The papers [5], [12], [3], [1], [6], [2], [10], [9], [4], [11], and [7] provide the notation and terminology for this paper. We introduce BCI stuctures with complements which are extensions of BCI structure with 0 and zero structure and are systems 〈 a carrier, an external complement, an internal complement, a zero 〉, where the carrier is a set, the external complement and the internal compleme...

We introduce Z-module structures which are extensions of additive loop structure and are systems 〈 a carrier, a zero, an addition, an external multiplication 〉, where the carrier is a set, the zero is an element of the carrier, the addition is a binary operation on the carrier, and the external multiplication is a function from Z× the carrier into the carrier. Let us mention that there exists a...

We present a finite element method for time-dependent convectiondiffusion equations. The method is explicit and is applicable with piecewise polynomials of degree n > 2 . In the limit of zero diffusion, it reduces to a recently analyzed finite element method for hyperbolic equations. Near optimal error estimates are derived. Numerical results are given.

In this paper new error estimates for an explicit finite element method for numerically solving the so-called zero-diffusion unipolar model (a one-dimensional simplified version of the drift-diffusion semiconductor device equations) are obtained. The method, studied in a previous paper, combines a mixed finite element method using a continuous piecewise-linear approximation of the electric fiel...

Let m be a non zero element of N, f be a partial function from Rm to R, k be an element of N, and Z be a set. We say that f is continuously differentiable up to order of k and Z if and only if (Def. 1) (i) Z ⊆ dom f , and (ii) f is partial differentiable up to order k and Z, and (iii) for every non empty finite sequence I of elements of N such that len I ¬ k and rng I ⊆ Segm holds f Z is contin...

A new higher order finite element method for elliptic partial differential equations on a stationary smooth surface Γ is introduced and analyzed. We assume Γ is characterized as the zero level of a level set function φ and only a finite element approximation φh (of degree k ≥ 1) of φ is known. For the discretization of the partial differential equation, finite elements (of degree m ≥ 1) on a pi...

We adopt the following convention: i, j, m, n denote natural numbers, K denotes a field, and a denotes an element of K. Next we state several propositions: (1) Let A, B be matrices over K, n1 be an element of Nn, and m1 be an element of Nm. If rng n1 × rngm1 ⊆ the indices of A, then Segm(A + B,n1,m1) = Segm(A,n1,m1) + Segm(B,n1,m1). (2) For every without zero finite subset P of N such that P ⊆ ...

Figure 1: Illustration of stimuli used during test trials. Functions are reconstructed from human clicked locations. F18 is the Dirac function with a non-zero element at-270.

In this paper, we obtain an explicit formula for the number of zero-sum k-element subsets in any finite abelian group.

Let A and B be lattices with zero. The classical tensor product, A ⊗ B, of A and B as join-semilattices with zero is a join-semilattice with zero; it is, in general, not a lattice. We define a very natural condition: A ⊗ B is capped (that is, every element is a finite union of pure tensors) under which the tensor product is always a lattice. Let Conc L denote the join-semilattice with zero of c...