INTERPOLATING BLASCHKE PRODUCTS AND ANGULAR DERIVATIVES

We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra H-infinity[(b) over bar : b has finite angular derivative everywhere. We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product. We conclude the paper with a method for constructing thin Blaschke products with infinite angular derivative everywhere.

Interpolating Blaschke Products and Angular Derivatives

We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra generated by the algebra of bounded analytic functions and the conjugates of Blaschke products with angular derivative finite everywhere. We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product. We conclude the paper with a method for constructing thin Blaschke products with infinite angular derivative everywhere.

On the composition of Frostman Blaschke products

We construct an infinite uniform Frostman Blaschke product B such that B composed with itself is also a uniform Frostman Blaschke product. We also show that the set of uniform Frostman Blaschke products is open in the set of inner functions with the uniform norm.

Decomposing Blaschke Products And Polynomials

The goal of this paper is to contribute to the understanding of complex polynomials and Blaschke products, two very important function classes in mathematics. For a polynomial, $f,$ of degree $n,$ we study when it is possible to write $f$ as a composition $f=g\circ h$, where $g$ and $h$ are polynomials, each of degree less than $n.$ A polynomial is defined to be \emph{decomposable }if such an $h$ and $g$ exist, and a polynomial is said to be \emph{indecomposable} if no such $h$ and $g$ exist. We apply the results of Rickards in \cite{key-2}. We show that $$C_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,(z-z_{1})(z-z_{2})...(z-z_{n})\,\mbox{is decomposable}\},$$ has measure $0$ when considered a subset of $\mathbb{R}^{2n}.$ Using this we prove the stronger result that $$D_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,\mbox{There exists\,}a\in\mathbb{C}\,\,\mbox{with}\,\,(z-z_{1})(z-z_{2})...(z-z_{n})(z-a)\,\mbox{decomposable}\},$$ also has measure zero when considered a subset of $\mathbb{R}^{2n}.$ We show that for any polynomial $p$, there exists an $a\in\mathbb{C}$ such that $p(z)(z-a)$ is indecomposable, and we also examine the case of $D_{5}$ in detail. The main work of this paper studies finite Blaschke products, analytic functions on $\overline{\mathbb{D}}$ that map $\partial\mathbb{D}$ to $\partial\mathbb{D}.$ In analogy with polynomials, we discuss when a degree $n$ Blaschke product, $B,$ can be written as a composition $C\circ D$, where $C$ and $D$ are finite Blaschke products, each of degree less than $n.$ Decomposable and indecomposable are defined analogously. Our main results are divided into two sections. First, we equate a condition on the zeros of the Blaschke product with the existence of a decomposition where the right-hand factor, $D,$ has degree $2.$ We also equate decomposability of a Blaschke product, $B,$ with the existence of a Poncelet curve, whose foci are a subset of the zeros of $B,$ such that the Poncelet curve satisfies certain tangency conditions. This result is hard to apply in general, but has a very nice geometric interpretation when we desire a composition where the right-hand factor is degree 2 or 3. Our second section of finite Blaschke product results builds off of the work of Cowen in \cite{key-3}. For a finite Blaschke product $B,$ Cowen defines the so-called monodromy group, $G_{B},$ of the finite Blaschke product. He then equates the decomposability of a finite Blaschke product, $B,$ with the existence of a nontrivial partition, $\mathcal{P},$ of the branches of $B^{-1}(z),$ such that $G_{B}$ respects $\mathcal{P}$. We present an in-depth analysis of how to calculate $G_{B}$, extending Cowen's description. These methods allow us to equate the existence of a decomposition where the left-hand factor has degree 2, with a simple condition on the critical points of the Blaschke product. In addition we are able to put a condition of the structure of $G_{B}$ for any decomposable Blaschke product satisfying certain normalization conditions. The final section of this paper discusses how one can put the results of the paper into practice to determine, if a particular Blaschke product is decomposable. We compare three major algorithms. The first is a brute force technique where one searches through the zero set of $B$ for subsets which could be the zero set of $D$, exhaustively searching for a successful decomposition $B(z)=C(D(z)).$ The second algorithm involves simply examining the cardinality of the image, under $B,$ of the set of critical points of $B.$ For a degree $n$ Blaschke product, $B,$ if this cardinality is greater than $\frac{n}{2}$, the Blaschke product is indecomposable. The final algorithm attempts to apply the geometric interpretation of decomposability given by our theorem concerning the existence of a particular Poncelet curve. The final two algorithms can be implemented easily with the use of an HTML

Prime and Semiprime Inner Functions

This paper studies the structure of inner functions under the operation of composition, and in particular the notions or primeness and semiprimeness. Results proved include the density of prime finite Blaschke products in the set of finite Blaschke products, the semiprimeness of finite products of thin Blaschke products and their approximability by prime Blaschke products. An example of a nonsemiprime Blaschke product that is a Frostman Blaschke product is also provided.

Prime and semiprime inner functions

Abstract This paper studies the structure of inner functions under the operation of composition, and in particular the notions or primeness and semiprimeness. Results proved include the density of prime finite Blaschke products in the set of finite Blaschke products, the semiprimeness of finite products of thin Blaschke products and their approximability by prime Blaschke products. An example of a nonsemiprime Blaschke product that is a Frostman Blaschke product is also provided.

Gut Bacteria Products Prevent Aki Induced By Ischemia-reperfusion.

Short-chain fatty acids (SCFAs) are fermentation end products produced by the intestinal microbiota and have anti-inflammatory and histone deacetylase-inhibiting properties. Recently, a dual relationship between the intestine and kidneys has been unraveled. Therefore, we evaluated the role of SCFA in an AKI model in which the inflammatory process has a detrimental role. We observed that therapy with the three main SCFAs (acetate, propionate, and butyrate) improved renal dysfunction caused by injury. This protection was associated with low levels of local and systemic inflammation, oxidative cellular stress, cell infiltration/activation, and apoptosis. However, it was also associated with an increase in autophagy. Moreover, SCFAs inhibited histone deacetylase activity and modulated the expression levels of enzymes involved in chromatin modification. In vitro analyses showed that SCFAs modulated the inflammatory process, decreasing the maturation of dendritic cells and inhibiting the capacity of these cells to induce CD4(+) and CD8(+) T cell proliferation. Furthermore, SCFAs ameliorated the effects of hypoxia in kidney epithelial cells by improving mitochondrial biogenesis. Notably, mice treated with acetate-producing bacteria also had better outcomes after AKI. Thus, we demonstrate that SCFAs improve organ function and viability after an injury through modulation of the inflammatory process, most likely via epigenetic modification.

Levels of yeast and its by-products on pacu juveniles feeding

This study was conducted to evaluate the inclusion of two levels (2.5 e 5.0%) of dried yeast (Saccharomyces cerevisiae) and its by-products, disrupted yeast cells and yeast cell wall in diets for juveniles of pacu (Piaractus mesopotamicus). Production performance, body and plasmatic composition indexes were evaluated. Seven isoproteic (26% digestible protein) and isoenergetic (3.100 kcal digestible energy) diets were formulated containing increased levels of each ingredient. The diets were supplied for 86 days, "ad libitum". Yeast and by-products increase feed efficiency and protein use, when compared to the control diet. Carcass composition and plasmatic (glucose, cortisol, uric acid, urea and plasmatic protein) levels are not affected by the test ingredient supplementation.

Electrochemical behavior of parent and photodegradation products of some selected pesticides

Electrochemical behavior of pesticides is extensively studied, but little attention has been given to the study of their degradation products (by-products) by electrochemical methods. However, the degradation products of pesticides can be even more toxic then the parent products and such studies should be encouraged. Therefore, the objective of this work was to evaluate the electroactivity of by-products of imazaquin, methylparathion, bentazon and atrazine, generated by UV irradiation and measured using cyclic and differential pulse voltammetry and UV-visible absorption spectrophotometry. Results have shown that several by-products exhibit electroactivity, allowing, in some cases, the simultaneous determination of both parent and degradation products.

Garlic (Allium sativum L.) and ready-to-eat garlic products: in vitro antioxidant activity

Garlic contains polyphenol and sulphur compounds, which are responsible for its antioxidant activity (AA). This study aimed at evaluating the AA of fresh garlic and its commercialised products and their shelf life. Fresh garlic (FG) and its products, i.e. chopped with salt (CGS), chopped without salt (CG), fried (FRG) and mixed garlic (FG with dehydrated garlic; MG) antioxidant activity was evaluated by three different methods: DPPH (1,1-diphenyl-2-picrylhydrazyl) assay, ß-carotene/linoleic acid assay and Rancimat® method. Amongst all the analysed products, fried garlic presented the highest antioxidant activity. The free radical-scavenging activity decreased during the shelf life of all analysed products that correlated with the decrease in the total polyphenol content. Our findings suggest that some compounds other than phenol may have contributed towards this outcome

Effect of glutamate and inosinate on sensory and instrumental texture of extruded products

Expanded products have been developed by extrusion of non-conventional highly nutritious raw materials such as amaranth and chickpea blended with bovine lung. As sensory acceptance of these snacks is restricted, this study aimed at improving their texture, through the addition of monosodium glutamate (MSG) and disodium inosinate (IMP) flavor enhancers to the feeding material, or to the flavor added after the extrusion. Sensory and mechanical analyses showed that both enhancers affected texture, assessed by sensory and instrumental methods. Addition of IMP together with MSG to the chickpea-based snacks presented the best results. This beneficial effect was not observed in the amaranth-based snack, suggesting that IMP and MSG can favorably impact texture of extruded products depending on the amount and type of protein present

Chemometric Studies on Natural Products as Potential Inhibitors of the NADH Oxidase from Trypanosoma cruzi Using the VolSurf Approach

Natural products have widespread biological activities, including inhibition of mitochondrial enzyme systems. Some of these activities, for example cytotoxicity, may be the result of alteration of cellular bioenergetics. Based on previous computer-aided drug design (CADD) studies and considering reported data on structure-activity relationships (SAR), an assumption regarding the mechanism of action of natural products against parasitic infections involves the NADH-oxidase inhibition. In this study, chemometric tools, such as: Principal Component Analysis (PCA), Consensus PCA (CPCA), and partial least squares regression (PLS), were applied to a set of forty natural compounds, acting as NADH-oxidase inhibitors. The calculations were performed using the VolSurf+ program. The formalisms employed generated good exploratory and predictive results. The independent variables or descriptors having a hydrophobic profile were strongly correlated to the biological data.

An AC-5 cathepsin B-like protease purified from Haemonchus contortus excretory secretory products shows protective antigen potential for lambs

The immunogenic properties of cysteine proteases obtained from excretory/secretory products (ES) of Haemonchus contortus were investigated with a fraction purified with a recombinant H. contortus cystatin affinity column. The enrichment of H. contortus ES for cysteine protease was confirmed with substrate SDS-PAGE gels since the cystatin-binding fraction activity was three times higher than total ES, despite representing only 3% of total ES. This activity was inhibited by a specific cysteine protease inhibitor (E64) and by recombinant cystatin. The one-dimensional profile of the cystatin-binding fraction displayed a single band with a molecular mass of 43 kDa. Mass spectrometry showed this to be AC-5, a cathepsin B-like cysteine protease which had not been identified in ES products of H. contortus before. The cystatin binding fraction was tested as an immunogen in lambs which were vaccinated three times (week 0, 2.5 and 5), challenged with 10 000 L3 H. contortus (week 6) before necropsy and compared to unvaccinated challenge controls and another group given total ES (n = 10 per group). The group vaccinated with cystatin-binding proteins showed 36% and 32% mean worm burden and eggs per gram of faeces (EPG) reductions, respectively, compared to the controls but total ES was almost without effect. After challenge the cystatin-binding proteins induced significantly higher local and systemic ES specific IgA and IgG responses.

Determination of Aflatoxins in Peanut Products in the Northeast Region of Sao Paulo, Brazil

The aim of the present study was to determine aflatoxin levels in peanut products traded in the Northeast region of Sao Paulo, Brazil. To this end, 240 samples of peanut products traded in the cities of Araras, Leme, Pirassununga and Porto Ferreira were collected from June 2006 to May 2007. The samples were analyzed for aflatoxins (AF) B(1), B(2), G(1) and G(2) by high performance liquid chromatography. Results showed 44.2% samples positive for AF at levels of 0.5 to 103.8 mu g.kg(-1). Nine of the positive samples (3.7% of the analysed samples) had total aflatoxin concentrations (B(1)+B(2)+G(1)+G(2)) higher than the limit established by Brazilian regulations (20 mu g.kg(-1)). Based on the above data, the probable mean daily intake (PDI(M)) of aflatoxins from peanut products in the Northeast region of Sao Paulo was estimated to be 0.23 ng kg b.w. day(-1). Although this PDI(M) value was relatively low, results indicate that aflatoxin contamination of peanut products may be a public health concern in Brazil, when considering the potential exposure of highly susceptible consumers. For example, it should be emphasized that children are potentially exposed to aflatoxins, since they consume large quantities of peanut candies, and these products had the highest number of samples positive for AFB(1).

Rapid formation of isoprene photo-oxidation products observed in Amazonia

Isoprene represents the single most important reactive hydrocarbon for atmospheric chemistry in the tropical atmosphere. It plays a central role in global and regional atmospheric chemistry and possible climate feedbacks. Photo-oxidation of primary hydrocarbons (e. g. isoprene) leads to the formation of oxygenated VOCs (OVOCs). The evolution of these intermediates affects the oxidative capacity of the atmosphere (by reacting with OH) and can contribute to secondary aerosol formation, a poorly understood process. An accurate and quantitative understanding of VOC oxidation processes is needed for model simulations of regional air quality and global climate. Based on field measurements conducted during the Amazonian Aerosol Characterization Experiment (AMAZE-08) we show that the production of certain OVOCs (e. g. hydroxyacetone) from isoprene photo-oxidation in the lower atmosphere is significantly underpredicted by standard chemistry schemes. Recently reported fast secondary production could explain 50% of the observed discrepancy with the remaining part possibly produced via a novel primary production channel, which has been proposed theoretically. The observations of OVOCs are also used to test a recently proposed HO(x) recycling mechanism via degradation of isoprene peroxy radicals. If generalized our observations suggest that prompt photochemical formation of OVOCs and other uncertainties in VOC oxidation schemes could result in uncertainties of modelled OH reactivity, potentially explaining a fraction of the missing OH sink over forests which has previously been largely attributed to a missing source of primary biogenic VOCs.