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.

scholarly journals An exact expression of positive periodic solution for a first-order singular equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yun Xin ◽  
Xiaoxiao Cui ◽  
Jie Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Lower Bounds ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Positive Periodic Solution ◽  
Exact Expression ◽  
Upper And Lower Bounds ◽  
Singular Equation ◽  
First Order

Abstract The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

scholarly journals WORLD VOLUME SOLITONS OF THE D3-BRANE IN THE BACKGROUND OF (p, q) FIVE-BRANES

2000 ◽  
Vol 15 (28) ◽  
pp. 4477-4498 ◽  
Author(s):  
P. M. LLATAS ◽  
A. V. RAMALLO ◽  
J. M. SÁNCHEZ DE SANTOS
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Brane World ◽  
Invariant Solutions ◽  
First Order ◽  
World Volume ◽  
The World ◽  
Energy Bound

We analyze the world volume solitons of a D3-brane probe in the background of parallel (p, q) five-branes. The D3-brane is embedded along the directions transverse to the five-branes of the background. By using the S duality invariance of the D3-brane, we find a first-order differential equation whose solutions saturate an energy bound. The SO(3) invariant solutions of this equation are found analytically. They represent world volume solitons which can be interpreted as formed by parallel (-q, p) strings emanating from the D3-brane world volume. It is shown that these configurations are 1/4 supersymmetric and provide a world volume realization of the Hanany–Witten effect.

scholarly journals On the integration processes of A. Huťa

1963 ◽  
Vol 3 (2) ◽  
pp. 202-206 ◽  
Author(s):  
J. C. Butcher
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Sixth Order ◽  
Order Accuracy ◽  
First Order ◽  
Runge Kutta ◽  
Image Position

Huta [1], [2] has given two processes for solving a first order differential equation to sixth order accuracy. His methods are each eight stage Runge-Kutta processes and differ mainly in that the later process has simpler coefficients occurring in it.

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