Left APP differential polynomial rings

A ring R is called a left APP-ring if for each element a∈R, the left annihilator l_R(Ra) is right s-unital as an ideal of R or equivalently R∕l_R(Ra) is flat as a left R-module. In this paper, we show that for a ring R and derivation δ of R, R is left APP if and only if R is δ-weakly rigid and the differential polynomial ring R[x;δ] is left APP. As a consequence, we see that if R is a left APP-ring, then the n^th Weyl algebra over R is left APP. Also we define δ-left APP (resp. p.q.-Baer) rings and we show that R is left APP (resp. p.q.-Baer) if and only if for each derivation δ of R, R is δ-weakly rigid and δ-left APP (resp. p.q.-Baer). Finally we prove that R[x;δ] is left APP (resp. p.q.-Baer) if and only if R is δ-left APP (resp. p.q.-Baer).     

On the invariance of small overlap hypotheses

Suppose thtS is a semigroup with a finite presentation (X; R). John Remmers has proved that the word problem for the presentation (X; R) is solvable if the presentation satisfies a certain small overlap hypothesis,C(n), forn≥3. Here we prove that, with trivial but numerous exceptions, if (X ₁;R ₁) and (X ₂;R ₂) are both finite presentations forS which satisfyC(2), then forn≥2, (X ₁;R ₁) satisfiesC(n) if and only if (X ₂;R ₂) satisfiesC(n).     

On (∈, ∈ ∨ q)‐fuzzy filters of R0‐algebras

In this paper, we introduce the notions of (∈, ∈ ∨ q)‐fuzzy filters and (∈, ∈ ∨ q)‐fuzzy Boolean (implicative) filters in R₀‐algebras and investigate some of their related properties. Some characterization theorems of these generalized fuzzy filters are derived. In particular, we prove that a fuzzy set in R₀‐algebras is an (∈, ∈ ∨ q)‐fuzzy Boolean filter if and only if it is an (∈, ∈ ∨ q)‐fuzzy implicative filter. Finally, we consider the concepts of implication‐based fuzzy Boolean (implicative) filters of R₀‐algebras (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the normalizer property for integral group rings

Let R(G) denote the intersection of all nonnormal subgroups of a group G. In this note, we prove that for every finite group G, if R(G) is not trivial, then the normalizer property holds forG.     

Automorphism Group of q-Quantum Torus Lie Algebra with q a Root of Unity*

Let α be an automorphism of a ring R. We study the skew Armendariz of Laurent series type rings (α-LA rings), as a generalization of the standard Armendariz condition from polynomials to skew Laurent series. We study on the relationship between the Baerness and p.p. property of a ring R and these of the skew Laurent series ring R[[x, x ^?1; α]], in case R is an α-LA ring. Moreover, we prove that for an α-weakly rigid ring R, R[[x, x ^?1; α]] is a left p.q.-Baer ring if and only if R is left p.q.-Baer and every countable subset of S _?(R) has a generalized countable join in R. Various types of examples of α-LA rings are provided.     

Quasi-Hopf twistors for elliptic quantum groups

The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type. On the basis of these solutions, two types of elliptic quantum groups have been introduced (Foda et al. [FIJKMY1], Felder [Fe]). Frønsdal [Fr1, Fr2] made a penetrating observation that both of them are quasi-Hopf algebras, obtained by twisting the standard quantum affine algebraU _q(g). In this paper we present an explicit formula for the twistors in the form of an infinite product of the universalR matrix ofU _q(g). We also prove the shifted cocycle condition for the twistors, thereby completing Frønsdal's findings.This construction entails that, for generic values of the deformation parameters, the representation theory forU _q(g) carries over to the elliptic algebras, including such objects as evaluation modules, highest weight modules and vertex operators. In particular, we confirm the conjectures of Foda et al. concerning the elliptic algebraA _q,p ( ).Dedicated to Professor Mikio Sato on the occasion of his seventieth birthday     

A(α)-acceptability of pade approximations to function exp (Q)

In this paper, a necessary and sufficient condition of A(a)-acceptability for rational approximations to the functionexp(q) and some sufficient conditions to guarantee A(α)-acceptability of Padé approximations[^(R)]_mⁿ (q)\hat R_m^n (q) to the functionexp(q) are given, where a ∈(0,π/2), n≤m,m≥2. Furthermore, it is proved that the condition of A(α)-acceptability of rational approximations toexp(q) is equivalent to the nonnegatively of a real polynomial in interval (−∞,0). Finally, we prove that[^(R)]₄¹ (q)\hat R_4^1 (q) is A(π/3)-acceptable. Based on this conclusion, two A(π/3)-stable multiderivative (hybrid) one-step methods are constructed.     

Sur la cohomologie des super algèbres de Lie étranges

In this paper we compute the cohomology with trivial coefficients for the Lie superalgebraspsl(n, n), p (n) andq(2n); we show that the cohomology ring ofq(2n+1) is of Krull dimension 1 and we calculate the ring forq(3) andq(5). The last section is devoted to a result about the cohomology of a Lie superalgebra with reductive even part with coefficients in a finite dimensional moduleM.     

The chromaticity of complete bipartite graphs with at most one edge deleted

Let K(p, q), p ≤ q, denote the complete bipartite graph in which the two partite sets consist of p and q vertices, respectively. In this paper, we prove that (1) the graph K(p, q) is chromatically unique if p ≥ 2; and (2) the graph K(p, q) - e obtained by deleting an edge e from K(p, q) is chromatically unique if p ≥ 3. The first result was conjectured by Salzberg, López, and Giudici, who also proved the second result under the condition that q - p ≤ 1.     

On r*-sequenceability and symmetric harmoniousness of groups. II

In this paper we investigate symmetric harmoniousness of groups and connections of this concept to the R*-sequenceability of groups. We prove that, under suitable assumptions, the direct product of a symmetric harmonious group with a group that is R*-sequenceable is R*-sequenceable; we discuss the symmetric harmoniousness of abelian and of nilpotent groups; we also prove that, for a fixed odd prime p, all but possibly finitely many of the nonabelian groups of order pq (q prime, q ≡ 1 (mod p)) are symmetric harmonious. © 1995 John Wiley & Sons, Inc.     

ltivariate Hausdorff operators on the spaces H1(Rn) and BMO(Rn)

Summary A multivariate Hausdorff operator H = H(, c, A) is defined in terms of a -finite Borel measure on Rⁿ, a Borel measurable function c on Rⁿ, and an n × n matrix A whose entries are Borel measurable functions on rⁿ and such that A is nonsingular -a.e. The operator H*:= H (, c | det A^-1|, A^-1) is the adjoint to H in a well-defined sense. Our goal is to prove sufficient conditions for the boundedness of these operators on the real Hardy space H¹(Rⁿ) and BMO (Rⁿ). Our main tool is proving commuting relations among H, H*, and the Riesz transforms R_j. We also prove commuting relations among H, H*, and the Fourier transform.     

Principally Quasi-Baer skew Generalized Power Series modules

Let R be a ring and S a strictly totally ordered monoid. Let ω: S → End(R) be a monoid homomorphism. Let M _R be an ω-compatible module and either R satisfies the ascending chain conditions (ACC) on left annihilator ideals or every S-indexed subset of right semicentral idempotents in R has a generalized S-indexed join. We show that M _R is p.q.-Baer if and only if the generalized power series module M[[S]] _{R[[S, ω]]} is p.q.-Baer. As a consequence, we deduce that for an ω-compatible ring R, the skew generalized power series ring R[[S, ω]] is right p.q.-Baer if and only if R is right p.q.-Baer and either R satisfies the ACC on left annihilator ideals or any S-indexed subset of right semicentral idempotents in R has a generalized S-indexed join in R. Examples to illustrate and delimit the theory are provided.     

Integral extensions of noncommutative rings

In this paper we study integral extensions of noncommutative rings. To begin, we prove that finite subnormalizing extensions are integral. This is done by proving a generalization of the Paré-Schelter result that a matrix ring is integral over the coefficient ring. Our methods are similar to those of Lorenz and Passman, who showed that finite normalizing extensions are integral. As corollaries we note that the (twisted) smash product over the restricted enveloping algebra of a finite dimensional restricted Lie algebra is integral over the coefficient ring and then prove a Going Up theorem for prime ideals in these ring extensions. Next we study automorphisms of rings. In particular, we prove an integrality theorem for algebraic automorphisms. Combining group gradings and actions, we show that if a ringR is graded by a finite groupG, andH is a finite group of automorphisms ofR that permute the homogeneous components, with the order ofH invertible inR, thenR is integral overR ₁ ^H , the fixed ring of the identity component. This, in turn, is used to prove our final result: Suppose that ifH is a finite dimensional semisimple cocommutative Hopf algebra over an algebraically closed field of positive characteristic. IfR is anH-module algebra, thenR is integral overR ^H , its subring of invariants.     

A lifting procedure for the asymmetric traveling salesman polytope and a large new class of facets

Given any family of valid inequalities for the asymmetric traveling salesman polytopeP(G) defined on the complete digraphG, we show that all members of are facet defining if the primitive members of (usually a small subclass) are. Based on this result we then introduce a general procedure for identifying new classes of facet inducing inequalities forP(G) by lifting inequalities that are facet inducing forP(G), whereG is some induced subgraph ofG. Unlike traditional lifting, where the lifted coefficients are calculated one by one and their value depends on the lifting sequence, our lifting procedure replaces nodes ofG with cliques ofG and uses closed form expressions for calculating the coefficients of the new arcs, which are sequence-independent. We also introduce a new class of facet inducing inequalities, the class of SD (source-destination) inequalities, which subsumes as special cases most known families of facet defining inequalities.Research supported by Grant DDM-8901495 of the National Science Foundation and Contract N00014-85-K-0198 of the U.S. Office of Naval Research.Research supported by M.U.R.S.T., Italy.     

On the least prime in an arithmetic progression

Letq, k be positive integers, (q, k)=1, andP(k, q) be the smallest prime number satisfyingpэk (modq) In this paper, we prove that forq sufficiently large, one hasP (k,q)≪q ⁸.     

Statistical procedures based on signed ranks ink samples with unequal variances

Ink samples with unequal variances, test procedures based on signed ranks for the homogeneity ofk location parameters are proposed. The asymptotic ²-distribution of the test statistics is shown. It is found that the asymptotic relative efficiency of the rank tests relative to Welch's test (1951,Biometrika,38, 330–336) under local alternatives agrees with that of the one-sample signed rank tests relative to thet-test. A simulation study for the goodness of the ²-approximate of significance points is done. Then, surprisingly it can be seen that the ²-approximate for the critical points of the proposed tests is better than that of Kruskal-Wallis test and the Welch-type test. NextR-estimators and weighted least squares estimators for common mean ofk samples under the homogeneity ofk location parameters are compared in the same way as the test case. Furthermore, positive-part shrinkage versions ofR-estimators for thek location parameters are considered along with a modified James-Stein estimation rule. The asymptotic distributional risks of the usualR-estimators, the positive-part shrinkageR-estimators (PSRE's), and the preliminary test and shrinkageR-versions under an arbitrary quadratic loss are derived. Under Mahalanobis loss, it is shown that the PSRE's dominate the otherR-estimators fork4. A simulation study leads strong support to the claims that the PSRE's dominate the other typeR-estimators and they are robust about outliers.     

On the tautological ring of ℳ g

We prove that any product of tautological classes of _g of degreed (in the Chow ring of _g with rational coefficients) vanishes ford>g–2 and is proportional to the class of the hyperelliptic locus in degreeg–2.Oblatum 28-I-1195 & 15-IV-1995In memory of Nicolaas H. Kuiper (1920–1994)     

Identities of semigroup rings over semilattices of completely (0-) simple semigroups

LetR be a ring with identity,S be a semigroup with the set of idempotentsE(S), and denote (E(S)) for the subsemigroup ofS generated byE(S). In this paper, we prove that ifS is a semilattice of completely 0-simple semigroups and completely simple semigroups, then the semigroup ringRS possesses an identity iff so doesR(E(S)); especially, the result is true forS being a completely regular semigroup.     

Limiting equations in asymptotic stability problems for nonautonomous differential equations

Summary By limiting equations, we prove some asymptotic stability theorems for the origin ofR ⁿ with respect to the solutions of a differential equation , also when the functionf is not defined forx=0. Further we examine similar problems concerning the asymptotic stability of a setM ofR ⁿ that can be unbounded.

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Riassunto Mediante le equazioni limiti, si dimostrano alcuni teoremi di stabilità asintotica per l'origine diR ⁿ rispetto alle soluzioni di un'equazione differenziale , anche quando la funzionef non è definita perx=0. Vengono inoltre esaminati analoghi problemi relativi alla stabilità asintotica di un insiemeM diR ⁿ anche non limitato.

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Work performed under the auspices of the Italian Council of Research (G.N.F.M. del C.N.R.).     

A recursive construction of asymmetric 1-factorizations

W. D. Wallis has recently shown that forn 4, the complete graph on 2n points (denotedK _2n ) has two non-isomorphic 1-factorizations. In this paper we prove that forn 5,K _2n has a 1-factorization with no symmetry at all and that as n increases without bound, the number of pairwise non-isomorphic asymmetric 1-factorizations ofK _2n also increases without bound.The work of B. A. Anderson was partially supported by an Arizona State University Summer Faculty Fellowship.