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In this note we provide the solution to a problem posed by the first author in a previous paper. In particular, we prove a result relating the number of nonzero coefficients of a certain functional equation to the order of any derivation satisfying that equation. 相似文献
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Jorge Gilberto Flores 《偏微分方程通讯》2013,38(10):1235-1263
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S. Mecheri 《Journal of Mathematical Sciences》2000,102(5):4429-4435
A generalized derivation
, is defined by the formula
, where
and
is the Banach algebra of bounded linear operators in a Hilbert space
. Sufficient conditions under which
and
are given. Bibliography: 8 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 20, 2000, pp. 111–119. 相似文献
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Given a finite-dimensional associative commutative algebra A over a field F, we define the structure of a Lie algebra using a nonzero derivation D of A. If A is a field and charF > 3; then the corresponding algebra is simple, presenting a nonisomorphic analog of the Zassenhaus algebra W 1(m). 相似文献
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Dulce M. Almeida 《Differential Geometry and its Applications》2006,24(2):178-190
A sub-Riemannian manifold is a differentiable manifold together with a smooth distribution which is equipped with a Riemannian metric. In this paper we attempt to study sub-Riemannian symmetric spaces (i.e., homogeneous sub-Riemannian manifolds admitting an involutive sub-Riemannian isometry at all points which is a central symmetry when restricted to the distribution) where the associated distribution is a codimension three fat distribution. We obtain a restricted classification theorem in dimension seven and we also construct a class of examples of quaternionic type in varying dimension. 相似文献
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Mu-Tao Wang 《Transactions of the American Mathematical Society》2003,355(1):265-271
Let be a minimal submanifold of that can be represented as the graph of a smooth map . We apply a formula that we derived in the study of mean curvature flow to obtain conditions under which must be an affine subspace. Our result covers all known ones in the general case. The conditions are stated in terms of the singular values of .
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We study codimension growth of infinite dimensional Lie algebras over a field of characteristic zero. We prove that if a Lie algebra L is an extension of a nilpotent algebra by a finite dimensional semisimple algebra then the PI-exponent of L exists and is a positive integer. 相似文献
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Summary It is shown that when (n–1) first integrals of a dynamical systemX inR
n
are known (and they are independent at any point ofR
n
) then one can have (n3) that certain orbits ofX are diffeomorphic to circles and others diffeomorphic to straight-lines. An analytical criterion is also given (involving only the first derivatives of the first integrals) in order thatall the orbits be diffeomorphic to straight lines. Therefore the criterion is sufficient in order to avoid the presence of geometrical chaos among the orbits of the dynamical systemX. 相似文献
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Leta, b, andc be the three sides of a triangleABC, a
i
,b
i
,c
i
anda
e
,b
e
, ce be the lengths of the three internal and external bisectors of the three anglesA, B, andC respectively. It is easy to express the bisectors as formulae of the sides. In this paper, we solve a problem proposed by H. Zassenhaus: for any three different bisectors in {ai, bi, ci, ae, be, ce}, finding the relations between each side of the triangle and the three chosen bisectors. We also prove that given any general values for three different bisectors (internal or external) of a triangle, we can not draw the triangle using a ruler and a pair of compasses alone. The formulae mentioned above are derived automatically using a general method of mechanical formula derivation.This work was partially supported by a Grant from Chinese NSF and by the NSF Grant CCR-917870. 相似文献
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Arizmendi-Peimbert Hugo Carrillo-Hoyo Angel Pérez-Tiscareño Reyna M. 《Rendiconti del Circolo Matematico di Palermo》1936,60(1):51-57
In Studia Math. 58:291–298, 1976, W. Żelazko gives a characterization of complex commutative complete unital m-convex algebras in which all maximal ideals are of codimension one. In these algebras every element has a bounded spectrum.
Here we present a similar result concerning sufficient conditions so that all maximal ideals of a complex commutative unital m-convex algebra to be of codimension one. Moreover, these conditions are proved to be equivalent to each other. We also give an example of a complex commutative unital advertibly complete m-convex algebra such that all its maximal ideals are of codimension one and has an element with unbounded spectrum.
相似文献20.
The amoeba of a complex algebraic set is its image under the projection onto the real subspace in the logarithmic scale. We study the homological properties of the complements of amoebas for sets of codimension higher than 1. In particular, we refine A. Henriques’ result saying that the complement of the amoeba of a codimension k set is (k ? 1)-convex. We also describe the relationship between the critical points of the logarithmic projection and the logarithmic Gauss map of algebraic sets. 相似文献