共查询到20条相似文献,搜索用时 15 毫秒
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Let F be a polynomial map in two variables over the complex field with nonzero constant Jacobian. Abhyankar proved that if F is smooth on generic lines then F is invertible. We sharpen Abhyankar’s result by proving that if F(𝕃) is smooth on one line 𝕃 then F is invertible. Criterion for smoothness of F(𝕃) is also discussed. 相似文献
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M. Amaglobeli 《Journal of Mathematical Sciences》2013,193(3):353-358
We prove that the tensor completion commutes with the operations of direct product and direct limit of exponential groups and, in general, does not commute with the Cartesian product and the inverse limit of exponential groups. 相似文献
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We establish a criterion for a spherical design associated with V. A. Yudin potentials. Thus we obtain an extremal property of spherical designs. 相似文献
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We show that if the number of directions not determined by a pointset
of
, of size q2 is at least pe q then every plane intersects
in 0 modulo pe+1 points and apply the result to ovoids of the generalised quadrangles
and
. 相似文献
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We classify all the indecomposable modules of dimension ≤ 5 over the quantum exterior algebra k(x, y)/(x^2, y^2, xy + qyx) in two variables, and all the indecomposable modules of dimension ≤3 over the quantum complete intersection k(x,y)/(x^m,y^n,xy + qyx) in two variables, where m or n ≥3, by giving explicitly their diagram presentations. 相似文献
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Indranil Biswas 《Bulletin des Sciences Mathématiques》2005,129(6):539-543
Let X be a smooth projective curve defined over an algebraically closed field of positive characteristic. We give a necessary and sufficient condition for a vector bundle over X to be ample. This generalizes a criterion given by Lange in [Math. Ann. 238 (1978) 193-202] for a rank two vector bundle over X to be ample. 相似文献
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Yasunori Fujikoshi Tamio Kan Shin Takahashi Tetsuro Sakurai 《Annals of the Institute of Statistical Mathematics》2011,63(2):387-403
Several criteria, such as CV, C
p
, AIC, CAIC, and MAIC, are used for selecting variables in linear regression models. It might be noted that C
p
has been proposed as an estimator of the expected standardized prediction error, although the target risk function of CV
might be regarded as the expected prediction error R
PE. On the other hand, the target risk function of AIC, CAIC, and MAIC is the expected log-predictive likelihood. In this paper,
we propose a prediction error criterion, PE, which is an estimator of the expected prediction error R
PE. Consequently, it is also a competitor of CV. Results of this study show that PE is an unbiased estimator when the true model
is contained in the full model. The property is shown without the assumption of normality. In fact, PE is demonstrated as
more faithful for its risk function than CV. The prediction error criterion PE is extended to the multivariate case. Furthermore,
using simulations, we examine some peculiarities of all these criteria. 相似文献
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Anatoliy P. Petravchuk 《Linear algebra and its applications》2010,433(3):574-579
It is well known that each pair of commuting linear operators on a finite dimensional vector space over an algebraically closed field has a common eigenvector. We prove an analogous statement for derivations of k[x] and k[x,y] over any field k of zero characteristic. In particular, if D1 and D2 are commuting derivations of k[x,y] and they are linearly independent over k, then either (i) they have a common polynomial eigenfunction; i.e., a nonconstant polynomial f∈k[x,y] such that D1(f)=λf and D2(f)=μf for some λ,μ∈k[x,y], or (ii) they are Jacobian derivations
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V. M. Petrichkovich 《Ukrainian Mathematical Journal》1997,49(6):963-965
We establish that a pair A, B, of nonsingular matrices over a commutative domain R of principal ideals can be reduced to their canonical diagonal forms D A and D B by the common transformation of rows and separate transformations of columns. This means that there exist invertible matrices U, V A, and V B over R such that UAV a=DA and UAV B=DB if and only if the matrices B *A and D * B DA where B * 0 is the matrix adjoint to B, are equivalent. 相似文献
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Marek Kȩpczyk 《Israel Journal of Mathematics》2017,221(1):481-487
We prove that a ring which is a sum of two PI subrings is a PI ring as well. This answers a question of K. I. Beidar and A. V. Mikhalev that has been open since 1995. 相似文献
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Classical orthogonal polynomials in two variables are defined as the orthogonal polynomials associated to a two-variable moment functional satisfying a matrix analogue of the Pearson differential equation. Furthermore, we characterize classical orthogonal polynomials in two variables as the polynomial solutions of a matrix second order partial differential equation.
AMS subject classification 42C05, 33C50Partially supported by Ministerio de Ciencia y Tecnología (MCYT) of Spain and by the European Regional Development Fund (ERDF) through the grant BFM2001-3878-C02-02, Junta de Andalucía, G.I. FQM 0229 and INTAS Project 2000-272. 相似文献
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设F是一个特征不等于2的域,A是,上的一个可除代数。本文研究了A上多项式环A[x1,X2,…,xn]中理想是有限生成的,以及它的Grobner基;也表明F[x1,x2,…,xn]中有限子集G是F[x1,x2,…,xn]的Griobner基当且仅当G是A[x1,x2,…,xn]中的Grobner基。 相似文献
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Adrian Vasiu 《Central European Journal of Mathematics》2005,3(1):14-25
We include short and elementary proofs of two theorems that characterize reductive group schemes over a discrete valuation
ring, in a slightly more general context. 相似文献