50,901 results
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2. Remarks on a recent paper titled: 'On the split common fixed point problem for strict pseudocontractive and asymptotically nonexpansive mappings in Banach spaces'
- Author
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Charles E. Chidume
- Subjects
Pure mathematics ,Smoothness (probability theory) ,Applied Mathematics ,lcsh:Mathematics ,Banach space ,Hilbert space ,Regular polygon ,010103 numerical & computational mathematics ,Fixed point ,lcsh:QA1-939 ,01 natural sciences ,Opial property ,010101 applied mathematics ,symbols.namesake ,Accretive ,Uniformly smooth ,Common fixed point ,symbols ,Discrete Mathematics and Combinatorics ,0101 mathematics ,Constant (mathematics) ,Analysis ,Mathematics - Abstract
In a recently published theorem on the split common fixed point problem for strict pseudocontractive and asymptotically nonexpansive mappings, Tang et al. (J. Inequal. Appl. 2015:305, 2015) studied a uniformly convex and 2-uniformly smooth real Banach space with the Opial property and best smoothness constant κ satisfying the condition $0 0 < κ < 1 2 , as a real Banach space more general than Hilbert spaces. A well-known example of a uniformly convex and 2-uniformly smooth real Banach space with the Opial property is $E=l_{p}$ E = l p , $2\leq p 2 ≤ p < ∞ . It is shown in this paper that, if κ is the best smoothness constant of E and satisfies the condition $0 0 < κ ≤ 1 2 , then E is necessarily $l_{2}$ l 2 , a real Hilbert space. Furthermore, some important remarks concerning the proof of this theorem are presented.
- Published
- 2021
3. 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
4. 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
5. On the Dispersions of the Gel’fand–Pinsker Channel and Dirty Paper Coding
- Author
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Jonathan Scarlett
- Subjects
Independent and identically distributed random variables ,Gaussian ,Variable-length code ,Data_CODINGANDINFORMATIONTHEORY ,Library and Information Sciences ,Computer Science Applications ,Gel’fand-Pinsker channel ,Combinatorics ,symbols.namesake ,Second-order coding rate ,Shannon–Fano coding ,Dirty paper coding ,symbols ,Channel dispersion ,Channels with state ,Algorithm ,Encoder ,Decoding methods ,Information Systems ,Mathematics ,Coding (social sciences) - Abstract
This paper studies the second-order coding rates for memoryless channels with a state sequence known non-causally at the encoder. In the case of finite alphabets, an achievability result is obtained using constant-composition random coding, and by using a small fraction of the block to transmit the empirical distribution of the state sequence. For error probabilities less than 0.5, it is shown that the second-order rate improves on an existing one based on independent and identically distributed random coding. In the Gaussian case (dirty paper coding) with an almost-sure power constraint, an achievability result is obtained using random coding over the surface of a sphere, and using a small fraction of the block to transmit a quantized description of the state power. It is shown that the second-order asymptotics are identical to the single-user Gaussian channel of the same input power without a state.
- Published
- 2015
6. A remark on a paper of P. B. Djakov and M. S. Ramanujan
- Author
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Murat Yurdakul and Elif Uyanik
- Subjects
Unbounded operator ,Combinatorics ,symbols.namesake ,Monotone polygon ,Basis (linear algebra) ,General Mathematics ,Bounded function ,Operator (physics) ,symbols ,Sequence space ,Continuous linear operator ,Ramanujan's sum ,Mathematics - Abstract
Let l be a Banach sequence space with a monotone norm in which the canonical system (e_{n}) is an unconditional basis. We show that if there exists a continuous linear unbounded operator between l-K\"{o}the spaces, then there exists a continuous unbounded quasi-diagonal operator between them. Using this result, we study in terms of corresponding K\"{o}the matrices when every continuous linear operator between l-K\"{o}the spaces is bounded. As an application, we observe that the existence of an unbounded operator between l-K\"{o}the spaces, under a splitting condition, causes the existence of a common basic subspace.
- Published
- 2019
7. 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
8. 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
9. 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
10. 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
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. 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
15. A new calculation method of feedback controller gain for bilinear paper-making process with disturbance
- Author
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I. Hamdan and Mohamed Hamdy
- Subjects
Lyapunov function ,Multivariable calculus ,Linear matrix inequality ,Bilinear interpolation ,Control engineering ,Industrial and Manufacturing Engineering ,Computer Science Applications ,Stability conditions ,symbols.namesake ,Control and Systems Engineering ,Control theory ,Modeling and Simulation ,Full state feedback ,symbols ,Schur complement ,Mathematics - Abstract
This paper presents a new method to calculate the feedback control gain for a class of multivariable bilinear system, and also applied this method on the control of two sections of paper-making process with disturbance. The robust H∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H∞ performance of the resulting closed-loop system are ensured. The controller turns out to be robust with respect to the disturbance in the plant. Utilizing the Schur complement and some variable transformations, the stability conditions of the multivariable bilinear systems are formulated in terms of Lyapunov function via the form of linear matrix inequality (LMI). The gain of controller will be calculated via LMI. Finally, the application examples of a headbox section and a dryer section of paper-making process are used to illustrate the applicability of the proposed method.
- Published
- 2014
16. Corrigendum to the papers on Exceptional orthogonal polynomials: J. Approx. Theory 182 (2014) 29–58, 184 (2014) 176–208 and 214 (2017) 9–48
- Author
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Antonio J. Durán
- Subjects
Numerical Analysis ,Pure mathematics ,Applied Mathematics ,General Mathematics ,Hilbert space ,Approx ,symbols.namesake ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Orthogonal polynomials ,symbols ,Analysis ,Mathematics - Abstract
We complete a gap in the proof that exceptional polynomials are complete orthogonal systems in the associated Hilbert spaces.
- Published
- 2020
17. Translation of Ludwig Boltzmann’s Paper 'On the Relationship between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability Calculations Regarding the Conditions for Thermal Equilibrium' Sitzungberichte der Kaiserlichen Akademie der Wissenschaften. Mathematisch-Naturwissen Classe. Abt. II, LXXVI 1877, pp 373-435 (Wien. Ber. 1877, 76:373-435). Reprinted in Wiss. Abhandlungen, Vol. II, reprint 42, p. 164-223, Barth, Leipzig, 1909
- Author
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Kim A. Sharp and Franz Matschinsky
- Subjects
Thermal equilibrium ,Fundamental theorem ,media_common.quotation_subject ,General Physics and Astronomy ,lcsh:Astrophysics ,Second law of thermodynamics ,Computer Science::Digital Libraries ,lcsh:QC1-999 ,Physics::History of Physics ,symbols.namesake ,second law of thermodynamics ,Ludwig Boltzmann ,Theory of heat ,lcsh:QB460-466 ,Boltzmann constant ,symbols ,lcsh:Q ,lcsh:Science ,entropy ,lcsh:Physics ,Mathematical physics ,Mathematics ,media_common - Abstract
Translation of the seminal 1877 paper by Ludwig Boltzmann which for the first time established the probabilistic basis of entropy. Includes a scientific commentary.
- Published
- 2015
18. Errata to the paper 'An Evolutionary Game Theoretic Framework for Femtocell Radio Resource Management'
- Author
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Rein Vesilo, Qimei Cui, Ahsan Saadat, and Wei Ni
- Subjects
business.industry ,Applied Mathematics ,020206 networking & telecommunications ,02 engineering and technology ,Computer Science Applications ,symbols.namesake ,Equilibrium selection ,Nash equilibrium ,0202 electrical engineering, electronic engineering, information engineering ,Selection (linguistics) ,Femtocell ,symbols ,Wireless ,Resource management ,Electrical and Electronic Engineering ,Radio resource management ,business ,Mathematical economics ,Game theory ,Mathematics - Abstract
The authors of [1] have become aware that several equations in [1] were presented with errors. As confirmed in this brief note, neither do the errors invalidate the game theoretic approach proposed in [1] , nor violate the equilibrium of the approach. However, the parameter selection, which is required to preserve the validity and unique equilibrium of the approach, is affected by the errors. We correct the equations with detailed mathematical derivations in the note.
- Published
- 2016
19. Addendum to the paper 'Real hypersurfaces in complex two-plane Grassmannians with ξ-invariant Ricci tensor'
- Author
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Hyunjin Lee, Young Jin Suh, and Gyu Jong Kim
- Subjects
Pure mathematics ,Plane (geometry) ,Mathematical analysis ,General Physics and Astronomy ,Ricci flow ,Characterization (mathematics) ,Einstein tensor ,symbols.namesake ,symbols ,Ricci decomposition ,Mathematics::Differential Geometry ,Geometry and Topology ,Invariant (mathematics) ,Mathematical Physics ,Distribution (differential geometry) ,Ricci curvature ,Mathematics - Abstract
In this paper, we introduce some notions of invariancy for the Ricci tensor on real hypersurfaces in complex two-plane Grassmannians G 2 ( C m + 2 ) , namely, F -invariant and invariant Ricci tensor. Using these notions, we give non-existence theorem and characterization for the special case among the real hypersurfaces of Type ( A ) in G 2 ( C m + 2 ) , respectively. Here the distribution F is defined by F = [ ξ ] ∪ D ⊥ where D ⊥ = Span { ξ 1 , ξ 2 , ξ 3 } and [ ξ ] = Span { ξ } .
- Published
- 2014
20. Corrections to the paper 'The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces'
- Author
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Rovshan A. Bandaliev
- Subjects
Discrete mathematics ,Mathematics::Functional Analysis ,Sublinear function ,General Mathematics ,Mathematics::Classical Analysis and ODEs ,Lebesgue's number lemma ,Type (model theory) ,symbols.namesake ,Operator (computer programming) ,Mathematics - Classical Analysis and ODEs ,Ordinary differential equation ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,symbols ,Standard probability space ,Lp space ,Variable (mathematics) ,Mathematics - Abstract
In this paper author was proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted variable Lebesgue space. Note that the proof of multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent don't contained any mistakes. But at the proving of the boundedness of certain sublinear operators on the weighted variable Lebesgue space Georgian colleagues discovered a small but significant error in this paper. This result is assigned as Theorem 5 in noted paper. In other words, sufficient conditions for general weights ensuring the validity of the two-weight strong type inequalities for some sublinear operator was found. In this theorem the inequality (9) isn't true. In this note we give the details of the correct argument. We presume that the reader is familiar with the contents and notation of our original paper. At the heart of our correction is the following Theorem which replaces Theorem 5.
- Published
- 2013
21. A survey of A. Yu. Ishlinsky’s papers on the occasion of his 100th birthday
- Author
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Victor Zhuravlev and Sergei Perelyaev
- Subjects
Viscoplasticity ,Plane (geometry) ,Mathematical analysis ,General Physics and Astronomy ,Plasticity ,Elasticity (physics) ,symbols.namesake ,Buckling ,Mechanics of Materials ,Euler's formula ,symbols ,Fracture (geology) ,Boundary value problem ,Mathematics - Abstract
A. Yu. Ishlinsky’s scientific publications impress one by the extremely wide scope of his scientific interests. Most of his results lie in two fundamental fields of research, mechanics of deformable bodies and mechanics of gyroscope and navigation systems; chronologically, they appeared mainly in this order. One of his first important results that became widely known was the construction of an exact theory of the Brinell test (1942). This theory dealt with determining the stress state under a rigid punch of spherical or plane shape penetrating into a perfectly plastic medium. The problem was solved in the rigorous statement in the framework of the Haar–von Karman complete plasticity hypothesis containing two relations between the principal stresses rather than one relation as in the Saint-Venant theory. The subsequent development of this problem led (1954) to construction of a general theory of plasticity which, in particular, allowed one to overcome the difficulties related to the derivation of the 3D strain equations beyond the elasticity range. A series of Ishlinsky’s papers (1940–1946) deals with imperfect elasticity, fracture theory, and plasticity theory. In this series, he constructed a description of aftereffect and relaxation generalizing the Maxwell and Thomson concepts on the basis of a linear differential relation between the stress and the strain. Plastic fracture models were also studied in these works. In particular, one of the fracture models was constructed for the example of a body whose one-dimensional strain obeys the law dσ/dt+ rσ= bde/dt+ bne, where σ is the stress and e is the strain. This model also admits a simple and illustrative interpretation as a damper with springs, which permits readily understanding the introduced fracture hypotheses and analyzing specific examples for various loading laws. Ishlinsky returned to plasticity and fracture theories in 1965–1968. The problem on the impact of a viscoplastic rod on a rigid obstacle is of interest. In the model accepted by Ishlinsky, the motion of the rod cross-sections is governed by heat equations with complex boundary conditions. It turned out unexpectedly that on impact the viscoplastic state does not instantly extend to the entire rod; instead, it runs away from the impact point and then returns without reaching the free end, thus leaving a rigid segment of the rod. In fracture theory of this time period, one should mention Ishlinsky’s paper of 1968, where two crack development models are compared. One model is the Griffith–Irvin model, and the other, which was developed later, is due to S. A. Khristianovich and G. I. Barenblatt. Ishlinsky showed that the latter model tends to the former as the range of the adhesion forces postulated in the latter tends to zero. Ishlinsky’s papers on the stability of elastic systems are of extreme importance. In a joint 1949 paper with M. A. Lavrent’ev, he theoretically explained the spectacular experiment in which a tube subjected to an underwater explosion loses its shape in such a way that the number of corrugations is the greater the closer they are to the explosion site. It turned out that the relationship between the characteristic exponents, the equilibrium mode number, and the applied external load constructed when studying the equilibrium modes permits one to maximize the buckling rate with respect to the mode number. The greater the applied force, the higher the mode number maximizing the characteristic exponent is. This result has numerous practical applications. The buckling problem for elastic systems, which goes back to Euler, is usually solved by methods of the theory of strength of materials for simplified models of rod or plate type. Ishlinsky studied this
- Published
- 2013
22. Averages of Ramanujan sums: note on two papers by E. Alkan
- Author
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László Tóth
- Subjects
Algebra and Number Theory ,Mathematics - Number Theory ,Logarithm ,Generalization ,Mathematics::Number Theory ,16. Peace & justice ,Ramanujan's sum ,Bernoulli polynomials ,Combinatorics ,symbols.namesake ,Identity (mathematics) ,11A25, 11B68, 33B15 ,symbols ,Arithmetic function ,Gamma function ,Binomial coefficient ,Mathematics - Abstract
We give a simple proof and a multivariable generalization of an identity due to E. Alkan concerning a weighted average of the Ramanujan sums. We deduce identities for other weighted averages of the Ramanujan sums with weights concerning logarithms, values of arithmetic functions for gcd's, the Gamma function, the Bernoulli polynomials, and binomial coefficients., Comment: 8 pages
- Published
- 2014
23. A Note on Recent Papers by Grafakos and Teschl, and Estrada
- Author
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Adam Nowak and Krzysztof Stempak
- Subjects
Hankel transform ,Partial differential equation ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,Function (mathematics) ,Transplantation ,symbols.namesake ,Radial function ,Fourier transform ,Fourier analysis ,symbols ,Analysis ,Mathematics - Abstract
We indicate how recent results of Grafakos and Teschl (J Fourier Anal Appl 19:167–179, 2013), and Estrada (J Fourier Anal Appl 20:301–320, 2014), relating the Fourier transform of a radial function in $$\mathbb R^n$$ and the Fourier transform of the same function in $$\mathbb R^{n+2}$$ and $$\mathbb R^{n+1}$$ , respectively, are located within known results on transplantation for Hankel transforms.
- Published
- 2014
24. Cycles with undistinguished actions and extended Rock–Paper–Scissors games
- Author
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Hans Haller and Eric Bahel
- Subjects
TheoryofComputation_MISCELLANEOUS ,Computer Science::Computer Science and Game Theory ,Economics and Econometrics ,Correlated equilibrium ,Normal-form game ,Trembling hand perfect equilibrium ,TheoryofComputation_GENERAL ,symbols.namesake ,Nash equilibrium ,Best response ,symbols ,Epsilon-equilibrium ,Folk theorem ,Risk dominance ,Mathematical economics ,Finance ,Mathematics - Abstract
This paper examines zero-sum games that are based on a cyclic preference relation defined over undistinguished actions. For each of these games, the set of Nash equilibria is characterized. When the number of actions is odd, a unique Nash equilibrium is always obtained. On the other hand, in the case of an even number of actions, every such game exhibits an infinite number of Nash equilibria. Our results give some insights as to the robustness of Nash equilibria with respect to perturbations of the action set.
- Published
- 2013
25. Comments on two papers concerning estimation of the parameters of the Pareto distribution in the presence of outliers
- Author
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David P. M. Scollnik
- Subjects
Statistics and Probability ,Estimation ,symbols.namesake ,Maximum likelihood ,Outlier ,Econometrics ,symbols ,Estimator ,State (functional analysis) ,Pareto distribution ,Mathematics - Abstract
In this paper, we examine and correct various results relating to estimation of a Pareto distribution in the presence of outliers according to a model introduced by Dixit and Jabbari Nooghabi (2011) [1] and further studied by Dixit and Jabbari Nooghabi (2011) [2] . In particular, Dixit and Jabbari Nooghabi (2011) [2] state that the maximum likelihood estimators for the parameters appearing in their model do not exist. We show that these estimators can in fact exist, and we present and illustrate a method for determining them when they do. Two numerical illustrations using actual insurance data are included.
- Published
- 2013
26. Limit cycles and the benefits of a short memory in rock-paper-scissors games
- Author
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James Burridge
- Subjects
Hopf bifurcation ,Computer Science::Computer Science and Game Theory ,education.field_of_study ,Recall ,media_common.quotation_subject ,Population ,Short-term memory ,Fixed point ,Asymmetry ,Computer Science::Multiagent Systems ,symbols.namesake ,Bifurcation theory ,symbols ,Limit (mathematics) ,education ,Mathematical economics ,Mathematics ,media_common - Abstract
When playing games in groups, it is an advantage for individuals to have accurate statistical information on the strategies of their opponents. Such information may be obtained by remembering previous interactions. We consider a rock-paper-scissors game in which agents are able to recall their last m interactions, used to estimate the behavior of their opponents. At critical memory length, a Hopf bifurcation leads to the formation of stable limit cycles. In a mixed population, agents with longer memories have an advantage, provided the system has a stable fixed point, and there is some asymmetry in the payoffs of the pure strategies. However, at a critical concentration of long memory agents, the appearance of limit cycles destroys their advantage. By introducing population dynamics that favors successful agents, we show that the system evolves toward the bifurcation point.
- Published
- 2015
27. Asymptotically stable equilibrium and limit cycles in the Rock–Paper–Scissors game in a population of players with complex personalities
- Author
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Jan Zakrzewski and Tadeusz Płatkowski
- Subjects
Statistics and Probability ,Hopf bifurcation ,Computer Science::Computer Science and Game Theory ,education.field_of_study ,Population ,Normal-form game ,Condensed Matter Physics ,Stability (probability) ,symbols.namesake ,Nonlinear Sciences::Adaptation and Self-Organizing Systems ,Exponential stability ,Stability theory ,symbols ,Quantitative Biology::Populations and Evolution ,Limit (mathematics) ,education ,Mathematical economics ,Bifurcation ,Mathematics - Abstract
We investigate a population of individuals who play the Rock–Paper–Scissors (RPS) game. The players choose strategies not only by optimizing their payoffs, but also taking into account the popularity of the strategies. For the standard RPS game, we find an asymptotically stable polymorphism with coexistence of all strategies. For the general RPS game we find the limit cycles. Their stability depends exclusively on two model parameters: the sum of the entries of the RPS payoff matrix, and a sensitivity parameter which characterizes the personality of the players. Apart from the supercritical Hopf bifurcation, we found the subcritical bifurcation numerically for some intervals of the parameters of the model.
- Published
- 2011
28. An Upper Bound on the Capacity of the Causal Dirty-Paper Channel
- Author
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M. Kesal and Uri Erez
- Subjects
Library and Information Sciences ,Precoding ,Noise (electronics) ,Upper and lower bounds ,Computer Science Applications ,Combinatorics ,symbols.namesake ,Channel capacity ,Interference (communication) ,Gaussian noise ,Bounded function ,symbols ,Computer Science::Information Theory ,Information Systems ,Mathematics ,Communication channel - Abstract
A bound on the capacity of the causal dirty-paper channel with arbitrary interference and general independent identically distributed additive noise is derived. In particular, it is shown that for the case of Gaussian noise, the capacity is upper bounded by log2(1+SNR/e) bits per real dimension. This bound is useful for SNR ≤ e(e-2) .
- Published
- 2011
29. A comment on the paper 'Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker–Planck equations' by T.D. Frank
- Author
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Joseph L. McCauley
- Subjects
Statistics and Probability ,Stochastic process ,Mathematical analysis ,Markov process ,Condensed Matter Physics ,Time reversibility ,Continuous-time Markov chain ,symbols.namesake ,Diffusion process ,symbols ,Applied mathematics ,Markov property ,Fokker–Planck equation ,Chapman–Kolmogorov equation ,Mathematics - Abstract
The purpose of this comment is to correct mistaken assumptions and claims made in the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker–Planck equations” by T. D. Frank [T.D. Frank, Stochastic feedback, non-linear families of Markov processes, and nonlinear Fokker–Planck equations, Physica A 331 (2004) 391]. Our comment centers on the claims of a “non-linear Markov process” and a “non-linear Fokker–Planck equation.” First, memory in transition densities is misidentified as a Markov process. Second, the paper assumes that one can derive a Fokker–Planck equation from a Chapman–Kolmogorov equation, but no proof was offered that a Chapman–Kolmogorov equation exists for the memory-dependent processes considered. A “non-linear Markov process” is claimed on the basis of a non-linear diffusion pde for a 1-point probability density. We show that, regardless of which initial value problem one may solve for the 1-point density, the resulting stochastic process, defined necessarily by the conditional probabilities (the transition probabilities), is either an ordinary linearly generated Markovian one, or else is a linearly generated non-Markovian process with memory. We provide explicit examples of diffusion coefficients that reflect both the Markovian and the memory-dependent cases. So there is neither a “non-linear Markov process”, nor a “non-linear Fokker–Planck equation” for a conditional probability density. The confusion rampant in the literature arises in part from labeling a non-linear diffusion equation for a 1-point probability density as “non-linear Fokker–Planck,” whereas neither a 1-point density nor an equation of motion for a 1-point density can define a stochastic process. In a closely related context, we point out that Borland misidentified a translation invariant 1-point probability density derived from a non-linear diffusion equation as a conditional probability density. Finally, in the Appendix A we present the theory of Fokker–Planck pdes and Chapman–Kolmogorov equations for stochastic processes with finite memory.
- Published
- 2007
30. Chaotic time series prediction for the game, Rock-Paper-Scissors
- Author
-
Paolo Patelli, Franco Salvetti, and Simone Nicolo
- Subjects
Computer Science::Computer Science and Game Theory ,Exploit ,business.industry ,ComputingMilieux_PERSONALCOMPUTING ,Chaotic ,Lyapunov exponent ,Chaos theory ,symbols.namesake ,symbols ,Entropy (information theory) ,Reinforcement learning ,Artificial intelligence ,Time series ,business ,Algorithm ,Game theory ,Software ,Mathematics - Abstract
Two players of Rock-Paper-Scissors are modeled as adaptive agents which use a reinforcement learning algorithm and exhibit chaotic behavior in terms of trajectories of probability in mixed strategies space. This paper demonstrates that an external super-agent can exploit the behavior of the other players to predict favorable moments to play against one of the other players the symbol suggested by a sub-optimal strategy. This third agent does not affect the learning process of the other two players, whose only goal is to beat each other. The choice of the best moment to play is based on a threshold associated with the Local Lyapunov Exponent or the Entropy, each computed by using the time series of symbols played by one of the other players. A method for automatically adapting such a threshold is presented and evaluated. The results show that these techniques can be used effectively by a super-agent in a game involving adaptive agents that exhibit collective chaotic behavior.
- Published
- 2007
31. Corrigendum to the paper 'Adjoining an Order Unit to a Matrix Ordered Space'
- Author
-
Anil Kumar Karn
- Subjects
Pure mathematics ,General Mathematics ,Mathematical analysis ,Operator theory ,Potential theory ,Theoretical Computer Science ,Strictly convex space ,symbols.namesake ,Matrix (mathematics) ,Fourier analysis ,Ordered space ,symbols ,Order (group theory) ,Unit (ring theory) ,Analysis ,Mathematics - Abstract
An error has been detected (and also corrected) in Theorem 2.8 of the paper entitled “Adjoining an Order Unit to a Matrix Ordered Space” (Positivity, (2005)9: 207–223; DOI 10.1007/s11117-003-2778-5). Accordingly, some of the results of the paper have been modified. Also, a notion of C*-matricially, Riesz normed spaces has been introduced.
- Published
- 2007
32. Modelling the dynamical behaviour of a paper web. Part II
- Author
-
Artem Kulachenko, Per Gradin, and H. Koivurova
- Subjects
Mechanical Engineering ,Skew ,Mixed finite element method ,Mechanics ,Aeroelasticity ,Finite element method ,Computer Science Applications ,Vibration ,symbols.namesake ,Acoustic theory ,Classical mechanics ,Critical speed ,Modeling and Simulation ,symbols ,General Materials Science ,Hamilton's principle ,Civil and Structural Engineering ,Mathematics - Abstract
In this paper, a finite element procedure is used to study the dynamic behaviour of a paper web in a free span between two rollers, including effects of transport velocity and surrounding air. The paper web is modelled as a three-dimensional orthotropic structure. The influence of air is accounted for by utilizing fluid-solid interaction analyses based on acoustic theory. The contribution of transport velocity is included through gyroscopic matrices and forces. The structural response on harmonic excitations has been studied using linear and non-linear models. Results show that air significantly reduces eigenfrequencies of the web. So called ''edge-flutter'' is nothing but the result of skew tension profile. Excessive web vibration can be eliminated by adjusting the web tension.
- Published
- 2007
33. Einstein's First Published Paper
- Author
-
Boris Iglewicz
- Subjects
Condensed Matter::Quantum Gases ,Statistics and Probability ,General Mathematics ,Proposition ,Epistemology ,symbols.namesake ,Graduate students ,Scientific method ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,symbols ,Calculus ,Data recording ,Statistics, Probability and Uncertainty ,Einstein ,Mathematics - Abstract
This article reviews Albert Einstein's first published paper, submitted for publication in 1900. At that time, Einstein was 21 and a recent college graduate. His paper uses modeling and least squares to analyze data in support of a scientific proposition. Einstein is shown to be well trained, for his day, in using statistics as a tool in his scientific research. This paper also shows his ability to make trivial arithmetic mistakes and some clumsiness in data recording. A major aim of this article is to help provide a better appreciation of Einstein as an active user of statistical arguments in this and other of his important publications.
- Published
- 2007
34. A note on a paper by A.G. Bratsos, M. Ehrhardt and I.Th. Famelis
- Author
-
A. G. Bratsos
- Subjects
Computational Mathematics ,Nonlinear system ,symbols.namesake ,Series (mathematics) ,Applied Mathematics ,Mathematical analysis ,Convergence (routing) ,symbols ,Soliton ,Adomian decomposition method ,Mathematics ,Schrödinger equation - Abstract
In this short note an addition to the paper [A.G. Bratsos, M. Ehrhardt, I.Th. Famelis, A discrete Adomian decomposition method for discrete nonlinear Schrodinger equations, Appl. Math. Comput. 197(1) (2008) 190-205] using the modulus of the terms evaluated from the Adomian decomposition method on p. 194 and their relation to the convergence of the resulting series is presented. Conclusions for the accuracy of the approximated solution are derived.
- Published
- 2009
35. Entropy Amplification Property and the Loss for Writing on Dirty Paper
- Author
-
Ram Zamir and A.S. Cohen
- Subjects
Discrete mathematics ,Difference set ,Speech recognition ,Gaussian ,Noise reduction ,Transmitter ,Library and Information Sciences ,Computer Science Applications ,symbols.namesake ,Additive white Gaussian noise ,Aperiodic graph ,symbols ,Probability distribution ,Entropy (information theory) ,Information Systems ,Mathematics - Abstract
Costa's celebrated ldquowriting on dirty paperrdquo (WDP) shows that the power-constrained channel Y=X+S+Z, with Gaussian Z, has the same capacity as the standard AWGN channel Y=X+Z, provided that the ldquointerferencerdquo S (no matter how strong it is) is known at the transmitter. While this ability for perfect interference cancelation is very appealing, it relies heavily on the Gaussianity of the (unknown) noise Z. We construct an example of ldquobadrdquo noise for writing on dirty paper, namely, ldquodifference set noiserdquo. If the interference S is strong, then difference-set noise limits the WDP capacity to at most 2 bits. At the same time, like in the AWGN case, the zero-interference capacity grows without bound with the input constraint. Thus almost 100% of the available capacity is lost in WDP in the presence of difference-set noise. This high capacity loss is due to the ldquoentropy amplification propertyrdquo (EAP) of noise with an aperiodic probability distribution. Using the EAP and the duality between WDP and Wyner-Ziv source coding, we also give an example of dramatic rate-loss in quantizing encrypted source.
- Published
- 2008
36. A Short note on the Paper (New Characterizations of the Pareto Distribution
- Author
-
Gholamhossein G. Hamedani and Mahdi Rasekhi
- Subjects
Statistics and Probability ,Mathematical optimization ,Pareto interpolation ,Characterizations ,Management Science and Operations Research ,Conditional expectation ,symbols.namesake ,Generalized Pareto distribution ,Pareto distribution ,Pareto distributions ,60E05, 60E15 ,lcsh:Statistics ,lcsh:HA1-4737 ,Mathematics ,Probability and Statistics ,lcsh:Mathematics ,Order statistic ,lcsh:QA1-939 ,Power (physics) ,Modeling and Simulation ,symbols ,Lomax distribution ,Statistics, Probability and Uncertainty ,Random variable - Abstract
Nofal and El Gebaly (2017), presented certain characterizations of the Pareto distribution based on the conditional expectations of power of the order statistics. In this short note we show that the same results can easily be obtained in terms of the power of the random variable.
- Published
- 2017
37. A Remark on a Paper of I. V. Latkin
- Author
-
M. N. Leont’eva
- Subjects
Discrete mathematics ,Logic ,Head (linguistics) ,Computation ,Value (computer science) ,Turing machine ,symbols.namesake ,symbols ,Symbol (formal) ,Analysis ,Inscribed figure ,Word (group theory) ,Counterexample ,Mathematics - Abstract
We will revisit the main theorem in [1] in which given a Turing machine program P and an input X, a formula Ω(X,P ) is constructed, about which it is asserted, among other things, that it is true iff the machine P accepts an input X in less than 2|X| steps. We claim that this is not true. Counterexample. As X we take a word 11 having length 2. The input inscribed on the tape before the computation starts consists of symbols 01100. . . (followed by zeros). We construct a Turing machine P accepting all nonempty words and rejecting the empty word: instruction M(0) : q10 → q3R, instruction M(1) : q30 → q2L, instruction M(2) : q31 → q0L, instruction M(3) : q00 → q00, instruction M(4) : q20 → q20. We show how P operates on input X. Before the first step, the head scans a cell with symbol 0 and sees 0. Step 1. Perform the instruction M(0) : q10 → q3R, after which the head scans cell 1 and sees 1. Step 2. Perform the instruction M(2) : q31 → q0L, after which the head scans cell 0 and sees 0. Step 3. Perform the instruction M(3) : q00 → q00, after which the head scans cell 0 and sees 0. Thus the Turing machine constructed accepts input X in less than 2|X| = 4 steps. Now consider a formula Ω(X,P ) constructed given a program P and an input X. Our goal is to check the value of a formula χ(0)&R(P ) → χ(ω) for the following values of variables
- Published
- 2013
38. A performance comparison of erasure tests with diversity reception for noncoherent M-ary FSK signaling [Transactions Papers]
- Author
-
Young Gil Kim and Norman C. Beaulieu
- Subjects
Frequency-shift keying ,business.industry ,Applied Mathematics ,Detector ,Viterbi algorithm ,Upper and lower bounds ,Computer Science Applications ,Diversity combining ,symbols.namesake ,Reed–Solomon error correction ,symbols ,Erasure ,Fading ,Electrical and Electronic Engineering ,Telecommunications ,business ,Algorithm ,Mathematics - Abstract
A l-Bayesian erasure test (BET) based on order statistics with diversity reception for noncoherent M-ary frequency shift keying (FSK) signaling is examined. In the l-BET, the M-ary FSK symbol is erased whenever the a posteriori probability of correct decision, which is a function of the l-largest sums of energy detector outputs, is less than a threshold. For binary FSK signaling in Rayleigh flat fading channels, the 2-BET is found to be the same as the difference threshold test (DTT), which declares an erasure whenever the difference between the largest and the second largest sums of energy detector outputs is less than a threshold. The output threshold test (OTT), which declares an erasure whenever the largest sum of energy detector outputs is less than a threshold, is proved equivalent to the 1-BET for the Rayleigh flat fading channel. Closed-form expressions for the probabilities of correct decision and symbol error for the DTT, Viterbi's ratio threshold test (RTT), and the OTT are derived when square-law combining (SLC) diversity is used. Several erasure tests including the Z-BET, the RTT, the OTT, and the DTT are compared in terms of probability of codeword error. The 2-BET provides almost the same performance as the BET that requires all the sums of energy detector outputs. The 2-BET provides power gains of 0.9 dB and 0.7 dB over the RTT for (7, 3) and (15, 7) Reed-Solomon (RS) codes, respectively, when the probability of codeword error is 10-3 and the diversity order is one.
- Published
- 2010
39. Remark on the paper of Park
- Author
-
Yuan Gong Sun
- Subjects
Lyapunov function ,Pure mathematics ,Differential equation ,Applied Mathematics ,Numerical analysis ,Mathematical analysis ,Linear matrix inequality ,Delay differential equation ,Computational Mathematics ,symbols.namesake ,Exponential stability ,symbols ,Lyapunov equation ,Delay time ,Mathematics - Abstract
This paper considers certain neutral differential equation with the distributed delayddt[x(t)+c(t)x([email protected])]+p(t)x(t)+q(t)x([email protected])+r(t)@!"t"-"@d^tx(s)ds=0.Without imposing a nonnegative restriction on coefficients of the equation, we establish a delay-dependent asymptotic stability condition for the equation by introducing a new Lyapunov function. The condition presented here is different from that of Park [J.H. Park, LMI optimization approach to asymptotic stability of certain neutral delay differential equation with time-varying coefficients, Appl. Math. Comput. 160 (2005) 355-361] in the sense that it is dependent on all delays of the equation. Numerical examples illustrate effectiveness and sharpness of our theoretical result.
- Published
- 2007
40. A remark on a paper of F. Luca and A. Sankaranarayanan
- Author
-
Imre Kátai
- Subjects
Set (abstract data type) ,Discrete mathematics ,symbols.namesake ,Number theory ,Statement (logic) ,General Mathematics ,Ordinary differential equation ,Multiplicative function ,Zero (complex analysis) ,symbols ,Calculus ,Euler's totient function ,Mathematics - Abstract
We generalize a result of F. Luca and A. Sankaranarayanan by proving that the set of n for which ϕ(1) + + ϕ(n) is squareful is of zero density. A similar statement holds for σ (n) instead of ϕ(n) and for some other multiplicative functions.
- Published
- 2008
41. A note on a paper by D.K.R. Babajee and M.Z. Dauhoo
- Author
-
Hongmin Ren
- Subjects
Discrete mathematics ,Iterative method ,Applied Mathematics ,Numerical analysis ,Third order convergence ,Mathematical analysis ,Mathematical proof ,Local convergence ,Computational Mathematics ,symbols.namesake ,symbols ,Always true ,Newton's method ,Counterexample ,Mathematics - Abstract
A counterexample is provided in this short note to show that some of local convergence theorems established in [D.K.R. Babajee, M.Z. Dauhoo, An analysis of the properties of the variants of Newton’s method with third order convergence, Appl. Math. Comput. 183 (2006) 659–684] are not always true. Some mistakes in the proofs of these theorems are pointed out.
- Published
- 2008
42. Revisiting Louis de Broglie's famous 1924 paper in thePhilosophical Magazine
- Author
-
P. Weinberger
- Subjects
symbols.namesake ,Theoretical physics ,symbols ,Matter wave ,Einstein ,Condensed Matter Physics ,Mathematics ,Epistemology - Abstract
De Broglie's contribution in the Philosophical Magazine from 1924 is fascinating from many standpoints: for its moderate use of mathematics, the close connection to Einstein's special theory of relativity, and of course for the proposal of matter waves. We revisit this mostly speculative publication, which contributed crucially to the birth of quantum mechanics.
- Published
- 2006
43. A Non-Gaussian Spatial Process Model for Opacity of Flocculated Paper
- Author
-
Patrick Brown, Robin Henderson, and Peter J. Diggle
- Subjects
Statistics and Probability ,Opacity ,Stochastic process ,Stochastic modelling ,Estimation theory ,Gaussian ,Covariance ,symbols.namesake ,Frequency domain ,Statistics ,symbols ,Statistical physics ,Statistics, Probability and Uncertainty ,Gaussian process ,Mathematics - Abstract
Product quality in the paper-making industry can be assessed by opacity of a linear trace through continuous production sheets, summarized in spectral form. We adopt a class of non-Gaussian stochastic models for continuous spatial variation to describe data of this type. The model has flexible covariance structure, physically interpretable parameters and allows several scales of variation for the underlying process. We derive the spectral properties of the model, and develop methods of parameter estimation based on maximum likelihood in the frequency domain. The methods are illustrated using sample data from a UK mill.
- Published
- 2003
44. Correction to the paper 'on the curvature of a generalization of a contact metric manifolds'
- Author
-
L. Di Terlizzi
- Subjects
Christoffel symbols ,Riemann curvature tensor ,symbols.namesake ,Mean curvature flow ,General Mathematics ,Mathematical analysis ,symbols ,Curvature form ,Sectional curvature ,Curvature ,Ricci curvature ,Scalar curvature ,Mathematics - Abstract
We considered in Example 3.1 of the paper [1] an S-structure on R2n+s . We concluded that when s > 1 this manifold cannot be of constant φ-sectional curvature. Unfortunately this result is wrong. In fact, essentially due to a sign mistake in defining the φ-structure and a consequent transposition of the elements of the φ-basis (3.2), some of the Christoffel’s symbols were incorrect. In the present rectification, using a more slendler tecnique, we prove that our manifold is of constant φ-sectional curvature −3s and then it is η-Einstein.
- Published
- 2009
45. Corrigendum to our paper 'On the asymptotic behaviour of the 2D Navier-Stokes equations with Navier friction conditions towards Euler equations.' [ZAMM 89(10), 810-822, 2009]
- Author
-
Gabriela Planas and Francisco Guillén-González
- Subjects
Physics::Fluid Dynamics ,symbols.namesake ,Applied Mathematics ,Mathematical analysis ,Mathematics::Analysis of PDEs ,Computational Mechanics ,Euler's formula ,symbols ,Navier–Stokes equations ,Euler equations ,Mathematics - Abstract
The authors would like to correct the proof of Theorem 3(a) in the original paper “On the asymptotic behaviour of the 2D Navier-Stokes equations with Navier friction conditions towards Euler equations.” [ZAMM 89(10), 810-822, 2009].
- Published
- 2015
46. A remark on a paper by Evans and Harris on the point spectra of Dirac operators
- Author
-
Karl Michael Schmidt
- Subjects
Dirac measure ,General Mathematics ,Dirac (software) ,Dirac algebra ,Clifford analysis ,Dirac operator ,symbols.namesake ,Dirac spinor ,symbols ,Point (geometry) ,QA ,Eigenvalues and eigenvectors ,Mathematical physics ,Mathematics - Abstract
This paper presents a sufficient condition for a one-dimensional Dirac operator with a potential tending to infinity at infinity to have no eigenvalues. It also provides a quick proof (and suggests variations) of a related criterion given by Evans and Harris.
- Published
- 2001
47. COAP 2004 Best Paper Award
- Author
-
Luca Bergamaschi, Jacek Gondzio, and Giovanni Zilli
- Subjects
Hessian matrix ,Control and Optimization ,Karush–Kuhn–Tucker conditions ,Iterative method ,Preconditioner ,Applied Mathematics ,Nonlinear programming ,Computational Mathematics ,symbols.namesake ,Biconjugate gradient stabilized method ,Saddle point ,Calculus ,symbols ,Applied mathematics ,Interior point method ,Mathematics - Abstract
for their paper “Preconditioning Indefinite Systems in Interior Point Methods for Optimization”, published in Volume 28, pages 149–171. This paper describes a class of indefinite preconditioners for reduced KKT systems arising in quadratic and nonlinear optimization with interior point methods. Spectral analysis of preconditioners is given and the improvements resulting from the use of primal-dual regularization are demonstrated. Computational results are reported for the application of the preconditioner to a variety of medium-size convex quadratic programming problems. Work on the paper began during the Summer of 2001, about a year after the authors had first met when Zilli invited Gondzio to give a series of lectures on interior point methods in Padova in September, 2000. The authors had complementary research backgrounds: Bergamaschi and Zilli worked on the theory and implementation of iterative methods for linear and nonlinear systems of equations [2], while Gondzio worked on the design and implementation of interior point methods for large-scale optimization [3]. This was essential since together, the three authors could tackle in depth a problem which required expertice in several areas. At that time Bergamaschi and Zilli were impressed with the recent development of Lukysan and Vlycek [6], who applied conjugate gradients to indefinite systems, and with the later analysis of Keller, Gould and Wathen [4] of indefinite constraint preconditioners. They convinced Gondzio to look into the issue. In the meantime, Rozlozn´ok and Simoncini [7] came up with an improved understanding of issues connected with indefinite preconditioning (in the context of saddle point problems arising in partial differential equation); these developments led the authors to take a closer look at the problem. Starting in July, 2001, the authors began to incorporate into Gondzio’s interior point code HOPDM (higher order primal dual methods) four iterative techniques: conjugate gradients, BiCGstab, GMRES and QMR. A description of these schemes can be found in Kelley’s book [5] and the references therein. The authors realized that the key difficulty in the solution of augmented systems of Newton equations in interior point methods for quadratic and nonlinear programming (otherwise known as reduced KKT systems) consisted in the loss of sparsity caused by the presence of the Hessian matrix Q in the system � (Q + � 1
- Published
- 2005
48. Contribution to the Discussion of the Paper ‘Geodesic Monte Carlo on Embedded Manifolds’
- Author
-
Babak Shahbaba, Shiwei Lan, and Jeffrey Streets
- Subjects
Statistics and Probability ,Simplex ,Geodesic ,Monte Carlo method ,Riemannian geometry ,Riemannian manifold ,Statistics::Computation ,Hybrid Monte Carlo ,symbols.namesake ,symbols ,Calculus ,Probability distribution ,Statistics, Probability and Uncertainty ,Gibbs sampling ,Mathematics - Abstract
We would like to start by congratulating Byrne and Girolami for writing such a thoughtful and extremely interesting paper. This is in fact a worthy addition to other high impact papers recently published by Professor Girolami’s lab in this field. The common theme of these papers is to use geometrically motivated methods to improve efficiency of sampling algorithms. In their seminal paper, Girolami & Calderhead (2011) proposed a novel Hamiltonian Monte Carlo (HMC) method, called Riemannian manifold HMC, that exploits the Riemannian geometry of the target distribution to improve standard HMC’s efficiency by automatically adapting to the local structure. Although this is a natural and beautiful idea, there are significant computational difficulties, which arise in effectively implementing this algorithm. In contrast, in this current contribution, Byrne and Girolami focused on special probability distributions, which give rise to particularly nice Riemannian geometries. In particular, the examples under consideration described in Section 4 allow for closed-form solutions to the geodesic equation, which can be used to reduce computational cost of geometrically motivated Monte Carlo methods. Although the proposed splitting algorithm is quiet interesting, we initially doubted its impact because Riemannian metrics with closed-form geodesics are extremely rare. However, we are now convinced that this approach will likely see application beyond what is outlined herein. For example, we believe that this approach can be used to improve computational efficiency of sampling algorithms when the parameter space is constrained. The standard HMC algorithm needs to evaluate each proposal to ensure that it is within the boundaries imposed by the constraints. Alternatively, as discussed by Neal (2011), one could modify standard HMC so the sampler bounces back after hitting the boundaries. In Appendix A, Byrne and Girolami discussed this approach for geodesic updates on the simplex. In many cases, a constrained parameter space can be bijectively mapped to a unit ball
- Published
- 2014
49. Comments on the paper 'Some new results on closed-loop stability in the presence of control saturation'
- Author
-
C. Burgat and Sophie Tarbou Riech
- Subjects
Control saturation ,Lyapunov function ,Control synthesis ,Linear system ,Open-loop controller ,Computer Science Applications ,symbols.namesake ,Exponential stability ,Control and Systems Engineering ,Control theory ,symbols ,Saturation (chemistry) ,Closed loop ,Mathematics - Abstract
In a paper by Lee and Hedrick (1995), some conditions for the global asymptotic stability of linear systems under saturating controls were presented as new. We show that most of the results of this paper are already well-known and published. Therefore they cannot be considered as new.
- Published
- 1997
50. On the Paper 'A Note on Spaces of Absolutely Convergent Fourier Transforms' by Björn G.Walther (this Issue). Letter to the Editor
- Author
-
S. V. Kislyakov
- Subjects
Algebra ,symbols.namesake ,Letter to the editor ,Partial differential equation ,Fourier transform ,Fourier analysis ,Applied Mathematics ,General Mathematics ,Mathematics education ,symbols ,Absolute convergence ,Analysis ,Mathematics - Published
- 2014
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