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Lipid disorders have been implicated in overweight and menopause. However, evidence on lipidomic analysis of fatty acids in erythrocytes of menopausal women is scarce. The aim of this study was to investigate the relationship between the body mass index within or beyond 5 years of menopause and erythrocyte fatty acid profile. This case-control study was conducted on out of 37 menopausal women total patients, 22 with body mass index ≥ 25 and 12 matched controls (body mass index 25 and non-physiological content of fatty acids, were richer in percentage of saturated fatty acids and poorer of monounsaturated fatty acids and polyunsaturated fatty acids than women with BMI25 than in women with BMI

This paper focuses on reducing the computational cost of a GNC Algorithm for deblurring images when dealing with full symmetric Toeplitz block matrices composed of Toeplitz blocks. Such a case is widespread in real cases when the PSF has a vast range. The analysis in this paper centers around the class of gamma matrices, which can perform vector multiplications quickly. The paper presents a theoretical and experimental analysis of how γ -matrices can accurately approximate symmetric Toeplitz matrices. The proposed approach involves adding a minimization step for a new approximation of the energy function to the GNC technique. Specifically, we replace the Toeplitz matrices found in the blocks of the blur operator with γ -matrices in this approximation. The experimental results demonstrate that the new GNC algorithm proposed in this paper reduces computation time by over 20 % compared with its previous version. The image reconstruction quality, however, remains unchanged. [ABSTRACT FROM AUTHOR]

We present the algebraic structures behind the approaches used to work with pairwise comparison matrices and, in general, the representation of preferences. We obtain a general definition of consistency and a universal decomposition in the space of PCMs, which allow us to define a consistency index. Also Arrow's theorem, which is presented in a general form, is relevant. All the presented results can be seen in the main formulations of PCMs, i.e., multiplicative, additive and fuzzy approach, by the fact that each of them is a particular interpretation of the more general algebraic structure needed to deal with these theories. [ABSTRACT FROM AUTHOR]

In this paper, we give a survey about recent versions of Korovkin-type theorems for modular function spaces, a class which includes Lp, Orlicz, Musielak-Orlicz spaces and many others. We consider various kinds of modular convergence, using certain summability processes, like triangular matrix statistical convergence, and filter convergence (which are generalizations of the statistical convergence). Finally, we consider an abstract axiomatic convergence which includes the previous ones and even almost convergence, which is not generated by any filter, as we show by an example. [ABSTRACT FROM AUTHOR]

We prove a Korovkin-type approximation theorem using abstract relative uniform filter convergence of a net of functions with respect to another fixed filter, a particular case of which is that of all neighborhoods of a point, belonging to the domain of the involved functions. We give some examples, in which we show that our results are strict generalizations of the classical ones. [ABSTRACT FROM AUTHOR]

We prove a Korovkin-type approximation theorem using the relative uniform convergence of a sequence of functions at a point, which is a method stronger than the classical ones. We give some examples on this new convergence method and we study also rates of convergence. [ABSTRACT FROM AUTHOR]

This paper deals with uncomplete unambiguous automata. In this setting, we investigate the minimal length of uncompletable words. This problem is connected with a well-known conjecture formulated by A. Restivo. We introduce the notion of relatively maximal row for a suitable monoid of matrices. We show that, if M is a monoid of {0, 1}-matrices of dimension n generated by a set S, then there is a matrix of M containing a relatively maximal row which can be expressed as a product of O(n3) matrices of S. As an application, we derive some upper bound to the minimal length of an uncompletable word of an uncomplete unambiguous automaton, in the case that its transformation monoid contains a relatively maximal row which is not maximal. Finally we introduce the maximal row automaton associated with an unambiguous automaton A. It is a deterministic automaton, which is complete if and only if A is. We prove that the minimal length of the uncompletable words of A is polynomially bounded by the number of states of A and the minimal length of the uncompletable words of the associated maximal row automaton. [ABSTRACT FROM AUTHOR]

We examine an instance of the blind source separation problem, namely, the reconstruction of digital documents degraded by bleed-through and show-through effects. We introduce a nonstationary, locally linear data model and a solution approach based on the assumption of cross-correlated ideal sources. In order to solve the ill-posed local linear problem, we impose that the sum of all rows of the mixture matrix is equal to one, and we assume that the ideal sources are nonnegative and with an estimated level of overlapping (i.e., estimated cross-correlation). The solutions we obtain are related to a factorization of the covariance matrix of the data, which allows the given constraints to be satisfied at best. Our experimental results confirm the effectiveness of the method we propose. [ABSTRACT FROM AUTHOR]

Some versions of Dieudonné-type convergence and uniform boundedness theorems are proved, for k-triangular and regular lattice group-valued set functions. We use sliding hump techniques and direct methods. We extend earlier results, proved in the real case. Furthermore, we pose some open problems. [ABSTRACT FROM AUTHOR]

Affine representations for archimedean $${\ell}$$ -groups and semisimple MV-algebras via embedding theorems are presented; they are simple to work with but powerful enough to express significant properties of our studied objects. Indeed, we focus on the space of particular homomorphisms between an archimedean $${\ell}$$ -group (a semisimple MV-algebra, respectively) and a vector lattice (a Riesz MV-algebra, respectively), i.e., the set of the generalized states, providing a general framework. [ABSTRACT FROM AUTHOR]

We investigate some properties of (uniformly) absolutely continuous, singular and non-concentrated k-subadditive lattice group-valued capacities, and we examine some relations between them. Furthermore, we pose some open problems. [ABSTRACT FROM AUTHOR]

Lp spaces are investigated for vector lattice-valued functions, with respect to filter convergence. As applications, some classical inequalities are extended to the vector lattice context, and some properties of the Brownian motion and the Brownian bridge are studied, to solve some stochastic differential equations. [ABSTRACT FROM AUTHOR]

We give necessary and sufficient conditions for exchange of limits of double-indexed families, taking values in sets endowed with an abstract structure of convergence, and for preservation of continuity or semicontinuity of the limit family, with respect to filter convergence. As a consequence, we give some filter limit theorems and some characterization of continuity and semicontinuity of the limit of a pointwise convergent family of set functions. Furthermore, we pose some open problems. [ABSTRACT FROM AUTHOR]

We deal with a new type of statistical convergence for double sequences, called Ψ-A-statistical convergence, and we prove a Korovkin-type approximation theorem with respect to this type of convergence in modular spaces. Finally, we give some application to moment-type operators in Orlicz spaces. [ABSTRACT FROM AUTHOR]

Some new types of limit theorems for topological group-valued measures are proved in the context of filter convergence for suitable classes of filters. We investigate (s)-boundedness, σ-additivity and regularity properties of topological group-valued measures. We consider also Schur-type theorems, using the sliding hump technique, and prove some convergence theorems in the particular case of positive measures. We deal with the notion of uniform filter exhaustiveness, by means of which we prove some theorems on existence of the limit measure, some other kinds of limit theorems and their equivalence, using known results on existence of countably additive restrictions of strongly bounded measures. Furthermore we pose some open problems. [ABSTRACT FROM AUTHOR]

We prove some versions of abstract Korovkin-type theorems in modular function spaces, with respect to filter convergence for linear positive operators, by considering several kinds of test functions. We give some results with respect to an axiomatic convergence, including almost convergence. An extension to non positive operators is also studied. Finally, we give some examples and applications to moment and bivariate Kantorovich-type operators, showing that our results are proper extensions of the corresponding classical ones. [ABSTRACT FROM AUTHOR]

Some types of compactness in the ideal context are defined and relations between ideal exhaustiveness and equicontinuity of measures are investigated. As applications, some versions of limit theorems involving ideal pointwise convergence of measure sequences and some weak compactness results related to integral functionals are presented. [ABSTRACT FROM AUTHOR]