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Generalized Compositions of Natural Numbers
optimal control optimal synthesis atom cooling
2011/2/21
Frictionless atom cooling in harmonic traps is formulated as a time-optimal control problem and a synthesis of optimal controlled trajectories is obtained.
Cutting Mutually Congruent Pieces from Convex Regions
Cutting Mutually Congruent Pieces Convex Regions
2011/1/21
What is the shape of the 2D convex region P from which, when 2 mutually congruent convex pieces with maximum possible area are cut out, the highest fraction of the area of P is left over? When P is re...
A homology plane of general type can have at most a cyclic quotient singularity
Homology plane of general type BMY inequality Zariski-Fujita decomposition
2011/2/22
We show that a homology plane of general type has at worst a single cyclic quotient singular point. An example of such a surface with a singular point does exist [MS, Theorem 3.1]. We
also show that ...
Expansions of subfields of the real field by a discrete set
Expansions of subfields real field discrete set
2011/2/21
Let K be a subfield of the real field, D K be a closed and discrete set and f : Dn ! K be such that f(Dn) is somewhere dense. Then (K, f) defines Z. We present several applications of this result. W...
Identities and congruences for a new sequence
congruence Euler polynomial identity p-regular function
2011/2/22
Let [x] be the greatest integer not exceeding x. In the paper we introduce the sequence {Un} given by U0 = 1 and Un = −2P[n/2] k=1 n 2kUn−2k (n 1), and establish many recursi...
Some Congruences of Kloosterman Sums and their Minimal Polynomials
Congruences of Kloosterman Sums Minimal Polynomials
2011/1/18
We prove two results on Kloosterman sums over finite fields, using Stickelberger’s theorem and the Gross-Koblitz formula. The first result concerns the minimal polynomial over Q of a Kloosterman sum, ...
Points rationnels sur les quotients d'Atkin-Lehner de courbes de Shimura de discriminant $pq$
Points rationnels quotients d’Atkin-Lehner
2011/2/21
Let p and q be two distinct prime numbers, and Xpq/wq be the quotient of the Shimura curve of discriminant pq by the Atkin-Lehner involution wq. We describe a way to verify in wide generality a criter...
Some remarks about the derivation operator and generalized Stirling numbers
formal power series derivation operator Stirling num-bers
2011/2/22
Studying expressions of the form (f(x)D)p, where D = d dx is the derivation operator, goes back to Scherk’s Ph.D.
Some inversion formulas and formulas for Stirling numbers
Inversion formula Inverse function Stirling number
2011/2/22
In the paper we present some new inversion formulas and two new formulas for Stirling numbers.
Let a and b be positive integers and let p be an odd prime such that p =ax2+by2 for some integers x and y.
Toda Molecule and Tomimatsu-Sato Solution $\sim$ Toward the complete proof of Nakamura's conjecture$\sim$
Toda Molecule Tomimatsu-Sato Solution $\sim$
2010/12/28
We discuss the Nakamura’s conjecture stating that the Tomimatsu-Sato black hole solution with deformation parameter n is composed of the special solutions of the Toda molecule equation at the n-th lat...
An inverse problem of Calderon type with partial data
inverse problem of Calderon type partial data
2011/2/24
A generalized variant of the Calder´on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension n 2...
Congruences concerning Legendre polynomials II
Legendre polynomial congruence character sum binary quadratic form
2011/2/22
Let p > 3 be a prime, and let m be an integer with p ∤ m. In the paper we solve some conjectures of Z.W.
Let p > 3 be a prime, and let m be an integer with p ∤ m. In the paper we solve some conjectures of Z.W. Sun concerning Pp−1 k=0 (6k)! mk(3k)!k!3 (mod p), and show that for integers m, n w...
Targetability of chaotic sets with small parameter perturbations
Chaotic set targetability Lie rank condition geometric control dynamical systems
2010/12/28
In this paper targetability of chaotic sets with small controls is discussed by virtue of some results of geometric control theory. It is proved that given a chaotic set Λ, it is possible to steer a o...