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1.1. The simplicial localization. The localization of a category C with respect to a subcategory W is the category C[W-‘1 which has the same objects as C and is obtained from C by formally inverting the maps of W. Our purpose here is to show that C[W-‘1 reflects just one aspect of a much richer object, the simplicial localization LC. This simplicial localization LC is a simplicial category with...

In this paper we will prove bounds for the fourth power moment in the t aspect over a short interval of automorphic L-functions L(s, g) for GL(2) on the central critical line Re s = 1/2. Here g is a fixed holomorphic or Maass Hecke eigenform for the modular group SL2(Z), or in certain cases, for the Hecke congruence subgroup Γ0(N ) with N > 1. The short interval is from a large K to K + K103/13...

We give an elementary, self-contained, and purely combinatorial proof of the Rayleigh monotonicity property of graphs. Consider a (linear, resistive) electrical network – this is a connected graph G = (V,E) and a set of positive real numbers y = {ye : e ∈ E} indexed by E. In this paper we allow graphs to have loops and/or multiple edges. The value of ye is interpreted as the electrical conducta...

Yielding elements (YE) are among those devices that not only help control structural damages, but make better seismic behavior by concentrating the frames in some removable part of the structures. YE are located at the intersection of Concentric Braced Frame (CBF) in a rectangular shape. In this paper, Seismic behavior of the frames with YE will be investigated. For this reason, 5 braced steel ...