Searching for a consensus similarity function for generalized trapezoidal fuzzy numbers

There is controversy regarding the use of the similarity functions proposed in the literature to compare generalized trapezoidal fuzzy numbers since conflicting similarity values are sometimes output for the same pair of fuzzy numbers. In this paper we propose a similarity function aimed at establishing a consensus. It accounts for the different approaches of all the similarity functions. It also has better properties and can easily incorporate new parameters for future improvements. The analysis is carried out on the basis of a large and representative set of pairs of trapezoidal fuzzy numbers.

The Proper Generalized Decomposition With Application In Problems Of Dynamics

In this paper we address the new reduction method called Proper Generalized Decomposition (PGD) which is a discretization technique based on the use of separated representation of the unknown fields, specially well suited for solving multidimensional parametric equations. In this case, it is applied to the solution of dynamics problems. We will focus on the dynamic analysis of an one-dimensional rod with a unit harmonic load of frequency (ω) applied at a point of interest. In what follows, we will present the application of the methodology PGD to the problem in order to approximate the displacement field as the sum of the separated functions. We will consider as new variables of the problem, parameters models associated with the characteristic of the materials, in addition to the frequency. Finally, the quality of the results will be assessed based on an example.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

Generalized flows, intrinsic stochasticity, and turbulent transport

The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows, which are families of probability distributions on the space of solutions to the associated ordinary differential equations which no longer satisfy the uniqueness theorem for ordinary differential equations. Two most natural regularizations of this problem, namely the regularization via adding small molecular diffusion and the regularization via smoothing out the velocity field, are considered. White-in-time random velocity fields are used as an example to examine the variety of phenomena that take place when the velocity field is not spatially regular. Three different regimes, characterized by their degrees of compressibility, are isolated in the parameter space. In the regime of intermediate compressibility, the two different regularizations give rise to two different scaling behaviors for the structure functions of the passive scalar. Physically, this means that the scaling depends on Prandtl number. In the other two regimes, the two different regularizations give rise to the same generalized flows even though the sense of convergence can be very different. The “one force, one solution” principle is established for the scalar field in the weakly compressible regime, and for the difference of the scalar in the strongly compressible regime, which is the regime of inverse cascade. Existence and uniqueness of an invariant measure are also proved in these regimes when the transport equation is suitably forced. Finally incomplete self similarity in the sense of Barenblatt and Chorin is established.

LXRα functions as a cAMP-responsive transcriptional regulator of gene expression

LXRα is a member of a nuclear receptor superfamily that regulates transcription. LXRα forms a heterodimer with RXRα, another member of this family, to regulate the expression of cholesterol 7α-hydroxylase by means of binding to the DR4-type cis-element. Here, we describe a function for LXRα as a cAMP-responsive regulator of renin and c-myc gene transcriptions by the interaction with a specific cis-acting DNA element, CNRE (an overlapping cAMP response element and a negative response element). Our previous studies showed that renin gene expression is regulated by cAMP, at least partly, through the CNRE sequence in its 5′-flanking region. This sequence is also found in c-myc and several other genes. Based on our cloning results using the yeast one-hybrid system, we discovered that the mouse homologue of human LXRα binds to the CNRE and demonstrated that it binds as a monomer. To define the function of LXRα on gene expression, we transfected the renin-producing renal As4.1 cells with LXRα expression plasmid. Overexpression of LXRα in As4.1 cells confers cAMP inducibility to reporter constructs containing the renin CNRE. After stable transfection of LXRα, As4.1 cells show a cAMP-inducible up-regulation of renin mRNA expression. In parallel experiments, we demonstrated that LXRα can also bind to the homologous CNRE in the c-myc promoter. cAMP promotes transcription through c-myc/CNRE:LXRα interaction in LXRα transiently transfected cells and increases c-myc mRNA expression in stably transfected cells. Identification of LXRα as a cAMP-responsive nuclear modulator of renin and c-myc expression not only has cardiovascular significance but may have generalized implication in the regulation of gene transcription.

Shared functions in vivo of a glycosyl-phosphatidylinositol-linked aspartyl protease, Mkc7, and the proprotein processing protease Kex2 in yeast.

The MKC7 gene was isolated as a multicopy suppressor of the cold-sensitive growth phenotype of a yeast kex2 mutant, which lacks the protease that cleaves pro-alpha-factor and other secretory proproteins at pairs of basic residues in a late Golgi compartment in yeast. MKC7 encodes an aspartyl protease most closely related to product of the YAP3 gene, a previously isolated multicopy suppressor of the pro-alpha-factor processing defect of a kex2 null. Multicopy MKC7 suppressed the alpha-specific mating defect of a kex2 null as well as multicopy YAP3 did, but multicopy YAP3 was a relatively weak suppressor of kex2 cold sensitivity. Overexpression of MKC7 resulted in production of a membrane-associated proteolytic activity that cleaved an internally quenched fluorogenic peptide substrate on the carboxyl side of a Lys-Arg site. Treatment with phosphatidylinositol-specific phospholipase C shifted Mkc7 activity from the detergent to the aqueous phase in a Triton X-114 phase separation, indicating that membrane attachment of Mkc7 is mediated by a glycosyl-phosphatidylinositol anchor. Although disruption of MKC7 or YAP3 alone resulted in no observable phenotype, mkc7 yap3 double disruptants exhibited impaired growth at 37 degrees C. Disruption of MKC7 and YAP3 in a kex2 null mutant resulted in profound temperature sensitivity and more generalized cold sensitivity. The synergism of mkc7, yap3, and kex2 null mutations argues that Mkc7 and Yap3 are authentic processing enzymes whose functions overlap those of Kex2 in vivo.

On some Generalizations of a Class of Discrete Functions

In this paper we examine discrete functions that depend on their variables in a particular way, namely the H-functions. The results obtained in this work make the “construction” of these functions possible. H-functions are generalized, as well as their matrix representation by Latin hypercubes.

First Order Characterizations of Pseudoconvex Functions

First order characterizations of pseudoconvex functions are investigated in terms of generalized directional derivatives. A connection with the invexity is analysed. Well-known first order characterizations of the solution sets of pseudolinear programs are generalized to the case of pseudoconvex programs. The concepts of pseudoconvexity and invexity do not depend on a single definition of the generalized directional derivative.

A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory

The first motivation for this note is to obtain a general version of the following result: let E be a Banach space and f : E → R be a differentiable function, bounded below and satisfying the Palais-Smale condition; then, f is coercive, i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references therein. A general result of this type was given in [3, Theorem 5.1] for a lower semicontinuous function defined on a Banach space, through an approach based on an abstract notion of subdifferential operator, and taking into account the “smoothness” of the Banach space. Here, we give (Theorem 1) an extension in a metric setting, based on the notion of slope from [11] and coercivity is considered in a generalized sense, inspired by [9]; our result allows to recover, for example, the coercivity result of [19], where a weakened version of the Palais-Smale condition is used. Our main tool (Proposition 1) is a consequence of Ekeland’s variational principle extending [12, Corollary 3.4], and deals with a function f which is, in some sense, the “uniform” Γ-limit of a sequence of functions.

Generalized Scalarizing Problems GENS and GENSLex of Multicriteria Optimization

* This paper is partially supported by the National Science Fund of Bulgarian Ministry of Education and Science under contract № I–1401\2004 "Interactive Algorithms and Software Systems Supporting Multicriteria Decision Making".

Weighted Theorems on Fractional Integrals in the Generalized Hölder Spaces via Indices mω and Mω

Mathematics Subject Classification: 26A16, 26A33, 46E15.

Fractional Calculus of the Generalized Wright Function

Mathematics Subject Classification: 26A33, 33C20.

Numerical Results for the Generalized Mittag-Leffler Function

Mathematics Subject Classification: 33E12, 33FXX PACS (Physics Abstracts Classification Scheme): 02.30.Gp, 02.60.Gf

Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function

2000 Mathematics Subject Classification: 26A33, 33C45

Generalized Sobolev Spaces of Exponential Type Associated with the Dunkl Operators

2000 Mathematics Subject Classification: 35E45