Some Connections between Topological and Modal Logic

We study modal logics based on neighbourhood semantics using methods and theorems having their origin in topological model theory. We thus obtain general results concerning completeness of modal logics based on neighbourhood semantics as well as the relationship between neighbourhood and Kripke semantics. We also give a new proof for a known interpolation result of modal logic using an interpolation theorem of topological model theory.     

On Some Connections between Potential Theory and Excursions of Reflecting Brownian Motion

We consider reflecting Brownian motion in a bounded domain with smooth boundary. Formulas for the moments of the excursion lengths are derived and connections between excursion theory of reflecting Brownian motion and notions from recurrent potential theory are explored.     

Connections between Romanovski and other polynomials

A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schrödinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given.     

Connections between congruence-lattices and polynomial properties

This paper gives characterisations of properties of varieties such as congruence-distributivity (CD), filtrality (FI), CD and having complemented principal congruences — these last two properties are shown to be equivalent- and having restricted equationally definable principal congruences (REDPC), in terms of the existence of some kind of polynomials. These are generalisations both of Jónsson's famous theorem characterizing CD as well as results concerning the (dual) discriminator. The methods are applied to show that REDPC implies CD, which was a problem asked in [2]. A generalisation of the concept of the Mal'cev condition — the so called Pixley-condition — is defined, and it is shown that filtrality and REDPC are Pixley-conditions. The relations between several concepts connected with the above ones are also investigated.The definitions can be found in section 2, and the results are contained in section 4, section 5, and section 6. We call attention to the figure at the end of the paper, which contains most of our results and gives a survey of the concepts examined.Presented by G. Grätzer.Thanks are also due to Peter Krauss, who called our attention to some gaps in our proofs in a previous version of the present paper.     

Connections between Size Functions and Critical Points

A mathematical approach to the concept of shape of a submanifold ℳ︁ of a Euclidean space had previously been given by means of ‘measuring functions’ (e.g. diameter or volume) and of the derived ‘size functions’. This paper relates the study and the computation of any such size function to the structure of critical points of the associated measuring function.     

Connections between projective geometry and superassociative algebra

This paper establishes a connection between projective geometry and the superassociative algebra of multiplace functions. In Part I a quaternary operation is defined for the points on a line j in a projective plane π relative to a fixed quadrangle and the result of operating on A,B,C,D is denoted by A(B,C,D). It is shown that π is a Pappus plane if and only if this operation is superassociative: (A(B,C,D))(E,F,G)=A(B(E,F,G),C(E,F,G),D(E,F,G)) for any points A,B,C,D,E,F,G on j. Desargues and certain special Desargues planes are also characterized by restrictions of the superassociative law. In Part II projective geometry is developed over superassociative systems.     

Connections between Deddens algebras and extended eigenvectors

A complex number λ is called an extended eigenvalue of the shift operator S, Sf = zf, on the disc algebra $C_A (\mathbb{D})$ if there exists a nonzero operator $A:{\text{ }}C_A (\mathbb{D}) \to C_A (\mathbb{D})$ satisfying the equation AS = λSA. We describe the set of all extended eigenvectors of S in terms of multiplication operators and composition operators. It is shown that there are connections between the Deddens algebra associated with S and the extended eigenvectors of S.     

Some Connections between Frames,Mutually Unbiased Bases,and POVM’s in Quantum Information Theory

This paper gives a very brief overview of some aspects of quantum information theory, then explains the relationship between a positive operator valued measure (POVM) and a frame. Some special types of POVM’s are defined and conjectures about them shown to be essentially conjectures about the existence of special types of frames. Finally, some connections with quantum channels and separable states are discussed.     

Connections between generalized graph entropies and graph energy

Dehmer and Mowshowitz introduced a class of generalized graph entropies using known information‐theoretic measures. These measures rely on assigning a probability distribution to a graph. In this article, we prove some extremal properties of such generalized graph entropies by using the graph energy and the spectral moments. Moreover, we study the relationships between the generalized graph entropies and compute the values of the generalized graph entropies for special graph classes. © 2014 Wiley Periodicals, Inc. Complexity 21: 35–41, 2015     

Connections between central factorial numbers and Bernoulli polynomials

In the paper, the author presents two finite discrete convolutions that combines central factorial numbers of both kinds and Bernoulli polynomials.     

The Ups and Downs of Percent (and Some Interesting Connections)

Percent is a standardized ratio comparison that is often used to describe relative amounts of increase and decrease. In this paper, the nonsymmetric relationship between percent of increase and percent of decrease is explored in several ways. Beginning with a simple graphical representation of the relationship, the functional relationship is developed, with relative decrease expressed as a function of relative increase. Once expressed in the form f(x) = 100x/(100 + x), an immediate connection is made to two other topics commonly found within the study of rates—the work problem and the harmonic mean. Finally, successive percents of increase or decrease are shown to be everyday applications of the geometric mean. This deeper look at a common mathematical concept has uncovered rich structural relationships between topics that are often isolated in the curriculum.     

Connections between Construction D and related constructions of lattices

Most practical constructions of lattice codes with high coding gains are multilevel constructions where each level corresponds to an underlying code component. Construction D, Construction \(\hbox {D}'\) , and Forney’s code formula are classical constructions that produce such lattices explicitly from a family of nested binary linear codes. In this paper, we investigate these three closely related constructions along with the recently developed Construction \(\hbox {A}'\) of lattices from codes over the polynomial ring \(\mathbb {F}_2[u]/u^a\) . We show that Construction by Code Formula produces a lattice packing if and only if the nested codes being used are closed under Schur product, thus proving the similarity of Construction D and Construction by Code Formula when applied to Reed–Muller codes. In addition, we relate Construction by Code Formula to Construction \(\hbox {A}'\) by finding a correspondence between nested binary codes and codes over \(\mathbb {F}_2[u]/u^a\) . This proves that any lattice constructible using Construction by Code Formula is also constructible using Construction \(\hbox {A}'\) . Finally, we show that Construction \(\hbox {A}'\) produces a lattice if and only if the corresponding code over \(\mathbb {F}_2[u]/u^a\) is closed under shifted Schur product.     

Connections between generalized,inexact and semi-infinite linear programming

This paper presents duality results between generalized and inexact linear programs and describes a special type of linear semi-infinite programs in connection with the programs above mentioned. In order to solve inexact linear programs a corresponding auxiliary problem can be formulated which is explicitly solvable. However, this auxiliary problem is a reformulation of the reduced semi-infinite problem. Therefore, all the numerical methods for solving semi-infinite linear programs can be used for the numerical treatment of inexact and generalized linear programs.

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Zusammenfassung Die vorliegende Arbeit zeigt Dualitätsergebnisse zwischen verallgemeinerten und inexakten linearen Programmen auf und beschreibt einen speziellen Typ linear-semi-infiniter Programme in Zusammenhang mit den oben erwähnten Optimierungsaufgaben. Um inexakte lineare Programme zu lösen wird ein Hilfsproblem aufgestellt, das explizit lösbar ist. Dieses Hilfsproblem ist eine Reformulierung des reduzierten semi-infiniten Problems. Daher können alle numerischen Methoden zur Lösung semi-infiniter linearer Programme auch zur numerischen Behandlung von inexakten und verallgemeinerten lineraren Programmen herangezogen werden.

     

Some Invariant Properties of Semi-symmetric Metric Recurrent Connections and Curvature Tensor Expressions

The projective transformation of the special semi-symmetric metric recurrent connection is studied in this paper. First of all, an invariant under this transformation is granted; Secondly, by inducing of the invariant and making use of the properties that the corresponding covariant derivative keeps being fixed under the distinctness connection, the curvature tensor expression of the Riemannian manifold is posed at the same time.     

Connections between two-variable Bernstein and Jacobi polynomials on the triangle

Connection coefficients between the two-variable Bernstein and Jacobi polynomial families on the triangle are given explicitly as evaluations of two-variable Hahn polynomials. Dual two-variable Bernstein polynomials are introduced. Explicit formula in terms of two-variable Jacobi polynomials and a recurrence relation are given.