scholarly journals A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution

2011 ◽  
Vol 2011 ◽  
pp. 1-20
Author(s):  
D. P. Siu ◽  
G. S. Ladde
Keyword(s):  
Closed Form ◽  
Dynamic Models ◽  
Type Systems ◽  
Probability Density Functions ◽  
Homogeneous Poisson Process ◽  
Closed Form Solutions ◽  
First Order ◽  
Solution Processes ◽  
Nonhomogeneous System ◽  
Non Homogeneous Poisson Process

In this work, a class of multidimensional stochastic hybrid dynamic models is studied. The system under investigation is a first-order linear nonhomogeneous system of Itô-Doob type stochastic differential equations with switching coefficients. The switching of the system is governed by a discrete dynamic which is monitored by a non-homogeneous Poisson process. Closed-form solutions of the systems are obtained. Furthermore, the major part of the work is devoted to finding closed-form probability density functions of the solution processes of linear homogeneous and Ornstein-Uhlenbeck type systems with jumps.

Jerk Limited Input Shapers

2004 ◽  
Vol 126 (1) ◽  
pp. 215-219 ◽  
Author(s):  
Tarunraj Singh
Keyword(s):  
Time Delay ◽  
Closed Form ◽  
Transfer Functions ◽  
Filter Design ◽  
Limited Time ◽  
Design Technique ◽  
Closed Form Solutions ◽  
First Order ◽  
Damped Systems

The focus of this paper is on the design of jerk limited input shapers (time-delay filters). Closed form solutions for the jerk limited time-delay filter for undamped systems is derived followed by the formulation of the problem for damped systems. Since the jerk limited filter involves concatenating an integrator to a time-delay filter, a general filter design technique is proposed where smoothing of the shaped input can be achieved by concatenating transfer functions of first order, harmonic systems, etc.

Thermal Stresses in Compliantly Joined Materials

1990 ◽  
Vol 112 (1) ◽  
pp. 24-29 ◽  
Author(s):  
J. C. Glaser
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Thermal Stresses ◽  
Material Interface ◽  
Element Mesh ◽  
Closed Form Solutions ◽  
First Order ◽  
The Past ◽  
Compliant Layer ◽  
Analytical Relations

In the past several years there have been a number of papers published which provide closed-form solutions for the stresses in bonded layers of materials. These closed-form solutions offer a rapid method to obtain first-order stresses for materials which are joined together and the compliant layer between them. However, before using them, it is desirable to have some feeling as to the accuracy of the results from these closed-form equations. Comparisons between these analytical relations and other approaches found in published works on bonding and to finite element solutions for several example problems are given. An attempt is made to qualify these closed-form equations in terms of their accuracy, as compared to other methods of analysis. The effects of finite element mesh refinement on the material interface stress results are also given.

scholarly journals Two Integrable Classes of Emden–Fowler Equations with Applications in Astrophysics and Cosmology

2018 ◽  
Vol 73 (9) ◽  
pp. 805-814
Author(s):  
Stefan C. Mancas ◽  
Haret C. Rosu
Keyword(s):  
General Relativity ◽  
Closed Form ◽  
Nonlinear Oscillator ◽  
Reduction Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Parametric Form ◽  
Closed Form Solutions ◽  
First Order ◽  
Class 1 ◽  
Elliptic Solutions

AbstractWe show that some Emden–Fowler (EF) equations encountered in astrophysics and cosmology belong to two EF integrable classes of the type ${\mathrm{d}^{2}}z/\mathrm{d}{\chi^{2}}=A{\chi^{-\lambda-2}}{z^{n}}$ for $\lambda=(n-1)/2$ (class 1), and $\lambda=n+1$ (class 2). We find their corresponding invariants which reduce them to first-order nonlinear ordinary differential equations. Using particular solutions of such EF equations, the two classes are set in the autonomous nonlinear oscillator the form ${\mathrm{d}^{2}}\nu/\mathrm{d}{t^{2}}+a\mathrm{d}\nu/\mathrm{d}t+b(\nu-{\nu^{n}})=0$, where the coefficients $a,b$ depend only on $\lambda,n$. For both classes, we write closed-form solutions in parametric form. The illustrative examples from astrophysics and general relativity correspond to two n = 2 cases from class 1 and 2, and one n = 5 case from class 1, all of them yielding Weierstrass elliptic solutions. It is also noticed that when n = 2, the EF equations can be studied using the Painlevé reduction method, since they are a particular case of equations of the type ${\mathrm{d}^{2}}z/\mathrm{d}{\chi^{2}}=F(\chi){z^{2}}$, where $F(\chi)$ is the Kustaanheimo-Qvist function.

scholarly journals Factorization method for some inhomogeneous Lienard equations

2021 ◽  
Vol 67 (3 May-Jun) ◽  
pp. 443
Author(s):  
O. Cornejo Perez ◽  
S. C. Mancas ◽  
H. C. Rosu ◽  
C. A. Rico-Olvera
Keyword(s):  
Differential Equations ◽  
Closed Form ◽  
Factorization Method ◽  
Closed Form Solutions ◽  
First Order ◽  
Liénard Equations ◽  
First Order Differential Equations

The factorization of inhomogeneous Li\'enard equations is performed showing that through the factorization conditions involved in the method one can obtain forcing terms for which closed-form solutions exist. Because of the reduction of order feature of factorization, the solutions are simultaneously solutions of first-order differential equations with polynomial nonlinearities. Several illustrative examples of such solutions are presented, generically having rational parts and consequently singularities.

The Artificial Hamiltonian, First Integrals, and Closed-Form Solutions of Dynamical Systems for Epidemics

2018 ◽  
Vol 73 (4) ◽  
pp. 323-330 ◽  
Author(s):  
Rehana Naz ◽  
Imran Naeem
Keyword(s):  
Dynamical Systems ◽  
Hamiltonian System ◽  
Closed Form ◽  
Hamiltonian Systems ◽  
Physical Structure ◽  
First Integrals ◽  
Second Order ◽  
Hamiltonian Structures ◽  
Closed Form Solutions ◽  
First Order

AbstractThe non-standard Hamiltonian system, also referred to as a partial Hamiltonian system in the literature, of the form ${\dot q^i} = \frac{{\partial H}}{{\partial {p_i}}},{\text{ }}{\dot p^i} = - \frac{{\partial H}}{{\partial {q_i}}} + {\Gamma ^i}(t,{\text{ }}{q^i},{\text{ }}{p_i})$ appears widely in economics, physics, mechanics, and other fields. The non-standard (partial) Hamiltonian systems arise from physical Hamiltonian structures as well as from artificial Hamiltonian structures. We introduce the term ‘artificial Hamiltonian’ for the Hamiltonian of a model having no physical structure. We provide here explicitly the notion of an artificial Hamiltonian for dynamical systems of ordinary differential equations (ODEs). Also, we show that every system of second-order ODEs can be expressed as a non-standard (partial) Hamiltonian system of first-order ODEs by introducing an artificial Hamiltonian. This notion of an artificial Hamiltonian gives a new way to solve dynamical systems of first-order ODEs and systems of second-order ODEs that can be expressed as a non-standard (partial) Hamiltonian system by using the known techniques applicable to the non-standard Hamiltonian systems. We employ the proposed notion to solve dynamical systems of first-order ODEs arising in epidemics.

Sign in / Sign up

Export Citation Format

Share Document