Discrete Clifford analysis is a higher dimensional discrete function theory based on skew Weyl relations. It is centered around the study of Clifford algebra valued null solutions, called discrete monogenic functions, of a discrete Dirac operator, i.e. a first order, Clifford vector valued difference operator. In this contribution, we establish a Cauchy-Kovalevskaya extension theorem for discre...

A modification of perturbation theory, known as delta-expansion (variationally improved perturbation), gave rigorously convergent series in some D = 1 models (oscillator energy levels) with factorially divergent ordinary perturbative expansions. In a generalization of variationally improved perturbation appropriate to renormalizable, asymptotically free theories, we show that the large expansio...

‎let $mathcal{a}$ be a unital banach algebra‎, ‎$mathcal{m}$ be a left $mathcal{a}$-module‎, ‎and $w$ in $mathcal{z}(mathcal{a})$ be a left separating point of $mathcal{m}$‎. ‎we show that if $mathcal{m}$ is a unital left $mathcal{a}$-module and $delta$ is a linear mapping from $mathcal{a}$ into $mathcal{m}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a jordan left de...

results 12 (14.8%) patients had positive results for both hdv rna and anti-hdv. the mean alt level was higher in hdv positive patients (75.9 u/ml) than hbv-mono-infected individuals; however, the mean hbv viral load was lower in coinfected patients than hbv-mono-infected patients. phylogenetically, genotype i was the only detected genotype, and the most closely related isolates were of turkish,...

The view of artificial neural networks as adaptive systems has lead to the development of ad-hoc generic procedures known as learning rules. The first of these is the Perceptron Rule (Rosenblatt, 1962), useful for single layer feed-forward networks and linearly separable problems. Its simplicity and beauty, and the existence of a convergence theorem made it a basic departure point in neural lea...

We develop a stochastic approximation-type algorithm to solve finite state/action, infinite-horizon, risk-aware Markov decision processes. Our has two loops. The inner loop computes the risk by solving saddle-point problem. outer performs $Q-$ learning compute an optimal policy. Several widely investigated measures (e.g., conditional value-at-risk, optimized certainty equivalent, and absolute s...

Let $G=(V,E)$, $V={1,2,ldots,n}$, $E={e_1,e_2,ldots,e_m}$,be a simple connected graph, with sequence of vertex degrees$Delta =d_1geq d_2geqcdotsgeq d_n=delta >0$ and Laplacian eigenvalues$mu_1geq mu_2geqcdotsgeqmu_{n-1}>mu_n=0$. Denote by $Kf(G)=nsum_{i=1}^{n-1}frac{1}{mu_i}$ and $t=t(G)=frac 1n prod_{i=1}^{n-1} mu_i$ the Kirchhoff index and number of spanning tree...

We study the elliptic equation with a line Dirac delta function as source term subject to Dirichlet boundary condition in two-dimensional domain. Such measure causes different types of solution singularities neighborhood fracture. establish new regularity results for class weighted Sobolev spaces and propose finite element algorithms that approximate singular at optimal convergence rate. Numeri...

Abstract We study pointwise convergence of the fractional Schrödinger means along sequences $t_{n}$ t n that converge to zero. Our main result is bounds on maximal function $\sup_{n} |e^{it_{n}(-\Delta )^{\alpha /2}} f| $ sup | <mml:msu...