Publikacje
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wszystkich: 101
Katalog Publikacji
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On the partition dimension of trees
PublikacjaGiven an ordered partition Π={P1,P2,…,Pt} of the vertex set V of a connected graph G=(V,E), the partition representation of a vertex v∈V with respect to the partition Π is the vector r(v|Π)=(d(v,P1),d(v,P2),…,d(v,Pt)), where d(v,Pi) represents the distance between the vertex vv and the set Pi. A partition Π of V is a resolving partition of G if different vertices of G have different partition representations, i.e., for every...
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On the mixing property and the ergodic principle for nonhomogeneous Markov chains
PublikacjaW pracy rozważane są różne typy zachowania granicznego nieskończenie wymiarowych niejednorodnych łańcuchów Markowa z czasem dyskretnym. Badana jest struktura geometryczna zbioru łańcuchów Markowa w normowej i mocnej topologii operatorowej.
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Changes in gene methylation patterns in neonatal murine hearts: Implications for the regenerative potential
PublikacjaBackground The neonatal murine heart is able to regenerate after severe injury; this capacity however, quickly diminishes and it is lost within the first week of life. DNA methylation is an epigenetic mechanism which plays a crucial role in development and gene expression regulation. Under investigation here are the changes in DNA methylation and gene expression patterns which accompany the loss of regenerative potential. Results The...
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On the super domination number of lexicographic product graphs
PublikacjaThe neighbourhood of a vertexvof a graphGis the setN(v) of all verticesadjacent tovinG. ForD⊆V(G) we defineD=V(G)\D. A setD⊆V(G) is called a super dominating set if for every vertexu∈D, there existsv∈Dsuch thatN(v)∩D={u}. The super domination number ofGis theminimum cardinality among all super dominating sets inG. In this article weobtain closed formulas and tight bounds for the super dominating number oflexicographic product...
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On mixing in the class of quadratic stochastic operators
PublikacjaWe study different types of limit behavior of quadratic stochastic operators acting on ℓ^1 (or ℓ^1_d) spaces in both strong and uniform topologies. The main motif of the paper is to express the uniform and strong asymptotic stability of the quadratic stochastic operator in terms of convergence of the associated (linear) nonhomogeneous Markov chain. We also examine which type of uniform convergence of iterates of the quadratic...
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Folate/homocysteine metabolism and lung cancer risk among smokers
PublikacjaBackground: Folate and homocysteine are involved in DNA synthesis and methylation processes, which are deregulated during carcinogenesis. Objectives: The aim of this study was to assess the relationship between folate/homocysteine concentrations, the functional polymorphisms of folate/homocysteine genes and lung cancer risk among cigarette smokers. Study design: The study included 132 lung cancer patients and 396 controls from...
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Result of the 6-min walk test is an independent prognostic factor of surgically treated non-small-cell lung cancer
PublikacjaPathological tumour, node and metastasis (TNM) stage remains the most significant prognostic factor of non-small-cell lung cancer (NSCLC). Meanwhile, age, gender, pulmonary function tests, the extent of surgical resection and the presence of concomitant diseases are commonly used to complete the prognostic profile of the patient with early stage of NSCLC. The aim of this study is to assess how the result of a 6-min walk test (6MWT)...
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Super Dominating Sets in Graphs
PublikacjaIn this paper some results on the super domination number are obtained. We prove that if T is a tree with at least three vertices, then n2≤γsp(T)≤n−s, where s is the number of support vertices in T and we characterize the extremal trees.
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Domination-Related Parameters in Rooted Product Graphs
PublikacjaAbstract A set S of vertices of a graph G is a dominating set in G if every vertex outside of S is adjacent to at least one vertex belonging to S. A domination parameter of G is related to those sets of vertices of a graph satisfying some domination property together with other conditions on the vertices of G. Here, we investigate several domination-related parameters in rooted product graphs.
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Total outer-connected domination in trees
PublikacjaW pracy przedstawiono dolne ograniczenie na liczbę dominowania totalnego zewnętrznie spójnego w grafach oraz scharakteryzowano wszystkie drzewa osiągające to ograniczenie.
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Crystallization of space: Space-time fractals from fractal arithmetic
PublikacjaFractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to the fractal in question, and one can formulate classical and quantum physics within the fractal set. In particular, fractals in space-time can be generated by means of homogeneous spaces associated...
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Quadratic stochastic operators on Banach lattices
PublikacjaWe study the convergence of iterates of quadratic stochastic operators that are mean monotonic. They are defined on the convex set of probability measures concentrated on a weakly compact order interval S = [0, f] of a fixed Banach lattice F. We study their regularity and identify the limits of trajectories either as the “infimum” or “supremum” of the support of initial distributions.
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Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus
PublikacjaFractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration, and complex structure. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the required basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.
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Quantum structure in competing lizard communities
PublikacjaAlmost two decades of research on applications of the mathematical formalism of quantum theory as a modeling tool in domains different from the micro-world has given rise to many successful applications in situations related to human behavior and thought, more specifically in cognitive processes of decision-making and the ways concepts are combined into sentences. In this article, we extend this approach to animal behavior, showing...
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Two almost homoclinic solutions for second-order perturbed Hamiltonian systems
PublikacjaW niniejszym artykule badamy problem istnienia rozwiązań prawie homoklinicznych (rozwiązań znikających w nieskończonościach) dla układów Hamiltonowskich drugiego rzędu (układów Newtonowskich) z zaburzeniem. Nasz wynik jest uogólnieniem twierdzenia Rabinowitza-Tanaki o istnieniu rozwiązania homoklinicznego dla układów bez zaburzenia [Math. Z. 206 (1991) 473-499]. O zaburzeniu zakładamy, że jest dostatecznie małe w przestrzeni funkcji...
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Prevalence Problem in the Set of Quadratic Stochastic Operators Acting on L1
PublikacjaThis paper is devoted to the study of the problem of prevalence in the class of quadratic stochastic operators acting on the L1 space for the uniform topology. We obtain that the set of norm quasi-mixing quadratic stochastic operators is a dense and open set in the topology induced by a very natural metric. This shows the typical long-term behaviour of iterates of quadratic stochastic operators.
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Comprehensive stabilization of all streams of solid residues formed during sewage sludge thermal treatment – Case study
PublikacjaModern wastewater treatment plants are currently struggling with the problem of processing and ecological management of sewage sludge. Thermal utilization is a frequently used practice of excess sludge utilization especially in large wastewater treatment plants, which seems to be a quite promising concept. However, during thermal treatment, fractions of ashes and dusts are generated. Such wastes, especially the dust fraction, can...
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A note on total reinforcement in graphs
PublikacjaIn this note we prove a conjecture and inprove some results presendet in a recent paper of N. Sridharan, M.D. Elias, V.S.A. Subramanian, Total reinforcement number of a graph, AKCE Int. J. Graphs Comb. 4 (2) (2007) 197-202.
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Total Domination Versus Domination in Cubic Graphs
PublikacjaA dominating set in a graph G is a set S of vertices of G such that every vertex not in S has a neighbor in S. Further, if every vertex of G has a neighbor in S, then S is a total dominating set of G. The domination number,γ(G), and total domination number, γ_t(G), are the minimum cardinalities of a dominating set and total dominating set, respectively, in G. The upper domination number, \Gamma(G), and the upper total domination...
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Certified domination
PublikacjaImagine that we are given a set D of officials and a set W of civils. For each civil x ∈ W, there must be an official v ∈ D that can serve x, and whenever any such v is serving x, there must also be another civil w ∈ W that observes v, that is, w may act as a kind of witness, to avoid any abuse from v. What is the minimum number of officials to guarantee such a service, assuming a given social network? In this paper, we introduce...