scholarly journals Algebraic definition of central dispersions of the 1st kind of the differential equation $y''=Q(t)y$

1966 ◽  
Vol 16 (1) ◽  
pp. 46-62
Author(s):  
Erich Barvínek
Keyword(s):  
Differential Equation ◽  
Definition Of

scholarly journals The allometric hypothesis when the size variable is uncertain: issues in the study of carcass composition by serial slaughter

1997 ◽  
Vol 38 (4) ◽  
pp. 477-488 ◽  
Author(s):  
A. B. Pleasants ◽  
G. C. Wake ◽  
A. L. Rae
Keyword(s):  
Differential Equation ◽  
Growth Rates ◽  
Allometric Equation ◽  
Carcass Composition ◽  
Farm Animals ◽  
Relative Growth ◽  
Relative Growth Rates ◽  
Definition Of ◽  
Maintenance Requirements ◽  
Size Variable

AbstractThe allometric hypothesis which relates the shape (y) of biological organs to the size of the plant or animal (x), as a function of the relative growth rates, is ubiquitous in biology. This concept has been especially useful in studies of carcass composition of farm animals, and is the basis for the definition of maintenance requirements in animal nutrition.When the size variable is random the differential equation describing the relative growth rates of organs becomes a stochastic differential equation, with a solution different from that of the deterministic equation normally used to describe allometry. This is important in studies of carcass composition where animals are slaughtered in different sizes and ages, introducing variance between animals into the size variable.This paper derives an equation that relates values of the shape variable to the expected values of the size variable at any point. This is the most easily interpreted relationship in many applications of the allometric hypothesis such as the study of the development of carcass composition in domestic animals by serial slaughter. The change in the estimates of the coefficients of the allometric equation found through the usual deterministc equation is demonstrated under additive and multiplicative errors. The inclusion of a factor based on the reciprocal of the size variable to the usual log - log regression equation is shown to produce unbiased estimates of the parameters when the errors can be assumed to be multiplicative.The consequences of stochastic size variables in the study of carcass composition are discussed.

On the theory and application of one-step numerical schemes for solving quantum stochastic differential equation (QSDE)

2014 ◽  
Vol 07 (03) ◽  
pp. 1450037
Author(s):  
T. O. Akinwumi ◽  
B. J. Adegboyegun
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Stochastic Differential Equation ◽  
Numerical Experiments ◽  
Numerical Schemes ◽  
Quantum Stochastic Differential Equation ◽  
One Step ◽  
Definition Of ◽  
Convergent Sequences ◽  
Solution Techniques

This paper presents one-step numerical schemes for solving quantum stochastic differential equation (QSDE). The algorithms are developed based on the definition of QSDE and the solution techniques yield rapidly convergent sequences which are readily computable. As well as developing the schemes, we perform some numerical experiments and the solutions obtained compete favorably with exact solutions. The solution techniques presented in this work can handle all class of QSDEs most especially when the exact solution does not exist.

scholarly journals Nonlinear definition of the shadowy mode in higher-order scalar-tensor theories

2021 ◽  
Vol 2021 (12) ◽  
pp. 020
Author(s):  
Antonio De Felice ◽  
Shinji Mukohyama ◽  
Kazufumi Takahashi
Keyword(s):  
Differential Equation ◽  
Coordinate System ◽  
Three Dimensional ◽  
Spacelike Hypersurface ◽  
Higher Order ◽  
Elliptic Differential Equation ◽  
Unitary Gauge ◽  
Definition Of

Abstract We study U-DHOST theories, i.e., higher-order scalar-tensor theories which are degenerate only in the unitary gauge and yield an apparently unstable extra mode in a generic coordinate system. We show that the extra mode satisfies a three-dimensional elliptic differential equation on a spacelike hypersurface, and hence it does not propagate. We clarify how to treat this “shadowy” mode at both the linear and the nonlinear levels.

scholarly journals Multiplication of Distributions and Algebras of Mnemofunctions

2019 ◽  
Vol 65 (3) ◽  
pp. 339-389
Author(s):  
A B Antonevich ◽  
T G Shagova
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Distribution Space ◽  
First Order ◽  
Space Of Distributions ◽  
Essential Properties ◽  
Definition Of ◽  
Distribution Spaces ◽  
Multiplication Of Distributions ◽  
General Method

In this paper, we discuss methods and approaches for definition of multiplication of distributions, which is not defined in general in the classical theory. We show that this problem is related to the fact that the operator of multiplication by a smooth function is nonclosable in the space of distributions. We give the general method of construction of new objects called new distributions, or mnemofunctions, that preserve essential properties of usual distributions and produce algebras as well. We describe various methods of embedding of distribution spaces into algebras of mnemofunctions. All ideas and considerations are illustrated by the simplest example of the distribution space on a circle. Some effects arising in study of equations with distributions as coefficients are demonstrated by example of a linear first-order differential equation.

Blast-off simulation sebagai alternatif media pembelajaran siswa dalam mempelajari mekanika gerak roket berbasis matlab

2020 ◽  
Vol 1 (1) ◽  
pp. 6-11
Author(s):  
Alpi Mahisha Nugraha ◽  
Nurullaeli Nurullaeli
Keyword(s):  
Differential Equation ◽  
User Interface ◽  
Driving Force ◽  
Order Differential Equation ◽  
Visual Media ◽  
Learning Effectiveness ◽  
Graphic User Interface ◽  
First Order ◽  
Definition Of

Blast-off or rocket launcher is a physics phenomena about mechanical of motion specially momentum principal. Unlike other flying objects like blimps and airplanes, blass-off uses the principle of changing momentum as a driving force to able fly in the air. The definition of force is a rate of changing momentum, the definition is illustrated by first-order differential equation which can be solved analytically or numerically. Unfortunately, during class learning, the equation is only used to solve collision problems instead of being used to explain blast-off phenomena which is very interesting to learn mostly. Moreover, if the explanation in the class uses visual media such as Graphic User Interface (GUI). Blast-off simulation is designed from the solving of the first differential numerically, and then the algorithm is compiled using Matlab aplication with an output in the form of a GUI so students become more interested in learning momentum and learning effectiveness will be incrised.

On the First Conjugate Point Function for Nonlinear Differential Equations

1975 ◽  
Vol 18 (4) ◽  
pp. 577-585 ◽  
Author(s):  
Allan C. Peterson ◽  
Dwight V. Sukup
Keyword(s):  
Differential Equation ◽  
Initial Value Problems ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Conjugate Point ◽  
Main Concern ◽  
Nonlinear Case ◽  
Point Function ◽  
Initial Value ◽  
Definition Of

AbstractWe are concerned with the nth order differential equation y(n) = (x, y, y′, …,y(n-1)), where it is assumed throughout that f is continuous on [α,β) × Rn, α < β≤∞, and that solutions of initial value problems are unique and exist on [α, β). The definition of the first conjugate point function η1(t) for linear homogeneous equations is extended to this nonlinear case. Our main concern is what properties of this conjugacy function are valid in the nonlinear case.

Continuous-time threshold AR(1) processes

1996 ◽  
Vol 28 (03) ◽  
pp. 728-746 ◽  
Author(s):  
O. Stramer ◽  
P. J. Brockwell ◽  
R. L. Tweedie
Keyword(s):  
Differential Equation ◽  
Weak Solution ◽  
Stochastic Differential Equation ◽  
Strong Solution ◽  
Piecewise Linear ◽  
Transition Probability ◽  
Unique Strong Solution ◽  
Direct Definition ◽  
Definition Of ◽  
Boundary Width

A threshold AR(1) process with boundary width 2δ &gt; 0 was defined by Brockwell and Hyndman [5] in terms of the unique strong solution of a stochastic differential equation whose coefficients are piecewise linear and Lipschitz. The positive boundary-width is a convenient mathematical device to smooth out the coefficient changes at the boundary and hence to ensure the existence and uniqueness of the strong solution of the stochastic differential equation from which the process is derived. In this paper we give a direct definition of a threshold AR(1) process with δ = 0 in terms of the weak solution of a certain stochastic differential equation. Two characterizations of the distributions of the process are investigated. Both express the characteristic function of the transition probability distribution as an explicit functional of standard Brownian motion. It is shown that the joint distributions of this solution with δ = 0 are the weak limits as δ ↓ 0 of the distributions of the solution with δ &gt; 0. The sense in which an approximating sequence of processes used by Brockwell and Hyndman [5] converges to this weak solution is also investigated. Some numerical examples illustrate the value of the latter approximation in comparison with the more direct representation of the process obtained from the Cameron–Martin–Girsanov formula and results of Engelbert and Schmidt [9]. We also derive the stationary distribution (under appropriate assumptions) and investigate stability of these processes.

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