945 resultados para piece-wise polynomials


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This article explores aspects of sustainability and the importance of sustainable development, including the place of the crucially important resource of fresh water and of freshwater ecosystems. It examines the treatment of natural resources by the economic system that underpins global business, outlines some progress towards more sustainable approaches to business, and recommends steps to re-establish science as the driver of wise policies that contribute to sustainable development.

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The authors report the record of Cyclops singularis collected from Peasemoor Piece, a seasonal pond on the outskirts of Oxford. This preliminary note is to alert others to the possibility that C singularis may occur in collections from seasonal ponds in the UK. The recent record of this species in Belgium (Alekseev et al. 2002) indicates that this species is not restricted to its type locality.

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It is often difficult to define ‘water quality’ with any degree of precision. One approach is that suggested by Battarbee (1997) and is based on the extent to which individual lakes have changed compared with their natural ‘baseline’ status. Defining the base-line status of artificial lakes and reservoirs however, is, very difficult. In ecological terms, the definition of quality must include some consideration of their functional characteristics and the extent to which these characteristics are self-sustaining. The challenge of managing lakes in a sustainable way is particularly acute in semi-arid, Mediterranean countries. Here the quality of the water is strongly influenced by the unpredictability of the rainfall as well as year-to-year variations in the seasonal averages. Wise management requires profound knowledge of how these systems function. Thus a holistic approach must be adopted and the factors influencing the seasonal dynamics of the lakes quantified over a range of spatial and temporal scales. In this article, the authors describe some of the ways in which both long-term and short-term changes in the weather have influenced the seasonal and spatial dynamics of phytoplankton in El Gergal, a water supply reservoir situated in the south of Spain. The quality of the water stored in this reservoir is typically very good but surface blooms of algae commonly appear during warm, calm periods when the water level is low. El Gergal reservoir is managed by the Empresa Municipal de Abastecimiento y Saneamiento (EMASESA) and supplies water for domestic, commercial and industrial use to an area which includes the city of Seville and twelve of its surrounding towns (ca. 1.3 million inhabitants). El Gergal is the last of two reservoirs in a chain of four situated in the Rivera de Huelva basin, a tributary of the Guadalquivir river. It was commissioned by EMASESA in 1979 and since then the company has monitored its main limnological parameters on, at least, a monthly basis and used this information to improve the management of the reservoir. As a consequence of these intensive studies the physical, chemical and biological information acquired during this period makes the El Gergal database one of the most complete in Spain. In this article the authors focus on three ‘weather-related’ effects that have had a significant impact on the composition and distribution of phytoplankton in El Gergal: (i) the changes associated with severe droughts; (ii) the spatial variations produced by short-term changes in the weather; (iii) the impact of water transfers on the seasonal dynamics of the dinoflagellate Ceratium.

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In this thesis, we consider two main subjects: refined, composite invariants and exceptional knot homologies of torus knots. The main technical tools are double affine Hecke algebras ("DAHA") and various insights from topological string theory.

In particular, we define and study the composite DAHA-superpolynomials of torus knots, which depend on pairs of Young diagrams and generalize the composite HOMFLY-PT polynomials from the full HOMFLY-PT skein of the annulus. We also describe a rich structure of differentials that act on homological knot invariants for exceptional groups. These follow from the physics of BPS states and the adjacencies/spectra of singularities associated with Landau-Ginzburg potentials. At the end, we construct two DAHA-hyperpolynomials which are closely related to the Deligne-Gross exceptional series of root systems.

In addition to these main themes, we also provide new results connecting DAHA-Jones polynomials to quantum torus knot invariants for Cartan types A and D, as well as the first appearance of quantum E6 knot invariants in the literature.

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通过在线形谐振腔中引入一段缠绕在压电陶瓷上的单模光纤作为正弦相位调制器,使得激射波长的损耗不固定,抑制由于掺铒光纤的均匀展宽效应引起的模式竞争,从而避免了在室温下不稳定的单波长激射,实现了多波长掺铒光纤激光器的稳定输出。为了获得平坦的多波长输出,在谐振腔里使用了一个损耗峰位于1530nm处的长周期光纤光栅,以获得较为平坦的增益谱。通过两个3dB耦合器制成的反射型梳状滤波器的滤波作用,实验中观察到稳定的多波长激射,相邻波长间隔约为0.45nm。中心9个波长的输出功率平坦度为10dB,边模抑制比大于25dB。

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We analyze mutual alignment errors due to wave-front aberrations. To solve the central obscured problem, we introduce modified Zernike polynomials, which are a set of complete orthogonal polynomials. It is found that different aberrations have different effects on mutual alignment errors. Some aberrations influence only the line of sight, while some aberrations influence both the line of sight and the intensity distributions. (c) 2005 Optical Society of America

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[ES]Este Trabajo de Fin de Grado tiene como objeto crear un programa que sirva como herramienta para los cálculos en las propiedades a fatiga de una pieza. El conjunto del trabajo se centra en su creación mediante la herramienta Excel. El programa cuenta con tres diferentes pestañas: una para los datos que debe introducir el usuario, otra correspondiente a los cálculos y por último una en la que aparecen los resultados. El usuario debe conocer las propiedades de la probeta del material a ensayar, así como el rango de ciclos en el cual se va a trabajar (siempre en un rango de ciclos medio alto). A partir de estas informaciones de la probeta, y gracias a la curva de Basquin y la ecuación de Marin, el programa será capaz de obtener la curva de resistencia a fatiga correspondiente para la pieza. Se incluyen también casos especiales en los que se realicen tratamientos mecánicos de mejora, con una tensión límite del proceso. Para obtener la curva S-N de la pieza se pedirá información en la pestaña de interfaz con el usuario sobre distintas propiedades de la pieza, que permitan así calcular los valores de los coeficientes de Marín gracias a la base de datos que contiene el programa. El usuario tiene también la opción de introducir él mismo los valores de los coeficientes para así obtener una curva que se aproxime más a sus resultados experimentales. En resumen, la función del programa es la de ser una calculadora de la resistencia fatiga de la pieza a partir de los datos que se disponen de la probeta.

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In this thesis an extensive study is made of the set P of all paranormal operators in B(H), the set of all bounded endomorphisms on the complex Hilbert space H. T ϵ B(H) is paranormal if for each z contained in the resolvent set of T, d(z, σ(T))//(T-zI)-1 = 1 where d(z, σ(T)) is the distance from z to σ(T), the spectrum of T. P contains the set N of normal operators and P contains the set of hyponormal operators. However, P is contained in L, the set of all T ϵ B(H) such that the convex hull of the spectrum of T is equal to the closure of the numerical range of T. Thus, NPL.

If the uniform operator (norm) topology is placed on B(H), then the relative topological properties of N, P, L can be discussed. In Section IV, it is shown that: 1) N P and L are arc-wise connected and closed, 2) N, P, and L are nowhere dense subsets of B(H) when dim H ≥ 2, 3) N = P when dimH ˂ ∞ , 4) N is a nowhere dense subset of P when dimH ˂ ∞ , 5) P is not a nowhere dense subset of L when dimH ˂ ∞ , and 6) it is not known if P is a nowhere dense subset of L when dimH ˂ ∞.

The spectral properties of paranormal operators are of current interest in the literature. Putnam [22, 23] has shown that certain points on the boundary of the spectrum of a paranormal operator are either normal eigenvalues or normal approximate eigenvalues. Stampfli [26] has shown that a hyponormal operator with countable spectrum is normal. However, in Theorem 3.3, it is shown that a paranormal operator T with countable spectrum can be written as the direct sum, N ⊕ A, of a normal operator N with σ(N) = σ(T) and of an operator A with σ(A) a subset of the derived set of σ(T). It is then shown that A need not be normal. If we restrict the countable spectrum of T ϵ P to lie on a C2-smooth rectifiable Jordan curve Go, then T must be normal [see Theorem 3.5 and its Corollary]. If T is a scalar paranormal operator with countable spectrum, then in order to conclude that T is normal the condition of σ(T) ≤ Go can be relaxed [see Theorem 3.6]. In Theorem 3.7 it is then shown that the above result is not true when T is not assumed to be scalar. It was then conjectured that if T ϵ P with σ(T) ≤ Go, then T is normal. The proof of Theorem 3.5 relies heavily on the assumption that T has countable spectrum and cannot be generalized. However, the corollary to Theorem 3.9 states that if T ϵ P with σ(T) ≤ Go, then T has a non-trivial lattice of invariant subspaces. After the completion of most of the work on this thesis, Stampfli [30, 31] published a proof that a paranormal operator T with σ(T) ≤ Go is normal. His proof uses some rather deep results concerning numerical ranges whereas the proof of Theorem 3.5 uses relatively elementary methods.

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[ES]Este es un Trabajo Fin de Grado interdisciplinar que aúna la Innovación y el Emprendimiento con la Econometría. En la parte teórica, se sintetiza la literatura relacionada con la innovación y el emprendimiento, los tipos y medidas de innovación, los factores que influyen tanto positiva como negativamente en la innovación, y se explica la importancia de innovar en las empresas. Se analizan también las bases de datos sobre innovación disponibles en Internet. Mientras que en la parte empírica, se analiza el impacto del Producto Interior Bruto sobre la actividad emprendedora total y por motivos de necesidad u oportunidad de 67 países a nivel mundial. Los países están divididos en tres tipos, dependiendo de cual es el motor impulsor de su economía: los factores tradicionales de producción, los factores que mejoran su eficiencia y las economías basadas en la sofisticación de sus empresas y la innovación. Así mismo, se analiza la influencia del PIB y otras variables macroeconómicas como el nivel de educación superior, la inversión pública y privada en I+D+i y el número de patentes PCT con el emprendimiento innovador. Para ello, se han teniendo en cuenta los datos aportados en los Informes Global Entrepreneurship Monitor (GEM) y Innovation Union Scoreboard (IUS) para el año 2012.

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Let F(θ) be a separable extension of degree n of a field F. Let Δ and D be integral domains with quotient fields F(θ) and F respectively. Assume that Δ D. A mapping φ of Δ into the n x n D matrices is called a Δ/D rep if (i) it is a ring isomorphism and (ii) it maps d onto dIn whenever d ϵ D. If the matrices are also symmetric, φ is a Δ/D symrep.

Every Δ/D rep can be extended uniquely to an F(θ)/F rep. This extension is completely determined by the image of θ. Two Δ/D reps are called equivalent if the images of θ differ by a D unimodular similarity. There is a one-to-one correspondence between classes of Δ/D reps and classes of Δ ideals having an n element basis over D.

The condition that a given Δ/D rep class contain a Δ/D symrep can be phrased in various ways. Using these formulations it is possible to (i) bound the number of symreps in a given class, (ii) count the number of symreps if F is finite, (iii) establish the existence of an F(θ)/F symrep when n is odd, F is an algebraic number field, and F(θ) is totally real if F is formally real (for n = 3 see Sapiro, “Characteristic polynomials of symmetric matrices” Sibirsk. Mat. Ž. 3 (1962) pp. 280-291), and (iv) study the case D = Z, the integers (see Taussky, “On matrix classes corresponding to an ideal and its inverse” Illinois J. Math. 1 (1957) pp. 108-113 and Faddeev, “On the characteristic equations of rational symmetric matrices” Dokl. Akad. Nauk SSSR 58 (1947) pp. 753-754).

The case D = Z and n = 2 is studied in detail. Let Δ’ be an integral domain also having quotient field F(θ) and such that Δ’ Δ. Let φ be a Δ/Z symrep. A method is given for finding a Δ’/Z symrep ʘ such that the Δ’ ideal class corresponding to the class of ʘ is an extension to Δ’ of the Δ ideal class corresponding to the class of φ. The problem of finding all Δ/Z symreps equivalent to a given one is studied.

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Let L be the algebra of all linear transformations on an n-dimensional vector space V over a field F and let A, B, ƐL. Let Ai+1 = AiB - BAi, i = 0, 1, 2,…, with A = Ao. Let fk (A, B; σ) = A2K+1 - σ1A2K-1 + σ2A2K-3 -… +(-1)KσKA1 where σ = (σ1, σ2,…, σK), σi belong to F and K = k(k-1)/2. Taussky and Wielandt [Proc. Amer. Math. Soc., 13(1962), 732-735] showed that fn(A, B; σ) = 0 if σi is the ith elementary symmetric function of (β4- βs)2, 1 ≤ r ˂ s ≤ n, i = 1, 2, …, N, with N = n(n-1)/2, where β4 are the characteristic roots of B. In this thesis we discuss relations involving fk(X, Y; σ) where X, Y Ɛ L and 1 ≤ k ˂ n. We show: 1. If F is infinite and if for each X Ɛ L there exists σ so that fk(A, X; σ) = 0 where 1 ≤ k ˂ n, then A is a scalar transformation. 2. If F is algebraically closed, a necessary and sufficient condition that there exists a basis of V with respect to which the matrices of A and B are both in block upper triangular form, where the blocks on the diagonals are either one- or two-dimensional, is that certain products X1, X2…Xr belong to the radical of the algebra generated by A and B over F, where Xi has the form f2(A, P(A,B); σ), for all polynomials P(x, y). We partially generalize this to the case where the blocks have dimensions ≤ k. 3. If A and B generate L, if the characteristic of F does not divide n and if there exists σ so that fk(A, B; σ) = 0, for some k with 1 ≤ k ˂ n, then the characteristic roots of B belong to the splitting field of gk(w; σ) = w2K+1 - σ1w2K-1 + σ2w2K-3 - …. +(-1)K σKw over F. We use this result to prove a theorem involving a generalized form of property L [cf. Motzkin and Taussky, Trans. Amer. Math. Soc., 73(1952), 108-114]. 4. Also we give mild generalizations of results of McCoy [Amer. Math. Soc. Bull., 42(1936), 592-600] and Drazin [Proc. London Math. Soc., 1(1951), 222-231].

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An investigation was conducted to estimate the error when the flat-flux approximation is used to compute the resonance integral for a single absorber element embedded in a neutron source.

The investigation was initiated by assuming a parabolic flux distribution in computing the flux-averaged escape probability which occurs in the collision density equation. Furthermore, also assumed were both wide resonance and narrow resonance expressions for the resonance integral. The fact that this simple model demonstrated a decrease in the resonance integral motivated the more detailed investigation of the thesis.

An integral equation describing the collision density as a function of energy, position and angle is constructed and is subsequently specialized to the case of energy and spatial dependence. This equation is further simplified by expanding the spatial dependence in a series of Legendre polynomials (since a one-dimensional case is considered). In this form, the effects of slowing-down and flux depression may be accounted for to any degree of accuracy desired. The resulting integral equation for the energy dependence is thus solved numerically, considering the slowing down model and the infinite mass model as separate cases.

From the solution obtained by the above method, the error ascribable to the flat-flux approximation is obtained. In addition to this, the error introduced in the resonance integral in assuming no slowing down in the absorber is deduced. Results by Chernick for bismuth rods, and by Corngold for uranium slabs, are compared to the latter case, and these agree to within the approximations made.

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A presente dissertação tem como objetivo mostrar como a literatura gótica pode ser atemporal, subvertendo as mentes e conceitos de seus leitores. Partindo do contexto histórico e cultural em que The Monk se inseriu, esse trabalho visa levantar as questões e elementos tão fortemente reprimidos em nossa sociedade desde o final do século XVIII, como as idéias de mal, abjeção e expressão do eu, em um diálogo permanente com a teoria de Michel Foucault, David Punter, Julia Kristeva, entre outros. Desta forma, a análise do romance se dá paralelamente a uma crítica social, visto que a obra gótica tem por um de seus fins denunciar e deslocar a realidade social. Em última instância, será feita a análise algumas personagens do romance e sua respectiva importância na obra

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[ES]El objeto del presente estudio de viabilidad es estudiar la eficiencia y productividad de la Central Hidroeléctrica de Plazakola aportando diversas alternativas posibles que puedan ser técnica y económicamente viables. Para cada una de las soluciones propuestas se analizará la producción de energía así como el presupuesto estimado de las obras y equipos necesarios, comparándose entre ellas y determinando la solución óptima, que será desarrollada en el anteproyecto.

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The effect of intermolecular coupling in molecular energy levels (electronic and vibrational) has been investigated in neat and isotopic mixed crystals of benzene. In the isotopic mixed crystals of C6H6, C6H5D, m-C6H4D2, p-C6H4D2, sym-C6H3D3, C6D5H, and C6D6 in either a C6H6 or C6D6 host, the following phenomena have been observed and interpreted in terms of a refined Frenkel exciton theory: a) Site shifts; b) site group splittings of the degenerate ground state vibrations of C6H6, C6D6, and sym-C6H3D3; c) the orientational effect for the isotopes without a trigonal axis in both the 1B2u electronic state and the ground state vibrations; d) intrasite Fermi resonance between molecular fundamentals due to the reduced symmetry of the crystal site; and e) intermolecular or intersite Fermi resonance between nearly degenerate states of the host and guest molecules. In the neat crystal experiments on the ground state vibrations it was possible to observe many of these phenomena in conjunction with and in addition to the exciton structure.

To theoretically interpret these diverse experimental data, the concepts of interchange symmetry, the ideal mixed crystal, and site wave functions have been developed and are presented in detail. In the interpretation of the exciton data the relative signs of the intermolecular coupling constants have been emphasized, and in the limit of the ideal mixed crystal a technique is discussed for locating the exciton band center or unobserved exciton components. A differentiation between static and dynamic interactions is made in the Frenkel limit which enables the concepts of site effects and exciton coupling to be sharpened. It is thus possible to treat the crystal induced effects in such a fashion as to make their similarities and differences quite apparent.

A calculation of the ground state vibrational phenomena (site shifts and splittings, orientational effects, and exciton structure) and of the crystal lattice modes has been carried out for these systems. This calculation serves as a test of the approximations of first order Frenkel theory and the atom-atom, pair wise interaction model for the intermolecular potentials. The general form of the potential employed was V(r) = Be-Cr - A/r6 ; the force constants were obtained from the potential by assuming the atoms were undergoing simple harmonic motion.

In part II the location and identification of the benzene first and second triplet states (3B1u and 3E1u) is given.