Maximum curves and isolated points of entire functions

Given M(r; f) =maxjzj=r (jf(z)j) , curves belonging to the set of points M = fz : jf(z)j = M(jzj; f)g were de�ned by Hardy to be maximum curves. Clunie asked the question as to whether the set M could also contain isolated points. This paper shows that maximum curves consist of analytic arcs and determines a necessary condition for such curves to intersect. Given two entire functions f1(z) and f2(z), if the maximum curve of f1(z) is the real axis, conditions are found so that the real axis is also a maximum curve for the product function f1(z)f2(z). By means of these results an entire function of in�nite order is constructed for which the set M has an in�nite number of isolated points. A polynomial is also constructed with an isolated point.

Applications of Feller-Reuter-Riley transition functions

A Feller–Reuter–Riley function is a Markov transition function whose corresponding semigroup maps the set of the real-valued continuous functions vanishing at infinity into itself. The aim of this paper is to investigate applications of such functions in the dual problem, Markov branching processes, and the Williams-matrix. The remarkable property of a Feller–Reuter–Riley function is that it is a Feller minimal transition function with a stable q-matrix. By using this property we are able to prove that, in the theory of branching processes, the branching property is equivalent to the requirement that the corresponding transition function satisfies the Kolmogorov forward equations associated with a stable q-matrix. It follows that the probabilistic definition and the analytic definition for Markov branching processes are actually equivalent. Also, by using this property, together with the Resolvent Decomposition Theorem, a simple analytical proof of the Williams' existence theorem with respect to the Williams-matrix is obtained. The close link between the dual problem and the Feller–Reuter–Riley transition functions is revealed. It enables us to prove that a dual transition function must satisfy the Kolmogorov forward equations. A necessary and sufficient condition for a dual transition function satisfying the Kolmogorov backward equations is also provided.

Hemolymph Functions In Mytilus-Californianus - Cytochemistry Of Hemocytes And Their Responses To Foreign Implants And Hemolymph Factors In Phagocytosis

The hemocytes of Mytilus californianus are of three types: small and large basophils and large granular acidophils. The basophils contain lysosomal enzymes and phagocytose colloidal carbon. Agglutinins for yeast and human A Rh+ve erythrocytes are present in plasma, but are not needed for effective phagocytosis; in vitro both acidophilic and basophilic hemocytes rapidly phagocytose these particles. Plasma proteins, analyzed electrophoretically, are under strong homeostatic control. When Mya arenaria mantle is placed orthotopically on M. californianus mantle, the implant is invaded by host hemocytes in a manner consistent with that described in other published reports on molluscan graft rejection. Steady state is achieved by 26 days postimplant. Second- and third-set implants are rejected more rapidly than are first-set implants, but this is not a specific response. Third-set implants elicit a host cellular response that is more localized than the response to first-set implants. These data do not permit conclusions with respect to memory in these molluscan immune responses, but do imply a qualitative “improvement” in this quasi-immune response of M. californianus.

Application-Specific Instruction Set Processor for SoC implementation of Modern Signal Processing Algorithms

A novel application-specific instruction set processor (ASIP) for use in the construction of modern signal processing systems is presented. This is a flexible device that can be used in the construction of array processor systems for the real-time implementation of functions such as singular-value decomposition (SVD) and QR decomposition (QRD), as well as other important matrix computations. It uses a coordinate rotation digital computer (CORDIC) module to perform arithmetic operations and several approaches are adopted to achieve high performance including pipelining of the micro-rotations, the use of parallel instructions and a dual-bus architecture. In addition, a novel method for scale factor correction is presented which only needs to be applied once at the end of the computation. This also reduces computation time and enhances performance. Methods are described which allow this processor to be used in reduced dimension (i.e., folded) array processor structures that allow tradeoffs between hardware and performance. The net result is a flexible matrix computational processing element (PE) whose functionality can be changed under program control for use in a wider range of scenarios than previous work. Details are presented of the results of a design study, which considers the application of this decomposition PE architecture in a combined SVD/QRD system and demonstrates that a combination of high performance and efficient silicon implementation are achievable. © 2005 IEEE.

On effective linearly ordered sets of comparison functions

Both the existence and the non-existence of a linearly ordered (by certain natural order relations) effective set of comparison functions (=dense comparison classes) are compatible with the ZFC axioms of set theory.

On the set of hypercyclic vectors for the differentiation

Let D be the differentiation operator Df = f' acting on the Fréchet space H of all entire functions in one variable with the standard (compact-open) topology. It is known since the 1950’s that the set H(D) of hypercyclic vectors for the operator D is non-empty. We treat two questions raised by Aron, Conejero, Peris and Seoane-Sepúlveda whether the set H(D) contains (up to the zero function) a non-trivial subalgebra of H or an infinite-dimensional closed linear subspace of H. In the present article both questions are answered affirmatively.

XOR-based hash functions

Bank conflicts can severely reduce the bandwidth of an interleaved multibank memory and conflict misses increase the miss rate of a cache or a predictor. Both occurrences are manifestations of the same problem: Objects which should be mapped to different indices are accidentally mapped to the same index. Suitable chosen hash functions can avoid conflicts in each of these situations by mapping the most frequently occurring patterns conflict-free. A particularly interesting class of hash functions are the XOR-based hash functions, which compute each set index bit as the exclusive-or of a subset of the address bits. When implementing an XOR-based hash function, it is extremely important to understand what patterns are mapped conflict-free and how a hash function can be constructed to map the most frequently occurring patterns without conflicts. Hereto, this paper presents two ways to reason about hash functions: by their null space and by their column space. The null space helps to quickly determine whether a pattern is mapped conflict-free. The column space is more useful for other purposes, e. g., to reduce the fan-in of the XOR-gates without introducing conflicts or to evaluate interbank dispersion in skewed-associative caches. Examples illustrate how these ideas can be applied to construct conflict-free hash functions.

Polynomial Functions and the Riesz Interpolation Property

Building on a proof by D. Handelman of a generalisation of an example due to L. Fuchs, we show that the space of real-valued polynomials on a non-empty set X of reals has the Riesz Interpolation Property if and only if X is bounded.

Modulational instability in asymmetric coupled wave functions

The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schrödinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and the group velocity dispersion terms) and the nonlinearity and coupling coefficients, on which no assumption is made. A generalized dispersion relation is obtained, relating the frequency and wave-number of a small perturbation around a coupled monochromatic (Stokes') wave solution. Explicitly stability criteria are obtained. The analysis reveals a number of possibilities. Two (individually) stable systems may be destabilized due to coupling. Unstable systems may, when coupled, present an enhanced instability growth rate, for an extended wave number range of values. Distinct unstable wavenumber windows may arise simultaneously.

Improving multi-site benefit functions via Bayesian model averaging: A new approach to benefit transfer

A benefit function transfer obtains estimates of willingness-to-pay (WTP) for the evaluation of a given policy at a site by combining existing information from different study sites. This has the advantage that more efficient estimates are obtained, but it relies on the assumption that the heterogeneity between sites is appropriately captured in the benefit transfer model. A more expensive alternative to estimate WTP is to analyze only data from the policy site in question while ignoring information from other sites. We make use of the fact that these two choices can be viewed as a model selection problem and extend the set of models to allow for the hypothesis that the benefit function is only applicable to a subset of sites. We show how Bayesian model averaging (BMA) techniques can be used to optimally combine information from all models. The Bayesian algorithm searches for the set of sites that can form the basis for estimating a benefit function and reveals whether such information can be transferred to new sites for which only a small data set is available. We illustrate the method with a sample of 42 forests from U.K. and Ireland. We find that BMA benefit function transfer produces reliable estimates and can increase about 8 times the information content of a small sample when the forest is 'poolable'. © 2008 Elsevier Inc. All rights reserved.

MAPPING SYSTEM LEVEL FUNCTIONS ON TO BIT LEVEL SYSTOLIC ARRAYS.

Bit-level systolic-array structures for computing sums of products are studied in detail. It is shown that these can be subdivided into two classes and that within each class architectures can be described in terms of a set of constraint equations. It is further demonstrated that high-performance system-level functions with attractive VLSI properties can be constructed by matching data-flow geometries in bit-level and word-level architectures.

STO and GTO field-induced polarization functions for H to Kr

Field-induced polarization (FIP) functions were proposed over two decades ago to improve the accuracy of calculated response properties, and the FIP functions in GTO form for H and C to F were tested on small molecules, with encouraging results. The concept of FIP,is now extended to all atoms up to Kr. New simplifying approximations for the description of asymptotic highest occupied atomic orbitals. (HOAOs) are introduced in this study. They provide the basis for STO and GTO exponents of a complete set of FIP functions from H to Kr, which are both listed for the convenience of the users. Tests on the polarizabilities of a series of atoms and molecules demonstrate that addition of the FIP basis functions to a series' of standard basis sets drastically improves the performance of all these basis sets compared to converged results. Moreover, the byproduct of this study (approximate asymptotic HOAOs) provides information for the construction of accurate basis sets for long-range ground state properties. (C) 2003 Wiley Periodicals, Inc.

Estimating fuzzy membership functions parameters by the levenberg-marquardt algorithm

In previous papers from the authors fuzzy model identification methods were discussed. The bacterial algorithm for extracting fuzzy rule base from a training set was presented. The Levenberg-Marquardt algorithm was also proposed for determining membership functions in fuzzy systems. In this paper the Levenberg-Marquardt technique is improved to optimise the membership functions in the fuzzy rules without Ruspini-partition. The class of membership functions investigated is the trapezoidal one as it is general enough and widely used. The method can be easily extended to arbitrary piecewise linear functions as well.

Desenvolvimento de um Code Set para a escrita manual baseado na classificação internacional de funcionalidade versão crianças e jovens

Compreender a funcionalidade de uma criança é um desafio persistente em contextos de saúde e educação. Na tentativa de superar esse desafio, em 2007, a Organização Mundial de Saúde desenvolveu a Classificação Internacional de Funcionalidade, Incapacidade e Saúde para Crianças e Jovens (CIF-CJ) como o primeiro sistema de classificação universal para documentar a saúde e funcionalidade da criança. Apesar de a CIF-CJ não ser um instrumento de avaliação e intervenção, tem, no entanto, a capacidade de servir de enquadramento para o desenvolvimento de ferramentas adaptadas às necessidades dos seus utilizadores. Considerando que no contexto escolar, a escrita manual encontra-se entre as atividades mais requeridas para a participação plena de uma criança, parece ser pertinente a definição de um conjunto de códigos destinados a caracterizar o perfil de funcionalidade de uma criança, no que se refere à escrita manual. O objetivo deste estudo foi, pois, o desenvolvimento de um conjunto preliminar de códigos baseado na CIF-CJ que possa vir a constituir um code set para a escrita manual. Dada a complexidade do tema e atendendo a que se pretende alcançar consenso entre os especialistas sobre quais as categorias da CIF-CJ que devem ser consideradas, optou-se pela utilização da técnica de Delphi. A escolha da metodologia seguiu a orientação dos procedimentos adotados pelo projeto Core Set CIF. De dezoito profissionais contactados, obtiveram-se respostas de sete terapeutas ocupacionais com experiência em pediatria, que participaram em todas as rondas. No total, três rondas de questionários foram realizadas para atingir um consenso, com um nível de concordância, previamente definido, de 70%. Deste estudo resultou um conjunto preliminar de códigos com 54 categorias da CIF-CJ (16 categorias de segundo nível, 14 categorias de terceiro nível e uma categoria de quarto nível), das quais 31 são categorias das funções do corpo, uma categoria das estruturas do corpo, 12 categorias de atividades e participação e 10 categorias de fatores ambientais. Este estudo é um primeiro passo para o desenvolvimento de um code set para a escrita manual baseado na CIF-CJ , sendo claramente necessário a realização de mais pesquisas no contexto do desenvolvimento e da validação deste code set.

Multiple Roots of Systems of Equations by Repulsion Merit Functions

In this paper we address the problem of computing multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function. The search procedure for a global minimizer of the merit function is carried out by a metaheuristic, known as harmony search, which does not require any derivative information. The multiple roots of the system are sequentially determined along several iterations of a single run, where the merit function is accordingly modified by penalty terms that aim to create repulsion areas around previously computed minimizers. A repulsion algorithm based on a multiplicative kind penalty function is proposed. Preliminary numerical experiments with a benchmark set of problems show the effectiveness of the proposed method.