On the Hilbert transform in the framework of generalized functions

In this paper, a definition of the Hilbert transform operating on Colombeau's temperated generalized functions is given. Similar results to some theorems that hold in the classical theory, or in certain subspaces of Schwartz distributions, have been obtained in this framework.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

DISTRIBUTION FUNCTIONS, MEAN SQUARED ERRORS, AND CONFIDENCE LIMITS FOR RIDGE REGRESSION ESTIMATORS

A large number of ridge regression estimators have been proposed and used with little knowledge of their true distributions. Because of this lack of knowledge, these estimators cannot be used to test hypotheses or to form confidence intervals.^ This paper presents a basic technique for deriving the exact distribution functions for a class of generalized ridge estimators. The technique is applied to five prominent generalized ridge estimators. Graphs of the resulting distribution functions are presented. The actual behavior of these estimators is found to be considerably different than the behavior which is generally assumed for ridge estimators.^ This paper also uses the derived distributions to examine the mean squared error properties of the estimators. A technique for developing confidence intervals based on the generalized ridge estimators is also presented. ^

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.

Basic mathematics in electrical communications. A treatise on conic section curves, exponentials, alternating current, electrical oscillations, transients and hyperbolic functions.

Mode of access: Internet.

Generalized Problem of Sratlikeness for Products of P-Valent Starlike Functions

∗ Partially supported by grant No. 433/94 NSF of the Ministry of Education and Science of the Republic of Bulgaria 1991 Mathematics Subject Classification:30C45

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".

Certain Properties of Fractional Calculus Operators Associated with Generalized Mittag-Leffler Function

Mathematics Subject Classification: 26A33, 33E12, 33C20.

Integral Representations of Generalized Mathieu Series Via Mittag-Leffler Type Functions

Mathematics Subject Classification: 33C05, 33C10, 33C20, 33C60, 33E12, 33E20, 40A30

Fractional Integration of the Product of Bessel Functions of the First Kind

Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09

Fractional Derivatives in Spaces of Generalized Functions

MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

Parameterized Link Functions in Generalized Linear Random Effect Models: a Case Study on Breast Cancer Treatment

In non-linear random effects some attention has been very recently devoted to the analysis ofsuitable transformation of the response variables separately (Taylor 1996) or not (Oberg and Davidian 2000) from the transformations of the covariates and, as far as we know, no investigation has been carried out on the choice of link function in such models. In our study we consider the use of a random effect model when a parameterized family of links (Aranda-Ordaz 1981, Prentice 1996, Pregibon 1980, Stukel 1988 and Czado 1997) is introduced. We point out the advantages and the drawbacks associated with the choice of this data-driven kind of modeling. Difficulties in the interpretation of regression parameters, and therefore in understanding the influence of covariates, as well as problems related to loss of efficiency of estimates and overfitting, are discussed. A case study on radiotherapy usage in breast cancer treatment is discussed.

On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.

Nonempirical hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound

A simple and completely general representation of the exact exchange-correlation functional of density-functional theory is derived from the universal Lieb-Oxford bound, which holds for any Coulomb-interacting system. This representation leads to an alternative point of view on popular hybrid functionals, providing a rationale for why they work and how they can be constructed. A similar representation of the exact correlation functional allows to construct fully nonempirical hyper-generalized-gradient approximations (HGGAs), radically departing from established paradigms of functional construction. Numerical tests of these HGGAs for atomic and molecular correlation energies and molecular atomization energies show that even simple HGGAs match or outperform state-of-the-art correlation functionals currently used in solid-state physics and quantum chemistry.

Piezoresistive sensor design using topology optimization

Piezoresistive materials, materials whose resistivity properties change when subjected to mechanical stresses, are widely utilized in many industries as sensors, including pressure sensors, accelerometers, inclinometers, and load cells. Basic piezoresistive sensors consist of piezoresistive devices bonded to a flexible structure, such as a cantilever or a membrane, where the flexible structure transmits pressure, force, or inertial force due to acceleration, thereby causing a stress that changes the resistivity of the piezoresistive devices. By applying a voltage to a piezoresistive device, its resistivity can be measured and correlated with the amplitude of an applied pressure or force. The performance of a piezoresistive sensor is closely related to the design of its flexible structure. In this research, we propose a generic topology optimization formulation for the design of piezoresistive sensors where the primary aim is high response. First, the concept of topology optimization is briefly discussed. Next, design requirements are clarified, and corresponding objective functions and the optimization problem are formulated. An optimization algorithm is constructed based on these formulations. Finally, several design examples of piezoresistive sensors are presented to confirm the usefulness of the proposed method.