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41.
A new kind of four-mode continuous variable coherent-entangled state is proposed in the Fock space by using the technique of integration within an ordered product,which exhibits both the properties of a coherent state and an entangled state,and spans a complete and orthonormal representation.The conjugate state of the four-mode continuous variable coherent-entangled state is derived by using the Fourier transformation.Moreover,a simple experimental protocol of generating a four-mode continuous variable coherent-entangled state is proposed by using beam splitters.As applications of this four-mode continuous variable coherent-entangled state,a four-mode entangled state and a four-mode squeezing-Fresnel operator are constructed. 相似文献
42.
Machiel Van Frankenhuysen 《Journal of Number Theory》2002,95(2):289-302
Following Elkies (Internat. Math. Res. Notices7 (1991) 99-109) and Bombieri (Roth's theorem and the abc-conjecture, preprint, ETH Zürich, 1994), we show that the ABC conjecture implies the one-dimensional case of Vojta's height inequality. The main geometric tool is the construction of a Belyǐ function. We take care to make explicit the effectivity of the result: we show that an effective version of the ABC conjecture would imply an effective version of Roth's theorem, as well as giving an (in principle) explicit bound on the height of rational points on an algebraic curve of genus at least two. 相似文献
43.
V. V. Kurta 《Mathematical Notes》1999,65(4):462-469
The main result of the paper is the nonexistence of integer positive solutions in wide classes of quasilinear elliptic equations
whose model examples are equations of the form {
}, where α>1 andq are some fixed real numbers.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 552–561, April, 1999. 相似文献
44.
Robert Gilmer William Heinzer Moshe Roitman 《Proceedings of the American Mathematical Society》1999,127(11):3141-3151
Suppose is a maximal ideal of a commutative integral domain and that some power of is finitely generated. We show that is finitely generated in each of the following cases: (i) is of height one, (ii) is integrally closed and , (iii) is a monoid domain over a field , where is a cancellative torsion-free monoid such that , and is the maximal ideal . We extend the above results to ideals of a reduced ring such that is Noetherian. We prove that a reduced ring is Noetherian if each prime ideal of has a power that is finitely generated. For each with , we establish existence of a -dimensional integral domain having a nonfinitely generated maximal ideal of height such that is -generated.
45.
Alberto Corso William Heinzer Craig Huneke 《Transactions of the American Mathematical Society》1998,350(12):5095-5109
We study content ideals of polynomials and their behavior under multiplication. We give a generalization of the Lemma of Dedekind-Mertens and prove the converse under suitable dimensionality restrictions.
46.
47.
48.
49.
Bob Hoogenboom 《Arkiv f?r Matematik》1982,20(1):69-85
Proofs are given of two theorems of Berezin and Karpelevič, which as far as we know never have been proved correctly. By using
eigenfunctions of the Laplace-Beltrami operator it is shown that the spherical functions on a complex Grassmann manifold are
given by a determinant of certain hypergeometric functions. By application of this result, it is proved that a certain system
of operators, fow which explicit expressions are given, generates the algebra of radial parts of invariant differential operators. 相似文献
50.
The N-heap Wythoffs game is a two-player impartial game with
N piles of tokens of sizes
Players take turns removing any number of tokens from a single pile, or removing
(a1,..., aN)
from all piles - ai tokens from the i-th pile,
providing that
where is the nim addition. The first player that cannot make a move loses. Denote all the
P-positions (i.e., losing positions) by
Two conjectures were proposed on the game by Fraenkel [7]. When
are fixed, i) there exists an integer N1
such that when
. ii) there exist integers N2
and _2 such that when
, the golden section.In this paper, we provide a sufficient condition for the conjectures to hold, and subsequently
prove them for the three-heap Wythoffs game with the first piles having up to 10 tokens.AMS Subject Classification: 91A46, 68R05. 相似文献