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81.
The aim of this paper is to study necessary conditions for existence of weak solutions of the inequality
82.
Regina Sandra Burachik B. F. Svaiter 《Proceedings of the American Mathematical Society》2003,131(8):2379-2383
Recently, the authors studied the connection between each maximal monotone operator and a family of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities.
The aim of this paper is to establish the converse of the latter fact. Namely, that every convex function satisfying those two particular inequalities is associated to a unique maximal monotone operator.
83.
84.
Let be a graph with diameter d 2. Recall is 1-homogeneous (in the sense of Nomura) whenever for every edge xy of the distance partition{{z V() | (z, y) = i, (x, z) = j} | 0 i, j d}is equitable and its parameters do not depend on the edge xy. Let be 1-homogeneous. Then is distance-regular and also locally strongly regular with parameters (v,k,,), where v = k, k = a
1, (v – k – 1) = k(k – 1 – ) and c
2 + 1, since a -graph is a regular graph with valency . If c
2 = + 1 and c
2 1, then is a Terwilliger graph, i.e., all the -graphs of are complete. In [11] we classified the Terwilliger 1-homogeneous graphs with c
2 2 and obtained that there are only three such examples. In this article we consider the case c
2 = + 2 3, i.e., the case when the -graphs of are the Cocktail Party graphs, and obtain that either = 0, = 2 or is one of the following graphs: (i) a Johnson graph J(2m, m) with m 2, (ii) a folded Johnson graph J¯(4m, 2m) with m 3, (iii) a halved m-cube with m 4, (iv) a folded halved (2m)-cube with m 5, (v) a Cocktail Party graph K
m × 2 with m 3, (vi) the Schläfli graph, (vii) the Gosset graph. 相似文献
85.
Mirko Lepović 《Journal of Applied Mathematics and Computing》2003,11(1-2):109-122
A tree is called starlike if it has exactly one vertex of degree greater than two. In [4] it was proved that two starlike treesG andH are cospectral if and only if they are isomorphic. We prove here that there exist no two non-isomorphic Laplacian cospectral starlike trees. Further, letG be a simple graph of ordern with vertex setV(G)={1,2, …,n} and letH={H 1,H 2, ...H n } be a family of rooted graphs. According to [2], the rooted productG(H) is the graph obtained by identifying the root ofH i with thei-th vertex ofG. In particular, ifH is the family of the paths $P_{k_1 } , P_{k_2 } , ..., P_{k_n } $ with the rooted vertices of degree one, in this paper the corresponding graphG(H) is called the sunlike graph and is denoted byG(k 1,k 2, …,k n ). For any (x 1,x 2, …,x n ) ∈I * n , whereI *={0,1}, letG(x 1,x 2, …,x n ) be the subgraph ofG which is obtained by deleting the verticesi 1, i2, …,i j ∈ V(G) (0≤j≤n), provided that $x_{i_1 } = x_{i_2 } = ... = x_{i_j } = 0$ . LetG(x 1,x 2,…, x n] be the characteristic polynomial ofG(x 1,x 2,…, x n ), understanding thatG[0, 0, …, 0] ≡ 1. We prove that $$G[k_1 , k_2 ,..., k_n ] = \Sigma _{x \in ^{I_ * ^n } } \left[ {\Pi _{i = 1}^n P_{k_i + x_i - 2} (\lambda )} \right]( - 1)^{n - (\mathop \Sigma \limits_{i = 1}^n x_i )} G[x_1 , x_2 , ..., x_n ]$$ where x=(x 1,x 2,…,x n );G[k 1,k 2,…,k n ] andP n (γ) denote the characteristic polynomial ofG(k 1,k 2,…,k n ) andP n , respectively. Besides, ifG is a graph with λ1(G)≥1 we show that λ1(G)≤λ1(G(k 1,k 2, ...,k n )) < for all positive integersk 1,k 2,…,k n , where λ1 denotes the largest eigenvalue. 相似文献
86.
Dragomir Ž. Đoković 《Combinatorica》1994,14(3):375-377
No Hadamard matrices of order 956 appear in the literature. In this note we construct two such matrices. They are both of Goethals-Seidel type. As a consequence of this and of a result of Seberry and Yamada, we conclude that there exist 4-Williamson type matrices of order 1913.This work was supported by NSERC of Canada Grants A-5285 and EQP0107539. 相似文献
87.
Vladimir Dobrić 《Journal of Theoretical Probability》1994,7(1):129-134
IfB is a weakly compactly generated Banach space andf: (S,S, ) satisfies the strong law of large numbers, thenf=f
1+f
2, wheref
1 is Bochner -integrable andf
2 is Pettis -integrable with Pettis norm 0. The decomposition is unique. 相似文献
88.
Ilija Lukačević 《General Relativity and Gravitation》1983,15(6):523-533
Two vector fields are considered, a timelike one,u
, and an arbitrary one, . The relative expansion and rotation are defined with respect to these fields, their mutual relations are studied, and some general formulas obtained. Applications are made, first to vector fields which are mutually nonrotating in a plane-symmetric metric, then to the electromagnetic field of an arbitrary magnetohydrodynamic fluid. 相似文献
89.
L. Janićijević 《Optical and Quantum Electronics》1985,17(2):125-138
Realized as an interferogram of a spherical and a cylindrical wave, the elliptical hologram is treated as a plane diffracting grating which produces Fresnel diffraction of a simple astigmatic gaussian incident wave. It is shown that if the principal axes of the incident beam coincide with the principal axes of the hologram, the diffracted wave field is composed of three different astigmatic gaussian waves, with their waists situated in parallel but distinct planes. The diffraction pattern, observed on a transverse screen, is the result of the interference of the three diffracted wave components. It consists of three systems of overlapped second-order curves, whose shape depends on the distance of the observation screen from the hologram, as well as on the parameters of the incident wave beam and the hologram. The results are specialized for gratings in the form of circular and linear holograms and for the case of a stigmatic gaussian incident wave, as well as for the normal plane-wave incidence on the three mentioned types of hologram. 相似文献
90.
We calculate the density of states for the nondegenerate Anderson model for various values ofu=U/ andn
f
using the perturbation theory withu as the expansion parameter. Summing all the -independent self-energy diagrams, we use the Friedel sum rule and Ward identities to express the physical quantities in terms of the remaining -dependent part of the self-energy, which we evaluate to the 2nd order. The results for the spin and charge susceptibilities obtained in such a way compare rather well with the Bethe-ansatz results. The density of states exhibits different features in different parts of the parameter space. In Kondo region (u>1,n
f
1, i.e., –
f
~U/2), we obtain a many-body resonance (half-width T
K
) around the Fermi level and two broad peaks () at about
f
+n
f
U and
f
+U. In the VF region (u>1, and |
f
|) we obtain only two peaks (), one at about
f
and one between
f
+n
f
U and
f
+U. The consequences regarding the shape of the photoemission and inverse photoemission spectra of Ce intermetallics are discussed. 相似文献