17 research outputs found
Conchoidal transform of two plane curves
The conchoid of a plane curve is constructed using a fixed circle in
the affine plane. We generalize the classical definition so that we obtain a
conchoid from any pair of curves and in the projective plane. We
present two definitions, one purely algebraic through resultants and a more
geometric one using an incidence correspondence in \PP^2 \times \PP^2. We
prove, among other things, that the conchoid of a generic curve of fixed degree
is irreducible, we determine its singularities and give a formula for its
degree and genus. In the final section we return to the classical case: for any
given curve we give a criterion for its conchoid to be irreducible and we
give a procedure to determine when a curve is the conchoid of another.Comment: 18 pages Revised version: slight title change, improved exposition,
fixed proof of Theorem 5.3 Accepted for publication in Appl. Algebra Eng.,
Commun. Comput
Equivalent birational embeddings II: divisors
Two divisors in are said to be Cremona equivalent if there is a
Cremona modification sending one to the other. We produce infinitely many non
equivalent divisorial embeddings of any variety of dimension at most 14. Then
we study the special case of plane curves and rational hypersurfaces. For the
latter we characterise surfaces Cremona equivalent to a plane.Comment: v2 Exposition improved, thanks to referee, unconditional
characterization of surfaces Cremona equivalent to a plan
Counting and computing regions of -decomposition: algebro-geometric approach
New methods for -decomposition analysis are presented. They are based on
topology of real algebraic varieties and computational real algebraic geometry.
The estimate of number of root invariant regions for polynomial parametric
families of polynomial and matrices is given. For the case of two parametric
family more sharp estimate is proven. Theoretic results are supported by
various numerical simulations that show higher precision of presented methods
with respect to traditional ones. The presented methods are inherently global
and could be applied for studying -decomposition for the space of parameters
as a whole instead of some prescribed regions. For symbolic computations the
Maple v.14 software and its package RegularChains are used.Comment: 16 pages, 8 figure
GUI Matlab para o cálculo de funções de Bessel usando frações continuadas
[EN] Higher order Bessel functions are prevalent in physics and engineering and there exist different methods to evaluate them quickly and efficiently. Two of these methods are Miller's algorithm and the continued fractions algorithm. Miller's algorithm uses arbitrary starting values and normalization constants to evaluate Bessel functions. The continued fractions algorithm directly computes each value, keeping the error as small as possible. Both methods respect the stability of the Bessel function recurrence relations. Here we outline both methods and explain why the continued fractions algorithm is more efficient. The goal of this paper is both (1) to introduce the continued fractions algorithm to physics and engineering students and (2) to present a MATLAB GUI (Graphic User Interface) where this method has been used for computing the Semi-integer Bessel Functions and their zeros.[PT] Funções de Bessel de ordem mais alta sĂŁo recorrentes em fĂsica e nas engenharias, sendo que há diferentes mĂ©todos para calculá-las de maneira rápida e eficiente. Dois destes mĂ©todos sĂŁo o algoritmo de Miller e o algoritmo de frações continuadas. O primeiro faz uso de valores iniciais e constantes de normalização arbitrários, enquanto o segundo o faz calculando cada valor diretamente, minimizando tanto quanto possĂvel o erro. Ambos respeitam a estabilidade das relações de recorrĂŞncia das funções de Bessel. Neste trabalho descrevemos ambos os mĂ©todos e explicamos a razĂŁo pela qual o algoritmo das frações continuadas Ă© mais eficiente. O objetivo do artigo Ă© (1) introduzir o algoritmo de frações continuadas para estudantes de fĂsica e das engenharias e (2) apresentar um GUI (Graphic User Interface) em Matlab no qual este mĂ©todo foi utilizado para calcular funções de Bessel semi-inteiras e seus zeros.The authors wish to thank the financial support received from the Universidad PolitĂ©cnica de Valencia under grant PAID-06-09-2734, from the Ministerio de Ciencia e InnovaciĂłn through grant ENE2008-00599 and specially from the Generalitat Valenciana under grant reference 3012/2009.Hernandez Vargas, E.; Commeford, K.; PĂ©rez Quiles, MJ. (2011). MATLAB GUI for computing Bessel functions using continued fractions algorithm. Revista Brasileira de Ensino de FĂsica. 33(1):1303-1311. https://doi.org/10.1590/S1806-11172011000100003S13031311331Giladi, E. (2007). Asymptotically derived boundary elements for the Helmholtz equation in high frequencies. Journal of Computational and Applied Mathematics, 198(1), 52-74. doi:10.1016/j.cam.2005.11.024Havemann, S., & Baran, A. J. (2004). Calculation of the phase matrix elements of elongated hexagonal ice columns using the T-matrix method. Journal of Quantitative Spectroscopy and Radiative Transfer, 89(1-4), 87-96. doi:10.1016/j.jqsrt.2004.05.014Segura, J., Fernández de CĂłrdoba, P., & Ratis, Y. L. (1997). A code to evaluate modified bessel functions based on thecontinued fraction method. Computer Physics Communications, 105(2-3), 263-272. doi:10.1016/s0010-4655(97)00069-6Bastardo, J. L., Abraham Ibrahim, S., Fernández de CĂłrdoba, P., UrchueguĂa Schölzel, J. F., & Ratis, Y. L. (2005). Evaluation of Fresnel integrals based on the continued fractions method. Applied Mathematics Letters, 18(1), 23-28. doi:10.1016/j.aml.2003.12.009Barnett, A. R., Feng, D. H., Steed, J. W., & Goldfarb, L. J. B. (1974). Coulomb wave functions for all real η and ϱ. Computer Physics Communications, 8(5), 377-395. doi:10.1016/0010-4655(74)90013-
Effects of Acute Febrile Diseases on the Periodontium of Rhesus Monkeys with Reference to Poliomyelitis
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67269/2/10.1177_00220345510300050301.pd