Double Biproduct Hom-Bialgebra and Related Quasitriangular Structures

Let(H, β) be a Hom-bialgebra such that β~2= id_H.(A, α_A) is a Hom-bialgebra in the left-left Hom-Yetter-Drinfeld category (_H~H)YD and(B, α_B) is a Hom-bialgebra in the right-right Hom-Yetter-Drinfeld category YD_H~H. The authors define the two-sided smash product Hom-algebra(A■H■B, α_A ? β ? α_B) and the two-sided smash coproduct Homcoalgebra(A◇H◇B, α_A ? β ? α_B). Then the necessary and sufficient conditions for(A■H■B, α_A ? β ? α_B) and(A◇H◇B, α_A ? β ? α_B) to be a Hom-bialgebra(called the double biproduct Hom-bialgebra and denoted by(A_◇~■H_◇~■B, α_A ? β ? α_B)) are derived. On the other hand, the necessary and sufficient conditions for the smash coproduct Hom-Hopf algebra(A◇H, α_A ? β) to be quasitriangular are given.     

Extension Principle and α-upper (α-lower) Fuzzy Set Category

In this paper the definitions of class of α-upper (resp. α-lower) fuzzy sets andweak extension principle and α-upper (resp. α-lower) fuzzy set category are givenand rationality of weak extension priuciple is illustrated. By the way we popularizeTheorem 2.3 in [1]. Let L be a complete lattice, 0 and 1 respectively the least and the greatestelement of L.     

CALCULATION OF α_3 COEFFICIENT OF SCALAR FIELD BY POINT SEPARATION METHOD

The α_3 coefficient of scalar field in arbitrary Riemann space-time background is calculated by point separation method in this article. The primary expression of α_3 involves 25 invariants. Using the identities derived in the appendix, we can reduce α_3 from 25 invariants to 17 invariants which agree with Gilkey's formula for α_s coefficient of the scalar field derived by geometric methods and reasons. Recently we derived two important invariant identilies, using these identities we can reduce α_3 from 17 invariants to 15 invariants which would much simplify the calculation of the energymomentum tensor of vacuum polarization.     

全平面上Laplace-Stieltjes变换所表示整函数的增长性（英文）

In the paper, the α-order of the Laplace-Stieltjes Transform is introducedfirstly, then we get the relationship between α-order represented by the maximum modulus and α-order represented by A_n^*, λ_n. Lastly, we obtain the relationship between type τrepresented by the maximum modulus and type τ represented by A_n^*, λ_n.     

斜Armendariz矩阵环

Let R be a ring.We show in the paper that the subring Un(R) of the upper triangular matrix ring Tn(R) is α-skew Armendariz if and only if R is α-rigid,also it is maximal in some non α-skew Armendariz rings,where α is a ring endomorphism of R with α(1) = 1.     

FROM REAL TO NONREAL SIGN PATTERN MATRICES

We extend some fundamental concepts of qualitative matrix analysis from sign patternclasses of real matrices to sign pattern classes of nonreal matrlces.Given two angles α≤β,we define a sector in the complex plane to be the set of allnonzero complex numbers whose arguments are in the interval from αto β.H α<β,theinterval could be closed,open,or half-open.Whenever α=β,the sector becomes a ray,     

α-TRANSIENCE AND α-RECURRENCE FOR RANDOM WALKS AND LEVY PROCESSES

The authors investigate the α-transience and α-recurrence for random walks and Levy processes by means of the associated moment generating function, give a dichotomy theorem for not one-sided processes and prove that the process X is quasi-symmetric if and only if X is not α-recurrent for all α< 0 which gives a probabilistic explanation of quasi-symmetry, a concept originated from C. J. Stone.     

On Skew Triangular Matrix Rings

Let α be a nonzero endomorphism of a ring R, n be a positive integer and T_n(R, α) be the skew triangular matrix ring. We show that some properties related to nilpotent elements of R are inherited by T_n(R, α). Meanwhile, we determine the strongly prime radical, generalized prime radical and Behrens radical of the ring R[x; α]/(x~n), where R[x; α] is the skew polynomial ring.     

Weighted Composition Operators from α-Bloch Spaces to H^∞

The article not only presents the boundedness and compactness of the weighted composition operator from α-Bloch spaces（or little α-Bloch spaces） to H^∞, but also gives some estimates for the norm of the weighted composition operator.     

On Affine Hypersurfaces with Parallel Cubic Form Relative to Affine α-connection

Similar to Nomizu-Pinkall’s geometric characterization of the Cayley surface and Hu-Li-Zhang’s characterization of the Cayley hypersurface,how can one characterize the generalized Cayley hypersurfaces?In this paper,by the affine α-connection of statistical manifolds,we study affine hypersurfaces with parallel cubic form relative to the affine α-connection.As the main results,we complete the classification of such hypersurfaces if its affine metric is either definite,or Lorentzian with α≠-1.Moreo...