Parasitic twins, a specific type of conjoined twins [6], occur when one twin ceases development during gestation [7] and becomes vestigial to the fully formed dominant twin, called the autositic twin. The underdeveloped twin is called parasitic because it is only partially formed, is not functional, or is wholly dependent on the autositic twin. In most cases, the phenotype of parasitic twins is...

The literature surrounding the Bell numbers is vast: see, for example, Comtet [1, Chapter 5]. Close cousins of the Bell numbers are the Uppuluri-Carpenter numbers (sometimes called the complementary Bell numbers); they count the excess of the number of set partitions of {1, . . . , n} into an even number of blocks over the number of partitions into an odd number of blocks. They are the integer ...

The purpose of this note is to propose and motivate a conjecture on the behavior of cohomological support loci for topologically trivial line bundles under derived equivalence, to verify it in the case of surfaces, and to explain further developments. The reason for such a conjecture is the desire to understand the relationship between the cohomology groups of (twists of) the canonical line bun...

We consider a family of slightly extended version of the Raynaud’s surfaces X over the field of positive characteristic with Mumford-Szpiro type polarizations Z, which have Kodaira non-vanishing H(X,Z) 6= 0. The surfaces are at least normal but smooth under a special condition. We compute the cohomologies H(X,Z) for i, n ∈ Z and study their (non-)vanishing. Finally, we give a fairly large famil...

when 0 < k ≤ p. We will say that a smooth projective variety X has Bott vanishing if for every ample line bundle L, i > 0 and j H(X,ΩjX ⊗ L) = 0 The purpose of this paper is to show that Bott vanishing is a simple consequence of a very specific condition on the Frobenius morphism in prime characteristic p. Recall that the absolute Frobenius morphism F : X → X on X, where X is a variety over Z/p...

This paper describes a method of interpreting three dimensional motion of an object by making use of r i g i d i t y assumption and orientation of i t s edge. We employ a vanishing point to determine the orientat ion. We propose a new idea of using cross ra t i o , i .e . one of the most fundamental concepts in projective geometry to f ind a vanishing point of a l ine . This allows to calculate...

The planar polynomial vector fields with a center at the origin can be written as an scalar differential equation, for example Abel equation. If the coefficients of an Abel equation satisfy the composition condition, then the Abel equation has a center at the origin. Also the composition condition is sufficient for vanishing the first order moments of the coefficients. The composition conjectur...

A finite element scheme for an entirely fractional Allen–Cahn equation with non-smooth initial data is introduced and analyzed. In the proposed nonlocal model, Caputo in-time derivative Laplacian replace standard local operators. Piecewise linear elements convolution quadratures are basic tools involved in presented numerical method. Error analysis implementation issues addressed together neede...

Abstract. This article is devoted to the study of the finite element approximation for a nonlocal nonlinear parabolic problem. Using a linearised Crank-Nicolson Galerkin finite element method for a nonlinear reaction-diffusion equation, we establish the convergence and error bound for the fully discrete scheme. Moreover, important results on exponential decay and vanishing of the solutions in f...

Horn recursion is a term used to describe when non-vanishing products of Schubert classes in the cohomology of flag varieties G/P are characterized by inequalities parameterized by similar non-vanishing products in the cohomology of “smaller” flag varieties. We consider the partial flag variety SLn/P and find that H ∗(SLn/P ) exhibits Horn recursion on a certain deformation of the cup product. ...