41,020 results
Search Results
2. On the paper 'On an identity for the zeros of Bessel functions' by Baricz et al
- Author
-
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
3. A Note on the Paper 'Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps'
- Author
-
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
4. 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
5. 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
6. 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
7. 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
8. 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
9. 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
10. 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
11. A note on the paper: 'Nonlinear integral equations with new admissibility types in b-metric spaces'
- Author
-
Ćemal B. Dolićanin, Vildan Ozturk, Tatjana Došenović, and Stojan Radenović
- Subjects
business.industry ,Applied Mathematics ,010102 general mathematics ,Fixed-point theorem ,Usability ,Fixed point ,Nonlinear integral equation ,Mathematical proof ,01 natural sciences ,Integral equation ,010101 applied mathematics ,Algebra ,Metric space ,Modeling and Simulation ,Geometry and Topology ,0101 mathematics ,business ,Mathematics ,Complement (set theory) - Abstract
In this paper we consider, discuss and slightly complement recent fixed point results for mappings in b-metric spaces established by Sintunavarat (J Fixed Point Theory Appl 18:397–416, 2016). Thus, all our results are with shorter proofs. In addition, an application to integral equations is given to illustrate the usability of our approach.
- Published
- 2017
12. Multiple limit cycles for the continuous model of the rock–scissors–paper game between bacteriocin producing bacteria
- Author
-
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
13. Estimates on the Minimal Stabilizing Horizon Length in Model Predictive Control for the Fokker-Planck Equation**This work was supported by the DFG project Model Predictive Control for the Fokker-Planck Equation, GR 1569/15-1. The paper was written while the second author was visiting the University of Newcastle, Australia
- Author
-
Lars Grüne and Arthur Fleig
- Subjects
0209 industrial biotechnology ,Partial differential equation ,Series (mathematics) ,Stochastic process ,010103 numerical & computational mathematics ,02 engineering and technology ,Optimal control ,01 natural sciences ,Controllability ,Model predictive control ,020901 industrial engineering & automation ,Control and Systems Engineering ,Control theory ,Stability theory ,Applied mathematics ,Fokker–Planck equation ,0101 mathematics ,Mathematics - Abstract
In a series of papers by Annunziato and Borzi, Model Predictive Control of the Fokker-Planck equation has been established as a numerically feasible way for controlling stochastic processes via their probability density functions. Numerical simulations suggest that the resulting controller yields an asymptotically stable closed loop system for optimization horizons looking only one time step into the future. In this paper we provide a formal proof of this fact for the Fokker-Planck equation corresponding to the controlled Ornstein-Uhlenbeck process using an L2 cost and control functions that are constant in space. The key step of the proof consists in the verification of an exponential controllability property with respect to the stage cost. Numerical simulations are provided to illustrate our results.
- Published
- 2016
14. On Nash’s unique contribution to analysis in just three of his papers
- Author
-
Sergiu Klainerman
- Subjects
Applied Mathematics ,General Mathematics ,010102 general mathematics ,0103 physical sciences ,010307 mathematical physics ,0101 mathematics ,01 natural sciences ,Mathematics - Published
- 2016
15. A Note on a Paper by Nieminen
- Author
-
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
16. Revisit to Fritz John’s paper on the blow-up of nonlinear wave equations
- Author
-
Xin Yang and Zhengfang Zhou
- Subjects
Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Type inequality ,35L70 ,Wave equation ,01 natural sciences ,Physics::History of Physics ,Mathematics - Analysis of PDEs ,Nonlinear wave equation ,0103 physical sciences ,FOS: Mathematics ,010307 mathematical physics ,0101 mathematics ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
In Fritz John's famous paper (1979), he discovered that for the wave equation $\Box u=|u|^p$, where $1, Comment: 11 pages, 3 figures
- Published
- 2016
17. A Note on the Paper 'A Common Fixed Point Theorem with Applications'
- Author
-
Jiangqian Zou and Hui Huang
- Subjects
Discrete mathematics ,Kantorovich inequality ,021103 operations research ,Control and Optimization ,Applied Mathematics ,010102 general mathematics ,0211 other engineering and technologies ,02 engineering and technology ,Management Science and Operations Research ,01 natural sciences ,Theory of computation ,Common fixed point ,Log sum inequality ,Rearrangement inequality ,0101 mathematics ,Mathematical economics ,Common fixed point theorem ,Mathematics - Abstract
In this note, we give affirmative answers to two open problems posed by Agarwal et al. in the paper (J Optim Theory Appl 163(2):482---490, 2014).
- Published
- 2015
18. A Note on the Paper 'Optimality Conditions for Optimistic Bilevel Programming Problem Using Convexifactors'
- Author
-
Bhawna Kohli
- Subjects
TheoryofComputation_MISCELLANEOUS ,Lemma (mathematics) ,021103 operations research ,Control and Optimization ,Applied Mathematics ,0211 other engineering and technologies ,TheoryofComputation_GENERAL ,010103 numerical & computational mathematics ,02 engineering and technology ,Management Science and Operations Research ,01 natural sciences ,Bilevel optimization ,Algebra ,Bellman equation ,Theory of computation ,0101 mathematics ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,Mathematics - Abstract
This note concerns about the conclusion of a lemma of a published paper of this journal.
- Published
- 2018
19. On D.Y. Gao and X. Lu paper 'On the extrema of a nonconvex functional with double-well potential in 1D'
- Author
-
Constantin Zălinescu
- Subjects
021103 operations research ,Applied Mathematics ,General Mathematics ,0211 other engineering and technologies ,General Physics and Astronomy ,Double-well potential ,02 engineering and technology ,Space (mathematics) ,01 natural sciences ,010101 applied mathematics ,Combinatorics ,Maxima and minima ,35J20, 35J60, 74G65, 74S30 ,Optimization and Control (math.OC) ,FOS: Mathematics ,Preprint ,0101 mathematics ,Constant (mathematics) ,Mathematics - Optimization and Control ,Subspace topology ,Mathematics - Abstract
The aim of this paper is to discuss the main result in the paper by D.Y. Gao and X. Lu [On the extrema of a nonconvex functional with double-well potential in 1D, Z. Angew. Math. Phys. (2016) 67:62]. More precisely we provide a detailed study of the problem considered in that paper, pointing out the importance of the norm on the space $C^{1}[a,b]$; because no norm (topology) is mentioned on $C^{1}[a,b]$ we look at it as being a subspace of $W^{1,p}(a,b)$ for $p\in [1,\infty]$ endowed with its usual norm. We show that the objective function has not local extrema with the mentioned constraints for $p\in [1,4)$, and has (up to an additive constant) only a local maximizer for $p=\infty$, unlike the conclusion of the main result of the discussed paper where it is mentioned that there are (up to additive constants) two local minimizers and a local maximizer. We also show that the same conclusions are valid for the similar problem treated in the preprint by X. Lu and D.Y. Gao [On the extrema of a nonconvex functional with double-well potential in higher dimensions, arXiv:1607.03995]., 12 pages; in this version we added the forgotten condition $F(x) \ne 0$ for $x\in (a,b)$ on page 3
- Published
- 2017
20. Entropy criteria and stability of extreme shocks: a remark on a paper of Leger and Vasseur
- Author
-
Kevin Zumbrun and Benjamin Texier
- Subjects
Conservation law ,Kullback–Leibler divergence ,Standard molar entropy ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Mathematics::Analysis of PDEs ,Regular polygon ,Min entropy ,Shock strength ,01 natural sciences ,010101 applied mathematics ,Mathematics - Analysis of PDEs ,FOS: Mathematics ,Uniqueness ,0101 mathematics ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
We show that a relative entropy condition recently shown by Leger and Vasseur to imply uniqueness and stable $L^2$ dependence on initial data of Lax 1- or $n$-shock solutions of an $n\times n$ system of hyperbolic conservation laws with convex entropy implies Lopatinski stability in the sense of Majda. This means in particular that Leger and Vasseur's relative entropy condition represents a considerable improvement over the standard entropy condition of decreasing shock strength and increasing entropy along forward Hugoniot curves, which, in a recent example exhibited by Barker, Freist\"uhler and Zumbrun, was shown to fail to imply Lopatinski stability, even for systems with convex entropy. This observation bears also on the parallel question of existence, at least for small $BV$ or $H^s$ perturbations, Comment: to appear in Proceedings of the AMS
- Published
- 2014
21. Some comments on the paper of Khuangsatung and Kangtunyakarn
- Author
-
Kanokwan Wongchan
- Subjects
010101 applied mathematics ,Nonlinear system ,Fixed point problem ,General Mathematics ,010102 general mathematics ,Convergence (routing) ,Applied mathematics ,0101 mathematics ,Fixed point ,01 natural sciences ,Mathematics - Abstract
In this paper, we discuss the validity of the result of Khuangsatung and Kangtunyakarn [Existence and convergence theorem for fixed point problem of various nonlinear mappings and variational inequality problems without some assumptions, Filomat 32(1) (2018) 305–309].
- Published
- 2018
22. Corrigendum to the paper: Existence and stability results for semilinear systems of impulsive stochastic differential equations with fractional Brownian motion. Stoch. Anal. Appl. 34 (2016), no. 5, 792–834
- Author
-
T. Blouhi, Tomás Caraballo, and Abdelghani Ouahab
- Subjects
Statistics and Probability ,Work (thermodynamics) ,Fractional Brownian motion ,Semilinear systems ,Applied Mathematics ,010102 general mathematics ,Stochastic difference equations ,Mathematical analysis ,Stability result ,Fixed point ,01 natural sciences ,010104 statistics & probability ,Stochastic differential equation ,0101 mathematics ,Statistics, Probability and Uncertainty ,Mathematics - Abstract
In this paper we correct an error made in our paper [Blouhi, T.; Caraballo, T.; Ouahab, A. Existence and stability results for semilinear systems of impulsive stochastic differential equations with fractional Brownian motion. Stoch. Anal. Appl. 34 (2016), no. 5, 792-834]. In fact, in this corrigendum we present the correct hypotheses and results, and highlight that the results can be proved using the same method used in the original work. The main feature is that we used a result which has been proved only when the diffusion term does not depend on the unknown.
- Published
- 2017
23. The non validity of the gaussian approximation for multi-user interference in ultra wide band impulse radio: from an inconvenience to an advantage - transactions papers
- Author
-
Daniele Domenicali, Jocelyn Fiorina, SUPELEC-Campus Gif, Ecole Supérieure d'Electricité - SUPELEC (FRANCE), and Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome]
- Subjects
Ultra-wideband ,02 engineering and technology ,Impulse (physics) ,01 natural sciences ,[SPI]Engineering Sciences [physics] ,010104 statistics & probability ,symbols.namesake ,Non-Gaussianity ,0202 electrical engineering, electronic engineering, information engineering ,0101 mathematics ,Electrical and Electronic Engineering ,Gaussian process ,Computer Science::Information Theory ,Mathematics ,business.industry ,Applied Mathematics ,020206 networking & telecommunications ,Computer Science Applications ,Gaussian approximation ,Multi user interference ,Additive white Gaussian noise ,Gaussian noise ,symbols ,Telecommunications ,business ,[SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing ,Algorithm - Abstract
International audience; The huge potential of ultra wide band impulse radio (UWB IR) with multiple access was initially evaluated using the standard Gaussian approximation which assumed that multi user interference could be approximated as classical Gaussian noise. Later the standard Gaussian approximation has been proved to be invalid in several cases. Thus the performance of the classical UWB IR correlation receiver dramatically reduces. We show in this paper how the non Gaussianity of the multi user interference can be exploited, turning the non Gaussianity into an advantage, increasing the performance with respect to the Gaussian interference case which was supposed to be too optimistic until now.
- Published
- 2009
24. Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities
- Author
-
Marius Mitrea and Fritz Gesztesy
- Subjects
Class (set theory) ,Pure mathematics ,Mathematics::Analysis of PDEs ,Boundary (topology) ,Spectral analysis ,Type (model theory) ,01 natural sciences ,Mathematics - Spectral Theory ,Mathematics - Analysis of PDEs ,FOS: Mathematics ,Boundary value problem ,0101 mathematics ,Spectral Theory (math.SP) ,Eigenvalues and eigenvectors ,Mathematics ,Applied Mathematics ,010102 general mathematics ,Nonlocal Robin Laplacians ,Eigenvalue inequalities ,Mathematics::Spectral Theory ,16. Peace & justice ,Lipschitz continuity ,010101 applied mathematics ,35P15, 47A10 (Primary) 35J25, 47A07 (Secondary) ,Dirichlet laplacian ,Bounded function ,Lipschitz domains ,Analysis ,Analysis of PDEs (math.AP) - Abstract
The aim of this paper is twofold: First, we characterize an essentially optimal class of boundary operators $\Theta$ which give rise to self-adjoint Laplacians $-\Delta_{\Theta, \Omega}$ in $L^2(\Omega; d^n x)$ with (nonlocal and local) Robin-type boundary conditions on bounded Lipschitz domains $\Omega\subset\bbR^n$, $n\in\bbN$, $n\geq 2$. Second, we extend Friedlander's inequalities between Neumann and Dirichlet Laplacian eigenvalues to those between nonlocal Robin and Dirichlet Laplacian eigenvalues associated with bounded Lipschitz domains $\Omega$, following an approach introduced by Filonov for this type of problems., Comment: 23 pages, added Remark 5.4
- Published
- 2009
- Full Text
- View/download PDF
25. Some comments on the paper: Controllability of fractional neutral stochastic functional differential systems, Z. Angew. Math. Phys. 65 (2014), no. 5, 941–959
- Author
-
Michelle Pierri and Donal O'Regan
- Subjects
Discrete mathematics ,Class (set theory) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,General Physics and Astronomy ,Differential systems ,01 natural sciences ,010101 applied mathematics ,Controllability ,Algebra ,0101 mathematics ,Differential (mathematics) ,Mathematics - Abstract
The abstract results and applications presented in “Controllability of fractional neutral stochastic functional differential systems, Z. Angew. Math. Phys. 65 (2014), no. 5, 941–959, are not correct. Moreover, the class of differential control problems studied in [1] is not H-controllable.
- Published
- 2016
26. Corrigendum to our paper ‘The Markov–Stieltjes transform on Hardy and Lebesgue spaces’
- Author
-
A. R. Mirotin and I. S. Kovalyova
- Subjects
Pure mathematics ,Markov chain ,Applied Mathematics ,010102 general mathematics ,Lebesgue's number lemma ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,symbols ,0101 mathematics ,Lp space ,Analysis ,Stieltjes transform ,Mathematics - Published
- 2017
27. A Note on the Paper 'The Asymptotic Behavior of the Composition of Firmly Nonexpansive Mappings'
- Author
-
David Ariza-Ruiz, Adriana Nicolae, and Genaro López-Acedo
- Subjects
Discrete mathematics ,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 ,Composition (combinatorics) ,01 natural sciences ,Theory of computation ,Applied mathematics ,0101 mathematics ,Mathematics - Abstract
In this note we correct an error in the paper (Ariza-Ruiz et al. in J Optim Theory Appl 167:409–429, 2015).
- Published
- 2017
28. Fractional Factorials and Prime Numbers (A Remark on the Paper 'On Prime Values of Some Quadratic Polynomials')
- Author
-
A. N. Andrianov
- Subjects
Statistics and Probability ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Prime element ,01 natural sciences ,Prime k-tuple ,Prime (order theory) ,010305 fluids & plasmas ,Combinatorics ,0103 physical sciences ,Prime factor ,Unique prime ,0101 mathematics ,Fibonacci prime ,Prime power ,Sphenic number ,Mathematics - Abstract
Congruences mod p for a prime p and partial products of the numbers 1,…, p − 1 are obtained. Bibliography: 2 titles.
- Published
- 2016
29. Correction of the paper 'Bicyclic graphs with extremal values of PI index'
- Author
-
Qiuju Bian and Gang Ma
- Subjects
Discrete mathematics ,Bicyclic molecule ,Applied Mathematics ,010102 general mathematics ,Bicyclic graphs ,0102 computer and information sciences ,01 natural sciences ,Graph ,Combinatorics ,010201 computation theory & mathematics ,Pi ,Discrete Mathematics and Combinatorics ,0101 mathematics ,Mathematics - Abstract
In Vukicevic and Stevanovic (2013), Theorem 2 is erroneous when m = 3 k + 1 for some integer k . The correct one is given now. That is, P I ( G ) ≥ m 2 − 3 m + 2 when m = 3 k + 1 for some integer k , where G is a connected bicyclic graph with m edges.
- Published
- 2016
30. Corrigendum to the paper 'Numerical approximation of fractional powers of regularly accretive operators'
- Author
-
Andrea Bonito and Joseph E. Pasciak
- Subjects
010101 applied mathematics ,Computational Mathematics ,Numerical approximation ,Applied Mathematics ,General Mathematics ,Calculus ,Applied mathematics ,010103 numerical & computational mathematics ,0101 mathematics ,01 natural sciences ,Mathematics - Published
- 2017
31. Remarks on a Paper by Giordano, Laforgia, and Pečarić
- Author
-
Mourad E. H. Ismail
- Subjects
symbols.namesake ,Applied Mathematics ,010102 general mathematics ,symbols ,Calculus ,Point (geometry) ,010103 numerical & computational mathematics ,0101 mathematics ,01 natural sciences ,Bessel function ,Analysis ,Mathematics - Abstract
We point out errors and oversights in a paper by Giordano, Laforgia, and Pecaric [3] on inequalities involving Bessel functions.
- Published
- 1997
- Full Text
- View/download PDF
32. On a paper by Khan and Majumdar
- Author
-
Nikolaos S. Papageorgiou
- Subjects
Mathematics::Functional Analysis ,Mathematics::Dynamical Systems ,Mathematics::Complex Variables ,Applied Mathematics ,010102 general mathematics ,05 social sciences ,Mathematics::Classical Analysis and ODEs ,Space (mathematics) ,01 natural sciences ,Computer Science::Computers and Society ,0502 economics and business ,Convergence (routing) ,Applied mathematics ,0101 mathematics ,Majumdar ,Mathematical economics ,Analysis ,050205 econometrics ,Mathematics - Abstract
In this paper we generalize two results of Khan and Majumdar on the weak sequential convergence of functions in the Lebesgue-Bochner space L X 1 (Ω) and on a Fatou-like convergence theorem.
- Published
- 1990
- Full Text
- View/download PDF
33. On a Method of Solution of Systems of Fractional Pseudo-Differential Equations
- Author
-
YangQuan Chen, Ravshan Ashurov, and Sabir Umarov
- Subjects
matrix symbol ,Differential equation ,Primary 35E15 ,33E12 ,01 natural sciences ,symbols.namesake ,solution operator ,Completeness (order theory) ,Mittag-Leffler function ,fractional order differential equation ,Applied mathematics ,fractional system of differential equations ,Uniqueness ,0101 mathematics ,Differential (infinitesimal) ,Secondary 35S10 ,Mathematics ,Applied Mathematics ,010102 general mathematics ,Linear system ,system of differential equations ,pseudo-differential operator ,Pseudo-differential operator ,010101 applied mathematics ,Sobolev space ,35R11 ,symbols ,Analysis ,Research Paper - Abstract
This paper is devoted to the general theory of linear systems of fractional order pseudo-differential equations. Single fractional order differential and pseudo-differential equations are studied by many authors and several monographs and handbooks have been published devoted to its theory and applications. However, the state of systems of fractional order ordinary and partial or pseudo-differential equations is still far from completeness, even in the linear case. In this paper we develop a new method of solution of general systems of fractional order linear pseudo-differential equations and prove existence and uniqueness theorems in the special classes of distributions, as well as in the Sobolev spaces.
- Published
- 2021
34. A study on fractional COVID‐19 disease model by using Hermite wavelets
- Author
-
Shaher Momani, Ranbir Kumar, Samir Hadid, and Sunil Kumar
- Subjects
General Mathematics ,coronavirus ,Value (computer science) ,Derivative ,34a34 ,01 natural sciences ,Caputo derivative ,convergence analysis ,Wavelet ,Special Issue Paper ,operational matrix ,Applied mathematics ,0101 mathematics ,26a33 ,Hermite wavelets ,Mathematics ,Hermite polynomials ,Collocation ,Special Issue Papers ,Basis (linear algebra) ,010102 general mathematics ,General Engineering ,34a08 ,010101 applied mathematics ,Algebraic equation ,Scheme (mathematics) ,60g22 ,mathematical model - Abstract
The preeminent target of present study is to reveal the speed characteristic of ongoing outbreak COVID-19 due to novel coronavirus. On January 2020, the novel coronavirus infection (COVID-19) detected in India, and the total statistic of cases continuously increased to 7 128 268 cases including 109 285 deceases to October 2020, where 860 601 cases are active in India. In this study, we use the Hermite wavelets basis in order to solve the COVID-19 model with time- arbitrary Caputo derivative. The discussed framework is based upon Hermite wavelets. The operational matrix incorporated with the collocation scheme is used in order to transform arbitrary-order problem into algebraic equations. The corrector scheme is also used for solving the COVID-19 model for distinct value of arbitrary order. Also, authors have investigated the various behaviors of the arbitrary-order COVID-19 system and procured developments are matched with exiting developments by various techniques. The various illustrations of susceptible, exposed, infected, and recovered individuals are given for its behaviors at the various value of fractional order. In addition, the proposed model has been also supported by some numerical simulations and wavelet-based results.
- Published
- 2021
35. Remarks on E. A. Rahmanov's paper 'on the asymptotics of the ratio of orthogonal polynomials'
- Author
-
Paul Nevai and Attila Máté
- Subjects
Discrete mathematics ,Mathematics(all) ,Numerical Analysis ,Statement (logic) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,010103 numerical & computational mathematics ,01 natural sciences ,Algebra ,Orthogonal polynomials ,0101 mathematics ,Analysis ,Mathematics ,Counterexample - Abstract
It is pointed out that the proof of the basic result of Rahmanov's paper has a serious gap. It is documented by original sources that a statement he relied on in the proof contains a misprint, and it is shown by a counterexample that this statement (with the misprint) is, in fact, false. A somewhat weaker statement is proved true.
- Published
- 1982
36. On a paper by Doeblin on non-homogeneous Markov chains
- Author
-
Harry Cohn
- Subjects
Statistics and Probability ,Pure mathematics ,Class (set theory) ,Markov chain ,Applied Mathematics ,010102 general mathematics ,Structure (category theory) ,Mathematical proof ,01 natural sciences ,Set (abstract data type) ,010104 statistics & probability ,Chain (algebraic topology) ,Examples of Markov chains ,0101 mathematics ,Representation (mathematics) ,Mathematics - Abstract
In [5] Doeblin considered some classes of finite non-homogeneous Markov chains and gave without proofs several results concerning their asymptotic behaviour. In the present paper we first attempt to make Doeblin's results precise and try to reconstruct his arguments. Subsequently we investigate more general situations, where a state space decomposition is provided by the sets occurring in the representation of the atomic sets of the tail or-field. We show that Doeblin's notion of an associated chain, as well as considerations regarding the tail ar-field structure of the chain, can be used to solve such cases. FINITE MARKOV CHAIN; FINAL CLASS; CYCLICALLY MOVING SUBCLASS; TAIL ar-FIELD; ATOMIC SET; RECURRENCE; WHIRLPOOL
- Published
- 1981
37. Fractional Model and Numerical Algorithms for Predicting COVID-19 with Isolation and Quarantine Strategies
- Author
-
Abdelilah Lamrani Alaoui, Elhoussine Azroul, and Abdelouahed Alla Hamou
- Subjects
Fractional differential equations ,65D05 ,Coronavirus disease 2019 (COVID-19) ,Caputo-Fabrizio derivative ,65R20 ,Fixed point ,01 natural sciences ,010305 fluids & plasmas ,Set (abstract data type) ,Fractional Adams–Bashforth method ,0103 physical sciences ,Isolation (database systems) ,Uniqueness ,0101 mathematics ,MATLAB ,computer.programming_language ,Mathematics ,Original Paper ,Applied Mathematics ,COVID-19 ,93E24 ,Fractional calculus ,010101 applied mathematics ,Computational Mathematics ,SEIR epidemic model ,Line (geometry) ,26A33 ,computer ,Algorithm - Abstract
In December 2019, a new outbreak in Wuhan, China has attracted world-wide attention, the virus then spread rapidly in most countries of the world, the objective of this paper is to investigate the mathematical modelling and dynamics of a novel coronavirus (COVID-19) with Caputo-Fabrizio fractional derivative in the presence of quarantine and isolation strategies. The existence and uniqueness of the solutions for the fractional model is proved using fixed point iterations, the fractional model are shown to have disease-free and an endemic equilibrium point.We construct a fractional version of the four-steps Adams-Bashforth method as well as the error estimate of this method. We have used this method to determine the numerical scheme of this model and Matlab program to illustrate the evolution of the virus in some countries (Morocco, Qatar, Brazil and Mexico) as well as to support theoretical results. The Least squares fitting is a way to find the best fit curve or line for a set of points, so we apply this method in this paper to construct an algorithm to estimate the parameters of fractional model as well as the fractional order, this model gives an estimate better than that of classical model.
- Published
- 2021
38. Some remarks on a paper of Kingman
- Author
-
R. K. Getoor
- Subjects
Discrete mathematics ,Statistics and Probability ,Zero set ,Subordinator ,Applied Mathematics ,010102 general mathematics ,Markov process ,Fixed point ,01 natural sciences ,symbols.namesake ,010104 statistics & probability ,Probability theory ,Joint probability distribution ,symbols ,State space ,0101 mathematics ,Finite set ,Mathematics - Abstract
We illustrate a technique for computing certain integrals that arise in probability theory by giving a new derivation of a formula of Kingman. This formula contains the joint distribution of the processes F(t) = inf {s: X(t + s) = b} and B(t) = inf{s: X(t - s) = b} where X is a time homogeneous, continuous parameter, Markov process and b is a fixed point in its state space. We then extend this formula to the situation in which b is replaced by a finite set {b 1, …, b n }.
- Published
- 1974
39. On a paper by A. I. Lee and J. M. Hill
- Author
-
Piero De Mottoni and Roberta Dal Passo
- Subjects
Applied Mathematics ,010102 general mathematics ,0103 physical sciences ,010307 mathematical physics ,0101 mathematics ,01 natural sciences ,Humanities ,Analysis ,Mathematics - Published
- 1985
- Full Text
- View/download PDF
40. Logical Rules as Fractions and Logics as Sketches
- Author
-
Dominique Duval, Calculs Algébriques et Systèmes Dynamiques (CASYS), Laboratoire Jean Kuntzmann (LJK ), and Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
- Subjects
FOS: Computer and information sciences ,Computer Science - Logic in Computer Science ,Logic ,Short paper ,Logical rules ,ComputerApplications_COMPUTERSINOTHERSYSTEMS ,0603 philosophy, ethics and religion ,01 natural sciences ,FOS: Mathematics ,Calculus ,Category Theory (math.CT) ,Limit (mathematics) ,0101 mathematics ,Category theory ,[MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT] ,Mathematics ,Applied Mathematics ,010102 general mathematics ,[INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO] ,Mathematics - Category Theory ,06 humanities and the arts ,16. Peace & justice ,Logic in Computer Science (cs.LO) ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,060302 philosophy ,Hardware_LOGICDESIGN - Abstract
In this short paper, using category theory, we argue that logical rules can be seen as fractions and logics as limit sketches.
- Published
- 2020
41. Computing isogenies between Jacobians of curves of genus 2 and 3
- Author
-
Enea Milio
- Subjects
Pure mathematics ,Algebra and Number Theory ,Mathematics::Number Theory ,Applied Mathematics ,Isotropy ,Prime number ,Theta function ,010103 numerical & computational mathematics ,Paper computing ,Mathematics::Geometric Topology ,01 natural sciences ,010101 applied mathematics ,Computational Mathematics ,Mathematics::Algebraic Geometry ,Genus (mathematics) ,0101 mathematics ,Algebraic number ,Quotient ,Mathematics - Abstract
We present a quasi-linear algorithm to compute isogenies between Jacobians of curves of genus 2 and 3 starting from the equation of the curve and a maximal isotropic subgroup of the l-torsion, for l an odd prime number, generalizing the Velu's formula of genus 1. This work is based from the paper Computing functions on Jacobians and their quotients of Jean-Marc Couveignes and Tony Ezome. We improve their genus 2 case algorithm, generalize it for genus 3 hyperelliptic curves and introduce a way to deal with the genus 3 non-hyperelliptic case, using algebraic theta functions.
- Published
- 2019
42. Algebraic bounds on the Rayleigh–Bénard attractor
- Author
-
Michael S. Jolly, Edriss S. Titi, Yu Cao, Jared P. Whitehead, Jolly, Michael S [0000-0002-7158-0933], Titi, Edriss S [0000-0002-5004-1746], Apollo - University of Cambridge Repository, Jolly, MS [0000-0002-7158-0933], and Titi, ES [0000-0002-5004-1746]
- Subjects
Paper ,General Mathematics ,General Physics and Astronomy ,global attractor ,Enstrophy ,01 natural sciences ,76F35 ,Attractor ,Periodic boundary conditions ,Boundary value problem ,0101 mathematics ,Algebraic number ,Rayleigh–Bénard convection ,math.AP ,Mathematical Physics ,Mathematics ,Rayleigh-Benard convection ,Plane (geometry) ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Statistical and Nonlinear Physics ,76E06 ,Nonlinear Sciences::Chaotic Dynamics ,010101 applied mathematics ,34D06 ,Homogeneous space ,Affine space ,synchronization ,35Q35 - Abstract
Funder: John Simon Guggenheim Memorial Foundation; doi: https://doi.org/10.13039/100005851, Funder: Einstein Visiting Fellow Program, The Rayleigh–Bénard system with stress-free boundary conditions is shown to have a global attractor in each affine space where velocity has fixed spatial average. The physical problem is shown to be equivalent to one with periodic boundary conditions and certain symmetries. This enables a Gronwall estimate on enstrophy. That estimate is then used to bound the L 2 norm of the temperature gradient on the global attractor, which, in turn, is used to find a bounding region for the attractor in the enstrophy–palinstrophy plane. All final bounds are algebraic in the viscosity and thermal diffusivity, a significant improvement over previously established estimates. The sharpness of the bounds are tested with numerical simulations.
- Published
- 2021
43. Data driven regularization by projection
- Author
-
Otmar Scherzer, Andrea Aspri, Yury Korolev, Korolev, Y [0000-0002-6339-652X], Scherzer, O [0000-0001-9378-7452], Apollo - University of Cambridge Repository, Korolev, Yury [0000-0002-6339-652X], and Scherzer, Otmar [0000-0001-9378-7452]
- Subjects
Paper ,Variational regularization ,010103 numerical & computational mathematics ,Gram–Schmidt orthogonalization ,01 natural sciences ,Regularization (mathematics) ,Theoretical Computer Science ,Data-driven ,FOS: Mathematics ,Applied mathematics ,Mathematics - Numerical Analysis ,Gram–Schmidt process ,Schmidt orthogonalization ,Gram– ,0101 mathematics ,data driven regularization ,Mathematical Physics ,Mathematics ,Gram– ,Generality ,Training set ,Radon transform ,inverse problems ,Applied Mathematics ,47A52, 65J20, 65J22, 65F22 ,variational regularization ,regularization by projection ,Numerical Analysis (math.NA) ,Inverse problem ,Computer Science Applications ,010101 applied mathematics ,Signal Processing - Abstract
We study linear inverse problems under the premise that the forward operator is not at hand but given indirectly through some input-output training pairs. We demonstrate that regularization by projection and variational regularization can be formulated by using the training data only and without making use of the forward operator. We study convergence and stability of the regularized solutions in view of Seidman (1980 J. Optim. Theory Appl. 30 535), who showed that regularization by projection is not convergent in general, by giving some insight on the generality of Seidman’s nonconvergence example. Moreover, we show, analytically and numerically, that regularization by projection is indeed capable of learning linear operators, such as the Radon transform.
- Published
- 2022
- Full Text
- View/download PDF
44. Stochastic contagion models without immunity: their long term behaviour and the optimal level of treatment
- Author
-
Kovacevic, Raimund M.
- Subjects
Original Paper ,Contagion ,Markov chain ,Markov processes ,010102 general mathematics ,Markov process ,Management Science and Operations Research ,Decision problem ,01 natural sciences ,Noise (electronics) ,Term (time) ,010101 applied mathematics ,Stochastic differential equation ,symbols.namesake ,Asymptotic properties ,Disease control ,Simple (abstract algebra) ,symbols ,Applied mathematics ,Uniqueness ,0101 mathematics ,Mathematics - Abstract
In this paper we analyze two stochastic versions of one of the simplest classes of contagion models, namely so-called SIS models. Several formulations of such models, based on stochastic differential equations, have been recently discussed in literature, mainly with a focus on the existence and uniqueness of stationary distributions. With applicability in view, the present paper uses the Fokker-Planck equations related to SIS stochastic differential equations, not only in order to derive basic facts, but also to derive explicit expressions for stationary densities and further characteristics related to the asymptotic behaviour. Two types of models are analyzed here: The first one is a version of the SIS model with external parameter noise and saturated incidence. The second one is based on the Kramers-Moyal approximation of the simple SIS Markov chain model, which leads to a model with scaled additive noise. In both cases we analyze the asymptotic behaviour, which leads to limiting stationary distributions in the first case and limiting quasistationary distributions in the second case. Finally, we use the derived properties for analyzing the decision problem of choosing the cost-optimal level of treatment intensity.
- Published
- 2018
45. The energy equality for weak solutions to the equations of non-Newtonian fluids
- Author
-
Jiaqi Yang
- Subjects
010101 applied mathematics ,Applied Mathematics ,Weak solution ,010102 general mathematics ,Short paper ,Thermodynamics ,0101 mathematics ,01 natural sciences ,Non-Newtonian fluid ,Mathematics - Abstract
In this short paper, we extend the result of Shinbrot (1974) to an incompressible fluid with shear dependent viscosity. It is shown that a weak solution to the equations of non-Newtonian fluids lying in a space L q ( 0 , T ; L p ) satisfies an energy equality, where 2 r r − 1 ≤ p ≤ 2 r r − 2 and 1 p + 1 q ≤ r − 1 r , if r > 2 ; p ≥ 2 r r − 1 and r − 1 p + 1 q = r − 1 2 , if 2 ( n + 1 ) n + 2 r ≤ 2 . In particular, our result implies that the weak solution must satisfy the energy equality when r ≥ 3 n + 2 n + 2 , which is consistent with the known fact.
- Published
- 2019
46. Existence and uniqueness of solutions of free boundary problems in heterogeneous environments
- Author
-
Mingxin Wang
- Subjects
010101 applied mathematics ,Applied Mathematics ,Ecology (disciplines) ,010102 general mathematics ,Short paper ,Quantitative Biology::Populations and Evolution ,Discrete Mathematics and Combinatorics ,Applied mathematics ,Boundary (topology) ,Uniqueness ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
In this short paper we study the existence and uniqueness of solutions of free boundary problems coming from ecology in heterogeneous environments.
- Published
- 2019
47. Convergence analysis of sample average approximation for a class of stochastic nonlinear complementarity problems: from two-stage to multistage
- Author
-
Hailin Sun, Bin Zhou, and Jie Jiang
- Subjects
Original Paper ,Class (set theory) ,Applied Mathematics ,Numerical analysis ,Two-stage ,010103 numerical & computational mathematics ,90C33 ,Multistage ,Lipschitz continuity ,Stochastic complementarity problems ,01 natural sciences ,90C15 ,010101 applied mathematics ,Convergence analysis ,Sample average approximation ,Theory of computation ,Convergence (routing) ,Nonlinear complementarity ,Applied mathematics ,Stage (hydrology) ,0101 mathematics ,Mathematics - Abstract
In this paper, we consider the sample average approximation (SAA) approach for a class of stochastic nonlinear complementarity problems (SNCPs) and study the corresponding convergence properties. We first investigate the convergence of the SAA counterparts of two-stage SNCPs when the first-stage problem is continuously differentiable and the second-stage problem is locally Lipschitz continuous. After that, we extend the convergence results to a class of multistage SNCPs whose decision variable of each stage is influenced only by the decision variables of adjacent stages. Finally, some preliminary numerical tests are presented to illustrate the convergence results.
- Published
- 2020
48. Looking for Pythagoras between the folds
- Author
-
Arsalan Wares
- Subjects
Mathematical logic ,Quantitative Biology::Biomolecules ,Mathematics::General Mathematics ,Applied Mathematics ,Mathematics::History and Overview ,010102 general mathematics ,05 social sciences ,Pythagorean theorem ,Short paper ,050301 education ,Folding (DSP implementation) ,01 natural sciences ,Education ,Algebra ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Mathematics (miscellaneous) ,Calculus ,0101 mathematics ,Mathematics instruction ,0503 education ,Mathematics - Abstract
The purpose of this short paper is to describe a new proof of the Pythagorean Theorem that involves paper folding.
- Published
- 2017
49. A case study of Covid-19 epidemic in India via new generalised Caputo type fractional derivatives
- Author
-
Pushpendra Kumar and Vedat Suat Erturk
- Subjects
Covid‐19 epidemic ,General Mathematics ,Banach space ,Fixed-point theorem ,new generalised Caputo non‐integer order derivative ,01 natural sciences ,92c60 ,Special Issue Paper ,Applied mathematics ,Uniform boundedness ,Uniqueness ,0101 mathematics ,26a33 ,Mathematics ,Special Issue Papers ,fixed point theory ,010102 general mathematics ,34c60 ,General Engineering ,Equicontinuity ,Fractional calculus ,010101 applied mathematics ,Norm (mathematics) ,92d30 ,Predictor‐Corrector scheme ,Epidemic model ,mathematical model - Abstract
The first symptomatic infected individuals of coronavirus (Covid-19) was confirmed in December 2020 in the city of Wuhan, China. In India, the first reported case of Covid-19 was confirmed on 30 January 2020. Today, coronavirus has been spread out all over the world. In this manuscript, we studied the coronavirus epidemic model with a true data of India by using Predictor-Corrector scheme. For the proposed model of Covid-19, the numerical and graphical simulations are performed in a framework of the new generalised Caputo sense non-integer order derivative. We analysed the existence and uniqueness of solution of the given fractional model by the definition of Chebyshev norm, Banach space, Schauder's second fixed point theorem, Arzel's-Ascoli theorem, uniform boundedness, equicontinuity and Weissinger's fixed point theorem. A new analysis of the given model with the true data is given to analyse the dynamics of the model in fractional sense. Graphical simulations show the structure of the given classes of the non-linear model with respect to the time variable. We investigated that the mentioned method is copiously strong and smooth to implement on the systems of non-linear fractional differential equation systems. The stability results for the projected algorithm is also performed with the applications of some important lemmas. The present study gives the applicability of this new generalised version of Caputo type non-integer operator in mathematical epidemiology. We compared that the fractional order results are more credible to the integer order results.
- Published
- 2020
50. On Ricci Curvature Pinching of Lagrangian Submanifolds in the Homogeneous Nearly Kähler $$\pmb {\mathbb {S}}^6(1)$$
- Author
-
Jiabin Yin, Zejun Hu, and Zeke Yao
- Subjects
Unit sphere ,Pure mathematics ,Applied Mathematics ,010102 general mathematics ,Short paper ,Characterization (mathematics) ,01 natural sciences ,Squeeze theorem ,010101 applied mathematics ,symbols.namesake ,Mathematics (miscellaneous) ,Homogeneous ,symbols ,Totally geodesic ,Mathematics::Differential Geometry ,0101 mathematics ,Ricci curvature ,Lagrangian ,Mathematics - Abstract
In this short paper, we study compact Lagrangian submanifolds of the homogeneous nearly Kahler 6-dimensional unit sphere $${\mathbb {S}}^6(1)$$. Following a strategy in Hu et al. (J Geom Phys 144:199–208, 2019), we shall establish an optimal pinching theorem in terms of the Ricci curvature so that a new characterization of the totally geodesic $${\mathbb {S}}^3(1)$$ and the Dillen–Verstraelen–Vrancken’s Berger sphere $$S^3$$ (described in J Math Soc Jpn 42:565–584, 1990) in $${\mathbb {S}}^6(1)$$ can be given.
- Published
- 2020
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.