The massive 3-loop fermion-loop corrections $\propto C_A N_f T_F^2$ and $C_F N_f T_F^2$ to the massive operator matrix elements $A_{Qg}$, $A_{Qq}^{\rm{PS}}$, $A_{qq,Q}^{\rm{PS}}$, $A_{qq,Q}^{\rm{NS}}$ and $A_{qq,Q}^{\rm{NS,TR}} have been obtained for general values of $N$. Thereby the corresponding contributions to the asymptotic heavy flavor Wilson coefficients of the structure function $F_2(x...

Abstract In this paper we provide non-smooth atomic decompositions of 2-microlocal Besov-type and Triebel–Lizorkin-type spaces with variable exponents $$B^{\varvec{w}, \phi }_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ B p ( · ) <mm...

The radio k-chromatic number $$rc_k(G)$$ of a graph G is the minimum integer $$\lambda $$ such that there exists function $$\phi : V(G) \rightarrow \{0,1,\cdots , \lambda \}$$ satisfying $$|\phi (u)-\phi (v)| \ge k+1 - d(u,v)$$ where d(u, v) denotes distance between u and v. To date, several upper lower bounds $$rc_k(\cdot )$$ established for different families. One most notable works in this d...

In the setting of non-type $\ty{II_1}$ representations, we propose a definition {\it deformed Fredholm module} $\big[D_\ct|D_\ct|^{-1}\,,\,{\bf\cdot}\,\big]_\ct$ for modular spectral triple $\ct$, where $D_\ct$ is Dirac operator. assumed to be invertible sake simplicity, and its domain an "essential" operator system $\ce_\ct$. According such definition, obtain $\big[D_\ct|D_\ct|^{-1}\,,\,{\bf\c...

The purpose of this paper is 1 a general nonlinear mixed set-valued inclusion framework for the over-relaxedA-proximal point algorithm based on the A, η -accretive mapping is introduced, and 2 it is applied to the approximation solvability of a general class of inclusions problems using the generalized resolvent operator technique due to Lan-Cho-Verma, and the convergence of iterative sequences...

In this paper, an iterative algorithm for finding a common point of the set of zeros of an accretive operator and the set of fixed points of a nonexpansive mapping is considered in a uniformly convex Banach space having a weakly continuous duality mapping. Under suitable control conditions, strong convergence of the sequence generated by proposed algorithm to a common point of two sets is estab...

The purpose of this paper is to study a strong convergence of multi-step iterative scheme to a common solution for a finite family of strongly accretive operator equations in a reflexive Banach space with weakly continuous duality map. As a consequence, the strong convergence theorem for the multi-step iterative sequence to a common fixed point for finite family of strongly pseudocontractive ma...

We prove an existence result for 7"-periodic mild solutions to nonlinear evolution equations of the form u(t) + Au(t) BF(t, u(t)) , t€R+. y Here (X, \\-\\) is a real Banach space, A: D(A) C X —> 2 is an operator with A — a! m-accretive for some a > 0 and such that -A. generates a compact semigroup, while F: R+ x D(A) —► X is a Carathéodory mapping which is T-periodic with respect to its first a...

In this work, we study the radiative and strong decay of $S$-wave $K\bar{K}_1(1400)$ molecular state within effective Lagrangians approach find relation between newly observed $\eta_1(1855)$ by comparing with BESIII observation. The prediction indicates that width can reach up to $182.97^{+2.79}_{-3.50}$ MeV, which be confronted experimental data. If could state, $K\bar{K}^{*}\pi$ three-body pr...