Geometrical logarithmic and trigonometric hypercomplex functions of quaternionic type

Quaternionic theory has greatly been developed in recent years [1-12]. Thus, in our view, the study of trigonometric and logarithmic type quaternionic functions is important for the determination and realization of a hyper complex theory. In this paper, we intend to give a geometrical foundation for both logarithmic and trigonometric hyper complex functions based on the exponential function of quaternionic type recently introduced by Borges, Marão and Machado in their paper entitled Geometrical octonions II: Hyper regularity and hyper periodicity of the exponential function appearing. © 2011 Pushpa Publishing House.

Zeros of classical orthogonal polynomials of a discrete variable

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Mapping an uncertainty zone between interpolated types of a categorical variable

Categorical data cannot be interpolated directly because they are outcomes of discrete random variables. Thus, types of categorical variables are transformed into indicator functions that can be handled by interpolation methods. Interpolated indicator values are then backtransformed to the original types of categorical variables. However, aspects such as variability and uncertainty of interpolated values of categorical data have never been considered. In this paper we show that the interpolation variance can be used to map an uncertainty zone around boundaries between types of categorical variables. Moreover, it is shown that the interpolation variance is a component of the total variance of the categorical variables, as measured by the coefficient of unalikeability. (C) 2011 Elsevier Ltd. All rights reserved.

Characterization of the procera Tomato Mutant Shows Novel Functions of the SlDELLA Protein in the Control of Flower Morphology, Cell Division and Expansion, and the Auxin-Signaling Pathway during Fruit-Set and Development

procera (pro) is a tall tomato (Solanum lycopersicum) mutant carrying a point mutation in the GRAS region of the gene encoding SlDELLA, a repressor in the gibberellin (GA) signaling pathway. Consistent with the SlDELLA loss of function, pro plants display a GA-constitutive response phenotype, mimicking wild-type plants treated with GA(3). The ovaries from both nonemasculated and emasculated pro flowers had very strong parthenocarpic capacity, associated with enhanced growth of preanthesis ovaries due to more and larger cells. pro parthenocarpy is facultative because seeded fruits were obtained by manual pollination. Most pro pistils had exserted stigmas, thus preventing self-pollination, similar to wild-type pistils treated with GA(3) or auxins. However, Style2.1, a gene responsible for long styles in noncultivated tomato, may not control the enhanced style elongation of pro pistils, because its expression was not higher in pro styles and did not increase upon GA(3) application. Interestingly, a high percentage of pro flowers had meristic alterations, with one additional petal, sepal, stamen, and carpel at each of the four whorls, respectively, thus unveiling a role of SlDELLA in flower organ development. Microarray analysis showed significant changes in the transcriptome of preanthesis pro ovaries compared with the wild type, indicating that the molecular mechanism underlying the parthenocarpic capacity of pro is complex and that it is mainly associated with changes in the expression of genes involved in GA and auxin pathways. Interestingly, it was found that GA activity modulates the expression of cell division and expansion genes and an auxin signaling gene (tomato AUXIN RESPONSE FACTOR7) during fruit-set.

Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.

Effect of constant and variable domain glycosylation on pharmacokinetics of therapeutic antibodies in mice

Previous studies on the effect of glycosylation on the elimination rate of antibodies have produced conflicting results. Here, we performed pharmacokinetic studies in mice with two preparations of a monoclonal IgG1 antibody enriched for complex type or high mannose type oligosaccharides at the Fc glycosylation site. No significant difference in the serum half-life was found between the two antibody glycoforms, nor was any difference observed in the serum half-lives of different complex type glycoforms. To evaluate the influence of glycosylation within the variable domain, a second monoclonal antibody, glycosylated in both the Fc and Fv domains, was separated into fractions containing different amounts of Fv-associated sialic acid and administered to mice. Again, no significant difference was found in the clearance rates of variants carrying different amounts of Fv-associated sialic acid or lacking Fv-glycosylation. These results suggest that glycosylation has little or no impact on the pharmacokinetic behavior of these two monoclonal antibodies in mice.

Knudsen effusion mass spectrometric determination of the complex vapor composition of samarium, europium, and ytterbium bromides

RATIONALE The vaporization of Sm, Eu, and Yb tri- and dibromides is accompanied by decomposition and disproportionation reactions. These result in complex vapor compositions whose analysis is an intricate problem for experimentalists. Approaches have been developed to interpret mass spectra and accurately determine the vapor composition of thermally unstable compounds. METHODS A sector type magnet instrument was used. A combined ion source allowed the study of both the molecular and ionic vapor compositions in the electron ionization (EI) and the thermionic emission (TE) modes. The methodological approaches were based on a joint analysis of the ionization efficiency functions, the temperature and time dependences of the ion currents, and special mathematical data evaluation. RESULTS The vaporization of SmBr3, YbBr3, SmBr2, EuBr2, and YbBr2 was studied in the temperature range of 850–1300 K. An initial stage of incongruent vaporization was observed in the case of the tribromides, SmBr2, and YbBr2. This eventually changed to a congruent vaporization stage. Various neutral (Ln, Br, Br2, LnBr, LnBr2, LnBr3, Ln2Br4, Ln2Br5, and Ln2Br6) and charged (Br–, LnBr3–, LnBr4–) species were detected at different vaporization stages. CONCLUSIONS The quantitative vapor composition of Sm, Eu, and Yb tri- and dibromides was determined. It was found that only EuBr2 was stable in the studied temperature range. The developed approaches can be useful in the case of other thermally unstable compounds.

FUNCTIONS OF DEADENYLATION FACTORS IN MRNA DECAY AND MRNA PROCESSING BODY FORMATION

Most newly synthesized messenger RNAs possess a 5’ cap and a 3’ poly(A) tail. The process of poly(A) tail shortening, also termed deadenylation, is important for post-transcriptional gene regulation, because deadenylation not only leads to mRNA translational inhibition but also is the first step of major mRNA degradation. Translationally inhibited mRNAs can be stored and/or degraded in dynamic cytoplasmic foci termed mRNA processing bodies, or P bodies, which are conserved in eukaryotes. To shed new light on the mechanisms of P body formation and P body functions, I focused on the link between deadenylation factors and P bodies. I found that the two major deadenylation complexes, Pan3-Pan2 and Ccr4-Caf1, can both be enriched in P bodies. The deadenylase activity of the Ccr4-Caf1 complex is prerequisite for P body formation. Pan3, but not the deadenylase Pan2, is essential for P body formation. While the C-terminal domain of Pan3 is important for interaction with Pan2, Pan3 N-terminal domain is important for Pan3 to form cytoplasmic foci colocalizing with P bodies and to promote mRNA decay. Interestingly, Pan3 N-terminal domain may be phosphorylated to regulate Pan3 localization and functions. Aside from the functions of the two deadenylation complexes in P bodies, I also studied all reported human P body proteins as a whole using bioinformatics. This effort not only has generated a comprehensive picture of the functions of and interactions among human P body proteins, but also has predicted proteins that may regulate P body formation and/or functions. In summary, my study has established a direct link between mRNA deadenylation and P body formation and has also led to new hypotheses to guide future research on how P body dynamics are controlled.

A study in the molecular and cellular functions of GSK3beta in prostate adenocarcinoma

Kinases are part of a complex network of signaling pathways that enable a cell to respond to changes in environmental conditions in a regulated and coordinated way. For example, Glycogen Synthase Kinase 3 beta (GSK3β) modulates conformational changes, protein-protein interaction, protein degradation, and activation of unique domains in proteins that transduce signals from the extracellular milieu to the nucleus. ^ In this project, I investigated the expression and function that GSK3β exhibits in prostate cells. The capacity of GSK3β to regulate two transcription factors (JUN and CREB), which are known to be inversely utilized in prostate tumor cells, was measured. JUN/AP1 is constitutively activated in PC-3 cells; whereas, CREB/CRE activity is ∼20 fold less than the former. GSK3β overexpression obliterates JUN/AP1 activity. With respect to CREB GSK3β increases CREB/CRE activity. Cellular levels of active GSK3β can determine whether JUN or CREB is preferentially active in the PC-3s. Theoretically, in response to a particular cellular context or stimulus, a cell may coordinate JUN and CREB function by regulating GSK3β.^ A comparison of various prostate cell lines showed that active GSK3β is less expressed in normal prostate epithelial cells than in tumor cells. Differentially expressed active (GSK3β) may correlate with progression of prostate carcinoma. If a known marker associated with carcinoma of the prostate could be shown to be regulated by GSK3β then, further study of GSK3β may lead to a better understanding of both possible prevention of the disease and improved therapy for advanced stages. ^ The androgen receptor (AR) is an intriguing phosphoprotein whose regulation is potentially determined by a variety of kinases. One of these is (GSK3β) I found that (GSK3β) is a regulator of the androgen receptor in both the unliganded and liganded states. It can inhibit AR function as measured by reporter assays. Also, GSK3β associates with the AR at the DNA binding domain because deletion constructs expressing either the n-terminus or the c-terminus (both having the DBD in common) immunoprecipitated with GSK3β. Increased understanding of how GSK3β functions in prostate cancer would provide clues into how (1) certain signal pathways are coordinated and (2) the androgen receptor may be regulated. ^

The functions of pitx2 and Bmp signaling in craniofacial development

The formation of the vertebrate face is an extremely complex developmental process, which needs to coordinate the outgrowth of several facial primordia. Facial primordia are small buds made up of mesenchymal masses enclosed by an epithelial layer that surrounds the primitive mouth. The upper jaw is formed by the maxillary process, the lateral nasal process, and the frontonasal process while the mandibular process forms the lower jaw. Recent experiments using genetics in mice and bead implantation approaches have shown that the pitx2 homeobox gene and Bmp signaling play important roles in this complex developmental process. However, the molecular mechanisms underlying the function of pitx2 and Bmp in these events are still unclear. Here, we show that pitx2 is required for oral epithelium maintenance, and branchial arch signaling is pitx2 dosage sensitive by using pitx2 allelic combinations that encode varying levels of pitx2. Maintenance of fgf8 signaling requires only low pitx2 dosage while repression of Bmp signaling requires high pitx2 levels. Different incisor and molar phenotypes in low level pitx2 mutant embryos suggest a distinct requirement for pitx2 in tooth-type development. The results show that pitx2 is required for craniofacial muscle formation and expanded Bmp signaling results in excess bone formation in pitx2 mutant embryos. Fate-mapping studies show that ectopic bone results from excessive bone growth, instead of muscle transformation. Moreover, by using cre/loxp system we show that partial loss of Bmpr-IA in the facial primordia results in cleft lip/palate, abnormal teeth, ectopic teeth and tooth transformation. These phenotypes suggest that Bmp signaling has multiple functions during craniofacial development. The mutant palate shelves can fuse with each other when cultured in vitro, suggesting that cleft palate is secondary to the partial loss of Bmpr-IA. Furthermore, we prove that Bmp4, one of the ligands of Bmpr-IA, plays a role during lip fusion developmental process and partial loss of Bmp4 in the facial primordia results in the lip fusion delay. These results have provided insight to understand the complex signaling cascades that regulate craniofacial development. ^

Nuclear functions of dynein light chain 1 in hormone action

It is widely accepted that the process of breast cancer tumorigenesis involves estrogen receptor-alpha (ER)-regulated stimulatory pathways, which feed into survival, cell cycle progression and proliferative response. Recent data from Kumar laboratory indicate that dynein light chain 1 (DLC1) plays a role in survival, motility and invasiveness, all of which are required for a successful tumorigenesis process. In the present research, we have discovered a mechanistic bidirectional regulatory link between the DLC1 and ER. We found that DLC1 facilitates ligand-induced ER transactivation involving the recruitment of the DLC1-ER complex to ER-target genes. To gain insights into the mechanism by which DLC1 regulates the ER pathway, we set out to identify novel DLC1-interacting proteins. Among other proteins, we identified KIBRA and Ciz1 as two novel DLC1-interacting proteins. We found that the KIBRA-DLC1 complex is recruited to ER-responsive promoters, and that KIBRA-DLC1 interaction is needed for the recruitment of ER to its targets as well as for ER's transactivation function. Finally, we found that KIBRA utilizes its histone H3interacting glutamic acid-rich region to regulate the transactivation activity of ER. During the course of this work, we also discovered that DLC1 interacts with Cdk2 and Ciz1, and such interactions play a direct accelerating role in the G1-S transition of breast cancer cells. While delineating the role of Ciz1 in hormone-responsive cancer cells, we found that Ciz1 is an estrogen-responsive gene, and acts as a co-regulator of ER. Accordingly, Ciz1 overexpression in breast cancer cells conferred estrogen hypersensitivity, promoted the growth-rate, anchorage-independency and tumorigenic properties. Collectively, findings made during the course of the present dissertation research introduced two new molecular players in the action of ER in breast cancer cells, with a particular focus on cell cycle progression and ER-chromatin target regulation. In addition, findings presented here provide novel mechanistic insight about the contribution of DLC1 and its interacting proteins in amplifying the hormone action and promoting the process of breast cancer tumorigenesis. ^

Developmental functions of XKaiso, a transcriptional repressor associating with the p120 catenin in Xenopus laevis

The Armadillo family catenin proteins function in multiple capacities including cadherin-mediated cell-cell adhesion and nuclear signaling. The newest catenin, p120 catenin, differs from the classical catenins and binds to the membrane-proximal domain of cadherins. Recently, a novel transcription factor Kaiso was found to interact with p120 catenin, suggesting that p120 catenin also possesses a nuclear function. We isolated the Xenopus homolog of Kaiso, XKaiso, from a Xenopus stage 17 cDNA library. XKaiso contains an amino-terminal BTB/POZ domain and three carboxyl-terminal zinc fingers. The XKaiso transcript was present maternally and expressed throughout early embryonic development. XKaiso's spatial expression was defined via in situ hybridization and was found localized to the brain, eye, ear, branchial arches, and spinal cord. Co-immunoprecipitation of Xenopus p120 catenin and XKaiso demonstrated their mutual association, while related experiments employing differentially epitope-tagged XKaiso constructs suggest that XKaiso also self-associates. On the functional level, reporter assays employing a chimera of XKaiso fused to the GAL4 DNA binding domain indicated that XKaiso is a transcriptional repressor. To better understand the significance of the Kaiso-p120 catenin complex in vertebrate development, Kaiso knock-down experiments were undertaken, and the modulatory role of p120 catenin in Kaiso function examined during Xenopus development. Using morpholino antisense oligonucleotides to block translation of XKaiso, XKaiso was found to be essential for Xenopus gastrulation, being required for correct morphogenetic movements in early embryogenesis. Molecular marker analyses indicated that one target gene of the Wnt/β-catenin pathway, Siamois, is significantly increased in embryos depleted for XKaiso, while other dorsal, ventral, and mesodermal cell fate markers were unaltered. In addition, the non-canonical Wnt-11, known to participate in planar cell polarity/convergent extension processes, was significantly upregulated following depletion of XKaiso. Such increased Wnt-11 expression likely contributed to the XKaiso depletion phenotype because a dominant negative form of Wnt-11 or of the downstream effector Dishevelled partially rescued the observed gastrulation defects. These results show that XKaiso is essential for proper gastrulation movements, resulting at least in part from its modulation of non-canonical Wnt signaling. The significance of the XKaiso-p120 catenin interaction has yet to be determined, but appears to include a role in modulating genes promoting canonical and non-canonical Wnt signals. ^

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.

RB and hbrm cooperate to repress the activation functions of E2F1

Forced expression of the retinoblastoma (RB) gene product inhibits the proliferation of cells in culture. A major target of the RB protein is the S-phase-inducing transcription factor E2F1. RB binds directly to the activation domain of E2F1 and silences it, thereby preventing cells from entering S phase. To induce complete G1 arrest, RB requires the presence of the hbrm/BRG-1 proteins, which are components of the coactivator SWI/SNF complex. This cooperation is mediated through a physical interaction between RB and hbrm/BRG-1. We show here that in transfected cells RB can contact both E2F1 and hbrm at the same time, thereby targeting hbrm to E2F1. E2F1 and hbrm are indeed found within the same complex in vivo. Furthermore, RB and hbrm cooperate to repress E2F1 activity in transient transfection assays. The ability of hbrm to cooperate with RB to repress E2F1 is dependent upon several distinct domains of hbrm, including the RB binding domain and the NTP binding site. However, the bromodomain seems dispensable for this activity. Taken together, our results point out an unexpected role of corepressor for the hbrm protein. The ability of hbrm and RB to cooperate in repressing E2F1 activity could be an underlying mechanism for the observed cooperation between hbrm and RB to induce G1 arrest. Finally, we demonstrate that the domain of hbrm that binds RB has transcriptional activation potential which RB can repress. This suggest that RB not only targets hbrm but also regulates its activity.

A chemical genomics approach toward understanding the global functions of the target of rapamycin protein (TOR)

The target of rapamycin protein (TOR) is a highly conserved ataxia telangiectasia-related protein kinase essential for cell growth. Emerging evidence indicates that TOR signaling is highly complex and is involved in a variety of cellular processes. To understand its general functions, we took a chemical genomics approach to explore the genetic interaction between TOR and other yeast genes on a genomic scale. In this study, the rapamycin sensitivity of individual deletion mutants generated by the Saccharomyces Genome Deletion Project was systematically measured. Our results provide a global view of the rapamycin-sensitive functions of TOR. In contrast to conventional genetic analysis, this approach offers a simple and thorough analysis of genetic interaction on a genomic scale and measures genetic interaction at different possible levels. It can be used to study the functions of other drug targets and to identify novel protein components of a conserved core biological process such as DNA damage checkpoint/repair that is interfered with by a cell-permeable chemical compound.