基于Zernike多项式表示色域边界的色域映射

在彩色图像的跨媒体复制中,由于不同媒体有不同的色域,所以在大多数情况下色域映射是不可避免的。不论采用何种映射算法,色域映射的第一步是确定有关媒体的色域边界。目前大多数的色域边界都是用一组测量的或用其它方法得到的离散数据来表示的。然而,由于这种表示方式是利用一组离散数据来实施色域映射的两个基本处理(即确定任一指定的等色调面平面中色域的边缘线以及确定色域边界与一条映射线的交点),比较复杂和费时,因此希望找到一种色域边界的解析表达式来解决这一问题。简述了不久前提出的一种解析函数色域边界表示方法,并用实例说明了如何利用这种解析表示(Zernike多项式)来实现上述的边缘线确定和交点确定。最后给出了几种映射算法的色域映射完整过程及其结果。     

Homology of Nilpotent Subalgebras of the Lie Superalgebra K(1,1).3

We calculate the dimensions of the second homology groups with trivial coefficients of nilpotent subalgebras of the Lie superalgebra , which is the natural superanalog of the Witt algebra. The proof is based on direct calculations of the rank of the differential. As an application, we find deformations of the maximal nilpotent subalgebra in .     

Iterative Algebras without Projections

We deal with iterative algebras of functions of -valued logic lacking projections, which we call algebras without projections. It is shown that a partially ordered set of algebras of functions of -valued logic, for , without projections contains an interval isomorphic to the lattice of all iterative algebras of functions of -valued logic. It is found out that every algebra without projections is contained in some maximal algebra without projections, which is the stabilizer of a semigroup of non-surjective transformations of the basic set. It is proved that the stabilizer of a semigroup of all monotone non-surjective transformations of a linearly ordered 3-element set is not a maximal algebra without projections, but the stabilizer of a semigroup of all transformations preserving an arbitrary non one-element subset of the basic set is.     

Standard Envelopes of Commutative Triple Systems

Under certain constraints on the characteristic of a field , the commutative standard enveloping q-algebra >B of a commutative triple system A over is defined. It is proved that(1) if the algebra B is simple, then the system A is simple;(2) if the system A is simple, then B either is simple or decomposes into the direct sum of two isomorphic simple subalgebras (as of ideals).     

Dynamical Lie algebra method for highly excited vibrational state of asymmetric linear tetratomic molecules

The highly excited vibrational states of asymmetric linear tetratomic molecules are studied in the framework of Lie algebra. By using symmetric groupU ₁(4)U ₂(4)⊗U ₃(4), we construct the Hamiltonian that includes not only Casimir operators but also Majorana operators M₁₂, M₁₃ and M₂₃, which are useful for getting potential energy surface and force constants in Lie algebra method. By Lie algebra treatment, we obtain the eigenvalues of the Hamiltonian, and make the concrete calculation for molecule C₂HF.     

Crystal Bases for Quantum Affine Algebras and Combinatorics of Young Walls

In this paper we give a realization of crystal bases for quantumaffine algebras using some new combinatorial objects which wecall the Young walls. The Young walls consist of colored blockswith various shapes that are built on a given ground-state walland can be viewed as generalizations of Young diagrams. Therules for building Young walls and the action of Kashiwara operatorsare given explicitly in terms of combinatorics of Young walls.The crystal graph of a basic representation is characterizedas the set of all reduced proper Young walls. The characterof a basic representation can be computed easily by countingthe number of colored blocks that have been added to the ground-statewall. 2000 Mathematical Subject Classification: 17B37, 17B65,81R50, 82B23.     

Dunkl Operators for Complex Reflection Groups

Dunkl operators for complex reflection groups are defined inthis paper. These commuting operators give rise to a parameterizedfamily of deformations of the polynomial De Rham complex. Thisleads to the study of the polynomial ring as a module over the‘rational Cherednik algebra’, and a natural contravariantform on this module. In the case of the imprimitive complexreflection groups G(m, p, N), the set of singular parametersin the parameterized family of these structures is describedexplicitly, using the theory of non-symmetric Jack polynomials.2000 Mathematical Subject Classification: 20F55 (primary), 52C35,05E05, 33C08 (secondary).     

Structure of Degenerate Block Algebras

Given a non-trivial torsion-free abelian group (A,+,Q), a field F of characteristic 0, and a non-degenerate bi-additive skew-symmetric map : A A F, we define a Lie algebra = (A, ) over F with basis {e_x | x A/{0}} and Lie product [e_x,e_y] = (x,y)e_x+y. We show that is endowed uniquely with a non-degenerate symmetric invariant bilinear form and the derivation algebra Der of is a complete Lie algebra. We describe the double extension D( , T) of by T, where T is spanned by the locally finite derivations of , and determine the second cohomology group H²(D( , T),F) using anti-derivations related to the form on D( , T). Finally, we compute the second Leibniz cohomology groups HL²( , F) and HL²(D( , T), F).2000 Mathematics Subject Classification: 17B05, 17B30This work was supported by the NNSF of China (19971044), the Doctoral Programme Foundation of Institution of Higher Education (97005511), and the Foundation of Jiangsu Educational Committee.     

Free Algebras of Automorphic Forms on the Upper Half-Plane

We find all pairs (,a) consisting of a cocompact Fuchsian group of genus zero and an automorphy factor a of for which the graded algebra of a--automorphic forms is free.