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1.
A standard completion γ assigns a closure system to each partially ordered set in such a way that the point closures are precisely
the (order-theoretical) principal ideals. If S is a partially ordered semigroup such that all left and all right translations
are γ-continuous (i.e., Y∈γS implies {x∈S:y·x∈Y}∈γS and {x∈S:x·y∈Y}∈γS for all y∈S), then S is called a γ-semigroup. If S
is a γ-semigroup, then the completion γS is a complete residuated semigroup, and the canonical principal ideal embedding of
S in γS is a semigroup homomorphism. We investigate the universal properties of γ-semigroup completions and find that under
rather weak conditions on γ, the category of complete residuated semigroups is a reflective subcategory of the category of
γ-semigroups. Our results apply, for example, to the Dedekind-MacNeille completion by cuts, but also to certain join-completions
associated with so-called “subset systems”. Related facts are derived for conditional completions.
A first draft of this paper by the second author, containing parts of Section 2, was received on August 9, 1985. 相似文献
2.
James M. Henle 《Israel Journal of Mathematics》1978,30(1-2):85-98
A number of related combinatorial properties of a cardinal κ contradicting AC are examined. Chief results include: (1) For
many ordinals γ, к → (к)γ implies к к (к)<γ. (2) For many ordinals γ, if к к (к)
γ
α
for all α<κ, then κ is γ-weakly ineffable. (3) For all infinite cardinals γ, к к (к)<γ implies κ is <γ-weakly ineffable.
Many of the results in this paper appeared originally in the author’s doctoral dissertation. 相似文献
3.
In the case of number fields the embedding problem of a p-extension with non-Abelian kernel of order p4 is studied. The two kernels of order 34 with generators α, γ and relations α9 = 1, [α,α]3=1,[α,αγγ]==1,[αγγ]=α3,γ3=1 or γ3=α3 and the kernel of order 24 with generators α, β, γ and relations α4=1 β2,[αγ]=1, [α,γ]=1,[βγ]=α2 are considered. For kernels of odd order the embedding problem is always solvable. For the kernel of order 16 the solvability
conditions are reduced to those for the associated problems at the Archimedean points, and to the compatibility condition.
Bibliography: 9 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 227, 1995, pp. 74–82. 相似文献
4.
Miguel Angel Javaloyes Levi Lopes de Lima Paolo Piccione 《Mathematische Zeitschrift》2008,260(2):277-303
Following the lines of Bott in (Commun Pure Appl Math 9:171–206, 1956), we study the Morse index of the iterates of a closed
geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic
Jacobi field. Given one such closed geodesic γ, we prove the existence of a locally constant integer valued map Λγ on the unit circle with the property that the Morse index of the iterated γ
N
is equal, up to a correction term εγ∈{0,1}, to the sum of the values of Λγ at the N-th roots of unity. The discontinuities of Λγ occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincaré map of γ.
We discuss some applications of the theory. 相似文献
5.
The discrete spectrum of the Hamiltonian of a pseudorelativistic system of two particles with finite masses is investigated
for a fixed total system momentum p and interaction potentials having the form Z|r12|−γ for large |r12|, where Z<0 and 0<γ≤2. The leading spectral asymptotic term is derived for γ<2. For γ=2, conditions are found for the finiteness
and infiniteness of the discrete spectrum that depend (for some Z) on the fixed momentum p, which radically distinguishes
the situation in question from the nonrelativistic case.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 2, pp. 297–306, November, 1999. 相似文献
6.
A. A. Borisenko Jr. 《Journal of Mathematical Sciences》1999,94(2):1147-1160
It is shown that the structure of a three-dimensional minimal parabolic surface is determined by the pair (V2, γ), where V2 is a minimal two-dimensional surface in Sn and γ satisfies Δγ+2γ=0 (here Δ is the Laplace operator in ℝ4). It is also shown that the singularities of the surface are determined by zeros of γ. Bibliography: 9 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 234, 1996, pp. 20–38. 相似文献
7.
Bischoff Wolfgang Hashorva Enkelejd Hüsler Jürg Miller Frank 《Annals of the Institute of Statistical Mathematics》2003,55(4):849-864
We consider a boundary crossing probability of a Brownian bridgeB
0 and a piecewise linear boundary functionu(t)−γh(t). The main result of this paper is an asymptotic expansion for γ→∞ of the boundary crossing probability thatB
0
(t) is larger than the piecewise linear boundary functionu(t)−γh(t) for somet. Such probabilities occur for instance in the context of change point problems when the Kolmogorov test is used. Examples
are discussed showing that the approximation is rather accurate even for small positive γ values.
Supported by the Swiss National Science Foundation Grant 20-55586.98. 相似文献
8.
Shaul K. Bar-Lev 《Annals of the Institute of Statistical Mathematics》1984,36(1):217-222
Summary Consider a truncated exponential family of absolutely continuous distributions with natural parameter θ and truncation parameter
γ. Strong consistency and asymptotic normality are shown to hold for the maximum likelihood and maximum conditional likelihood
estimates of θ with γ unknown. Moreover, these two estimates are also shown to have the same limiting distribution, coinciding
with that of the maximum likelihood estimate for θ when γ is assumed to be known. 相似文献
9.
F. Pillichshammer 《Acta Mathematica Hungarica》2003,98(4):311-321
We ask for the maximum σ
n
γ
of Σ
i,j=1
n
‖x
i-x
j‖γ, where x
1,χ,x
n are points in the Euclidean plane R
2 with ‖xi-xj‖ ≦1 for all 1≦ i,j ≦ n and where ‖.‖γ denotes the γ-th power of the Euclidean norm, γ ≧ 1. (For γ =1 this question was stated by L. Fejes Tóth in [1].) We calculate
the exact value of σ
n
γ
for all γ γ 1,0758χ and give the distributions which attain the maximum σ
n
γ
. Moreover we prove upper bounds for σ
n
γ
for all γ ≧ 1 and calculate the exact value of σ
4
γ
for all γ ≧ 1.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
10.
V. A. Belonogov 《Algebra and Logic》2005,44(6):357-369
Let P(n) be the set of all partitions of a natural number n. In the representation theory of symmetric groups, for every partition
α ∈ P(n), the partition h(α) ∈ P(n) is defined so as to produce a certain set of zeros in the character table for Sn. Previously, the analog f(α) of h(α) was obtained pointing out an extra set of zeros in the table mentioned. Namely, h(α)
is greatest (under the lexicographic ordering ≤) of the partitions β of n such that χα(gβ) ≠ 0, and f(α) is greatest of the partitions γ of n that are opposite in sign to h(α) and are such that χα(gγ) ≠ 0, where χα is an irreducible character of Sn, indexed by α, and gβ is an element in the conjugacy class of Sn, indexed by β. For α ∈ P(n), under some natural restrictions, here, we construct new partitions h′(α) and f′(α) of n possessing
the following properties. (A) Let α ∈ P(n) and n ⩾ 3. Then h′(α) is identical is sign to h(α), χα(gh′(α)) ≠ 0, but χα(gγ) = 0 for all γ ∈ P(n) such that the sign of γ coincides with one of h(α), and h′(α) < γ < h(α). (B) Let α ∈ P(n), α ≠ α′,
and n ⩾ 4. Then f′(α) is identical in sign to f(α), χα(gf′(α)) ≠ 0, but χα(gγ) = 0 for all γ ∈ P(n) such that the sign of γ coincides with one of f(α), and f′(α) < γ < f(α). The results obtained are
then applied to study pairs of semiproportional irreducible characters in An.
Supported by RFBR grant No. 04-01-00463.
__________
Translated from Algebra i Logika, Vol. 44, No. 6, pp. 643–663, November–December, 2005. 相似文献
11.
A properk-coloring of a graph is acyclic if every 2-chromatic subgraph is acyclic. Borodin showed that every planar graph has an acyclic
5-coloring. This paper shows that the acyclic chromatic number of the projective plane is at most 7. The acyclic chromatic
number of an arbitrary surface with Euler characteristic η=−γ is at mostO(γ4/7). This is nearly tight; for every γ>0 there are graphs embeddable on surfaces of Euler characteristic −γ whose acyclic chromatic
number is at least Ω(γ4/7/(logγ)1/7). Therefore, the conjecture of Borodin that the acyclic chromatic number of any surface but the plane is the same as its
chromatic number is false for all surfaces with large γ (and may very well be false for all surfaces).
This author's research was supported in part by a United States Israeli BSF grant.
This author's research was supported by the Ministry of Research and Technology of Slovenia, Research Project P1-0210-101-92.
This author's research was supported by the Office of Naval Research, grant number N00014-92-J-1965. 相似文献
12.
E. Marušic-Paloka 《Applied Mathematics and Optimization》2001,44(3):245-272
We consider an injection of incompressible viscous fluid in a curved pipe with a smooth central curve γ . The one-dimensional model is obtained via singular perturbation of the Navier—Stokes system as ɛ , the ratio between the cross-section area and the length of the pipe, tends to zero. An asymptotic expansion of the flow
in powers of ɛ is computed. The first term in the expansion depends only on the tangential injection along the central curve γ of the pipe and the velocity as well as the pressure drop are in the tangential direction. The second term contains the
effects of the curvature (flexion) of γ in the direction of the tangent while the effects of torsion appear in the direction of the normal and the binormal to γ . The boundary layers at the ends of the pipe are studied. The error estimate is proved.
Accepted 21 March 2001. Online publication 9 August 2001. 相似文献
13.
Summary We introduce the concepts of γ-semi-open set, γs-set, γs-set, generalized γs-set, generalized γs-set, semi-T1γspace and semi-R0γspace by using γ-open-sets. 相似文献
14.
We present examples of flag homology spheres whose γ-vectors satisfy the Kruskal–Katona inequalities. This includes several families of well-studied simplicial complexes, including
Coxeter complexes and the simplicial complexes dual to the associahedron and to the cyclohedron. In these cases, we construct
explicit flag simplicial complexes whose f-vectors are the γ-vectors in question, and so a result of Frohmader shows that the γ-vectors satisfy not only the Kruskal–Katona inequalities but also the stronger Frankl–Füredi–Kalai inequalities. In another
direction, we show that if a flag (d−1)-sphere has at most 2d+3 vertices its γ-vector satisfies the Frankl–Füredi–Kalai inequalities. We conjecture that if Δ is a flag homology sphere then γ(Δ) satisfies the Kruskal–Katona, and further, the Frankl–Füredi–Kalai inequalities. This conjecture is a significant refinement
of Gal’s conjecture, which asserts that such γ-vectors are nonnegative. 相似文献
15.
This paper undertakes a study of asymptotic behavior of solutions corresponding to von Karman thermoelastic plates. A distinct
feature of the work is that the model considered has no added dissipation—particularly mechanical dissipation typically added to plate equation when long time-behavior is considered. Thus, the model
consists of undamped oscillatory plate equation strongly coupled with heat equation. Nevertheless we are able to show that the ultimate (asymptotic)
behavior of the von Karman evolution is described by finite dimensional global attractor. In addition, the obtained estimate for the dimension and the size of the attractor are independent of the rotational inertia parameter γ and heat/thermal capacity κ, where the former is known to change the character of dynamics from hyperbolic (γ>0) to parabolic like (γ=0). Other properties of attractors such as additional smoothness and upper-semicontinuity with respect to parameters γ and κ are also established. The main ingredients of the proofs are (i) sharp regularity of Airy’s stress function, and (ii) newly
developed (Chueshov and Lasiecka in Memoirs of AMS, in press) “compensated” compactness methods applicable to non-compact
dynamics.
I. Lasiecka’s research partially supported by the NSF Grant DMS-0104305 and ARO Grant DAAD19-02-10179. 相似文献
16.
H. Dym 《Israel Journal of Mathematics》1974,18(4):391-398
It is proved that ifj is an inner function and ρ(T)=sup|∫(eiγT/j(γ))f(γ)dγ| overf in the unit ball ofH
1, then eitherρ ≡ 1 for allT≧0, or elseρ(T) ↓ 0 exponentially fast asT ↑ ∞. The inner functionsj corresponding to each alternative are classified. 相似文献
17.
Ákos Császár 《Acta Mathematica Hungarica》2006,113(4):325-332
Summary There is a formula for the interior of a set in a generalized topology composed of the γ-open sets, where γ is a monotonic
map in the power set of X. There are known conditions for a γ assuring that this formula is valid. The paper gives essential generalizations for these
conditions and contains some applications. 相似文献
18.
Abstract. A dihedral (trihedral) wedge is the intersection of two (resp. three) half-spaces in R
3
. It is called α-fat if the angle (resp., solid angle) determined by these half-spaces is at least α>0 . If, in addition, the sum of the three face angles of a trihedral wedge is at least γ >4π/3 , then it is called (γ,α)-substantially fat . We prove that, for any fixed γ>4π/3, α>0 , the combinatorial complexity of the union of n (a) α -fat dihedral wedges, and (b) (γ,α) -substantially fat trihedral wedges is at most O(n^ 2+ ɛ ) , for any ɛ >0 , where the constants of proportionality depend on ɛ , α (and γ ). We obtain as a corollary that the same upper bound holds for the combinatorial complexity of the union of n (nearly) congruent cubes in R
3
. These bounds are not far from being optimal. 相似文献
19.
Characterizations of γ-open sets and locally γ-regular sets are given. We generalize some already established results and answer an open question by giving a characterization
to γ-quasi-open sets.
相似文献
20.
The Union of Congruent Cubes in Three Dimensions 总被引:1,自引:1,他引:0
Abstract. A dihedral (trihedral) wedge is the intersection of two (resp. three) half-spaces in R
3
. It is called α-fat if the angle (resp., solid angle) determined by these half-spaces is at least α>0 . If, in addition, the sum of the three face angles of a trihedral wedge is at least γ >4π/3 , then it is called (γ,α)-substantially fat . We prove that, for any fixed γ>4π/3, α>0 , the combinatorial complexity of the union of n (a) α -fat dihedral wedges, and (b) (γ,α) -substantially fat trihedral wedges is at most O(n^ 2+ ɛ ) , for any ɛ >0 , where the constants of proportionality depend on ɛ , α (and γ ). We obtain as a corollary that the same upper bound holds for the combinatorial complexity of the union of n (nearly) congruent cubes in R
3
. These bounds are not far from being optimal. 相似文献