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1.
In Lowen and Wuyts (Appl Categ Struct 8:235–245, 2000) the authors studied the simultaneously concretely reflective and concretely coreflective subconstructs of the category Ap of approach spaces. For the sake of shortness we call such subconstructs stable. Using a technique introduced in Herrlich and Lowen (1999) it was possible to explicitly describe such stable subconstructs by a condition on the objects which used certain subsets
of [0, ∞ ]. Thus each stable subconstruct Ap
m
described in [9] corresponds to the subset {0} ∪ [m, ∞ ] ⊂ [0, ∞ ] for m ∈ [0, ∞ ]. Although this characterization is correct, Theorem 4.7 in [9] stating that the subconstructs Ap
m
were the only stable subconstructs of Ap is not. The main results, which together prove that the only stable subconstructs are those where a restriction is put on
the range of the distances of the objects, are upheld, but it turns out that not only the sets {0} ∪ [m, ∞ ], but actually each closed subsemigroup of [0, ∞ ] determines a stable subconstruct (albeit again in exactly the same
way as characterized in [9]). In the first part of our paper, Sections 1 and 2, we develop the general technique, which is totally different to the
one from [3], and in Theorem 2.13 we prove the main result for the case of approach spaces. The technique which we develop is also applicable
to other cases. Thus, in Section 3, more precisely in Theorems 3.9 and 3.11, we give the complete solution to the corresponding
characterization problem for the constructs pq
Met
∞ of pseudo-quasi-metric spaces and p
Met
∞ of pseudometric spaces and in Section 4 we briefly sketch how the technique can be adapted and used to also completely solve
the problem in the case of more general types of approach spaces and metric spaces. At the same time, in all cases, we are
able to give necessary and sufficient conditions under which two stable subconstructs of one of these topological constructs
are concretely isomorphic. It turns out that in all cases there are 2à02^{\aleph_0} non-concretely isomorphic stable subconstructs. 相似文献
2.
Kathrin Bacher 《Potential Analysis》2010,32(1):1-15
In this paper we introduce the notion of a Borell-Brascamp-Lieb inequality for metric measure spaces (M,d,m) denoted by BBL(K,N) for two numbers K,N ∈ ℝ with N ≥ 1. In the first part we prove that BBL(K,N) holds true on metric measure spaces satisfying a curvature-dimension condition CD(K,N) developed and studied by Lott and Villani in (Ann Math 169:903–991, 2007) as well as by Sturm in (Acta Math 196(1):133–177, 2006). The aim of the second part is to show that BBL(K,N) is stable under convergence of metric measure spaces with respect to the L
2-transportation distance. 相似文献
3.
4.
S. F. Kamornikov 《Mathematical Notes》1996,60(1):18-21
The structure of the totally local formation,ℓ
∞ formG, generated by a simple non-Abelian groupG is described. By applying this result we prove the existence of totally local formations that are not idempotents of the
semigroupG
∞ of all totally local formations and are not representable as the product of finitely many indecomposable elements ofG
∞. We also describe totally local formations all of whose totally local subformations are hereditary.
Translated fromMatematicheskie Zametki, Vol. 60, No. 1, pp. 24–29, July, 1996. 相似文献
5.
For a finite poset P = (V, ≤ ), let _s(P){\cal B}_s(P) consist of all triples (x,y,z) ∈ V
3 such that either x < y < z or z < y < x. Similarly, for every finite, simple, and undirected graph G = (V,E), let Bs(G){\cal B}_s(G) consist of all triples (x,y,z) ∈ V
3 such that y is an internal vertex on an induced path in G between x and z. The ternary relations Bs(P){\cal B}_s(P) and Bs(G){\cal B}_s(G) are well-known examples of so-called strict betweennesses. We characterize the pairs (P,G) of posets P and graphs G on the same ground set V which induce the same strict betweenness relation Bs(P)=Bs(G){\cal B}_s(P)={\cal B}_s(G). 相似文献
6.
Endre Boros Khaled Elbassioni Vladimir Gurvich Hans Raj Tiwary 《Annals of Operations Research》2011,188(1):63-76
Given a graph G=(V,E) and a weight function on the edges w:E→ℝ, we consider the polyhedron P(G,w) of negative-weight flows on G, and get a complete characterization of the vertices and extreme directions of P(G,w). Based on this characterization, and using a construction developed in Khachiyan et al. (Discrete Comput. Geom. 39(1–3):174–190,
2008), we show that, unless P=NP, there is no output polynomial-time algorithm to generate all the vertices of a 0/1-polyhedron. This strengthens the NP-hardness
result of Khachiyan et al. (Discrete Comput. Geom. 39(1–3):174–190, 2008) for non 0/1-polyhedra, and comes in contrast with the polynomiality of vertex enumeration for 0/1-polytopes (Bussiech and
Lübbecke in Comput. Geom., Theory Appl. 11(2):103–109, 1998). As further applications, we show that it is NP-hard to check if a given integral polyhedron is 0/1, or if a given polyhedron
is half-integral. Finally, we also show that it is NP-hard to approximate the maximum support of a vertex of a polyhedron
in ℝ
n
within a factor of 12/n. 相似文献
7.
Ehud Meir 《Algebras and Representation Theory》2012,15(2):391-405
We define a notion of complexity for modules over group rings of infinite groups. This generalizes the notion of complexity
for modules over group algebras of finite groups. We show that if M is a module over the group ring kG, where k is any ring and G is any group, and M has f-complexity (where f is some complexity function) over some set of finite index subgroups of G, then M has f-complexity over G (up to a direct summand). This generalizes the Alperin-Evens Theorem, which states that if the group G is finite then the complexity of M over G is the maximal complexity of M over an elementary abelian subgroup of G. We also show how we can use this generalization in order to construct projective resolutions for the integral special linear
groups, SL(n, ℤ), where n ≥ 2. 相似文献
8.
Iddo Eliazar 《Queueing Systems》2007,55(1):71-82
We explore M/G/∞ systems ‘fed’ by Poissonian inflows with infinite arrival rates. Three processes – corresponding to the system's state, workload, and queue-size – are studied and analyzed. Closed form formulae characterizing the system's stationary structure and correlation structure are derived. And, the issues of queue finiteness, workload summability, and Long Range Dependence are investigated.
We then turn to devise a ‘reverse engineering’ scheme for the design of the system's correlation structure. Namely: how to construct an M/G/∞ system with a pre-desired ‘target’ workload/queue auto-covariance function. The ‘reverse engineering’ scheme is applied
to various examples, including ones with infinite queues and non-summable workloads.
AMS Subject Classifications Primary: 60K25; Secondary: 60G55, 60G10 相似文献
9.
We will simplify earlier proofs of Perelman’s collapsing theorem for 3-manifolds given by Shioya–Yamaguchi (J. Differ. Geom.
56:1–66, 2000; Math. Ann. 333: 131–155, 2005) and Morgan–Tian ( [math.DG], 2008). A version of Perelman’s collapsing theorem states: “Let
{M3i}\{M^{3}_{i}\}
be a sequence of compact Riemannian 3-manifolds with curvature bounded from below by (−1) and
$\mathrm{diam}(M^{3}_{i})\ge c_{0}>0$\mathrm{diam}(M^{3}_{i})\ge c_{0}>0
. Suppose that all unit metric balls in
M3iM^{3}_{i}
have very small volume, at most
v
i
→0 as
i→∞, and suppose that either
M3iM^{3}_{i}
is closed or has possibly convex incompressible toral boundary. Then
M3iM^{3}_{i}
must be a graph manifold for sufficiently large
i”. This result can be viewed as an extension of the implicit function theorem. Among other things, we apply Perelman’s critical
point theory (i.e., multiple conic singularity theory and his fibration theory) to Alexandrov spaces to construct the desired
local Seifert fibration structure on collapsed 3-manifolds. 相似文献
10.
A group is said to be p-rigid, where p is a natural number, if it has a normal series of the form G = G
1 > G
2 > … > G
p
> G
p+1 = 1, whose quotients G
i
/G
i+1 are Abelian and are torsion free when treated as
\mathbbZ \mathbb{Z} [G/G
i
]-modules. Examples of rigid groups are free soluble groups. We point out a recursive system of universal axioms distinguishing
p-rigid groups in the class of p-soluble groups. It is proved that if F is a free p-soluble group, G is an arbitrary p-rigid group, and W is an iterated wreath product of p infinite cyclic groups, then ∀-theories for these groups satisfy the inclusions A(F) ê A(G) ê A(W) \mathcal{A}(F) \supseteq \mathcal{A}(G) \supseteq \mathcal{A}(W) . We construct an ∃-axiom distinguishing among p-rigid groups those that are universally equivalent to W. An arbitrary p-rigid group embeds in a divisible decomposed p-rigid group M = M(α1,…, α
p
). The latter group factors into a semidirect product of Abelian groups A
1
A
2…A
p
, in which case every quotient M
i
/M
i+1 of its rigid series is isomorphic to A
i
and is a divisible module of rank αi over a ring
\mathbbZ \mathbb{Z} [M/M
i
]. We specify a recursive system of axioms distinguishing among M-groups those that are Muniversally equivalent to M. As a consequence, it is stated that the universal theory of M with constants in M is decidable. By contrast, the universal theory of W with constants is undecidable. 相似文献
11.
Liangping Jiang 《Journal of Mathematical Sciences》2011,177(3):395-401
The classical criterion of asymptotic stability of the zero solution of equations x′ = f(t, x) is that there exists a function V (t, x), a(∥x∥) ≤ V (t, x) ≤ b(∥x∥) for some a, b ∈ K such that [(V)\dot] \dot{V} (t, x) ≤ −c(∥x∥) for some c ∈ K. In this paper, we prove that if V(m + 1) \mathop {V}\limits^{(m + {1})} (t, x) is bounded on some set [tk − T, tk + T] × BH(tk → +∞ as k → ∞), then the condition that [(V)\dot] \dot{V} (t, x) ≤ −c(∥x∥) can be weakened and replaced by that [(V)\dot] \dot{V} (t, x) ≤ 0 and − (−[(V)\dot] \dot{V} (tk, x)| + − [(V)\ddot] \ddot{V} (tk, x)| + ⋯ + − V(m) \mathop {V}\limits^{(m)} (tk, x)|) ≤ −c′(∥x∥) for some c′ ∈ K. Moreover, the author also presents a corresponding instability criterion. [1–10] 相似文献
12.
Sara Westreich 《Algebras and Representation Theory》2008,11(1):63-82
We study pointed Hopf algebras of the form U(R
Q
), (Faddeev et al., Quantization of Lie groups and Lie algebras. Algebraic Analysis, vol. I, Academic, Boston, MA, pp. 129–139, 1988; Faddeev et al., Quantum groups. Braid group, knot theory and statistical mechanics. Adv. Ser. Math. Phys., vol. 9, World Science, Teaneck, NJ, pp. 97–110, 1989; Larson and Towber, Commun. Algebra 19(12):3295–3345, 1991), where R
Q
is the Yang–Baxter operator associated with the multiparameter deformation of GL
n
supplied in Artin et al. (Commun. Pure Appl. Math. 44:8–9, 879–895, 1991) and Sudbery (J. Phys. A, 23(15):697–704, 1990). We show that U(R
Q
) is of type A
n
in the sense of Andruskiewitsch and Schneider (Adv. Math. 154:1–45, 2000; Pointed Hopf algebras. Recent developments in Hopf Algebras Theory, MSRI Series, Cambridge University Press, Cambridge, 2002). We consider the non-negative part of U(R
Q
) and show that for two sets of parameters, the corresponding Hopf sub-algebras can be obtained from each other by twisting
the multiplication if and only if they possess the same groups of grouplike elements. We exhibit families of finite-dimensional
Hopf algebras arising from U(R
Q
) with non-isomorphic groups of grouplike elements. We then discuss the case when the quantum determinant is central in A(R
Q
) and show that under some assumptions on the group of grouplike elements, two finite-dimensional Hopf algebras U(R
Q
), U(R
Q′) can be obtained from each other by twisting the comultiplication if and only if In the last part we show that U
Q
is always a quotient of a double crossproduct.
I wish to thank UIC, where some of the work was done, for hospitality. 相似文献
13.
Let G = GL
N
or SL
N
as reductive linear algebraic group over a field k of characteristic p > 0. We prove several results that were previously established only when N ⩽ 5 or p > 2
N
: Let G act rationally on a finitely generated commutative k-algebra A and let grA be the Grosshans graded ring. We show that the cohomology algebra H
*(G, grA) is finitely generated over k. If moreover A has a good filtration and M is a Noetherian A-module with compatible G action, then M has finite good filtration dimension and the H
i
(G, M) are Noetherian A
G
-modules. To obtain results in this generality, we employ functorial resolution of the ideal of the diagonal in a product
of Grassmannians. 相似文献
14.
E. I. Zelenov 《Theoretical and Mathematical Physics》2008,157(3):1707-1712
We consider C*-algebras of commutation relations over the fields ℚ
p, p = 2, 3, 5, …, ∞. We describe all the irreducible separable representations of these algebras. We prove that the algebras
are not isomorphic at different p.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 3, pp. 406–412, December, 2008. 相似文献
15.
Olav Arnfinn Laudal 《Acta Appl Math》2008,101(1-3):191-204
In the papers (Laudal in Contemporary Mathematics, vol. 391, [2005]; Geometry of time-spaces, Report No. 03, [2006/2007]), we introduced the notion of (non-commutative) phase algebras (spaces) Ph
n
(A), n=0,1,…,∞ associated to any associative algebra A (space), defined over a field k. The purpose of this paper is to study this construction in some more detail. This seems to give us a possible framework
for the study of non-commutative partial differential equations. We refer to the paper (Laudal in Phase spaces and deformation
theory, Report No. 09, [2006/2007]), for the applications to non-commutative deformation theory, Massey products and for the construction of the versal family
of families of modules. See also (Laudal in Homology, Homotopy, Appl. 4:357–396, [2002]; Proceedings of NATO Advanced Research Workshop, Computational Commutative and Non-Commutative Algebraic Geometry, [2004]).
相似文献
16.
One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the
Gray tensor product. In this paper we begin to adapt the machinery of globular operads (Batanin, Adv Math 136:39–103, 1998) to this task. We present a general construction of a tensor product on the category of n-globular sets from any normalised (n + 1)-operad A, in such a way that the algebras for A may be recaptured as enriched categories for the induced tensor product. This is an important step in reconciling the globular
and simplicial approaches to higher category theory, because in the simplicial approaches one proceeds inductively following
the idea that a weak (n + 1)-category is something like a category enriched in weak n-categories. In this paper we reveal how such an intuition may be formulated in terms of globular operads. 相似文献
17.
Ascher H. Shapiro 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1958,9(5-6):637-641
Zusammenfassung Es wird ein expliziter Ausdruck für die Wirbelst?rkeω hinter einem gekrümmten Verdichtungsstoss für den Fall der zweidimensionalen Str?mung eines idealen Gases in Termen der Geschwindigkeit
der ungest?rten Str?mungV
∞, ihrer Mach-ZahlM
∞, des Stosswinkelsσ und des Krümmungsradiusr
s
des Verdichtungsstosses im betrachteten Punkt aufgestellt.
Die dimensionslose Wirbelst?rkeω
r
s
/V
∞ h?ngt nur vonM
∞ undσ ab. Bei festgehaltenemM
∞ treten bei einem Stosswinkel von 90° (senkrechter Verdichtungsstoss) und auch dann, wenn der Stosswinkel dem Mach-Winkel
der ungest?rten Str?mung gleich ist (Verdichtungsstoss der Intensit?t Null), keine Wirbel auf. Für einen dazwischenliegenden
Winkel, der von 68° fürM
∞=1,5 bis zu 36° fürM
∞=10 variiert, wird die Wirbelst?rke ein Maximum.
相似文献
18.
19.
Francesco Catino Salvatore Siciliano Ernesto Spinelli 《Algebras and Representation Theory》2010,13(6):653-660
Let L be a non-abelian restricted Lie algebra over a field of characteristic p > 0 and let u(L) denote its restricted enveloping algebra. In Siciliano (Publ Math (Debr) 68:503–513, 2006) it was proved that if u(L) is Lie solvable then the Lie derived length of u(L) is at least ⌈log2(p + 1)⌉. In the present paper we characterize the restricted enveloping algebras whose Lie derived length coincides with this
lower bound. 相似文献
20.
We study additive representability of orders on multisets (of size k drawn from a set of size n) which satisfy the condition of independence of equal submultisets (IES) introduced by Sertel and Slinko (Ranking committees,
words or multisets. Nota di Laboro 50.2002. Center of Operation Research and Economics. The Fundazione Eni Enrico Mattei,
Milan, 2002, Econ. Theory 30(2):265–287, 2007). Here we take a geometric view of those orders, and relate them to certain combinatorial objects which we call discrete
cones. Following Fishburn (J. Math. Psychol., 40:64–77, 1996) and Conder and Slinko (J. Math. Psychol., 48(6):425–431, 2004), we define functions f(n,k) and g(n,k) which measure the maximal possible deviation of an arbitrary order satisfying the IES and an arbitrary almost representable
order satisfying the IES, respectively, from a representable order. We prove that g(n,k) = n − 1 whenever n ≥ 3 and (n, k) ≠ (5, 2). In the exceptional case, g(5,2) = 3. We also prove that g(n,k) ≤ f(n,k) ≤ n and establish that for small n and k the functions g(n,k) and f(n,k) coincide.
相似文献