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2. On the Controversy over the Logical Correctness of Einstein’s First Paper on Mass-Energy Equivalence
- Author
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Lixian Yan, Patrick Moylan, and Michael Gironda
- Subjects
symbols.namesake ,Correctness ,Circular reasoning ,General Engineering ,symbols ,Criticism ,Mass–energy equivalence ,Energy–momentum relation ,Logic error ,Einstein ,Mathematical economics ,Mathematics ,Simple (philosophy) - Abstract
It is well-known that Einstein’s first attempt to explain E = mc2 which was published in Annalen der Physik in 1905, has been criticized as problematic. In particular, it has been shown by Ives and reiterated by Jammer that it suffers from the error of circular reasoning. Attempts have been made in the scientific literature to discount the circular reasoning objection of Ives, Jammer, Arzelies and others. Fritz Rohrlich in 1990 gave a remarkably simple and concise derivation of E = mc2 along lines similar to Einstein’s but based on both momentum and energy conservation, in contrast to Einstein’s which uses only energy considerations. Rohrlich’s approach using momentum conservation is an alternative to Einstein’s, which is free from objection in logical error, and we make it quite clear on the importance of the implicit assumption of momentum conservation in any attempt to refute the circular reasoning error in Einstein’s paper. It is our contention that this point is overlooked or altogether avoided by those who have attempted to uproot the circular reasoning criticism of Einstein’s paper.
- Published
- 2021
3. 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
4. Folding a Paper Strip to Minimize Thickness
- Author
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Hiro Ito, Erik D. Demaine, Anna Lubiw, David Eppstein, Ryuhei Uehara, Yushi Uno, Adam Hesterberg, Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science, and Massachusetts Institute of Technology. Department of Mathematics
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Computational Geometry (cs.CG) ,FOS: Computer and information sciences ,paper folding ,0102 computer and information sciences ,02 engineering and technology ,Topology ,01 natural sciences ,Theoretical Computer Science ,NP completeness ,symbols.namesake ,Exponential growth ,crease width ,Computer Science - Data Structures and Algorithms ,0202 electrical engineering, electronic engineering, information engineering ,Discrete Mathematics and Combinatorics ,Data Structures and Algorithms (cs.DS) ,Mathematics ,NP-complete ,computational origami ,Planar graph ,rigid origami ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,symbols ,Computer Science - Computational Geometry ,020201 artificial intelligence & image processing ,linkage ,optimization problem - Abstract
In this paper, we study how to fold a specified origami crease pattern in order to minimize the impact of paper thickness. Specifically, origami designs are often expressed by a mountain-valley pattern (plane graph of creases with relative fold orientations), but in general this specification is consistent with exponentially many possible folded states. We analyze the complexity of finding the best consistent folded state according to twometrics:minimizing the total number of layers in the folded state (so that a “flat folding” is indeed close toflat), andminimizing the total amount of paper required to execute the folding (where “thicker” creases consume more paper). We prove both problems strongly NP-complete even for 1D folding. On the other hand, we prove the first problem fixed-parameter tractable in 1D with respect to the number of layers., National Science Foundation (U.S.). Origami Design for Integration of Self-assembling Systems for Engineering Innovation (grant EFRI- 124038), National Science Foundation (U.S.). Expedition grant (CCF-1138967), United States. Department of Defense. National Defense Science and Engineering Graduate (NDSEG) Fellowship (32 CFR 168a)
- Published
- 2015
5. On the 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. Annotated Translations of Three of the Euler’s Papers on Celestial Mechanics
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Sylvio R. Bistafa
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General Engineering ,Motion (geometry) ,Lagrangian point ,Three-body problem ,Celestial mechanics ,symbols.namesake ,Orbit ,Classical mechanics ,Physics::Space Physics ,Euler's formula ,symbols ,Astrophysics::Earth and Planetary Astrophysics ,Center of mass ,Mathematics ,Syzygy (astronomy) - Abstract
Annotated translations from Latin of three of the Euler’s papers on celestial mechanics are presented, which fall into the category of three-body problems. The first translation deals with an exact solution of three bodies that move around the common center of mass and always line up. This is considered the first work from which the three collinear Lagrange points could be obtained. The second translation deals with motions of Sun, Earth and Moon in syzygy and Moon libration as well, where, for the first time, Euler introduces an archaic form of a Fourier sine series expansion to describe the Moon’s wagging motion. The last translation relates to a paper that was written with the goal of alleviating astronomical computations of the perturbed motion of the Moon around the Earth by the Sun, ending up with eight coupled differential equations for resolving the perturbed motion of this celestial body. Despite showing great analytical skills, Euler gave no indications on how this system of equations could be solved, which renders his efforts practically useless in the determination of the variations of the nodal line and inclination of the Moon’s orbit.
- 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
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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
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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 Generalized Zero-Forcing Precoder with Successive Dirty-Paper Coding in MISO Broadcast Channels
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Sha Hu and Fredrik Rusek
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Discrete mathematics ,FOS: Computer and information sciences ,Computer Science - Information Theory ,Applied Mathematics ,Information Theory (cs.IT) ,020206 networking & telecommunications ,020302 automobile design & engineering ,02 engineering and technology ,Maximization ,Main diagonal ,Computer Science Applications ,symbols.namesake ,0203 mechanical engineering ,Broadcast channels ,Lagrange multiplier ,0202 electrical engineering, electronic engineering, information engineering ,Zero Forcing Equalizer ,symbols ,Dirty paper coding ,Electrical and Electronic Engineering ,Mathematics ,Coding (social sciences) ,Communication channel - Abstract
In this paper, we consider precoder designs for multiuser multiple-input-single-output (MISO) broadcasting channels. Instead of using a traditional linear zero-forcing (ZF) precoder, we propose a generalized ZF (GZF) precoder in conjunction with successive dirty-paper coding (DPC) for data-transmissions, namely, the GZF-DP precoder, where the suffix \lq{}DP\rq{} stands for \lq{}dirty-paper\rq{}. The GZF-DP precoder is designed to generate a band-shaped and lower-triangular effective channel $\vec{F}$ such that only the entries along the main diagonal and the $\nu$ first lower-diagonals can take non-zero values. Utilizing the successive DPC, the known non-causal inter-user interferences from the other (up to) $\nu$ users are canceled through successive encoding. We analyze optimal GZF-DP precoder designs both for sum-rate and minimum user-rate maximizations. Utilizing Lagrange multipliers, the optimal precoders for both cases are solved in closed-forms in relation to optimal power allocations. For the sum-rate maximization, the optimal power allocation can be found through water-filling, but with modified water-levels depending on the parameter $\nu$. While for the minimum user-rate maximization that measures the quality of the service (QoS), the optimal power allocation is directly solved in closed-form which also depends on $\nu$. Moreover, we propose two low-complexity user-ordering algorithms for the GZF-DP precoder designs for both maximizations, respectively. We show through numerical results that, the proposed GZF-DP precoder with a small $\nu$ ($\leq\!3$) renders significant rate increments compared to the previous precoder designs such as the linear ZF and user-grouping based DPC (UG-DP) precoders., Comment: 31 pages, 13 figures, submitted to IEEE Transactions on Wireless Communications in Aug. 2016
- Published
- 2017
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10. A remark on a paper of P. B. Djakov and M. S. Ramanujan
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Murat Yurdakul and Elif Uyanik
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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
11. Universal scaling law of an origami paper spring
- Author
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Bohua Sun
- Subjects
Environmental Engineering ,Biomedical Engineering ,Computational Mechanics ,Aerospace Engineering ,FOS: Physical sciences ,Ocean Engineering ,Poisson distribution ,01 natural sciences ,Square (algebra) ,010305 fluids & plasmas ,symbols.namesake ,Physics - General Physics ,0103 physical sciences ,010306 general physics ,Civil and Structural Engineering ,Mathematics ,Mechanical Engineering ,Mathematical analysis ,Extension (predicate logic) ,Poisson's ratio ,Power (physics) ,Nonlinear system ,General Physics (physics.gen-ph) ,Mechanics of Materials ,Spring (device) ,lcsh:TA1-2040 ,symbols ,Curve fitting ,lcsh:Engineering (General). Civil engineering (General) - Abstract
This letter solves an open question of origami paper spring risen by Yoneda et al.(Phys. Rev. E 2019). By using both dimensional analysis and data fitting, a universal scaling law of a paper spring is formulated. The scaling law shows that origami spring force obeys power square law of spring extension, however strong nonlinear to the total twist angle. The study has also successfully generalized the scaling law from the Poisson ratio 0.3 to an arbitrary Poisson's ratio with the help of dimensional analysis., Comment: 3 pages, 3 figues and 1 table
- Published
- 2020
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12. Reply to 'Critical Comments on the Paper ‘On the Logical Inconsistency of the Special Theory of Relativity’'
- Author
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Stephen J. Crothers
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Sobolev space ,symbols.namesake ,Simultaneity ,Lorentz transformation ,Rebuttal ,symbols ,Special relativity ,Einstein ,Tacit assumption ,Mathematical economics ,Cosmology ,Mathematics - Abstract
It has been critically argued by V. A. Leus (Sobolev Institute of Mathematics, Novosibirsk, Russia) that in my proof that Einstein’s Special Theory of Relativity is logically inconsistent and therefore false, I violated the basic tenets of Special Relativity and foisted an alternative theory upon Einstein’s. A careful study of the critical analysis reveals however a failure to address the key arguments I adduced to prove Special Relativity logically inconsistent, and a concomitant invocation of Einstein’s theory to try to argue that my analysis is incorrect because it does not concur with Einstein. There is therefore no proof advanced of any alleged error in my analysis. In my paper I did not introduce an alternative theory. The aforementioned critical paper affords opportunity in rebuttal to amplify the invalidity of A. Einstein’s tacit assumption, in constructing the Special Theory of Relativity, that systems of clock-synchronised stationary observers consistent with Lorentz Transformation can be mathematically constructed. Since such systems of observers have in fact no mathematical existence the Special Theory of Relativity is logically inconsistent. It is therefore invalid. The consequences for physics, astronomy, and cosmology, are significant.
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- 2018
13. 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
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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
14. Reduced linear fractional representation of nonlinear systems for stability analysis ⁎ ⁎The research was partially supported by the grant K115694 of the National Research, Development and Innovation Office - NKFIH. The project has also been supported by the European Union, co-financed by the European Social Fund through the grant EFOP-3.6.3-VEKOP-16-2017-00002. The research leading to the results presented in the paper was supported (also) by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences
- Author
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Gábor Szederkényi, Péter Polcz, and Tamás Péni
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Lyapunov stability ,Lyapunov function ,0209 industrial biotechnology ,Stability (learning theory) ,Parameterized complexity ,02 engineering and technology ,Nonlinear system ,symbols.namesake ,020901 industrial engineering & automation ,Control and Systems Engineering ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Algebra representation ,Applied mathematics ,020201 artificial intelligence & image processing ,Representation (mathematics) ,Differential (mathematics) ,Mathematics - Abstract
Based on symbolic and numeric manipulations, a model simplification technique is proposed in this paper for the linear fractional representation (LFR) and for the differential algebraic representation introduced by Trofino and Dezuo (2013). This representation is needed for computational Lyapunov stability analysis of uncertain rational nonlinear systems. The structure of the parameterized rational Lyapunov function is generated from the linear fractional representation (LFR) of the system model. The developed method is briefly compared to the n-D order reduction technique known from the literature. The proposed model transformations does not affect the structure of Lyapunov function candidate, preserves the well-posedness of the LFR and guarantees that the resulting uncertainty block is at most the same dimensional as the initial one. The applicability of the proposed method is illustrated on two examples.
- Published
- 2018
15. A Remark on the Paper 'Properties of Intersecting Families of Ordered Sets' by O. Einstein
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Sounggun Wee and Sang-il Oum
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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
16. A trio of heteroclinic bifurcations arising from a model of spatially-extended Rock-Paper-Scissors
- Author
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Claire M. Postlethwaite and Alastair M. Rucklidge
- Subjects
Population ,General Physics and Astronomy ,FOS: Physical sciences ,Pattern Formation and Solitons (nlin.PS) ,01 natural sciences ,symbols.namesake ,0101 mathematics ,education ,Quantitative Biology - Populations and Evolution ,Mathematical Physics ,Saddle ,Mathematics ,Hopf bifurcation ,Equilibrium point ,education.field_of_study ,Partial differential equation ,37G15, 34C37, 37C29, 91A22 ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Ode ,Populations and Evolution (q-bio.PE) ,Heteroclinic cycle ,Statistical and Nonlinear Physics ,Nonlinear Sciences - Pattern Formation and Solitons ,010101 applied mathematics ,Ordinary differential equation ,FOS: Biological sciences ,symbols - Abstract
One of the simplest examples of a robust heteroclinic cycle involves three saddle equilibria: each one is unstable to the next in turn, and connections from one to the next occur within invariant subspaces. Such a situation can be described by a third-order ordinary differential equation (ODE), and typical trajectories approach each equilibrium point in turn, spending progressively longer to cycle around the three points but never stopping. This cycle has been invoked as a model of cyclic competition between populations adopting three strategies, characterised as Rock, Paper and Scissors. When spatial distribution and mobility of the populations is taken into account, waves of Rock can invade regions of Scissors, only to be invaded by Paper in turn. The dynamics is described by a set of partial differential equations (PDEs) that has travelling wave (in one dimension) and spiral (in two dimensions) solutions. In this paper, we explore how the robust heteroclinic cycle in the ODE manifests itself in the PDEs. Taking the wavespeed as a parameter, and moving into a travelling frame, the PDEs reduce to a sixth-order set of ODEs, in which travelling waves are created in a Hopf bifurcation and are destroyed in three different heteroclinic bifurcations, depending on parameters, as the travelling wave approaches the heteroclinic cycle. We explore the three different heteroclinic bifurcations, none of which have been observed in the context of robust heteroclinic cycles previously. These results are an important step towards a full understanding of the spiral patterns found in two dimensions, with possible application to travelling waves and spirals in other population dynamics models., Comment: 36 pages, 8 figures
- Published
- 2019
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17. 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
18. Refined exponential stability analysis of a coupled system * *The paper was partially supported by the ANR projects LimICoS and SCIDIS. Corresponding author. Fax +33-561336411
- Author
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Alexandre Seuret, Mohammed Safi, and Lucie Baudouin
- Subjects
Lyapunov function ,Lyapunov stability ,0209 industrial biotechnology ,Mathematical analysis ,02 engineering and technology ,Lyapunov exponent ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,020901 industrial engineering & automation ,Exponential stability ,Control and Systems Engineering ,Stability theory ,Ordinary differential equation ,symbols ,Lyapunov equation ,0101 mathematics ,Lyapunov redesign ,Mathematics - Abstract
The objective of this contribution is to improve recent stability results for a system coupling ordinary differential equations to a vectorial transport partial differential equation by proposing a new structure of Lyapunov functional. Following the same process of most of the investigations in literature, that are based on an a priori selection of Lyapunov functionals and use the usual integral inequalities (Jensen, Wirtinger, Bessel...), we will present an efficient method to estimate the exponential decay rate of this coupled system leading to a tractable test expressed in terms of linear matrix inequalities. These LMI conditions stem from the new design of a candidate Lyapunov functional, but also the inherent properties of the Legendre polynomials, that are used to build a projection of the infinite dimensional part of the state of the system. Based on these polynomials and using the appropriate Bessel-Legendre inequality, we will prove an exponential stability result and in the end, we will show the efficiency of our approach on academic example.
- Published
- 2017
19. Cooperative object detection in road traffic 1 1The research for this paper was financially supported by the Hollósi Ferenc Tudástámogató Alapítvány
- Author
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Olivér Törő, Tamás Bécsi, Szilárd Aradi, and Péter Gáspár
- Subjects
020301 aerospace & aeronautics ,business.industry ,Gaussian ,Recursion (computer science) ,020206 networking & telecommunications ,02 engineering and technology ,Object detection ,Nonlinear system ,Noise ,symbols.namesake ,0203 mechanical engineering ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,State space ,Computer vision ,Artificial intelligence ,Affine transformation ,business ,Particle filter ,Mathematics - Abstract
Multi-sensor object detection and tracking on a highway scene with radar measurements is presented. The estimation algorithm is the random finite set based Bernoulli filter, working in the Bayesian framework. The recursion for calculating the Bayes estimation is implemented as a particle filter. A method is presented for calculating the likelihoods, suitable for particle filtering performed with moving sensors, assuming additive Gaussian measurement noise. In our approach, for calculating the posterior estimate of the object state, the measurement likelihoods are computed in the state space, instead of the measurement space, by mapping each measurement to the global coordinate system. The map consists of a nonlinear and an affine part. While the affine transformation trivially preserves the Gaussian nature, the nonlinear is well-proven to be approximated as affine too. This approach allows the particles to be drawn directly from the state space, hence the evaluation of the measurement model is not needed, which saves computational power.
- Published
- 2017
20. Abstracts of the Papers Published in Journal of the Japan Society for Aeronautical and Space Sciences (Vol. 67, No. 6, Dec. 2019)
- Author
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Hikaru Aono, Katsutoshi Kondo, Akira Oyama, Masayuki Anyoji, Kozo Fujii, Taku Nonomura, and Makoto Yamamoto
- Subjects
Thesaurus (information retrieval) ,symbols.namesake ,Wing ,Space and Planetary Science ,business.industry ,symbols ,Aerospace Engineering ,Reynolds number ,Bioinspiration ,Aerodynamics ,Aerospace engineering ,business ,Mathematics - Published
- 2020
21. Remarks on a paper by Gavrilov: Grad-Shafranov equations, steady solutions of the three dimensional incompressible Euler equations with compactly supported velocities, and applications
- Author
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Peter Constantin, Vlad Vicol, and Joonhyun La
- Subjects
010102 general mathematics ,Mathematical analysis ,Euler flow ,01 natural sciences ,Euler equations ,010101 applied mathematics ,symbols.namesake ,Mathematics - Analysis of PDEs ,Physics::Plasma Physics ,Physics::Space Physics ,symbols ,FOS: Mathematics ,Incompressible euler equations ,Geometry and Topology ,0101 mathematics ,GEOM ,35Q30, 35Q35, 35Q92 ,Analysis ,Mathematics ,Analysis of PDEs (math.AP) - Abstract
We describe a method to construct smooth and compactly supported solutions of 3D incompressible Euler equations and related models. The method is based on localizable Grad–Shafranov equations and is inspired by the recent result (Gavrilov in A steady Euler flow with compact support. Geom Funct Anal 29(1):90–197, [Gav19]).
- Published
- 2019
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22. The approximate capacity for the 3-receiver writing on random dirty paper channel
- Author
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Stefano Rini and Shlomo Shamai
- Subjects
Gaussian ,020206 networking & telecommunications ,Data_CODINGANDINFORMATIONTHEORY ,02 engineering and technology ,State (functional analysis) ,Upper and lower bounds ,Superposition principle ,symbols.namesake ,Additive white Gaussian noise ,Transmission (telecommunications) ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Algorithm ,Realization (systems) ,Computer Science::Information Theory ,Mathematics ,Communication channel - Abstract
In this paper, the approximate capacity of the 3-receiver “writing on random dirty paper” (WRDP) channel is derived. In the M-receiver WRDP channel, the channel output is obtained as the sum of the channel input, white Gaussian noise and a channel state sequence randomly selected among a set of M independent Gaussian sequences. The transmitter has non-causal knowledge of the set of possible state sequences but does not know which one is selected to produce the channel output. In the following, we derive upper and lower bounds to the capacity of the 3-receiver WRDP channel which are to within a distance of at most 3 bits-per-channel-use (bpcu) for all channel parameters. In the achievability proof, the channel input is composed of the superposition of three codewords: the receiver opportunistically decodes a different set of codewords, depending on the variance of the channel state appearing in the channel output. Time-sharing among multiple transmission phases is employed to guarantee that transmitted message can be decoded regardless of the state realization. In the converse proof, we derive a novel outer bound which matches the pre-log coefficient arising in the achievability proof due to time-sharing. Although developed for the case of three possible state realizations, our results can be extended the general WRDP.
- Published
- 2017
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23. Einstein’s Approach to Statistical Mechanics: The 1902–04 Papers
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Raúl Rechtman and Luca Peliti
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Thermal equilibrium ,Basis (linear algebra) ,Physics - History and Philosophy of Physics ,Equations of motion ,Statistical and Nonlinear Physics ,Statistical mechanics ,01 natural sciences ,Sketch ,010305 fluids & plasmas ,Theoretical physics ,symbols.namesake ,0103 physical sciences ,symbols ,Einstein ,010306 general physics ,Focus (optics) ,Mathematical Physics ,Mathematics - Abstract
We summarize the papers published by Einstein in the Annalen der Physik in the years 1902-04 on the derivation of the properties of thermal equilibrium on the basis of the mechanical equations of motion and of the calculus of probabilities. We point out the line of thought that led Einstein to an especially economical foundation of the discipline, and to focus on fluctuations of the energy as a possible tool for establishing the validity of this foundation. We also sketch a comparison of Einstein's approach with that of Gibbs, suggesting that although they obtained similar results, they had different motivations and interpreted them in very different ways., Comment: 22 pages, submitted to JSP
- Published
- 2016
24. An Upper Bound on the Capacity of Vector Dirty Paper with Unknown Spin and Stretch
- Author
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David T. H. Kao and Ashutosh Sabharwal
- Subjects
010302 applied physics ,FOS: Computer and information sciences ,business.industry ,Gaussian ,Computer Science - Information Theory ,Information Theory (cs.IT) ,Scalar (mathematics) ,Significant difference ,Transmitter ,020206 networking & telecommunications ,02 engineering and technology ,Topology ,01 natural sciences ,Upper and lower bounds ,Dirty paper ,Channel capacity ,symbols.namesake ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Zero-forcing precoding ,Telecommunications ,business ,Mathematics ,Computer Science::Information Theory - Abstract
Dirty paper codes are a powerful tool for combating known interference. However, there is a significant difference between knowing the transmitted interference sequence and knowing the received interference sequence, especially when the channel modifying the interference is uncertain. We present an upper bound on the capacity of a compound vector dirty paper channel where although an additive Gaussian sequence is known to the transmitter, the channel matrix between the interferer and receiver is uncertain but known to lie within a bounded set. Our bound is tighter than previous bounds in the low-SIR regime for the scalar version of the compound dirty paper channel and employs a construction that focuses on the relationship between the dimension of the message-bearing signal and the dimension of the additive state sequence. Additionally, a bound on the high-SNR behavior of the system is established., Comment: to be presented at ISIT 2013
- Published
- 2013
- Full Text
- View/download PDF
25. Analogy and Invention Some Remarks on Poincaré’s Analysis Situs Papers
- Author
-
Claudio Bartocci
- Subjects
Pure mathematics ,symbols.namesake ,Situs ,Betti number ,Poincaré conjecture ,symbols ,Analogy ,Homology sphere ,Mathematics - Abstract
The primary role played by analogy in Henri Poincare’s work, and in particular in his “analysis situs” papers, is emphasized. Poincare’s “sixth example” (showing that Betti numbers do not suffice to classify 3-manifolds) and his construction of the homology sphere are discussed in detail.
- Published
- 2018
26. 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
-
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
27. 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
-
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
28. Convergence Results of Galerkin Optimal Control with Legendre Test Function∗∗The work and views expressed in this paper are those of the authors and do not reflect the oficial policy or position of the U.S. Department of the Army, the U.S. Department of the Navy, the U.S. Department of Defense or the U.S. Government
- Author
-
Randy Boucher and Wei Kang
- Subjects
Mathematical optimization ,Discretization ,MathematicsofComputing_NUMERICALANALYSIS ,Optimal control ,symbols.namesake ,Control and Systems Engineering ,Discontinuous Galerkin method ,symbols ,Test functions for optimization ,Piecewise ,Gaussian quadrature ,Galerkin method ,Legendre polynomials ,Mathematics - Abstract
A Galerkin-based family of numerical formulations is presented for solving nonlinear optimal control problems. This paper introduces a family of direct methods that calculate optimal trajectories by discretizing the system dynamics using Galerkin numerical techniques and approximate the cost function with Gaussian quadrature. In this numerical approach, the analysis is based on L 2 -norms. An important result in the theoretical foundation is that the feasibility and consistency theorems are proved for problems with piecewise continuous controls. Galerkin methods may be formulated in a number of ways that allow for eficiency and/or improved accuracy while solving a wide range of optimal control problems with a variety of state and control constraints. Numerical formulations using Legendre test functions are derived. One formulation allows for a weak enforcement of boundary conditions, which imposes end conditions only up to the accuracy of the numerical approximation itself. Finally, a numerical example is shown to demonstrate the exponential convergence of Galerkin optimal control.
- Published
- 2015
29. Design of PD Observer-Based Fault Estimator for a Class of Takagi-Sugeno Descriptor Systems∗∗The work presented in this paper was supported by VEGA, the Grant Agency of the Ministry of Education and the Academy of Science of Slovak Republic, under Grant No. 1/0348/14. This support is very gratefully acknowledged
- Author
-
Dusan Krokavec and Anna Filasova
- Subjects
Lyapunov function ,symbols.namesake ,Nonlinear system ,Observer (quantum physics) ,Control and Systems Engineering ,Control theory ,Convex optimization ,Convergence (routing) ,symbols ,Estimator ,State observer ,Mathematics ,System model - Abstract
A generalized approach to design a proportional and derivative system faults fuzzy observer for continuous-time nonlinear systems described in the Takagi-Sugeno descriptor statespace form is presented in the paper. Considering measurable premise variables, the problem addressed is formulated as an enhanced concept to descriptor systems design, implying the asymptotic convergence both the state observer error as fault estimate error. Presented in the sense of the second Lyapunov method, an associated structure of linear matrix inequalities is outlined to possess the global observer asymptotic dynamic properties with compiling the local insiders by inference through the membership functions equal those of the system model. The proposed design conditions are verified by simulations in the numerical illustrative example.
- Published
- 2015
30. On the Capacity of the Carbon Copy onto Dirty Paper Channel
- Author
-
Shlomo Shamai Shitz and Stefano Rini
- Subjects
Independent and identically distributed random variables ,FOS: Computer and information sciences ,Computer Science - Information Theory ,02 engineering and technology ,Library and Information Sciences ,01 natural sciences ,Precoding ,010305 fluids & plasmas ,Channel capacity ,symbols.namesake ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,Fading ,Mathematics ,Channel use ,Computer Science::Information Theory ,business.industry ,Information Theory (cs.IT) ,020206 networking & telecommunications ,Computer Science Applications ,Additive white Gaussian noise ,Gaussian noise ,symbols ,Telecommunications ,business ,Algorithm ,Information Systems ,Communication channel - Abstract
The "Carbon Copy onto Dirty Paper" (CCDP) channel is the compound "writing on dirty paper" channel in which the channel output is obtained as the sum of the channel input, white Gaussian noise and a Gaussian state sequence randomly selected among a set possible realizations. The transmitter has non-causal knowledge of the set of possible state sequences but does not know which sequence is selected to produce the channel output. We study the capacity of the CCDP channel for two scenarios: (i) the state sequences are independent and identically distributed, and (ii) the state sequences are scaled versions of the same sequence. In the first scenario, we show that a combination of superposition coding, time-sharing and Gel'fand-Pinsker binning is sufficient to approach the capacity to within three bits per channel use for any number of possible state realizations. In the second scenario, we derive capacity to within four bits-per-channel-use for the case of two possible state sequences. This result is extended to the CCDP channel with any number of possible state sequences under certain conditions on the scaling parameters which we denote as "strong fading" regime. We conclude by providing some remarks on the capacity of the CCDP channel in which the state sequences have any jointly Gaussian distribution.
- Published
- 2017
- Full Text
- View/download PDF
31. Analysis and Design of Dirty Paper Coding by Transformation of Noise
- Author
-
Sae-Young Chung and Young-Seung Lee
- Subjects
Block code ,Concatenated error correction code ,Data_CODINGANDINFORMATIONTHEORY ,Binary erasure channel ,Linear code ,symbols.namesake ,Additive white Gaussian noise ,Electronic engineering ,symbols ,Dirty paper coding ,Low-density parity-check code ,Algorithm ,Decoding methods ,Computer Science::Information Theory ,Mathematics - Abstract
We design a coding scheme for Costa's dirty paper coding (DPC) (M.H.M. Costa, 1983) using a channel and a shaping code. We show that by transforming the channel noise distribution the DPC channel can be converted into the binary erasure channel (BEC) with binary interference with memory. Furthermore, the messages exchanged during the iterative decoding between the channel and shaping codes become one dimensional under the new model. We analyze the iterative decoding and find good shaping and channel code pairs using some closed-form extrinsic information transfer (EXIT) curves. We verify that our dirty paper codes designed using this method are also good for the original DPC channel with the additive white Gaussian noise (AWGN) and arbitrary interference. Our implementation of DPC uses short block codes such as repetition codes for shaping codes. Although the shaping gains of such codes are not very high, they may provide a better complexity-performance trade-off for simple practical implementations of DPC. Furthermore, we show accurate theoretical analysis is possible for such codes under our channel model.
- Published
- 2007
32. A new calculation method of feedback controller gain for bilinear paper-making process with disturbance
- Author
-
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
33. Corrections to the paper 'The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces'
- Author
-
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
34. Note on A. Barbour’s paper on Stein’s method for diffusion approximations
- Author
-
Andrew B. Duncan, Mikołaj Kasprzak, and Sebastian J. Vollmer
- Subjects
Statistics and Probability ,Pure mathematics ,60B10 ,Statistics & Probability ,Gaussian ,Banach space ,Stein’s method ,01 natural sciences ,010104 statistics & probability ,symbols.namesake ,FOS: Mathematics ,60J65 ,60E05 ,0101 mathematics ,QA ,60J60 ,Mathematics ,Semigroup ,0104 Statistics ,010102 general mathematics ,Probability (math.PR) ,Stein's method ,Heavy traffic approximation ,60F17 ,Primary: 60B10, 60F17, Secondary: 60J60, 60J65, 60E05 ,Norm (mathematics) ,symbols ,Stein equation ,Mathematics [G03] [Physical, chemical, mathematical & earth Sciences] ,Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre] ,Statistics, Probability and Uncertainty ,Donsker’s theorem ,Mathematics - Probability ,diffusion approximations - Abstract
In (Barbour, 1990) foundations for diffusion approximation via Stein's method are laid. This paper has been cited more than 130 times and is a cornerstone in the area of Stein's method. A semigroup argument is used therein to solve a Stein equation for Gaussian diffusion approximation. We prove that, contrary to the claim in (Barbour, 1990), the semigroup considered therein is not strongly continuous on the Banach space of continuous, real-valued functions on D[0,1] growing slower than a cubic, equipped with an appropriate norm. We also provide a proof of the exact formulation of the solution to the Stein equation of interest, which does not require the aforementioned strong continuity. This shows that the main results of (Barbour, 1990) hold true., Comment: 8 pages
- Published
- 2017
35. Physics in Riemann’s Mathematical Papers
- Author
-
Athanase Papadopoulos
- Subjects
Physics ,Physical reasoning ,Mathematics::Complex Variables ,Riemann surface ,Mathematics::History and Overview ,010102 general mathematics ,Face (sociological concept) ,06 humanities and the arts ,Riemannian geometry ,Space (mathematics) ,01 natural sciences ,Physics::History of Physics ,symbols.namesake ,Riemann hypothesis ,060105 history of science, technology & medicine ,symbols ,Calculus ,0601 history and archaeology ,0101 mathematics ,Relation (history of concept) ,Mathematics - Abstract
Riemann’s mathematical papers contain many ideas that arise in physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann’s ideas in mathematics from there in physics. Furthermore, Riemann’s philosophical ideas are often in the background of his work on science. The aim of this chapter is to give an overview of Riemann’s mathematical results based on physical reasoning or motivated by physics. We also elaborate on the relation with philosophy. While we discuss some of Riemann’s philosophical points of view, we review some ideas on the same subjects emitted by Riemann’s predecessors, and in particular Greek philosophers, mainly the pre-socratics and Aristotle.
- Published
- 2017
36. About the Performance of Practical Dirty Paper Coding Schemes in Gaussian MIMO Broadcast Channels
- Author
-
Julien Dumont, G. R. Mohammad-Khani, and Samson Lasaulce
- Subjects
symbols.namesake ,Single antenna interference cancellation ,Gaussian ,MIMO ,Bit error rate ,Electronic engineering ,symbols ,Dirty paper coding ,Version vector ,Encoder ,Decoding methods ,Mathematics - Abstract
This paper describes a way of implementing DPC in a Gaussian MIMO broadcast channel. The outer encoder is based on a vector TCQ designed to possess certain "good properties". Simpler schemes such as the Tomlinson Harashima or Scalar Costa's scheme are also considered by a way of comparison. The inner encoder is implemented through a vector version of the ZF-DPC and the MMSE-DPC. The BER performance of the DPC schemes is evaluated and compared to that of conventional interference cancellers (pre-ZF, pre-MMSE). From simulation results the choices of the inner encoder, the outer encoder (THS/SCS/TCQ) and the interference cancellation technique (conventional or DPC) are discussed.
- Published
- 2006
37. Bending Paper and the Möbius Strip
- Author
-
Sören Bartels and Peter Hornung
- Subjects
symbols.namesake ,Mathematics::Combinatorics ,Mechanics of Materials ,Mathematics::Number Theory ,Mechanical Engineering ,Plate theory ,symbols ,General Materials Science ,Geometry ,Möbius strip ,Bending ,Nonlinear elasticity ,Mathematics - Abstract
We present some rigorous results about the bending behaviour of paper. By adapting these results to the Mobius strip, we obtain some qualitative properties of developable Mobius strips which minimize the bending energy. We also provide some numerical simulations which illustrate and strengthen the analytic results.
- Published
- 2014
38. Addendum to the paper 'Real hypersurfaces in complex two-plane Grassmannians with ξ-invariant Ricci tensor'
- Author
-
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
39. Lp-solution for BSDEs with jumps in the case p<2 : Corrections to the paper ‘BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration’
- Author
-
Alexandre Popier and Thomas Kruse
- Subjects
Statistics and Probability ,Generator (computer programming) ,010102 general mathematics ,Monotonic function ,Poisson distribution ,01 natural sciences ,010104 statistics & probability ,symbols.namesake ,Stochastic differential equation ,Monotone polygon ,Modeling and Simulation ,Mathematik ,symbols ,Filtration (mathematics) ,Applied mathematics ,Uniqueness ,0101 mathematics ,Brownian motion ,Mathematics - Abstract
In T. Kruse and A. Popier, we established existence and uniqueness of solutions of backward stochastic differential equations in under a monotonicity condition on the generator and in a general filtration. There was a mistake in the case . Here we give a corrected proof. Moreover the quasi-left continuity condition on the filtration is removed.
- Published
- 2017
40. Erratum to the paper 'L∞(L∞)-boundedness and convergence of DG(p)-solutions for nonlinear conservation laws with boundary conditions'
- Author
-
Christian Henke and Lutz Angermann
- Subjects
Conservation law ,Pure mathematics ,Lemma (mathematics) ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,Lebesgue integration ,Computational Mathematics ,Nonlinear system ,symbols.namesake ,Convergence (routing) ,symbols ,Boundary value problem ,Affine transformation ,Constant (mathematics) ,Mathematics - Abstract
In the paper (HA14), unfortunately, a computational error occurred in one estimate. Although the wrong estimate does not affect the main results, we want to present the necessary corrections. Essentially, Lemma 5.2 has to be corrected and, since it is used in the proof of Theorem 5.1, the proof of this theorem also requires an adaptation. (i) The corrected formulation of Lemma 5.2 is as follows. Lemma 5.2 For Lagrange finite elements with a shape-regular family of affine meshes { T n h } h>0 there is a constant C > 0 independent of q and h such that for all w ∈ Wh and q = 2m, m ∈N: CΛq−2 p (∇w,∇Ip h (wq−1))T ∫ T ‖∇w‖l2‖w‖ q−2 0,∞,T dx, ∀T ∈ T n h , (5.1) where Λp = ‖ ∑ndof i=1 |φi|‖0,∞,T is the Lebesgue constant.
- Published
- 2015
41. A commentary on Teichmüller’s paper Extremale quasikonforme Abbildungen und quadratische Differentiale
- Author
-
Athanase Papadopoulos, Weixu Su, and Vincent Alberge
- Subjects
Teichmüller space ,Fuchsian group ,Quasiconformal mapping ,Riemann surface ,010102 general mathematics ,06 humanities and the arts ,01 natural sciences ,Beltrami equation ,Moduli ,Algebra ,symbols.namesake ,060105 history of science, technology & medicine ,symbols ,0601 history and archaeology ,0101 mathematics ,Uniformization (set theory) ,Mathematics - Abstract
We provide a commentary on Teichmuller's paper "Extremale quasikonforme Abbildungen und quadratische Differentiale" (Extremal quasiconformal mappings of closed oriented Riemann surfaces), Abh. Preuss. Akad. Wiss., Math.-Naturw. Kl. 1940, No.22, 1-197 (1940). The paper is quoted in several works, although it was read by very few people. Some of the results it contains were rediscovered later on and published without any reference to Teichmuller. In this commentary, we highlight the main results and the main ideas contained in that paper and we describe some of the important developments they gave rise to.
- Published
- 2016
42. A commentary on Teichmüller’s paper Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Flächen
- Author
-
Athanase Papadopoulos, Annette A'Campo-Neuen, Norbert A'Campo, and Vincent Alberge
- Subjects
Fuchsian group ,Teichmüller space ,Quasiconformal mapping ,Pure mathematics ,Euclidean space ,Riemann surface ,010102 general mathematics ,Surface (topology) ,Mathematics::Geometric Topology ,01 natural sciences ,Algebra ,symbols.namesake ,Invariance of domain ,0103 physical sciences ,Uniformization theorem ,symbols ,010307 mathematical physics ,0101 mathematics ,Mathematics - Abstract
This is a mathematical commentary on Teichmuller's paper ``Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Flachen" (Determination of extremal quasiconformal maps of closed oriented Riemann surfaces). This paper is among the last (and may be the last one) that Teichmuller wrote on the theory of moduli. It contains the proof of the so-called Teichmuller existence theorem for a closed surface of genus at least 2. For this proof, the author defines a mapping between a space of equivalence classes of marked Riemann surfaces (the Teichmuller space) and a space of equivalence classes of certain Fuchsian groups (the so-called Fricke space). After that, he defines a map between the latter and the Euclidean space of dimension 6g-6 Using Brouwer's theorem of invariance of domain, he shows that this map is a homeomorphism. This involves in particular a careful definition of the topologies of Fricke space, the computation of its dimension, and comparison results between hyperbolic distance and quasiconformal dilatation. The use of the invariance of domain theorem is in the spirit of Poincare and Klein's use of the so-called ``continuity principle" in their attempts to prove the uniformization theorem.
- Published
- 2016
43. Averages of Ramanujan sums: note on two papers by E. Alkan
- Author
-
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
44. A note on O. Frolkina’s paper 'pairwise disjoint moebius bands in space'
- Author
-
Sergey A. Melikhov
- Subjects
Algebra and Number Theory ,010102 general mathematics ,Disjoint sets ,Space (mathematics) ,01 natural sciences ,Combinatorics ,symbols.namesake ,Simple (abstract algebra) ,0103 physical sciences ,symbols ,010307 mathematical physics ,Möbius strip ,0101 mathematics ,Algebraic number ,Mathematics - Abstract
We note a simple algebraic proof of Frolkina’s result that [Formula: see text] does not contain uncountably many pairwise disjoint copies of the Möbius band, and of a similar result in higher dimensions.
- Published
- 2019
45. Cycles with undistinguished actions and extended Rock–Paper–Scissors games
- Author
-
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
46. Series representation of the Riemann zeta function and other results: Complements to a paper of Crandall
- Author
-
Mark W. Coffey
- Subjects
Pure mathematics ,Algebra and Number Theory ,Polylogarithm ,Mathematics - Number Theory ,Mathematics::Number Theory ,Applied Mathematics ,Mathematical analysis ,Mathematics::Classical Analysis and ODEs ,Stieltjes constants ,FOS: Physical sciences ,Mathematical Physics (math-ph) ,Riemann zeta function ,Riemann Xi function ,Hurwitz zeta function ,Computational Mathematics ,Arithmetic zeta function ,symbols.namesake ,Riemann hypothesis ,11M06, 11M35, 11Y35, 11Y60 ,FOS: Mathematics ,symbols ,Number Theory (math.NT) ,Mathematical Physics ,Prime zeta function ,Mathematics - Abstract
We supplement a very recent paper of R. Crandall concerned with the multiprecision computation of several important special functions and numbers. We show an alternative series representation for the Riemann and Hurwitz zeta functions providing analytic continuation through out the whole complex plane. Additionally we demonstrate some series representations for the initial Stieltjes constants appearing in the Laurent expansion of the Hurwitz zeta function. A particular point of elaboration in these developments is the hypergeometric form and its equivalents for certain derivatives of the incomplete Gamma function. Finally, we evaluate certain integrals including $\int_{\tiny{Re} s=c} {{\zeta(s)} \over s} ds$ and $\int_{\tiny{Re} s=c} {{\eta(s)} \over s} ds$, with $\zeta$ the Riemann zeta function and $\eta$ its alternating form., Comment: 17 pages, no figures
- Published
- 2013
47. Constructing the Cubus simus and the Dodecaedron simum via paper folding
- Author
-
Klaudia Kwickert and Urs Hartl
- Subjects
Snub dodecahedron ,Hyperbolic geometry ,Metric Geometry (math.MG) ,Folding (DSP implementation) ,Snub cube ,Archimedean solid ,Combinatorics ,symbols.namesake ,Dodecahedron ,Mathematics - Metric Geometry ,Differential geometry ,FOS: Mathematics ,symbols ,Geometry and Topology ,51M15 (Primary) 51M20 (Secondary) ,Projective geometry ,Mathematics - Abstract
The archimedean solids Cubus simus (snub cube) and Dodecaedron simum (snub dodecahedron) cannot be constructed by ruler and compass. We explain that for general reasons their vertices can be constructed via paper folding on the faces of a cube, respectively dodecahedron, and we present explicit folding constructions. The construction of the Cubus simus is particularly elegant. We also review and prove the construction rules of the other Archimedean solids., Comment: 13 pages, 12 figures, v2: as published in Geometriae Dedicata
- Published
- 2012
48. An Upper Bound on the Capacity of the Causal Dirty-Paper Channel
- Author
-
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
49. A comment on the paper 'Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker–Planck equations' by T.D. Frank
- Author
-
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
50. Chaotic time series prediction for the game, Rock-Paper-Scissors
- Author
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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
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