The Jacobson and Brown—McCoy Radicals of Certain Group Rings

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A note on embedding of classes H ω

Among others, we extend an interesting theorem of M. V. Medvedeva pertaining to the embedding relation H BV, where BV denotes the set of the functions of -bounded variation.     

弱加法范畴的特殊根和Brown—McCoy根

引言 [1]中将象元类是I的加法范畴记作A=∪_αA_β,其中_αA_β表示Hom(α,β)中所有态射之集。据范畴的定义,对于任意α∈I,_αA_α中必有单位元_α|_α,从而对于范畴中规定的加法和乘法来说,_αA_α作成一个有单位元的结合环,今将加法范畴中去掉_αA_α必有单     

A note on θ-tightness

In questo lavoro chiariamo il ruolo che la θ-tightness (introdotta dagli autori in [2]) ha nel determinare alcune estensioni di sottoinsiemi di uno spazio topologico.     

A note on Marino-Vafa formula

Hodge integrals over moduli spaces of curves appear naturally during the localization procedure in computation of Gromov-Witten invariants. A remarkable formula of Marino-Vafa expresses a generation function of Hodge integrals via some combinatorial and algebraic data seemingly unrelated to these apriori algebraic geometric objects. We prove in this paper by directly expanding the formula and estimating the involved terms carefully that except a specific type all the other Hodge integrals involving up to three Hodge classes can be calculated from this formula. This implies that amazingly rich information about moduli spaces and Gromov-Witten invariants is encoded in this complicated formula. We also give some low genus examples which agree with the previous results in literature. Proofs and calculations are elementary as long as one accepts Mumford relations on the reductions of products of Hodge classes.     

A note on β-connectedness

An example is given to show that there exists a generalized topological space which is irreducible but not β-connected. This gives an answer to Question 2.8 in [6]. Besides, some characterizations of β-connectedness are obtained.     

A note on Weil index

Let F be a non-archimedean local field of characteristic 0 and(?)a nontrivial additive character.Weil first defined the Weil indexγ(a,(?))(a∈F~*)in his famous paper,from which we know thatγ(a,(?))γ(b,(?))=γ(ab,(?))γ(1,(?))(a,b)andγ(a,(?))~4 =(-1,-1),where(a,b)is the Hilbert symbol for F.The Weil index plays an important role in the theory of theta series and in the general representation theory.In this paper,we establish an identity relating the Weil indexγ(a,(?))and the Gauss sum.     

A note on the selection of Benders’ cuts

A new cut selection criterion for Benders’ cuts is proposed and computationally analyzed. The results show that the new criterion is more robust—and often considerably faster—than the standard ones.     

A note on Iwasawa µ-invariants of elliptic curves

Suppose that E ₁ and E ₂ are elliptic curves defined over ℚ and p is an odd prime where E ₁ and E ₂ have good ordinary reduction. In this paper, we generalize a theorem of Greenberg and Vatsal [3] and prove that if E ₁[p ⁱ ] and E ₂[p ⁱ ] are isomorphic as Galois modules for i = μ(E ₁), then μ(E ₁) ≤ μ(E ₂). If the isomorphism holds for i = μ(E ₁) + 1, then both the curves have same μ-invariants. We also discuss one numerical example.     

A note on the uniqueness theorem of meromorphic mappings

In this article, some uniqueness theorems of meromorphic mappings are proved.     

A note on degrees of irreducible π-Brauer characters

In this note, we first investigate the degrees of irreducible π-Brauer characters of a finite π-separable group G. Then we relate degrees of irreducible π-Brauer characters to class lengths of π-regular elements of G. Received: 4 April 2008     

A note on nonstable monomorphisms¶of vector bundles

In this paper we consider the question of the existence of a nonstable vector bundle monomorphism u:α→β over a closed, connected and smooth manifold M, when dimension of α= 3, dimension of β= dimension of M=n≡ 0(4). The singularity method provides the full obstruction to this problem and under some homological hypothesis we can compute it in terms of well known invariants. Received: 31 May 1999     

A note on curvature of α-connections of a statistical manifold

The family of α-connections ∇^(α) on a statistical manifold equipped with a pair of conjugate connections and is given as . Here, we develop an expression of curvature R ^(α) for ∇^(α) in relation to those for . Immediately evident from it is that ∇^(α) is equiaffine for any when are dually flat, as previously observed in Takeuchi and Amari (IEEE Transactions on Information Theory 51:1011–1023, 2005). Other related formulae are also developed. The work was conducted when the author was on sabbatical leave as a visiting research scientist at the Mathematical Neuroscience Unit, RIKEN Brain Science Institute, Wako-shi, Saitama 351-0198, Japan.     

A note on λ-compact spaces

We extend the well-known and important fact that “a topological space X is compact if and only if every ideal in C(X) is fixed”, to more general topological spaces. Some interesting consequences are also observed. In particular, the maximality of compact Hausdorff spaces with respect to the property of compactness is generalized and the topological spaces with this generalized property are characterized.