Search results

article

The Taylor series method of order p and Adams–Bashforth method on time scales

Svetlin G. Georgiev, İnci M. Erhan

Mathematical Methods in the Applied Sciences > 46 > 1 > 304 - 320

A recent study on the Taylor series method of second order and the trapezoidal rule for dynamic equations on time scales has been continued by introducing a derivation of the Taylor series method of arbitrary order

p

on time scales. The error and convergence analysis of the method is also obtained. The 2‐step Adams–Bashforth method for dynamic equations on time scales is concluded and applied...

article

Periodicity on isolated time scales

Martin Bohner, Jaqueline Mesquita, Sabrina Streipert

Mathematische Nachrichten > 295 > 2 > 259 - 280

In this work, we formulate the definition of periodicity for functions defined on isolated time scales. The introduced definition is consistent with the known formulations in the discrete and quantum calculus settings. Using the definition of periodicity, we discuss the existence and uniqueness of periodic solutions to a family of linear dynamic equations on isolated time scales. Examples in quantum...

article

On oscillatory behaviour of third-order half-linear dynamic equations on time scales

Said R. Grace, Gokula Nanda Chhatria

Opuscula Mathematica > 2022 > Vol. 42, no. 6 > 849--865

In this work, we study the oscillation and asymptotic behaviour of third-order nonlinear dynamic equations on time scales. The findings are obtained using an integral criterion as well as a comparison theorem with the oscillatory properties of a first-order dynamic equation. As a consequence, we give conditions which guarantee that all solutions to the aforementioned problem are only oscillatory,...

article

Nonoscillation of half‐linear dynamic equations on time scales

Petr Hasil, Jozef Kisel'ák, Michal Pospíšil, Michal Veselý

Mathematical Methods in the Applied Sciences > 44 > 11 > 8775 - 8797

The research contained in this paper belongs to the qualitative theory of dynamic equations on time scales. Via the detailed analysis of solutions of the associated Riccati equation and an advanced averaging technique, we provide the description of domain of nonoscillation of very general equations. The results are formulated and proved for half‐linear equations (i.e., equations connected to PDEs...

article

A generalized delta derivative on time scale with applications

Shekhar Singh Negi, Syed Abbas, Muslim Malik

Mathematical Methods in the Applied Sciences > 43 > 15 > 9046 - 9079

Inspired by a well‐known “Hilger‐derivative” on time scale introduced by Stephan Hilger, we introduce a new derivative on the time scale, called “black delta (or in notation

▴

)‐derivative.” It is an adaptive unified approach of derivative of continuous and discrete calculus. Several important nontrivial results concerning this derivative are obtained. Also, a necessary and sufficient condition for...

article

An asymptotic result for a certain type of delay dynamic equation with biological background

Halis Can Koyuncuoğlu, Nezihe Turhan, Murat Adıvar

Mathematical Methods in the Applied Sciences > 43 > 12 > 7303 - 7310

Inspired by Cooke and York's work, we concentrate on the delay dynamic equation on a nonempty, arbitrary, closed set of real numbers, so‐called a time scale. The utilization of an abstract delay function δ in the above‐given equation relaxes the condition that each individual has a fixed constant life span when it fits a growth process. The main result is obtained by establishing a linkage between...

article

A class of new nonlinear dynamic integral inequalities containing integration on infinite interval on time scales

Haidong Liu, Cuiyuan Li, Feichao Shen

Advances in Difference Equations > 2019 > 2019 > 1 > 1-11

In this paper, we investigate some new nonlinear dynamic integral inequalities containing integration on infinite interval on time scales, which provide explicit bounds on unknown functions. Our results not only generalize some dynamic inequalities in related literature, but also are new even for the continuous and discrete time cases. Two examples are given to illustrate the present results.

article

Oscillation for a nonlinear neutral dynamic equations on time‐scales with variable exponents

Shekhar Singh Negi, Syed Abbas, Muslim Malik

Mathematical Methods in the Applied Sciences > 42 > 12 > 4146 - 4169

In the present manuscript, we study the oscillation theory for a first‐order nonlinear neutral dynamic equations on timescales with variable exponents of the form where ξ is a quotient of odd positive integers;

t_{*} \in T

be a fixed number;

[t_{*}, {\infty)}_{T}

is a timescale interval; η,τ_m > 0;

f_{m} \in C (R, R)

for m = 1,2,…,n such that

x f_{m} (x) > 0 \forall x \in R \ {0}; R, T \in C_{r d} ([t_{*}, {\infty)}_{T}, R)

, and the variable exponents α_m(t) satisfy...

article

Sharp oscillation and nonoscillation tests for delay dynamic equations

Basak Karpuz

Mathematical Methods in the Applied Sciences > 42 > 9 > 2993 - 3001

In this paper, we give new sufficient conditions for both oscillation and nonoscillation of the delay dynamic equation where

p \in C_{rd} ([t_{0}, {\infty)}_{T}, R_{0}^{+})

and

τ \in C_{rd} ([t_{0}, {\infty)}_{T}, T)

satisfy τ(t) ≤ σ(t) for all large t and

\lim_{t \to \infty} τ (t) = \infty

. As an important corollary, we obtain the time scale invariant integral condition for nonoscillation:

\int_{τ (t)}^{σ (t)} p (η) Δ η \leq \frac{1}{e}

for all large t. Also, with some examples, we show that...

article

Improved GNN Models for Constant Matrix Inversion

Predrag S. Stanimirović, Marko D. Petković

Neural Processing Letters > 2019 > 50 > 1 > 321-339

It was shown that the multiplication of the left hand side of the classical Zhang neural network design rule by an appropriate positive definite matrix generates a new neural design with improved convergence rate. Our intention is to apply similar principle on the standard gradient neural network (GNN) model. To that goal, we discover that some of proposed models can be considered as the multiplication...

article

Oscillation result for half‐linear dynamic equations on timescales and its consequences

Petr Hasil, Michal Veselý

Mathematical Methods in the Applied Sciences > 42 > 6 > 1921 - 1940

We study oscillatory properties of half‐linear dynamic equations on timescales. Via the combination of the Riccati technique and an averaging method, we find the domain of oscillation for many equations. The presented main result is not the conversion of a known result from the theory of differential or difference equations, ie, we obtain new results for the timescales

T = R

(for differential equations)...

article

The Karamata integration theorem on time scales and its applications in dynamic and difference equations

Pavel Řehák

Applied Mathematics and Computation > 2018 > 338 > C > 487-506

We derive a time scale version of the well-known result from the theory of regular variation, namely the Karamata integration theorem. We show an application of this theorem in asymptotic analysis of linear second order dynamic equations. We obtain a classification and asymptotic formulae for all (positive) solutions, which unify, extend, and improve the existing results. In addition, we utilize these...

article

A novel computer-oriented dynamical approach with efficient formulations for multibody systems including ignorable coordinates

Hossein Nejat Pishkenari, Siamak Heidarzadeh

Applied Mathematical Modelling > 2018 > 62 > C > 461-475

Based on Lagrangian mechanics, we present a novel and computationally efficient set of equations of motion in the matrix notation, for unconstrained or constrained mechanical systems including ignorable coordinates. The equations are applicable to multibody systems including holonomic or nonholonomic constraints. It is shown that by appropriate selection of generalized speeds as a new set of motion...

article

Oscillation of Emden–Fowler type nonlinear neutral delay dynamic equation on time scales

Ying Sui, Shurong Sun

Journal of Applied Mathematics and Computing > 2019 > 60 > 1-2 > 291-301

In this paper, we consider the following Emden–Fowler type nonlinear neutral delay dynamic equation of the form $$\begin{aligned} \left( r(t)\left( (y(t)+p(t)y(\tau (t)))^\Delta \right) ^\alpha \right) ^\Delta +q(t)y^\beta (m(t))=0 \end{aligned}$$ r ( t ) ( y ( t ) + p ( t ) y ( τ ( t ) ) ) Δ α Δ + q ( t ) y β ( m ( t ) ) = 0 on time scales, where ...

article

Gradient Neural Network with Nonlinear Activation for Computing Inner Inverses and the Drazin Inverse

Predrag S. Stanimirović, Marko D. Petković, Dimitrios Gerontitis

Neural Processing Letters > 2018 > 48 > 1 > 109-133

Two gradient-based recurrent neural networks (GNNs) for solving two matrix equations are presented and investigated. These GNNs can be used for generating various inner inverses, including the Moore–Penrose, and in the computation of the Drazin inverse. Convergence properties of defined GNNs are considered. Certain conditions which impose convergence towards the pseudoinverse, and the Drazin inverse...

article

Recurrent neural network for computing the W-weighted Drazin inverse

Xue-Zhong Wang, Haifeng Ma, Predrag S. Stanimirović

Applied Mathematics and Computation > 2017 > 300 > C > 1-20

Two gradient based recurrent neural networks (RNNs) for computing the W-weighted Drazin inverse of a real rectangular matrix are proposed and considered. Usage of the first RNN is limited by a specific constraint on the spectrum of a certain matrix. The second RNN is usable without restrictions. The stability of the recurrent neural networks as well as their convergence are considered. Numerical examples...

article

A two-component dynamic stand model of natural thinning

Tatiana V. Stankova, Ulises Diéguez-Aranda

Forest Ecology and Management > 2017 > 385 > C > 264-280

Our investigation aims (1) to derive a dynamic model for mean volume and biomass growth projection over time, considering the competition-induced tree mortality (dynamic size-density model), (2) to design a compatible two-component modelling system composed of the dynamic size-density model and an appropriate density decrease function, and (3) to examine the applicability of this composite natural...

article

Nonlinearly Activated Recurrent Neural Network for Computing the Drazin Inverse

Xue-Zhong Wang, Haifeng Ma, Predrag S. Stanimirović

Neural Processing Letters > 2017 > 46 > 1 > 195-217

Four gradient-based recurrent neural networks for computing the Drazin inverse of a square real matrix are developed. Theoretical analysis shows that any monotonically-increasing odd activation function ensures the global convergence performance of defined neural network models. The computer simulation results further substantiate that the considered neural networks could compute the Drazin inverse...

article

Dynamic equations of tritium concentration during wastewater (light water) containing tritium electrolysis

Junbo Zhou, Yang Liu, Chao Wang

International Journal of Hydrogen Energy > 2016 > 41 > 36 > 16014- 16018

Nuclear facilities often produce some wastewater containing tritium, which cannot be discharged directly because of the radioactivity of the tritium. It is of great significance to study the dynamic change rules of tritium concentration during wastewater containing tritium electrolysis with SPE for tritium enrichment for the estimation of the environmental tritium concentration and the recovery of...

chapter

Structure design and dynamic modelling of a novel modular self-reconfigurable robot

Jie Huang, Weimin Ge, Xiaofeng Wang, Jun Liu

2016 IEEE International Conference on Mechatronics and Automation > 2284 - 2289

2016 IEEE International Conference on Mechatronics and Automation

Reconfigurability of the modular robot is becoming curial to be a high flexibility for the wide varieties of tasks and environments. In this paper, a novel self-reconfigurable modular robot called M²sbot is designed, which has the approximate cuboid shaping structure. The unit model is with one active and five passive connection surfaces, compact structure and flexible motion. It is characterized...

INFONA - science communication portal

Search results

The Taylor series method of order p and Adams–Bashforth method on time scales

Periodicity on isolated time scales

On oscillatory behaviour of third-order half-linear dynamic equations on time scales

Nonoscillation of half‐linear dynamic equations on time scales

A generalized delta derivative on time scale with applications

An asymptotic result for a certain type of delay dynamic equation with biological background

A class of new nonlinear dynamic integral inequalities containing integration on infinite interval on time scales

Oscillation for a nonlinear neutral dynamic equations on time‐scales with variable exponents

Sharp oscillation and nonoscillation tests for delay dynamic equations

Improved GNN Models for Constant Matrix Inversion

Oscillation result for half‐linear dynamic equations on timescales and its consequences

The Karamata integration theorem on time scales and its applications in dynamic and difference equations

A novel computer-oriented dynamical approach with efficient formulations for multibody systems including ignorable coordinates

Oscillation of Emden–Fowler type nonlinear neutral delay dynamic equation on time scales

Gradient Neural Network with Nonlinear Activation for Computing Inner Inverses and the Drazin Inverse

Recurrent neural network for computing the W-weighted Drazin inverse

A two-component dynamic stand model of natural thinning

Nonlinearly Activated Recurrent Neural Network for Computing the Drazin Inverse

Dynamic equations of tritium concentration during wastewater (light water) containing tritium electrolysis

Structure design and dynamic modelling of a novel modular self-reconfigurable robot

Filter options

Publication date

Content availability

Publication type

Publication language

Keywords

Data set

INFONA - science communication portal

Search results

Add recipient

Sending message cancelled

Are you sure you want to cancel sending this message?

Send message

Filter options

Publication date

Date range setting

Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.

Content availability

Publication type

Publication language

Keywords

Data set

Reporting an error / abuse

Sending the report failed

Accessibility options