Let u t = ∇ 2 u − q(x)u := Lu in D × [0, ∞), where D ⊂ R 3 is a bounded domain with a smooth connected boundary S, and q(x) ∈ L 2 (S) is a real-valued function with compact support in D. is the outer normal to S, one can find q(x) uniquely. A similar result is obtained for the heat equation u t = Lu := ∇ · (a∇u). These results are based on new versions of Property C.

We investigate functions f over a finite field Fq, with q prime, with the property that the map x goes to f(x) + cx is a permutation for at least 2 √ q − 1 elements c of the field. We also consider the case in which q is not prime and f is a function in many variables and pairs of functions (f, g) with the property that the map x goes to f(x) + cg(x) + dx is a permutation for many pairs (c, d) ...

We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the q-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials. The function is evaluated at points which are in geometric progression in ]0, 1[. Numerous properties of the modified Bernstein Polynomials are extended to their q-analogues: simultaneous approximation, p...

The aim of this paper is to derive (by using two operators, representable by a Jacobi matrix) a family of q-orthogonal polynomials, which turn to be dual to alternative q-Charlier polynomials. A discrete orthogonality relation and a three-term recurrence relation for these dual polynomials are explicitly obtained. The completeness property of dual alternative q-Charlier polynomials is also esta...

Let P and Q be additive and hereditary graph properties and let r, s be integers such that r ≥ s. Then an r s -fractional (P,Q)-total coloring of a finite graph G = (V,E) is a mapping f , which assigns an s-element subset of the set {1, 2, . . . , r} to each vertex and each edge, moreover, for any color i all vertices of color i induce a subgraph with property P, all edges of color i induce a s...

The aim of this note is to give a simpler proof result Avsec, which states that $q$-Gaussian algebras have the complete metric approximation property.

We construct a l-factorizalion of the complement .E, of the linear Hamming code of length m:m,--2'-l in the z-cube Q^, for r ) 2,havitg the following equitable property: its component l-factors intersect each Cayley parallel l-factor of Q^ at a constant number of edges, (namely 2mr-r-t edges). In the way to that construction, we flnd an equitable m,-t-factorization of 2, formed by two factors Q...

Suppose that X is a generalized n-manifold, n 5, satisfying the disjoint disks property, and M and Q are topologicalmand q-manifolds, respectively, 1-LCC embedded in X, with n m 3 and n q 3. We de ne what it means for M to be stably transverse to Q in X. In the metastable range, 3m 2(n 1) and 3(m+ q) < 4(n 1), we show that there is an arbitrarily small homotopy of M to a 1-LCC embedding that is...

Abstract A (folklore?) conjecture states that no holomorphic modular form $F(\tau )=\sum _{n=1}^{\infty } a_nq^n\in q\mathbb Z[[q]]$ exists, where $q=e^{2\pi i\tau }$ , such its anti-derivative $\sum a_nq^n/n$ has integral coefficients in the q -expansion. recent observation of Broadhurst and Zudilin, rigorously accomplished by Li Neururer, led to examples meromorphic forms possessing integrali...

It is well known that one can construct a family of q 2 ?q 2 Miquelian inversive planes on the same pointset such that any two share exactly the blocks through a xed point. Further, Ebert 10] has shown that this family can be augmented for even q by adding some Suzuki-Tits inversive planes. We wish to apply the method of Ebert combined with a technique from Dover 7] to obtain a family of unital...