In this study, we introduce the expression dλ(x,y):=λ∥x∥+(1−λ)∥y∥−∥λx+(1−λ)y∥ on real normed space X(X,∥·∥), where x,y∈X and λ∈R. We characterize find various estimates of it. also obtain a generalization some refinements Maligranda’s inequality. Finally, give relations between dλ(x,y) several types angular distances two nonzero vectors in space.

We show that for any lattice L ⊆ Rn and vectors x, y ∈ Rn, ρ(L+ x)2ρ(L+ y)2 ≤ ρ(L)2ρ(L+ x + y)ρ(L+ x− y) , where ρ is the Gaussian mass function ρ(A) := ∑w∈A exp(−π‖w‖ ). We show a number of applications, including bounds on the moments of the discrete Gaussian distribution, various monotonicity properties of the heat kernel on flat tori, and a positive correlation inequality for Gaussian measu...

This paper presents a numerical study of a stochastic augmented Lagrangian algorithm to solve continuous constrained global optimization problems. The algorithm approximately solves a sequence of bound constrained subproblems whose objective function penalizes equality and inequality constraints violation and depends on the Lagrange multiplier vectors and a penalty parameter. Each subproblem is...

background: despite the enhancement in health outcomes worldwide, health inequity and inequality is one of the most relevant topics both for health policy and public health. this research was designed to decompose the health inequality of people living in shiraz, south-west iran. methods: data were obtained from a multistage-sample survey conducted in shiraz from april to may 2012, to find dete...

This article concerns the stability and periodicity of solutions to the delay dynamic system x4(t) = A(t)x(t) + F (t, x(t), x(g(t))) + C(t) on a time scale. By the inequality technique for vectors, we obtain some stability criteria for the above system. Then, using the Horn fixed point theorem, we present some conditions under which our system is asymptotically periodic and its periodic solutio...

In recent years, sequential optimality conditions are frequently used for convergence of iterative methods to solve nonlinear constrained optimization problems. The sequential optimality conditions do not require any of the constraint qualications. In this paper, We present the necessary sequential complementary approximate Karush Kuhn Tucker (CAKKT) condition for a point to be a solution of a ...

Kalman smoothers obtain state estimates in a system with stochastic dynamics and measurement noise. We consider the smoothing problem in a distributed setting, present a cooperative smoothing algorithm for Gauss-Markov linear models, and provide a convergence analysis for the algorithm. An extension of the algorithm that maximizes the likelihood with respect to a sequence of state vectors subje...

We point out that the inequality det E > 0 distinguishes the kinematical phase space of canonical connection gravity from that of a gauge field theory, and characterize the eigen-vectors with positive, negative and zero-eigenvalue of the corresponding quantum operator in a lattice-discretized version of the theory. The diagonalization ofˆdet E is simplified by classifying its eigenvectors accor...