Quasiconformal mappings and inequalities involving special functions

This PhD thesis in Mathematics belongs to the field of Geometric Function Theory. The thesis consists of four original papers. The topic studied deals with quasiconformal mappings and their distortion theory in Euclidean n-dimensional spaces. This theory has its roots in the pioneering papers of F. W. Gehring and J. Väisälä published in the early 1960’s and it has been studied by many mathematicians thereafter. In the first paper we refine the known bounds for the so-called Mori constant and also estimate the distortion in the hyperbolic metric. The second paper deals with radial functions which are simple examples of quasiconformal mappings. These radial functions lead us to the study of the so-called p-angular distance which has been studied recently e.g. by L. Maligranda and S. Dragomir. In the third paper we study a class of functions of a real variable studied by P. Lindqvist in an influential paper. This leads one to study parametrized analogues of classical trigonometric and hyperbolic functions which for the parameter value p = 2 coincide with the classical functions. Gaussian hypergeometric functions have an important role in the study of these special functions. Several new inequalities and identities involving p-analogues of these functions are also given. In the fourth paper we study the generalized complete elliptic integrals, modular functions and some related functions. We find the upper and lower bounds of these functions, and those bounds are given in a simple form. This theory has a long history which goes back two centuries and includes names such as A. M. Legendre, C. Jacobi, C. F. Gauss. Modular functions also occur in the study of quasiconformal mappings. Conformal invariants, such as the modulus of a curve family, are often applied in quasiconformal mapping theory. The invariants can be sometimes expressed in terms of special conformal mappings. This fact explains why special functions often occur in this theory.

Vorlesungen über die Theorie der elliptischen Modulfunctionen,

Available on demand as hard copy or computer file from Cornell University Library.

Les fonctions polyédriques et modulaires.

Available on demand as hard copy or computer file from Cornell University Library.

A Gag peptide encompassing B- and T-cell epitopes of the caprine arthritis encephalitis virus functions as modular carrier peptide

Short synthetic peptides are important tools in biomedical research permitting to generate hapten specific polyclonal sera for analytical purposes or functional studies. In this paper we provide proof of principle that a peptide located in a highly conserved portion of the Gag protein of the caprine arthritis encephalitis virus and carrying an immunodominant T helper cell epitope functions as an efficient carrier peptide, mediating a strong antibody response to a peptidic hapten encompassing a well-characterized B cell epitope of Env. The carrier and hapten peptides were collinearly synthesized permutating their molecular arrangement. While the antibody response to the hapten was similar for both constructs, the antibody response to a B cell epitope overlapping the T helper cell epitope of the Gag carrier peptide was considerably different. This permits a modular use of the carrier peptide to generate antibody directed exclusively to the hapten peptide or a strong humoral response to both carrier- and hapten-peptide. Finally, we have mapped the epitopes involved in this polarized antibody response and discussed the potential immunological implications.

Towards modular and coordinated manufacturing systems oriented to services

Nowadays, there is a trend for industry reorganization in geographically dispersed systems, carried out of their activities with autonomy. These systems must maintain coordinated relationship among themselves in order to assure an expected performance of the overall system. Thus, a manufacturing system is proposed, based on ""web services"" to assure an effective orchestration of services in order to produce final products. In addition, it considers special functions, such as teleoperation and remote monitoring, users` online request, among others. Considering the proposed system as discrete event system (DES), techniques derived from Petri nets (PN), including the Production Flow Schema (PFS), can be used in a PFS/PN approach for modeling. The system is approached in different levels of abstraction: a conceptual model which is obtained by applying the PFS technique and a functional model which is obtained by applying PN. Finally, a particular example of the proposed system is presented.

A modular tethering complex for endosomal recycling.

How proteins migrate through the interconnected organelles of the endolysosomal system is poorly understood. A piece of the puzzle has been added with the identification of a complex of tethering factors that functions in the recycling of proteins towards the cell surface.

Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two

The Rankin convolution type Dirichlet series D-F,D-G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series D-F,D-G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of the same weight are not linear combinations of those. In order to conduct these experiments a numerical method to compute the Petersson scalar products of Jacobi Forms is developed and discussed in detail.

Desarrollo de un sistema hardware modular que implemente los instrumentos de un laboratorio de electrónica

El poder disponer de la instrumentación y los equipos electrónicos resulta vital en el diseño de circuitos analógicos. Permiten realizar las pruebas necesarias y el estudio para el buen funcionamiento de estos circuitos. Los equipos se pueden diferenciar en instrumentos de excitación, los que proporcionan las señales al circuito, y en instrumentos de medida, los que miden las señales generadas por el circuito. Estos equipos sirven de gran ayuda pero a su vez tienen un precio elevado lo que impide en muchos casos disponer de ellos. Por esta principal desventaja, se hace necesario conseguir un dispositivo de bajo coste que sustituya de alguna manera a los equipos reales. Si el instrumento es de medida, este sistema de bajo coste puede ser implementado mediante un equipo hardware encargado de adquirir los datos y una aplicación ejecutándose en un ordenador donde analizarlos y presentarlos en la pantalla. En el caso de que el instrumento sea de excitación, el único cometido del sistema hardware es el de proporcionar las señales cuya configuración ha enviado el ordenador. En un equipo real, es el propio equipo el que debe realizar todas esas acciones: adquisición, procesamiento y presentación de los datos. Además, la dificultad de realizar modificaciones o ampliaciones de las funcionalidades en un instrumento tradicional con respecto a una aplicación de queda patente. Debido a que un instrumento tradicional es un sistema cerrado y uno cuya configuración o procesamiento de datos es hecho por una aplicación, algunas de las modificaciones serían realizables modificando simplemente el software del programa de control, por lo que el coste de las modificaciones sería menor. En este proyecto se pretende implementar un sistema hardware que tenga las características y realice las funciones del equipamiento real que se pueda encontrar en un laboratorio de electrónica. También el desarrollo de una aplicación encargada del control y el análisis de las señales adquiridas, cuya interfaz gráfica se asemeje a la de los equipos reales para facilitar su uso. ABSTRACT. The instrumentation and electronic equipment are vital for the design of analogue circuits. They enable to perform the necessary testing and study for the proper functioning of these circuits. The devices can be classified into the following categories: excitation instruments, which transmit the signals to the circuit, and measuring instruments, those in charge of measuring the signals produced by the circuit. This equipment is considerably helpful, however, its high price often makes it hardly accessible. For this reason, low price equipment is needed in order to replace real devices. If the instrument is measuring, this low cost system can be implemented by hardware equipment to acquire the data and running on a computer where analyzing and present on the screen application. In case of an excitation the instrument, the only task of the hardware system is to provide signals which sent the computer configuration. In a real instrument, is the instrument itself that must perform all these actions: acquisition, processing and presentation of data. Moreover, the difficulty of making changes or additions to the features in traditional devices with respect to an application running on a computer is evident. This is due to the fact that a traditional instrument is a closed system and its configuration or data processing is made by an application. Therefore, certain changes can be made just by modifying the control program software. Consequently, the cost of these modifications is lower. This project aims to implement a hardware system with the same features and functions of any real device, available in an electronics laboratory. Besides, it aims to develop an application for the monitoring and analysis of acquired signals. This application is provided with a graphic interface resembling those of real devices in order to facilitate its use.

Modular organization of the Friend murine leukemia virus envelope protein underlies the mechanism of infection

Retrovirus infection is initiated by receptor-dependent fusion of the envelope to the cell membrane. The modular organization of the envelope protein of C type retroviruses has been exploited to investigate how binding of the surface subunit (SU) to receptor triggers fusion mediated by the transmembrane (TM) subunit. We show that deletion of the receptor-binding domain (RBD) from SU of Friend murine leukemia virus (Fr-MLV) abolishes infection that is restored by supplying RBD as a soluble protein. Infection by this mechanism remains dependent on receptor expression. When membrane attachment of the virus lacking RBD is reestablished by inserting the hormone erythropoietin, infection remains dependent on the RBD/receptor complex. However, infection increases 50-fold to 5 × 105 units/ml on cells that also express the erythropoietin receptor. Soluble RBD from Fr-MLV also restores infection by amphotropic and xenotropic MLVs in which RBD is deleted. These experiments demonstrate that RBD has two functions: mediating virus attachment and activating the fusion mechanism. In addition, they indicate that receptor engagement triggers fusion by promoting a subgroup-independent functional interaction between RBD and the remainder of SU and/or TM.

SMART, a simple modular architecture research tool: Identification of signaling domains

Accurate multiple alignments of 86 domains that occur in signaling proteins have been constructed and used to provide a Web-based tool (SMART: simple modular architecture research tool) that allows rapid identification and annotation of signaling domain sequences. The majority of signaling proteins are multidomain in character with a considerable variety of domain combinations known. Comparison with established databases showed that 25% of our domain set could not be deduced from SwissProt and 41% could not be annotated by Pfam. SMART is able to determine the modular architectures of single sequences or genomes; application to the entire yeast genome revealed that at least 6.7% of its genes contain one or more signaling domains, approximately 350 greater than previously annotated. The process of constructing SMART predicted (i) novel domain homologues in unexpected locations such as band 4.1-homologous domains in focal adhesion kinases; (ii) previously unknown domain families, including a citron-homology domain; (iii) putative functions of domain families after identification of additional family members, for example, a ubiquitin-binding role for ubiquitin-associated domains (UBA); (iv) cellular roles for proteins, such predicted DEATH domains in netrin receptors further implicating these molecules in axonal guidance; (v) signaling domains in known disease genes such as SPRY domains in both marenostrin/pyrin and Midline 1; (vi) domains in unexpected phylogenetic contexts such as diacylglycerol kinase homologues in yeast and bacteria; and (vii) likely protein misclassifications exemplified by a predicted pleckstrin homology domain in a Candida albicans protein, previously described as an integrin.

Modular cis-regulatory organization of developmentally expressed genes: two genes transcribed territorially in the sea urchin embryo, and additional examples.

The cis-regulatory systems that control developmental expression of two sea urchin genes have been subjected to detailed functional analysis. Both systems are modular in organization: specific, separable fragments of the cis-regulatory DNA each containing multiple transcription factor target sites execute particular regulatory subfunctions when associated with reporter genes and introduced into the embryo. The studies summarized here were carried out on the CyIIIa gene, expressed in the embryonic aboral ectoderm and on the Endo16 gene, expressed in the embryonic vegetal plate, archenteron, and then midgut. The regulatory systems of both genes include modules that control particular aspects of temporal and spatial expression, and in both the territorial boundaries of expression depend on a combination of negative and positive functions. In both genes different regulatory modules control early and late embryonic expression. Modular cis-regulatory organization is widespread in developmentally regulated genes, and we present a tabular summary that includes many examples from mouse and Drosophila. We regard cis-regulatory modules as units of developmental transcription control, and also of evolution, in the assembly of transcription control systems.

Design and analysis of an all-optical processor for modular arithmetic

We present a logical design of an all-optical processor that performs modular arithmetic. The overall design is based a set of interconnected modules that use all-optical gates to perform simple logical functions. The all-optical logic gates are based on the semiconductor optical amplifier nonlinear loop. Simulation results are presented and some practical design issues are discussed.

Central-tapped node linked modular fault-tolerance topology for SRM applications

Electric vehicles (EVs) and hybrid electric vehicles (HEVs) can reduce greenhouse gas emissions while switched reluctance motor (SRM) is one of the promising motor for such applications. This paper presents a novel SRM fault-diagnosis and fault-tolerance operation solution. Based on the traditional asymmetric half-bridge topology for the SRM driving, the central tapped winding of the SRM in modular half-bridge configuration are introduced to provide fault-diagnosis and fault-tolerance functions, which are set idle in normal conditions. The fault diagnosis can be achieved by detecting the characteristic of the excitation and demagnetization currents. An SRM fault-tolerance operation strategy is also realized by the proposed topology, which compensates for the missing phase torque under the open-circuit fault, and reduces the unbalanced phase current under the short-circuit fault due to the uncontrolled faulty phase. Furthermore, the current sensor placement strategy is also discussed to give two placement methods for low cost or modular structure. Simulation results in MATLAB/Simulink and experiments on a 750-W SRM validate the effectiveness of the proposed strategy, which may have significant implications and improve the reliability of EVs/HEVs.

Mathematical methods for the configuration of transportation systems with a focus on continuous and modular matrix conveyors

The lack of flexibility in logistic systems currently on the market leads to the development of new innovative transportation systems. In order to find the optimal configuration of such a system depending on the current goal functions, for example minimization of transport times and maximization of the throughput, various mathematical methods of multi-criteria optimization are applicable. In this work, the concept of a complex transportation system is presented. Furthermore, the question of finding the optimal configuration of such a system through mathematical methods of optimization is considered.

Congruences in modular, Jacobi, Siegel, and mock modular forms with applications

We study congruences in the coefficients of modular and other automorphic forms. Ramanujan famously found congruences for the partition function like p(5n+4) = 0 mod 5. For a wide class of modular forms, we classify the primes for which there can be analogous congruences in the coefficients of the Fourier expansion. We have several applications. We describe the Ramanujan congruences in the counting functions for overparitions, overpartition pairs, crank differences, and Andrews' two-coloured generalized Frobenius partitions. We also study Ramanujan congruences in the Fourier coefficients of certain ratios of Eisenstein series. We also determine the exact number of holomorphic modular forms with Ramanujan congruences when the weight is large enough. In a chapter based on joint work with Olav Richter, we study Ramanujan congruences in the coefficients of Jacobi forms and Siegel modular forms of degree two. Finally, the last chapter contains a completely unrelated result about harmonic weak Maass forms.