We present a concealing method in which an anti-point spread function (APSF) is generated using binary optics, which produces a large-scale dark area in the focal region that can hide any object located within it. This result is achieved by generating two identical PSFs of opposite signs, one consisting of positive electromagnetic waves from the zero-phase region of the binary optical element a...

The solutions of fluid-structure interaction problems, using displacement-based finite element formulations for acoustic fluids, may contain spurious non-zero frequencies. To remove this deficiency, we present here a new formulation based on a three-field discretization using displacements, pressure and a “vorticity moment” as variables with an appropriate treatment of the boundary conditions. ...

Let Zp be the finite field of prime order p and A be a subsequence of Zp. We prove several classification results about the following questions: (1) When can one represent zero as a sum of some elements of A ? (2) When can one represent every element of Zp as a sum of some elements of A ? (3) When can one represent every element of Zp as a sum of l elements of A ?

We analyse the error of interpolation of functions from the space H(a, c) in the nodes a < b < c of a regular quadratic Lagrange finite element in 1D by interpolants from the local function space of this finite element. We show that the order of the error depends on the way in which the mutual positions of nodes a, b, c change as the length of interval [a, c] approaches zero.

A front-fixing finite element method is developed for the valuation of American put options on zero-coupon bonds under a class of one-factor models of short interest rates. Numerical results are presented to examine our method and to compare it with the usual finite element method. A conjecture concerning the behavior of the early exercise boundary near the option expiration date is proposed ac...

(i) is the most important one. We showed that extensions < = are classified by >@?A& 1 B DCE GF ( . The element 0 corresponded to a splitting. If one element is a non-zero multiple of the other, they correspond to the same , although different extensions. As an application, we proved: Proposition. Every rank 2 locally free sheaf on ? is a direct sum of invertible sheaves. I can’t remember if I ...

Finite element methods for a family of systems of singular perturbation problems of a saddle point structure are discussed. The system is approximately a linear Stokes problem when the perturbation parameter is large, while it degenerates to a mixed formulation of Poisson’s equation as the perturbation parameter tends to zero. It is established, basically by numerical experiments, that most of ...

Let d be a Turing degree, R[d] and Q[d] denote respectively classes of recursively enumerable (r.e.) and all degrees in which d is relatively enumerable. We proved in [ta] that there is a degree d containing differences of r.e.sets (briefly, d.r.e.degree) such that R[d] possess a least element m>0. Now we show the existence of a d.r.e. d such that R[d] has no a least element. We prove also that...

The one-lie Rényi-Ulam liar game is a 2-player perfect information zero sum game, lasting q rounds, on the set [n] := {1, . . . , n}. In each round Paul chooses a subset A ⊆ [n] and Carole either assigns 1 lie to each element of A or to each element of [n] \ A. Paul wins the regular (resp. pathological) game if after q rounds there is at least one (resp. at most one) element with one or fewer l...

We introduce a mixed discontinuous/continuous finite element pair for ocean modelling, with continuous quadratic layer thickness and discontinuous velocity. We investigate the finite element pair applied to the linear shallow-water equations on an f -plane. The element pair has the property that all geostrophically balanced states which strongly satisfy the boundary conditions have discrete div...