A shuffling theorem for reflectively symmetric tilings

The author and Rohatgi recently proved a ‘shuffling theorem’ for doubly-dented hexagons. In particular, they showed that shuffling removed unit triangles along a horizontal axis in a hexagon changes the tiling number by only a simple multiplicative factor. In this paper, we consider a similar phenomenon for a symmetry class of tilings, namely, the reflectively symmetric tilings. We also prove several shuffling theorems for halved hexagons.     

Some Examples of Nonhypoelliptic Infinitely Degenerate Elliptic Differential Operators

This paper contains examples of nonhypoelliptic infinitely degenerate elliptic differential operators. Global nonsmooth solutions of the corresponding homogeneous equations are constructed.     

Non-linear eigenvalue problems for <Emphasis Type="Italic">p</Emphasis>-Laplacian with variable domain

In this work we consider some eigenvalue problems for p-Laplacian with variable domain. Eigenvalues of this operator are taken as a functional of the domain. We calculate the first variation of this functional, using the obtained formula investigate behavior of the eigenvalues when the domain varies. Then we consider one shape optimization problem for the first eigenvalue, prove the necessary condition of optimality relatively domain, offer an algorithm for the numerical solution of this problem.     

Semilinear perturbation of powers of the mizohata operators

ABSTRACT

We study the Cauchy Problem associated to a class of quasilinear Schrödinger equations which have been derived as models of several physical phenomenas. We prove local existence in arbitrary space dimension N without any smallness condition on the initial data.     

General one-loop formulas for $$H\rightarrow f\bar{f}\gamma $$ H → f f ¯ γ and its applications

The European Physical Journal C - Considering supergravity theory is a natural step in the development of gravity models. This paper follows the “algebraic“ path and constructs possible...     

An expedient synthesis of the fibril binding compound FSB via sequential Pd-catalyzed coupling reactions

The styryl benzene derivative (E, E)-1-fluoro-2,5-bis(3-hydroxycarbonyl-4-hydroxy)styrylbenzene (FSB), well-known for its binding to beta-amyloid peptide fibrils, was synthesized in an efficient manner exploiting two sequential palladium(0)-catalyzed coupling reactions in a 34% overall yield. This is a substantial improvement to the previously reported synthesis of FSB in 1.1%.     

Chemical constituents from the leaves of Manglietia phuthoensis and their effects on osteoblastic MC3T3-E1 cells

Two new phenyl glycosides, mangliesides A and B (1, 2), a new ionol glycoside, manglieside C (3), two new lignan glycosides, mangliesides D and E (4, 5), were isolated from the leaves of Manglietia phuthoensis, along with two known lignans, 3-methoxymagnolol (6) and obovatol (7). Their structures were established by means of 1D and 2D NMR, electrospray ionization (ESI)-MS and HR-ESI-MS experiments. Among them, compounds 2 and 5 significantly (p<0.05) increased the growth and differentiation of osteoblastic MC3T3-E1 cells in vitro.