In this paper, the geometric interpolation of planar data points and boundary tangent directions by a cubic $G^2$ Pythagorean-hodograph (PH) spline curve is studied. It is shown that such an interpolant exists under some natural assumptions on the data. The construction of the spline is based upon the solution of a tridiagonal system of nonlinear equations. The asymptotic approximation order 4 is confirmed.
COBISS.SI-ID: 15262809
We investigate representations of a rat. func. R \in k(x), which is a field of char. zero, in the form R = K \cdot \sigma S/S. Here K,S \in k(x), and \sigma is an automorphism of k(x) mapping k[x] onto k[x]. We show that the degrees of the num. and denom. of K are simultaneously minimized iff K = r/s where r, s \in k[x] and r is coprime with \sigma^n s for all n \in \mathbb{Z}. Subject to certain assumptions we present an algorithm for minimizing w(\deg{num}(S), \deg{den}(S)). We show how to use these representations of rat. functions to obtain succinct repr. of \sigma-hypergeometric terms.
COBISS.SI-ID: 15580505
Naj bo A matrika povezanosti, G graf, D matrika razdalj in V diagonalna matrika valenc. V članku študiramo možnosti za razločevanje med grafi z enakim spektrom glede na spektralne lastnosti določenih dodatnih matrik Ugotovili smo, da matrike oblike A^m - V, katerih elementi štejejo nezaključene sprehode dolžine m v grafu, razločujejo nekatere izospektralne grafe. Par grafov z ujemajočimi lastnimi vrednostmi različnih matrik imenujemo krepko izospektralen ali S-izospektralni grafi, za razliko od tistih, ki so manj podobni. Z drugimi besedami, nekateri grafi so bolj S-izospektralni kot drugi.
COBISS.SI-ID: 516139289
We obtain the following characterization of Q-polynomial distance-regular graphs (DRG). Let G be a DRG with diameter d ? 3. Let E denote a min. idempotent of G which is not the trivial idempotent E0. Let ?*0, ..., ?*d denote the dual eigenvalue sequence for E. We show that E is Q-polynomial iff (i) the entry-wise product E?E is a linear comb. E0, E, and at most one other min. idempotent of G;(ii) there exists a complex scalar ß such that ?*i-1-ß ?*i+?*i+1 is independent of i for1?i? d-1;(iii) ?*i??*0 for 1?i? d. If any of these three conditions is omitted, E is not necessarily Q-polynomial.
COBISS.SI-ID: 15688537
This article represents a continuation of our ongoing effort toward quantitative understanding of the microwave catalytic effect. It provides a derivation of an analytical solution for the microwave catalysis. The obtained expression is compared with the results of the Monte Carlo simulation and is applied to reproduce the microwave catalytic effect experimentally observed in the polyethylene terephthalate solvolysis. Implications for the interactions of microwaves with living organisms in the context of widespread mobile telephony are also discussed.
COBISS.SI-ID: 1851882