共查询到20条相似文献,搜索用时 31 毫秒
1.
Peter J. Slater 《Discrete Mathematics》1981,34(2):185-193
The concept of a k-sequential graph is presented as follows. A graph G with ∣V(G)∪ E(G)∣=t is called k-sequential if there is a bijection such that for each edgein E(G) one has. A graph that is 1-sequential is called simply sequential, and, in particular the author has conjectured that all trees are simply sequential. In this paper an introductory study of k-sequential graphs is made. Further, several variations on the problems of gracefully or sequentially numbering the elements of a graph are discussed. 相似文献
2.
A finite set A = {a1 < … <an}? ? is said to be convex if the sequence (ai ? ai?1)ni=2 is strictly increasing. Using an estimate of the additive energy of convex sets, one can estimate the size of the sumset as ∣A + A∣ ? ∣A∣102/65, which slightly sharpens Shkredov’s latest result ∣A + A∣ ? ∣A∣58/37.
相似文献3.
J. Qian D.Q. Miao Z.H. Zhang W. Li 《International Journal of Approximate Reasoning》2011,52(2):212-230
Attribute reduction is one of the key issues in rough set theory. Many heuristic attribute reduction algorithms such as positive-region reduction, information entropy reduction and discernibility matrix reduction have been proposed. However, these methods are usually computationally time-consuming for large data. Moreover, a single attribute significance measure is not good for more attributes with the same greatest value. To overcome these shortcomings, we first introduce a counting sort algorithm with time complexity O(∣C∣ ∣U∣) for dealing with redundant and inconsistent data in a decision table and computing positive regions and core attributes (∣C∣ and ∣U∣ denote the cardinalities of condition attributes and objects set, respectively). Then, hybrid attribute measures are constructed which reflect the significance of an attribute in positive regions and boundary regions. Finally, hybrid approaches to attribute reduction based on indiscernibility and discernibility relation are proposed with time complexity no more than max(O(∣C∣2∣U/C∣), O(∣C∣∣U∣)), in which ∣U/C∣ denotes the cardinality of the equivalence classes set U/C. The experimental results show that these proposed hybrid algorithms are effective and feasible for large data. 相似文献
4.
It is shown in this paper that the Schrodinger operator with a potential satisfying ∣V(x)∣ ≤ M/∣x∣2a.e. in the unit ball B has the strong unique continuation property in H2,2(B) for for n≥2. 相似文献
5.
A Lyapunov transformation is a linear transformation on the set n of hermitian matrices H ? n,n of the form A(H) = A1H + HA, where A ?n,n. Given a positive stable A ?n,n, the Stein-Pfeffer Theorem characterizes those K ? n for which K = B(H), where B is similar to A and H is positive definite. We give a new proof of this result, and extend it in several directions. The proofs involve the idea of a controllability subspace, employed previously in this context by Snyders and Zakai. 相似文献
6.
Let V be an n-dimentional unitary space with inner product (·,·) and S the set {x∈V:(x, x)=1}. For any A∈Hom(V, V) and with ∣q∣?1, we define . If q=1, then W(A:q) is just the classical numerical range {(Ax, x):x∈S}, the convexity of which is well known. Another generalization of the numerical range is the C-numerical range, which is defined to be the set where C∈Hom(V, V). In this note, we prove that W(A:q) is always convex and that WC(A) is convex for all A if rank C=1 or n=2. 相似文献
7.
Stephen M. Paneitz 《Journal of Functional Analysis》1981,41(3):315-326
Let Sp() be the symplectic group for a complex Hibert space . Its Lie algebra sp() contains an open invariant convex cone C0; each element of C0 commutes with a unique sympletic complex structure. The Cayley transform : X∈ sp()→(I + X)1∈ Sp() is analyzed and compared with the exponential mapping. As an application we consider equations of the form is strongly continuous, and show that if ∝?∞∞ ∥A(t)∥ dt < 2 and ∝? t8∞A(t) dt?C0, the (scattering) operator , where St′(t) is the solution such that St′(t′) = I, is in the range of restricted to C0. It follows that S leaves invariant a unique complex structure; in particular, it is conjugate in Sp() to a unitary operator. 相似文献
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9.
Let M = (S, I) be a matroid of finite character on the infinite set S. Let be any system of subsets of S each having finite rank and let be a finite system of sets of arbitrary rank. Necessary and sufficient conditions are given for the system ? to have an independent system of distinct representatives. 相似文献
10.
The matrix equation is studied, under the assumption that (A, B1) is controllable, but allowing nonhermitian S. An inequality is given relating the dimensions of the eigenspaces of A and of the null space of S. In particular, if B has rank 1 and S is nonsingular, then S is hermitian, and the inertias of A and S are equal. Other inertial results are obtained, the role of the controllability of (A1, B1S1) is studied, and a class of D-stable matrices is determined. 相似文献
11.
Derek W Robinson 《Journal of Functional Analysis》1983,51(3):268-284
Let (, +, ∥ · ∥) denote a Banach space , ordered by a proper norm-closed convex cone +, with a Riesz norm ∥ · ∥, and define the canonical half-norm N associated with + by . The analogs of the Hille-Yosida and Feller-Miyadera-Phillips theorems characterizing the generators H of C0- or C01-semigroups S = {St}t ? 0 of positive operators, i.e., operators such that St+?+, are proved. In these theorems conditions of norm-dissipativity, e.g., are replaced by N-dissipativity, i.e., . 相似文献
12.
The sample size required for determination of a given degree of difference between two therapies or modalities A and B being compared with each other, supposing that the sample sizes are equal, is given by Here Cα/2 is the upper α/2 percentile point of the standard normal distribution, C1?β is the abscissa cutting off the proportion 1?β in its upper tail and β in its lower tail; pA and pB are the probabilities of favorable response to A and B; if p?A and p?B are the corresponding measured proportions, then = (p?A + p?B); and the Q's are 1 minus the p's. When it is desirable to use unequal size groups, the sample sizes n1 相似文献
13.
Gary H Meisters 《Journal of Functional Analysis》1977,26(1):68-88
In an earlier paper (Translation-invariant linear forms and a formula for the Dirac measure, J. Functional Analysis8 (1971), 173–188) the author proved that the ratio of two real numbers is a non-Liouville number if and only if there exist two Schwartz distributions A and B with compact supports on the real line such that δ′ = A ? ταA + B ? τβB. The present paper presents (in Section 3) a completely new and more elementary proof of this result (stated fully as Theorems 1 and 2 at the end of Section 1) based on some fundamental properties of the mapping H0 = ? Δ and H = H0 + T, where T which are established in Section 2. Further connections with Diophantine approximation (badly approximable numbers and Roth's Theorem) are presented in Section 4 where it is proved that the orders of the distributions A and B are always ?2 (Theorem 3) and almost always =3 (Theorem 4). Section 5 contains some partial results (Theorem 5 and Corollary 2 of Theorem 6) on the analogous question (as yet unsettled) for the Banach space C(T) of all continuous functions on the circle group T, and connects this problem with Sidon sets of integers. 相似文献
14.
Gerd Wittstock 《Journal of Functional Analysis》1981,40(2):127-150
We generalize Arveson's extension theorem for completely positive mappings [1] to a Hahn-Banach principle for matricial sublinear functionals with values in an injective C1-algebra or an ideal in B(). We characterize injective W1-algebras by a matricial order condition. We illustrate the matricial Hahn-Banach principle by three applications: (1) Let be unital C1-algebras, a subalgebra of and injective. If ?: → is a completely bounded self-adjoint -bihomomorphism, then it can be expressed as the difference of two completely positive -bihomomorphism. (2) Let be a W1-algebra, containing 1, on a Hilbert space . If is finite and hyperfinite, there exists an invariant expectation mapping P of B() onto ′. P is an extension of the center trace. (3) Combes [7] proved, that a lower semicontinuous scalar weight on a C1-algebra is the upper envelope of bounded positive functionals. We generalize this result to unbounded completely positive mappings with values in an injective W1-algebra. 相似文献
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16.
Ryuzaburo Noda 《Journal of Combinatorial Theory, Series A》1978,24(1):89-95
t?(2k, k, λ) designs having a property similar to that of Hadamard 3-designs are studied. We consider conditions (i), (ii), or (iii) for t?(2k, k, λ) designs: (i) The complement of each block is a block. (ii) If A and B are a complementary pair of blocks, then ∥ A ∩ C ∥ = ∥ B ∩ C ∥ ± u holds for any block C distinct from A and B, where u is a positive integer. (iii) if A and B are a complementary pair of blocks, then ∥ A ∩ C ∥ = ∥ B ∩ C ∥ or ∥ A ∩ C ∥ = ∥ B ∩ C ∥ ± u holds for any block C distinct from A and B, where u is a positive integer. We show that a t?(2k, k, λ) design with t ? 2 and with properties (i) and (ii) is a 3?(2u(2u + 1), u(2u + 1), u(2u2 + u ? 2)) design, and that a t?(2k, k, λ) design with t ? 4 and with properties (i) and (iii) is the 5-(12, 6, 1) design, the 4-(8, 4, 1) design, a design, or a design. 相似文献
17.
Jean-Bernard Baillon 《Journal of Functional Analysis》1978,29(2):199-213
Let C be a closed convex subset of a uniformly smooth Banach space. Let S(t) : C → C be a semigroup of type ω. Then the generator A0 of S(t) has a dense domain in C. Moreover there is is an operator A such that: (i) A0 ? A and accretive, (iii) R(I + λA) ? C for λ > 0 and ωλ < 1, (iv) for every x?C. 相似文献
18.
Peter Bundschuh 《Journal of Number Theory》1984,18(1):91-98
In two previous papers Nettler proved the transcendence of the continued fractions , as well as the transcendence of the numbers A + B, A ? B, AB, where the a's and b's are positive integers satisfying a certain mutual growth condition. In the present paper even the algebraic independence of A and B is proved under almost the same condition and furthermore a result concerning the transcendency of AB is established. 相似文献
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20.
Kenneth R Davidson 《Journal of Functional Analysis》1982,48(1):20-42
Given a commuting pair 1, 2 of abelian subalgebras of the Calkin algebra, we look for a commuting pair 1,2 of subalgebras of which project onto 1 and 2. We do not insist that i, be abelian, so i, may contain nontrivial compact operators. If X is the joint spectrum σ(1, 2), it is shown that the existence of a pair 1, 2 depends only on the element τ in Ext(X) determined by 1, 2. The set L(X) of those τ in Ext(X) which “lift” in this sense is shown to be a subgroup of Ext(X) when Ext(X) is Hausdorff, and also when i are singly generated. In this latter case, L(X) can be explicitly calculated for large classes of joint spectra. These results are applied to lift certain pairs of commuting elements of the Calkin algebra to pairs of commuting operators. 相似文献