Related papers: Some integral inequalities on time scales
The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index $GA_1$ and…
This paper aims to improve existing results about using averaging method for analysis of dynamic systems on time scales. We obtain a more accurate estimate for proximity between solutions of original and averaged systems regarding…
We establish an inequality of different metrics for algebraic polynomials.
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
In this article, we explore the celebrated Gr\"{u}ss inequality, where we present a new approach using the Gr\"{u}ss inequality to obtain new refinements of operator means inequalities. We also present several operator Gr\"{u}ss-type…
The formalizations of periods of time inside a linear model of Time are usually based on the notion of intervals, that may contain or may not their endpoints. This is not enought when the periods are written in terms of coarse granularities…
We study more general variational problems on time scales. Previous results are generalized by proving necessary optimality conditions for (i) variational problems involving delta derivatives of more than the first order, and (ii) problems…
We study arithmetic inequalities for multiplicative, sub(super)-multiplicative, sub(super)-homogeneous functions. Applications for the classical arithmetic functions are pointed out.
Some inequalities and reverses of classic H\"{o}lder and Minkowski types are obtained for scalar Birkhoff weak integrable functions with respect to a non-additive measure.
In this paper, we establish several new inequalities for n- time differentiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality.
We provide an overview of the connections between Bell's inequalities and algebraic structure.
We consider systems of ordinary differential equations with multiple scales in time. In general, we are interested in the long time horizon of a slow variable that is coupled to solution components that act on a fast scale. Although the…
In this paper we explore a new method of analysis of associative algebras.
Recent explainable artificial intelligence (XAI) methods for time series primarily estimate point-wise attribution magnitudes, while overlooking the directional impact on predictions, leading to suboptimal identification of significant…
We present a new time-stepping algorithm for nonlinear PDEs that exhibit scale separation in time. Our scheme combines asymptotic techniques (which are inexpensive but can have insufficient accuracy) with parallel-in-time methods (which,…
The theory and applications of dynamic derivatives on time scales has recently received considerable attention. The primary purpose of this paper is to give basic properties of diamond-$\alpha$ derivatives which are a linear combination of…
In this paper, a nonlinear system of fractional ordinary differential equations with multiple scales in time is investigated. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the…
We prove a version of the Euler-Lagrange equations for certain problems of the calculus of variations on time scales with higher-order delta derivatives.
We give norm inequalities for some classical operators in amalgams spaces and in some subspace of Morrey space.
This paper analyzes effects of time-dependence in the Bell inequality. A generalized inequality is derived for the case when coincidence and non-coincidence [and hence whether or not a pair contributes to the actual data] is controlled by…