Towards a maximal extension of Pelczynski`s decomposition method in Banach spaces

l Suppose that X, Y. A and B are Banach spaces such that X is isomorphic to Y E) A and Y is isomorphic to X circle plus B. Are X and Y necessarily isomorphic? In this generality. the answer is no, as proved by W.T. Cowers in 1996. In the present paper, we provide a very simple necessary and sufficient condition on the 10-tuples (k, l, m, n. p, q, r, s, u, v) in N with p+q+u >= 3, r+s+v >= 3, uv >= 1, (p,q)$(0,0), (r,s)not equal(0,0) and u=1 or v=1 or (p. q) = (1, 0) or (r, s) = (0, 1), which guarantees that X is isomorphic to Y whenever these Banach spaces satisfy X(u) similar to X(p)circle plus Y(q), Y(u) similar to X(r)circle plus Y(s), and A(k) circle plus B(l) similar to A(m) circle plus B(n). Namely, delta = +/- 1 or lozenge not equal 0, gcd(lozenge, delta (p + q - u)) divides p + q - u and gcd(lozenge, delta(r + s - v)) divides r + s - v, where 3 = k - I - in + n is the characteristic number of the 4-tuple (k, l, m, n) and lozenge = (p - u)(s - v) - rq is the discriminant of the 6-tuple (p, q, r, s, U, v). We conjecture that this result is in some sense a maximal extension of the classical Pelczynski`s decomposition method in Banach spaces: the case (1, 0. 1, 0, 2. 0, 0, 2. 1. 1). (C) 2009 Elsevier Inc. All rights reserved.

The bound quiver of a split extension

In this paper, we give a sufficient (which is also necessary under a compatibility hypothesis) condition on a set of arrows in the quiver of an algebra A so that A is a split extension of A/M, where M is the ideal of A generated by the classes of these arrows. We also compare the notion of split extension with that of semiconvex extension of algebras.

UNIQUENESS OF THE EXTENSION OF 2-HOMOGENEOUS POLYNOMIALS

Homogeneous polynomials of degree 2 on the complex Banach space c(0)(l(n)(2)) are shown to have unique norm-preserving extension to the bidual space. This is done by using M-projections and extends the analogous result for c(0) proved by P.-K. Lin.

On Approximate KKT Condition and its Extension to Continuous Variational Inequalities

In this work, we introduce a necessary sequential Approximate-Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality, and we prove its relation with the Approximate Gradient Projection condition (AGP) of Garciga-Otero and Svaiter. We also prove that a slight variation of the AKKT condition is sufficient for a convex problem, either for variational inequalities or optimization. Sequential necessary conditions are more suitable to iterative methods than usual punctual conditions relying on constraint qualifications. The AKKT property holds at a solution independently of the fulfillment of a constraint qualification, but when a weak one holds, we can guarantee the validity of the KKT conditions.

Fire Incidences, Water Bodies, and Population in Maine

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FIRE HAZARD IN COCONINO COUNTY, ARIZONA

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The Strider Years: An Extension of the History of Colby College

Beloved Colby historian Ernest Cummings Marriner '13 documents Robert E. Lee Strider's nineteen years as president of Colby College. Marriner is also the author of the definitive History of Colby, which covers the period up to the Strider presidency.

Extension And Testing Of A 2D Hydrodynamic Model For Direct Rainfall Runoff Simulation

While the simulation of flood risks originating from the overtopping of river banks is well covered within continuously evaluated programs to improve flood protection measures, flash flooding is not. Flash floods are triggered by short, local thunderstorm cells with high precipitation intensities. Small catchments have short response times and flow paths and convective thunder cells may result in potential flooding of endangered settlements. Assessing local flooding and pathways of flood requires a detailed hydraulic simulation of the surface runoff. Hydrological models usually do not incorporate surface runoff at this detailedness but rather empirical equations are applied for runoff detention. In return 2D hydrodynamic models usually do not allow distributed rainfall as input nor are any types of soil/surface interaction implemented as in hydrological models. Considering several cases of local flash flooding during the last years the issue emerged for practical reasons but as well as research topics to closing the model gap between distributed rainfall and distributed runoff formation. Therefore, a 2D hydrodynamic model, depth-averaged flow equations using the finite volume discretization, was extended to accept direct rainfall enabling to simulate the associated runoff formation. The model itself is used as numerical engine, rainfall is introduced via the modification of waterlevels at fixed time intervals. The paper not only deals with the general application of the software, but intends to test the numerical stability and reliability of simulation results. The performed tests are made using different artificial as well as measured rainfall series as input. Key parameters of the simulation such as losses, roughness or time intervals for water level manipulations are tested regarding their impact on the stability.

Brand image co-creation and individual identity extension in online environments: a Facebook investigation

In this thesis I investigate the extent to which companies can build a more communal environment out of their fan pages while also evaluating the corresponding brand value that may come from having such a communal environment. My research is comprised in three articles: in the first article, I describe how the brand image is created or augmented in the fan page environment, therefore providing demonstrable evidence of value creation. In the second article, I describe how individuals use fan page semiotic elements to communicate their identities. Finally, in the third article, I describe the possible communal characteristics of a fan page and the conditions that enable it to evolve to the virtual brand community concept. As a result, I will contribute to the marketing literature on the use of Facebook for communicating brand identity, on the co-creation of the brand image in social media context, and on the conceptual definition of fan pages as a communal environment.

Line extension influence on brand image: a study on the alcoholic beverage market in Brazil

The present study has the objective of understanding the influence of line extensions on the image of vodka brands. The research was performed by organizing various focus groups with vodka consumers in São Paulo. These focus groups allowed exploring and analyzing how the last line extensions of vodka brands have modified the image the consumers had of the brand. Three hypotheses were distinguished as an outcome of the research: (1) The influence of a line extension on brand image depends heavily on the initial image the consumers have of the brand. For a vodka brand with an average or bad image, launching a line extension with a perceived average or bad quality does not modify the brand image. On the contrary, for a vodka brand with a positive initial brand image, launching a line extension with perceived high quality led to a positive change in the brand image. (2) For vodka brands, a vertical line extension recognized as having high authenticity provokes a transfer of attributes from the extended product to the brand. (3) Among Keller’s (1993) dimensions of brand image, non-product related attributes and especially packaging are the one that are the most influenced by line extensions of vodka brands.

Estudo da flamabilidade e resistência à chama de compósito de poliéster insaturado e fibra da folha do abacaxizeiro (PALF)

In the present research work, composites were prepared using pine apple leaf fibres (PALF) as reinforcement with unsaturated polyester resin as matrix, incorporating with fire retardant at different compositions. The PALF was obtained from the decortication of pine apple leaves obtained from Ramada 4 from Ielmo Marinho in the State of Rio Grande do Norte. The unsaturated polyester resin and the catalyzer were bought from the local establishment. The fire retardant, aluminium tri-hydroxide - Al(OH)3 was donated by Alcoa Alumínio S.A and was used in the proportions of 20%, 40% and 60% w/w. Initially the fibres were treated with 2% NaOH for 1 hour, to remove any impurities present on the fibre surface, such as wax, fat, pectin and pectate, in order to have a better adsorption of the fibres with the matrix as well as the flame retardant. The fibre mat was prepared in a mat preparator by immersion, developed in the Textile Engineering Laboratory, at the UFRN. The composites (300x300x3 mm) were prepared by compression molding and the samples (150x25x3 mm) for analysis of the properties were cut randomly using a laser cutter. Some of the cut samples were used to measure the smoke emission and fire resistance using UL94 standard. Mechanical tension-extension and flexural properties were carried in CTGás RN and the Laboratório de Metais e Ensaios Mecânicos Engenharia de Materiais UFRN , as well as SEM studies were carried out at Núcleo de Estudos em Petróleo e Gás Natural - UFRN . From the observed results, it was noted that, there was no marked influence of the fire retardant on the mechanical properties. Also in the water absorption test, the quantity of water absorbed was less in the sample with higher concentration of fire retardant. It was also observed that the increase in the proportion of the fire retardant increased the time of burning, may be due to the compactness of the composite due to the presence of fire retardant as a filling material even though it was meant to reduce the rate of inflammability of the composite

On the zeros of polynomials: An extension of the Enestrom-Kakeya theorem

This paper presents an extension of the Enestrom-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K, L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994)[6]. (C) 2011 Elsevier B.V. All rights reserved.

On extension theorems for holomorphic generalized functions

We present two extension theorems for holomorphic generalized functions. The first one is a version of the classic Hartogs extension theorem. In this, we start from a holomorphic generalized function on an open neighbourhood of the bounded open boundary, extending it, holomorphically, to a full open. In the second theorem a generalized version of a classic result is obtained, done independently, in 1943, by Bochner and Severi. For this theorem, we start from a function that is holomorphic generalized and has a holomorphic representative on the bounded domain boundary, we extend it holomorphically the function, for the whole domain.