For a fixed SL(3,Z) Maass form φ, we consider the family of L-functions L(φ× uj, s) where uj runs over the family of Hecke-Maass cusp forms on SL(2,Z). We obtain an estimate for the second moment of this family of L-functions at the special points 1 2 + itj consistent with the Lindelöf Hypothesis. We also obtain a similar upper bound on the sixth moment of the family of Hecke-Maass cusp forms a...

Abstract This paper investigates the spatial behavior of the solutions of the Laplace equation on a semi-infinite cylinder when dynamical nonlinear boundary conditions are imposed on the lateral side of the cylinder. We prove a Phragmén-Lindelöf alternative for the solutions. To be precise, we see that the solutions increase in an exponential way or they decay as a polynomial. To give a complet...

We continue Mizar formalization of general topology according to the book [16] by Engelking. In the article, we present the final theorem of Section 4.1. Namely, the paper includes the formalization of theorems on the correspondence between the cardinalities of the basis and of some open subcover, and a discreet (closed) subspaces, and the weight of that metrizable topological space. We also de...

In [23], Todorcevic gives a survey of basis problems in combinatorial set theory, listing nine theorems and six working conjectures — all in the presence of PFA — including the following three of interest to us here: Conjecture 1 (Todorcevic; [23]). If R is a binary relation, then either R ≤ א0 ·ω1 or [ω1]0 ≤ R. Conjecture 2 (Hajnal, Juhasz; [5]). If X is a regular Hausdorff space, then the fol...

In this paper, we have dened and studied a generalized form of topological vector spaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is proved that every s-topological vector space is generalized homogeneous space. Every open subspace of an s-topological vector space is...

We give some necessary and sufficient conditions for the character of spaces to be preserved under closed maps. Introduction. Recall the following result due to K. Morita and S. Hanai [11] or A. H. Stone [14]: Let Y be the image of a metric space X under a closed map/. Then Y is first countable (or metrizable) if and only if every boundary df~x(y) of the point-inverse/"'^) is compact. E. Michae...

Let (G, u) be an Archimedean norm-complete dimension group with order-unit. Continuing a previous paper, we study intervals (i.e., nonempty upward directed lower subsets) of G which are closed with respect to the canonical norm of (G, u). In particular, we establish a canonical one-to-one correspondence between closed intervals of G and certain affine lower semicontinuous functions on the state...