相关论文: Combined dynamic Gruss inequalities on time scales
Trace conjunction integrals are introduced and studied. They appear in trace conjunction inequalities which unify the Hardy inequality on a halfspace and the classical Gagliardo trace inequality. At the endpoint they satisfy a…
The aim of this paper is to generalize the Hermite--Hadamard inequality for functions convex on the coordinates. Our composite result generalizes the result of Dragomir in \cite{Drag}. Many other interesting inequalities can be derived from…
We study a long-recognised but under-appreciated symmetry called "dynamical similarity" and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a…
The Douglas-Rachford algorithm is a very popular splitting technique for finding a zero of the sum of two maximally monotone operators. However, the behaviour of the algorithm remains mysterious in the general inconsistent case, i.e., when…
We prove existence of solution to a nonlinear first-order nabla dynamic equation on an arbitrary bounded time scale with boundary conditions, where the right-hand side of the dynamic equation is a continuous function.
We generalize the differential representation of the operators of the Galilean algebras to include fractional derivatives. As a result a whole new class of scale invariant Galilean algebras are obtained. The first member of this class has…
Two time scale stochastic approximation is analyzed when the iterates on either or both time scales do not necessarily converge.
A class of numerical quadrature rules is derived, with equally-spaced nodes, and unit weights except at a few points at each end of the series, for which "corrections" (not using any further information about the integrand) are added to the…
Normal and anomalous diffusion are ubiquitous in many complex systems [1] . Here, we define a time and space generalized diffusion equation (GDE), which uses fractional-time derivatives and transformed d-path Laplacian operators on…
We study a general class of weighted shifts whose weights $\alpha$ are given by $\alpha_n = \sqrt{\frac{p^n + N}{p^n + D}}$, where $p > 1$ and $N$ and $D$ are parameters so that $(N,D) \in (-1, 1)\times (-1, 1)$. Some few examples of these…
The Grey System Theory (GST) is a powerful mathematical framework employed for modeling systems with uncertain or incomplete information. This paper proposes an integration of the GST with time scales, a generalized approach that…
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…
To predict allowable time-step size for the fully discretized nonlinear differential equations, a stability theory is developed using exact determination of an infinite perturbation series. Mathematical induction is used to determine the…
New reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces are pointed out. These results complement the recent ones obtained by the author in an earlier paper. Further, they are employed to establish new Gruss…
We analyze approaches to the partial or complete unification of gauge symmetries in theories with dynamical symmetry breaking. Several types of models are considered, including those that (i) involve sufficient unification to quantize…
We consider a class of of massless gradient Gibbs measures, in dimension greater or equal to three, and prove a decoupling inequality for these fields. As a result, we obtain detailed information about their geometry, and the percolative…
When averages of different experimental determinations of the same quantity are computed, each with statistical and systematic error components, then frequently the statistical and systematic components of the combined error are quoted…
We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open question raised by Geers et al. in [GPPS13]. The proof of…
We generalize the tree-confluent graphs to a broader class of graphs called Delta-confluent graphs. This class of graphs and distance-hereditary graphs, a well-known class of graphs, coincide. Some results about the visualization of…
This paper studies clustering algorithms for dynamically evolving graphs $\{G_t\}$, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper…