247,591 results
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2. Mass Balance Equations for Retention and Basis Weight in a Paper Machine
- Author
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Pradeep Kumar Juneja, Gauri Yadav, Neha Belwal, Mayank Chaturvedi, and A. K. Ray
- Subjects
Paper machine ,business.product_category ,Mass balance ,Applied mathematics ,Process control ,business ,Stock (geology) ,Mathematics - Abstract
In a paper industry, especially in thick stock wet end process, the two most important variables are retention in forming section of a paper machine and basis weight of the thick stock. Present paper attempts to understand the governing mass balance equations which may be required to deduce an appropriate process model.
- Published
- 2019
3. Comments on 'A Note on the Paper 'Optimality Conditions for Optimistic Bilevel Programming Problem Using Convexifactors''
- Author
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N. Gadhi
- Subjects
Mathematical optimization ,021103 operations research ,Control and Optimization ,Applied Mathematics ,0211 other engineering and technologies ,010103 numerical & computational mathematics ,02 engineering and technology ,Management Science and Operations Research ,01 natural sciences ,Bilevel optimization ,Bellman equation ,Theory of computation ,0101 mathematics ,Mathematics - Abstract
Necessary optimality conditions for a bilevel optimization problem are given in the paper by Kohli (J Optim Theory Appl 152: 632–651, 2012). Recently, the same author corrected his results in the note (J Optim Theory Appl 181:706–707, 2019). In this work, we have pointed out that some of the new modifications are wrong. We correct the flaws and present an alternative proof for the main result.
- Published
- 2021
4. Multivariate extremes and max-stable processes: discussion of the paper by Zhengjun Zhang
- Author
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R. L. Smith
- Subjects
Statistics and Probability ,Multivariate statistics ,Computational Theory and Mathematics ,Applied Mathematics ,Maximum likelihood ,Zhàng ,Context (language use) ,Statistics, Probability and Uncertainty ,Extreme value theory ,Mathematical economics ,Analysis ,Mathematics - Abstract
This discussion reviews the paper by Zhengjun Zhang in the context of broader research on multivariate extreme value theory and max-stable processes.
- Published
- 2021
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. Corrigendum to a Paper by Charak and Laine
- Author
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Kuldeep Singh Charak and Ilpo Laine
- Subjects
Discrete mathematics ,Class (set theory) ,Applied Mathematics ,General Mathematics ,Entire function ,Prime (order theory) ,Mathematics - Abstract
This is a corrigendum to our paper, “On a class of prime entire functions”, published in Acta Math. Sin., Engl. Ser., 25, 1647–1652 (2009).
- Published
- 2020
7. Addendum to the paper 'High‐order symmetric cubature rules for tetrahedra and pyramids'
- Author
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Jan Jaśkowiec and N. Sukumar
- Subjects
Combinatorics ,Numerical Analysis ,Applied Mathematics ,General Engineering ,Tetrahedron ,Addendum ,High order ,Mathematics - Published
- 2021
8. Ramsey, Paper, Scissors
- Author
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Jacob Fox, Xiaoyu He, and Yuval Wigderson
- Subjects
Computer Science::Computer Science and Game Theory ,Applied Mathematics ,General Mathematics ,Combinatorial game theory ,0102 computer and information sciences ,01 natural sciences ,Computer Graphics and Computer-Aided Design ,Upper and lower bounds ,Combinatorics ,010201 computation theory & mathematics ,TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY ,FOS: Mathematics ,Mathematics - Combinatorics ,Graph (abstract data type) ,Combinatorics (math.CO) ,Ramsey's theorem ,Null graph ,Software ,MathematicsofComputing_DISCRETEMATHEMATICS ,Mathematics ,Independence number - Abstract
We introduce a graph Ramsey game called Ramsey, Paper, Scissors. This game has two players, Proposer and Decider. Starting from an empty graph on $n$ vertices, on each turn Proposer proposes a potential edge and Decider simultaneously decides (without knowing Proposer's choice) whether to add it to the graph. Proposer cannot propose an edge which would create a triangle in the graph. The game ends when Proposer has no legal moves remaining, and Proposer wins if the final graph has independence number at least $s$. We prove a threshold phenomenon exists for this game by exhibiting randomized strategies for both players that are optimal up to constants. Namely, there exist constants $0B\sqrt{n}\log{n}$. This is a factor of $\Theta(\sqrt{\log{n}})$ larger than the lower bound coming from the off-diagonal Ramsey number $r(3,s)$.
- Published
- 2020
9. Correcting mistakes in the paper 'A mass formula for negacyclic codes of length 2k and some good negacyclic codes over $\mathbb {Z}_{4}+u\mathbb {Z}_{4}$' [Cryptogr. Commun. (2017) 9: 241–272]
- Author
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Rama Krishna Bandi, Yuan Cao, Yonglin Cao, and Fang-Wei Fu
- Subjects
Mass formula ,Combinatorics ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,Computer Networks and Communications ,Applied Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,020206 networking & telecommunications ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Mathematics - Abstract
We correct some mistakes in the paper “A mass formula for negacyclic codes of length 2k and some good negacyclic codes over $\mathbb {Z}_{4}+u\mathbb {Z}_{4}$ ” (Bandi et al. Cryptogr. Commun. 9, 241–272, 2017).
- Published
- 2020
10. On the Paper 'On hyperideals of ordered semihypergroups' by ZeGu in Ital. J. Pure Appl. Math
- Author
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Niovi Kehayopulu
- Subjects
Statistics and Probability ,Numerical Analysis ,Lemma (mathematics) ,Pure mathematics ,Algebra and Number Theory ,Corollary ,Applied Mathematics ,Semiprime ,Ideal (order theory) ,Geometry and Topology ,Prime (order theory) ,Theoretical Computer Science ,Mathematics - Abstract
Giving the proper citations, it is shown that, except of Lemma 2.4 and Theorem 2.6, almost all the results of the paper in the title have been previously published for ordered hypersemigroups in Eur. J. Pure Appl. Math. and they are not new. There are also two results obtained from ordered semigroups just putting a ``$\circ$" instead of ``$\cdot$" (that isn't a correct way to work), without reference to ordered semigroups on which the results on ordered hypersemigroups are based. One of them can be obtained as corollary to a theorem in Eur. J. Pure Appl. Math. as well, and it is not new.
- Published
- 2019
11. Some remarks on the paper 'Fixed point theorems for generalized contractive mappings in metric spaces'
- Author
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Ovidiu Popescu
- Subjects
Pure mathematics ,Metric space ,Applied Mathematics ,Modeling and Simulation ,Fixed-point theorem ,Geometry and Topology ,Mathematics - Abstract
In this work, we improve and correct some results in the paper by Proinov (J Fixed Point Theory Appl 22:1–27, 2020).
- Published
- 2021
12. Measurement of some properties of pulp and paper made from date palm midribs and wheat straw by soda-AQ pulping process
- Author
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Mohamed A. Abdel-Aal, Salim Hiziroglu, Hamad A. Al-Mefarrej, N. D. Shetta, Ibrahim M. Aref, and Ramadan A. Nasser
- Subjects
biology ,Applied Mathematics ,Pulp (paper) ,Raw material ,Juniperus procera ,Straw ,engineering.material ,Condensed Matter Physics ,biology.organism_classification ,Pulp and paper industry ,chemistry.chemical_compound ,Cedar wood ,chemistry ,Phoenix dactylifera ,engineering ,Lignin ,Hemicellulose ,Electrical and Electronic Engineering ,Instrumentation ,Mathematics - Abstract
The objective of this study was to characterize the properties of pulp and paper manufactured from two agricultural residues namely, wheat straw (Triticum aestivum L. em Thell.) and date palm midribs (Phoenix dactylifera L.) widely available in Saudi Arabia by employing soda-anthraquinone (AQ) pulping process. Specimens from cedar wood (Juniperus procera Hochst. ex Endl.) wood was also used as control samples. Chemical and the morphological characteristics of all three types of raw materials in addition to basic properties of hand sheets made from such resources were evaluated. The results indicated that wheat straw had the highest hemicellulose and ash values of 35% and 7% and the lowest lignin content value of 18%, respectively. The fibre length of the both palm fronds and wheat straw was lower than that of 2.2 mm which was found for J. procera. Overall strength properties of the handsheet made from two agricultural raw materials were significantly lower than those made from J. procera pulp. Wheat straw handsheets also had higher strength properties than those made from date palm midribs with an exception of their tear index. Based on the results of this study it appears that both types of raw materials, date palm midribs and wheat straw could have a potential to manufacture pulp and paper with accepted properties so that such underutilized species can be converted into value-added products.
- Published
- 2015
13. Some comments on Chen Xu, Mengmei Xi, Xuejun Wang and Hao Xia's paper 'L^r convergence for weighted sums of extended negatively dependent random variables'
- Author
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da Silva and João Lita
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Discrete mathematics ,L(R) ,Chen ,biology ,Convergence of random variables ,Applied Mathematics ,General Mathematics ,Dependent random variables ,Convergence (routing) ,biology.organism_classification ,Mathematics - Abstract
This work is a contribution to the Project UIDB/04035/2020, funded by FCT - Fundacao para a Ciencia e a Tecnologia, Portugal.
- Published
- 2020
14. 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
15. Metapopulation model of rock-scissors-paper game with subpopulation-specific victory rates stabilized by heterogeneity
- Author
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Genki Ichinose, Takashi Nagatani, and Kei-ichi Tainaka
- Subjects
0301 basic medicine ,Statistics and Probability ,General Immunology and Microbiology ,Applied Mathematics ,Victory ,Metapopulation ,General Medicine ,Models, Theoretical ,Random walk ,01 natural sciences ,General Biochemistry, Genetics and Molecular Biology ,Graph ,Combinatorics ,03 medical and health sciences ,030104 developmental biology ,Game Theory ,Homogeneous ,Modeling and Simulation ,0103 physical sciences ,Neutral stability ,Computer Simulation ,010306 general physics ,General Agricultural and Biological Sciences ,Mathematics - Abstract
Recently, metapopulation models for rock-paper-scissors games have been presented. Each subpopulation is represented by a node on a graph. An individual is either rock (R), scissors (S) or paper (P); it randomly migrates among subpopulations. In the present paper, we assume victory rates differ in different subpopulations. To investigate the dynamic state of each subpopulation (node), we numerically obtain the solutions of reaction-diffusion equations on the graphs with two and three nodes. In the case of homogeneous victory rates, we find each subpopulation has a periodic solution with neutral stability. However, when victory rates between subpopulations are heterogeneous, the solution approaches stable focuses. The heterogeneity of victory rates promotes the coexistence of species.
- Published
- 2018
16. A Note on the Paper 'Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps'
- Author
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Farid Bozorgnia and Allahkaram Shafie
- Subjects
Discrete mathematics ,021103 operations research ,Control and Optimization ,Applied Mathematics ,0211 other engineering and technologies ,Regular polygon ,010103 numerical & computational mathematics ,02 engineering and technology ,Management Science and Operations Research ,Mathematical proof ,01 natural sciences ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,Vector optimization ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Metrization theorem ,Theory of computation ,FOS: Mathematics ,0101 mathematics ,Mathematics ,Vector space ,Counterexample - Abstract
In this work, some counterexamples are given to refute some results reported in the paper by Guo and Li [8] (J Optim Theory Appl 162,(2014), 821-844). We correct the faulty in some of their theorems and we present alternative proofs. Moreover, we extend the definition of approximately pseudo-dissipative in the setting of metrizable topological vector spaces.
- Published
- 2019
17. Metapopulation dynamics in the rock-paper-scissors game with mutation: Effects of time-varying migration paths
- Author
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Kei-ichi Tainaka, Genki Ichinose, and Takashi Nagatani
- Subjects
0301 basic medicine ,Statistics and Probability ,Mutation rate ,Phase transition ,Population Dynamics ,Population ,Metapopulation ,General Biochemistry, Genetics and Molecular Biology ,03 medical and health sciences ,0302 clinical medicine ,Game Theory ,Mutation Rate ,Animals ,Quantitative Biology::Populations and Evolution ,Statistical physics ,Diffusion (business) ,education ,Mathematics ,Chronobiology Phenomena ,education.field_of_study ,General Immunology and Microbiology ,Applied Mathematics ,General Medicine ,Models, Theoretical ,Random walk ,030104 developmental biology ,Modeling and Simulation ,Mutation (genetic algorithm) ,Path (graph theory) ,Animal Migration ,General Agricultural and Biological Sciences ,030217 neurology & neurosurgery - Abstract
Migration paths of animals are rarely the same. The paths may change according to seasonal and circadian rhythms. We study the effect of temporal migration on population dynamics of rock-paper-scissors (RPS) games with mutation by using the metapopulation dynamic model with two patches. Via mutation, an individual R changes to S with rate μ. All agents move by random walk between two patches and the RPS game is performed in each patch. The migration path between two patches is switched on or off periodically. The dynamics are represented by the reaction-diffusion equations with time-dependent diffusion coefficients in diffusively coupled reactors. We obtain the solutions of time-dependent reaction-diffusion equations numerically and analytically. The time-varying migration path induces complex behavior for the RPS dynamics, depending on the frequency of the periodical path. We find that the phase transitions occur by varying mutation rate μ. The phase transition depends highly on the frequency.
- Published
- 2019
18. Critical perspectives on provable security: Fifteen years of 'another look' papers
- Author
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Neal Koblitz and Alfred Menezes
- Subjects
Provable security ,Algebra and Number Theory ,Computer Networks and Communications ,business.industry ,Applied Mathematics ,020206 networking & telecommunications ,Subject (documents) ,Cryptography ,0102 computer and information sciences ,02 engineering and technology ,Computer security ,computer.software_genre ,Mathematical proof ,01 natural sciences ,Microbiology ,010201 computation theory & mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Discrete Mathematics and Combinatorics ,business ,computer ,Mathematics - Abstract
We give an overview of our critiques of "proofs" of security and a guide to our papers on the subject that have appeared over the past decade and a half. We also provide numerous additional examples and a few updates and errata.
- Published
- 2019
19. 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
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20. A note on the paper 'A novel approach of graphical rectangular b-metric spaces with an application to the vibrations of a vertical heavy hanging cable'
- Author
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Fei He, Ning Lu, and Shu-Fang Li
- Subjects
Algebra ,Vibration ,Metric space ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Applied Mathematics ,Modeling and Simulation ,Fixed-point theorem ,Geometry and Topology ,Fundamental lemma ,Mathematical proof ,Counterexample ,Mathematics - Abstract
In this work, a counterexample is given to refute a result in the paper by Younis et al. (J Fixed Point Theory Appl 21:1–33, 2019). Furthermore, applying this counterexample, we give negative answers to some of the open problems in their paper. Recently, Baradol et al. give a new theorem to rectify the result of Younis et al. However, we find that there are some gaps in the proofs of their results. Finally, we introduce a fundamental lemma and fill these gaps.
- Published
- 2020
21. Physics driven behavioural clustering of free-falling paper shapes
- Author
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Fumiya Iida, Toby Howison, Josie Hughes, Fabio Giardina, Howison, Toby [0000-0001-8548-5550], Iida, Fumiya [0000-0001-9246-7190], and Apollo - University of Cambridge Repository
- Subjects
Inertia ,Physiology ,Physical system ,Social Sciences ,computer.software_genre ,Systems Science ,01 natural sciences ,010305 fluids & plasmas ,Physical Phenomena ,Physical phenomena ,Medicine and Health Sciences ,Psychology ,Cluster Analysis ,Moment of Inertia ,Multidisciplinary ,Applied Mathematics ,Simulation and Modeling ,theoretical model ,article ,Classical Mechanics ,Dynamical Systems ,Variety (cybernetics) ,Free falling ,machine learning ,Physical Sciences ,Medicine ,physics ,Algorithms ,Research Article ,Paper ,Computer and Information Sciences ,Reynolds Number ,Science ,Fluid Mechanics ,Research and Analysis Methods ,Machine learning ,Continuum Mechanics ,Motion ,Machine Learning Algorithms ,Artificial Intelligence ,0103 physical sciences ,010306 general physics ,Set (psychology) ,Cluster analysis ,Behavior ,Biological Locomotion ,business.industry ,Biology and Life Sciences ,Fluid Dynamics ,Models, Theoretical ,Nonlinear Dynamics ,Artificial intelligence ,business ,computer ,Mathematics - Abstract
Many complex physical systems exhibit a rich variety of discrete behavioural modes. Often, the system complexity limits the applicability of standard modelling tools. Hence, understanding the underlying physics of different behaviours and distinguishing between them is challenging. Although traditional machine learning techniques could predict and classify behaviour well, typically they do not provide any meaningful insight into the underlying physics of the system. In this paper we present a novel method for extracting physically meaningful clusters of discrete behaviour from limited experimental observations. This method obtains a set of physically plausible functions that both facilitate behavioural clustering and aid in system understanding. We demonstrate the approach on the V-shaped falling paper system, a new falling paper type system that exhibits four distinct behavioural modes depending on a few morphological parameters. Using just 49 experimental observations, the method discovered a set of candidate functions that distinguish behaviours with an error of 2.04%, while also aiding insight into the physical phenomena driving each behaviour. © 2019 Howison et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
- Published
- 2019
22. Special issue: Selected papers of CMMSE
- Author
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Jorge Eduardo Macías-Díaz, Raquel Garcia-Rubio, and Jesús Vigo-Aguiar
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Computational Mathematics ,Applied Mathematics ,Mathematics education ,Mathematics - Published
- 2019
23. Ten Simple Rules for writing algorithmic bioinformatics conference papers
- Author
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Paul Medvedev
- Subjects
0301 basic medicine ,Computer and Information Sciences ,Computer science ,QH301-705.5 ,Bioinformatics ,Writing ,Gene Identification and Analysis ,Genetic Networks ,Research and Analysis Methods ,Field (computer science) ,03 medical and health sciences ,Cellular and Molecular Neuroscience ,Database and Informatics Methods ,Clustering Algorithms ,0302 clinical medicine ,Computer software ,Genetics ,Humans ,Prototypes ,Biology (General) ,Molecular Biology ,Ecology, Evolution, Behavior and Systematics ,Simple (philosophy) ,Publishing ,Ecology ,Information Dissemination ,Software Tools ,Applied Mathematics ,Simulation and Modeling ,Computational Biology ,Software Engineering ,Biology and Life Sciences ,Congresses as Topic ,030104 developmental biology ,Editorial ,Technology Development ,Computational Theory and Mathematics ,Modeling and Simulation ,Physical Sciences ,Engineering and Technology ,Sequence Analysis ,Sequence Alignment ,030217 neurology & neurosurgery ,Algorithms ,Mathematics ,Network Analysis - Abstract
Author summary Conferences are great venues for disseminating algorithmic bioinformatics results, but they unfortunately do not offer an opportunity to make major revisions in the way that journals do. As a result, it is not possible for authors to fix mistakes that might be easily correctable but nevertheless can cause the paper to be rejected. As a reviewer, I wish that I had the opportunity to tell the authors, “Hey, you forgot to do this really important thing, without which it is hard to accept the paper, but if you could go back and fix it, you might have a great paper for the conference.” This lack of a back and forth can be especially problematic for first-time submitters or those from outside the field, e.g., biologists. In this article, I outline Ten Simple Rules to follow when writing an algorithmic bioinformatics conference paper to avoid having it rejected.
- Published
- 2020
24. Extension of Kalman Filtering to Semilinear PDE Systems-Application to Pulp and Paper
- Author
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Ivan Francisco Yupanqui Tello, Alain Vande Wouver, and Daniel Coutinho
- Subjects
Spatial variable ,0209 industrial biotechnology ,Observer (quantum physics) ,02 engineering and technology ,Kalman filter ,Chemical reactor ,Nonlinear system ,020901 industrial engineering & automation ,Distributed parameter system ,0202 electrical engineering, electronic engineering, information engineering ,Riccati equation ,Pulp bleaching ,Applied mathematics ,020201 artificial intelligence & image processing ,Mathematics - Abstract
This paper deals with the observer design of nonlinear tubular chemical reactor models. The analysis is performed on a linearized version of the model around a steady-state profile, in which some coefficients are a function of the spatial variable. The study starts from a general model of chemical tubular reactors that will serve as a benchmark model for the formulation in the infinite dimensional Hilbert state space. The optimal output injection operator associated to the proposed observer is computed via the solution of the infinite-dimensional Riccati equation in the space variable. The performance of the observer is illustrated through numerical experiments of an industrial pulp bleaching tubular reactor model.
- Published
- 2020
25. (CMMSE paper) A finite‐difference model for indoctrination dynamics
- Author
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María G. Medina-Guevara, Héctor Vargas-Rodríguez, and Pedro B. Espinoza-Padilla
- Subjects
Agent-based model ,Finite difference model ,Opinion dynamics ,General Mathematics ,Dynamics (mechanics) ,Indoctrination ,General Engineering ,Applied mathematics ,Mathematics - Published
- 2018
26. Call for Papers: T.C. Machine-Learning Mathematical Structures
- Author
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Rafał Abłamowicz
- Subjects
business.industry ,Applied Mathematics ,Artificial intelligence ,Mathematical structure ,business ,Mathematics - Published
- 2021
27. Pride and Passion: Remarks on Thomas L. Saaty’s Final Papers
- Author
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Barış Kiremitci and Eyüp Çetin
- Subjects
Statistics and Probability ,Numerical Analysis ,Pride ,Algebra and Number Theory ,business.industry ,Applied Mathematics ,media_common.quotation_subject ,Analytic network process ,Life satisfaction ,Analytic hierarchy process ,Passion ,Theoretical Computer Science ,Management ,Analytics ,Publishing ,Honor ,Geometry and Topology ,business ,media_common ,Mathematics - Abstract
Thomas L. Saaty, a world-renowned scholar and our beloved Advisory Editor, passed away on August 14, 2017 at the age of 91.  He has made many fundamental contributions to operations research, analytics, business and mathematics. Despite his heavy illness for 14 months, as passionate about science, he has also enthusiastically published his research. We review his final works published in 2017 and 2018. We are also honored to reveal and publish his final statements on neural firing and synthesis in making comparisons & life satisfaction, respectively, in his final two papers; the previous one submitted by him just before his passing and the other one submitted by his co-authors after his death to European Journal of Pure and Applied Mathematics (EJPAM).We just would like to remember and honor Saaty’s memory by publishing his final papers at EJPAM and this humble remarks dedicated to the memory of Thomas L. Saaty on the occasion of the first anniversary of his passing, August 14, 2018.
- Published
- 2018
28. Comments on the paper 'A conservative linear difference scheme for the 2D regularized long-wave equation', by Xiaofeng Wang, Weizhong Dai and Shuangbing Guo [Applied Mathematics and Computation, 342 (2019) 55-70]
- Author
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Asma Rouatbi and Khaled Omrani
- Subjects
0209 industrial biotechnology ,Applied Mathematics ,Computation ,020206 networking & telecommunications ,02 engineering and technology ,Wave equation ,Computational Mathematics ,020901 industrial engineering & automation ,Norm (mathematics) ,Scheme (mathematics) ,Convergence (routing) ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,Mathematics - Abstract
In the above article, a second-order convergence in the maximum norm of the two-dimensional regularized long-wave equation is proved. However, due to a wrong inequality in Lemma 3.3 used in X. Wang et al.[1], there are some fundamental errors in this paper, in particular the proof of Theorem 3.3 and the convergence Theorem are no longer correct. The present brief paper contains clarifying comments.
- Published
- 2021
29. Evolutionary dynamics of rock-paper-scissors game in the patchy network with mutations
- Author
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Tina Verma and Arvind Kumar Gupta
- Subjects
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
30. Wet paper codes and the dual distance in steganography
- Author
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Carlos Munuera, Morgan Barbier, Universidad de Valladolid [Valladolid] (UVa), Algorithmic number theory for cryptology (TANC), Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and This work was supported in part by Junta de CyL under grant VA065A07 and by Spanish Ministry for Science and Technology under grants MTM2007-66842-C02-01 and MTM 2007-64704
- Subjects
FOS: Computer and information sciences ,Computer Science - Cryptography and Security ,Computer Networks and Communications ,Computer Science - Information Theory ,Microbiology ,Image (mathematics) ,[INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR] ,ACM: E.: Data/E.4: CODING AND INFORMATION THEORY/E.4.1: Error control codes ,Distortion ,Discrete Mathematics and Combinatorics ,Steganography ,wet paper codes ,Mathematics ,Algebra and Number Theory ,Information Theory (cs.IT) ,Applied Mathematics ,[MATH.MATH-IT]Mathematics [math]/Information Theory [math.IT] ,Coding theory ,Linear code ,ACM: G.: Mathematics of Computing/G.2: DISCRETE MATHEMATICS/G.2.3: Applications ,dual distance ,[INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT] ,Embedding ,Orthogonal array ,Error detection and correction ,Error-correcting codes ,Cryptography and Security (cs.CR) ,Algorithm - Abstract
In 1998 Crandall introduced a method based on coding theory to secretly embed a message in a digital support such as an image. Later, in 2005, Fridrich et al. improved this method to minimize the distortion introduced by the embedding; a process called wet paper. However, as previously emphasized in the literature, this method can fail during the embedding step. Here we find sufficient and necessary conditions to guarantee a successful embedding, by studying the dual distance of a linear code. Since these results are essentially of combinatorial nature, they can be generalized to systematic codes, a large family containing all linear codes. We also compute the exact number of embedding solutions and point out the relationship between wet paper codes and orthogonal arrays.
- Published
- 2012
31. Bifurcation analysis of the rock–paper–scissors game with discrete-time logit dynamics
- Author
-
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
32. Comments on Paper 'On the Relation Between Two Approaches to Necessary Optimality Conditions in Problems with State Constraints'
- Author
-
Dmitry Karamzin
- Subjects
0209 industrial biotechnology ,021103 operations research ,Control and Optimization ,Relation (database) ,Applied Mathematics ,0211 other engineering and technologies ,Subject (philosophy) ,02 engineering and technology ,State (functional analysis) ,Management Science and Operations Research ,Optimal control ,020901 industrial engineering & automation ,Maximum principle ,Theory of computation ,Mathematical economics ,Mathematics - Abstract
This Forum Note concerns the question of necessary optimality conditions in optimal control problems subject to state constraints. Some critical remarks about a recently published paper are made.
- Published
- 2018
33. Paper folding and trigonometric ratios
- Author
-
Arsalan Wares
- Subjects
Mathematical logic ,Applied Mathematics ,010102 general mathematics ,05 social sciences ,050301 education ,Folding (DSP implementation) ,01 natural sciences ,Education ,Algebra ,Mathematics (miscellaneous) ,Concept learning ,0101 mathematics ,Trigonometry ,Mathematics instruction ,0503 education ,Mathematics - Abstract
The purpose of this note is to discuss how paper folding can be used to find the exact trigonometric ratios of the following four angles: 22.5°, 67.5°, 27°, and 63°.
- Published
- 2018
34. 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
-
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
35. Response to 'Comments on the paper by B. E. <scp>Grossman‐Ponemon</scp> , L. M. Keer, and A. J. Lew ‘A method to compute mixed‐mode stress intensity factors for nonplanar cracks in three dimensions’ ( Int. J. Numer. Methods Eng ., 2020)'
- Author
-
Adrian J. Lew and Benjamin E. Grossman-Ponemon
- Subjects
Numerical Analysis ,Grossman ,Applied Mathematics ,INT ,General Engineering ,Mixed mode ,Stress intensity factor ,Mathematics ,Mathematical physics - Published
- 2021
36. A Note on Solvable Time-Homogeneous Stochastic Volatility Models (Working Paper)
- Author
-
Mahir Lokvancic
- Subjects
Constant coefficients ,Distribution function ,Stochastic volatility ,Homogeneous ,Valuation of options ,Applied mathematics ,Asset (economics) ,Diffusion (business) ,Mathematics ,Heston model - Abstract
We revisit well-known stochastic volatility models with constant coefficients for single asset driven by one factor stochastic volatility as homogeneous diffusion and demonstrate an alternative to the classifications provided in Albanese and Lawi, and Henry-Labord`ere, to deduce asset price distribution function, at a fixed time, in an analytic form.
- Published
- 2020
37. A Look at Robustness and Stability of $\ell_{1}$-versus $\ell_{0}$-Regularization: Discussion of Papers by Bertsimas et al. and Hastie et al
- Author
-
Peter Bühlmann, Armeen Taeb, and Yuansi Chen
- Subjects
Statistics and Probability ,latent variables ,low-rank estimation ,General Mathematics ,Linear model ,020206 networking & telecommunications ,Feature selection ,02 engineering and technology ,Latent variable ,01 natural sciences ,Regularization (mathematics) ,010104 statistics & probability ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,Distributional robustness ,0101 mathematics ,Statistics, Probability and Uncertainty ,high-dimensional estimation ,Mathematics ,variable selection - Abstract
We congratulate the authors Bertsimas, Pauphilet and van Parys (hereafter BPvP) and Hastie, Tibshirani and Tibshirani (hereafter HTT) for providing fresh and insightful views on the problem of variable selection and prediction in linear models. Their contributions at the fundamental level provide guidance for more complex models and procedures.
- Published
- 2020
- Full Text
- View/download PDF
38. Performance Analysis of Binned Orthogonal/Bi-Orthogonal Block Code as Dirty-Paper Code for Digital Watermarking Application
- Author
-
Kah Chan Teh, Xiaotian Xu, and Yong Liang Guan
- Subjects
Block code ,Theoretical computer science ,Applied Mathematics ,Code word ,Data_CODINGANDINFORMATIONTHEORY ,Code rate ,Signal Processing ,Code (cryptography) ,Bit error rate ,Dirty paper coding ,Hardware_ARITHMETICANDLOGICSTRUCTURES ,Electrical and Electronic Engineering ,Digital watermarking ,Algorithm ,Decoding methods ,Computer Science::Information Theory ,Mathematics - Abstract
A binned dirty-paper code (DPC) divides a set of codewords into a number of bins. The codeword in the bin that has the maximum correlation with the side information is selected as the transmitted dirty-paper codeword. This letter derives and verifies the analytical bit-error rate (BER) expression of binned orthogonal block code used as DPC in watermarking applications. The BER trends of such orthogonal DPC under constant code length or constant code rate constrains are analyzed. Finally, we propose a new class of DPC based on binned bi-orthogonal codes and demonstrate its BER performance gain over orthogonal DPC.
- Published
- 2009
39. Comments on the paper: Bilinear form and exact solutions for a new extended (2 + 1)-dimensional Boussinesq equation by Ping Cui [Results Phys 22 (2021) 103919]
- Author
-
Lazhar Bougoffa
- Subjects
010302 applied physics ,Ping (video games) ,Exact solution ,Physics ,QC1-999 ,One-dimensional space ,Hirota bilinear form ,General Physics and Astronomy ,02 engineering and technology ,Bilinear form ,021001 nanoscience & nanotechnology ,01 natural sciences ,Extended (2 + 1)-dimensional Boussinesq equation ,Exact solutions in general relativity ,0103 physical sciences ,Applied mathematics ,0210 nano-technology ,Bilinear Bell polynomial ,Mathematics - Abstract
The purpose of this comment paper is to show that the results of the paper (Cui, 2021) are incorrect.
- Published
- 2021
40. Corrigendum to the paper: A way to model stochastic perturbations in population dynamics models with bounded realizations. Commun Nonlinear Sci Numer Simulat, 77 (2019), 239–257
- Author
-
Javier López-de-la-Cruz, Alain Rapaport, Renato Colucci, and Tomás Caraballo
- Subjects
Numerical Analysis ,education.field_of_study ,Stochastic process ,Applied Mathematics ,Dynamics (mechanics) ,Population ,Process (computing) ,Random perturbation ,01 natural sciences ,010305 fluids & plasmas ,Nonlinear system ,Modeling and Simulation ,Bounded function ,0103 physical sciences ,Applied mathematics ,010306 general physics ,education ,Mathematics - Abstract
In this corrigendum we correct an error in our paper [T. Caraballo, R. Colucci, J. Lopez-de-la-Cruz and A. Rapaport. A way to model stochastic perturbations in population dynamics models with bounded realizations, Commun Nonlinear Sci Numer Simulat, 77(2019) 239–257]. We present a correct way to model real noisy perturbations by considering a slightly different stochastic process based, as in the original paper, on the Ornstein-Uhlenbeck process. Namely, we correct the formulae that generates the noisy realizations to ensure the boundedness property to be satisfied with probability one (which turns out not to be true in our original paper even though it was observed in all the simulations).
- Published
- 2021
41. Mistakes can stabilise the dynamics of rock-paper-scissors games
- Author
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Krishnendu Chatterjee, Maria Kleshnina, Jerzy A. Filar, and Sabrina Streipert
- Subjects
Evolutionary Genetics ,0301 basic medicine ,Computer science ,Population Dynamics ,Social Sciences ,Stable equilibrium ,Cognition ,0302 clinical medicine ,Psychology ,050207 economics ,Biology (General) ,Strategy execution ,0303 health sciences ,Animal Behavior ,Ecology ,Applied Mathematics ,05 social sciences ,Biological Evolution ,Computational Theory and Mathematics ,Dynamics (music) ,Modeling and Simulation ,Physical Sciences ,Probability distribution ,Mathematical economics ,Game theory ,Research Article ,QH301-705.5 ,Decision Making ,Microbiology ,03 medical and health sciences ,Cellular and Molecular Neuroscience ,Game Theory ,0502 economics and business ,Genetics ,Humans ,Animal behavior ,Evolutionary dynamics ,Molecular Biology ,Ecology, Evolution, Behavior and Systematics ,030304 developmental biology ,Behavior ,Evolutionary Biology ,Population Biology ,Cognitive Psychology ,Biology and Life Sciences ,Probability Theory ,Probability Distribution ,Organismal Evolution ,030104 developmental biology ,Microbial Evolution ,Cognitive Science ,Zoology ,Mathematics ,030217 neurology & neurosurgery ,Neuroscience - Abstract
A game of rock-paper-scissors is an interesting example of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow individuals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving. We consider two cases: completely random mistakes when individuals have no bias towards any strategy and a general form of mistakes. Then, we determine conditions for a strategy to dominate all other strategies. However, given that individuals who adopt a dominating strategy are still prone to behavioural mistakes in the observed behaviour, we may still observe extinct strategies. That is, behavioural mistakes in strategy execution stabilise evolutionary dynamics leading to an evolutionary stable and, potentially, mixed co-existence equilibrium., Author summary A game of rock-paper-scissors is more than just a children’s game. This type of interactions is often used to describe competition among animals or humans. A special feature of such an interaction is that none of the pure strategies dominates, resulting in a cyclic pattern. However, in wild communities such interactions are rarely observed by biologists. Our results suggest that this lack of cyclicity may stem from imperfectness of interacting individuals. In other words, we show analytically that heterogeneity in behavioural patterns may break a cyclic relationship and lead to a stable equilibrium in pure or mixed strategies.
- Published
- 2021
42. Remarks on two connected papers about Keller–Segel systems with nonlinear production
- Author
-
Giuseppe Viglialoro, Tomomi Yokota, and Yuya Tanaka
- Subjects
010101 applied mathematics ,Nonlinear system ,Sublinear function ,Applied Mathematics ,Signal production ,010102 general mathematics ,Applied mathematics ,Production (computer science) ,Nonlinear diffusion ,0101 mathematics ,01 natural sciences ,Analysis ,Mathematics - Abstract
These notes aim to provide a deeper insight on the specifics of two articles dealing with chemotaxis models with nonlinear production. More precisely, we are referring to the papers “Boundedness of solutions to a quasilinear parabolic–parabolic chemotaxis model with nonlinear signal production” by Tao et al. (2019) [2] and “Boundedness for a fully parabolic Keller–Segel model with sublinear segregation and superlinear aggregation” by Frassu and Viglialoro (2021) [1] . These works, independently published in these last years, present results leaving open room for further improvement. Indeed, in the first a gap in the proof of the main claim appears, whereas the cornerstone assumption in the second is not sharp. In these pages we give a more complete picture to the relative underlying comprehension.
- Published
- 2021
43. Comment on the paper 'Heat and mass transfer in unsteady MHD slip flow of Casson fluid over a moving wedge embedded in a porous medium in the presence of chemical reaction: Numerical solutions using Keller‐Box method, Imran Ullah, Ilyas Khan, Sharidan Shafie, Numerical Methods for Partial Differential Equations , November 2017, https://doi.org/10.1002/num.22221'
- Author
-
Asterios Pantokratoras
- Subjects
Numerical Analysis ,business.product_category ,Applied Mathematics ,010103 numerical & computational mathematics ,Mechanics ,01 natural sciences ,Chemical reaction ,Wedge (mechanical device) ,010101 applied mathematics ,Computational Mathematics ,Ullah ,Mass transfer ,Slip flow ,Casson fluid ,0101 mathematics ,Magnetohydrodynamics ,business ,Porous medium ,Analysis ,Mathematics - Published
- 2018
44. Comment on the paper 'Preserves of eigenvalue inclusion sets of matrix products'
- Author
-
K.Sant aram, Sandeep Kanodia, Manoj Joshi, and K.N.Rajesh wari
- Subjects
Matrix (mathematics) ,Applied mathematics ,Inclusion (mineral) ,Eigenvalues and eigenvectors ,Mathematics - Published
- 2018
45. Allowable delay sets for the stability analysis of linear time-varying delay systems using a delay-dependent reciprocally convex lemma * *This paper was supported by the ANR Project SCIDiS, contract number
- Author
-
Alexandre Seuret and Frédéric Gouaisbaut
- Subjects
0209 industrial biotechnology ,Linear system ,Stability (learning theory) ,02 engineering and technology ,Function (mathematics) ,Upper and lower bounds ,Stability conditions ,020901 industrial engineering & automation ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,Convex combination ,Constant (mathematics) ,Time complexity ,Mathematics - Abstract
This paper addresses the stability analysis of linear systems subject to a time-varying delay. The contribution of this paper is twofolds. First, we aim at presenting a new matrix inequality, which can be seen as an improved version of the reciprocally convex combination, which provides a more accurate delay-dependent lower bound. When gathering this new inequality with the Wirtinger-based integral inequality, efficient stability conditions expressed in terms of LMI are designed and show a clear reduction of the conservatism with a reasonable associated computational cost. The second original contribution of this paper consists in noting that stability conditions issued from the Wirtinger-based integral inequality depends in an affine manner on the bounds of the delay function and also on its derivative. This allows to refine the definition of allowable delay set and to relax usual convex on the delay function. As a result of this new characterization, the LMI conditions allows obtaining stability regions for slow time-varying delay systems which are very closed to the constant delay case.
- Published
- 2017
46. A Note on the Paper 'The Algebraic Structure of the Arbitrary-Order Cone'
- Author
-
Yen Chi Roger Lin, Xin-He Miao, and Jein Shan Chen
- Subjects
Pure mathematics ,021103 operations research ,Control and Optimization ,Algebraic structure ,Applied Mathematics ,0211 other engineering and technologies ,Structure (category theory) ,Order (ring theory) ,010103 numerical & computational mathematics ,02 engineering and technology ,Management Science and Operations Research ,01 natural sciences ,Cone (formal languages) ,Combinatorics ,Operator (computer programming) ,Product (mathematics) ,Light cone ,0101 mathematics ,Mathematics ,Counterexample - Abstract
In this short paper, we look into a conclusion drawn by Alzalg (J Optim Theory Appl 169:32---49, 2016). We think the conclusion drawn in the paper is incorrect by pointing out three things. First, we provide a counterexample that the proposed inner product does not satisfy bilinearity. Secondly, we offer an argument why a pth-order cone cannot be self-dual under any reasonable inner product structure on $$\mathbb {R}^n$$Rn. Thirdly, even under the assumption that all elements operator commute, the inner product becomes an official inner product and the arbitrary-order cone can be shown as a symmetric cone, we think this condition is still unreasonable and very stringent so that the result can only be applied to very few cases.
- Published
- 2017
47. On the comparison of inventory replenishment policies with time-varying stochastic demand for the paper industry
- Author
-
David Ciprés, Lorena Polo, and David Escuín
- Subjects
0209 industrial biotechnology ,Operations research ,Build to order ,Applied Mathematics ,Supply chain ,Time horizon ,010103 numerical & computational mathematics ,02 engineering and technology ,01 natural sciences ,Computational Mathematics ,020901 industrial engineering & automation ,Production planning ,Service level ,Vendor-managed inventory ,Inventory theory ,Perpetual inventory ,0101 mathematics ,Mathematics - Abstract
The aim of this paper is the development of a mathematical model to compute the optimal inventory mix to face stochastic demand at minimum cost in a two-level supply chain. The paper addresses a multi-product dynamic lot-sizing problem under stochastic demand subject to capacity and service level constraints. This model is executed to compare a Make To Order (MTO) strategy to a Vendor Managed Inventory (VMI) partnership between the supplier and their customers. Both strategies provide the demand order to be produced. A schedule of production orders is determined over the planning horizon in order to minimize the inventory holding costs of the supply chain, taking into consideration that the supplier is also responsible of initiating the replenishment orders and deliveries of their customers according to the VMI partnership. The simulation model is illustrated empirically using a real case study: a paper manufacturing company that pursues to improve customer service level and supply chain inventory costs through a proper production planning of their paper machines and a suitable VMI order replenishment schedule.
- Published
- 2017
48. 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
49. Analysis of paper pressing: the saturated one-dimensional case
- Author
-
D. Bežanovic, E.F. Kaasschieter, C.J. van Duijn, Center for Analysis, Scientific Computing & Appl., and Applied Analysis - BURGERS
- Subjects
Pressing ,Paper machine ,business.product_category ,Diffusion equation ,Applied Mathematics ,Mathematical analysis ,Computational Mechanics ,Boundary (topology) ,Nonlinear diffusion ,Geometry ,Uniqueness ,business ,Mathematics - Abstract
We derive a one-dimensional model that describes pressing of water saturated paper in the press-section of the paper machine. The model involves two nonlinear diffusion equations which are coupled across an internal boundary. Existence and uniqueness as a number of qualitative properties are demonstrated. Further, computational results for a concrete case are discussed.
- Published
- 2006
50. A two-phase parameter estimation method for radiative transfer problems in paper industry applications
- Author
-
Per Edström
- Subjects
Scattering ,Estimation theory ,Applied Mathematics ,media_common.quotation_subject ,Mathematical analysis ,General Engineering ,Phase (waves) ,Inverse problem ,Pulp and paper industry ,Asymmetry ,Computer Science Applications ,Convergence (routing) ,Radiative transfer ,Point (geometry) ,media_common ,Mathematics - Abstract
A two-phase method for estimation of the scattering and absorption coefficients and the asymmetry factor (σ s , σ a and g) in the radiative transfer problem is presented. The first phase parameterizes σ s and σ a through g via a simplified model and performs–at a relatively low cost–a scalar optimization over g. It is shown that this gives such a good starting point that the second phase can be accurately performed by a simple Gauss-Newton method. It is also shown that as a part of the first phase can be used on its own when only σ s and σ a are wanted, and it is noted that this gives higher accuracy than the commonly used Kubelka–Munk method when using standardized paper industry reflectance factor measurements. The parameter estimation problem is shown to be non-trivial and ill-conditioned, and its character is analysed. It is discussed that as standard optimization methods are so sensitive to the choice of starting point for this problem that it is hard to find a starting point that gives convergence a...
- Published
- 2008
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