Let T be a Noetherian ring and f a nonzerodivisor on T . We study concrete necessary and sufficient conditions for a module over R = T/(f) to be weakly liftable to T , in the sense of Auslander, Ding and Solberg. We focus on cyclic modules and get various positive and negative results on the lifting and weak lifting problems. For a module over T we define the loci for certain properties: liftab...

A function f :R → {0, 1} is weakly symmetric (weakly symmetrically continuous) at x ∈ R provided there is a sequence hn → 0 such AMS classification numbers: Primary 26A15; Secondary 03E50, 03E35.

1. Preliminaries. Let X be the class of compact 1 connected semisimple Lie groups; 3C'C3C is the following set of groups, Sp(w), SU(w), Spin(w), G2, F*, EQ, E7, Es, U*(X) the weakly complex bordism of X [ l ] and A the ring U*(pt) = Z[Fi , F2, • • • ]. A is the weakly complex bordism ring defined by Milnor. The generators F,are weakly complex manifolds of dim 2i. The bordism class of a weakly c...

In this paper, we prove an existence theorem for the pseudo-nonlocal Cauchy problem x′(t) + Ax(t) = f(t, x(t), ∫ t t0 k(t, s, x(s))ds), x0(t0) = x0−g(x), where A is the infinitesimal generator of a C0 semigroup of operator {T (t)}t>0 on a Banach space. The functions f, g are weakly-weakly sequentially continuous and the integral is taken in the sense of Pettis.

We define traces associated to a weakly holomorphic modular form f of arbitrary negative even integral weight and show that these traces appear as coefficients of certain weakly holomorphic forms of half-integral weight. If the coefficients of f are integral, then these traces are integral as well. We obtain a negative weight analogue of the classical Shintani lift and give an application to a ...

For this paper we assume familiarity with the basics of the theory of modular forms as may be found, for instance, in Serre’s classic introduction [12]. A weakly holomorphic modular form of weight k ∈ 2Z for Γ = PSL2(Z) is a holomorphic function f on the upper half-plane that satisfies f( cτ+d ) = (cτ + d)f(τ) for all ( a b c d ) ∈ Γ and that has a q-expansion of the form f(τ) = ∑ n≥n0 a(n)q , ...

We study the weak* lower semicontinuity properties of functionals of the form F (u) = ess sup x∈Ω f(x,Du(x)) where Ω is a bounded open set of R and u ∈ W 1,∞(Ω). Without a continuity assumption on f(·, ξ) we show that the supremal functional F is weakly* lower semicontinuous if and only if it is a level convex functional (i.e. it has convex sub levels). In particular if F is weakly* lower semic...

in this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. we prove that if $n$ is a weakly prime subtractive ternary subsemimodule of a ternary $r$-semimodule $m$, then either $n$ is a prime ternary subsemimodule or $(n : m)(n : m)n = 0$. if $n$ is a $q$-...

For a countable, weakly minimal theory T , we show that the SchröderBernstein property (any two elementarily bi-embeddable models are isomorphic) is equivalent to each of the following: 1. For any U -rank-1 type q ∈ S(acl(∅)) and any automorphism f of the monster model C, there is some n < ω such that f(q) is not almost orthogonal to q ⊗ f(q)⊗ . . .⊗ fn−1(q); 2. T has no infinite collection of ...

In this paper we study the log structures on generalized semistable varieties, generalize the result by F. Kato and M. Olsson, and prove the canonicity of log structure when it can be expected. In out text we first give the definitions of local chart and weakly normal crossing morphism. Then we study the invariants of complete noetherian local ring coming from weakly normal crossing morphisms. ...