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91.
Using a probabilistic approach, the parallel dynamics of fully connected Q-Ising neural networks is studied for arbitrary Q. A novel recursive scheme is set up to determine the time evolution of the order parameters through the evolution of the distribution of the local field, taking into account all feedback correlations. In contrast to extremely diluted and layered network architectures, the local field is no longer normally distributed but contains a discrete part. As an illustrative example, an explicit analysis is carried out for the first four time steps. For the case of the Q = 2 and Q = 3 model the results are compared with extensive numerical simulations and excellent agreement is found. Finally, equilibrium fixed-point equations are derived and compared with the thermodynamic approach based upon the replica-symmetric mean-field approximation. 相似文献
92.
Abstract Let D be arbitrary simply connected domain with at least two boundary points.We have introduced a kind of analytic functions' space H_■~V (D) (p≥1, q>0)and shown that it is a complete linear space with respect to the norm ■·||_(H_q~p(D)). 相似文献
93.
Eric L. McDowell 《Proceedings of the American Mathematical Society》1998,126(12):3733-3741
The notion of a multi-valued absolute fixed point set (MAFS) will be defined and characterized in the setting of set-valued maps with images containing multiple components.
94.
We construct connected, locally connected, almost regular, countable, Urysohn spaces. This answers a problem of G.X. Ritter. We show that there are 2c such non-homeomorphic spaces. We also show that there are 2c non-homeomorphic spaces which are further rigid. We discuss the group of homeomorphisms of such spaces.The following question was raised by G.X. Ritter: Does there exist a countable connected locally connected Urysohn space which is almost regular? We answer this question in the affirmative and in fact, show that not only are there as many as 2c such spaces but that there are just as many rigid spaces with the same properties. Furthermore we show that every countable Urysohn space is a subspace of such a space. We also prove that every countable group is isomorphic to the group of autohomeomorphisms of some connected locally connected almost regular Urysohn space. Examples are given of groups of order c which can be represented in this manner. 相似文献
95.
A new metric diameter for a locally connected metric frame is constructed which is finer than the original one. Amongst other results, this construction allows a proof that the category of uniformly locally connected metric frames and uniform frame maps is reflective in the category of locally connected metric frames and uniform frame maps.
Mathematics Subject Classification (2000) 54A05. 相似文献
96.
Shin Satoh 《Proceedings of the American Mathematical Society》2005,133(2):613-616
Any surface-knot in 4-space can be projected into 3-space with a finite number of triple points, and its triple point number, , is defined similarly to the crossing number of a classical knot. By definition, we have for the connected sum. In this paper, we give infinitely many pairs of surface-knots for which this equality does not hold.
97.
A finite algebra is said to be order-primal if its clone of all term operations is the set of all operations defined on A which preserve a given partial order ≤ on A. In this paper we study algebraic properties of order-primal algebras for connected ordered sets (A; ≤). Such order-primal algebras are constantive, simple and have no non-identical automorphisms. We show that in this case cannot have only unary fundamental operations or only one at least binary fundamental operation. We prove several properties of the varieties and the quasi-varieties generated by constantive and simple algebras and apply these properties to order-primal algebras. Further, we use the properties of order-primal algebras to formulate new primality criteria for finite algebras.* Research supported by the Hungarian research grant No. TO34137 and by the János Bolyai grant.** Research supported by the Thailand Research Fund. 相似文献
98.
An automated quasi three-dimensional finite element grid generation method is presented for particular three-dimensional complex connected domain, across which some are simply connected two-dimensional.regions and some are multiply connected two-dimensional regions. A subdivision algorithm based on the variational principle has been developed to ascertain the smoothness and orthogonality of the generated grid in any cross sections. Smooth transition between the simply and multiply connected regions is maintained. For illustration, the method is applied to generate a finite element three-dimensional grid for human above knee stump. 相似文献
99.
100.