p-adic MRA and GMRA are important tools for constructing wavelet frames in L2(R+). That a nested subspace sequence in L2(R+) has trivial intersection and L2(R+) union is a fundamental requirement for it to form a p-adic MRA and GMRA. This paper addresses the intersection and union of p-adic dilates of a singly generated p-adic shift-invariant subspace. We prove that, for a singly generated p-adic shift-invariant subspace, the intersection of its p-adic dilates is 0, and the union of its p-adic dilates is a Walsh p-adic reducing subspace of L2(R+) if the generator φ is Walsh p-adic refinable in addition. In particular, the dilates form a p-adic GMRA for L2(R+) if and only if ∪j∈Zpjsupp(Fφ)=R+, where F is the Walsh p-adic Fourier transform on L2(R+). It is worth noticing that our results are similar to the case of usual L2(R), while their proofs are nontrivial. It is because the p-adic addition ⊕ on R+ is different from the usual addition + on R.
We prove that every nonlinear mixed Lie triple derivable mapping from any factor von Neumann algebra A into itself is an additive *-derivation, with the classical derivable mapping and matrix block.
We consider the asymptotic behavior of non-autonomous stochastic fractional wave equations on an unbounded domain Rn. We firstly transform the equation into a random equation whose solutions generate a random one system. Then we establish the asymptotical compactness of the system by the splitting technique. Finally the existence of random attractors is proved.
We first discuss two special quasi-cyclic modules over principal ideal domains and then investigate the structures of vector spaces of finite A-width. We show that the poset of A-invariant subspaces of a vector space of finite A-width must satisfy the minimal condition, and give a sufficient and necessary condition for a vector space (as a F[λ]-module) to be a quasi-cyclic module.
Let λ1, λ2, λ3, λ4 be non-zero real numbers, not all negative, and let λ1/λ2 be irrational and algebraic. Let V be a well-spaced sequence and δ > 0. We prove that for any given ε > 0, the number of v satisfying v ∈ V and v ≤ X for which|λ1p12+λ2p22+λ3p33+λ4p43-v|<v-δ has no solution in primes p1, p2, p3, p4 does not exceed O(X7/8+2δ+ε). This gives an improvement of an earlier result.
We explicitly compute the first and second cohomology groups of the Super Schrödinger algebra J (1/1) with coefficients in the trivial module and the finitedimentional irreducible modules. We also show that the first and second cohomology groups of J (1/1) with coefficients in the universal enveloping algebras U(J (1/1)) (under the adjoint action) are infinite dimensional.
Let H4 be the Sweedler's 4-dimensional Hopf algebra. In this paper by the definition and property of Rota-Baxter operator, we establish the system of quadratic equations of the matrix elements of Rota-Baxter operators of H4 with weight λ for a given base. By solving the system of the equations with weight λ=0 and λ=1 the matrix forms of Rota-Baxter operators are given.Keywords Sweedler's algebra; weight; Rota-Baxter algebra
We propose a joint modeling approach for the analysis of recurrent event data with a terminal event, where an additive-multiplicative rates model is specified for the recurrent event process, the Cox hazards frailty model is specified for the terminal event, and the shared frailty is used to account for the association between the two processes. An estimating equation approach is developed for estimating the model parameters. The asymptotic properties of the proposed estimators are established. Simulation studies are constructed to examine performances of the proposed estimators under finite samples. Finally, we use the proposed method to analyze a medical cost study of chronic heart failure patients.Keywords additive-multiplicative rates model; estimating equation; frailty; recurrent event; terminal event
Partially linear additive panel data models with strong interpretability and flexibility have been widely used in a variety of research fields. Considered a fixed effects partially linear additive panel data model with correlation structure within subjects, we derived the estimators by using penalized quadratic inference functions method under the basis of combining exponential spline function and LSDV method; the asymptotic normality of parametric estimators and convergence of nonparametric estimators were proved under suitable regular conditions; Monte Carlo simulations show that our estimates have good performances in small sample cases; meanwhile, the estimation techniques were used to analyse a real data set.
In this paper, using theory of value distribution, we investigate whether a class of order n complex differential-difference equation
ω(n)(z)2 +[αω(z + c) - βω(z)]2=1
and a class of systems of order n complex differential-difference equations
have entire solutions with finite order or not. Our results extend and improve the results due to Gao Lingyun and Liu Kai et al.
In this paper, we study the analytical solutions for the extended generalized two-component Dullin-Gottwald-Holm shallow water system. By the resulting of Emden equation, we investigate the global existence and finite-time blowup phenomena. Furthermore, the perturbation method and characteristic method are used to construct two types of exact solutions for this system.
Let A be an abelian category and X a subcategory of A. Sather-Wagstaff, Sharif and White introduced the Gorenstein subcategory G (X). Denote by PP the class of pure-projective R-modules and by P the class of projective R-modules. We show that there are some rings such that G (P) ⊆ G(PP), which gives a negative answer to the Question that whether G (W) is contained in G (X) provided that W is a subcategory of X. In addition, we give some characterizations of when G (P) ⊆ G (PP) and G (PP) ⊆ G (P) hold.
We investigate a scalarizing function's continuity and convexity under K-conditions. Utilizing that function, we convert set-valued optimization problems into equilibrium problems, and then study existence of efficient solutions of set-valued optimization problems with constraints, the upper semicontinuity and lower semicontinuity of strongly approximate solution mappings to the parametric set-valued optimization problems. As compared with relevant literatures, our methods are new, our conclusions and conditions are more general.
We study univalent functions f for which log f' belongs to the analytic Morrey spaces. We establish some new characterizations of the analytic Morrey domains.