共查询到20条相似文献,搜索用时 31 毫秒
1.
R. N. Miroshin 《Vestnik St. Petersburg University: Mathematics》2016,49(2):122-129
The bilinear Chapman–Kolmogorov equation determines the dynamical behavior of Markov processes. The task to solve it directly (i.e., without linearizations) was posed by Bernstein in 1932 and was partially solved by Sarmanov in 1961 (solutions are represented by bilinear series). In 2007–2010, the author found several special solutions (represented both by Sarmanov-type series and by integrals) under the assumption that the state space of the Markov process is one-dimensional. In the presented paper, three special solutions have been found (in the integral form) for the multidimensional- state Markov process. Results have been illustrated using five examples, including an example that shows that the original equation has solutions without a probabilistic interpretation. 相似文献
2.
In this paper, we have applied modified cubic B-spline based differential quadrature method to get numerical solutions of one dimensional reaction-diffusion systems such as linear reaction-diffusion system, Brusselator system, Isothermal system and Gray-Scott system. The models represented by these systems have important applications in different areas of science and engineering. The most striking and interesting part of the work is the solution patterns obtained for Gray Scott model, reminiscent of which are often seen in nature. We have used cubic B-spline functions for space discretization to get a system of ordinary differential equations. This system of ODE’s is solved by highly stable SSP-RK43 method to get solution at the knots. The computed results are very accurate and shown to be better than those available in the literature. Method is easy and simple to apply and gives solutions with less computational efforts. 相似文献
3.
O. V. Ilyin 《Computational Mathematics and Mathematical Physics》2016,56(12):2079-2083
The evolution of the concentrations of particles of two types that annihilate at collision is considered. The kinetic model describing the dynamics of the mixture is represented by a system of two first-order nonlinear partial differential equations. It is shown that the solutions of this model are related to the solutions of the inhomogeneous transport equations by the Bäcklund transform. Analytic solutions of the problem about penetration of particles of the first type from the left half-plane into the right half-plane occupied by the particles of the second type (the two-dimensional penetration problem or molecular beam problem) and of the problem of outflow of the particles of the first type from a circular source into a domain occupied by the particles of the second type are obtained. Possible generalizations of the model are discussed. 相似文献
4.
The first integrals and exact solutions of mathematical models of epidemiology: a susceptible‐infected‐recovered‐infected (SIRI) model and a tuberculosis model with demographic growth are analyzed. These models are represented by systems of first‐order nonlinear ordinary differential equations, and this system is replaced by one which contains a second‐order ordinary differential equation. The partial Lagrangian approach is then utilized to derive the first integrals of these models. Several cases arise. Then, we utilize the derived first integrals to construct exact solutions for the models under investigation and determine new solutions. The dynamic properties of these models are studied too. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
5.
Shiang-Tai Liu 《TOP》2016,24(1):1-18
The coefficient of variation is a useful statistical measure, which has long been widely used in many areas. In real-world applications, there are situations where the observations are inexact and imprecise in nature and they have to be estimated. This paper investigates the sample coefficient of variation (CV) with uncertain observations, which are represented by interval values. Since the observations are interval-valued, the derived CV should be interval-valued as well. A pair of mathematical programs is formulated to calculate the lower bound and upper bound of the CV. Originally, the pair of mathematical programs is nonlinear fractional programming problems, which do not guarantee to have global optimum solutions. By model reduction and variable substitutions, the mathematical programs are transformed into a pair of quadratic programs. Solving the pair of quadratic programs produces the global optimum solutions and constructs the interval of the CV. The given example shows that the proposed model is indeed able to help the manufacturer select the most suitable manufacturing process with interval-valued observations. 相似文献
6.
Present address: Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada. Numerical solutions are obtained for a quasi-steady model ofthe electrochemcial machining process for two-dimensional problemswith the electrodes being represented by closed curves, oneinside the other. The accuracy of the procedure is checked bythe solutions obtained by it for a particular case with a perturbationsolution. The two solutions agree well. The applicability ofthe numerical procedure is indicated by presenting results whichshow the making of a notch in a circular cylinder. 相似文献
7.
The introductory part of this paper contains an overview of known results about elementary and delta shock solutions to Riemann problem for well known Chaplygin gas model (nowadays used in cosmological theories for dark energy) in terms of entropic shadow waves. Shadow waves are introduced in [17] and they are represented by shocks depending on a small parameter ε with unbounded amplitudes having a distributional limit involving the Dirac delta function. In a search for admissible solutions to all possible cases of mutual interactions of waves arising from double Riemann initial data we found same cases that cannot be resolved with already known types of elementary or shadow wave solutions. These cases are resolved by introducing a sequence of higher order shadow waves depending on integer powers of ε. It is shown that such waves have a distributional limit but only until some finite time T. 相似文献
8.
J. E. Macías-Díaz 《Journal of Difference Equations and Applications》2013,19(4):319-335
Departing from a complex system of nonlinear partial differential equations that models the growth dynamics of biological films, we provide a finite-difference model to approximate its solutions. The variables of interest are measured in absolute scales, whence the need of preserving the positivity of the solutions is a mathematical constraint that must be observed. In this work, we provide a numerical discretization of our mathematical model which is capable of preserving the non-negative character of approximations under suitable conditions on the model and computational parameters. As opposed to the nonlinear model which motivates this report, our numerical technique is a linear method which, under suitable circumstances, may be represented by an M-matrix. The fact that our method is a positivity-preserving scheme is established using the inverse-positive properties of these matrices. Computer simulations corroborate the validity of the theoretical findings. 相似文献
9.
van den Broek W. A. Engwerda J. C. Schumacher J. M. 《Journal of Optimization Theory and Applications》2003,119(3):565-595
Equilibria in dynamic games are formulated often under the assumption that the players have full knowledge of the dynamics to which they are subject. Here, we formulate equilibria in which players are looking for robustness and take model uncertainty explicitly into account in their decisions. Specifically, we consider feedback Nash equilibria in indefinite linear-quadratic differential games on an infinite time horizon. Model uncertainty is represented by a malevolent input which is subject to a cost penalty or to a direct bound. We derive conditions for the existence of robust equilibria in terms of solutions of sets of algebraic Riccati equations. 相似文献
10.
In this paper after having obtained the Lax pair of a hierarchy of soliton equations,we discuss the parametric representation for finite-band solutions of the stationary solitonequation, and prove it can be represented as a Hamiltonian system which is integrable inLiouville sense. The nonconfocal involutive integral representations {Fm} are obtained also.In the condition of finite-band solutions of the soliton equation, the time and space can bedevided inio two Hamiltonian systems, so the fi… 相似文献
11.
In this paper, we obtain accurate analytic free vibration solutions of rectangular thin cantilever plates by using an up-to-date rational superposition method in the symplectic space. To the authors’ knowledge, these solutions were not available in the literature due to the difficulty in handling the complex mathematical model. The Hamiltonian system-based governing equation is first constructed. The eigenvalue problems of two fundamental vibration problems are formed for a cantilever plate. By symplectic expansion, the fundamental solutions are obtained. Superposition of these solutions are equal to that of the cantilever plate, which yields the analytic frequency equation. The mode shapes are then readily obtained. The developed method yields the benchmark analytic solutions with fast convergence and satisfactory accuracy by rigorous derivation, without assuming any trial solutions; thus, it is regarded as rational, and its applicability to more boundary value problems of partial differential equations represented by plates’ vibration, bending and buckling may be expected. 相似文献
12.
This work presents a general state-space representation of a multi-machine, multi-order power system model, which may be used to carry out small-signal stability assessments. Computational software coded in MATLAB has been developed in order to find and analyse the solution of an arbitrary number of synchronous generators in the network. Each generator is represented by a pre-defined model. The model choice is tailored to fit the available data for each generator. The software has provisions for conducting power flow solutions and the calculation of the initial state that the generators keep prior to the disturbance. The state-space representation and the equivalent transfer function matrix of the system are generated automatically. Eigenvalue analysis may be carried out using the standard MATLAB functionality. The paper is one of a tutorial nature and in order to check on the sanity of the results given by the new software, two text-book networks have been examined. The results were also compared with those generated using commercial industrial-grade software. 相似文献
13.
Pablo Aguirre Eduardo González-Olivares Soledad Torres 《Nonlinear Analysis: Real World Applications》2013,14(1):768-779
We study a predator–prey model with the Allee effect on prey and whose dynamics is described by a system of stochastic differential equations assuming that environmental randomness is represented by noise terms affecting each population. More specifically, we consider a term that expresses the variability of the growth rate of both species due to external, unpredictable events. We assume that the intensities of these perturbations are proportional to the population size of each species. With this approach, we prove that the solutions of the system have sample pathwise uniqueness and bounded moments. Moreover, using an Euler–Maruyama-type numerical method we obtain approximated solutions of the system with different intensities for the random noise and parameters of the model. In the presence of a weak Allee effect, we show that long-term survival of both populations can occur. On the other hand, when a strong Allee effect is considered, we show that the random perturbations may induce the non-trivial attracting-type invariant objects to disappear, leading to the extinction of both species. Furthermore, we also find the Maximum Likelihood estimators for the parameters involved in the model. 相似文献
14.
Speckle noise contamination is a common issue in ultrasound imaging system. Due to the edge-preserving feature, total variation (TV) regularization-based techniques have been extensively utilized for speckle noise removal. However, TV regularization sometimes causes staircase artifacts as it favors solutions that are piecewise constant. In this paper, we propose a new model to overcome this deficiency. In this model, the regularization term is represented by a combination of total variation and high-order total variation, while the data fidelity term is depicted by a generalized Kullback-Leibler divergence. The proposed model can be efficiently solved by alternating direction method with multipliers (ADMM). Compared with some state-of-the-art methods, the proposed method achieves higher quality in terms of the peak signal to noise ratio (PSNR) and the structural similarity index (SSIM). Numerical experiments demonstrate that our method can remove speckle noise efficiently while suppress staircase effects on both synthetic images and real ultrasound images. 相似文献
15.
M. Fampa L. A. Barroso D. Candal L. Simonetti 《Computational Optimization and Applications》2008,39(2):121-142
In this paper, we present a bilevel programming formulation for the problem of strategic bidding under uncertainty in a wholesale
energy market (WEM), where the economic remuneration of each generator depends on the ability of its own management to submit
price and quantity bids. The leader of the bilevel problem consists of one among a group of competing generators and the follower
is the electric system operator. The capability of the agent represented by the leader to affect the market price is considered
by the model. We propose two solution approaches for this non-convex problem. The first one is a heuristic procedure whose
efficiency is confirmed through comparisons with the optimal solutions for some instances of the problem. These optimal solutions
are obtained by the second approach proposed, which consists of a mixed integer reformulation of the bilevel model. The heuristic
proposed is also compared to standard solvers for nonlinearly constrained optimization problems. The application of the procedures
is illustrated in case studies with configurations derived from the Brazilian power system. 相似文献
16.
Yuesheng Xu & Taishan Zeng 《高等学校计算数学学报(英文版)》2023,16(1):58-78
More competent learning models are demanded for data processing due
to increasingly greater amounts of data available in applications. Data that we encounter often have certain embedded sparsity structures. That is, if they are represented in an appropriate basis, their energies can concentrate on a small number
of basis functions. This paper is devoted to a numerical study of adaptive approximation of solutions of nonlinear partial differential equations whose solutions may
have singularities, by deep neural networks (DNNs) with a sparse regularization
with multiple parameters. Noting that DNNs have an intrinsic multi-scale structure
which is favorable for adaptive representation of functions, by employing a penalty
with multiple parameters, we develop DNNs with a multi-scale sparse regularization
(SDNN) for effectively representing functions having certain singularities. We then
apply the proposed SDNN to numerical solutions of the Burgers equation and the
Schrödinger equation. Numerical examples confirm that solutions generated by the
proposed SDNN are sparse and accurate. 相似文献
17.
Underactuated robotic locomotion systems are commonly represented by nonholonomic constraints where in mixed systems, these constraints are also combined with momentum evolution equations. Such systems have been analyzed in the literature by exploiting symmetries and utilizing advanced geometric methods. These works typically assume that the shape variables are directly controlled, and obtain the system’s solutions only via numerical integration. In this work, we demonstrate utilization of the perturbation expansion method for analyzing a model example of mixed locomotion system—the twistcar toy vehicle, which is a variant of the well-studied roller-racer model. The system is investigated by assuming small-amplitude oscillatory inputs of either steering angle (kinematic) or steering torque (mechanical), and explicit expansions for the system’s solutions under both types of actuation are obtained. These expressions enable analyzing the dependence of the system’s dynamic behavior on the vehicle’s structural parameters and actuation type. In particular, we study the reversal in direction of motion under steering angle oscillations about the unfolded configuration, as well as influence of the choice of actuation type on convergence properties of the motion. Some of the findings are demonstrated qualitatively by reporting preliminary motion experiments with a modular robotic prototype of the vehicle. 相似文献
18.
19.
《European Journal of Operational Research》2002,138(3):545-553
This paper considers an inventory control model for a single perishable product with a fuzzy shortage cost and a fuzzy outdating cost. This model is a single-period horizon model. Due to fuzziness of shortage and outdating costs, an expected profit function is represented with a fuzzy set. The purpose of this paper is to find the solution maximizing the expected profit function. After defining a nondominated ordering quantity based on fuzzy max order, we seek some of them and investigate an effect of the fuzziness on the obtained solutions. 相似文献
20.
Svetlana Jankovi? Jasmina Djordjevi?Miljana Jovanovi? 《Applied mathematics and computation》2011,217(21):8754-8764
In this paper, a new class of backward doubly stochastic differential equations is studied. This type of equations has a more general form of the forward Itô integrals compared to the ones which have been studied until now. We conclude that unique solutions of these equations can be represented with the help of solutions of the corresponding backward doubly stochastic differential equations, considered earlier in paper [5] by Pardoux and Peng. Some comparison theorems are also given, as well as a probabilistic interpretation for solutions of the corresponding quasilinear stochastic partial differential equations. 相似文献