相关论文: Diamond-alpha Integral Inequalities on Time Scales
A numerical setup for the Bell-CHSH inequality for causal diamonds in $1+1$ Minkowski spacetime is presented. Upon choosing a suitable set of test functions supported in the diamonds, sensible violations are reported for the correlation…
The fundamental problem of the calculus of variations on time scales concerns the minimization of a delta-integral over all trajectories satisfying given boundary conditions. In this paper we prove the second Euler-Lagrange necessary…
In this paper, we introduce the nabla fractional derivative and fractional integral on time scales in the Riemann-Liouville sense. We also introduce the nabla fractional derivative in Gr\"unwald-Letnikov sense. Some of the basic properties…
This document introduces a generalization of calculus that treats both continuous and discrete variables on an equal footing. This generalization of calculus was developed independently of the "Calculus on Time Scales" literature but may be…
We introduce a discrete-time fractional calculus of variations on the time scales $\mathbb{Z}$ and $(h\mathbb{Z})_a$. First and second order necessary optimality conditions are established. Some numerical examples illustrating the use of…
We study problems of the calculus of variations and optimal control within the framework of time scales. Specifically, we obtain Euler-Lagrange type equations for both Lagrangians depending on higher order delta derivatives and…
We first prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial…
We introduce a nabla, a delta, and a symmetric fractional calculus on arbitrary nonempty closed subsets of the real numbers. These fractional calculi provide a study of differentiation and integration of noninteger order on discrete,…
This paper studies alpha testing in a high-dimensional conditional time-varying factor model with temporally dependent observations. Both factor loadings and alpha processes are allowed to vary smoothly over time, and the cross-sectional…
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…
In this paper we obtain the estimates on some dynamic integral inequalities in three variables which can be used to study certain dynamic equations. We give some applications to convey the importance of our result.
In calculus of variations on general time scales, an integral Euler-Lagrange equation is usually derived in order to characterize the critical points of non shifted Lagrangian functionals, see e.g. [R.A.C. Ferreira and co-authors,…
This article deals with variational optimal-control problems on time scales in the presence of delay in the state variables. The problem is considered on a time scale unifying the discrete, the continuous and the quantum cases. Two examples…
We formulate certain inequalities for the geometric quantities characterizing causal diamonds in curved and Minkowski spacetimes. These inequalities involve the red-shift factor which, as we show explicitly in the spherically symmetric…
In the present paper we will give some new notions, such as {\Delta}-convergence and {\Delta}-Cauchy, by using the {\Delta}-density and investigate their relations. It is important to say that, the results presented in this work generalize…
We prove the Euler-Lagrange delta-differential equations for problems of the calculus of variations on arbitrary time scales with delta-integral functionals depending on higher-order delta derivatives.
A generalization of the H\"older inequality is considered. Its relations with a previously obtained improvement of the Cauchy--Schwarz inequality are discussed.
We establish some nonlinear integral inequalities for functions defined on a time scale. The results extend some previous Gronwall and Bihari type inequalities on time scales. Some examples of time scales for which our results can be…
We establish necessary optimality conditions for variational problems with an action depending on the free endpoints. New transversality conditions are also obtained. The results are formulated and proved using the recent and general theory…
There have been many proposed forms of fractional calculus, which can be grouped into a few broad classes of operators. By replacing the kernel of the power function with another kernel function, the traditional Riemann-Liouville formula…