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

The group of invariants of an inner function with finite spectrum

This paper determines the group of continuous invariants corresponding to an inner function circle dot with finitely many singularities on the unit circle T; that is, the continuous mappings g : T -> T such that circle dot o g = circle dot on T. These mappings form a group under composition.

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.

Antioxidant And Antiproliferative Activities Of Methanolic Extract From A Neglected Agricultural Product: Corn Cobs.

Neglected agricultural products (NAPs) are defined as discarded material in agricultural production. Corn cobs are a major waste of agriculture maize. Here, a methanolic extract from corn cobs (MEC) was obtained. MEC contains phenolic compounds, protein, carbohydrates (1.4:0.001:0.001). We evaluated the in vitro and in vivo antioxidant potential of MEC. Furthermore, its antiproliferative property against tumor cells was assessed through MTT assays and proteins related to apoptosis in tumor cells were examined by western blot. MEC showed no hydroxyl radical scavenger capacity, but it showed antioxidant activity in Total Antioxidant Capacity and DPPH scavenger ability assays. MEC showed higher Reducing Power than ascorbic acid and exhibited high Superoxide Scavenging activity. In tumor cell culture, MEC increased catalase, metallothionein and superoxide dismutase expression in accordance with the antioxidant tests. In vivo antioxidant test, MEC restored SOD and CAT, decreased malondialdehyde activities and showed high Trolox Equivalent Antioxidant Capacity in animals treated with CCl4. Furthermore, MEC decreased HeLa cells viability by apoptosis due an increase of Bax/Bcl-2 ratio, caspase 3 active. Protein kinase C expression increased was also detected in treated tumor cells. Thus, our findings pointed out the biotechnological potential of corn cobs as a source of molecules with pharmacological activity.

Systematic Management of Variability in UML-based Software Product Lines

This paper presents SMarty, a variability management approach for UML-based software product lines (PL). SMarty is supported by a UML profile, the SMartyProfile, and a process for managing variabilities, the SMartyProcess. SMartyProfile aims at representing variabilities, variation points, and variants in UML models by applying a set of stereotypes. SMartyProcess consists of a set of activities that is systematically executed to trace, identify, and control variabilities in a PL based on SMarty. It also identifies variability implementation mechanisms and analyzes specific product configurations. In addition, a more comprehensive application of SMarty is presented using SEI's Arcade Game Maker PL. An evaluation of SMarty and related work are discussed.

Width of exotics from QCD sum rules : Tetraquarks or molecules?

We investigate the widths of the recently observed charmonium like resonances X(3872), Z(4430), and Z(2)(4250) using QCD sum rules. Extending previous analyses regarding these states as diquark-antiquark states or molecules of D mesons, we introduce the Breit-Wigner function in the pole term. We find that introducing the width increases the mass at the small Borel window region. Using the operator-product expansion up to dimension 8, we find that the sum rules based on interpolating current with molecular components give a stable Borel curve from which both the masses and widths of these resonances can be well obtained. Thus the QCD sum rule approach strongly favors the molecular description of these states.

ON THE THREE-DIMENSIONAL BLASCHKE-LEBESGUE PROBLEM

The width of a closed convex subset of n-dimensional Euclidean space is the distance between two parallel supporting hyperplanes. The Blaschke-Lebesgue problem consists of minimizing the volume in the class of convex sets of fixed constant width and is still open in dimension n >= 3. In this paper we describe a necessary condition that the minimizer of the Blaschke-Lebesgue must satisfy in dimension n = 3: we prove that the smooth components of the boundary of the minimizer have their smaller principal curvature constant and therefore are either spherical caps or pieces of tubes (canal surfaces).

Direct evidence of singlet molecular oxygen generation from peroxynitrate, a decomposition product of peroxynitrite

The decomposition of peroxynitrite to nitrite and dioxygen at neutral pH follows complex kinetics, compared to its isomerization to nitrate at low pH. Decomposition may involve radicals or proceed by way of the classical peracid decomposition mechanism. Peroxynitrite (ONOOH/ONOO(-)) decomposition has been proposed to involve formation of peroxynitrate (O(2)NOOH/O(2)NOO(-)) at neutral pH (D. Gupta, B. Harish, R. Kissner and W. H. Koppenol, Dalton Trans., 2009, DOI: 10.1039/b905535e, see accompanying paper in this issue). Peroxynitrate is unstable and decomposes to nitrite and dioxygen. This study aimed to investigate whether O(2)NOO(-) formed upon ONOOH/ONOO(-) decomposition generates singlet molecular oxygen [O(2) ((1)Delta(g))]. As unequivocally revealed by the measurement of monomol light emission in the near infrared region at 1270 nm and by chemical trapping experiments, the decomposition of ONOO(-) or O(2)NOOH at neutral to alkaline pH generates O(2) ((1)Delta(g)) at a yield of ca. 1% and 2-10%, respectively. Characteristic light emission, corresponding to O(2) ((1)Delta(g)) monomolecular decay was observed for ONOO(-) and for O(2)NOOH prepared by reaction of H(2)O(2) with NO(2)BF(4) and of H(2)O(2) with NO(2)(-) in HClO(4). The generation of O(2) ((1)Delta(g)) from ONOO(-) increased in a concentration-dependent manner in the range of 0.1-2.5 mM and was dependent on pH, giving a sigmoid pro. le with an apparent pK(a) around pD 8.1 (pH 7.7). Taken together, our results clearly identify the generation of O(2) ((1)Delta(g)) from peroxynitrate [O(2)NOO(-) -> NO(2)(-) + O(2) ((1)Delta(g))] generated from peroxynitrite and also from the reactions of H(2)O(2) with either NO(2)BF(4) or NO(2)(-) in acidic media.

Fermentation of cacao (Theobroma cacao L.) seeds with a hybrid Kluyveromyces marxianus strain improved product quality attributes

Fermentation of Theobroma cacao (cacao) seeds is an absolute requirement for the full development of chocolate flavor precursors. An adequate aeration of the fermenting cacao seed mass is a fundamental prerequisite for a satisfactory fermentation. Here, we evaluated whether a controlled inoculation of cacao seed fermentation using a Kluyveromyces marxianus hybrid yeast strain, with an increased pectinolytic activity, would improve an earlier liquid drainage (`sweatings`) from the fermentation mass, developing a superior final product quality. Inoculation with K. marxianus increased by one third the volume of drained liquid and affected the microorganism population structure during fermentation, which was detectable up to the end of the process. Introduction of the hybrid yeast affected the profile of total seed protein degradation evaluated by polyacrylamide gel electrophoresis, with improved seed protein degradation, and reduction of titrable acidity. Sensorial evaluation of the chocolate obtained from beans fermented with the K. marxianus inoculation was more accepted by analysts in comparison with the one from cocoa obtained through natural fermentation. The increase in mass aeration during the first 24 h seemed to be fundamental for the improvement of fermentation quality, demonstrating the potential application of this improved hybrid yeast strain with superior exogenous pectinolytic activity.

Efficiency and feasibility of product disassembly: A case-based study

The productivity associated with commonly available disassembly methods today seldomly makes disassembly the preferred end-of-life solution for massive take back product streams. Systematic reuse of parts or components, or recycling of pure material fractions are often not achievable in an economically sustainable way. In this paper a case-based review of current disassembly practices is used to analyse the factors influencing disassembly feasibility. Data mining techniques were used to identify major factors influencing the profitability of disassembly operations. Case characteristics such as involvement of the product manufacturer in the end-of-life treatment and continuous ownership are some of the important dimensions. Economic models demonstrate that the efficiency of disassembly operations should be increased an order of magnitude to assure the competitiveness of ecologically preferred, disassembly oriented end-of-life scenarios for large waste of electric and electronic equipment (WEEE) streams. Technological means available to increase the productivity of the disassembly operations are summarized. Automated disassembly techniques can contribute to the robustness of the process, but do not allow to overcome the efficiency gap if not combined with appropriate product design measures. Innovative, reversible joints, collectively activated by external trigger signals, form a promising approach to low cost, mass disassembly in this context. A short overview of the state-of-the-art in the development of such self-disassembling joints is included. (c) 2008 CIRP.

Integrating technology roadmapping and portfolio management at the front-end of new product development

Many authors point out that the front-end of new product development (NPD) is a critical success factor in the NPD process and that numerous companies face difficulties in carrying it out appropriately. Therefore, it is important to develop new theories and proposals that support the effective implementation of this earliest phase of NPD. This paper presents a new method to support the development of front-end activities based on integrating technology roadmapping (TRM) and project portfolio management (PPM). This new method, called the ITP Method, was implemented at a small Brazilian high-tech company in the nanotechnology industry to explore the integration proposal. The case study demonstrated that the ITP Method provides a systematic procedure for the fuzzy front-end and integrates innovation perspectives into a single roadmap, which allows for a better alignment of business efforts and communication of product innovation goals. Furthermore, the results indicated that the method may also improve quality, functional integration and strategy alignment. (C) 2010 Elsevier Inc. All rights reserved.