ct. Guy and Harary (1967) have shown that, for k > 3, the graph P[2k, k] is homeomorphic to the Möbius ladder M2k, so that its crossing number is one; it is well known that P[2k, 2] is planar. Exoo, Harary and Kabell (1981) have shown hat the crossing number of P[2k + 1, 2] is three, for k ≥ 2. Fiorini (1986) and Richter and Salazar (2002) have shown that P[9, 3] has crossing number two and that P[3k, 3] has crossing number k, provided k ≥ 4. We extend this result by showing that P[3k, k] also has crossing number k for all k ≥ 4.
The article studies the cubic mapping graph $\Gamma (n)$ of $\mathbb {Z}_n[{\rm i}]$, the ring of Gaussian integers modulo $n$. For each positive integer $n>1$, the number of fixed points and the in-degree of the elements $\overline 1$ and $\overline 0$ in $\Gamma (n)$ are found. Moreover, complete characterizations in terms of $n$ are given in which $\Gamma _{2}(n)$ is semiregular, where $\Gamma _{2}(n)$ is induced by all the zero-divisors of $\mathbb {Z}_n[{\rm i}]$.
We study the use of a GPU for the numerical approximation of the curvature dependent flows of graphs - the mean-curvature flow and the Willmore flow. Both problems are often applied in image processing where fast solvers are required. We approximate these problems using the complementary finite volume method combined with the method of lines. We obtain a system of ordinary differential equations which we solve by the Runge-Kutta-Merson solver. It is a robust solver with an automatic choice of the integration time step. We implement this solver on CPU but also on GPU using the CUDA toolkit. We demonstrate that the mean-curvature flow can be successfully approximated in single precision arithmetic with the speed-up almost 17 on the Nvidia GeForce GTX 280 card compared to Intel Core 2 Quad CPU. On the same card, we obtain the speed-up 7 in double precision arithmetic which is necessary for the fourth order problem - the Willmore flow of graphs. Both speed-ups were achieved without affecting the accuracy of the approximation. The article is structured in such way that the reader interested only in the implementation of the Runge-Kutta-Merson solver on the GPU can skip the sections containing the mathematical formulation of the problems.
The view that the goddess Asherah was venerated by a considerable part of the ancient Israelite population up to the time of exile, enjoying the unique status of being Yahweh´s consort, appears to have been gaining ground among a number of students of the ancient Istraelite religion in recent years. They have compiled abundant evidence of various types, all of which is worth careful examination. I am aware that it is unrealistic to attempt to draw out the many complexities of the scholarly arguments, the aim of this short study is to examine the major data and consider it they are sufficient to aqward the goddess this "controversial" role, something which presents a serious challenge to the character of the ancient Israelite religion and has implicaitions for biblical theology.
The effect of aqueous and ether Chelidonium majus haulms extract on cervical HeLa tumor cells, mammary adenocarcinoma MCF 7 tumor cells and acute lymphoblastic leukemia CEM tumor cells in vitro have been studied. The purpose of this research was to compare the effect of aqueous and ether Chelidonium majus haulms extract on selected tumor cells. Colorimetric MTT assay have been used for the study of the antiproliferative effect of aqueous and ether haulms extract of Chelidonium majus on cell viability in vitro. The results of the experiments have shown the cytotoxic effect of the aqueous and the ether Chelidonium majus haulms extract on the individual tumor cells. The aqueous Chelidonium majus haulms extract was the most effective on CEM cells, it was less effective on MCF 7 cells and it was the least effective on HeLa cells. The ether haulms extract of Chelidonium majus was the most effective at all of studied concentrations on CEM cells and MCF 7 cells in comparison with HeLa cells, where it was significantly effective only at the highest concentration. Aqueous and ether haulms extract of Chelidonium majus tested in vitro indicated their cytotoxic activity. Both haulms extract of Chelidonium majus were more efficient on CEM cells. It is assumed that higher antiproliferative activity of ether haulms extract of Chelidonium majus is the result of higher antiproliferative activity of lipophilic substances. The lipophilic substances pass through membrane and bind to various proteins and change their biological activity., Vladimíra Tomečková, Veronika Tkáčová, Peter Urban, Marek Stupák, and Literatura
This paper argues whether the Czech Constitutional Court should be the example of Activism, and whether the Japanese Supreme Court should be characterised as the example of Restraint in the context of constitutional justice. For instance, the former has declared numerous laws unconstitutional in the past two decades, while the latter has declared only a limited number unconstitutional in the past 68 years. We will examine the appropriateness of these characterisations by comparing and contrasting their brief histories, competences, and the nomination processes and precedents, in order to discuss their roles in the transitional period towards the new constitutionalism, paying specific attention to the extent politicisation has impacted each Courts.