Fuchs and collaborators [1, 2] showed that when a high voltage is applied between two electrodes, immersed in two beakers containing twice distilled water, a water bridge between the two containers is formed. We observed that a copper ions flow can pass through the bridge if the negative electrode is a copper electrode. The direction of the flux is not only depending on the direction of the applied electrostatic field but on the relative electronegativity of the electrodes too. The fact seems to suggest new perspectives in understanding the structure of water and the mechanisms concerning the arising of ions fluxes in living matter.
For two vertices $u$ and $v$ of a connected graph $G$, the set $I(u, v)$ consists of all those vertices lying on a $u$–$v$ geodesic in $G$. For a set $S$ of vertices of $G$, the union of all sets $I(u,v)$ for $u, v \in S$ is denoted by $I(S)$. A set $S$ is a convex set if $I(S) = S$. The convexity number $\mathop {\mathrm con}(G)$ of $G$ is the maximum cardinality of a proper convex set of $G$. A convex set $S$ in $G$ with $|S| = \mathop {\mathrm con}(G)$ is called a maximum convex set. A subset $T$ of a maximum convex set $S$ of a connected graph $G$ is called a forcing subset for $S$ if $S$ is the unique maximum convex set containing $T$. The forcing convexity number $f(S, \mathop {\mathrm con})$ of $S$ is the minimum cardinality among the forcing subsets for $S$, and the forcing convexity number $f(G, \mathop {\mathrm con})$ of $G$ is the minimum forcing convexity number among all maximum convex sets of $G$. The forcing convexity numbers of several classes of graphs are presented, including complete bipartite graphs, trees, and cycles. For every graph $G$, $f(G, \mathop {\mathrm con}) \le \mathop {\mathrm con}(G)$. It is shown that every pair $a$, $ b$ of integers with $0 \le a \le b$ and $b \ge 3$ is realizable as the forcing convexity number and convexity number, respectively, of some connected graph. The forcing convexity number of the Cartesian product of $H \times K_2$ for a nontrivial connected graph $H$ is studied.
For an ordered set W = {w1, w2,...,wk} of vertices and a vertex v in a connected graph G, the (metric) representation of v with respect to W is the k-vector r(v|W)=(d(v,w1), d(v, w2),...,d(v, wk)), where d(x, y) represents the distance between the vertices x and y. The set W is a resolving set for G if distinct vertices of G have distinct representations. A resolving set of minimum cardinality is a basis for G and the number of vertices in a basis is its (metric) dimension dim(G). For a basis W of G, a subset S of W is called a forcing subset of W if W is the unique basis containing S. The forcing number fG(W, dim) of W in G is the minimum cardinality of a forcing subset for W, while the forcing dimension f(G, dim) of G is the smallest forcing number among all bases of G. The forcing dimensions of some well-known graphs are determined. It is shown that for all integers a, b with 0 ≤ a ≤ b and b ≥1, there exists a nontrivial connected graph G with f(G) = a and dim(G) = b if and only if {a, b} ≠ {0, 1}.
In this paper, it is proved that the Fourier integral operators of order $m$, with $-n < m \leq -(n-1)/2$, are bounded from three kinds of Hardy spaces associated with Herz spaces to their corresponding Herz spaces.
Doctor David J. Webb MD, DSc, FRCP, FRSE, FMedSci, a clinical pharmacologist specialising in the management of cardiovascular disease, is the recipient of The Fourth Tomoh Masaki Award , a bi-annual prize presented on the occasion of the International Conferences on Endothelin to scientists for outstanding contributions and achievements in the field of endothelin research. The Fourth Tomoh Masaki Award was presented to Doctor Webb at the Fifteenth International Conference on Endothelin which was held at Duo Hotel, Prague, Czech Republic, in October 2017. The award was granted to Dr. Webb during the Award Ceremony in Troja Chateau “In Recognition of his Outstanding Contributions to Science and Endothelin Research in Particular”. This article summarises the career and the scientific achievements of David J. Webb viewed by his former student Dr. Neeraj Dhaun, known to everybody as ‘Bean’., N. Dhaun., and Seznam literatury
It is well known that every $x\in (0,1]$ can be expanded to an infinite Lüroth series in the form of $$x=\frac {1}{d_1(x)}+\cdots +\frac {1}{d_1(x)(d_1(x)-1)\cdots d_{n-1}(x)(d_{n-1}(x)-1)d_n(x)}+\cdots , $$ where $d_n(x)\geq 2$ for all $n\geq 1$. In this paper, sets of points with some restrictions on the digits in Lüroth series expansions are considered. Mainly, the Hausdorff dimensions of the Cantor sets $$ F_{\phi }=\{x\in (0,1]\colon d_n(x)\geq \phi (n), \ \forall n\geq 1\} $$are completely determined, where $\phi $ is an integer-valued function defined on $\mathbb N$, and $\phi (n)\to \infty $ as $n\to \infty $.
This paper considers the problem of determining linear relations from data affected by additive noise in the context of the Frisch scheme. The loci of solutions of the Frisch scheme and their properties are first described in the algebraic case. In this context two main problems are analyzed: the evaluation of the maximal number of linear relations compatible with data affected by errors and the determination of the linear relation actually linking the noiseless data. Subsequently the extension of the Frisch scheme to the identification of dynamical systems is considered for both SISO and MIMO cases and the problem of its application to real processes is investigated. For this purpose suitable identification criteria and model parametrizations are described. Finally two classical identification problems are mapped into the Frisch scheme, the blind identification of FIR channels and the identification of AR + noise models. This allows some theoretical and practical extensions.
For a finite commutative ring $R$ and a positive integer $k\geqslant 2$, we construct an iteration digraph $G(R, k)$ whose vertex set is $R$ and for which there is a directed edge from $a\in R$ to $b\in R$ if $b=a^k$. Let $R=R_1\oplus \ldots \oplus R_s$, where $s>1$ and $R_i$ is a finite commutative local ring for $i\in \{1, \ldots , s\}$. Let $N$ be a subset of $\{R_1, \dots , R_s\}$ (it is possible that $N$ is the empty set $\emptyset $). We define the fundamental constituents $G_N^*(R, k)$ of $G(R, k)$ induced by the vertices which are of the form $\{(a_1, \dots , a_s)\in R\colon a_i\in {\rm D}(R_i)$ if $R_i\in N$, otherwise $a_i\in {\rm U}(R_i), i=1,\ldots ,s\},$ where U$(R)$ denotes the unit group of $R$ and D$(R)$ denotes the zero-divisor set of $R$. We investigate the structure of $G_N^*(R, k)$ and state some conditions for the trees attached to cycle vertices in distinct fundamental constituents to be isomorphic.
Up to present for modelling and analyzing of random phenomenons, some statistical distributions are proposed. This paper considers a new general class of distributions, generated from the logit of the gamma random variable. A special case of this family is the \textit{Gamma-Uniform} distribution. We derive expressions for the four moments, variance, skewness, kurtosis, Shannon and Rényi entropy of this distribution. We also discuss the asymptotic distribution of the extreme order statistics, simulation issues, estimation by method of maximum likelihood and the expected information matrix. We show that the Gamma-Uniform distribution provides great flexibility in modelling for negatively and positively skewed, convex-concave shape and reverse `J' shaped distributions. The usefulness of the new distribution is illustrated through two real data sets by showing that it is more flexible in analysing of the data than of the Beta Generalized-Exponential, Beta-Exponential, Beta-Pareto, Generalized Exponential, Exponential Poisson, Beta Generalized Half-Normal and Generalized Half-Normal distributions. and Na konci článku uvedena podoba jména Narges Montazeri Hedesh