共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, the following facts are stated in the setting of b-metric spaces.
相似文献
- (1)The contraction constant in the Banach contraction principle fully extends to [0, 1), but the contraction constants in Reich’s fixed point theorem and many other fixed point theorems do not fully extend to [0, 1), which answers the early stated question on transforming fixed point theorems in metric spaces to fixed point theorems in b-metric spaces.
- (2) Caristi’s theorem does not fully extend to b-metric spaces, which is a negative answer to a recent Kirk–Shahzad’s question (Remark 12.6) [Fixed Point Theory in Distance Spaces. Springer, 2014].
2.
Let K be a Hausdorff space and C
b
(K) be the Banach algebra of all complex bounded continuous functions on K. We study the Gateaux and Fréchet differentiability of subspaces of C
b
(K). Using this, we show that the set of all strong peak functions in a nontrivial separating separable subspace H of C
b
(K) is a dense G
δ subset of H, if K is compact. This gives a generalized Bishop’s theorem, which says that the closure of the set of all strong peak points for
H is the smallest closed norming subset of H. The classical Bishop’s theorem was proved for a separating subalgebra H and a metrizable compact space K. 相似文献
3.
Banaschewski’s theorem concerns subdirect product decompositions of lattice ordered groups. In the present paper we deal with
the analogous investigation for the case of generalized MV -algebras (GMV -algebras, in short); we apply this notion in the sense studied by Galatos and Tsinakis. 相似文献
4.
We use the method of local representation and original method of Brauer to study the block with K(B)−L(B)=1, and get some properties on the defect group and the structure of this kind of blocks. Then, we show that K(B) conjecture holds for this kind of blocks. 相似文献
5.
Shin-ichi Ohta 《Journal of Geometric Analysis》2016,26(3):2067-2096
We extend the range of N to negative values in the (K, N)-convexity (in the sense of Erbar–Kuwada–Sturm), the weighted Ricci curvature \(\mathop {\mathrm {Ric}}\nolimits _N\) and the curvature-dimension condition \(\mathop {\mathrm {CD}}\nolimits (K,N)\). We generalize a number of results in the case of \(N>0\) to this setting, including Bochner’s inequality, the Brunn–Minkowski inequality and the equivalence between \(\mathop {\mathrm {Ric}}\nolimits _N \ge K\) and \(\mathop {\mathrm {CD}}\nolimits (K,N)\). We also show an expansion bound for gradient flows of Lipschitz (K, N)-convex functions. 相似文献
6.
Claudia Alfes 《The Ramanujan Journal》2010,22(2):163-169
Recently, Bruinier and Ono investigated the arithmetic of the coefficients of Ramanujan’s mock theta function ω(q). In Ramanujan J. (submitted) they obtained congruences with respect to the modulus 512. Here we show that ω(q) modulo 5 is dictated by an elliptic curve. 相似文献
7.
V. K. Chaubey A. Mishra 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2017,52(1):1-7
In the present paper we study the Finslerian hypersurfaces of a Finsler space with a special (α, β) metric, and examine the hypersurfaces of this special metric as a hyperplane of first, second and third kinds. 相似文献
8.
Let x and y be two variables satisfying the commutation relation xy=qyx+hf(y), where f(y) is a polynomial. In this paper, using Young diagrams and generating functions techniques, we study the binomial formula
(x+y)
n
and we present an identity for x
m
y. The connection to Operator Calculus is discussed and several special cases are treated explicitly. 相似文献
9.
Jiri Rohn 《Optimization Letters》2012,6(3):585-591
A theorem of the alternatives for the equation \({|Ax|-|B||x|=b\ (A,B\in{\mathbb{R}}^{n\times n},\, b\in{\mathbb{R}}^n)}\) is proved and several consequences are drawn. In particular, a class of matrices A, B is identified for which the equation has exactly 2 n solutions for each positive right-hand side b. 相似文献
10.
We prove the modularity of certain residually reducible p-adic Galois representations of an imaginary quadratic field assuming the uniqueness of the residual representation. We obtain
an R = T theorem using a new commutative algebra criterion that might be of independent interest. To apply the criterion, one needs
to show that the quotient of the universal deformation ring R by its ideal of reducibility is cyclic Artinian of order no greater than the order of the congruence module T/J, where J is an Eisenstein ideal in the local Hecke algebra T. The inequality is proven by applying the Main conjecture of Iwasawa Theory for Hecke characters and using a result of Berger
[Compos Math 145(3):603–632, 2009]. This strengthens our previous result [Berger and Klosin, J Inst Math Jussieu 8(4):669–692,
2009] to include the cases of an arbitrary p-adic valuation of the L-value, in particular, cases when R is not a discrete valuation ring. As a consequence we show that the Eisenstein ideal is principal and that T is a complete intersection. 相似文献
11.
This paper presents an approach using a recursive algorithm for packing (?, w)-rectangles into larger rectangular and L-shaped pieces. Such a problem has actual applications for non-guillotine cutting and pallet/container loading. Our motivation for developing the L-approach is based on the fact that it can solve difficult pallet loading instances. Indeed, it is able to solve all testing problems (more than 20 000 representatives of infinite equivalence classes of the literature), including the 18 hard instances unresolved by other heuristics. We conjecture that the L-approach always finds optimum packings of (?, w)-rectangles into rectangular pieces. Moreover, the approach may also be useful when dealing with cutting and packing problems involving L-shaped pieces. 相似文献
12.
The aim of the paper is to obtain some theoretical and numerical properties of Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices (PRM). In the case of 3 × 3 PRM, a differentiable one-to-one correspondence is given between Saaty’s inconsistency ratio and Koczkodaj’s inconsistency index based on the elements of PRM. In order to make a comparison of Saaty’s and Koczkodaj’s inconsistencies for 4 × 4 pairwise comparison matrices, the average value of the maximal eigenvalues of randomly generated
n × n
PRM is formulated, the elements a
ij
(i < j) of which were randomly chosen from the ratio scale
with equal probability 1/(2M − 1) and a
ji
is defined as 1/a
ij
. By statistical analysis, the empirical distributions of the maximal eigenvalues of the PRM depending on the dimension number are obtained. As the dimension number increases, the shape of distributions gets similar
to that of the normal ones. Finally, the inconsistency of asymmetry is dealt with, showing a different type of inconsistency. 相似文献
13.
We investigate the relation between analytic Campanato spaces \(\mathcal {AL}_{p,s}\) and the spaces F(p, q, s), characterize the bounded and compact Riemann–Stieltjes operators from \(\mathcal {AL}_{p,s}\) to \(F(p,p-s-1,s)\). We also describe the corona theorem and the interpolating sequences for the class \(F(p,p-2,s)\), which is the Möbius invariant subspace of the analytic Besov type spaces \(B_p(s)\). 相似文献
14.
It is proved unconditionally that every sufficiently large positive integer satisfying some necessary congruence conditions can be represented as the sum of s almost equal k-th powers of prime numbers for 2 ≤ k ≤ 10 and s =2k + 1, which gives a short interval version of Hun's theorem. 相似文献
15.
In this paper, the structure of the critical group of the graph K
m
× C
n
is determined, where m, n ≥ 3. 相似文献
16.
Crossing numbers of graphs are in general very difficult to compute. There are several known exact results on the crossing
number of the Cartesian products of paths, cycles or stars with small graphs. In this paper we study cr(Km □ Pn), the crossing number of the Cartesian product Km □ Pn. We prove that
for m ≥ 3,n ≥ 1 and cr(Km □ Pn)≥ (n − 1)cr(Km+2 − e) + 2cr(Km+1). For m≤ 5, according to Klešč, Jendrol and Ščerbová, the equality holds. In this paper, we also prove that the equality holds for
m = 6, i.e., cr(K6 □ Pn) = 15n + 3.
Research supported by NFSC (60373096, 60573022). 相似文献
17.
David J. Grynkiewicz 《Israel Journal of Mathematics》2010,177(1):413-439
Let t ≥ 1, let A and B be finite, nonempty subsets of an abelian group G, and let $
A\mathop + \limits_i B
$
A\mathop + \limits_i B
denote all the elements c with at least i representations of the form c = a + b, with a ∈ A and b ∈ B. For |A|, |B| ≥ t, we show that either
$
\sum\limits_{i = 1}^t {|A\mathop + \limits_i B| \geqslant t|A| + t|B| - 2t^2 + 1,}
$
\sum\limits_{i = 1}^t {|A\mathop + \limits_i B| \geqslant t|A| + t|B| - 2t^2 + 1,}
相似文献
18.
The notion of derivatives for smooth representations of GL(n, ? p ) was defined in [BZ77]. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations in [Sah89] and called the “adduced” representation. In this paper we define derivatives of all orders for smooth admissible Fréchet representations of moderate growth. The real case is more problematic than the p-adic case; for example, arbitrary derivatives need not be admissible. However, the highest derivative continues being admissible, and for irreducible unitarizable representations coincides with the space of smooth vectors of the adduced representation.In the companion paper [AGS] we prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations.We apply those results to finish the computation of adduced representations for all irreducible unitary representations and to prove uniqueness of degenerate Whittaker models for unitary representations, thus completing the results of [Sah89, Sah90, SaSt90, GS13a]. 相似文献
19.
We show, conditional on a uniform version of the prime k-tuples conjecture, that there are x/(log x)1+o(1) numbers not exceeding x common to the ranges of φ and σ. Here φ is Euler’s totient function and σ is the sum-of-divisors function. 相似文献
20.
Jingjing Ma 《Algebra Universalis》2011,65(4):341-351
It is shown that a unital finite-dimensional ℓ-simple ℓ-algebra with a distributive basis is isomorphic to a lattice-ordered matrix algebra with the entrywise lattice order over
a lattice-ordered twisted group algebra of a finite group with the coordinatewise lattice order. It is also shown that the
isomorphism is unique. 相似文献
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