Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R

2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63

On the Generalized Associated Legendre Functions

Mathematics Subject Classification: 33C60, 33C20, 44A15

Calculating the derivative of piecewise functions

Exercises involving the calculation of the derivative of piecewise defined functions are common in calculus, with the aim of consolidating beginners’ knowledge of applying the definition of the derivative. In such exercises, the piecewise function is commonly made up of two smooth pieces joined together at one point. A strategy which avoids using the definition of the derivative is to find the derivative function of each smooth piece and check whether these functions agree at the chosen point. Showing that this strategy works together with investigating discontinuities of the derivative is usually beyond a calculus course. However, we shall show that elementary arguments can be used to clarify the calculation and behaviour of the derivative for piecewise functions.

Taylor Spectrum and Characteristic Functions of Commuting 2-Contractions

2000 Mathematics Subject Classification: 47A10, 47A13.

Comparison of Linear Functions in Middle Grades Textbooks from Singapore and the United States

Many U.S. students do not perform well on mathematics assessments with respect to algebra topics such as linear functions, a building-block for other functions. Poor achievement of U.S. middle school students in this topic is a problem. U.S. eighth graders have had average mathematics scores on international comparison tests such as Third International Mathematics Science Study, later known as Trends in Mathematics and Science Study, (TIMSS)-1995, -99, -03, while Singapore students have had highest average scores. U.S. eighth grade average mathematics scores improved on TIMMS-2007 and held steady onTIMMS-2011. Results from national assessments, PISA 2009 and 2012 and National Assessment of Educational Progress of 2007, 2009, and 2013, showed a lack of proficiency in algebra. Results of curriculum studies involving nations in TIMSS suggest that elementary textbooks in high-scoring countries were different than elementary textbooks and middle grades texts were different with respect to general features in the U.S. The purpose of this study was to compare treatments of linear functions in Singapore and U.S. middle grades mathematics textbooks. Results revealed features currently in textbooks. Findings should be valuable to constituencies who wish to improve U.S. mathematics achievement. Portions of eight Singapore and nine U.S. middle school student texts pertaining to linear functions were compared with respect to 22 features in three categories: (a) background features, (b) general features of problems, and (c) specific characterizations of problem practices, problem-solving competency types, and transfer of representation. Features were coded using a codebook developed by the researcher. Tallies and percentages were reported. Welch's t-tests and chi-square tests were used, respectively, to determine whether texts differed significantly for the features and if codes were independent of country. U.S. and Singapore textbooks differed in page appearance and number of pages, problems, and images. Texts were similar in problem appearance. Differences in problems related to assessment of conceptual learning. U.S. texts contained more problems requiring (a) use of definitions, (b) single computation, (c) interpreting, and (d) multiple responses. These differences may stem from cultural differences seen in attitudes toward education. Future studies should focus on density of page, spiral approach, and multiple response problems.

Locally recurrent functions, density topologies and algebraic genericity

We study the algebraic and topological genericity of certain subsets of locally recurrent functions, obtaining (among other results) algebrability and spaceability within these classes.

Locally recurrent functions, density topologies and algebraic genericity

We study the algebraic and topological genericity of certain subsets of locally recurrent functions, obtaining (among other results) algebrability and spaceability within these classes.

IL-10-producing Regulatory B Cell Development in Human Autoimmune Disease

B cell abnormalities contribute to the development and progress of autoimmune disease. Traditionally, the role of B cells in autoimmune disease was thought to be predominantly limited to the production of autoantibodies. Nevertheless, in addition to autoantibody production, B cells have other functions potentially relevant to autoimmunity. Such functions include antigen presentation to and activation of T cells, expression of costimulatory molecules and cytokine production. Recently, the ability of B cells to negatively regulate cellular immune responses and inflammation has been described and the concept of “regulatory B cells” has emerged. A variety of cytokines produced by regulatory B cell subsets have been reported with interleukin-10 (IL-10) being the most studied. IL-10-producing regulatory B cells predominantly localize within a rare CD1dhiCD5+ B cell subset in mice and the CD24hiCD27+ B cell subset in adult humans. This specific IL-10-producing subset of regulatory B cells have been named “B10 cells” to highlight that the regulatory function of these rare B cells is primarily mediated by IL-10, and to distinguish them from other regulatory B cell subsets that regulate immune responses through different mechanisms. B10 cells have been studies in a variety of animal models with autoimmune disease and clinical settings of human autoimmunity. There are many unsolved questions related to B10 cells including their surface phenotype, their origin and development in vivo, and their role in autoimmunity.

In Chapter 3 of this dissertation, the role of the B cell receptor (BCR) in B10 cell development is highlighted. First, the BCR repertoire of mouse peritoneal cavity B10 cells is examined by single cell sequencing; peritoneal cavity B10 cells have clonally diverse germline BCRs that are predominantly unmutated. Second, mouse B10 cells are shown to have higher frequencies of λ+ BCRs compared to non-B10 cells which may indicate the involvement of BCR light chain editing early in the process of B10 cell development in vivo. Third, human peripheral blood B10 cells are examined and are also found to express higher frequencies of λ chains compared to non-b10 cells. Therefore, B10 cell BCRs are clonally diverse and enriched for unmutated germline sequences and λ light chains.

In Chapter 4 of this dissertation, B10 cells are examined in the healthy developing human across the entire age range of infancy, childhood and adolescence, and in a large cohort of children with autoimmunity. The study of B10 cells in the developing human documents a massive transient expansion during middle childhood when up to 30% of blood B cells were competent to produce IL-10. The surface phenotype of pediatric B10 cells was variable and reflective of overall B cell development. B10 cells down-regulated CD4+ T cell interferon-gamma (IFN-γ) production through IL-10-dependent pathways and IFN-γ inhibited whereas interleukin-21 (IL-21) promoted B cell IL-10 competency in vitro. Children with autoimmunity had a contracted B10 cell compartment, along with increased IFN-γ and decreased IL-21 serum levels compared to age-matched healthy controls. The decreased B10 cell frequencies and numbers in children with autoimmunity may be partially explained by the differential regulation of B10 cell development by IFN-γ and IL-21 and alterations in serum cytokine levels. The age-related changes of the B10 cell compartment during normal human development provide new insights into immune tolerance mechanisms involved in inflammation and autoimmunity.

These studies collectively demonstrate that BCR signals are the most important early determinant of B10 cell development in vivo, that human B10 cells are not a surface phenotype defined developmental B cell subset but a functionally defined regulatory B cell subset that regulates CD4+ T IFN-γ production through IL-10-dependent pathways and that human B10 cell development can be regulated by soluble factors in vivo such as the cytokine milieu. The findings of these studies provide new insights into immune tolerance mechanisms involved in human autoimmunity and the potent effects of IL-21 on human B cell IL-10 competence in vitro open new horizons in the development of autologous B10 cell-based therapies as an approach to treat human autoimmune disease in the future.

Transient Receptor Potential Vanilloid 4 Ion Channel Functions as a Pruriceptor in Epidermal Keratinocytes to Evoke Histaminergic Itch.

TRPV4 ion channels function in epidermal keratinocytes and in innervating sensory neurons; however, the contribution of the channel in either cell to neurosensory function remains to be elucidated. We recently reported TRPV4 as a critical component of the keratinocyte machinery that responds to ultraviolet B (UVB) and functions critically to convert the keratinocyte into a pain-generator cell after excess UVB exposure. One key mechanism in keratinocytes was increased expression and secretion of endothelin-1, which is also a known pruritogen. Here we address the question of whether TRPV4 in skin keratinocytes functions in itch, as a particular form of "forefront" signaling in non-neural cells. Our results support this novel concept based on attenuated scratching behavior in response to histaminergic (histamine, compound 48/80, endothelin-1), not non-histaminergic (chloroquine) pruritogens in Trpv4 keratinocyte-specific and inducible knock-out mice. We demonstrate that keratinocytes rely on TRPV4 for calcium influx in response to histaminergic pruritogens. TRPV4 activation in keratinocytes evokes phosphorylation of mitogen-activated protein kinase, ERK, for histaminergic pruritogens. This finding is relevant because we observed robust anti-pruritic effects with topical applications of selective inhibitors for TRPV4 and also for MEK, the kinase upstream of ERK, suggesting that calcium influx via TRPV4 in keratinocytes leads to ERK-phosphorylation, which in turn rapidly converts the keratinocyte into an organismal itch-generator cell. In support of this concept we found that scratching behavior, evoked by direct intradermal activation of TRPV4, was critically dependent on TRPV4 expression in keratinocytes. Thus, TRPV4 functions as a pruriceptor-TRP in skin keratinocytes in histaminergic itch, a novel basic concept with translational-medical relevance.

Winter sea surface temperature reconstruction from planktic foraminiferal transfer functions in the northeastern Arabian Sea over the last two millennia

The Indian monsoon system is an important climate feature of the northern Indian Ocean. Small variations of the wind and precipitation patterns have fundamental influence on the societal, agricultural, and economic development of India and its neighboring countries. To understand current trends, sensitivity to forcing, or natural variation, records beyond the instrumental period are needed. However, high-resolution archives of past winter monsoon variability are scarce. One potential archive of such records are marine sediments deposited on the continental slope in the NE Arabian Sea, an area where present-day conditions are dominated by the winter monsoon. In this region, winter monsoon conditions lead to distinctive changes in surface water properties, affecting marine plankton communities that are deposited in the sediment. Using planktic foraminifera as a sensitive and well-preserved plankton group, we first characterize the response of their species distribution on environmental gradients from a dataset of surface sediment samples in the tropical and sub-tropical Indian Ocean. Transfer functions for quantitative paleoenvironmental reconstructions were applied to a decadal-scale record of assemblage counts from the Pakistan Margin spanning the last 2000?years. The reconstructed temperature record reveals an intensification of winter monsoon intensity near the year 100 CE. Prior to this transition, winter temperatures were >1.5°C warmer than today. Conditions similar to the present seem to have established after 450 CE, interrupted by a singular event near 950 CE with warmer temperatures and accordingly weak winter monsoon. Frequency analysis revealed significant 75-, 40-, and 37-year cycles, which are known from decadal- to centennial-scale resolution records of Indian summer monsoon variability and interpreted as solar irradiance forcing. Our first independent record of Indian winter monsoon activity confirms that winter and summer monsoons were modulated on the same frequency bands and thus indicates that both monsoon systems are likely controlled by the same driving force.

Series representations of the remainders in the expansions for certain functions with applications

We present a summary of the series representations of the remainders in the expansions in ascending powers of t of 2/(et+1)2/(et+1) , sech t and coth t and establish simple bounds for these remainders when t>0t>0 . Several applications of these expansions are given which enable us to deduce some inequalities and completely monotonic functions associated with the ratio of two gamma functions. In addition, we derive a (presumably new) quadratic recurrence relation for the Bernoulli numbers Bn.

Caracterização estrutural e avaliação das atividades farmacológicas da fucana B extraída da alga Dictyota menstrualis

Seaweeds are a major source of biologically active compounds . In the extracellular matrix of these organisms are sulfated polysaccharides that functions as structural components preventing it against dehydration. The fraction 0.9 (FucB) rich in sulfated fucans obtained from brown seaweed Dictyota menstrualis was chemical characterized and evaluated for pharmacological activity by testing anticoagulant activity, stimulatory action on the synthesis of an antithrombotic heparan sulfate, antioxidant activity and its effects in cell proliferation. The main components were FucB carbohydrates (49.80 ± 0.10 %) and sulfate (42.30 ± 0.015 %), with phenolic compounds ( 3.86 ± 0.016 %) and low protein contamination ( 0.58 ± 0.001 % ) . FucB showed polydisperse profile and analysis of signals in the infrared at 1262, 1074 and 930 cm -1 and 840 assigned to S = O bonds sulfate esters , CO bond presence of 3,6- anhydrogalactose , β -D- galactose non- sulfated sulfate and the axial position of fucose C4 , respectively. FucB exhibited moderate anticoagulant activity , the polysaccharides prolonged time (aPTT ) 200 ug ( > 90s ) partial thromboplastin FucB no effect on prothrombin time (PT), which corresponds to the extrinsic pathway of coagulation was observed. This stimulation promoted fraction of about 3.6 times the synthesis of heparan sulfate (HS) by endothelial cells of the rabbit aorta ( RAEC ) in culture compared with cells not treated with FucB . This has also been shown to compete for the binding site with heparin. The rich fraction sulfated fucans exhibited strong antioxidant activity assays on total antioxidant (109.7 and 89.5 % compared with BHT and ascorbic acid standards ) , reducing power ( 71 % compared to ascorbic acid ) and ferric chelation ( 71 , comparing with 5 % ascorbic acid). The fraction of algae showed cytostatic activity on the RAEC cells revealed that the increase of the synthesis of heparan sulfate is not related to proliferation. FucB showed antiproliferative action on cell lines modified as Hela and Hep G2 by MTT assay . These results suggest that FucB Dictyota menstrualis have anticoagulant , antithrombotic , antioxidant potential as well as a possible antitumor action, promoting the stimulation of the synthesis of antithrombotic HS by endothelial cells and is useful in the prevention of thrombosis, also due to its inhibitory action on species reactive oxygen ( ROS ) in some in vitro systems , being involved in promoting a hypercoagulable state

Holomorphic functions on non-Runge domains and related problems.

Let U be a domain in CN that is not a Runge domain. We study the topological and algebraic properties of the family of holomorphic functions on U which cannot be approximated by polynomials.

Protein markers of B. xylophilus Steiner & Buhrer, 1934 (Nickle, 1970) populations using quantitative proteomics and character compatibility.

The Pine Wood Nematode (PWN) Bursaphelenchus xylophilus is a severe forest pathogen in countries where it has been introduced and is considered a worldwide quarantine organism. In this study, protein markers for differentiating populations of this nematode were identified by studying differences among four selected Iberian and one American population. These populations were compared by quantitative proteomics (iTRAQ). From a total of 2860 proteins identified using the public database from the B. xylophilus genome project, 216 were unambiguous and significantly differentially regulated in the studied populations. Comparisons of their pairwise ratio were statistically treated and supported in order to convert them into discrete character states, suggesting that 141 proteins were not informative as population specific markers. Application of the Character Compatibility methodology on the remaining 75 proteins (belonging to families with different biological functions) excludes 27 which are incompatible among them. Considering only the compatible proteins, the method selects a subset of 30 specific unique protein markers which allowed the compared classification of the Iberian isolates. This approach makes it easier search for diagnostic tools and phylogenetic inference within species and populations of a pathogen exhibiting a high level of genetic diversity.