共查询到20条相似文献,搜索用时 15 毫秒
1.
Let S° be an inverse semigroup with semilattice biordered set E° of idempotents and E a weakly inverse biordered set with a subsemilattice Ep = { e ∈ E | arbieary f ∈ E, S(f , e) loheain in w(e)} isomorphic to E° by θ:Ep→E°. In this paper, it is proved that if arbieary f, g ∈E, f ←→ g→→ f°θD^s° g°θand there exists a mapping φ from Ep into the symmetric weakly inverse semigroup P J(E∪ S°) satisfying six appropriate conditions, then a weakly inverse semigroup ∑ can be constructed in P J(S°), called the weakly inverse hull of a weakly inverse system (S°, E, θ, φ) with I(∑) ≌ S°, E(∑) ∽- E. Conversely, every weakly inverse semigroup can be constructed in this way. Furthermore, a sufficient and necessary condition for two weakly inverse hulls to be isomorphic is also given. 相似文献
2.
Given a multiplicative band of idempotents S in a ring R, for all e,f∈S the ∇-product e
∇
f=e+f+fe−efe−fef is an idempotent that lies roughly above e and f in R just as ef and fe lie roughly below e and f. In this paper we study ∇-bands in rings, that is, bands in rings that are closed under ∇, giving various criteria for ∇ to be associative, thus making the band a skew lattice. We also consider when a given band S in R generates a ∇-band. 相似文献
3.
Bart De Bruyn 《Annals of Combinatorics》2010,14(3):307-318
Let f be an isometric embedding of the dual polar space ${\Delta = DQ(2n, {\mathbb K})}Let f be an isometric embedding of the dual polar space
D = DQ(2n, \mathbb K){\Delta = DQ(2n, {\mathbb K})} into
D¢ = DQ(2n, \mathbb K¢){\Delta^\prime = DQ(2n, {\mathbb K}^\prime)}. Let P denote the point-set of Δ and let
e¢: D¢? S¢ @ PG(2n - 1, \mathbb K¢){e^\prime : \Delta^\prime \rightarrow {\Sigma^\prime} \cong {\rm PG}(2^n - 1, {{\mathbb K}^\prime})} denote the spin-embedding of Δ′. We show that for every locally singular hyperplane H of Δ, there exists a unique locally singular hyperplane H′ of Δ′ such that f(H) = f(P) ?H¢{f(H) = f(P) \cap H^\prime}. We use this to show that there exists a subgeometry
S @ PG(2n - 1, \mathbb K){\Sigma \cong {\rm PG}(2^n - 1, {\mathbb K})} of Σ′ such that: (i) e¢°f (x) ? S{e^\prime \circ f (x) \in \Sigma} for every point x of D; (ii) e : = e¢°f{\Delta; ({\rm ii})\,e := e^\prime \circ f} defines a full embedding of Δ into Σ, which is isomorphic to the spin-embedding of Δ. 相似文献
4.
For a regular semigroup with an inverse transversal, we have Saito’s structureW(I,S
o, Λ, *, {α, β}). We represent congruences on this kind of semigroups by the so-called congruence assemblage which consist
of congruences on the structure component partsI,S
o and Λ. The structure of images of this type of semigroups is also presented.
This work is supported by Natural Science Foundation of Guangdong Province 相似文献
5.
On the divisibility of power LCM matrices by power GCD matrices 总被引:3,自引:0,他引:3
Jianrong Zhao Shaofang Hong Qunying Liao K. P. Shum 《Czechoslovak Mathematical Journal》2007,57(1):115-125
Let S = {x
1, ..., x
n
} be a set of n distinct positive integers and e ⩾ 1 an integer. Denote the n × n power GCD (resp. power LCM) matrix on S having the e-th power of the greatest common divisor (x
i
, x
j
) (resp. the e-th power of the least common multiple [x
i
, x
j
]) as the (i, j)-entry of the matrix by ((x
i
, x
j
)
e
) (resp. ([x
i
, x
j
]
e
)). We call the set S an odd gcd closed (resp. odd lcm closed) set if every element in S is an odd number and (x
i
, x
j
) ∈ S (resp. [x
i
, x
j
] ∈ S) for all 1 ⩽ i, j ⩽ n. In studying the divisibility of the power LCM and power GCD matrices, Hong conjectured in 2004 that for any integer e ⩾ 1, the n × n power GCD matrix ((x
i
, x
j
)
e
) defined on an odd-gcd-closed (resp. odd-lcm-closed) set S divides the n × n power LCM matrix ([x
i
, x
j
]
e
) defined on S in the ring M
n
(ℤ) of n × n matrices over integers. In this paper, we use Hong’s method developed in his previous papers [J. Algebra 218 (1999) 216–228;
281 (2004) 1–14, Acta Arith. 111 (2004), 165–177 and J. Number Theory 113 (2005), 1–9] to investigate Hong’s conjectures.
We show that the conjectures of Hong are true for n ⩽ 3 but they are both not true for n ⩾ 4.
Research is partially supported by Program for New Century Excellent Talents in University, by SRF for ROCS, SEM, China and
by the Lady Davis Fellowship at the Technion, Israel
Research is partially supported by a UGC (HK) grant 2160210 (2003/05). 相似文献
6.
L. Sobrero 《Annali di Matematica Pura ed Applicata》1935,14(1):139-148
Sunto Due funzionif(x, y) e ϕ(x, y), biarmoniche (e cioè soddisfacenti all'equazione ΔΔ=0), rispettivamente definite nei semipianix>0 edx<0, le cui derivate seconde si annullano all'infinito, e tali che nei punti dell'assey risultif=ϕ e∂f/∂x=∂ϕ/∂x, si dicono l'una ? riflessa ? dell'altra attorno all'assey. Da ognuna delle due funzionif e ϕ l'altra si ottiene con sole operazioni di sostituzione e derivazione (indicando, precisamente, con{f}, {∂f/∂x} e{Δf} le funzioni che si ottengono daf, ∂f/∂x eΔf ponendo, in queste, in luogo dix il suo contrario −x, si ha ϕ={f}+2x{∂f/∂x}+x
2
{Δf} e, reciprocamente,f={ϕ}+2x{∂ϕ/∂x}+x
2{Δϕ}). In modo analogo si definisce una operazione di riflessione analitica attorno a un cerchio. La retta potendosi riguardare
come cerchio degenere (di raggio infinito) l'operazione di rifiessione analitica attorno alla retta viene ottenuta, nel testo,
come caso limite di quella di riflessione attorno al cerchio. L'operazione di riflessione analitica trova applicazione in
alcuni problemi di elasticità piana (perturbazione prodotta da un foro circolare nella sollecitazione di un sistema piano;
determinazione degli sforzi in un semipiano elastico sollecitato da una forza applicata in un punto interno). 相似文献
7.
In this paper we investigate a certain linear combination K([(x)\vec])=K(a;b,c,d;e,f,g)K(\vec{x})=K(a;b,c,d;e,f,g) of two Saalschutzian hypergeometric series of type 4
F
3(1). We first show that K([(x)\vec])K(\vec{x}) is invariant under the action of a certain matrix group G
K
, isomorphic to the symmetric group S
6, acting on the affine hyperplane V={(a,b,c,d,e,f,g)∈ℂ7:e+f+g−a−b−c−d=1}. We further develop an algebra of three-term relations for K(a;b,c,d;e,f,g). We show that, for any three elements μ
1,μ
2,μ
3 of a certain matrix group M
K
, isomorphic to the Coxeter group W(D
6) (of order 23040) and containing the above group G
K
, there is a relation among K(m1[(x)\vec])K(\mu_{1}\vec{x}), K(m2[(x)\vec])K(\mu_{2}\vec{x}), and K(m3[(x)\vec])K(\mu_{3}\vec{x}), provided that no two of the μ
j
’s are in the same right coset of G
K
in M
K
. The coefficients in these three-term relations are seen to be rational combinations of gamma and sine functions in a,b,c,d,e,f,g. 相似文献
8.
A semiring S whose additive reduct is a semilattice is called a k-regular semiring if for every a∈S there is x∈S such that a+axa=axa. For a semigroup F, the power semiring P(F) is a k-regular semiring if and only if F is a regular semigroup. An element e∈S is a k-idempotent if e+e
2=e
2. Basic properties of k-regular semirings whose k-idempotents are commutative have been studied. 相似文献
9.
Daniel Berend 《Israel Journal of Mathematics》1988,62(1):32-36
LetP andQ be real polynomials of degreesd ande, respectively, andf a periodic function. It is shown that, iff iss times differentiable atQ(0), wheres≧7de
3 log 14e
3, then for every ɛ>0 the diophantine inequality ≧FF5C;P(x)f(Q(x)) -P(0)f(Q(0)) -y≧ εx≠0, has a solution. This settles in particular a question raised by Furstenberg and Weiss [6]. 相似文献
10.
Peter Clifford 《Annals of Combinatorics》2005,9(3):281-291
Motivated by recent results of Stanley, we generalize the rank of a partition λ to the rank of a shifted partition S(λ). We show that the number of bars required in a minimal bar tableau of S(λ) is max(o, e + (ℓ(λ) mod 2)), where o and e are the number of odd and even rows of λ. As a consequence we show that the irreducible projective characters of Sn vanish on certain conjugacy classes. Another corollary is a lower bound on the degree of the terms in the expansion of Schur’s
Qλ symmetric functions in terms of the power sum symmetric functions.
Received November 20, 2003 相似文献
11.
Robert S. Strichartz 《Journal d'Analyse Mathématique》2006,99(1):333-353
For certain Cantor measures μ on ℝn, it was shown by Jorgensen and Pedersen that there exists an orthonormal basis of exponentialse
2πiγ·x for λεΛ. a discrete subset of ℝn called aspectrum for μ. For anyL
1 functionf, we define coefficientsc
γ(f)=∝f(y)e
−2πiγiy
dμ(y) and form the Mock Fourier series ∑λ∈Λcλ(f)e
2πiλ·x
. There is a natural sequence of finite subsets Λn increasing to Λ asn→∞, and we define the partial sums of the Mock Fourier series by
We prove, under mild technical assumptions on μ and Λ, thats
n(f) converges uniformly tof for any continuous functionf and obtain the rate of convergence in terms of the modulus of continuity off. We also show, under somewhat stronger hypotheses, almost everywhere convergence forfεL
1.
Research supported in part by the National Science Foundation, Grant DMS-0140194. 相似文献
12.
For a positive integer n and a subset S⊆[n−1], the descent polytope DP
S
is the set of points (x
1,…,x
n
) in the n-dimensional unit cube [0,1]
n
such that x
i
≥x
i+1 if i∈S and x
i
≤x
i+1 otherwise. First, we express the f-vector as a sum over all subsets of [n−1]. Second, we use certain factorizations of the associated word over a two-letter alphabet to describe the f-vector. We show that the f-vector is maximized when the set S is the alternating set {1,3,5,…}∩[n−1]. We derive a generating function for F
S
(t), written as a formal power series in two non-commuting variables with coefficients in ℤ[t]. We also obtain the generating function for the Ehrhart polynomials of the descent polytopes. 相似文献
13.
Mario Petrich 《Czechoslovak Mathematical Journal》2006,56(1):27-46
Let S be a regular semigroup and E(S) be the set of its idempotents. We call the sets S(e, f)f and eS(e, f) one-sided sandwich sets and characterize them abstractly where e, f ∈ E(S). For a, a′ ∈ S such that a = aa′a, a′ = a′aa′, we call S(a) = S(a′a, aa′) the sandwich set of a. We characterize regular semigroups S in which all S(e; f) (or all S(a)) are right zero semigroups (respectively are trivial) in several ways including weak versions of compatibility of the natural
order.
For every a ∈ S, we also define E(a) as the set of all idempotets e such that, for any congruence ϱ on S, aϱa
2 implies that aϱe. We study the restrictions on S in order that S(a) or
be trivial. For
, we define
on S by a
b if
. We establish for which S are
or
congruences. 相似文献
14.
15.
On any compact Riemannian manifold (M,g) of dimension n, the L
2-normalized eigenfunctions φ
λ
satisfy
||fl||¥ £ Cl\fracn-12\|\phi_{\lambda}\|_{\infty}\leq C\lambda^{\frac{n-1}{2}} where −Δφ
λ
=λ
2
φ
λ
. The bound is sharp in the class of all (M,g) since it is obtained by zonal spherical harmonics on the standard n-sphere S
n
. But of course, it is not sharp for many Riemannian manifolds, e.g., flat tori ℝ
n
/Γ. We say that S
n
, but not ℝ
n
/Γ, is a Riemannian manifold with maximal eigenfunction growth. The problem which motivates this paper is to determine the
(M,g) with maximal eigenfunction growth. In an earlier work, two of us showed that such an (M,g) must have a point x where the set ℒ
x
of geodesic loops at x has positive measure in S*xMS^{*}_{x}M. We strengthen this result here by showing that such a manifold must have a point where the set ℛ
x
of recurrent directions for the geodesic flow through x satisfies |{ℛ}
x
|>0. We also show that if there are no such points, L
2-normalized quasimodes have sup-norms that are o(λ
(n−1)/2), and, in the other extreme, we show that if there is a point blow-down x at which the first return map for the flow is the identity, then there is a sequence of quasimodes with L
∞-norms that are Ω(λ
(n−1)/2). 相似文献
16.
A function f : GF(2
r
) → GF(2
r
) is called crooked if the sets {f(x) + f(x + a)|x ∈ GF(2
r
)} is an affine hyperplane for any nonzero a ∈ GF(2
r
). We prove that a crooked binomial function f(x) = x
d
+ ux
e
defined on GF(2
r
) satisfies that both exponents d, e have 2-weights at most 2.
相似文献
17.
Boris Rubin 《Journal d'Analyse Mathématique》1999,77(1):105-128
Explicit inversion formulas are obtained for the hemispherical transform(FΜ)(x) = Μ{y ∃S
n :x. y ≥ 0},x ∃S
n, whereS
n is thendimensional unit sphere in ℝn+1,n ≥ 2, and Μ is a finite Borel measure onS
n. If Μ is absolutely continuous with respect to Lebesgue measuredy onS
n, i.e.,dΜ(y) =f(y)dy, we write(F f)(x) = ∫
x.y> 0
f(y)dy and consider the following cases: (a)f ∃C
∞(Sn); (b)f ∃ Lp(S
n), 1 ≤ p < ∞; and (c)f ∃C(Sn). In the case (a), our inversion formulas involve a certain polynomial of the Laplace-Beltrami operator. In the remaining
cases, the relevant wavelet transforms are employed. The range ofF is characterized and the action in the scale of Sobolev spacesL
p
γ
(Sn) is studied. For zonalf ∃ L1(S
2), the hemispherical transformF f was inverted explicitly by P. Funk (1916); we reproduce his argument in higher dimensions.
Partially sponsored by the Edmund Landau Center for Research in Mathematical Analysis, supported by the Minerva Foundation
(Germany). 相似文献
18.
Jipu Ma 《Frontiers of Mathematics in China》2008,3(2):305-316
Let E and F be Banach spaces, f: U ⊂ E → F be a map of C
r
(r ⩾ 1), x
0 ∈ U, and ft (x
0) denote the FréLechet differential of f at x
0. Suppose that f′(x
0) is double split, Rank(f′(x
0)) = ∞, dimN(f′(x
0)) > 0 and codimR(f′(x
0)) s> 0. The rank theorem in advanced calculus asks to answer what properties of f ensure that f(x) is conjugate to f′(x
0) near x
0. We have proved that the conclusion of the theorem is equivalent to one kind of singularities for bounded linear operators,
i.e., x
0 is a locally fine point for f′(x) or generalized regular point of f(x); so, a complete rank theorem in advanced calculus is established, i.e., a sufficient and necessary condition such that the
conclusion of the theorem to be held is given.
相似文献
19.
An Application of a Mountain Pass Theorem 总被引:3,自引:0,他引:3
We are concerned with the following Dirichlet problem:
−Δu(x) = f(x, u), x∈Ω, u∈H
1
0(Ω), (P)
where f(x, t) ∈C (×ℝ), f(x, t)/t is nondecreasing in t∈ℝ and tends to an L
∞-function q(x) uniformly in x∈Ω as t→ + ∞ (i.e., f(x, t) is asymptotically linear in t at infinity). In this case, an Ambrosetti-Rabinowitz-type condition, that is, for some θ > 2, M > 0,
0 > θF(x, s) ≤f(x, s)s, for all |s|≥M and x∈Ω, (AR)
is no longer true, where F(x, s) = ∫
s
0
f(x, t)dt. As is well known, (AR) is an important technical condition in applying Mountain Pass Theorem. In this paper, without assuming
(AR) we prove, by using a variant version of Mountain Pass Theorem, that problem (P) has a positive solution under suitable
conditions on f(x, t) and q(x). Our methods also work for the case where f(x, t) is superlinear in t at infinity, i.e., q(x) ≡ +∞.
Received June 24, 1998, Accepted January 14, 2000. 相似文献
20.
This paper gives lower estimates for the frequency modules of almost periodic solutions to equations of the form
, where A generates a strongly continuous semigroup in a Banach space
, F(t,x) is 2π-periodic in t and continuous in (t,x), and f is almost periodic. We show that the frequency module ℳ(u) of any almost periodic mild solution u of (*) and the frequency module ℳ(f) of f satisfy the estimate e
2π
iℳ(f)⊂e
2π
iℳ(u). If F is independent of t, then the estimate can be improved: ℳ(f)⊂ℳ(u). Applications to the nonexistence of quasi-periodic solutions are also given. 相似文献