3,780 results
Search Results
2. Addenda to the book “Critical points at infinity in some variational problems” and to the paper “The scalar-curvature problem on the standard three-dimensional sphere”.
- Author
-
Bahri, Abbes
- Subjects
- *
SCALAR field theory , *PROBLEM solving , *MATHEMATICAL analysis , *DIFFERENTIAL equations , *NUMERICAL analysis - Published
- 2016
- Full Text
- View/download PDF
3. A note on the paper global optimization of nonlinear sum of ratios
- Author
-
Jiao, Hongwei and Shen, Peiping
- Subjects
- *
MATHEMATICAL programming , *DIFFERENTIAL equations , *MATHEMATICAL analysis , *COMPLEX numbers - Abstract
Abstract: In this technical note, we give a short extension application for nonlinear sum of ratios problem (P) considered in [Y.J. Wang, K.C. Zhang, Global optimization of nonlinear sum of ratios problem, Applied Mathematics and Computation 158 (2004) 319–330]. Actually our result is slightly more general, since we do not specify additional positive coefficient for each ratio. In this note, we use different equivalent problem as done in Wang and Zhang (2004). Our method introduce p variables less than other method (Wang and Zhang, 2004), and our approach need not additional special program to obtain the upper and lower bound of numerator and denominator for each ratio in the objective function. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
4. Second-Order Modified Nonstandard Explicit Euler and Explicit Runge–Kutta Methods for n -Dimensional Autonomous Differential Equations.
- Author
-
Alalhareth, Fawaz K., Gupta, Madhu, Kojouharov, Hristo V., and Roy, Souvik
- Subjects
FINITE differences ,MATHEMATICAL analysis ,DYNAMICAL systems ,DIFFERENTIAL equations ,BIOLOGICAL systems - Abstract
Nonstandard finite-difference (NSFD) methods, pioneered by R. E. Mickens, offer accurate and efficient solutions to various differential equation models in science and engineering. NSFD methods avoid numerical instabilities for large time steps, while numerically preserving important properties of exact solutions. However, most NSFD methods are only first-order accurate. This paper introduces two new classes of explicit second-order modified NSFD methods for solving n-dimensional autonomous dynamical systems. These explicit methods extend previous work by incorporating novel denominator functions to ensure both elementary stability and second-order accuracy. This paper also provides a detailed mathematical analysis and validates the methods through numerical simulations on various biological systems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
5. Advances in mathematical analysis for solving inhomogeneous scalar differential equation.
- Author
-
Albidah, Abdulrahman B., Alsulami, Ibraheem M., El-Zahar, Essam R., and Ebaid, Abdelhalim
- Subjects
FUNCTIONAL equations ,INITIAL value problems ,ORDINARY differential equations ,DIFFERENTIAL equations ,MATHEMATICAL analysis - Abstract
This paper considered a functional model which splits to two types of equations, mainly, advance equation and delay equation. The advance equation was solved using an analytical approach. Different types of solutions were obtained for the advance equation under specific conditions of the model’s parameters. These solutions included the polynomial solutions of first and second degrees, the periodic solution and the hyperbolic solution. The periodic solution was invested to establish the analytical solution of the delay equation. The characteristics of the solution of the present model were discussed in detail. The results showed that the solution was continuous in the domain of the problem, under a restriction on the given initial condition, while the first derivative was discontinuous at a certain point and lied within the domain of the delay equation. In addition, some existing results in the literature were recovered as special cases of the current ones. The present successful analysis can be further generalized to include complex functional equations with an arbitrary function as an inhomogeneous term. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
6. Differential Transform Method and Neural Network for Solving Variational Calculus Problems.
- Author
-
Brociek, Rafał and Pleszczyński, Mariusz
- Subjects
CALCULUS of variations ,ORDINARY differential equations ,MATHEMATICAL analysis ,DIFFERENTIAL equations ,ANALYTICAL solutions - Abstract
The history of variational calculus dates back to the late 17th century when Johann Bernoulli presented his famous problem concerning the brachistochrone curve. Since then, variational calculus has developed intensively as many problems in physics and engineering are described by equations from this branch of mathematical analysis. This paper presents two non-classical, distinct methods for solving such problems. The first method is based on the differential transform method (DTM), which seeks an analytical solution in the form of a certain functional series. The second method, on the other hand, is based on the physics-informed neural network (PINN), where artificial intelligence in the form of a neural network is used to solve the differential equation. In addition to describing both methods, this paper also presents numerical examples along with a comparison of the obtained results.Comparingthe two methods, DTM produced marginally more accurate results than PINNs. While PINNs exhibited slightly higher errors, their performance remained commendable. The key strengths of neural networks are their adaptability and ease of implementation. Both approaches discussed in the article are effective for addressing the examined problems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
7. Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity II: Dynamics.
- Author
-
Bringmann, Bjoern
- Subjects
GIBBS' equation ,WAVE equation ,NONLINEAR analysis ,MATHEMATICAL analysis ,DIFFERENTIAL equations - Abstract
In this two-paper series, we prove the invariance of the Gibbs measure for a threedimensional wave equation with a Hartree nonlinearity. The novelty lies in the singularity of the Gibbs measure with respect to the Gaussian free field. In this paper, we focus on the dynamical aspects of our main result. The local theory is based on a paracontrolled approach, which combines ingredients from dispersive equations, harmonic analysis, and random matrix theory. The main contribution, however, lies in the global theory. We develop a new globalization argument, which addresses the singularity of the Gibbs measure and its consequences. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
8. A nonconservative kinetic framework under the action of an external force field: Theoretical results with application inspired to ecology.
- Author
-
Carbonaro, Bruno and Menale, Marco
- Subjects
EVOLUTION equations ,MATHEMATICAL analysis ,CLIMATE change ,PARTICLE interactions ,AGRICULTURAL productivity - Abstract
The present paper deals with the kinetic-theoretic description of the evolution of systems consisting of many particles interacting not only with each other but also with the external world, so that the equation governing their evolution contains an additional term representing such interaction, called the 'forcing term'. Firstly, the interactions between pairs of particles are both conservative and nonconservative; the latter represents, among others, birth/death rates. The 'forcing term' does not express a 'classical' force exerted by the external world on the particles, but a more general influence on the effects of mutual interactions of particles, for instance, climate changes, that increase or decrease the different agricultural productions at different times, thus altering the economic relationships between different subsystems, that in turn can be also perturbed by stock market fluctuations, sudden wars, periodic epidemics, and so on. Thus, the interest towards these problems moves the mathematical analysis of the effects of different kinds of forcing terms on solutions to equations governing the collective (that is statistical) behaviour of such nonconservative many-particle systems. In the present paper, we offer a study of the basic mathematical properties of such solutions, along with some numerical simulations to show the effects of forcing terms for a classical prey–predator model in ecology. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
9. Numerical solution of time‐fraction modified equal width wave equation
- Author
-
Merdan, Mehmet, Yildirim, Ahmet, and Gökdoğan, Ahmet
- Published
- 2012
- Full Text
- View/download PDF
10. Binary Opinion Space in the SCARDO Model.
- Author
-
Gezha, Vladislav N. and Kozitsin, Ivan V.
- Subjects
DIFFERENTIAL equations ,APPROXIMATION theory ,PARAMETER estimation ,MATHEMATICAL formulas ,MATHEMATICAL analysis - Abstract
The paper presents the analysis of the SCARDO model in the case of the binary opinion space. The model itself and the conditions under which the analysis is performed are described and discussed in details. Analytical solutions are found for the mean field approximation. The fixed points as well as their stability properties are characterized. Furthermore, we precisely describe the hyperplane in the parameter space that defines which opinion will gather more supporters. Extensive computational experiments are performed to demonstrate the applicability of our theoretical results. Experiments suggest that the mean-field approximation can fairly accurately predict the behavior of the model provided there is a nonzero probability of anticonformity-type opinion changes. At the end of the paper, we outline the possible direction for future studies. [ABSTRACT FROM AUTHOR]
- Published
- 2022
11. Solutions of some typical nonlinear differential equations with Caputo-Fabrizio fractional derivative.
- Author
-
Zhoujin Cui
- Subjects
FRACTIONAL differential equations ,DIFFERENTIAL equations ,FRACTIONAL calculus ,MATHEMATICAL analysis ,KERNEL functions - Abstract
In this paper, the solutions of some typical nonlinear fractional differential equations are discussed, and the implicit analytical solutions are obtained. The fractional derivative concerned here is the Caputo-Fabrizio form, which has a nonsingular kernel. The calculation results of different fractional orders are compared through images. In addition, by comparing the results obtained in this paper with those under Caputo fractional derivative, it is found that the solutions change relatively gently under Caputo-Fabrizio fractional derivative. It can be concluded that the selection of appropriate fractional derivatives and appropriate fractional order is very important in the modeling process. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
12. LETTER TO THE EDITOR: ON BORWEIN'S PAPER, 'ADJOINT PROCESS DUALITY'
- Author
-
Zălinescu, Constantin
- Subjects
DUALITY theory (Mathematics) ,ALGEBRA ,MATHEMATICAL analysis ,TOPOLOGY ,GEOMETRY ,SET theory ,ADJOINT differential equations ,DIFFERENTIAL equations ,MATHEMATICS - Abstract
We give counterexamples for some statements of Borwein and sufficient conditions for the validity of these. [ABSTRACT FROM AUTHOR]
- Published
- 1986
13. A Mechanistic Model for Long COVID Dynamics.
- Author
-
Derrick, Jacob, Patterson, Ben, Bai, Jie, and Wang, Jin
- Subjects
POST-acute COVID-19 syndrome ,COVID-19 ,POPULATION dynamics ,MATHEMATICAL analysis ,DIFFERENTIAL equations ,LOTKA-Volterra equations - Abstract
Long COVID, a long-lasting disorder following an acute infection of COVID-19, represents a significant public health burden at present. In this paper, we propose a new mechanistic model based on differential equations to investigate the population dynamics of long COVID. By connecting long COVID with acute infection at the population level, our modeling framework emphasizes the interplay between COVID-19 transmission, vaccination, and long COVID dynamics. We conducted a detailed mathematical analysis of the model. We also validated the model using numerical simulation with real data from the US state of Tennessee and the UK. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
14. Analysis of Within-Host Mathematical Models of Toxoplasmosis That Consider Time Delays.
- Author
-
Sultana, Sharmin, González-Parra, Gilberto, and Arenas, Abraham J.
- Subjects
BASIC reproduction number ,MATHEMATICAL models ,TOXOPLASMOSIS ,MATHEMATICAL analysis ,ORDINARY differential equations ,DIFFERENTIAL equations - Abstract
In this paper, we investigate two within-host mathematical models that are based on differential equations. These mathematical models include healthy cells, tachyzoites, and bradyzoites. The first model is based on ordinary differential equations and the second one includes a discrete time delay. We found the models' steady states and computed the basic reproduction number R 0 . Two equilibrium points exist in both models: the first is the disease-free equilibrium point and the second one is the endemic equilibrium point. We found that the initial quantity of uninfected cells has an impact on the basic reproduction number R 0 . This threshold parameter also depends on the contact rate between tachyzoites and uninfected cells, the contact rate between encysted bradyzoite and the uninfected cells, the conversion rate from tachyzoites to bradyzoites, and the death rate of the bradyzoites- and tachyzoites-infected cells. We investigated the local and global stability of the two equilibrium points for the within-host models that are based on differential equations. We perform numerical simulations to validate our analytical findings. We also demonstrated that the disease-free equilibrium point cannot lose stability regardless of the value of the time delay. The numerical simulations corroborated our analytical results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
15. EXISTENCE AND UNIQUENESS RESULTS OF IMPULSIVE FRACTIONAL NEUTRAL PANTOGRAPH INTEGRO DIFFERENTIAL EQUATIONS WITH DELAY.
- Author
-
ILAVARASI, RAVI and MALAR, KANDASAMY
- Subjects
UNIQUENESS (Philosophy) ,PANTOGRAPH ,DIFFERENTIAL equations ,MATHEMATICAL analysis ,VISCOELASTIC materials - Abstract
In this paper, we study the existence and uniqueness results of Impulsive fractional neutral pantograph integro-differential equations with delay. The results are obtained by using the Krasnoselskii fixed point theorem. Finally examples are given to illustrate the main result obtained in this article. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
16. Editorial.
- Author
-
Chleboun, Jan
- Subjects
NUMERICAL analysis ,MATHEMATICAL models ,MATHEMATICAL analysis ,INVERSE problems ,DIFFERENTIAL equations - Published
- 2018
- Full Text
- View/download PDF
17. A Robust Proof of the Instability of Naked Singularities of a Scalar Field in Spherical Symmetry.
- Author
-
Liu, Jue and Li, Junbin
- Subjects
MATHEMATICS theorems ,DIFFERENTIAL equations ,NUMERICAL analysis ,MATHEMATICAL analysis ,MATHEMATICAL models - Abstract
Published in 1999, Christodoulou proved that the naked singularities of a self-gravitating scalar field are not stable in spherical symmetry and therefore the cosmic censorship conjecture is true in this context. The original proof is by contradiction and sharp estimates are obtained strictly depending on spherical symmetry. In this paper, appropriate a priori estimates for the solution are obtained. These estimates are more relaxed but sufficient for giving another robust argument in proving the instability, in particular not by contradiction. In a companion paper, we are able to prove certain instability theorems of the spherically symmetric naked singularities of a scalar field under gravitational perturbations without symmetries. The argument given in this paper plays a central role. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
18. Explicit Solution for Constrained Scalar-State Stochastic Linear-Quadratic Control With Multiplicative Noise.
- Author
-
Wu, Weiping, Gao, Jianjun, Li, Duan, and Shi, Yun
- Subjects
RICCATI equation ,DIFFERENTIAL equations ,H2 control ,STOCHASTIC control theory ,MATHEMATICAL analysis - Abstract
We study in this paper, a class of constrained linear-quadratic (LQ) optimal control problem formulations for the scalar-state stochastic system with multiplicative noise, which has various applications, especially in the financial risk management. The linear constraint on both the control and state variables considered in our model destroys the elegant structure of the conventional LQ formulation and has blocked the derivation of an explicit control policy so far in the literature. We successfully derive in this paper, the analytical control policy for such a class of problems by utilizing the state separation property induced from its structure. We reveal that the optimal control policy is a piecewise affine function of the state and can be computed offline efficiently by solving two coupled Riccati equations. Under some mild conditions, we also obtain the stationary control policy for an infinite time horizon. We demonstrate the implementation of our method via some illustrative examples and show how to calibrate our model to solve dynamic constrained portfolio optimization problems. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
19. TRANSFORMATION OPERATORS FOR IMPEDANCE STURM-LIOUVILLE OPERATORS ON THE LINE.
- Author
-
KAZANIVSKIY, M., MYKYTYUK, YA., and SUSHCHYK, N.
- Subjects
HILBERT space ,STURM-Liouville equation ,DIFFERENTIAL equations ,MATHEMATICAL analysis ,MATHEMATICAL functions - Abstract
In the Hilbert space H := L2(R), we consider the impedance Sturm-Liouville operator T: H → H generated by the differential expression -p d/dx 1/p² d/dxp, where the function p: R → R
+ is of bounded variation on R and infx∈R p(x) > 0. Existence of the transformation operator for the operator T and its properties are studied. In the paper, we suggest an efficient parametrization of the impedance function p in term of a real-valued bounded measure μ ∈M via pμ (x) := eμ([x,∞)) , x ∈ R. For a measure μ ∊M, we establish existence of the transformation operator for the Sturm-Liouville operator Tμ , which is constructed with the function pμ . Continuous dependence of the operator Tμ on μ is also proved. As a consequence, we deduce that the operator Tμ is unitarily equivalent to the operator T0 := -d²/dx². [ABSTRACT FROM AUTHOR]- Published
- 2023
- Full Text
- View/download PDF
20. ON EQUIVALENCE OF P-HENSTOCK-TYPE INTEGRALS FOR INTERVAL VALUED FUNCTIONS.
- Author
-
Iluebe, Victor Odalochi, Mogbademu, Adesanmi Alao, Ajilore, Joshua Olugbenga, and Esan, Olumide Afolabi
- Subjects
MEASURE theory ,DIFFERENTIAL equations ,MATHEMATICAL analysis ,INTEGRATION (Theory of knowledge) ,HENSTOCK-Kurzweil integral - Abstract
In this paper, we use the p-norm to define the interval p-Henstock integral, introduce the interval p-Sequential Henstock integrals and show the equivalence of the interval p-Henstock-type integrals. The p-norm provides an alternative approach to defining the Henstock-type integrals of interval valued functions and the p-integral of interval valued functions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
21. The Development of Managerial Ability: A Mathematical Analysis
- Author
-
Patz, Alan L.
- Published
- 1975
22. Analysis of stochastic pantograph differential equations with generalized derivative of arbitrary order.
- Author
-
Vivek, Devaraj, Elsayed, Elsayed M., and Kanagarajan, Kuppusamy
- Subjects
DIFFERENTIAL equations ,STOCHASTIC analysis ,MATHEMATICAL formulas ,MATHEMATICAL models ,MATHEMATICAL analysis - Abstract
In this paper, we mainly study the existence of analytical solutions of stochastic pantograph differential equations. The standard Picard's iteration method is used to obtain the theory. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
23. Ill-Posedness Issue on a Multidimensional Chemotaxis Equations in the Critical Besov Spaces.
- Author
-
Li, Jinlu, Yu, Yanghai, and Zhu, Weipeng
- Subjects
CHEMOTAXIS ,MATHEMATICS ,DIFFERENTIAL equations ,MATHEMATICAL analysis ,MATHEMATICAL models - Abstract
In this paper, we aim to solving the open question left in [Nie, Yuan: Nonlinear Anal 196 (2020); J. Math. Anal. Appl 505 (2022) and Xiao, Fei: J. Math. Anal. Appl 514 (2022)]. We prove that a multidimensional chemotaxis system is ill-posedness in B ˙ 2 d , r - 3 2 × ( B ˙ 2 d , r - 1 2 ) d when 1 ≤ r < d due to the lack of continuity of the solution. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
24. The Geometry of Bézier Curves in Minkowski 3--Space.
- Author
-
Ceylan, Ayşe Yılmaz
- Subjects
MINKOWSKI space ,CURVATURE ,GEOMETRY ,DIFFERENTIAL equations ,MATHEMATICAL analysis - Abstract
The scope of this paper is to look at some aspects of the differential geometry of Bézier curves in Minkowski space. For that purpose, we firstly introduce Frenet Bézier curve in Minkowski 3--space. Especially, we investigate the Serret-Frenet frame, curvature and torsion of the Frenet Bézier curves at all points. Moreover, we give the Frenet apparatus of these curves at the end points. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
25. On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport.
- Author
-
Scarpa, Luca and Signori, Andrea
- Subjects
BIOLOGICAL transport ,TUMOR growth ,REACTION-diffusion equations ,CHEMOTAXIS ,MATHEMATICAL analysis ,DIFFERENTIAL equations - Abstract
This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell adhesion by a non-local term and may be seen as non-local variants of the corresponding local model proposed by Garcke et al (2016). The model in consideration couples a non-local Cahn–Hilliard equation for the tumor phase variable with a reaction–diffusion equation for the nutrient concentration, and takes into account also significant mechanisms such as chemotaxis and active transport. The system depends on two relaxation parameters: a viscosity coefficient and parabolic-regularization coefficient on the chemical potential. The first part of the paper is devoted to the analysis of the system with both regularizations. Here, a rich spectrum of results is presented. Weak well-posedness is first addressed, also including singular potentials. Then, under suitable conditions, existence of strong solutions enjoying the separation property is proved. This allows also to obtain a refined stability estimate with respect to the data, including both chemotaxis and active transport. The second part of the paper is devoted to the study of the asymptotic behavior of the system as the relaxation parameters vanish. The asymptotics are analyzed when the parameters approach zero both separately and jointly, and exact error estimates are obtained. As a by-product, well-posedness of the corresponding limit systems is established. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
26. THE DISTRIBUTION OF THE TIME REQUIRED TO REDUCE SOME PREASSIGNED LEVEL A SINGLE-CHANNEL QUEUE CHARACTERIZED BY A TIME-DEPENDENT POISSON-DISTRIBUTED ARRIVAL RATE AND A GENERAL CLASS OF HOLDING TIMES .
- Author
-
Luchak, George
- Subjects
QUEUING theory ,OPERATIONS research ,POISSON distribution ,MATHEMATICAL analysis ,DIFFERENTIAL equations ,ANALYSIS of variance ,PRODUCTION scheduling - Abstract
This paper provides the solution to the problem of the distribution of busy periods of the single-channel queue characterized by a time-dependent Poisson-distributed arrival rate and a general class of holding times. The notation is chosen in such a fashion that the main body of computations and mathematical analysis is identical with what was required in the solution of the general queuing equations considered in a previous paper which should be read first
[4] . The solution of the problem for winch the traffic intensity is constant and the holding time distribution is Pearson type III is derived in closed form in terms of the In k functions introduced previously. [ABSTRACT FROM AUTHOR]- Published
- 1957
- Full Text
- View/download PDF
27. Improved collision detection of MD5 with additional sufficient conditions.
- Author
-
Fang, Linan, Wu, Ting, Qi, Yongxing, Shen, Yanzhao, Zhang, Peng, Lin, Mingmin, and Dong, Xinfeng
- Subjects
COLLISION detection (Computer animation) ,CRYPTOGRAPHY ,ALGORITHMS ,MATHEMATICAL analysis ,DIFFERENTIAL equations - Abstract
One application of counter-cryptanalysis is detecting whether a message block is involved in a collision attack, such as the detection of MD5 and SHA-1. Stevens and Shumow speeded up the detection of SHA-1 by introducing unavoidable conditions in message blocks. They left a challenge: how to determine unavoidable conditions for MD5. Later, Shen et al. found that the unavoidable conditions of MD5 were the sufficient conditions located in the last round of differential paths. In this paper, we made further work. We discover sufficient conditions in the second round that can also be used as unavoidable conditions. With additional sufficient conditions, we subdivide three sets and distinguish seven more classes. As a result, compared with Shen's collision detection algorithm, our improved algorithm reduces the collision detection cost by 8.18%. Finally, we find that they do exist in the differential paths constructed by the automatic tool "HashClash". [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
28. Runge and His Legacy.
- Author
-
Butcher, John
- Subjects
RUNGE-Kutta formulas ,NUMERICAL analysis ,APPROXIMATION theory ,DIFFERENTIAL equations ,MATHEMATICAL analysis - Abstract
Carl David Tolmé Runge was a German mathematician. In 1895 he brought about a revolution in the science of what has become numerical analysis. Numerical approximation to the solution of ordinary differential equations had been based on the method of Euler. but it suffered from a low convergence rate. Runge's discovery in his 1895 paper brought the so-called order from 1 up to 2. This development was followed within a few years by extensions of his techniques which brought the possible order up to 4. The analysis of order conditions for early work on Runge-Kutta methods was based on the use of a scalar test problem y' = f (x, y), but for high order method derivations and other applications, it is appropriate to use instead an autonomous high dimensional test problem y' = f (y). Because of the special requirements of stiff problems, implicit Runge-Kutta methods have an importance of their own and these developments are briefly surveyed. The intricate manipulations required to analyse the order of complicated methods has lead to an algebraic theory and its formulation as B-series. Finally, the special applications to structure-preserving algorithms are introduced. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
29. Research on AMSAA-BISE model—An answer to Mei Men-Hua.
- Author
-
Zhou Yuan-quan
- Subjects
DIFFERENTIAL equations ,MATHEMATICAL analysis ,LINEAR algebra ,APPROXIMATION theory ,FUNCTIONAL analysis - Abstract
The AMSAA-BISE model is derived from another approach. This certainly shows the correctness of the AMSAA-BISE model, and indicates the incorrectness of the approximate model given in this paper. The engineering example illustrating these conclusions is given. Merits and demerits of AMSAA and AMSAA-BISE model are discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2001
- Full Text
- View/download PDF
30. Reduction Theorems for Hybrid Dynamical Systems.
- Author
-
Maggiore, Manfredi, Sassano, Mario, and Zaccarian, Luca
- Subjects
DYNAMICAL systems ,LYAPUNOV functions ,DIFFERENTIAL equations ,NUMERICAL analysis ,MATHEMATICAL analysis - Abstract
This paper presents reduction theorems for stability, attractivity, and asymptotic stability of compact subsets of the state space of a hybrid dynamical system. Given two closed sets $\Gamma _1 \subset \Gamma _2 \subset \mathbb {R}^n$ , with $\Gamma _1$ compact, the theorems presented in this paper give conditions under which a qualitative property of $\Gamma _1$ that holds relative to $\Gamma _2$ (stability, attractivity, or asymptotic stability) can be guaranteed to also hold relative to the state space of the hybrid system. As a consequence of these results, sufficient conditions are presented for the stability of compact sets in cascade-connected hybrid systems. We also present a result for hybrid systems with outputs that converge to zero along solutions. If such a system enjoys a detectability property with respect to a set $\Gamma _1$ , then $\Gamma _1$ is globally attractive. The theory of this paper is used to develop a hybrid estimator for the period of oscillation of a sinusoidal signal. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
31. Min-max differential game with partial differential equation.
- Author
-
Youness, Ebrahim. A., Megahed, Abd El-Monem. A., Eladdad, Elsayed. E., and Madkour, Hanem. F. A.
- Subjects
INITIAL value problems ,BOUNDARY value problems ,DIFFERENTIAL equations ,DIFFERENTIAL games ,GAME theory ,MATHEMATICAL analysis - Abstract
In this paper, we are concerned with a min-max differential game with Cauchy initial value problem (CIVP) as the state trajectory for the differential game, we studied the analytical solution and the approximate solution by using Picard method (PM) of this problem. We obtained the equivalent integral equation to the CIVP. Also, we suggested a method for solving this problem. The existence, uniqueness of the solution and the uniform convergence are discussed for the two methods. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
32. On differential analysis of spacelike flows on normal congruence of surfaces.
- Author
-
Erdoğdu, Melek and Yavuz, Ayşe
- Subjects
LORENTZIAN function ,PARTIAL differential equations ,DIFFERENTIAL equations ,FINITE volume method ,MATHEMATICAL analysis - Abstract
The present paper examines the differential analysis of flows on normal congruence of spacelike curves with spacelike normal vector in terms of anholonomic coordinates in three dimensional Lorentzian space. Eight parameters, which are related by three partial differential equations, are discussed. Then, it is seen that the curl of tangent vector field does not include any component with principal normal direction. Thus there exists a surface which contains both s--lines and b -- lines. Also, we examine a normal congruence of surfaces containing the s -- lines and b -- lines. By compatibility conditions, Gauss-Mainardi-Codazzi equations are obtained for this normal congruence of surface. Intrinsic geometric properties of this normal congruence of surfaces are given. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
33. Searching for An Optimal Switched Reluctance Motor Design.
- Author
-
Jażdżyński, Wiesław and Majchrowicz, Michał
- Subjects
MOTOR design & construction ,MATHEMATICAL optimization ,MATHEMATICAL analysis ,ORDINARY differential equations ,DIFFERENTIAL equations - Abstract
An approach helpful when developing an optimized construction of a 6/4 type switched reluctance motor (SRM) is described in the paper. The analytical modeling procedure, based on the reluctance network method and analytical solution of an ordinary differential equation, enables applying a gradient optimization routine and better control of optimization process. The model allows for estimation of the efficiency, torque, and acoustic noise of the motor taking into account the magnetic non-linearity and the control algorithm to keep a constant input power. A bicriterial optimization routine has been applied to find optimal constructions. Eleven geometric and winding parameters are supposed to be the optimization quantities. Analyzed constructions - the initial one and the optimized ones, were validated by means of FEM calculations. The proposed approach can be employed in designing the SRM to be a drive motor in an electrical vehicle, at least as a first attempt. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
34. Disturbance Observer Design for Nonlinear Systems Represented by Input–Output Models.
- Author
-
Ding, Shihong, Chen, Wen-Hua, Mei, Keqi, and Murray-Smith, David J.
- Subjects
NONLINEAR systems ,NONLINEAR dynamical systems ,INPUT-output analysis ,LINEAR systems ,TANKS ,MATHEMATICAL analysis ,DIFFERENTIAL equations - Abstract
A new approach to the design of nonlinear disturbance observers (DOBs) for a class of nonlinear systems described by input–output differential equations is presented in this paper. In contrast with established forms of nonlinear DOBs, the most important feature of this new type of DOB is that only measurement of the output variable is required, rather than the state variables. An inverse simulation model is first constructed based on knowledge of the structure and parameters of a conventional model of the system. The disturbance can then be estimated by comparing the output of the inverse model and the input of the original nonlinear system. Mathematical analysis demonstrates the convergence of this new form of nonlinear DOB. The approach has been applied to disturbance estimation for a linear system and a new form of linear DOB has been developed. The differences between the proposed linear DOB and the conventional form of frequency-domain DOB are discussed through a numerical example. Finally, the nonlinear DOB design method is illustrated through an application involving a simulation of a jacketed continuous stirred tank reactor system. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
35. A COUPLED PDE MODEL OF HIGH INTENSITY ULTRASOUND HEATING OF BIOLOGICAL TISSUE, PART I: WELL-POSEDNESS.
- Author
-
EFENDIEV, M. A., MURLEY, J., and SIVALOGANATHAN, S.
- Subjects
HIGH intensity lasers ,ULTRASONIC imaging ,BIOLOGICAL mathematical modeling ,MATHEMATICAL analysis ,DIFFERENTIAL equations - Abstract
Over the past decade, High Intensity Focused Ultrasound (HIFU) has emerged as an important novel therapeutic modality in the treatment of cancers, that avoids many of the associated negative side effects of more well-established cancer therapies (eg chemotherapy and radiotherapy). In this paper, a coupled system of partial differential equations is used to model the interaction of HIFU with biological tissue. The mathematical model takes into account the effects of both diffusive and convective transport on the temperature field, when acoustic (ultrasound) energy is deposited at a particular location (focal point) in the biological tissue. The model poses significant challenges in establishing existence and uniqueness of solutions, which we consider to be a crucial first step in any realistic, applied mathematical study of HIFU therapy. In this paper, we establish well-posedness of our model, using the Leray-Schauder principle, together with a-priori estimates. [ABSTRACT FROM AUTHOR]
- Published
- 2020
36. Basic Properties of Fractional Fourier Transformation.
- Author
-
Nikolova, Yanka
- Subjects
FOURIER transforms ,FOURIER analysis ,DIFFERENTIAL equations ,INTEGRAL equations ,INTEGRAL theorems ,MATHEMATICAL analysis ,HEAT equation ,FRACTIONAL calculus - Abstract
In this paper we give a generalization of the classical Fourier transformation, known as fractional Fourier transformation (FRFT). We also prove main properties of the FRFT and discuss some of its applications. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
37. Application of reproducing kernel Hilbert space method for generalized 1-D linear telegraph equation.
- Author
-
Abbasbandy, S. and Khodabandehlo, H. R.
- Subjects
HILBERT space ,DIFFERENTIAL equations ,ORTHOGONALIZATION ,MATHEMATICAL models ,MATHEMATICAL analysis - Abstract
This paper presents a generalized 1-D linear telegraph equation. We have solved this equation by the Reproducing Kernel Hilbert Space (RKHS) method and compared it with other methods such as fourth-order compact difference and alternating direction implicit schemes and meshless local radial point interpolation (MLRPI). Comparing the results of these three methods and comparing the exact solution, indicating the efficiency and validity of RKHS. The uniformly converges of the computed solution to the analytical solution are proved. Note that the procedure is easy to implement, and it no need discretization, and is mesh-free too. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
38. Existence, uniqueness and continuous dependence of solution to random delay differential equation of fractional order.
- Author
-
Ho Vu and Le Si Dong
- Subjects
DIFFERENTIAL equations ,UNIQUENESS (Mathematics) ,MEAN square algorithms ,APPROXIMATION theory ,MATHEMATICAL analysis - Abstract
In this paper, we aim to prove the existence, uniqueness of the solution to the random delay differential equation of fractional order involving the successive approximation method. Moreover, using the Gronwall inequality, we study the continuous dependence of solution in the mean square sense of the problem. Finally, the fractional ϵ-approximate solution in the mean square sense is also considered. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
39. The Effect of Mutual Interaction and Harvesting on Food Chain Model.
- Author
-
Hassan, Sarab Kazim and Jawad, Shireen Rasool
- Subjects
FOOD chains ,PREDATION ,HARVESTING ,MATHEMATICAL analysis ,DIFFERENTIAL equations ,COEXISTENCE of species - Abstract
Copyright of Iraqi Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Published
- 2022
- Full Text
- View/download PDF
40. Fractional harmonic maps into manifolds in odd dimension n > 1.
- Author
-
Da Lio, Francesca
- Subjects
FRACTIONAL calculus ,HARMONIC analysis (Mathematics) ,MANIFOLDS (Mathematics) ,CONTINUITY ,MATHEMATICAL analysis ,DIFFERENTIAL equations ,DIFFERENTIAL geometry - Abstract
In this paper we consider critical points of the following nonlocal energy $$\begin{array}{ll}{\mathcal{L}}_n(u) = \int_{{I\!\!R}^n}| ({-\Delta})^{n/4} u(x)|^2 dx, \qquad(1)\end{array}$$ where $${u \in \dot{H}^{n/2}({I\!\!R}^n,{\mathcal{N}}), {\mathcal{N}} \subset {I\!\!R}^m}$$ is a compact k dimensional smooth manifold without boundary and n > 1 is an odd integer. Such critical points are called n/2-harmonic maps into $${{\mathcal{N}}}$$ . We prove that $${(-\Delta) ^{n/4} u\in L^p_{loc}({I\!\!R}^n)}$$ for every p ≥ 1 and thus $${u \in C^{0,\alpha}_{loc}({I\!\!R}^n)}$$ , for every 0 < α < 1. The local Hölder continuity of n/2-harmonic maps is based on regularity results obtained in [ 4 ] for nonlocal Schrödinger systems with an antisymmetric potential and on some new 3-terms commutators estimates. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
41. Characterization of Lindley distribution by truncated moments.
- Author
-
Ahsanullah, M., Ghitany, M. E., and Al-Mutairi, D. K.
- Subjects
DISTRIBUTION (Probability theory) ,EXPONENTIAL functions ,MATHEMATICAL functions ,MATHEMATICAL analysis ,DIFFERENTIAL equations - Abstract
In the past few years, the Lindley distribution has gained popularity for modeling lifetime data as an alternative to the exponential distribution. This paper provides two new characterizations of the Lindley distribution. The first characterization is based on a relation between left truncated moments and failure rate function. The second characterization is based on a relation between right truncated moments and reversed failure rate function. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
42. Existence and uniqueness of solution of the differential equation describing the TASEP-LK coupled transport process.
- Author
-
Li, Jingwei and Zhang, Yunxin
- Subjects
- *
DIFFERENTIAL equations , *PARTIAL differential equations , *MATHEMATICAL analysis , *NUMERICAL calculations , *BOUNDARY layer (Aerodynamics) , *MAXIMUM principles (Mathematics) , *MONTE Carlo method - Abstract
We study the existence and uniqueness of solution of a evolutionary partial differential equation originating from the continuum limit of a coupled process of totally asymmetric simple exclusion process (TASEP) and Langmuir kinetics (LK). In the fields of physics and biology, the TASEP-LK coupled process has been extensively studied by Monte Carlo simulations, numerical computations, and detailed experiments. However, no rigorous mathematical analysis so far has been given for the corresponding differential equations, especially the existence and uniqueness of their solutions. In this paper, we prove the existence of the C ∞ [ 0 , 1 ] steady-state solution by the method of upper and lower solution, and the uniqueness in both W 1 , 2 (0 , 1) and L ∞ (0 , 1) by a generalized maximum principle. We further prove the global existence and uniqueness of the time-dependent solution in C ([ 0 , 1 ] × [ 0 , + ∞)) ∩ C 2 , 1 ([ 0 , 1 ] × (0 , + ∞)) , which, for any continuous initial value, converges to the steady-state solution in C [ 0 , 1 ] (global attractivity). Our results support the numerical calculations and Monte Carlo simulations, and provide theoretical foundations for the TASEP-LK coupled process, especially the most important phase diagram of particle density along the travel track under different model parameters, which is difficult because the boundary layers (at one or both boundaries) and domain wall (separating high and low particle densities) may appear as the length of the travel track tends to infinity. The methods used in this paper may be instructive for studies of the more general cases of the TASEP-LK process, such as the one with multiple travel tracks and/or multiple particle species. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
43. Post inhibitory rebound spike related to nearly vertical nullcline for small homoclinic and saddle-node bifurcations.
- Author
-
Wang, Xianjun and Gu, Huaguang
- Subjects
NEURONS ,BIFURCATION theory ,DIFFERENTIAL equations ,MATHEMATICAL formulas ,MATHEMATICAL analysis - Abstract
A spike induced by inhibitory stimulation instead of excitatory stimulation, called post-inhibitory rebound (PIR) spike, has been found in multiple neurons with important physiological functions, which presents counterintuitive behavior mainly related to focus near Hopf bifurcation. In the present paper, the condition for the PIR spike is extended to small homoclinic orbit (SHom) and saddle-node (SN) bifurcations, and the underlying mechanism is acquired in a neuron model. Firstly, PIR spike is evoked from a stable node near the SHom or SN bifurcation by a strong inhibitory stimulation. Then, the dynamics of threshold curve for a spike, vector fields, and nullcline of recovery variable are used to well explain the cause for the PIR spike. The shape of threshold curve for the node resembles that of focus. The nullcline plays an important role in forming PIR spike, which is analytically identified at last. Besides, a sufficient condition is acquired from the integration to a differential equation, and the range of parameters for the PIR spike is presented. The extended bifurcation types and the underlying mechanisms for the PIR spike such as the nullcline present comprehensive and deep understandings for the PIR spike, which also provides potential strategy to modulate the PIR phenomenon and even related physiological functions of neurons. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
44. Integral backstepping Lyapunov redesign control of uncertain nonlinear systems.
- Author
-
Jalalabadi, Esmaeil, Paylakhi, Seyedeh Zahra, Rahimi‐kian, Ashkan, and Moshiri, Behzad
- Subjects
LYAPUNOV exponents ,DIFFERENTIAL equations ,MATHEMATICAL optimization ,MATHEMATICAL analysis ,ELECTRICAL engineering - Abstract
This paper intends to design an integral backstepping Lyapunov redesign controller (IBLRC) for various uncertain strict‐feedback‐form nonlinear systems. The pros and cons of backstepping Lyapunov redesign resulted in the design idea. An integral term is incorporated in conventional backstepping with Lyapunov redesign to indirectly decrease chattering and steady‐state error of a reference signal tracking when unknown static parameters and matched and unmatched dynamic uncertainties exist. The closed‐loop system is mathematically confirmed as stable in a Lyapunov frame, and we ultimately reach uniformly semi‐global boundedness of all signals. Simulation results of the proposed IBLRC are juxtaposed with those of the classic backstepping with the Lyapunov redesign. The proposed IBLRC realizes excellent tracking and enhanced robust performance than the BLRC for time‐varying and step tracking references. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
45. Convergence and center manifolds for differential equations driven by colored noise.
- Subjects
DIFFERENTIAL equations ,STOCHASTIC convergence ,MANIFOLDS (Mathematics) ,BURGERS' equation ,MATHEMATICAL analysis - Abstract
In this paper, we study the convergence and pathwise dynamics of random differential equations driven by colored noise. We first show that the solutions of the random differential equations driven by colored noise with a nonlinear diffusion term uniformly converge in mean square to the solutions of the corresponding Stratonovich stochastic differential equation as the correlation time of colored noise approaches zero. Then, we construct random center manifolds for such random differential equations and prove that these manifolds converge to the random center manifolds of the corresponding Stratonovich equation when the noise is linear and multiplicative as the correlation time approaches zero. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
46. COMPARISON OF TWO NEURAL NETWORK APPROACHES TO MODELING PROCESSES IN A CHEMICAL REACTOR.
- Author
-
SHEMYAKINA, Tatiana, TARKHOV, Dmitriy, VASILYEV, Alexander, and VELICHKO, Yulia
- Subjects
DIFFERENTIAL equations ,NEURAL circuitry ,CHEMICAL reactors ,ARTIFICIAL intelligence ,MATHEMATICAL analysis - Abstract
In this paper, we conduct the comparative analysis of two neural network approaches to the problem of constructing approximate neural network solutions of non-linear differential equations. The first approach is connected with building a neural network with one hidden layer by minimization of an error functional with regeneration of test points. The second approach is based on a new continuous analog of the shooting method. In the first step of the second method, we apply our modification of the corrected Euler method, and in the second and subsequent steps, we apply our modification of the Störmer method. We have tested our methods on a boundary value problem for an ODE which describes the processes in the chemical reactor. These methods allowed us to obtain simple formulas for the approximate solution of the problem, but the problem is special because it is highly non-linear and also has ambiguous solutions and vanishing solutions if we change the parameter value. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
47. A global random walk on spheres algorithm for transient heat equation and some extensions.
- Author
-
Sabelfeld, Karl K.
- Subjects
BOUNDARY value problems ,ALGORITHMS ,DIFFERENTIAL equations ,MATHEMATICAL analysis ,FINITE element method - Abstract
We suggest in this paper a global Random Walk on Spheres (gRWS) method for solving transient boundary value problems, which, in contrast to the classical RWS method, calculates the solution in any desired family of m prescribed points. The method uses only N trajectories in contrast to mN trajectories in the conventional RWS algorithm. The idea is based on the symmetry property of the Green function and a double randomization approach. We present the gRWS method for the heat equation with arbitrary initial and boundary conditions, and the Laplace equation. Detailed description is given for 3D problems; the 2D problems can be treated analogously. Further extensions to advection-diffusion-reaction equations will be presented in a forthcoming paper. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
48. Difference of generalized integration operators on the space of Cauchy transforms.
- Author
-
Wang, Maofa and Guo, Xin
- Subjects
DIRICHLET forms ,DIFFERENTIAL equations ,MATHEMATICAL analysis ,NUMERICAL analysis ,MATHEMATICAL functions - Abstract
In this paper, the boundedness and compactness of the differences of generalized integration operators from the space of Cauchy integral transforms to the Bloch-type spaces and the weighted Dirichlet spaces are investigated. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
49. Characterizing the strange term in critical size homogenization: Quasilinear equations with a general microscopic boundary condition.
- Author
-
Díaz, Jesus Ildefonso, Gómez-Castro, David, Podol'skii, Alexander V., and Shaposhnikova, Tatiana A.
- Subjects
QUASILINEARIZATION ,DIFFERENTIAL equations ,BOUNDARY value problems ,NUMERICAL analysis ,MATHEMATICAL analysis - Abstract
The aim of this paper is to consider the asymptotic behavior of boundary value problems in n-dimensional domains with periodically placed particles, with a general microscopic boundary condition on the particles and a p-Laplace diffusion operator on the interior, in the case in which the particles are of critical size. We consider the cases in which 1 < p < n, n ≥ 3. In fact, in contrast to previous results in the literature, we formulate the microscopic boundary condition in terms of a Robin type condition, involving a general maximal monotone graph, which also includes the case of microscopic Dirichlet boundary conditions. In this way we unify the treatment of apparently different formulations, which before were considered separately. We characterize the so called "strange term" in the homogenized problem for the case in which the particles are balls of critical size. Moreover, by studying an application in Chemical Engineering, we show that the critically sized particles lead to a more effective homogeneous reaction than noncritically sized particles. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
50. Periodic impulsive fractional differential equations.
- Author
-
Fečkan, Michal and Wang, Jin Rong
- Subjects
DIFFERENTIAL equations ,BOUNDARY value problems ,COMPLEX variables ,NUMERICAL analysis ,MATHEMATICAL analysis - Abstract
This paper deals with the existence of periodic solutions of fractional differential equations with periodic impulses. The first part of the paper is devoted to the uniqueness, existence and asymptotic stability results for periodic solutions of impulsive fractional differential equations with varying lower limits for standard nonlinear cases as well as for cases of weak nonlinearities, equidistant and periodically shifted impulses. We also apply our result to an impulsive fractional Lorenz system. The second part extends the study to periodic impulsive fractional differential equations with fixed lower limit. We show that in general, there are no solutions with long periodic boundary value conditions for the case of bounded nonlinearities. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.