A Note on Solvability of the Nonlinear Abstract Viscoelastic Problem in Banach Spaces

In this work we are concerned with the existence of integral solution for a nonlinear abstract viscoelastic problem in Banach space, where the operator is accretive dependent on time.     

${[\ell_p]}_{e.r}$ Euler-Riesz Difference Sequence Spaces

Başar and Braha [1], introduced the sequence spaces $\breve{\ell}_\infty$, $\breve{c}$ and $\breve{c}_0$ of Euler-Cesáro bounded, convergent and null difference sequences and studied their some properties. Then, in [2], we introduced the sequence spaces ${[\ell_\infty]}_{e.r}, {[c]}_{e.r}$ and ${[c_0]}_{e.r}$ of Euler-Riesz bounded, convergent and null difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. The main purpose of this study is to introduce the sequence space ${[\ell_p]}_{e.r}$ of Euler-Riesz $p-$absolutely convergent series, where $1 \leq p <\infty$, difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. Furthermore, the inclusion $\ell_p\subset{[\ell_p]}_{e.r}$ hold, the basis of the sequence space ${[\ell_p]}_{e.r}$ is constructed and $\alpha-$, $\beta-$ and $\gamma-$duals of the space are determined. Finally, the classes of matrix transformations from the ${[\ell_p]}_{e.r}$ Euler-Riesz difference sequence space to the spaces $\ell_\infty, c$ and $c_0$ are characterized. We devote the final section of the paper to examine some geometric properties of the space ${[\ell_p]}_{e.r}$.     

Strong Converse Inequality for the Meyer-König and Zeller-Durrmeyer Operators

In this paper we give a strong converse inequality of type B in terms of unified $K$-functional $K^α_λ (f, t^2) (0 ≤ λ ≤ 1, 0 < α < 2)$ for the Meyer-König and Zeller-Durrmeyer type operators.     

Reducing Subspaces of Toeplitz Operators on $N_ϕ$-Type Quotient Modules on the Torus

In this paper, we prove that the Toeplitz operator with finite Blaschke product symbol $S_{ψ(z)}$ on $N_ϕ$ has at least $m$ non-trivial minimal reducing subspaces, where $m$ is the dimension of $H^2(Γ_ω) ⊖ ϕ(ω)H^2 (Γ_ω)$. Moreover, the restriction of $S_{ψ(z)}$ on any of these minimal reducing subspaces is unitary equivalent to the Bergman shift $M_z$.     

REPRESENTATION OF GENERALIZED TRANSLATIONS OF THE PRODUCT OF TWO FUNCTIONS ON SIGNED HYPERGROUPS ON THE REAL LINE

In this paper,we consider the generalized translations associated with the Dunkl and the Jacobi-Dunkl differential-difference operators on the real line which provide the structure of signed hrpergroups on R.Especially,we study the representation of the generalized translations of the product of two functions for these signed hypergroups.     

利用具有非常规插入场的QCD求和规则计算核子张量荷

利用外张量场下的QCD求和规则计算了核子张量荷,其中核子插入场的核子流算符取最一般形式或称为非常规型,计算包括至维度8的项的贡献.详细分析了不同核子插入场及张量磁化率对计算核子张量荷求和规则的影响.计算表明,改变核子插入场及张量磁化率仍不能得到求和规则的稳定解,但如取最佳插入场的形式,对同位旋矢量和同位旋标量的求和规则解的稳定性有所改善.给出了在通常的对核子“QCD求和规则窗口”标度下核子张量荷的平均值.     

相干态统计特性的弱测量结构研究

理论分析相干态位移参数估计在弱测量方法下的放大效应.引入偏振态作为附属态(Ancilla States),分别进行初选择和后选择,中间的相互作用采用了偏振相关的弱位移操作算符.通过最后检测光子数的分布来估计位移参数;在牺牲检测光子强度的情况下可以有效提高放大效应.