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991.
Following the definition of Gr?bner bases in rings of differential operators given by Insa and Pauer (1998), we discuss some
computational properties of Gr?bner bases arising when the coefficient set is a ring. First we give examples to show that
the generalization of S-polynomials is necessary for computation of Gr?bner bases. Then we prove that under certain conditions
the G-S-polynomials can be reduced to be simpler than the original one. Especially for some simple case it is enough to consider
S-polynomials in the computation of Gr?bner bases. The algorithm for computation of Gr?bner bases can thus be simplified.
Last we discuss the elimination property of Gr?bner bases in rings of differential operators and give some examples of solving
PDE by elimination using Gr?bner bases.
This work was supported by the NSFC project 60473019. 相似文献
992.
For operators with homogeneous disorder, it is generally expected that there is a relation between the spectral characteristics of a random operator in the infinite setup and the distribution of the energy gaps in its finite volume versions, in corresponding energy ranges. Whereas pure point spectrum of the infinite operator goes along with Poisson level statistics, it is expected that purely absolutely continuous spectrum would be associated with gap distributions resembling the corresponding random matrix ensemble. We prove that on regular rooted trees, which exhibit both spectral types, the eigenstate point process has always Poissonian limit. However, we also find that this does not contradict the picture described above if that is carefully interpreted, as the relevant limit of finite trees is not the infinite homogenous tree graph but rather a single-ended ‘canopy graph.’ For this tree graph, the random Schrödinger operator is proven here to have only pure-point spectrum at any strength of the disorder. For more general single-ended trees it is shown that the spectrum is always singular – pure point possibly with singular continuous component which is proven to occur in some cases. 相似文献
993.
CUI Jianlian & HOU Jinchuan Department of Mathematical Science Tsinghua University Beijing China Department of Applied Mathematics Taiyuan University of Technology Taiyuan China Department of Mathematics Shanxi Teachers University Linfen China 《中国科学A辑(英文版)》2005,(12)
Let H be an infinite dimensional complex Hilbert space. Denote by B(H) the algebra of all bounded linear operators on H, and by I(H) the set of all idempo-tents in B(H). Suppose that Φ is a surjective map from B(H) onto itself. If for every λ ∈ {-1,1,2,3,1/2,1/3} and A, B ∈ B(H), A - λB ∈ I(H) (?) Φ(A) - λΦ(B) ∈ I(H), then Φ is a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that Φ(A) = TAT-1 for all A ∈ B(H), or Φ(A) = TA*T-1 for all A ∈ B(H); if, in addition, A-iB ∈ I(H) (?) Φ(A) -ιΦ(B) ∈ I(H), here ι is the imaginary unit, then Φ is either an automorphism or an anti-automorphism. 相似文献
994.
Generalized OWA Aggregation Operators 总被引:7,自引:0,他引:7
Ronald R. Yager 《Fuzzy Optimization and Decision Making》2004,3(1):93-107
We extend the ordered weighted averaging (OWA) operator to a provide a new class of operators called the generalized OWA (GOWA) operators. These operators add to the OWA operator an additional parameter controlling the power to which the argument values are raised. We look at some special cases of these operators. One important case corresponds to the generalized mean and another special case is the ordered weighted geometric operator. 相似文献
995.
996.
997.
998.
M. Yu. Tyaglov 《Journal of Applied Mechanics and Technical Physics》2007,48(5):649-655
The convection of an isothermally incompressible fluid in a horizontal layer with free undeformable boundaries kept at a constant
temperature is considered. Under the fairly common assumptions of the temperature dependence of the specific volume, it is
shown that the monotonicity principle holds and that the spectrum of critical Rayleigh numbers is countable and prime. Models
with linear and quadratic temperature dependences of the specific volume are given as examples. The results on the spectrum
of the critical Rayleigh numbers are also valid for some other boundary conditions.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 35–42, September–October, 2007. 相似文献
999.
Let H be an infinite dimensional complex Hilbert space. Denote by B(H)the algebra of all bounded linear operators on H, and by I(H) the set of all idempotents in B(H). Suppose that φ is a surjective map from B(H) onto itself. If for everyλ∈ {-1, 1, 2, 3, 1/2, 1/3} and A, B ∈ B(H), A - λB ∈ I(H) (→)φ(A) - λφ(B) ∈ I(H), then φis a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that φ(A) = TAT-1 for all A ∈ B(H), or φ(A) = TA*T-1 for all A ∈ B(H); if, in addition, A - iB ∈ I(H) (→)φ(A) - iφ(B) ∈ I(H), here i is the imaginary unit, then φ is either an automorphism or an anti-automorphism. 相似文献
1000.
A. Fernndez F. Mayoral F. Naranjo C. Sez E.A. Snchez-Prez 《Journal of Mathematical Analysis and Applications》2007,330(2):1249-1263
We use the integration structure of the spaces of scalar integrable functions with respect to a vector measure to provide factorization theorems for operators between Banach function spaces through Hilbert spaces. A broad class of Banach function spaces can be represented as spaces of scalar integrable functions with respect to a vector measure, but this representation (the vector measure) is not unique. Since our factorization depends on the vector measure that is used for the representation we also give a characterization of those vector measures whose corresponding spaces of integrable functions coincide. 相似文献