In this work the complexity of a feasible variant of a Linear Programming Predictor-Corrector algorithm specialized for transportation and assignment problems is explored. A O(n |log (ϵ )|) iteration complexity was achieved by proving that the step size computed by the studied algorithm is bounded at each iteration by θ (4-3θ )(1-θ )^2/n , where θ∈ [0,1[ . Therefore, allowing to conclude that the analyzed Predictor-Corrector algorithm that uses the 2-norm neighborhood has polynomial iteration complexity and is Q-linearly convergent.

In this study, we introduce an elliptic biquaternionic sequence with Vietoris' numbers as its components and discuss some of its properties. Also, the generating function and some identities in terms of elliptic biquaternionic sequence with Vietoris' numbers are given. Furthermore, the construction of this elliptic biquaternion sequence is presented using matrices that generate the quaternionic sequence where the components are Vietoris' number, and also by applying the determinant to a special kind of matrices.

The main purpose of this paper is to study some properties of Vietoris’ number sequence and present some techniques, using special types of matrices that generates this number sequence.

Special integers sequences have been the center of attention for many researchers, as well as the sequences of quaternions where its components are the elements of these sequences. Motivated by a rational sequence, we consider the quaternions with components Vietoris? numbers and investigate some of its properties. For this sequence a two and three term recurrence relation is established, as well as a Binet?s type formula. Moreover the generating function for this sequence is introduced and also the determinant of some tridiagonal matrices are used in order to find elements of this sequence.

In this paper, we introduce different kinds of growth orders for the set of entire solutions to the most general framework of higher‐dimensional polynomial Cauchy‐Riemann equations , where is the hypercomplex Cauchy‐Riemann operator, λi are arbitrarily chosen nonzero complex constants, and ki are arbitrarily chosen positive integers. The core ingredient is a projection formula that establishes a relation to the ki‐monogenic component functions, which are null‐solutions to iterates of the Cauchy‐Riemann operator that we studied in earlier works. Furthermore, we briefly outline the analogies of the Lindelöf‐Pringsheim theorem in this context.

In this paper we study same basic properties of growth types for solutions to polynomial Cauchy-Riemann equations.

In this paper we introduce generalized growth orders and growth types in the sense of Shah and Seremeta in the context of polymonogenic functions. They provide a refinement of previously introduced growth orders in the study of the asymptotic growth behavior of functions satisfying higher dimensional Cauchy–Riemann type equations. We prove a number of insight giving inequalities and manage to extend some basic results that were recently proved for the context of the usual first order Cauchy–Riemann system in Clifford analysis.

In this paper we design a model based method to locate a leakage and estimate its size in a gas network, using a linearised version of an hyperbolic PDE. To do this, the problem is reduced to two identical ODEs, allowing in this way for a representation of the pressure as well as the mass flow in terms of its system of fundamental solutions. Then using the available measurements at the grid boundary points, the correspondent coefficients can be determined. Assuming pressure continuity, we check for consistency of the coefficients in order to find faulty pipelines. Thence, the location of the leakage can be found either graphically or using a numerical method for a specific pipe. Next, its size can also be estimated.

In this paper, we introduce generalizations of the classical growth order and the growth type of analytic functions in the context of polymonogenic functions. Polymonogenic functions are null-solutions of higher integer order iterates of a generalized higher dimensional Cauchy-Riemann operator. One of the main goals is to prove generalizations of the famous Lindelof-Pringsheim theorem linking explicitly these growth orders and growth types with the Taylor series coefficients in the context of this function class.

In this study, the main characteristics of research works on Mathematical / Operations Research techniques applied to cancer and involving the temperature are described and analyzed. The information contained in those works was cataloged in accordance with specific key elements previously chosen. The developments on the theme are evaluated, observing what was done, describing the related applications, procedures and their practical implementation.

For entire axially monogenic functions, which are monogenic in the whole space, the lower order and type are defined, as in the complex case, in terms of the maximum modulus of the functions and the Taylor coefficients. The study carried out in this paper bears certain novelty to the familiar literature concerning the Clifford valued functions.

In this paper we deal with paravector valued multiperiodic solutions to the Dirac–Hodge equation on the upper half-space of Rn which linearizes the Laplace–Beltrami operator. These functions provide basic building blocks for classes of hypermonogenic Eisenstein series on arithmetic subgroups of the Ahlfors–Vahlen group. In turn they can be regarded as hypermonogenic generalizations of the classical cotangent function and the elliptic functions. The goal of this paper is to develop explicit representations of the Fourier coefficients of these functions. The Fourier coefficients are composed by sums over Bell polynomials evaluated in lattice points multiplied by binomial coefficients.

We report on the development of a high energy and high average power de-multiplexed femtosecond fiber amplifier tailored for thin film CIGS solar cell scribing. The obtained machining results will be presented and discussed.

Solidification of an alloy has many industrial applications, such as foundry technology, crystal growth, coating and purification of materials, welding process, etc. Unlike the classical Stefan problem for pure metals, alloy solidification involves complex heat and mass transport phenomena. For most metal alloys, there could be three regions, namely, solid region, mushy zone (dendrite arms and interdendritic liquid) and liquid region in solidification process. Solidification of binary mixtures does not exhibit a distinct front separating solid and liquid phases. Instead, the solid is formed as a permeable, fluid saturated, crystal-line-like matrix. The structure and extent of this mushy region, depends on numerous factors, such as the specific boundary and initial conditions. During solidification, latent energy is released at the interfaces which separate the phases within the mushy region. The distribution of this energy therefore depends on the specific structure of the multiphase region. Latent energy released during solidification is transferred by conduction in the solid phase, as well as by the combined effects of conduction and convection in the liquid phase. To investigate the heat and mass transfer during the solidification process of an alloy, a few models have been proposed. They can be roughly classified into the continuummodel and the volume-averaged model. Based on principles of classical mixture theory, Bennon & Incropera (1987) developed a continuum model for momentum, heat and species transport in the solidification process of a binary alloy. Voller et al. (1989) and Rappaz & Voller (1990) modified the continuum model by considering the solute distribution on microstructure, the so-called Scheil approach. Beckermann & Viskanta (1988) reported an experimental study on dendritic solidification of an ammonium chloride-water solution. A numerical simulation for the same physical configuration was also performed using a volumetric averaging technique. Subsequently, the volumetric averaging technique was systematically derived by Ganesan & Poirier (1990) and Ni & Beckermann (1991). Detailed discussions onmicrostructure formation andmathematical modelling of transport phenomenon during solidification of binary systems can be found in 5

Dairy, dairy, quite contrary: further evidence to support a role for calcium in counteracting the cholesterol

We present some results on the asymptotic growth behavior of entire special monogenic functions. A generalization of the classical Valiron inequality for this class of functions and some basic properties related to the lower order are discussed.

In this paper we study the asymptotic growth behavior of solutions to the Dirac–Hodge equation on upper half-space of Rn+1. By means of the Fourier transform we introduce lower and upper growth orders and generalizations of the maximum term and central index for this function class. Together with a Cauchy estimate we obtain an explicit lower and upper bound estimate of the maximum modulus M(xn,f) in terms of these notions.

Each paper should commence with an accurate and informative abstract, written as a single paragraph. It should be complete in itself and intelligible without reference to the text or figures, and should not exceed 250 words. Tables. Tables should be reduced to the simplest form, and should not duplicate information in the text or figures. They should be typed on separate pages, one page for each Table, at the end of the article and carry headings describing their content. Illustrations. The original illustrations should accompany the submitted typescript. Text figures, line drawings, computer-generated figures and graphs should be of sufficient size and quality to allow for reduction by half or two-thirds. Half-tone photographs are acceptable where they clearly contribute to the text. All figures should be numbered and legends should be provided. Note that authors will be charged 350 GBP for the publication of colour figures. Authors from countries entitled to free journal access through HINARI will be exempt from these charges. References. References should be based on the numbered (Vancouver) system. When an article has more than ten authors, only the names of the first three should be given followed by et al.; give abbreviated journal titles and conform to the following styles: Goel V, Cheema SK, Agellon LB, Ooraikul B & Basu TK (1999) Dietary rhubabrb (Rheum rhaponticum) stalk fibre stimulates cholesterol 7α-hydroxylase gene expression and bile acid excretion in cholesterol-fed C57BL/6J mice. Br J Nutr 81, 65–71. Jenkins DJ, Kendall CW, Marchie A, et al. (2003) The effect of combining plant sterols, soy protein, viscous fibres, and almonds in treating hypercholesterolemia. Metabolism 52, 1478–1483. Brandtzaeg P (2003) Role of local immunity and breast-feeding in mucosal homoeostasis and defence against infections. In Nutrition and Immune Function, pp. 273–320 [PC Calder, CJ Field and HS Gill, editors]. Wallingford, Oxon: CAB International. Stock M & Rothwell NJ (1982) Obesity and Leanness: Basic Aspects. London: John Libbey. Citations should be numbered consecutively in the order in which they first appear in the text using superscript Arabic numerals in parentheses, e.g. ‘The conceptual difficulty of this approach has recently been highlighted(1,2–4). If a reference is cited more than once the same number should be used each time. Referees. Authors are asked to submit the names of up to four scientists who would be well-qualified to review the paper; however, no more than one such reviewer will be used. The email addresses and institutions of the named reviewers should be given. Proofs. PDF page proofs will be emailed to authors for checking, and should be returned within 3 days (by fax or Express mail) to the BJN Production Editor, Cambridge University Press, The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU, UK; fax +44 1223 325802, email bjnproduction@cambridge.org Typescripts. The British Journal of Nutrition operates an on-line submission and reviewing system (eJournalPress). Authors should submit to the following address: http://bjn.msubmit.net/ If any difficulties are encountered please contact the Publications Office (details above) immediately. Professor Philip Calder Editor-in-Chief British Journal of Nutrition The Nutrition Society 10 Cambridge Court 210 Shepherds Bush Road London W6 7NJ UK Tel: +44 (0)20 7605 6555 Fax: +44 20 7602 1756 Email: edoffice@nutsoc.org.uk British Journal of Nutrition Directions to Contributors Concise Version (Revised August 2007) British Journal of Nutrition, published by Cambridge University Press on behalf of the Nutrition Society 2010© British Journal of Nutrition An International Journal of Nutritional Science Volume 104, 2010 ISSN: 0007-1145 Aims and Scope The British Journal of Nutrition is an international, peer-reviewed journal publishing original papers, review articles, short communications and technical notes on human and clinical nutrition, animal nutrition and basic science as applied to nutrition. Correspondence is encouraged in a Nutrition Discussion Forum. The Journal recognizes the multidisciplinary nature of nutritional science and encourages the submission of material from all of the specialities involved in research and clinical practice. The Journal also publishes supplements on topics of particular interest. The British Journal of Nutrition is published twice monthly by Cambridge University Press on behalf of The Nutrition Society. The British Journal of Nutrition is available online to subscribers at journals.cambridge.org/bjn Tables of contents and abstracts are available free at the same website.

In this paper, we develop the basic concepts for a generalized Wiman–Valiron theory for Clifford algebra valued functions that satisfy inside an n + 1-dimensional ball the higher dimensional Cauchy-Riemann system \({\frac{\partial f}{\partial x_0} + \sum_{i=1}^n e_i\frac{\partial f}{\partial x_i}=0}\) . These functions are called monogenic or Clifford holomorphic inside the ball. We introduce growth orders, the maximum term and a generalization of the central index for monogenic Taylor series of finite convergence radius. Our goal is to establish explicit relations between these entities in order to estimate the asymptotic growth behavior of a monogenic function in a ball in terms of its Taylor coefficients. Furthermore, we exhibit a relation between the growth order of such a function f and the growth order of its partial derivatives.

It is well known that the Joukowski transformation plays an important role in physical applications of conformal mappings, in particular in the study of flows around airfoils. We present, for n≥2, an n-dimensional hypercomplex analogue of the Joukowski transformation and describe in some detail the 3D case. A generalized 3D Joukowski profile, produced with Maple, is included.