Let X be a smooth projective variety of dimension n over an algebraically closed field k with char(k) = p > 0 and F : X → X1 be the relative Frobenius morphism. For any vector bundle W on X , we prove that instability of F∗W is bounded by instability of W ⊗ T(Ω X ) (0 ≤ l ≤ n(p − 1))(Corollary 4.8). When X is a smooth projective curve of genus g ≥ 2, it implies F∗W being stable whenever W is st...

This exposition explains the basic ideas of Stein’s method for Poisson random variable approximation and Poisson process approximation from the point of view of the immigration-death process and Palm theory. The latter approach also enables us to define local dependence of point processes [Chen and Xia (2004)] and use it to study Poisson process approximation for locally dependent point process...

The cutwidth of a graph G is defined to be the smallest integer k such that the vertices of G can be arranged in a vertex ordering [v1, . . . , vn] in a way that, for every i = 1, . . . , n−1, there are at most k edges with the one endpoint in {v1, . . . , vi} and the other in {vi+1, . . . , vn}. We examine the problem of computing in polynomial time the cutwidth of a partial w-tree with bounde...

We develop an approach to fabricate monodisperse water-in-water-in-water (w/w/w) double emulsion in microfluidic devices. A jet of aqueous solution containing two incompatible solutes, dextran and polyethylene glycol (PEG), is periodically perturbed into water-in-water (w/w) droplets. By extracting water out of the w/w droplet, the solute concentrations in the droplet phase increase; when the c...

The purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of Sturm-Liouville problem with equation of the form w??=(?2f(x)?R(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in C2(a,b which has a single zero (so called turning point) at point 0x=x and R(x) is a continuously differentiable function. ...

and Applied Analysis 3 We are interested in the following optimal control problem: min u∈Uad⊂X J ( u, y u ) 1 2 {∫T 0 ∥ ∥y − zd ∥ ∥2 0,Ωdt ∫T 0 ‖u‖0,ΩUdt } , 2.1 subject to yt − div ( A∇yt D∇y ∫ t 0 C t, τ ∇y x, τ dτ ) f Bu, in Ω × 0, T , y 0, on ∂Ω × 0, T , y|t 0 y0, in Ω, 2.2 where u is control, y is state, zd is the observation, Uad is a closed convex subset, f x, t ∈ L2 0, T ;L2 Ω , and zd ...

The principal specialization ?w=Sw(1,…,1) of the Schubert polynomial at w, which equals degree matrix variety corresponding to has attracted a lot attention in recent years. In this paper, we show that ?w is bounded below by 1+p132(w)+p1432(w) where pu(w) number occurrences pattern u strengthening previous result A. Weigandt. We then make conjecture relating polynomials containment. Finally, ch...

for some l > 0 and for all x E 0 and C; E R" . We also assume a;j = aj;. For such operators, the Dirichlet problem is solvable in n if and only if it is solvable for the Laplace operator, according to a theorem of Littman, Stampacchia and Weinberger [I]. This means that if n ~ R" is a sufficiently nice bounded region (the unit ball, B, is an example) and J is a given continuous function on the ...

The two well-known numerical radius inequalities for the tensor product $$A \otimes B$$ acting on $${\mathbb {H}} {\mathbb {K}}$$ , where A and B are bounded linear operators defined complex Hilbert spaces $$ {K}},$$ respectively \frac{1}{2} \Vert A\Vert B\Vert \le w(A B) w(A)w(B) \min \{ w(A) w(B) \}. In this article, we develop new lower upper bounds $$w(A B)$$ of study equality conditions th...