Some inclusion theorems for absolute summability

In this work the inclusion relations between absolute summability domains of a normal matrix A and certain factorable matrices are described. Thus, some classes of factorable matrices transforming the absolute summability domain of A into a set of convergent or absolutely convergent series are characterized. As an application, the special case where A is the Cesàro matrix is considered.     

New inequalities of Hermite-Hadamard type via s-convex functions in the second sense with applications

In this paper, we establish some new inequalities of Hermite-Hadamard type whose derivatives in absolute value are s-convex in the second sense. Finally some applications to special means of positive real numbers are given.     

Bounds for the signless Laplacian energy

The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. The Laplacian (respectively, the signless Laplacian) energy of G is the sum of the absolute values of the differences between the eigenvalues of the Laplacian (respectively, signless Laplacian) matrix and the arithmetic mean of the vertex degrees of the graph. In this paper, among some results which relate these energies, we point out some bounds to them using the energy of the line graph of G. Most of these bounds are valid for both energies, Laplacian and signless Laplacian. However, we present two new upper bounds on the signless Laplacian which are not upper bounds for the Laplacian energy.     

Epireflections and supercompact cardinals

We prove that the existence of arbitrarily large supercompact cardinals implies that every absolute epireflective class of objects in a balanced accessible category is a small-orthogonality class. In other words, if L is a localization functor on a balanced accessible category such that the unit morphism X→LX is an epimorphism for all X and the class of L-local objects is defined by an absolute formula, then the existence of a sufficiently large supercompact cardinal implies that L is a localization with respect to some set of morphisms.     

Redundant objective functions in linear vector maximum problems and their determination

Suppose that in a multicriteria linear programming problem among the given objective functions there are some which can be deleted without influencing the set E of all efficient solutions. Such objectives are said to be redundant. Introducing systems of objective functions which realize their individual optimum in a single vertex of the polyhedron generated by the restriction set, the notion of relative or absolute redundant objectives is defined. A theory which describes properties of absolute and relative redundant objectives is developed. A method for determining all the relative and absolute redundant objectives, based on this theory, is given. Illustrative examples demonstrate the procedure.     

Energy image density property and the lent particle method for Poisson measures

We introduce a new approach to absolute continuity of laws of Poisson functionals. It is based on the energy image density property for Dirichlet forms. The associated gradient is a local operator and gives rise to a nice formula called the lent particle method which consists in adding a particle and taking it back after some calculation.     

Complexity of single machine scheduling problems under scenario-based uncertainty

We present algorithmic and computational complexity results for several single machine scheduling problems where some job characteristics are uncertain. This uncertainty is modeled through a finite set of well-defined scenarios. We use here the so-called absolute robustness criterion to select among feasible solutions.     

On the absolute ruin problem in a Sparre Andersen risk model with constant interest

In this paper, we extend the work of Mitric and Sendova (2010), which considered the absolute ruin problem in a risk model with debit and credit interest, to renewal and non-renewal structures. Our first results apply to MAP processes, which we later restrict to the Sparre Andersen renewal risk model with interclaim times that are generalized Erlang (n) distributed and claim amounts following a Matrix-Exponential (ME) distribution (see for e.g. Asmussen and O’Cinneide (1997)). Under this scenario, we present a general methodology to analyze the Gerber-Shiu discounted penalty function defined at absolute ruin, as a solution of high-order linear differential equations with non-constant coefficients. Closed-form solutions for some absolute ruin related quantities in the generalized Erlang (2) case complement the results obtained under the classical risk model by Mitric and Sendova (2010).     

On the total absolute curvature of an immersed sphere

A recent result of Tobias Ekholm [T. Ekholm, Regular homotopy and total curvature II: Sphere immersions into 3-space, Alg. Geom. Topol. 6 (2006) 493-513] shows that for every ?>0 it is possible to construct a sphere eversion such that the total absolute curvature of the immersed spheres are always less than 8π+?. It is an open question whether this is the best possible. The paper contains results relating to this conjecture. As an interesting consequence of these methods it is shown that if during an eversion the total absolute curvature does not exceed 12π then a certain topological event must take place, namely the immersion must become non-simple at some point. An immersion f in general position is simple if for any irreducible self-intersection curve of f in 3-space, its two pre-image curves in the sphere are disjoint.     

Non-Existence of Subordinate Solutions for Jacobi Operators in Some Critical Cases

We show a method of repairing some gaps in proofs of the absolute continuity of the spectrum of Jacobi operators. Such gaps have been found in several recent papers, dealing mainly with the so-called critical case (i.e., Jordan box case). We solve the problem by proving that the subordinate solution does not exist for many cases with two linearly independent generalised eigenvectors possessing “similar” asymptotic behaviour.     

Über die Führer von Gaußschen Summen als Größencharaktere

Let K be an absolute abelian number field. The conductor of the Hecke characters of K formed by Gaussian sums is investigated. In some cases we obtain formulas for this conductor while in others a bound is given. These enable us to obtain a general upper bound for the conductor in terms of the class field theoretic conductor of K. Our bound is an improvement on existing bounds in the literature.     

Small extensions of models of o-minimal theories and absolute homogeneity

We obtain some results on existence of small extensions of models of weakly o-minimal atomic theories. In particular, we find a sharp upper estimate for the Hanf number of such a theory for omitting an arbitrary family of pure types. We also find a sharp upper estimate for cardinalities of weakly o-minimal absolutely homogeneous models and a sufficient condition for absolute homogeneity.     

Finite groups with a given absolute central factor group

Let G be a group and L(G) be the absolute center of G, that is, the set of all elements of G fixed by all automorphisms of G. In this paper, we classify all finite groups G whose absolute central factors are isomorphic to a cyclic group, \({\mathbb{Z}_p \times \mathbb{Z}_p}\) , D ₈, Q ₈, or a non-abelian group of order pq for some distinct primes p and q.     

The absolute order of a permutation representation of a Coxeter group

A permutation representation of a Coxeter group W naturally defines an absolute order. This family of partial orders (which includes the absolute order on W) is introduced and studied in this paper. Conditions under which the associated rank generating polynomial divides the rank generating polynomial of the absolute order on W are investigated when W is finite. Several examples, including a symmetric group action on perfect matchings, are discussed. As an application, a well-behaved absolute order on the alternating subgroup of W is defined.     

Class groups of quadratic fields of 3-rank at least 2: Effective bounds

In this paper, we give parametric families of both real and complex quadratic number fields whose class group has 3-rank at least 2. As a consequence, we obtain that for all large positive real numbers x, the number of both real and complex quadratic fields whose class group has 3-rank at least 2 and absolute value of the discriminant ?x is >cx1/3, where c is some positive constant.     

Linear operators with compact supports, probability measures and Milyutin maps

The notion of a regular operator with compact supports between function spaces is introduced. On that base we obtain a characterization of absolute extensors for 0-dimensional spaces in terms of regular extension operators having compact supports. Milyutin maps are also considered and it is established that some topological properties, like paracompactness, metrizability and κ-metrizability, are preserved under Milyutin maps.     

Duality of nonconvex optimization with positively homogeneous functions

We consider an optimization problem with positively homogeneous functions in its objective and constraint functions. Examples of such positively homogeneous functions include the absolute value function and the p-norm function, where p is a positive real number. The problem, which is not necessarily convex, extends the absolute value optimization proposed in Mangasarian (Comput Optim Appl 36:43–53, 2007). In this work, we propose a dual formulation that, differently from the Lagrangian dual approach, has a closed-form and some interesting properties. In particular, we discuss the relation between the Lagrangian duality and the one proposed here, and give some sufficient conditions under which these dual problems coincide. Finally, we show that some well-known problems, e.g., sum of norms optimization and the group Lasso-type optimization problems, can be reformulated as positively homogeneous optimization problems.     

Torsion Abelian RAI-Groups

A subgroup A of an Abelian group G is called its absolute ideal if A is an ideal of any ring on G. An Abelian group is called an RAI-group if there exists a ring on it in which every ideal is absolute. The problem of describing RAI-groups was formulated by L. Fuchs (Problem 93). In this paper, absolute ideals of torsion Abelian groups and torsion Abelian RAI-groups are described.     

The energy of random graphs

In 1970s, Gutman introduced the concept of the energy E(G) for a simple graph G, which is defined as the sum of the absolute values of the eigenvalues of G. This graph invariant has attracted much attention, and many lower and upper bounds have been established for some classes of graphs among which bipartite graphs are of particular interest. But there are only a few graphs attaining the equalities of those bounds. We however obtain an exact estimate of the energy for almost all graphs by Wigner’s semi-circle law, which generalizes a result of Nikiforov. We further investigate the energy of random multipartite graphs by considering a generalization of Wigner matrix, and obtain some estimates of the energy for random multipartite graphs.     

Sufficient conditions for the Lebesgue integrability of Fourier transforms

We give sufficient conditions for the Lebesgue integrability of the Fourier transform of a function f ∈ L ^p (?) for some 1 < p ≤ 2. These sufficient conditions are in terms of the L ^p integral modulus of continuity of f; in particular, they apply for functions in the integral Lipschitz class Lip(α, p) and for functions of bounded s-variation for some 0 < s < p. Our theorems are nonperiodic versions of the classical theorems of Bernstein, Szász, Zygmund and Salem, and recent theorems of Gogoladze and Meskhia on the absolute convergence of Fourier series.