Processing and Characterization of Nano-biocomposites Based on Mater-Bi® with Layered Silicates

The development of new nano-biocomposites has been one of the main research areas of interest in polymer science in recent years, since they can combine the intrinsic biodegradable nature of matrices with the ability to modify their properties by the addition of selected nano-reinforcements. In this work, the addition of mineral nanoclays (montmorillonites and sepiolites) to a commercial starch-based matrix is proposed. A complete study on their processing by melt-intercalation techniques and further evaluation of the main properties of nano-biocomposites has been carried out. The results reported show an important influence of the nano-biocomposites morphology on their final properties. In particular, the rheological and viscoelastic characteristics of these systems are very sensitive to the dispersion level of the nanofiller, but it is possible to assess that the material processing behaviour is not compromised by the presence of these nano-reinforcements. In general, both nanofillers had a positive influence in the materials final properties. Mechanical performance shows improvements in terms of elastic modulus, without important limitations in terms of ductility. Thermal properties are improved in terms of residual mass after degradation and low improvements are also observed in terms of oxygen barrier properties.

Cube factorizations of complete graphs

A cube factorization of the complete graph on n vertices, K-n, is a 3-factorization of & in which the components of each factor are cubes. We show that there exists a cube factorization of & if and only if n equivalent to 16 (mod 24), thus providing a new family of uniform 3 -factorizations as well as a partial solution to an open problem posed by Kotzig in 1979. (C) 2004 Wiley Periodicals, Inc.

A probabilistic switch model of information flow in social networks: Application for virtual circuits to organizational design

Network building and exchange of information by people within networks is crucial to the innovation process. Contrary to older models, in social networks the flow of information is noncontinuous and nonlinear. There are critical barriers to information flow that operate in a problematic manner. New models and new analytic tools are needed for these systems. This paper introduces the concept of virtual circuits and draws on recent concepts of network modelling and design to introduce a probabilistic switch theory that can be described using matrices. It can be used to model multistep information flow between people within organisational networks, to provide formal definitions of efficient and balanced networks and to describe distortion of information as it passes along human communication channels. The concept of multi-dimensional information space arises naturally from the use of matrices. The theory and the use of serial diagonal matrices have applications to organisational design and to the modelling of other systems. It is hypothesised that opinion leaders or creative individuals are more likely to emerge at information-rich nodes in networks. A mathematical definition of such nodes is developed and it does not invariably correspond with centrality as defined by early work on networks.

In vitro hydrolytic degradation of centrifugally spun polyhydroxybutyrate-pectin composite fibres

BACKGROUND: Centrifugal spinning is a novel fibre-forming process that readily permits the incorporation of additives while avoiding the thermal damage often associated with conventional melt spinning. Centrifugal spinning of a viscous solution of poly(3-hydroxybutyrate) (PHB) mixed with pectin was used to fabricate a range of fibres containing different concentrations of this biologically active agent. The influence of this blending on fibre morphology and in vitro degradation in an accelerated hydrolytic model at 70 ?C and pH of 10.6 is reported. RESULTS: Blending influenced the physiochemical properties of the fibres, andthis significantly affected thedegradation profile of both the fibre and its PHB constituent. A greater influence on degradation was exerted by the type of pectin and its degree of esterification than by variations in its loading. CONCLUSION: Centrifugal spinning permits the fabrication of composite fibrous matrices from PHB and pectin. Incorporation of the polysaccharide into the fibres can be used to manipulate degradation behaviour and demonstrates a model for doping of matrices with active biological constituents. The unique features of the centrifugal spinning process, as illustrated by the structure of the fibres and the degradation profiles, suggest possible applications of centrifugally spun biopolymers as wound scaffolding devices and in tissue engineering.

On the Asymptotic Behavior of the Ratio between the Numbers of Binary Primitive and Irreducible Polynomials

This work was presented in part at the 8th International Conference on Finite Fields and Applications Fq^8 , Melbourne, Australia, 9-13 July, 2007.

Some Examples of Rigid Representations

*Research partially supported by INTAS grant 97-1644.

Examples Illustrating some Aspects of the Weak Deligne-Simpson Problem

Research partially supported by INTAS grant 97-1644

Matricial Model for the Study of Lower Bounds

Let V be an array. The range query problem concerns the design of data structures for implementing the following operations. The operation update(j,x) has the effect vj ← vj + x, and the query operation retrieve(i,j) returns the partial sum vi + ... + vj. These tasks are to be performed on-line. We define an algebraic model – based on the use of matrices – for the study of the problem. In this paper we establish as well a lower bound for the sum of the average complexity of both kinds of operations, and demonstrate that this lower bound is near optimal – in terms of asymptotic complexity.

Factorizations of some Groups of Lie Type of Lie Rank 4

Еленка Генчева, Цанко Генчев В настоящата работа се разглеждат крайни прости групи G , които могат да се представят като произведение на две свои собствени неабелеви прости подгрупи A и B. Всяко такова представяне G = AB е прието да се нарича факторизация на G, а тъй като множителите A и B са избрани да бъдат прости подгрупи на G, то разглежданите факторизации са известни още като прости факторизации на G. Тук се предполага, че G е проста група от лиев тип и лиев ранг 4 над крайно поле GF (q). Ключови думи: крайни прости групи, групи от лиев тип, факторизации на групи.

Closed Form Solutions of Integrable Nonlinear Evolution Equations

2010 Mathematics Subject Classification: 35Q55.

On Majorization for Matrices

In this paper, we give several results for majorized matrices by using continuous convex function and Green function. We obtain mean value theorems for majorized matrices and also give corresponding Cauchy means, as well as prove that these means are monotonic. We prove positive semi-definiteness of matrices generated by differences deduced from majorized matrices which implies exponential convexity and log-convexity of these differences and also obtain Lypunov's and Dresher's type inequalities for these differences.

Exploring the joint compositional variability of major components and trace elements in the Tellus soil geochemistry survey (Northern Ireland)

The complexity of modern geochemical data sets is increasing in several aspects (number of available samples, number of elements measured, number of matrices analysed, geological-environmental variability covered, etc), hence it is becoming increasingly necessary to apply statistical methods to elucidate their structure. This paper presents an exploratory analysis of one such complex data set, the Tellus geochemical soil survey of Northern Ireland (NI). This exploratory analysis is based on one of the most fundamental exploratory tools, principal component analysis (PCA) and its graphical representation as a biplot, albeit in several variations: the set of elements included (only major oxides vs. all observed elements), the prior transformation applied to the data (none, a standardization or a logratio transformation) and the way the covariance matrix between components is estimated (classical estimation vs. robust estimation). Results show that a log-ratio PCA (robust or classical) of all available elements is the most powerful exploratory setting, providing the following insights: the first two processes controlling the whole geochemical variation in NI soils are peat coverage and a contrast between “mafic” and “felsic” background lithologies; peat covered areas are detected as outliers by a robust analysis, and can be then filtered out if required for further modelling; and peat coverage intensity can be quantified with the %Br in the subcomposition (Br, Rb, Ni).

Flowers of Gomphrena globosa L. as an alternatve source of betacyanins: optimization of the extraction using response surface methodology

Betacyanins are betalain pigments that display a red-violet colour which have been reported to be three times stronger than the red-violet dye produced by anthocyanins [1]. The applications of betacyanins cover a wide range of matrices, mainly as additives or ingredients in the food industry, cosmetics, pharmaceuticals and livestock feed. Although, being less commonly used than anthocyanins and carotenoids, betacyanins are stable between pH 3 to 7 and suitable for colouring in low acid matrices. In addition, betacyanins have been reported to display interesting medicinal character as powerful antioxidant and chemopreventive compounds either in vitro or in vivo models [2]. Betacyanins are obtained mainly from the red beet of Beta vulgaris plant (between I 0 to 20 mg per I 00 g pulp) but alternative primary sources are needed [3]. In addition, independently of the source used, the effect of the variables that affect the extraction of betacyanins have not been properly described and quantified. Therefore, the aim of this study was to identifY and optimize the conditions that maximize betacyanins extraction using the tepals of Gomphrena globosa L. flowers as an alternative source. Assisted by the statistical technique of response surface methodology, an experimental design was developed for testing the significant explanatory variables of the extraction (time, temperature, solid-liquid ratio and ethanolwater ratio). The identification was performed using high-performance liquid chromatography coupled with a photodiode array detector and mass spectrometry with electron spray ionization (HPLC-PDAMS/ ESI) and the response was measured by the quantification of these compounds using HPLC-PDA. Afterwards, a response surface analysis was performed to evaluate the results. The major betacyanin compounds identified were gomphrenin 11 and Ill and isogomphrenin IJ and Ill. The highest total betacyanins content was obtained by using the following conditions: 45 min of extraction. time, 35•c, 35 g/L of solid-liquid ratio and 25% of ethanol. These values would not be found without optimizing the conditions of the betacyanins extraction, which moreover showed contrary trends to what it has been described in the scientific bibliography. More specifically, concerning the time and temperature variables, an increase of both values (from the common ones used in the bibliography) showed a considerable improvement on the betacyanins extraction yield without displaying any type of degradation patterns.

Development of procedures for the triazole fungicides determination in fruits and liquid samples using microextraction techniques and chromatographic separation

Agricultural crops can be damaged by funguses, insects, worms and other organisms that cause diseases and decrease the yield of production. The effect of these damaging agents can be reduced using pesticides. Among them, triazole compounds are effective substances against fungus; for example, Oidium. Nevertheless, it has been detected that the residues of these fungicides in foods as well as in derivate products can affect the health of the consumers. Therefore, the European Union has established several regulations fixing the maximum residue of pesticide levels in a wide range of foods trying to assure the consumer safety. Hence, it is very important to develop adequate methods to determine these pesticide compounds. In most cases, gas or liquid chromatographic (GC, LC) separations are used in the analysis of the samples. But firstly, it is necessary to use proper sample treatments in order to preconcentrate and isolate the target analytes. To reach this aim, microextraction techniques are very effective tools; because allow to do both preconcentration and extraction of the analytes in one simple step that considerably reduces the source of errors. With these objectives, two remarkable techniques have been widely used during the last years: solid phase microextraction (SPME) and liquid phase microextraction (LPME) with its different options. Both techniques that avoid the use or reduce the amount of toxic solvents are convenient coupled to chromatographic equipments providing good quantitative results in a wide number of matrices and compounds. In this work simple and reliable methods have been developed using SPME and ultrasound assisted emulsification microextraction (USAEME) coupled to GC or LC for triazole fungicides determination. The proposed methods allow confidently determine triazole concentrations of μg L‐1 order in different fruit samples. Chemometric tools have been used to accomplish successful determinations. Firstly, in the selection and optimization of the variables involved in the microextraction processes; and secondly, to overcome the problems related to the overlapping peaks. Different fractional factorial designs have been used for the screening of the experimental variables; and central composite designs have been carried out to get the best experimental conditions. Trying to solve the overlapping peak problems multivariate calibration methods have been used. Parallel Factor Analysis 2 (PARAFAC2), Multivariate Curve Resolution (MCR) and Parallel Factor Analysis with Linear Dependencies (PARALIND) have been proposed, the adequate algorithms have been used according to data characteristics, and the results have been compared. Because its occurrence in Basque Country and its relevance in the production of cider and txakoli regional wines the grape and apple samples were selected. These crops are often treated with triazole compounds trying to solve the problems caused by the funguses. The peel and pulp from grape and apple, their juices and some commercial products such as musts, juice and cider have been analysed showing the adequacy of the developed methods for the triazole determination in this kind of fruit samples.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.