Let $p(x)$ be a nondecreasing real-valued continuous function
 on $R_+:=[0,\infty)$ such that $p(0)=0$ and $p(x) \to \infty$ as $x \infty$.
 Given real or complex-valued integrable function $f$ in Lebesgue's sense every bounded interval $(0,x)$
 for $x>0$, symbol $f \in L^1_{loc} (R_+)$, we set
 $$
 s(x)=\int _{0}^{x}f(u)du
 and
 \sigma _{p}(s(x))=\frac{1}{...

Let F be a distribution inD′ and let f be a locally summable function. The composition F f x of F and f is said to exist and be equal to the distribution h x if the limit of the sequence {Fn f x } is equal to h x , where Fn x F x ∗ δn x for n 1, 2, . . . and {δn x } is a certain regular sequence converging to the Dirac delta function. In the ordinary sense, the composition δ s sinh−1x r does no...

in this research, a two-phase algorithm based on the artificial neural network (ann) and a harmony search (hs) algorithm has been developed with the aim of assessing the reliability of structures with implicit limit state functions. the proposed method involves the generation of datasets to be used specifically for training by finite element analysis, to establish an ann model using a proven an...

capacity of a road facility as an important characteristic in transportation and traffic studies is defined as the maximum rate of flow that could be held by that facility, which has been supposed to have a constant and certain value. this assumption, although necessary for most traffic studies, has also caused some problems, like that of demand exceeding capacity in many road facilities. resea...

Let A = (ank)∞n,k=1 be an infinite matrix and x = (xk) ∞ k=1 a sequence of real or complex numbers. Then the A-transform of x is a sequence Ax = (An(x))where An(x) = ∑ ∞ k=1 ankxk provided that the series converges for each n; and the sequence x is said to be A-summable if Ax is convergent. In this paper we define statistical A-summability of x, that is, x is said to be statistically A-summable...

In functional analysis the notion of a summable family (with sum x) is well-known. If (x i) i2I is a family of points from a normed space, (x i) is called summable to x ii for each " > 0 there exits a nite set F 0 I such that kx ? P i2F x i k < " for each nite set F, F 0 F I. But we can interprete this deenition as the convergence of a suitable net. In a normed commutative group we characterize...

We provide an overview of the tools and techniques resurgence theory used in Borel-Ecalle resummation method, which we then apply to massless Wess–Zumino model. Starting from already known results on anomalous dimension model, solve its renormalisation group equation for two-point function a space formal series. show that this solution is 1-Gevrey Borel transform resurgent. The Schwinger–Dyson ...

In this paper, we first introduce the notion of summability of an infinite set of vectors of real Hilbert space, without using index sets. Further we introduce the notion of weak summability, which is weaker than that of summability. Then, several statements for summable sets and weakly summable ones are proved. In the last part of the paper, we give a necessary and sufficient condition for sum...

This paper considers ergodicity properties of certain adaptive Markov chain Monte Carlo (MCMC) algorithms for multidimensional target distributions, in particular Adaptive Metropolis and Adaptive Metropoliswithin-Gibbs. It was previously shown by Roberts and Rosenthal (2007) that Diminishing Adaptation and Containment imply ergodicity of adaptive MCMC. We derive various sufficient conditions to...