For a nontrivial connected graph G of order n, the detour distance D(u, v) between two vertices u and v in G is the length of a longest u − v path in G. Detour distance is a metric on the vertex set of G. For each integer k with 1 ≤ k ≤ n−1, a coloring c : V (G) → N is a k-metric coloring of G if |c(u) − c(v)| + D(u, v) ≥ k + 1 for every two distinct vertices u and v of G. The value χ k m(c) of a k-metric coloring c is the maximum color assigned by c to a vertex of G and the k-metric chromatic number χ k m(G) of G is the minimum value of a k-metric coloring of G. For every nontrivial connected graph G of order n, χ 1m(G) ≤ χ 2m(G) ≤ . . . ≤ χ n−1 m (G). Metric chromatic numbers provide a generalization of several well-studied coloring parameters in graphs. Upper and lower bounds have been established for χ k m(G) in terms of other graphical parameters of a graph G and exact values of k-metric chromatic numbers have been determined for complete multipartite graphs and cycles. For a nontrivial connected graph G, the anti-diameter adiam(G) is the minimum detour distance between two vertices of G. We show that the adiam(G)-metric chromatic number of a graph G provides information on the Hamiltonian properties of the graph and investigate realization results and problems on this parameter.
The earthquakes of magnitudes ML=5.0 and 5.3 in the Kaliningrad enclave of Russia on September 21, 2004 were unexpected in a very low-seismicity area. The earthquakes caused minor damage in the Kaliningrad enclave, in northern Poland and in southwestern Lithuania, and macroseismic intensities of 6-7 (EMS) close to the epicenters. The earthquakes were felt up to 800 km distance. The events have been located under the central-northern part of the Sambia Penninsula at 16 and 20 km depth. Their source mechanism has been found to be a right lateral strike slip on a direction parallel to the edge of the Fennoscandian Shield and the East European Craton. The possible cause of the earthquakes is discussed. With the glaciotectonic cause unlikely, it seems the earthquakes evidence tectonic patterns, possibly resulting from stress propagating all across Europe from the Mediterranean region. Historical information seems to evidence past seismic activity in the region, which together with the 2004 earthquakes show the need to reassess seismic hazard in the area., Paweł Wiejacz., and Obsahuje bibliografii
Let $T\in {\mathcal{L}}(X)$ be a bounded operator on a complex Banach space $X$. If $V$ is an open subset of the complex plane such that $\lambda -T$ is of Kato-type for each $\lambda \in V$, then the induced mapping $f(z)\mapsto (z-T)f(z)$ has closed range in the Fréchet space of analytic $X$-valued functions on $V$. Since semi-Fredholm operators are of Kato-type, this generalizes a result of Eschmeier on Fredholm operators and leads to a sharper estimate of Nagy’s spectral residuum of $T$. Our proof is elementary; in particular, we avoid the sheaf model of Eschmeier and Putinar and the theory of coherent analytic sheaves.
KL-Miner [9] is a datarnining procedure that, given input data matrix
M. and a set of parameters, generates patterns of the form R ~ C/7. Here R and C are categorial attributes corresponding to the columns of M, and 7 is a Boolean condition defined in terms of the remaining colums of Ai. The pattern R C means that R and C are strongly correlated on the submatrix of M formed by all the rows of M that satisfy 7. What is meant by “strong correlation” and how are R, C and 7 generated is determined by the input parameters of the procedure. KL-Miner conforms to the GUHA principle forinulated in [1]. It revives two older GUHA procedures described in [2]; it is very much related to CORREL and contains a new implementation of COLLAPS as a module.
In this paper, we mention the motivation that leads to designing of KL-Miner, describing our new implementation of COLLAPS and giving application exarnples that illustrate the main features of KL-Miner.
A Northwest Iranian dialect, Aftari, is grouped both diachronically and typologically together with the other dialects spoken around the town of Semnān, east of Tehran. For this group the designation “Komisenian”, after the old name of the province, is proposed in the article. As is the case with the neighboring Caspian dialects to the north, Aftari is the language of postpositions, and it has a relatively elaborate system of personal and demonstrative pronouns. Aftari shares with Tabari the element -enn- in the present indicative, a remnant of the Old Iranian present participle * -ant-. In terms of ergativity, Aftari holds a position somewhere between Tabari, which has none, and the Central Plateau Dialects which have preserved the system. Remnants of the Middle Iranian ergativity remain in Aftari as a distinct set of personal endings for the past transitive; in the past, these acted as agents of transitive verbs. Thus, transitivity still plays a role in the past conjugation, but there are indications that the difference is fading away, most notably in 3rd person singular forms. The intransitive past tenses are marked by -št- preceding the personal endings, except for the 3rd person singular, which has neither. The perfect tense has various constructions, often merging with the preterit, and thus may not be authentic to Aftari.
This paper generalizes the results of papers which deal with the Kurzweil-Henstock construction of an integral in ordered spaces. The definition is given and some limit theorems for the integral of ordered group valued functions defined on a Hausdorff compact topological space $T$ with respect to an ordered group valued measure are proved in this paper.
Certain financial market strategies are known to exhibit a hysteretic structure similar to the memory observed in plasticity, ferromagnetism, or magnetostriction. The main difference is that in financial markets, the spontaneous occurrence of discontinuities in the time evolution has to be taken into account. We show that one particular market model considered here admits a representation in terms of Prandtl-Ishlinskii hysteresis operators, which are extended in order to include possible discontinuities both in time and in memory. The main analytical tool is the Kurzweil integral formalism, and the main result proves the well-posedness of the process in the space of right-continuous regulated functions.
We propose an extended version of the Kurzweil integral which contains both the Young and the Kurzweil integral as special cases. The construction is based on a reduction of the class of δ-fine partitions by excluding small sets.
The Kurzweil-Henstock approach has been successful in giving an alternative definition to the classical Itô integral, and a simpler and more direct proof of the Itô Formula. The main advantage of this approach lies in its explicitness in defining the integral, thereby reducing the technicalities of the classical stochastic calculus. In this note, we give a unified theory of stochastic integration using the Kurzweil-Henstock approach, using the more general martingale as the integrator. We derive Henstock's Lemmas, absolute continuity property of the primitive process, integrability of stochastic processes and convergence theorems for the Kurzweil-Henstock stochastic integrals. These properties are well-known in the classical (non-stochastic) integration theory but have not been explicitly derived in the classical stochastic integration.
T. Almada and J. Vaz de Carvalho (2001) stated the problem to investigate if these Lukasiewicz algebras are algebras of some logic system. In this article an affirmative answer is given and the L m n -propositional calculus, denoted by ℓ m n , is introduced in terms of the binary connectives → (implication), ։ (standard implication), ∧ (conjunction), ∨ (disjunction) and the unary ones f (negation) and Di , 1 ≤ i ≤ n − 1 (generalized Moisil operators). It is proved that ℓ m n belongs to the class of standard systems of implicative extensional propositional calculi. Besides, it is shown that the definitions of L m n -algebra and ℓ m n -algebra are equivalent. Finally, the completeness theorem for ℓ m n is obtained.