154,937 results
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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. 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
5. 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
6. Folding a Paper Strip to Minimize Thickness
- Author
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Hiro Ito, Erik D. Demaine, Anna Lubiw, David Eppstein, Ryuhei Uehara, Yushi Uno, Adam Hesterberg, Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science, and Massachusetts Institute of Technology. Department of Mathematics
- Subjects
Computational Geometry (cs.CG) ,FOS: Computer and information sciences ,paper folding ,0102 computer and information sciences ,02 engineering and technology ,Topology ,01 natural sciences ,Theoretical Computer Science ,NP completeness ,symbols.namesake ,Exponential growth ,crease width ,Computer Science - Data Structures and Algorithms ,0202 electrical engineering, electronic engineering, information engineering ,Discrete Mathematics and Combinatorics ,Data Structures and Algorithms (cs.DS) ,Mathematics ,NP-complete ,computational origami ,Planar graph ,rigid origami ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,symbols ,Computer Science - Computational Geometry ,020201 artificial intelligence & image processing ,linkage ,optimization problem - Abstract
In this paper, we study how to fold a specified origami crease pattern in order to minimize the impact of paper thickness. Specifically, origami designs are often expressed by a mountain-valley pattern (plane graph of creases with relative fold orientations), but in general this specification is consistent with exponentially many possible folded states. We analyze the complexity of finding the best consistent folded state according to twometrics:minimizing the total number of layers in the folded state (so that a “flat folding” is indeed close toflat), andminimizing the total amount of paper required to execute the folding (where “thicker” creases consume more paper). We prove both problems strongly NP-complete even for 1D folding. On the other hand, we prove the first problem fixed-parameter tractable in 1D with respect to the number of layers., National Science Foundation (U.S.). Origami Design for Integration of Self-assembling Systems for Engineering Innovation (grant EFRI- 124038), National Science Foundation (U.S.). Expedition grant (CCF-1138967), United States. Department of Defense. National Defense Science and Engineering Graduate (NDSEG) Fellowship (32 CFR 168a)
- Published
- 2015
7. 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
8. 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
9. Annotated Translations of Three of the Euler’s Papers on Celestial Mechanics
- Author
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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
10. Evolutionary dynamics of rock-paper-scissors game in the patchy network with mutations
- Author
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Tina Verma and Arvind Kumar Gupta
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Hopf bifurcation ,education.field_of_study ,General Mathematics ,Applied Mathematics ,Population ,Evolutionary game theory ,Biodiversity ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Metapopulation ,symbols.namesake ,Transcritical bifurcation ,Evolutionary biology ,Mutation (genetic algorithm) ,symbols ,education ,Evolutionary dynamics ,Mathematics - Abstract
Connectivity is the safety network for biodiversity conservation because connected habitats are more effective for saving the species and ecological functions. The nature of coupling for connectivity also plays an important role in the co-existence of species in cyclic-dominance. The rock-paper-scissors game is one of the paradigmatic mathematical model in evolutionary game theory to understand the mechanism of biodiversity in cyclic-dominance. In this paper, the metapopulation model for rock-paper-scissors with mutations is presented in which the total population is divided into patches and the patches form a network of complete graph. The migration among patches is allowed through simple random walk. The replicator-mutator equations are used with the migration term. When migration is allowed then the population of the patches will synchronized and attain stable state through Hopf bifurcation. Apart form this, two phases are observed when the strategies of one of the species mutate to other two species: co-existence of all the species phase and existence of one kind of species phase. The transition from one phase to another phase is taking place due to transcritical bifurcation. The dynamics of the population of species of rock, paper, scissors is studied in the environment of homogeneous and heterogeneous mutation. Numerical simulations have been performed when mutation is allowed in all the patches (homogeneous mutation) and some of the patches (heterogeneous mutation). It has been observed that when the number of patches is increased in the case of heterogeneous mutation then the population of any of the species will not extinct and all the species will co-exist.
- Published
- 2021
11. 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
12. 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
13. A Generalized Zero-Forcing Precoder with Successive Dirty-Paper Coding in MISO Broadcast Channels
- Author
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Sha Hu and Fredrik Rusek
- Subjects
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
- Full Text
- View/download PDF
14. Riemann’s Shockwave Paper
- Author
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Jeremy Gray
- Subjects
Physics::Fluid Dynamics ,Riemann hypothesis ,symbols.namesake ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Partial differential equation ,symbols ,Mathematics ,Mathematical physics - Abstract
Riemann’s account of shockwaves and his novel approach to hyperbolic partial differential equations are described, as is Darboux’s later explanation.
- Published
- 2021
15. Bifurcation analysis of the rock–paper–scissors game with discrete-time logit dynamics
- Author
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Yosuke Umezuki
- Subjects
Computer Science::Computer Science and Game Theory ,Sociology and Political Science ,05 social sciences ,General Social Sciences ,01 natural sciences ,010305 fluids & plasmas ,symbols.namesake ,Bifurcation theory ,Discrete time and continuous time ,Nash equilibrium ,Best response ,0502 economics and business ,0103 physical sciences ,Attractor ,symbols ,Applied mathematics ,050207 economics ,Statistics, Probability and Uncertainty ,Invariant (mathematics) ,General Psychology ,Bifurcation ,Saddle ,Mathematics - Abstract
In this study, we investigate a discrete-time version of logit dynamics, as applied to the rock–paper–scissors (RPS) game. First, we show that around the Nash equilibrium point, an attracting closed invariant curve appears due to the Neimark–Sacker bifurcation. Next, near the resonance point, we find a period-three attracting cycle, which can be thought of as a counterpart to the cyclically stable set in the RPS game with best response dynamics. Moreover, we show that the cycle can coexist with an attracting closed invariant curve, a period-three saddle cycle, and the attracting or repelling Nash equilibrium point. Finally, we use the codimension-two bifurcation theory to specify the set of heteroclinic bifurcations that destroy the coexistence of the attractors.
- Published
- 2018
16. 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
17. 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
18. Universal scaling law of an origami paper spring
- Author
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Bohua Sun
- Subjects
Environmental Engineering ,Biomedical Engineering ,Computational Mechanics ,Aerospace Engineering ,FOS: Physical sciences ,Ocean Engineering ,Poisson distribution ,01 natural sciences ,Square (algebra) ,010305 fluids & plasmas ,symbols.namesake ,Physics - General Physics ,0103 physical sciences ,010306 general physics ,Civil and Structural Engineering ,Mathematics ,Mechanical Engineering ,Mathematical analysis ,Extension (predicate logic) ,Poisson's ratio ,Power (physics) ,Nonlinear system ,General Physics (physics.gen-ph) ,Mechanics of Materials ,Spring (device) ,lcsh:TA1-2040 ,symbols ,Curve fitting ,lcsh:Engineering (General). Civil engineering (General) - Abstract
This letter solves an open question of origami paper spring risen by Yoneda et al.(Phys. Rev. E 2019). By using both dimensional analysis and data fitting, a universal scaling law of a paper spring is formulated. The scaling law shows that origami spring force obeys power square law of spring extension, however strong nonlinear to the total twist angle. The study has also successfully generalized the scaling law from the Poisson ratio 0.3 to an arbitrary Poisson's ratio with the help of dimensional analysis., Comment: 3 pages, 3 figues and 1 table
- Published
- 2020
- Full Text
- View/download PDF
19. ‘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
20. 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
- Subjects
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.
- Published
- 2018
21. Schrödinger’s Reaction to the EPR Paper
- Author
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Jos Uffink
- Subjects
symbols.namesake ,Theoretical physics ,Argument ,Completeness (order theory) ,Biorthogonal system ,Single measurement ,symbols ,Quantum Physics ,Einstein ,Physics::History of Physics ,Schrödinger's cat ,Outcome (probability) ,Mathematics - Abstract
I discuss Schrodinger’s response to the Einstein-Podolsky-Rosen (EPR) paper of 1935. In particular, it is argued, based on an unpublished notebook, that while Schrodinger sympathized with the EPR argument he worried about its lack of emphasis on the role of biorthogonal expansions and on the distinction between conclusions dependent on the particular outcome obtained in a single measurement, versus those that quantify over all possible outcomes of a measurement procedure. I also discuss the different views between Schrodinger and Einstein on the issue of the completeness of quantum mechanics. Finally, I discuss the question whether Schrodinger borrowed from his correspondence with Einstein to come up with his famous Cat Paradox.
- Published
- 2020
22. Comments on the paper 'Asymptotic behavior for a fourth-order parabolic equation involving the Hessian. Z. Angew. Math. Phys., (2018) 69: 147'
- Author
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Jun Zhou and Hang Ding
- Subjects
Hessian matrix ,symbols.namesake ,Fourth order ,Applied Mathematics ,General Mathematics ,symbols ,General Physics and Astronomy ,Applied mathematics ,Finite time ,Mathematics ,Energy functional ,Blowing up - Abstract
In this note, we make two revisions of the paper [2]. The first one is the asymptotic behavior of the energy functional as $$t\rightarrow T$$ (see [2, Theorem 1.6]), where T is the blow-up time. The second one is the equivalent conditions for the solutions blowing up in finite time or existing globally (see [2, Theorem 1.8]).
- Published
- 2019
23. 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
- Subjects
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
24. 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
25. Respond to the comment letter by Romano and Barretta on the paper 'Exact solution of Eringen's nonlocal integral model for bending of Euler–Bernoulli and Timoshenko beams'
- Author
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Meral Tuna and Mesut Kirca
- Subjects
Generalized function ,Heaviside step function ,Mechanical Engineering ,General Engineering ,Dirac delta function ,02 engineering and technology ,Bending ,021001 nanoscience & nanotechnology ,symbols.namesake ,Bernoulli's principle ,020303 mechanical engineering & transports ,Exact solutions in general relativity ,0203 mechanical engineering ,Mechanics of Materials ,Step function ,Calculus ,symbols ,Euler's formula ,General Materials Science ,0210 nano-technology ,Mathematics - Abstract
This letter is proposed to provide answers to the concerns raised by Romano and Baretta (2016) in their comment letter. While the criticism about the title of the paper is partly reasonable, the other issues including the improper manipulations of the generalized functions (i.e. Dirac delta and Heaviside step functions), inappropriate approximations and incorrect expressions and results are totally denied by providing reasonable justifications and relevant references from the literature. The detailed answers to each concern are given within the following paragraphs.
- Published
- 2017
26. Comment on the paper 'Interaction of delta shock waves for the Chaplygin Euler equations of compressible fluid flow with split delta functions, Yu Zhang, Yanyan Zhang, Jinhuan Wang Mathematical Methods in the Applied Sciences , 2018; 41 :7678–7697'
- Author
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Asterios Pantokratoras
- Subjects
Delta ,Shock wave ,symbols.namesake ,General Mathematics ,Mathematical analysis ,Zhàng ,General Engineering ,symbols ,Applied science ,Compressible fluid flow ,Mathematics ,Euler equations - Published
- 2020
27. Ludwig Prandtl’s 1933 Paper Concerning Wings for Minimum Induced Drag, Translation and Commentary
- Author
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Douglas F. Hunsaker and Warren F. Phillips
- Subjects
symbols.namesake ,Classical mechanics ,Lift-induced drag ,Prandtl number ,symbols ,Translation (geometry) ,Mathematics - Published
- 2020
28. Evolutionary dynamics in the rock-paper-scissors system by changing community paradigm with population flow
- Author
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Junpyo Park
- Subjects
Hopf bifurcation ,education.field_of_study ,General Mathematics ,Applied Mathematics ,Population ,General Physics and Astronomy ,Robustness (evolution) ,Statistical and Nonlinear Physics ,Fixed point ,symbols.namesake ,symbols ,Outflow ,Statistical physics ,Balanced flow ,Evolutionary dynamics ,education ,Multistability ,Mathematics - Abstract
Classic frameworks of rock-paper-scissors game have been assumed in a closed community that a density of each group is only affected by internal factors such as competition interplay among groups and reproduction itself. In real systems in ecological and social sciences, however, the survival and a change of a density of a group can be also affected by various external factors. One of common features in real population systems in ecological and social sciences is population flow that is characterized by population inflow and outflow in a group or a society, which has been usually overlooked in previous works on models of rock-paper-scissors game. In this paper, we suggest the rock-paper-scissors system by implementing population flow and investigate its effect on biodiversity. For two scenarios of either balanced or imbalanced population flow, we found that the population flow can strongly affect group diversity by exhibiting rich phenomena. In particular, while the balanced flow can only lead the persistent coexistence of all groups which accompanies a phase transition through supercritical Hopf bifurcation on different carrying simplices, the imbalanced flow strongly facilitates rich dynamics such as alternative stable survival states by exhibiting various group survival states and multistability of sole group survivals by showing not fully covered but spirally entangled basins of initial densities due to local stabilities of associated fixed points. In addition, we found that, the system can exhibit oscillatory dynamics for coexistence by relativistic interplay of population flows which can capture the robustness of the coexistence state. Applying population flow in the rock-paper-scissors system can ultimately change a community paradigm from closed to open one, and our foundation can eventually reveal that population flow can be also a significant factor on a group density which is independent to fundamental interactions among groups.
- Published
- 2021
29. 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
30. 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
-
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
31. 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
32. A trio of heteroclinic bifurcations arising from a model of spatially-extended Rock-Paper-Scissors
- Author
-
Claire M. Postlethwaite and Alastair M. Rucklidge
- Subjects
Population ,General Physics and Astronomy ,FOS: Physical sciences ,Pattern Formation and Solitons (nlin.PS) ,01 natural sciences ,symbols.namesake ,0101 mathematics ,education ,Quantitative Biology - Populations and Evolution ,Mathematical Physics ,Saddle ,Mathematics ,Hopf bifurcation ,Equilibrium point ,education.field_of_study ,Partial differential equation ,37G15, 34C37, 37C29, 91A22 ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Ode ,Populations and Evolution (q-bio.PE) ,Heteroclinic cycle ,Statistical and Nonlinear Physics ,Nonlinear Sciences - Pattern Formation and Solitons ,010101 applied mathematics ,Ordinary differential equation ,FOS: Biological sciences ,symbols - Abstract
One of the simplest examples of a robust heteroclinic cycle involves three saddle equilibria: each one is unstable to the next in turn, and connections from one to the next occur within invariant subspaces. Such a situation can be described by a third-order ordinary differential equation (ODE), and typical trajectories approach each equilibrium point in turn, spending progressively longer to cycle around the three points but never stopping. This cycle has been invoked as a model of cyclic competition between populations adopting three strategies, characterised as Rock, Paper and Scissors. When spatial distribution and mobility of the populations is taken into account, waves of Rock can invade regions of Scissors, only to be invaded by Paper in turn. The dynamics is described by a set of partial differential equations (PDEs) that has travelling wave (in one dimension) and spiral (in two dimensions) solutions. In this paper, we explore how the robust heteroclinic cycle in the ODE manifests itself in the PDEs. Taking the wavespeed as a parameter, and moving into a travelling frame, the PDEs reduce to a sixth-order set of ODEs, in which travelling waves are created in a Hopf bifurcation and are destroyed in three different heteroclinic bifurcations, depending on parameters, as the travelling wave approaches the heteroclinic cycle. We explore the three different heteroclinic bifurcations, none of which have been observed in the context of robust heteroclinic cycles previously. These results are an important step towards a full understanding of the spiral patterns found in two dimensions, with possible application to travelling waves and spirals in other population dynamics models., Comment: 36 pages, 8 figures
- Published
- 2019
- Full Text
- View/download PDF
33. Combining mid infrared spectroscopy and paper spray mass spectrometry in a data fusion model to predict the composition of coffee blends
- Author
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Rodinei Augusti, Camila Assis, Leandro S. Oliveira, Hebert Vinicius Pereira, Victoria Silva Amador, and Marcelo M. Sena
- Subjects
Multivariate statistics ,Spectrophotometry, Infrared ,Food Handling ,Infrared spectroscopy ,Reproducibility of Results ,Feature selection ,Coffea ,General Medicine ,Sensor fusion ,Mass spectrometry ,Coffee ,Analytical Chemistry ,symbols.namesake ,Fourier transform ,Partial least squares regression ,Spectroscopy, Fourier Transform Infrared ,symbols ,Biological system ,Spectroscopy ,Food Analysis ,Food Science ,Mathematics - Abstract
This paper describes a robust multivariate model for quantifying and characterizing blends of Robusta and Arabica coffees. At different degrees of roasting, 120 ground coffee blends (0.0–33.0%) were formulated. Spectra were obtained by two different techniques, attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy and paper spray mass spectrometry (PS-MS). Partial least squares (PLS) models were built individually with the two types of spectra. Nevertheless, better predictions were obtained by low and medium-level data fusion, taking advantage from the synergy between these two data sets. Data fusion models were improved by variable selection, using genetic algorithms (GA) and ordered predictors selection (OPS). The smallest prediction errors were provided by OPS low-level data fusion model. The number of variables used for regression was reduced from 2145 (full spectra) to 230. Model interpretation was performed by assigning some of the selected variables to specific coffee components, such as trigonelline and chlorogenic acids.
- Published
- 2018
34. 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
35. Einstein’s Approach to Statistical Mechanics: The 1902–04 Papers
- Author
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Raúl Rechtman and Luca Peliti
- Subjects
Thermal equilibrium ,Basis (linear algebra) ,Physics - History and Philosophy of Physics ,Equations of motion ,Statistical and Nonlinear Physics ,Statistical mechanics ,01 natural sciences ,Sketch ,010305 fluids & plasmas ,Theoretical physics ,symbols.namesake ,0103 physical sciences ,symbols ,Einstein ,010306 general physics ,Focus (optics) ,Mathematical Physics ,Mathematics - Abstract
We summarize the papers published by Einstein in the Annalen der Physik in the years 1902-04 on the derivation of the properties of thermal equilibrium on the basis of the mechanical equations of motion and of the calculus of probabilities. We point out the line of thought that led Einstein to an especially economical foundation of the discipline, and to focus on fluctuations of the energy as a possible tool for establishing the validity of this foundation. We also sketch a comparison of Einstein's approach with that of Gibbs, suggesting that although they obtained similar results, they had different motivations and interpreted them in very different ways., Comment: 22 pages, submitted to JSP
- Published
- 2016
36. 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
37. A Note on a Paper by Nieminen
- Author
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Marcel Roman and Adrian Sandovici
- Subjects
Pure mathematics ,Mathematics::Operator Algebras ,Applied Mathematics ,010102 general mathematics ,Linear operators ,Hilbert space ,Mathematics::Spectral Theory ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,Mathematics (miscellaneous) ,symbols ,0101 mathematics ,Mathematics - Abstract
A criteria due to Toivo Nieminen concerning selfadjoint linear operators in complex Hilbert spaces is extended to the case of linear relations.
- Published
- 2019
38. Remarks on a paper by Gavrilov: Grad-Shafranov equations, steady solutions of the three dimensional incompressible Euler equations with compactly supported velocities, and applications
- Author
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Peter Constantin, Vlad Vicol, and Joonhyun La
- Subjects
010102 general mathematics ,Mathematical analysis ,Euler flow ,01 natural sciences ,Euler equations ,010101 applied mathematics ,symbols.namesake ,Mathematics - Analysis of PDEs ,Physics::Plasma Physics ,Physics::Space Physics ,symbols ,FOS: Mathematics ,Incompressible euler equations ,Geometry and Topology ,0101 mathematics ,GEOM ,35Q30, 35Q35, 35Q92 ,Analysis ,Mathematics ,Analysis of PDEs (math.AP) - Abstract
We describe a method to construct smooth and compactly supported solutions of 3D incompressible Euler equations and related models. The method is based on localizable Grad–Shafranov equations and is inspired by the recent result (Gavrilov in A steady Euler flow with compact support. Geom Funct Anal 29(1):90–197, [Gav19]).
- Published
- 2019
- Full Text
- View/download PDF
39. Closed-Form Capacity Bounds for the Exponential Version of the Dirty Paper Channel
- Author
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Mostafa Monemizadeh and Hamed Fehri
- Subjects
Gaussian ,020208 electrical & electronic engineering ,020206 networking & telecommunications ,02 engineering and technology ,Interference (wave propagation) ,Upper and lower bounds ,Noise (electronics) ,Exponential function ,Superposition principle ,symbols.namesake ,Signal-to-noise ratio ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Applied mathematics ,Electrical and Electronic Engineering ,Computer Science::Information Theory ,Communication channel ,Mathematics - Abstract
This letter presents closed-form capacity bounds for an exponential version of the dirty paper channel (EDPC). The EDPC can be used to model the non-coherent Gaussian dirty paper channel (GDPC). First, a superposition modulation-like technique is used to obtain a capacity upper bound for the EDPC. Then, a closed-form capacity lower bound for the EDPC is obtained by using a Costa-like strategy. Using this lower bound and exploiting the asymptotic properties of high signal to noise ratios (SNRs), we obtain the high-SNR capacity of the EDPC which is intriguingly analogous to the complex-valued GDPC. Finally, a closed-form capacity lower bound for the EDPC is given which is useful in the weak interference regime.
- Published
- 2020
40. The approximate capacity for the 3-receiver writing on random dirty paper channel
- Author
-
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
- Full Text
- View/download PDF
41. 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
42. An Upper Bound on the Capacity of Vector Dirty Paper with Unknown Spin and Stretch
- Author
-
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
43. 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
44. WASP (Write a Scientific Paper): Probability – Poisson and binomial distributions
- Author
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Neville Calleja and Victor Grech
- Subjects
020205 medical informatics ,Binomial (polynomial) ,Obstetrics and Gynecology ,02 engineering and technology ,Biostatistics ,Poisson distribution ,Medical Writing ,Measure (mathematics) ,Binomial Distribution ,03 medical and health sciences ,symbols.namesake ,0302 clinical medicine ,030225 pediatrics ,Pediatrics, Perinatology and Child Health ,Statistics ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Poisson Distribution ,Mathematics - Abstract
This paper outlines Binomial and Poisson distributions which are both used to measure the occurrence of a number of random events within a certain period.
- Published
- 2018
45. 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
46. Determination of Poisson’s Ratio of Kraft Paper Using Digital Image Correlation
- Author
-
Zhongchen Bi, Xing Wei, Xiaolong Cao, and Yong Xie
- Subjects
symbols.namesake ,Digital image correlation ,Containerboard ,Mathematical analysis ,symbols ,Analytical chemistry ,Deformation (meteorology) ,Anisotropy ,Poisson distribution ,Measure (mathematics) ,Kraft paper ,Poisson's ratio ,Mathematics - Abstract
Kraft paper is the most popular raw material for based-paper packaging containers. Poisson’s ratio is an important index to indicate the inherent property of materials. There were many difficulties to measure Poisson’s ratio of kraft paper using the traditional contract methods, because of its micro deformation and anisotropy. A simple and efficient non-contract method had been proposed to solve this problem using DIC(Digital Image Correlation) method in this paper. Obtained the relative deformation of samples by calibrated CCD images, Poisson’s ratio could be computed. The test results indicated that Poisson’s ratios of corrugating medium in the MD(Machine Direction) and CD (Cross-machine Direction) were 0.275 and 0.119, and ones of linerboard were 0.275 and 0.119 in MD and CD, respectively. This study showed that DIC was a new approach to measure Poisson’s ratio of kraft paper.
- Published
- 2012
47. Interference channels with source cooperation in the strong cooperation regime: Symmetric capacity to within 2 bits/s/Hz with Dirty Paper Coding
- Author
-
Daniela Tuninetti and Shuang Yang
- Subjects
Gaussian ,Interference (wave propagation) ,Topology ,Channel capacity ,Superposition principle ,symbols.namesake ,Encoding (memory) ,Electronic engineering ,symbols ,Dirty paper coding ,Point (geometry) ,Computer Science::Information Theory ,Communication channel ,Mathematics - Abstract
The capacity region of the Gaussian interference channel with two source-destination pairs where the sources can cooperate is not known. Prabhakaran and Viswanath showed that the sum-rate capacity can be achieved to within 19 bits/s/Hz by using a combination of superposition coding and zero-forcing. This paper only focuses on the symmetric capacity, i.e., the maximum equal rate point that the two sources can simultaneously achieve in a Gaussian interference channel with symmetric channel gains, in the strong cooperation regime, i.e., when the cooperation link is stronger than either the direct link or the interference link. In this setting, it is showed that the “binning+superposition” achievable scheme of Yang and Tuninetti, implemented with Gaussian codebooks and Dirty Paper Coding, achieves the symmetric capacity to within 2 bits/s/Hz-thereby considerably reducing the previously known gap. The extension of this gap-result to other regimes is also discussed.
- Published
- 2011
48. 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
49. Correspondence related to the paper by Busemann and Feller, Zur Differentiation der Lebesgueschen Integrale [On the differentiation of Lebesgue’s integrals]. Fundamenta Mathematicae 22 (1934) 226–256
- Author
-
Manfred Karbe
- Subjects
Pure mathematics ,symbols.namesake ,symbols ,Lebesgue integration ,Mathematics - Published
- 2018
50. 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
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