The decomposition of Kv into K2×K5''''s

The decomposition of the complete graph Kv into Kr×Kc's, the products of Kr and Kc,is originated from the use of DNA library screening. In this paper, we consider the case where r=2 and c = 5, and show that such a decomposition exists if and only if v ≡ 1 (mod 25).     

QK空间的插值序列

本文研究了Q_K空间的插值问题.利用复分析和调和分析的方法,获得了单位圆盘上的一个序列{z_n}是Q_K∩H^∞空间的插值序列的一个充分必要条件,推广了Q_p空间的部分结果.     

On the structure of the K2 of the ring of integers in a number field

For any prime p, the p-primary part of the tame and the wild kernel of a number field F is described in terms of ideal class groups of p-power cyclotomic extensions of F.     

A conjecture on a class of elements of finite order in K2Fp

For a local field F the finite subgroups of K₂ F are expressed by a class of special elements of finite order, which makes a famous theorem built by Moore, Carroll, Tate and Merkurjev more explicit and also disproves a conjecture posed by Browkin.     

ComplexK-theory ofBSL3(Z)

ComplexK-theory ofBSL₃(Z) andBSt₃(Z) are computed. We first study a Brown-Peterson (BP) version of Soulé's arguments. Then we consider complexK-theory by using a Conner-Floyd type theorem.     

E -Theoretic Duality for Higher Rank Graph Algebras

We prove that there is a Poincaré type duality in E-theory between higher rank graph algebras associated with a higher rank graph and its opposite correspondent. We obtain an r-duality, that is the fundamental classes are in E^r. The basic tools are a higher rank Fock space and higher rank Toeplitz algebra which has a more interesting ideal structure than in the rank 1 case. The K-homology fundamental class is given by an r-fold exact sequence whereas the K-theory fundamental class is given by a homomorphism. The E-theoretic products are essentially pull-backs so that the computation is done at the level of exact sequences. Mathematics Subject Classification (2000): 46L80.     

On A(X) → TC(X) for some X

Let X be a connected based space and p be a two-regular prime number. If the fundamental group of X has order p, we compute the two-primary homotopy groups of the homotopy fiber of the trace map A(X) → TC(X) relating algebraic K-theory of spaces to topological cyclic homology. The proof uses a theorem of Dundas and an explicit calculation of the cyclotomic trace map K(ℤ[C_p])→ TC(ℤ[C_p]).     

On the K shortest path trees problem

We address the problem of finding the K best path trees connecting a source node with any other non-source node in a directed network with arbitrary lengths. The main result in this paper is the proof that the kth shortest path tree is adjacent to at least one of the previous (k-1) shortest path trees. Consequently, we design an O(f(n,m,C_max)+Km) time and O(K+m) space algorithm to determine the K shortest path trees, in a directed network with n nodes, m arcs and maximum absolute length C_max, where O(f(n,m,C_max)) is the best time needed to solve the shortest simple paths connecting a source node with any other non-source node.     

The weight twoK-theory of fields

We verify the weight-two portion of the Quillen-Lichtenbaum conjectures, relating the modn weight-twoK-groups of a field with the appropriate étale cohomology groups. This extends the work of Merkurjev and Suslin onK ₂ of a field, and the works of Suslin and the author on the indecomposableK ₃ of a field.Partially supported by the NSF.     

SU(2)-equivariantk-theory of a class ofC*-algebras and nonhomogeneous random walks

The SU(2) equivariantK ₀-Theory of a class ofC*-algebras is studied. These algebras arise from nonhomogeneous actions of SU(2) or SO(3) on uniformly hyperfinite algebras. The problems are shown to be equivalent to studying nonhomogeneous random walks associated with infinite products of characters — in particular, properties related to unimodality and positivity. Concrete sufficient conditions are developed for reducing the problem to the maximal torus action, for which extensive results are known; these become necessary and sufficient when there is a bound on the degree of the characters, or a strong unimodality assumption is made. When the degrees are unbounded, examples are constructed to indicate the range of behavior possible when reduction to the maximal torus is impossible. Finally, limit ratio theorems are obtained for the distribution of irreducibles in products of characters having a unimodality property.Supported in part by an operating grant from NSERC, Canada.     

Torsion in Boundary Coinvariants and K -Theory for Affine Buildings

Let (G, I, N, S) be an affine topological Tits system, and let Γ be a torsion-free cocompact lattice in G. This article studies the coinvariants H ₀(Γ; C(Ω,Z)), where Ω is the Furstenberg boundary of G. It is shown that the class [1] of the identity function in H ₀(Γ; C(Ω, Z)) has finite order, with explicit bounds for the order. A similar statement applies to the K ₀ group of the boundary crossed product C ^*-algebra C(Ω)Γ. If the Tits system has type ? ₂, exact computations are given, both for the crossed product algebra and for the reduced group C ^*-algebra.     

K2 of a Ring via the G-Construction

We interpret the Steinberg symbols x_i,j(a) as homotopies contracting the elementary matrices e_i,j(a), the latters being represented by certain arcs in a simplicial model of the K-theory. We further prove the Steinberg relations for these homotopies. This provides an explicit map from K₂ of a ring, defined classically as ker(St(R) → GL(R)), to π₂ of the G-construction assigned to R. Though the two groups are known to be isomorphic, a certain work is to be done to prove that this explicit map is an isomorphism. Mathematics Subject Classification 1991: Primary 19B99, 19D99; secondary 18E10, 18F25.     

Approximations for the delay probability in the M/G/s queue

This paper develops approximations for the delay probability in an M/G/s queue. For M/G/s queues, it has been well known that the delay probability in the M/M/s queue, i.e., the Erlang delay formula, is usually a good approximation for other service-time distributions. By using an excellent approximation for the mean waiting time in the M/G/s queue, we provide more accurate approximations of the delay probability for small values of s. To test the quality of our approximations, we compare them with the exact value and the Erlang delay formula for some particular cases.     

Poisson formulas for circular functions on some groups of type H

Explicit Poisson kernels are found for the subelliptic Dirichlet problem with boundary data satisfying certain symmetry conditions on balls and halfspaces in some Heisenberg type groups. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

A New Inequality for Weakly （K1, K2）-Quasiregular Mappings

We obtain a new inequality for weakly （K1,K2）-quasiregular mappings by using the McShane extension method. This inequality can be used to derive the self-improving regularity of （K1, K2）-Quasiregular Mappings.     

On the K0 groups of nest algebras

In this paper we compute the K ₀ group of any nest subalgebra of ().     

The Lower Algebraic K -theory of Γ3

We explicitly compute the lower algebraic K-theory of Γ₃ a discrete subgroup of the group of isometries of hyperbolic 3-space. An erratum to this article is available at .     

Note on theK0 of rings with Zariskian filtration

For a noncommutative Zariski ringR with associated graded ringG(R) of finite global dimension there is an injectionK _o(R) K _o (G(R)). The result applies to certain rings of differential operators, in particular to the ring of germs of microlocal differential operators that also provides an example of a nonpositively filtered Zariski ring.Research fellow at UIA, supported by a grant from the Province of Antwerp.Supported by an NFWO grant.     

The real spectrum of an ideal and KO-theory exact sequences

A construction in abstract real algebra is used to define invariants S _n(A) of commutative rings, with or without identity. If A=C(X) is the ring of continuous real functions on a compact space, then S _n(A) = k0^–n(X), and, for any A, S _n(A) Z[1/2]-W _n(A) Z[1/2], where the W _n(A) are the Witt groups of A. In addition, a short exact sequence of rings yields a long exact sequence of the groups S _n. The functors S _n(A) thus provide a solution of a problem proposed by Karoubi. This paper primarily deals with the exact sequences involving a ring A and an ideal I A. Work supported in part by NSF Grant DMS85-06816.     

Dimension Theory and Nonstable K1 of Quadratic Modules

Employing Bak's dimension theory, we investigate the nonstable quadratic K-group K _1,2n (A, ) = G _2n (A, )/E _2n (A, ), n 3, where G _2n (A, ) denotes the general quadratic group of rank n over a form ring (A, ) and E _2n (A, ) its elementary subgroup. Considering form rings as a category with dimension in the sense of Bak, we obtain a dimension filtration G _2n (A, ) G _2n ⁰(A, ) ; G _2n ¹(A, ) ... E _2n (A, ) of the general quadratic group G _2n (A, ) such that G _2n (A, )/G _2n ⁰(A, ) is Abelian, G _2n ⁰(A, ) G _2n ¹(A, ) ... is a descending central series, and G _2n ^d(A)(A, ) = E _2n (A, ) whenever d(A) = (Bass–Serre dimension of A) is finite. In particular K _1,2n (A, ) is solvable when d(A) < .