We study the real components of modular curves. Our main result is an abstract group-theoretic description of the real components of a modular curve defined by a congruence subgroup of level N in terms of the corresponding subgroup of SL2(Z/NZ). We apply this result to several families of modular curves (such as X0(N), X1(N), etc.) to obtain formulas for the number of real components. Somewhat ...

in this paper, photovoltaic (pv) grid-connected inverter which is the core device in pv grid-connected system has been in depth research.an improved predictive current controller has been developed by the authors for single-phase grid-connected voltage source inverters (vsi).based on dsp tms320lf2407a, a 10 kw single-phase grid-connected inverter has been built in this paper.thus is aimed at us...

We consider the linearization of the three-dimensional water waves equation with surface tension about a flat interface. Using oscillatory integral methods, we prove that solutions of this equation demonstrate dispersive decay at the somewhat surprising rate of t−5/6. This rate is due to competition between surface tension and gravitation at O(1) wave numbers and is connected to the fact that, ...

For any two graphs G and H Lovász has defined a cell complex Hom (G,H) having in mind the general program that the algebraic invariants of these complexes should provide obstructions to graph colorings. Here we announce the proof of a conjecture of Lovász concerning these complexes with G a cycle of odd length. More specifically, we show that If Hom (C2r+1, G) is k-connected, then χ(G) ≥ k + 4....

Having consented to read a paper on Plague, it occurred to me that the occasion would be a fitting one for obtaining the benefit of the opinion of the Society on several questions connected with the epidemiology of Plague, which are somewhat obscure, and which are deserving of discussion. To begin with : there is the comparatively rapid retrogression of Plague from Western Europe in the latter ...

The Pb(II) atom in the title compound, [Pb(C(10)H(6)NO(2))(2)], is N,O-chelated by two quinoline-2-carboxyl-ate anions in a distorted Ψ-trigonal-bipyramidal environment; four atoms are connected to the Pb(II) atom by regular coordination bonds. The structure also features two somewhat long Pb⋯O inter-actions [2.952 (3) and 3.014 (3) Å]. These long inter-actions give rise to a layer coordination...

In this paper we propose a topological data structure for quadtrees, TopQT. This data structure is somewhat different from others very common in cell-complexes representations such as the famous half-edge. In the main result of this paper, we show that given a cell in the quadtree, TopQT is able to find all four connected neighbor cells in constant time. We give some pseudo algorithms to explai...