection (COVID-19) detected in India, and the total statistic of cases continuously increased to 7 128 268 cases including 109 285 deceases to October 2020, where 860 601 cases are active in India. In this study, we use the Hermite wavelets basis in order to solve the COVID-19 model with time- arbitrary Caputo derivative. The discussed framework is based upon Hermite wavelets. The operational matrix incorporated with the collocation scheme is used in order to transform arbitrary-order problem into algebraic equations. The corrector scheme is also used for solving the COVID-19 model for distinct value of arbitrary order. Also, authors have investigated the various behaviors of the arbitrary-order COVID-19 system and procured developments are matched with exiting developments by various techniques. The various illustrations of susceptible, exposed, infected, and recovered individuals are given for its behaviors at the various value of fractional order. In addition, the proposed model has been also supported by some numerical simulations and wavelet-based results.
- Published
- 2021
29. 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
30. Algebraic bounds on the Rayleigh–Bénard attractor
- Author
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Michael S. Jolly, Edriss S. Titi, Yu Cao, Jared P. Whitehead, Jolly, Michael S [0000-0002-7158-0933], Titi, Edriss S [0000-0002-5004-1746], Apollo - University of Cambridge Repository, Jolly, MS [0000-0002-7158-0933], and Titi, ES [0000-0002-5004-1746]
- Subjects
Paper ,General Mathematics ,General Physics and Astronomy ,global attractor ,Enstrophy ,01 natural sciences ,76F35 ,Attractor ,Periodic boundary conditions ,Boundary value problem ,0101 mathematics ,Algebraic number ,Rayleigh–Bénard convection ,math.AP ,Mathematical Physics ,Mathematics ,Rayleigh-Benard convection ,Plane (geometry) ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Statistical and Nonlinear Physics ,76E06 ,Nonlinear Sciences::Chaotic Dynamics ,010101 applied mathematics ,34D06 ,Homogeneous space ,Affine space ,synchronization ,35Q35 - Abstract
Funder: John Simon Guggenheim Memorial Foundation; doi: https://doi.org/10.13039/100005851, Funder: Einstein Visiting Fellow Program, The Rayleigh–Bénard system with stress-free boundary conditions is shown to have a global attractor in each affine space where velocity has fixed spatial average. The physical problem is shown to be equivalent to one with periodic boundary conditions and certain symmetries. This enables a Gronwall estimate on enstrophy. That estimate is then used to bound the L 2 norm of the temperature gradient on the global attractor, which, in turn, is used to find a bounding region for the attractor in the enstrophy–palinstrophy plane. All final bounds are algebraic in the viscosity and thermal diffusivity, a significant improvement over previously established estimates. The sharpness of the bounds are tested with numerical simulations.
- Published
- 2021
31. Variations on a Theme in Paper Folding
- Author
-
Burkard Polster
- Subjects
General Mathematics ,010102 general mathematics ,0103 physical sciences ,010307 mathematical physics ,Folding (DSP implementation) ,0101 mathematics ,01 natural sciences ,Linguistics ,Theme (narrative) ,Mathematics - Published
- 2004
32. Fractional Factorials and Prime Numbers (A Remark on the Paper 'On Prime Values of Some Quadratic Polynomials')
- Author
-
A. N. Andrianov
- Subjects
Statistics and Probability ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Prime element ,01 natural sciences ,Prime k-tuple ,Prime (order theory) ,010305 fluids & plasmas ,Combinatorics ,0103 physical sciences ,Prime factor ,Unique prime ,0101 mathematics ,Fibonacci prime ,Prime power ,Sphenic number ,Mathematics - Abstract
Congruences mod p for a prime p and partial products of the numbers 1,…, p − 1 are obtained. Bibliography: 2 titles.
- Published
- 2016
33. Corrigendum to the paper 'Numerical approximation of fractional powers of regularly accretive operators'
- Author
-
Andrea Bonito and Joseph E. Pasciak
- Subjects
010101 applied mathematics ,Computational Mathematics ,Numerical approximation ,Applied Mathematics ,General Mathematics ,Calculus ,Applied mathematics ,010103 numerical & computational mathematics ,0101 mathematics ,01 natural sciences ,Mathematics - Published
- 2017
34. The geometry of folding paper dolls
- Author
-
Brigitte Servatius
- Subjects
Grade school ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,people.profession ,Art ,Folding (DSP implementation) ,Sister ,01 natural sciences ,Visual arts ,Girl ,0101 mathematics ,Dressmaker ,people ,media_common - Abstract
When a parent sees a little girl sitting on the floor cutting paper dolls, many thoughts may come to mind: ‘She’s keeping out of trouble’ or ‘She’s making a mess’ or even ‘There go my tax returns’. The thought that should have come to my parent’s mind, however, was ‘One day she’ll be a mathematician’. My grandmother, who worked as a dressmaker, often allowed my sister and me to use her razor sharp scissors on the strips of leftover tracing paper. This paper is inspired by a notebook that I kept in grade school when I ‘studied’ paper dolls, and the figures are based on dolls found pressed between the pages.
- Published
- 1997
35. Separating Hyperplanes and the Authorship of the Disputed Federalist Papers
- Author
-
Robert Bosch and Jason A. Smith
- Subjects
021103 operations research ,Federalist ,Hyperplane ,General Mathematics ,Philosophy ,0211 other engineering and technologies ,010103 numerical & computational mathematics ,02 engineering and technology ,0101 mathematics ,01 natural sciences ,Genealogy - Abstract
(1998). Separating Hyperplanes and the Authorship of the Disputed Federalist Papers. The American Mathematical Monthly: Vol. 105, No. 7, pp. 601-608.
- Published
- 1998
36. Bioremediation of Hydrocarbon Using Bacterial Lipase from Waste Biomass
- Author
-
Enketeswara Subudhi, Anshuman Sahu, and Rajesh Kumar Sahoo
- Subjects
0301 basic medicine ,food.ingredient ,Central composite design ,General Mathematics ,030106 microbiology ,General Physics and Astronomy ,Biomass ,01 natural sciences ,03 medical and health sciences ,chemistry.chemical_compound ,food ,Bioremediation ,Response surface methodology ,0101 mathematics ,Lipase ,chemistry.chemical_classification ,biology ,010102 general mathematics ,General Chemistry ,Pulp and paper industry ,Hydrocarbon ,chemistry ,biology.protein ,General Earth and Planetary Sciences ,Peanut oil ,Petroleum ,General Agricultural and Biological Sciences - Abstract
Hydrocarbons originated from automobile oils are significant polluting agents of the soil. Lipase-mediated catalytic degradation of hydrocarbons from this used automobile oil is attempted in the present approach. Lipase was produced from peanut oil industry waste biomass using thermophilic alkaline-tolerant Pseudomonas sp. S1 obtained from sediment of Taptapani hot spring, Odisha. The experiments were designed as per central composite design, which is response surface methodology, to study the effect of the parameters and their interaction on the activity. A quadratic regression was found to be best with the experimental data, R2 = 0.899741 and the maximum lipase production of 51.3 IU/g was predicted from peanut oil seed waste biomass at an optimum pH of 8.31, temperature of 50.58 °C, moisture content of 50.8%, and biosurfactant content of 1.051 mg. The significant interaction of pH and moisture content with biosurfactant during lipase production was observed through the contour plots and 3D surface responses. Pseudomonas sp. S1 could degrade 92.6% of the used automobile oil after incubation for 24 h under optimum pH of 8.31 and temperature of 50.58 °C. Degradation of petroleum hydrocarbons by this thermophilic isolate could be effective due to the ability of lipase to utilize the used automobile oils as sole source of carbon and energy.
- Published
- 2020
37. Special Ulrich bundles on regular Weierstrass fibrations
- Author
-
Joan Pons-Llopis and Rosa M. Miró-Roig
- Subjects
Pure mathematics ,Class (set theory) ,Mathematics::Commutative Algebra ,General Mathematics ,010102 general mathematics ,Short paper ,Elliptic surfaces ,Ulrich bundles ,01 natural sciences ,Mathematics::Algebraic Geometry ,Simple (abstract algebra) ,0103 physical sciences ,Weierstrass fibrations ,Rank (graph theory) ,010307 mathematical physics ,0101 mathematics ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
The main goal of this short paper is to prove the existence of rank 2 simple and special Ulrich bundles on a wide class of elliptic surfaces: namely, on regular Weierstrass fibrations \(\pi : S\rightarrow \mathbb {P}^1\). Alongside we also show the existence of rank 2 weakly Ulrich sheaves on arbitrary Weierstrass fibrations \(S\rightarrow C_0\) and we deal with the (non-)existence of rank one Ulrich bundles on them.
- Published
- 2019
38. On the Characterizations of Wave Front Sets in Terms of the Short-Time Fourier Transform
- Author
-
Stevan Pilipović and Bojan Prangoski
- Subjects
Wavefront ,General Mathematics ,010102 general mathematics ,Short paper ,Mathematical analysis ,Short-time Fourier transform ,02 engineering and technology ,01 natural sciences ,Sobolev space ,symbols.namesake ,020303 mechanical engineering & transports ,Fourier transform ,0203 mechanical engineering ,symbols ,0101 mathematics ,Mathematics - Abstract
© 2019, Pleiades Publishing, Ltd. It is well known that the classical and Sobolev wave fronts were extended to nonequivalent global versions by the use of the short-time Fourier transform. In this very short paper, we give complete characterizations of the former wave front sets in terms of the short-time Fourier transform.
- Published
- 2019
39. On Dyakonov’s paper 'Equivalent normos on Lipschitz-type spaces of homorphic functions'
- Author
-
Miroslav Pavlović
- Subjects
010101 applied mathematics ,Pure mathematics ,Unit circle ,General Mathematics ,010102 general mathematics ,Holomorphic function ,0101 mathematics ,Type (model theory) ,Lipschitz continuity ,01 natural sciences ,Complex plane ,Unit disk ,Mathematics - Published
- 1999
40. A case study of Covid-19 epidemic in India via new generalised Caputo type fractional derivatives
- Author
-
Pushpendra Kumar and Vedat Suat Erturk
- Subjects
Covid‐19 epidemic ,General Mathematics ,Banach space ,Fixed-point theorem ,new generalised Caputo non‐integer order derivative ,01 natural sciences ,92c60 ,Special Issue Paper ,Applied mathematics ,Uniform boundedness ,Uniqueness ,0101 mathematics ,26a33 ,Mathematics ,Special Issue Papers ,fixed point theory ,010102 general mathematics ,34c60 ,General Engineering ,Equicontinuity ,Fractional calculus ,010101 applied mathematics ,Norm (mathematics) ,92d30 ,Predictor‐Corrector scheme ,Epidemic model ,mathematical model - Abstract
The first symptomatic infected individuals of coronavirus (Covid-19) was confirmed in December 2020 in the city of Wuhan, China. In India, the first reported case of Covid-19 was confirmed on 30 January 2020. Today, coronavirus has been spread out all over the world. In this manuscript, we studied the coronavirus epidemic model with a true data of India by using Predictor-Corrector scheme. For the proposed model of Covid-19, the numerical and graphical simulations are performed in a framework of the new generalised Caputo sense non-integer order derivative. We analysed the existence and uniqueness of solution of the given fractional model by the definition of Chebyshev norm, Banach space, Schauder's second fixed point theorem, Arzel's-Ascoli theorem, uniform boundedness, equicontinuity and Weissinger's fixed point theorem. A new analysis of the given model with the true data is given to analyse the dynamics of the model in fractional sense. Graphical simulations show the structure of the given classes of the non-linear model with respect to the time variable. We investigated that the mentioned method is copiously strong and smooth to implement on the systems of non-linear fractional differential equation systems. The stability results for the projected algorithm is also performed with the applications of some important lemmas. The present study gives the applicability of this new generalised version of Caputo type non-integer operator in mathematical epidemiology. We compared that the fractional order results are more credible to the integer order results.
- Published
- 2020
41. On sums of squares of primes and a k-th power of prime
- Author
-
Zhixin Liu and Rui Zhang
- Subjects
Discrete mathematics ,010505 oceanography ,General Mathematics ,010102 general mathematics ,Short paper ,Sander ,01 natural sciences ,Prime (order theory) ,Power (physics) ,Integer ,Congruence (manifolds) ,0101 mathematics ,0105 earth and related environmental sciences ,Mathematics - Abstract
In this short paper, we consider the exceptional set of integers, not restricted by elementary congruence conditions, which cannot be represented as sums of two squares of primes and a k-th power of prime for any integer $$k \ge 3$$ . Our results improve the recent results due to Brudern (in: Sander, Steuding, Steuding (eds) From arithmetic to zeta-functions, Springer, Cham 2016). The similar method can be also applied to some related questions in this direction, and this can improve the previous results.
- Published
- 2018
42. A remark on the Navier-Stokes equations with the Coriolis force
- Author
-
Hengjun Zhao and Yin-Xia Wang
- Subjects
Physics ,Body force ,General Mathematics ,010102 general mathematics ,Short paper ,Mathematics::Analysis of PDEs ,General Engineering ,01 natural sciences ,Physics::Geophysics ,Physics::Fluid Dynamics ,010101 applied mathematics ,Rossby number ,Classical mechanics ,Fictitious force ,Initial value problem ,0101 mathematics ,Navier–Stokes equations ,Shallow water equations ,Physics::Atmospheric and Oceanic Physics - Abstract
In this short paper, the initial value problem for the Navier-Stokes equations with the Coriolis force is investigated. The Coriolis force appears in almost all of the models of meteorology and geophysics dealing with large-scale phenomena. We prove that existence of uniform global large solutions to the Navier-Stokes equations with the Coriolis force for a class of special initial data. The results obtained in this paper are different from the previous 2 types of results.
- Published
- 2017
43. Assessment of fatty acid composition and response surface optimization of ultrasonic-assisted extraction of phenolic compounds from Pouteria campechiana pulp
- Author
-
Mariani Abdul Hamid, Roswanira Abdul Wahab, and Nur Haziqah Che Marzuki
- Subjects
0301 basic medicine ,chemistry.chemical_classification ,Chromatography ,Linolenic acid ,General Mathematics ,Pulp (paper) ,010102 general mathematics ,Extraction (chemistry) ,General Physics and Astronomy ,Myristic acid ,Fatty acid ,General Chemistry ,engineering.material ,01 natural sciences ,General Biochemistry, Genetics and Molecular Biology ,Palmitic acid ,03 medical and health sciences ,chemistry.chemical_compound ,Oleic acid ,030104 developmental biology ,chemistry ,engineering ,Gallic acid ,0101 mathematics ,General Agricultural and Biological Sciences - Abstract
Pouteria campechiana (PC) pulp was analyzed for its fatty acid composition. Fourteen different kinds of fatty acids were found with the major fatty acids viz. palmitic acid (C16:0), oleic acid (C18:1), myristic acid (C14:0) and linolenic acid (C18:2), making up approximately 73.8 % of the total fatty acid content (TPC). An ultrasonic-assisted extraction (UAE) of the polyphenolic bioactive components in PC pulp powder were statistically optimized using the Central Composite Design (CCD). Factors that gave maximized TPC in the crude extract of PC pulp powder were assessed for factors, ratio of ethanol:water, extraction temperature and extraction time. The established optimum conditions of the CCD model with R2 = 0.8833 were within the studied range and agreed well with the predicted values. Under an optimized condition [30 min, 35 °C and ratio of ethanol:water, 60:40 (%, v/v)], the highest TPC was 1162.80 mg GAE/100 g in comparison to the predicted 1115.06 mg GAE/100 g. High Performance Liquid Chromatography confirmed that gallic acid and its derivatives were the major components, comprising a ⁓0.03 % (w/w) of the PC pulp crude extract. Pertinently, a high recovery value in the HPLC validation data (109.84 %, R2 = 0.9995) suggests the method was accurate.
- Published
- 2018
44. Global optimization in Hilbert space
- Author
-
Benoît Chachuat, Boris Houska, Engineering & Physical Science Research Council (EPSRC), and Commission of the European Communities
- Subjects
Technology ,Optimization problem ,Mathematics, Applied ,0211 other engineering and technologies ,CONVEX COMPUTATION ,010103 numerical & computational mathematics ,02 engineering and technology ,ELLIPSOIDS ,01 natural sciences ,90C26 ,93B40 ,Convergence analysis ,0102 Applied Mathematics ,Branch-and-lift ,CUT ,Mathematics ,65K10 ,021103 operations research ,Full Length Paper ,Operations Research & Management Science ,0103 Numerical and Computational Mathematics ,Bounded function ,Physical Sciences ,symbols ,49M30 ,Calculus of variations ,INTEGRATION ,SET ,Complexity analysis ,Complete search ,Operations Research ,General Mathematics ,APPROXIMATIONS ,Set (abstract data type) ,symbols.namesake ,Applied mathematics ,ALGORITHM ,0101 mathematics ,INTERSECTION ,Global optimization ,0802 Computation Theory and Mathematics ,Science & Technology ,Infinite-dimensional optimization ,Hilbert space ,Computer Science, Software Engineering ,Constraint (information theory) ,Computer Science ,Software - Abstract
We propose a complete-search algorithm for solving a class of non-convex, possibly infinite-dimensional, optimization problems to global optimality. We assume that the optimization variables are in a bounded subset of a Hilbert space, and we determine worst-case run-time bounds for the algorithm under certain regularity conditions of the cost functional and the constraint set. Because these run-time bounds are independent of the number of optimization variables and, in particular, are valid for optimization problems with infinitely many optimization variables, we prove that the algorithm converges to an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon $$\end{document}ε-suboptimal global solution within finite run-time for any given termination tolerance \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon > 0$$\end{document}ε>0. Finally, we illustrate these results for a problem of calculus of variations.
- Published
- 2017
45. U(X) as a ring for metric spaces X
- Author
-
Javier Cabello Sánchez
- Subjects
Ring (mathematics) ,021103 operations research ,General Mathematics ,010102 general mathematics ,Short paper ,0211 other engineering and technologies ,02 engineering and technology ,Function (mathematics) ,Space (mathematics) ,01 natural sciences ,Combinatorics ,Uniform continuity ,Metric space ,Bounded function ,0101 mathematics ,Mathematics - Abstract
In this short paper, we will show that the space of real valued uniformly continuous functions defined on a metric space (X,d) is a ring if and only if every subset A ? X has one of the following properties: ? A is Bourbaki-bounded, i.e., every uniformly continuous function on X is bounded on A. ? A contains an infinite uniformly isolated subset, i.e., there exist ? > 0 and an infinite subset F ? A such that d(a,x) ? ? for every a ? F, x ? X n \{a}.
- Published
- 2017
46. Self-contracted curves in spaces with weak lower curvature bound
- Author
-
Shin-ichi Ohta, Vladimir Zolotov, and Nina Lebedeva
- Subjects
Pure mathematics ,Class (set theory) ,General Mathematics ,Flag (linear algebra) ,010102 general mathematics ,Metric Geometry (math.MG) ,Paper based ,Curvature ,01 natural sciences ,Angle condition ,010101 applied mathematics ,Metric space ,51F99 ,Mathematics - Metric Geometry ,Bounded function ,FOS: Mathematics ,Mathematics::Differential Geometry ,0101 mathematics ,Snowflake ,Mathematics - Abstract
We show that bounded self-contracted curves are rectifiable in metric spaces with weak lower curvature bound in a sense we introduce in this article. This class of spaces is wide and includes, for example, finite-dimensional Alexandrov spaces of curvature bounded below and Berwald spaces of nonnegative flag curvature. (To be more precise, our condition is regarded as a strengthened doubling condition and holds also for a certain class of metric spaces with upper curvature bound.) We also provide the non-embeddability of large snowflakes into (balls in) metric spaces in the same class. We follow the strategy of the last author's previous paper based on the small rough angle condition, where spaces with upper curvature bound are considered. The results in this article show that such a strategy applies to spaces with lower curvature bound as well., Comment: A goofy mistake in formulations of Theorem 2 and 4 is fixed
- Published
- 2019
- Full Text
- View/download PDF
47. On some previous results for the Drazin inverse of block matrices
- Author
-
Jelena Višnjić
- Subjects
Combinatorics ,General Mathematics ,010102 general mathematics ,Drazin inverse ,Short paper ,Block (permutation group theory) ,Block matrix ,010103 numerical & computational mathematics ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
This short paper is motivated by the paper of Bu et al. [C. Bu, C. Feng, P. Dong, A note on computational formulas for the Drazin inverse of certain block matrices, J. Appl. Math. Comput.(38) (2012) 631-640], where the authors gave additive formula for Drazin inverse for matrices under new conditions, and two representations under some specific conditions. Here is shown that the additive formula is not valid for all matrices which satisfy given conditions. Also, here is proved that the representations which were given in mentioned paper do not extend the results given by Hartwig et al. [R. Hartwig, X. Li, Y. Wei, Representations for the Drazin inverse of a 2 _ 2 block matrix, SIAM J. Matrix. Anal. Appl. (27)(2006) 757-771 ], in fact they are equivalent.
- Published
- 2016
48. A Note on 'Impossible' Paper Folding
- Author
-
Thomas C. Hull
- Subjects
Computer science ,General Mathematics ,010102 general mathematics ,0103 physical sciences ,010307 mathematical physics ,Folding (DSP implementation) ,Statistical physics ,0101 mathematics ,01 natural sciences - Abstract
(1996). A Note on “Impossible” Paper Folding. The American Mathematical Monthly: Vol. 103, No. 3, pp. 240-241.
- Published
- 1996
49. d-Hermite rings and skew $$\textit{PBW}$$ PBW extensions
- Author
-
Oswaldo Lezama and Claudia Gallego
- Subjects
Hermite polynomials ,Rank (linear algebra) ,General Mathematics ,010102 general mathematics ,Short paper ,Skew ,010103 numerical & computational mathematics ,01 natural sciences ,Combinatorics ,symbols.namesake ,Computational Theory and Mathematics ,Kronecker delta ,symbols ,Kronecker's theorem ,Finitely-generated abelian group ,0101 mathematics ,Statistics, Probability and Uncertainty ,Mathematics - Abstract
In this short paper we study the d-Hermite condition about stably free modules for skew $$\textit{PBW}$$ extensions. For this purpose, we estimate the stable rank of these non-commutative rings. In addition, and closely related with these questions, we will prove Kronecker’s theorem about the radical of finitely generated ideals for some particular types of skew $$\textit{PBW}$$ extensions.
- Published
- 2015
50. A Remark on the Local Cohomology Modules of a Union of Disjoint Matroids
- Author
-
Cong Minh Nguyen and Minh Cong Nguyen
- Subjects
Discrete mathematics ,Ideal (set theory) ,Mathematics::Commutative Algebra ,General Mathematics ,010102 general mathematics ,Short paper ,0102 computer and information sciences ,Disjoint sets ,Local cohomology ,01 natural sciences ,Matroid ,Simplicial complex ,010201 computation theory & mathematics ,0101 mathematics ,Mathematics - Abstract
Let I be the Stanley–Reisner ideal of a simplicial complex Δ. In this short paper, we shall give a formula of vanishing of the local cohomology modules for S/I(r) in the case Δ is a union of disjoint matroids, where I(r) is the rth symbolic power of I. As an application, we will improve a previous result in Minh and Nakamura (Nagoya Math. J. 213, 127–140, 2014) for the k-Buchsbaumness of S/I(r).
- Published
- 2015
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