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Comptes Rendus Mathematique
The Thue–Morse–Pascal double sequence and similar structures2011 •
If a recurrent two-dimensional sequence with initial conditions defined by linear substitution and a two-dimensional sequence that is generated by planar substitution are identical over a sufficiently large initial square, then they will coincide over all. After proving this general principle, we apply it to some concrete examples. One of them, the Thue–Morse–Pascal two-dimensional sequence, is defined by two copies of the Prouhet–Thue–Morse sequence as pair of initial conditions and by the Pascal Triangle Addition modulo 2 as rule of recurrence. As it follows, the Thue–Morse–Pascal two-dimensional sequence is the result of 15 substitution rules, each of them consisting of the substitution of some 4×44×4 matrix with an 8×88×8 matrix.Si une suite bidimensionnelle récurrente avec conditions initiales définies par substitution linéaire et une suite bidimensionnelle engendrée par substitution plane sont identiques sur un carré initial assez grand, alors elles coïncident partout. Après avoir démontré ce principe on lʼapplique à quelques exemples concrets. Lʼun dʼentre-eux est la suite bidimensionnelle de Thue–Morse–Pascal définie par deux exemplaires de la suite de Prouhet–Thue–Morse comme couple de conditions initiales et lʼaddition du triangle de Pascal modulo 2 comme règle de récurrence. Il sʼensuit que la suite bidimensionnelle de Thue–Morse–Pascal est le résultat de 15 règles de substitution, chacune dʼentre-elles consistant de la substitution dʼune certaine matrice 4×44×4 avec une matrice 8×88×8.
Fractals-complex Geometry Patterns and Scaling in Nature and Society
RECURRENT DOUBLE SEQUENCES THAT CAN BE PRODUCED BY CONTEXT-FREE SUBSTITUTIONS2010 •
International Journal of Rf and Microwave Computer-aided Engineering
Mathematical foundations of frequency-domain modeling of nonlinear circuits and systems using the arithmetic operator method2003 •
The arithmetic operator method (AOM) is a method for performing arithmetic operations on one or more signals that are described by their spectra. By extension, any analytic functional operation on the signals can be performed in the frequency domain using matrix-vector operations. The mathematical foundation of AOM is presented as a numerically efficient convolution-like procedure in this article. It is directly applicable to the behavioral modeling of nonlinear RF and microwave circuits and systems. © 2003 Wiley Periodicals, Inc. Int J RF and Microwave CAE 13, 473–495, 2003.
Monatshefte für Mathematik
Exhaustive search methods for CNS polynomials2008 •
In this paper, we present a method for finding all expansive polynomials with a prescribed degree n and constant term c 0. Our research is motivated by the fact that expansivity is a necessary condition for number system constructions. We use the ...
Designs, Codes and Cryptography
Theta functions and symmetric weight enumerators for codes over imaginary quadratic fields2014 •
We prove that every quasi-smooth hypersurface in the 95 families of weighted Fano threefold hypersurfaces is birationally rigid.
2010 •
Let $\F_q$ be a field of characteristic $p$ with $q$ elements. It is known that the degrees of the irreducible characters of the Sylow $p$-subgroup of $GL_n(\F_q)$ are powers of $q$ by Issacs. On the other hand Sangroniz showed that this is true for a Sylow $p$-subgroup of a classical group defined over $\F_q$ if and only if $p$ is odd. For the classical groups of Lie type $B$, $C$ and $D$ the only bad prime is 2. For the exceptional groups there are others. In this paper we construct irreducible characters for the Sylow $p$-subgroups of the Chevalley groups $D_4(q)$ with $q=2^f$ of degree $q^3/2$. Then we use an analogous construction for $E_6(q)$ with $q=3^f$ to obtain characters of degree $q^7/3$, and for $E_8(q)$ with $q=5^f$ to obtain characters of degree $q^{16}/5.$ This helps to explain why the primes 2, 3 and 5 are bad for the Chevalley groups of type $E$ in terms of the representation theory of the Sylow $p$-subgroup.
Computing Research Repository - CORR
A Public Key Block Cipher Based on Multivariate Quadratic Quasigroups2008 •
We have designed a new class of public key algorithms based on quasigroup string trans- formations using a speciflc class of quasigroups called multivariate quadratic quasigroups (MQQ). Our public key algorithm is a bijective mapping, it does not perform message expansions and can be used both for encryption and signatures. The public key consist of n quadratic polynomials with n variables where n = 140;160;:::. A particular characteristic of our public key algorithm is that it is very fast and highly parallelizable. More concretely, it has the speed of a typical modern symmetric block cipher { the reason for the phrase "A Public Key Block Cipher" in the title of this paper. Namely the reference C code for the 160{bit variant of the algorithm performs decryption in less than 11,000 cycles (on Intel Core 2 Duo { using only one processor core), and around 6,000 cycles using two CPU cores and OpenMP 2.0 library. However, implemented in Xilinx Virtex-5 FPGA that is running on ...
Computational Optimization and Applications
Lower bounds on the global minimum of a polynomial2014 •
2000 •
Journal of Physics A: Mathematical and Theoretical
Ising n -fold integrals as diagonals of rational functions and integrality of series expansions2013 •
2002 •
2004 •
International Journal of Computational Intelligence and Applications
Support Vector Regression and Functional Networks for Viscosity and Gas/Oil Ratio Curves Estimation2011 •
2012 •
Engineering Letters
New Polynomial Classes for #2SAT Established Via Graph-Topological Structure2007 •
2019 •
Lecture Notes in Computer Science
Advanced Meet-in-the-Middle Preimage Attacks: First Results on Full Tiger, and Improved Results on MD4 and SHA-22010 •
Finite Fields and Their Applications
Cyclotomic numbers and primitive idempotents in the ring GF(q)[x]/(xpn-12004 •
Molecular and Cellular Endocrinology
Modeling of glucose regulation and insulin-signaling pathways2009 •
Mathematics of Computation
Perturbing polynomials with all their roots on the unit circle2000 •
Nuclear Physics B - NUCL PHYS B
Correlation lengths and E8 mass spectrum of the dilute A3 lattice model1998 •
J. Korean Math. Soc. 50 (2013), No. 2, pp. 275-306
Invariant differential operators on the Minkowski-Euclid spaceJournal of Physics A: Mathematical and Theoretical
Diagonal Ising susceptibility: elliptic integrals, modular forms and Calabi–Yau equations2012 •
2006 •
Journal of Statistical Mechanics: Theory and Experiment
On the three state Potts model with competing interactions on the Bethe lattice2006 •
Mihai Prunescu