Riemannian metric and geometric mean for positive semidefinite matrices of fixed rank

This paper introduces a new metric and mean on the set of positive semidefinite matrices of fixed-rank. The proposed metric is derived from a well-chosen Riemannian quotient geometry that generalizes the reductive geometry of the positive cone and the associated natural metric. The resulting Riemannian space has strong geometrical properties: it is geodesically complete, and the metric is invariant with respect to all transformations that preserve angles (orthogonal transformations, scalings, and pseudoinversion). A meaningful approximation of the associated Riemannian distance is proposed, that can be efficiently numerically computed via a simple algorithm based on SVD. The induced mean preserves the rank, possesses the most desirable characteristics of a geometric mean, and is easy to compute. © 2009 Society for Industrial and Applied Mathematics.

A comparison of silicon oxide and nitride as host matrices on the photoluminescence from Er3+ ions

This paper compares the properties of silicon oxide and nitride as host matrices for Er ions. Erbium-doped silicon nitride films were deposited by a plasma-enhanced chemical-vapour deposition system. After deposition, the films were implanted with Er3+ at different doses. Er-doped thermal grown silicon oxide films were prepared at the same time as references. Photoluminescence features of Er3+ were inspected systematically. It is found that silicon nitride films are suitable for high concentration doping and the thermal quenching effect is not severe. However, a very high annealing temperature up to 1200 degrees C is needed to optically activate Er3+ which may be the main obstacle to impede the application of Er-doped silicon nitride.

Calculation of the band structure of semiconductor quantum wells using scattering matrices

The transfer-matrix method widely used in the calculation of the band structure of semiconductor quantum wells is found to have limitations due to its intrinsic numerical instability. It is pointed out that the numerical instability arises from free-propagating transfer matrices. A new scattering-matrix method is developed for the multiple-band Kane model within the envelope-function approximation. Compared with the transfer-matrix method, the proposed algorithm is found to be more efficient and stable. A four-band Kane model is used to check the validity of the method and the results are found to be in good agreement with earlier calculations.

Substitution Matrices of Residue Triplets Derived from Protein Blocks.

In protein sequence alignment, residue similarity is usually evaluated by substitution matrix, which scores all possible exchanges of one amino acid with another. Several matrices are widely used in sequence alignment, including PAM matrices derived from homologous sequence and BLOSUM matrices derived from aligned segments of BLOCKS. However, most matrices have not addressed the high-order residue-residue interactions that are vital to the bioproperties of protein.With consideration for the inherent correlation in residue triplet, we present a new scoring scheme for sequence alignment. Protein sequence is treated as overlapping and successive 3-residue segments. Two edge residues of a triplet are clustered into hydrophobic or polar categories, respectively. Protein sequence is then rewritten into triplet sequence with 2 · 20 · 2 = 80 alphabets. Using a traditional approach, we construct a new scoring scheme named TLESUMhp (TripLEt SUbstitution Matrices with hydropobic and polar information) for pairwise substitution of triplets, which characterizes the similarity of residue triplets. The applications of this matrix led to marked improvements in multiple sequence alignment and in searching structurally alike residue segments. The reason for the occurrence of the ‘‘twilight zone,’’ i.e., structure explosion of lowidentity sequences, is also discussed.

Dendrimer films as matrices for electrochemical fabrication of novel gold/palladium bimetallic nanostructures

Electrodeposition of novel Au/Pd bimetallic nanostructures with dendrimer films as matrices has been reported. The dendrimers exhibited highly open structures arising from protonation of amines and this made them have good penetrability for solvent molecules. The unique properties of dendrimers obviously affected the morphologies and compositions of deposited bimetallic nanostructures compared with those from unmodified surfaces. Field-emitted scanning electron microscopy, energy dispersive spectroscopy, X-ray photoelectron spectroscopy and UV-vis spectroscopy were used to characterize these nanostructures.

Electrochemical biosensors based on advanced bioimmobilization matrices

Biosensors have experienced rapid, extensive development. To maintain the bioactivity of biomolecules and to give the electrochemical output signal required, appropriate bioimmobilization matrices for biomolecules are critical.In this review, we describe some advanced membrane materials (including hydrogels, sol-gel-derived organic-inorganic composites and lipid membranes), introduce electrochemical biosensors based on bioimmobilization materials and describe their performance.Biosensors operating in extreme conditions and displaying direct electron transfer with electrodes based on these advanced membrane materials are attractive. Recent developments in nanomaterials include biosensors, so we emphasize the intersection of nanomaterials with advanced membrane materials in biosensors.

Relationship between luminescence and matrices in the system Al2O3-B2O3-Ce2O3

The system Al2O3-B2O3-Ce2O3, with Al/B ratio varying from 4.5 to 2 and Ce/(Al + B) = 0.02, has been prepared at the temperature from 1 200 to 1 400 degrees C. Relationship between luminescence and matrices in the system Al2O3-B2O3-Ce2O3 was investigated. It was found that some changes of the matrices occurred with Al/B ratio varying from 4.5 to 2. These results lead to a great change in luminescence properties, indicating variation of Ce-surroundings of crystal field. With the decrease of the ratio from 3 to 2, the excitation and emission peaks shift to shorter wavelengths. it was also found that a new type of rare earth luminescent materials was obtained with appropriate Al/B ratio.

Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices

B.M. Brown, M. Marletta, S. Naboko, I. Wood: Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices, J. London Math. Soc., June 2008; 77: 700-718. The full text of this article will be made available in this repository in June 2009 Sponsorship: EPSRC,INTAS

Diseño y desarrollo de herramientas en cerámica, La Calera. Asistencia técnica para el mejoramiento de la pasta cerámica y proceso de secado de piezas de alfarería San Sebastián. Mejoramiento de la pasta cerámica y proceso de secado de piezas de alfarería. Acondicionamiento y manejo de hornos, Momil. Mejoramiento de la pasta cerámica y proceso de secado de piezas de alfarería. Asistencia para la elaboración de matrices y moldes para piezas de cerámica acondicionamiento y manejo de hornos, Ciénaga De Oro y Planeta Rica.

[152] hojas : ilustraciones.

An Independent-Connection Model for Traffic Matrices

A common assumption made in traffic matrix (TM) modeling and estimation is independence of a packet's network ingress and egress. We argue that in real IP networks, this assumption should not and does not hold. The fact that most traffic consists of two-way exchanges of packets means that traffic streams flowing in opposite directions at any point in the network are not independent. In this paper we propose a model for traffic matrices based on independence of connections rather than packets. We argue that the independent connection (IC) model is more intuitive, and has a more direct connection to underlying network phenomena than the gravity model. To validate the IC model, we show that it fits real data better than the gravity model and that it works well as a prior in the TM estimation problem. We study the model's parameters empirically and identify useful stability properties. This justifies the use of the simpler versions of the model for TM applications. To illustrate the utility of the model we focus on two such applications: synthetic TM generation and TM estimation. To the best of our knowledge this is the first traffic matrix model that incorporates properties of bidirectional traffic.

Sugar matrices in stabilization of bioactives by dehydration

Development of functional foods with bioactive components requires component stability in foods and ingredients. Stabilization of sensitive bioactive components can be achieved by entrapment or encapsulation of these components in solid food matrices. Lactose or trehalose was used as the structure-forming material for the entrapment of hydrophilic ascorbic acid and thiamine hydrochloride or the encapsulation of oil particles containing hydrophobic α-tocopherol. In the delivery of hydrophobic components, milk protein isolate, soy protein isolate, or whey protein isolate were used as emulsifiers and, in some cases, applied in excess amount to form matrices together with sugars. Dehydrated amorphous structures with bioactives were produced by freezing and freeze-drying. Experimental results indicated that: (i) lactose and trehalose showed similar water sorption and glass transition but very different crystallization behavior as pure sugars; (ii) the glass transition of sugar-based systems was slightly affected by the presence of other components in anhydrous systems but followed closely that of sugar after water plasticization; (iii) sugar crystallization in mixture systems was composition-dependent; (iv) the stability of bioactives was better retained in the amorphous matrices, although small losses of stability were observed for hydrophilic components above glass transition and for hydrophobic components as a function of water activity; (v) sugar crystallization caused significant loss of hydrophilic bioactives as a result of the exclusion from the continuous crystalline phase; (vi) loss of hydrophobic bioactives upon sugar crystallization was a result of dramatic change of emulsion properties and the exclusion of oil particles from the protecting structure; (vii) the double layers at the hydrophilic-hydrophobic interfaces improved the stability of hydrophobic bioactives in dehydrated systems. The present study provides information on the physical and chemical stability of sugar-based dehydrated delivery systems, which could be helpful in designing foods and ingredients containing bioactive components with improved storage stability.

Matrices de sentido para las nociones de velocidad y tiempo

Las distancias entre saberes de la vida diaria, los escolares y los eruditos, afincan sus raíces en matrices de sentido de epistemes propias. Tal ocurre para las nociones de velocidad y tiempo de la matemática del cambio. Una didáctica crítica es desafiada a deconstruirlos, desentrañando su presencia en el sentido común del estudiantado y en los saberes escolares de los que debe apropiarse éste, de modo de proporcionar antecedentes para diseñar y validar puentes de diálogo entre estos cuerpos de saberes. Para colaborar en esta línea, se presentan matrices de sentido para las nociones de velocidad y de tiempo obtenidas en investigaciones de la Matemática del Cambio.

Códigos secretos: otra forma de aplicar las matrices en bachillerato (16-18)

Tras una breve introducción para hacer referencia a distintos tipos de códigos secretos, el articulo estudia con detalle, esquemáticamente y mediante ejemplos, los códigos matriciales. Se expone, además, una forma de automatizar dichos códigos en el aula, mediante un programa escrito en dBASE III Plus. La parte final consta de unas preguntas sobre sus posibilidades didácticas.