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Search results for: SEIBERG-WITTEN INVARIANTS
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Seiberg-Witten invariants the topological degree and wall crossing formula
PublicationFollowing S. Bauer and M. Furuta we investigate finite dimensional approximations of a monopole map in the case b 1 = 0. We define a certain topological degree which is exactly equal to the Seiberg-Witten invariant. Using homotopy invariance of the topological degree a simple proof of the wall crossing formula is derived.
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On Invariants of Fluid Mechanics Tensors
PublicationThis paper presents physical interpretations of the first and second invariants of tensors of fluid mechanics. Some examples of elementary applications and meanings are also given.
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Product Graph Invariants with Applications in the Theory of Information
PublicationThere are a large number of graph invariants. In the paper, we consider some of them, e.g. the independence and chromatic numbers. It is well know that we cannot efficiently calculate these numbers for arbitrary graphs. In the paper we present relations between these invariants and concepts from the theory of information. Concepts such as source coding and transmission over a noisy channel with zero probability of error are modeled...
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Topological invariants for equivariant flows: Conley index and degree
PublicationAbout forty years have passed since Charles Conley defined the homotopy index. Thereby, he generalized the ideas that go back to the calculus of variations work of Marston Morse. Within this long time the Conley index has proved to be a valuable tool in nonlinear analysis and dynamical systems. A significant development of applied methods has been observed. Later, the index theory has evolved to cover such areas as discrete dynamical...
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On the super domination number of lexicographic product graphs
PublicationThe 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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Algebraic periods and minimal number of periodic points for smooth self-maps of 1-connected 4-manifolds with definite intersection forms
PublicationLet M be a closed 1-connected smooth 4-manifolds, and let r be a non-negative integer. We study the problem of finding minimal number of r-periodic points in the smooth homotopy class of a given map f: M-->M. This task is related to determining a topological invariant D^4_r[f], defined in Graff and Jezierski (Forum Math 21(3):491–509, 2009), expressed in terms of Lefschetz numbers of iterations and local fixed point indices of...
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Identity verification using complex representations of handwritten signature
PublicationThis paper is devoted to handwritten signature verification using the cross-correlation approach (adopted by the authors from telecommunications) and dynamic time warping. The following invariants of the handwritten signature: the net signature, the instantaneous complex frequency and the complex cepstrum are analyzed. The problem of setting the threshold for deciding whether the current signature is authentic or forged is discussed....
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General solution of quantum mechanical equations of motion with time-dependent Hamiltonians: A Lie algebraic approach
PublicationThe unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic techniques in this context and elaborate the theory for SU(2) and SU(1,1). In these cases we give explicit formulae for obtaining general solutions from special ones. We show that the constructions...
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Persistences: analysis of the image of Gdańsk and its cultural identity through survey processes and digital architectural representation
PublicationThe aim of the research was to analyse the historical legacy/heritage of the city of Gdańsk in order to characterise the narrative tools which can be used to promote the cultural identity of the urban landscape. The main focus was on the city's defence system - a cultural route that is spatially limited to a relatively small area, but temporally spanning almost a millennium. The fortifications demarcate a spatial boundary, limiting...
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Minimum order of graphs with given coloring parameters
PublicationA complete k-coloring of a graph G=(V,E) is an assignment F: V -> {1,...,k} of colors to the vertices such that no two vertices of the same color are adjacent, and the union of any two color classes contains at least one edge. Three extensively investigated graph invariants related to complete colorings are the minimum and maximum number of colors in a complete coloring (chromatic number χ(G) and achromatic number ψ(G), respectively),...