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商洛学院数学与计算机应用学院初等数论课件Chapter 1 Prime Numbers.
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.
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.
Real-Time Sorting of Binary Numbers on One-Dimensional CA
Real-Time Sorting of Binary Numbers One-Dimensional CA
2010/12/28
Abstract. A new fast (real time) sorter of binary numbers by one-dimensional cellular automata is proposed. It sorts a list of n numbers represented by k-bits each in exactly nk steps. This is only on...
On a unified theory of numbers
unified theory numbers
2010/12/13
In 1873 James Clerk Maxwell combined electricity and magnetism using the Maxwell's Equations into a single force called electromagnetism and since then,physicists have been trying to discover the elus...
Corrigendum --- Quadratic Class Numbers Divisible by 3
Corrigendum Quadratic Class Numbers Divisible by 3
2010/12/10
In attempting to handle N+(X) the paper states that the Scholz reflection principle “yields 3|h(k) for any positive integer for which 3|h(−3k)”. This is not correct, and one cannot establish a r...
We define a new sequence of positive integers, associated with Catalan numbers and Narayana polynomials.
On fractional parts of powers of real numbers close to 1
fractional parts of powers real numbers close to 1
2010/12/10
We prove that there exist arbitrarily small positive real num-bers " such that every integral power (1 + ")n is at a distance greater than 2−17"| log "|−1 to the set of rational integers. ...