We study the poles and residues of the complex zeta function fs of a plane curve. We prove that most non-rupture divisors do not contribute to poles of fs or roots of the Bernstein-Sato polynomial ...bf(s) of f. For plane branches we give an optimal set of candidates for the poles of fs from the rupture divisors and the characteristic sequence of f. We prove that for generic plane branches fgen all the candidates are poles of fgens. As a consequence, we prove Yano's conjecture for any number of characteristic exponents if the eigenvalues of the monodromy of f are different.
J3Gen: a PRNG for low-cost passive RFID Melià-Seguí, Joan; Garcia-Alfaro, Joaquin; Herrera-Joancomartí, Jordi
Sensors (Basel, Switzerland),
03/2013, Volume:
13, Issue:
3
Journal Article
Peer reviewed
Open access
Pseudorandom number generation (PRNG) is the main security tool in low-cost passive radio-frequency identification (RFID) technologies, such as EPC Gen2. We present a lightweight PRNG design for ...low-cost passive RFID tags, named J3Gen. J3Gen is based on a linear feedback shift register (LFSR) configured with multiple feedback polynomials. The polynomials are alternated during the generation of sequences via a physical source of randomness. J3Gen successfully handles the inherent linearity of LFSR based PRNGs and satisfies the statistical requirements imposed by the EPC Gen2 standard. A hardware implementation of J3Gen is presented and evaluated with regard to different design parameters, defining the key-equivalence security and nonlinearity of the design. The results of a SPICE simulation confirm the power-consumption suitability of the proposal.
U ovome radu prezentirani su Jacobijevi polinomi, njihova osnovna svojstva i specijalni slučajevi kao što su Legendreovi, Čebiševljevi i Gegenbauerovi polinomi. Osim toga, pokazana je primjena ...Jacobijevih polinoma pri računanju momenata nekih neprekidnih slučajnih varijabli.
The existence and uniqueness of a Kronrod type extension to the wellknown Gauss-Turan quadrature formulas were proved by Li (1994, pp.71- 83). For the generalized Chebyshev weight functions and for ...the GoriMicchelli weight function, we found explicit formulas of the corresponding generalized Stieltjes polynomials. General real Kronrod extensions of the Gaussian quadrature formulas with multiple nodes are introduced. In some cases, the explicit expressions of the polynomials, whose zeros are the nodes of the considered quadratures, are determined. / Уникальное применение теории расширения функций Конрода относительно квадратурной формулы Гаусс-Тюрана доказал Ли (Li, 1994, стр.71-83). Определены эксплицитные выражения для обобщенных подмножеств Стилтьесапо отношению квесовым функциям Чебышева и весовым функциям Гори-Мишелли. Определено расширение функций Конрода по квадратурной формуле Гаусса с узлами многочлена. В отдельных случаях определены эксплицитные выражения множеств, нули которых являются узлами исследуемых квадратур. / Egzistenciju i jedinstvenost Kronrodovih ekstenzija za dobro poznate Gaus-Turanove kvadraturne formule dokazao je Li (Li, 1994, str.71-83). Određeni su eksplicitni izrazi za uopštene Stiltjesove polinome u odnosu na Čebiševljeve težinske funkcije, kao i u odnosu na težinsku funkciju Gori-Mičeli. Definisana je Kronrodova ekstenzija za Gausove kvadraturne formule sa višestrukim čvorovima. U nekim slučajevima određeni su eksplicitni izrazi polinoma, čije su nule čvorovi posmatranih kvadratura.
Orthogonal polynomials are a widely used class of mathematical functions that are helpful in the solution of many important technical problems. This book provides, for the first time, a systematic ...development of computational techniques, including a suite of computer programs in Matlab downloadable from the Internet, to generate orthogonal polynomials of a great variety.
Field Arithmetic Fried, Michael D; Jarden, Moshe
2008, 2004, 2004-10-31, 2008-05-05, Volume:
11
eBook
Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite ...groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC, and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)? The third edition improves the second edition in two ways: First it removes many typos and mathematical inaccuracies that occur in the second edition (in particular in the references). Secondly, the third edition reports on five open problems (out of thirtyfour open problems of the second edition) that have been partially or fully solved since that edition appeared in 2005.
U radu je izložena primjena Čebiševljevih polinoma prve i druge vrste kod dokazivanja ne-racionalnosti nekih vrijednosti trigonometrijskih funkcija.
Odnosno, dat je osvrt na određivanja brojeva koji ...su racionalni višekratnici broja π, a za koje su vrijednosti sinusa, kosinusa i tangensa racionalni odnosno iracionalni brojevi. Pokazano je, da ako je \( \cos \alpha \) racionalan broj tada je i \( \cos n\alpha \) racionalan broj za svaki prirodan broj n, a ako su i \( \sin \alpha \) i \( \cos \alpha \) racionalni brojevi, tada je i \( \sin n\alpha \) racionalan broj. Nadalje, pokazano je, da ako su m, n relativno prosti brojevi i \(\cos \frac{n}{m}\pi\) racionalan broj, tada je i \(\cos \frac{\pi}{m}\) racionalan broj, kao i da je za svaki prirodan broj m veći od 3, broj \(\cos \frac{\pi}{m}\)
iracionalan. Razmatrana je također racionalnost i iracionalnost brojeva \(tg\frac{2\pi }{n}\).
Positive Polynomials in Control originates from an invited session presented at the IEEE CDC 2003 and gives a comprehensive overview of existing results in this quickly emerging area. This carefully ...edited book collects important contributions from several fields of control, optimization, and mathematics, in order to show different views and approaches of polynomial positivity. The book is organized in three parts, reflecting the current trends in the area: 1. applications of positive polynomials and LMI optimization to solve various control problems, 2. a mathematical overview of different algebraic techniques used to cope with polynomial positivity, 3. numerical aspects of positivity of polynomials, and recently developed software tools which can be employed to solve the problems discussed in the book.
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