Stieltjes functions and discrete classical orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Vector spaces of entire functions of unbounded type

Let E be an infinite dimensional complex Banach space. We prove the existence of an infinitely generated algebra, an infinite dimensional closed subspace and a dense subspace of entire functions on E whose non-zero elements are functions of unbounded type. We also show that the τδ topology on the space of all holomorphic functions cannot be obtained as a countable inductive limit of Fr´echet spaces. RESUMEN. Sea E un espacio de Banach complejo de dimensión infinita y sea H(E) el espacio de funciones holomorfas definidas en E. En el artículo se demuestra la existencia de un álgebra infinitamente generada en H(E), un subespacio vectorial en H(E) cerrado de dimensión infinita y un subespacio denso en H(E) cuyos elementos no nulos son funciones de tipo no acotado. También se demuestra que el espacio de funciones holomorfas con la topología ? no es un límite inductivo numberable de espacios de Fréchet.

On real analytic functions of unbounded type

In this paper we prove several results on the existence of analytic functions on an infinite dimensional real Banach space which are bounded on some given collection of open sets and unbounded on others. In addition, we also obtain results on the density of some subsets of the space of all analytic functions for natural locally convex topologies on this space. RESUMEN. Los autores demuestran varios resultados de existencia de funciones analíticas en espacios de Banach reales de dimensión infinita que están acotadas en un colección de subconjuntos abiertos y no acotadas en los conjuntos de otra colección. Además, se demuestra la densidad de ciertos subconjuntos de funciones analíticas para varias topologías localmente convexas.

Estimation of Symmetric Channels for Discrete Cosine Transform Type-I Multicarrier Systems: A Compressed Sensing Approach

The problem of channel estimation for multicarrier communications is addressed. We focus on systems employing the Discrete Cosine Transform Type-I (DCT1) even at both the transmitter and the receiver, presenting an algorithm which achieves an accurate estimation of symmetric channel filters using only a small number of training symbols. The solution is obtained by using either matrix inversion or compressed sensing algorithms. We provide the theoretical results which guarantee the validity of the proposed technique for the DCT1. Numerical simulations illustrate the good behaviour of the proposed algorithm.

Targeting of a Germ Cell-specific Type 1 Hexokinase Lacking a Porin-binding Domain to the Mitochondria as Well as to the Head and Fibrous Sheath of Murine Spermatozoa

Multiple isoforms of type 1 hexokinase (HK1) are transcribed during spermatogenesis in the mouse, including at least three that are presumably germ cell specific: HK1-sa, HK1-sb, and HK1-sc. Each of these predicted proteins contains a common, germ cell-specific sequence that replaces the porin-binding domain found in somatic HK1. Although HK1 protein is present in mature sperm and is tyrosine phosphorylated, it is not known whether the various potential isoforms are differentially translated and localized within the developing germ cells and mature sperm. Using antipeptide antisera against unique regions of HK1-sa and HK1-sb, it was demonstrated that these isoforms were not found in pachytene spermatocytes, round spermatids, condensing spermatids, or sperm, suggesting that HK1-sa and HK1-sb are not translated during spermatogenesis. Immunoreactivity was detected in protein from round spermatids, condensing spermatids, and mature sperm using an antipeptide antiserum against the common, germ cell-specific region, suggesting that HK1-sc was the only germ cell-specific isoform present in these cells. Two-dimensional SDS-PAGE suggested that all of the sperm HK1-sc was tyrosine phosphorylated, and that the somatic HK1 isoform was not present. Immunoelectron microscopy revealed that HK1-sc was associated with the mitochondria and with the fibrous sheath of the flagellum and was found in discrete clusters in the region of the membranes of the sperm head. The unusual distribution of HK1-sc in sperm suggests novel functions, such as extramitochondrial energy production, and also demonstrates that a hexokinase without a classical porin-binding domain can localize to mitochondria.

Calcineurin and vacuolar-type H+-ATPase modulate macrophage effector functions

While effector molecules produced by activated macrophages (including nitric oxide, tumor necrosis factor α, interleukin 1, etc.) help to eliminate pathogens, high levels of these molecules can be deleterious to the host itself. Despite their importance, the mechanisms modulating macrophage effector functions are poorly understood. This work introduces two key negative regulators that control the levels and duration of macrophage cytokine production. Vacuolar-type H+-ATPase (V-ATPase) and calcineurin (Cn) constitutively act in normal macrophages to suppress expression of inflammatory cytokines in the absence of specific activation and to inhibit macrophage cytokine responses induced by bacterial lipopolysaccharide (V-ATPase), interferon γ (V-ATPase and Cn), and calcium (Ca2+) flux (Cn). Cn and V-ATPase modulate effector gene expression at the mRNA level by inhibiting transcription factor NF-κB. This negative regulation by Cn is opposite to its crucial positive role in T cells, where it activates NFAT transcription factor(s) leading to expression of interleukin 2, tumor necrosis factor α, and other cytokine genes. The negative effects of V-ATPase and Cn on NF-κB-dependent gene expression are not limited to the macrophage lineage, as similar effects have been seen with a murine fibroblast cell line and with primary astrocytes.

Molecular characterization and assembly of the needle complex of the Salmonella typhimurium type III protein secretion system

Many bacterial pathogens of plants and animals have evolved a specialized protein-secretion system termed type III to deliver bacterial proteins into host cells. These proteins stimulate or interfere with host cellular functions for the pathogen's benefit. The Salmonella typhimurium pathogenicity island 1 encodes one of these systems that mediates this bacterium's ability to enter nonphagocytic cells. Several components of this type III secretion system are organized in a supramolecular structure termed the needle complex. This structure is made of discrete substructures including a base that spans both membranes and a needle-like projection that extends outward from the bacterial surface. We demonstrate here that the type III secretion export apparatus is required for the assembly of the needle substructure but is dispensable for the assembly of the base. We show that the length of the needle segment is determined by the type III secretion associated protein InvJ. We report that InvG, PrgH, and PrgK constitute the base and that PrgI is the main component of the needle of the type III secretion complex. PrgI homologs are present in type III secretion systems from bacteria pathogenic for animals but are absent from bacteria pathogenic for plants. We hypothesize that the needle component may establish the specificity of type III secretion systems in delivering proteins into either plant or animal cells.

Identification of Two Type V Myosins in Fission Yeast, One of Which Functions in Polarized Cell Growth and Moves Rapidly in the Cell

We characterized the novel Schizosaccharomyces pombe genes myo4+ and myo5+, both of which encode myosin-V heavy chains. Disruption of myo4 caused a defect in cell growth and led to an abnormal accumulation of secretory vesicles throughout the cytoplasm. The mutant cells were rounder than normal, although the sites for cell polarization were still established. Elongation of the cell ends and completion of septation required more time than in wild-type cells, indicating that Myo4 functions in polarized growth both at the cell ends and during septation. Consistent with this conclusion, Myo4 was localized around the growing cell ends, the medial F-actin ring, and the septum as a cluster of dot structures. In living cells, the dots of green fluorescent protein-tagged Myo4 moved rapidly around these regions. The localization and movement of Myo4 were dependent on both F-actin cables and its motor activity but seemed to be independent of microtubules. Moreover, the motor activity of Myo4 was essential for its function. These results suggest that Myo4 is involved in polarized cell growth by moving with a secretory vesicle along the F-actin cables around the sites for polarization. In contrast, the phenotype of myo5 null cells was indistinguishable from that of wild-type cells. This and other data suggest that Myo5 has a role distinct from that of Myo4.

A planar geometrical model for representing multidimensional discrete spaces and multiple-valued logic functions /

Bibliography: p. 37-38.

Structure and regulation of type 2 transglutaminase in relation to its physiological functions and pathological roles

This chapter contains sections titled: Introduction Structure and Regulation Physiologic Functions of TG2 Disruption of TG2 Functions in Pathologic Conditions Perspectives for Pharmacologic Interventions Concluding Comments Acknowledgements References

Finding the Relationship between a Search Algorithm and a Class of Functions on Discrete Space by Exhaustive Search

* The work is supported by RFBR, grant 04-01-00858-a.

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

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

Association between mean residual life (MRL) and failure rate functions for continuous and discrete lifetime distributions

The purpose of this study was to correct some mistakes in the literature and derive a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. It was also desired to find the conditions under which the discrete failure rate function has an upside-down bathtub shape if corresponding MRL function has a bathtub shape. The study showed that if discrete MRL has a bathtub shape, then under some conditions the corresponding failure rate function has an upside-down bathtub shape. Also the study corrected some mistakes in proofs of Tang, Lu and Chew (1999) and established a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. Similarly, some mistakes in Gupta and Gupta (2000) are corrected, with the ensuing results being expanded and proved thoroughly to establish the relationship between the crossing points of the failure rate and associated MRL functions. The new results derived in this study will be useful to model various lifetime data that occur in environmental studies, medical research, electronics engineering, and in many other areas of science and technology.

Parametric CAD model based shape optimization using adjoint functions

Adjoint methods have proven to be an efficient way of calculating the gradient of an objective function with respect to a shape parameter for optimisation, with a computational cost nearly independent of the number of the design variables [1]. The approach in this paper links the adjoint surface sensitivities (gradient of objective function with respect to the surface movement) with the parametric design velocities (movement of the surface due to a CAD parameter perturbation) in order to compute the gradient of the objective function with respect to CAD variables.
For a successful implementation of shape optimization strategies in practical industrial cases, the choice of design variables or parameterisation scheme used for the model to be optimized plays a vital role. Where the goal is to base the optimization on a CAD model the choices are to use a NURBS geometry generated from CAD modelling software, where the position of the NURBS control points are the optimisation variables [2] or to use the feature based CAD model with all of the construction history to preserve the design intent [3]. The main advantage of using the feature based model is that the optimized model produced can be directly used for the downstream applications including manufacturing and process planning.
This paper presents an approach for optimization based on the feature based CAD model, which uses CAD parameters defining the features in the model geometry as the design variables. In order to capture the CAD surface movement with respect to the change in design variable, the “Parametric Design Velocity” is calculated, which is defined as the movement of the CAD model boundary in the normal direction due to a change in the parameter value.
The approach presented here for calculating the design velocities represents an advancement in terms of capability and robustness of that described by Robinson et al. [3]. The process can be easily integrated to most industrial optimisation workflows and is immune to the topology and labelling issues highlighted by other CAD based optimisation processes. It considers every continuous (“real value”) parameter type as an optimisation variable, and it can be adapted to work with any CAD modelling software, as long as it has an API which provides access to the values of the parameters which control the model shape and allows the model geometry to be exported. To calculate the movement of the boundary the methodology employs finite differences on the shape of the 3D CAD models before and after the parameter perturbation. The implementation procedure includes calculating the geometrical movement along a normal direction between two discrete representations of the original and perturbed geometry respectively. Parametric design velocities can then be directly linked with adjoint surface sensitivities to extract the gradients to use in a gradient-based optimization algorithm.
The optimisation of a flow optimisation problem is presented, in which the power dissipation of the flow in an automotive air duct is to be reduced by changing the parameters of the CAD geometry created in CATIA V5. The flow sensitivities are computed with the continuous adjoint method for a laminar and turbulent flow [4] and are combined with the parametric design velocities to compute the cost function gradients. A line-search algorithm is then used to update the design variables and proceed further with optimisation process.