Related papers: Some new dynamic Inequality on time scales in thre…

This paper studies the Hardy-type inequalities on the discrete intervals. The first result is the variational formulas of the optimal constants. Using these formulas, one may obtain an approximating procedure and the known basic estimates…

We consider certain systems of three linked simultaneous diagonal equations in ten variables with total degree exceeding five. By means of a complification argument, we obtain an asymptotic formula for the number of integral solutions of…

Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.

Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and…

The determination of a dynamic law of cut is complex and often very difficult to develop. Several formulations were developed, in very complex ways being given that 3 AD crosses from there, the number of variables is much higher than out of…

This paper uses differential spaces to obtain some new results in integrable Hamiltonian systems

The discrete, the quantum, and the continuous calculus of variations, have been recently unified and extended by using the theory of time scales. Such unification and extension is, however, not unique, and two approaches are followed in the…

Imputation models sometimes use auxiliary variables that, though not part of the planned analysis, can improve the accuracy of imputed values and the efficiency of point estimates. A recent article, using evidence from simulations, argued…

We consider the inverse dynamic problem for the wave equation with a potential on a real line. The forward initial-boundary value problem is set up with a help of boundary triplets. As an inverse data we use an analog of a response operator…

In this paper, new refinements for integral and sum forms of H\"older inequality are established. We note that many existing inequalities related to the H\"older inequality can be improved via obtained new inequalities in here, we show this…

We use the integrable deformations method for a three-dimensional system of differential equations to obtain deformations of the T system. We analyze a deformation given by particular deformation functions. We point out that the obtained…

In this paper, the Authors establish a new identity for differentiable functions. By the well-known H\"older and power mean inequality, they obtain some integral inequalities related to the convex functions and apply these inequalities to…

In this paper, we established a new Ostrowski-type inequality involving functions of two independent variables.

Complex systems display variability over a broad range of spatial and temporal scales. Some scales are unresolved due to computational limitations. The impact of these unresolved scales on the resolved scales needs to be parameterized or…

Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…

The scaling of the spatio-temporal response of coarsening systems is studied through simulations of the 2D and 3D Ising model with Glauber dynamics. The scaling functions agree with the prediction of local scale invariance, extending…

We obtain variance inequalities for quadratic forms of weakly dependent random variables with bounded fourth moments. We also discuss two application. Namely, we use these inequalities for deriving the limiting spectral distribution of a…

Testing for causation, defined as the preceding impact of the past values of one variable on the current value of another one when all other pertinent information is accounted for, is increasingly utilized in empirical research of the…

We introduce a fractional calculus on time scales using the theory of delta (or nabla) dynamic equations. The basic notions of fractional order integral and fractional order derivative on an arbitrary time scale are proposed, using the…

In this paper we study well posedness of a certain nonlinear Volterra-Fredholm dynamic integral and integro-dynamic equations on unbounded interval from arbitrary time scale. We derive the time scale analogue of certain integral…