Revistas académicas de la Universidad Católica del Norte
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Partial actions and quotient rings
No full textIn this paper we study the Martindale ring of α-quotients Q associated with the partial action (R,α). Among other results we extend the partial action to Q and prove that it can be identified with an ideal of Q, the Martindale ring of β-quotients of T , where (T, β) denotes the enveloping action of (R,α). We prove that, in general, (Q, β) is not the enveloping action of (Q,α) and study the relationship between the rings R, Q, T and Q. Finally, we establish some properties related to the center of Q and the extended α-centroid of R
Cycle connectivity in weighted graphs
No full textSome new connectivity concepts in weighted graphs are introduced in this article. The concepts of strong arc, partial cutnode, bridge and block are introduced. Also three different types of cycles namely locamin cycle, multimin cycle and strongest strong cycle are introduced. Partial blocks in weighted graphs are characterized using strongest paths. Also a set of necessary conditions for a weighted graph to be a partial block involving strong cycles and a sufficient condition for a weighted graph to be a partial block involving strongest strong cycles are obtained. A new connectivity parameter called cycle connectivity and a new type of weighted graphs called θ - weighted graphs are introduced and partial blocks in θ - weighted graphs are fully characterized
Examples of Morse decompositions for semigroups actions
No full textThe concepts of Morse decompositions and dynamic Morse decompositions are equivalent for flows. In this paper we show that these concepts are not equivalent for Morse decompositions of semigroups of homeomorphisms on topological spaces.We give an example of a dynamic Morse decompositions on compactifications of topological spaces. Other examples of Morse decompositions are also provided.
A quantum mechanical proof of the fourier inversion formula
No full textThe translation of the observable, position and momentum, of a given particle in the real line, at a certain time t, from Classical Mechanics, into the operators, position and momentum, in Quantum Mechanics, gives us the inspiration to make a proof of the existence of the Fourier's Inverse Transform, using algebraic relations involving these operators (position and momentum), a few of Linear Algebra and Analysis, without resorting to the classical technics like Fubini's Theorem and Lebesgue's Dominated Convergence Theorem
On graphs whose chromatic transversal domination number is two
No full textIn this paper we characterize the class of trees, block graphs, cactus graphs and cubic graphs for which the chromatic transversal domination number is equal to two
Finite topologies and digraphs
No full textIn this paper we study the relation between finite topologies and digraphs. We associate a digraph to a topology by means of the “specialization” relation between points in the topology. Reciprocally, we associate a topology to each digraph, taking the sets of vertices adjacent (in the digraph) to v, for all vertex v, as a subbasis of closed sets for the topology. We use these associations to examine the relation between a simple digraph and its homologous topology. We also extend this relation to the functions preserving the structure between these classes of objects
Bipartite theory of irredundant set
No full textThe bipartite version of irredundant set, edge-vertex irredundant set and vertex-edge irredundant set are introduced. Using the bipartite theory of graph, IRve(G)+Υ(G) = |V| and Υve(G)+IR(G) = |V| are proved
On strongly faint e-continuous functions
No full textA new class of functions, called strongly faint e-continuous function, has been defined and studied. Relationships among strongly faint e-continuous functions and econnected spaces, e-normal spaces and e-compact spaces are investigated. Furthermore, the relationships between strongly faint e-continuous functions and graphs are also investigated
On the instability of solutions of an eighth order nonlinear differential equation of retarded type
No full textIn this paper, we give some sufficient conditions on the instability of the zero solution of a kind of eighth order nonlinear differential equations of retarded type by using the Lyapunov direct method. The obtained sufficient conditions improve an existing result in the literature
Numerical range of a pair of strictly upper triangular matrices
No full textGiven two strictly upper triangular matrices X, Y ∈ Cm×m, we study the range WY (X) = {trnXn-1Y* : n ∈ N}, where N is the group of unit upper triangular matrices in Cm×m. We prove that it is either a point or the whole complex plane. We characterize when it is a point. We also obtain some convexity result for a similar range, where N is replaced by any ball of Ck(k = m(m - 1)/2) embedded in N , m = 4