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101.
J. Płonka 《Algebra Universalis》1995,33(4):441-457
Presented by B. Jónsson. 相似文献
102.
Jarosław Cel 《Journal of Geometry》1995,53(1-2):28-36
It is proved for a nonempty proper subset S of a real topological linear space L that kerS ={convAz: z bdryS} and for a close connected nonconvex subset S of L that kerS ={convAz: z slncS}, where bdryS and slncS denote the sets of boundary points and strong local nonconvexity points of S, respectively, and Az = {s S: z is clearly visible from s via S}.This extends previous results and, combined with standard techniques, yields among others two Krasnosel'skii-type characterizations for the dimension of kerS in Rd in case of a nonempty proper set S with bdryS bounded and a closed connected nonconvex set S with lncS bounded.The assumption of boundedness of S turns out to be irrelevant in these criteria.Herrn Professor Dr. Wilhelm Stoll gewidmetResearch partially supported by the grant PB 2 1140 91 01 相似文献
103.
We prove that certain two-point Padé approximants occupying the diagonal of the Padé table form monotone sequences of lower and upper bounds uniformly converging to a Stieltjes function. The results can be applied to the theory of inhomogeneous media for the calculation of the bounds on the effective transport coefficients of heterogeneous materials. 相似文献
104.
Jarosław Pykacz 《International Journal of Theoretical Physics》1994,33(7):1403-1416
A new, physically more plausible definition of a fuzzy quantum logic is proposed. It is shown that this definition coincides with the previously studied definition of a fuzzy quantum logic; therefore it defines objects which are traditional quantum logics with ordering sets of states. The new definition is expressed exclusively in terms of fuzzy set operations which are generated by connectives of multiple-valued logic studied by ukasiewicz at the beginning of the 20th century. Therefore, the logic of quantum mechanics is recognized as a version of infinite-valued ukasiewicz logic. 相似文献
105.
106.
Let u(x, y) be defined in B
1×B
2 where B
1
m
and B
2
n
, and assume that u(x, ·) harmonic for every fixed x and u(·, y) is subharmonic for every fixed y. We show that if u(·, y) is, in addition, C
2 for each y then u is subharmonic in B
1×B
2 in both variables jointly. 相似文献
107.
The linear ordering problem is an NP-hard combinatorial problem with a large number of applications. Contrary to another very popular problem from the same category, the traveling salesman problem, relatively little space in the literature has been devoted to the linear ordering problem so far. This is particularly true for the question of developing good heuristic algorithms solving this problem.In the paper we propose a new heuristic algorithm solving the linear ordering problem. In this algorithm we made use of the sorting through insertion pattern as well as of the operation of permutation reversal. The surprisingly positive effect of the reversal operation, justified in part theoretically and confirmed in computational examples, seems to be the result of a unique property of the problem, called in the paper the symmetry of the linear ordering problem. This property consists in the fact that if a given permutation is an optimal solution of the problem with the criterion function being maximized, then the reversed permutation is a solution of the problem with the same criterion function being minimized. 相似文献
108.
This paper is devoted to a discussion of the notion of localizability for phonons, i.e., quasiparticles arising from the harmonic vibrations of a system ofn atoms bound to one another by elastic forces. The natural tools for the analysis of localizability are the projection operatorsÊ() acting on the Hilbert space of one-phonon states, where is an arbitrary subset of the set that consists ofn vectors specifying the equilibrium positions ofn atoms. The expectation value ofÊ() is the probability that the phonon belongs to the atoms whose equilibrium positions are characterized by the elements of . For a strongly localizable phonon all of the projection operatorsÊ() commute with one another, whereas in the case of a weakly localizable phonon the operatorsÊ(1) andÊ(2) do not commute when 1 and 2 overlap. With the aid of the Jauch-Piron quantum theory of localization in space, the present paper describes the method of obtainingÊ() and also shows that if in the system ofn atoms there exist normal modes of zero frequency, then the phonon is only weakly localizable. Given the explicit expression forÊ(), one can define the number-of-phonons operator as well as the quasiparticle analogue (given in a companion paper) of the Wigner distribution function. 相似文献
109.
Paweł Hitczenko 《Israel Journal of Mathematics》1993,84(1-2):161-178
Letf
n
= Σ
k=1
n
v
k
r
k
,n=1,…, be a martingale transform of a Rademacher sequence (r
n)and let (r
n
′
) be an independent copy of (r
n).The main result of this paper states that there exists an absolute constantK such that for allp, 1≤p<∞, the following inequality is true:
In order to prove this result, we obtain some inequalities which may be of independent interest. In particular, we show that
for every sequence of scalars (a
n)one has
where
is theK-interpolation norm between ℓ1 and ℓ2. We also derive a new exponential inequality for martingale transforms of a Rademacher sequence.
This research was supported in part by an NSF grant and an FRPD grant at NCSU. 相似文献
110.