共查询到20条相似文献,搜索用时 46 毫秒
1.
Nijjwal Karak 《Czechoslovak Mathematical Journal》2017,67(1):143-150
In many recent articles, medians have been used as a replacement of integral averages when the function fails to be locally integrable. A point x in a metric measure space (X, d, μ) is called a generalized Lebesgue point of a measurable function f if the medians of f over the balls B(x, r) converge to f(x) when r converges to 0. We know that almost every point of a measurable, almost everywhere finite function is a generalized Lebesgue point and the same is true for every point of a continuous function. We show that a function f ∈ M s,p (X), 0 < s ≤ 1, 0 < p < 1, where X is a doubling metric measure space, has generalized Lebesgue points outside a set of \(\mathcal{H}^h\)-Hausdorff measure zero for a suitable gauge function h. 相似文献
2.
A. B. Kostin 《Differential Equations》2016,52(2):220-239
We study the inverse problem of the reconstruction of the coefficient ?(x, t) = ?0(x, t) + r(x) multiplying ut in a nonstationary parabolic equation. Here ?0(x, t) ≥ ?0 > 0 is a given function, and r(x) ≥ 0 is an unknown function of the class L∞(Ω). In addition to the initial and boundary conditions (the data of the direct problem), we pose the problem of nonlocal observation in the form ∫0Tu(x, t) dμ(t) = χ(x) with a known measure dμ(t) and a function χ(x). We separately consider the case dμ(t) = ω(t)dt of integral observation with a smooth function ω(t). We obtain sufficient conditions for the existence and uniqueness of the solution of the inverse problem, which have the form of ready-to-verify inequalities. We suggest an iterative procedure for finding the solution and prove its convergence. Examples of particular inverse problems for which the assumptions of our theorems hold are presented. 相似文献
3.
Let μ be a Radon measure on Rd which may be non–doubling. The only condition satisfied by μ is that μ(B(x, r)) ≤ Cr n for all x ∈ ? d , r > 0 and some fixed 0 < n ≤ d. In this paper, the authors prove that the boundedness from H 1(μ) into L 1,∞(μ) of a singular integral operator T with Calderón–Zygmund kernel of Hörmander type implies its L 2(μ)–boundedness. 相似文献
4.
I. V. Boikov 《Siberian Mathematical Journal》2016,57(3):425-441
Optimal cubature formulas are constructed for calculations of multidimensional integrals in weighted Sobolev spaces. We consider some classes of functions defined in the cube Ω = [-1, 1]l, l = 1, 2,..., and having bounded partial derivatives up to the order r in Ω and the derivatives of jth order (r < j ≤ s) whose modulus tends to infinity as power functions of the form (d(x, Г))-(j-r), where x ∈ Ω Г, x = (x1,..., xl), Г = ?Ω, and d(x, Г) is the distance from x to Г. 相似文献
5.
Let μ be a nonnegative Radon measure on ? d which only satisfies μ (B(x, r)) ? C 0 r n for all x ∈ ? d , r > 0, with some fixed constants C 0 > 0 and n ∈ (0, d]. In this paper, a new characterization for the space RBMO(μ) of Tolsa in terms of the John-Strömberg sharp maximal function is established. 相似文献
6.
T. R. Gadyl’shin 《Mathematical Notes》2015,98(5-6):900-908
This paper deals with boundary-value problems on the closed interval [a, b] for the Schrödinger equation with potential of the form q(x, μ ?1 x) + ε ?1 Q(ε ?1 x), where q(x, ζ) is a 1-periodic (in ζ) function, Q(ξ) is a compactly supported function, 0 ∈ (a, b), and μ, ε are small positive parameters. The solutions of these boundary-value problemsup to O(ε +μ) are constructed by combining the homogenization method and the method of matching asymptotic expansions. 相似文献
7.
Let {Q n (α,β) (x)} n=0 ∞ denote the sequence of polynomials orthogonal with respect to the non-discrete Sobolev inner product where λ>0 and d μ α,β(x)=(x?a)(1?x)α?1(1+x)β?1 dx, d ν α,β(x)=(1?x) α (1+x) β dx with a1, α,β>0. Their inner strong asymptotics on (?1,1), a Mehler-Heine type formula as well as some estimates of the Sobolev norms of Q n (α,β) are obtained.
相似文献
$\langle f,g\rangle=\int_{-1}^{1}f(x)g(x)d\mu_{\alpha,\beta}(x)+\lambda\int_{-1}^{1}f'(x)g'(x)d\nu_{\alpha,\beta}(x)$
8.
Malkhaz Ashordia 《Czechoslovak Mathematical Journal》2017,67(3):579-608
A general theorem (principle of a priori boundedness) on solvability of the boundary value problem dx = dA(t) · f(t, x), h(x) = 0 is established, where f: [a, b]×R n → R n is a vector-function belonging to the Carathéodory class corresponding to the matrix-function A: [a, b] → R n×n with bounded total variation components, and h: BVs([a, b],R n ) → R n is a continuous operator. Basing on the mentioned principle of a priori boundedness, effective criteria are obtained for the solvability of the system under the condition x(t1(x)) = B(x) · x(t 2(x))+c 0, where t i: BVs([a, b],R n ) → [a, b] (i = 1, 2) and B: BVs([a, b], R n ) → R n are continuous operators, and c 0 ∈ R n . 相似文献
9.
Let G be a graph, and g, f: V (G) → Z+ with g(x) ≤ f(x) for each x ∈ V (G). We say that G admits all fractional (g, f)-factors if G contains an fractional r-factor for every r: V (G) → Z+ with g(x) ≤ r(x) ≤ f(x) for any x ∈ V (G). Let H be a subgraph of G. We say that G has all fractional (g, f)-factors excluding H if for every r: V (G) → Z+ with g(x) ≤ r(x) ≤ f(x) for all x ∈ V (G), G has a fractional r-factor F h such that E(H) ∩ E(F h ) = θ, where h: E(G) → [0, 1] is a function. In this paper, we show a characterization for the existence of all fractional (g, f)-factors excluding H and obtain two sufficient conditions for a graph to have all fractional (g, f)-factors excluding H. 相似文献
10.
Let d ≥ 1 and Z be a subordinate Brownian motion on R~d with infinitesimal generator ? + ψ(?),where ψ is the Laplace exponent of a one-dimensional non-decreasing L′evy process(called subordinator). We establish the existence and uniqueness of fundamental solution(also called heat kernel) pb(t, x, y) for non-local operator L~b= ? + ψ(?) + b ?, where Rb is an Rd-valued function in Kato class K_(d,1). We show that p~b(t, x, y)is jointly continuous and derive its sharp two-sided estimates. The kernel pb(t, x, y) determines a conservative Feller process X. We further show that the law of X is the unique solution of the martingale problem for(L~b, C_c~∞(R~d)) and X is a weak solution of Xt = X0+ Zt + integral from n=0 to t(b(Xs)ds, t ≥ 0).Moreover, we prove that the above stochastic differential equation has a unique weak solution. 相似文献
11.
In this paper we present an infeasible-interior-point algorithm, based on a new wide neighbourhood N(τ1, τ2, η), for linear programming over symmetric cones. We treat the classical Newton direction as the sum of two other directions. We prove that if these two directions are equipped with different and appropriate step sizes, then the new algorithm has a polynomial convergence for the commutative class of search directions. In particular, the complexity bound is O(r1.5logε?1) for the Nesterov-Todd (NT) direction, and O(r2logε?1) for the xs and sx directions, where r is the rank of the associated Euclidean Jordan algebra and ε > 0 is the required precision. If starting with a feasible point (x0, y0, s0) in N(τ1, τ2, η), the complexity bound is \(O\left( {\sqrt r \log {\varepsilon ^{ - 1}}} \right)\) for the NT direction, and O(rlogε?1) for the xs and sx directions. When the NT search direction is used, we get the best complexity bound of wide neighborhood interior-point algorithm for linear programming over symmetric cones. 相似文献
12.
The problem considered here can be viewed as the analogue in higher dimensions of the one variable polynomial interpolation of Lagrange and Newton. Let x1,...,xr be closed points in general position in projective spacePn, then the linear subspaceV ofH0 (?n,O(d)) (the space of homogeneous polynomials of degreed on ?n) formed by those polynomials which are singular at eachxi, is given by r(n + 1) linear equations in the coefficients, expressing the fact that the polynomial vanishes with its first derivatives at x1,...,xr. As such, the “expected” value for the dimension ofV is max(0,h0(O(d))?r(n+1)). We prove thatV has the “expected” dimension for d≥5 (theorem A). This theorem was first proven in [A] using a very complicated induction with many initial cases. Here we give a greatly simplified proof using techniques developed by the authors while treating the corresponding problem in lower degrees. 相似文献
13.
Let G =(V,E) be a locally finite graph,whose measure μ(x) has positive lower bound,and A be the usual graph Laplacian.Applying the mountain-pass theorem due to Ambrosetti and Rabinowitz(1973),we establish existence results for some nonlinear equations,namely △u+hu=f(x,u),x∈V.In particular,we prove that if h and f satisfy certain assumptions,then the above-mentioned equation has strictly positive solutions.Also,we consider existence of positive solutions of the perturbed equation △u+hu=f(x,u)+∈g.Similar problems have been extensively studied on the Euclidean space as well as on Riemannian manifolds. 相似文献
14.
Alain Escassut Ta Thi Hoai An 《P-Adic Numbers, Ultrametric Analysis, and Applications》2018,10(1):12-31
Let IK be an algebraically closed field of characteristic 0 complete for an ultrametric absolute value. Following results obtained in complex analysis, here we examine problems of uniqueness for meromorphic functions having finitely many poles, sharing points or a pair of sets (C.M. or I.M.) defined either in the whole field IK or in an open disk, or in the complement of an open disk. Following previous works in C, we consider functions fn(x)fm(ax + b), gn(x)gm(ax + b) with |a| = 1 and n ≠ m, sharing a rational function and we show that f/g is a n + m-th root of 1 whenever n + m ≥ 5. Next, given a small function w, if n, m ∈ IN are such that |n ? m|∞ ≥ 5, then fn(x)fm(ax + b) ? w has infinitely many zeros. Finally, we examine branched values for meromorphic functions fn(x)fm(ax + b). 相似文献
15.
A. S. Pushnyakov 《Computational Mathematics and Mathematical Physics》2018,58(4):612-620
A compact metric space with a bounded Borel measure is considered. Any measurable set of diameter not exceeding r is called r-cluster. The existence of a collection consisting of a fixed number of 2r-clusters possessing the following properties is investigated: the clusters are located at the distance r from each other and the collection measure (the total measure of the clusters in the collection) is close to the measure of the entire space. It is proved that there exists a collection with a maximum measure among such collections. The concept of r-parametric discretization of the distribution of distances into short, medium, and long distances is defined. In terms of this discretization, a lower bound on the measure of the maximum-measure collection is obtained. 相似文献
16.
Basudeb Dhara 《Czechoslovak Mathematical Journal》2018,68(1):95-119
Let R be a noncommutative prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, let F, G and H be three generalized derivations of R, I an ideal of R and f(x1,..., x n ) a multilinear polynomial over C which is not central valued on R. If for all r = (r1,..., r n ) ∈ I n , then one of the following conditions holds:
相似文献
$$F(f(r))G(f(r)) = H(f(r)^2 )$$
- (1)there exist a ∈ C and b ∈ U such that F(x) = ax, G(x) = xb and H(x) = xab for all x ∈ R
- (2)there exist a, b ∈ U such that F(x) = xa, G(x) = bx and H(x) = abx for all x ∈ R, with ab ∈ C
- (3)there exist b ∈ C and a ∈ U such that F(x) = ax, G(x) = bx and H(x) = abx for all x ∈ R
- (4)f(x1,..., x n )2 is central valued on R and one of the following conditions holds
- (a)there exist a, b, p, p’ ∈ U such that F(x) = ax, G(x) = xb and H(x) = px + xp’ for all x ∈ R, with ab = p + p’
- (b)there exist a, b, p, p’ ∈ U such that F(x) = xa, G(x) = bx and H(x) = px + xp’ for all x ∈ R, with p + p’ = ab ∈ C.
- (a)
17.
A. V. Lipnitskii 《Differential Equations》2008,44(8):1072-1081
We construct a linear differential system \(\dot x\) = (A(t) + μB(t))x, x ∈ ?2, t ≥ 0, with almost periodic coefficients which is almost reducible for all μ ∈ ? except for an at most countable set and whose singular and higher characteristic exponents treated as functions of the parameter μ are discontinuous at some point. 相似文献
18.
ZhangJie Wang 《中国科学 数学(英文版)》2017,60(4):593-612
Given a large positive number x and a positive integer k, we denote by Qk(x) the set of congruent elliptic curves E(n): y2= z3- n2 z with positive square-free integers n x congruent to one modulo eight,having k prime factors and each prime factor congruent to one modulo four. We obtain the asymptotic formula for the number of congruent elliptic curves E(n)∈ Qk(x) with Mordell-Weil ranks zero and 2-primary part of Shafarevich-Tate groups isomorphic to(Z/2Z)2. We also get a lower bound for the number of E(n)∈ Qk(x)with Mordell-Weil ranks zero and 2-primary part of Shafarevich-Tate groups isomorphic to(Z/2Z)4. The key ingredient of the proof of these results is an independence property of residue symbols. This property roughly says that the number of positive square-free integers n x with k prime factors and residue symbols(quadratic and quartic) among its prime factors being given compatible values does not depend on the actual values. 相似文献
19.
David Kalaj 《Israel Journal of Mathematics》2005,150(1):241-251
We give the new inequality related to the J. C. C. Nitsche conjecture (see [6]). Moreover, we consider the two- and three-dimensional case. LetA(r, 1)={z:r<|z|<1}. Nitsche's conjecture states that if there exists a univalent harmonic mapping from an annulusA(r, 1), to an annulusA(s, 1), thens is at most 2r/(r 2+1).Lyzzaik's result states thats<t wheret is the length of the Grötzsch's ring domain associated withA(r, 1) (see [5]). Weitsman's result states thats≤1/(1+1/2(r logr)2) (see [8]).Our result for two-dimensional space states thats≤1/(1+1/2 log2 r) which improves Weitsman's bound for allr, and Lyzzaik's bound forr close to 1. For three-dimensional space the result states thats≤1/(r?logr). 相似文献
20.
We consider the Neumann problem outside a small neighborhood of a planar disk in the three-dimensional space. The surface of this neighborhood is assumed to be smooth, and its thickness is characterized by a small parameter ε. A uniform asymptotic expansion of the solution of this problem with respect to ε is constructed by the matching method. Since the problem turned out to be bisingular, an additional inner asymptotic expansion in the so-called stretched variables is constructed near the edge of the disk. A physical interpretation of the solution of this boundary value problem is the velocity potential of a laminar flow of an ideal fluid around a thin body, which is the neighborhood of the disk. It is assumed that this flow has unit velocity at a large distance from the disk, which is equivalent to the following condition for the potential: u(x1, x2, x3, ε) = x3+O(r?2) as r → ∞, where r is the distance to the origin. The boundary condition of this problem is the impermeability of the surface of the body: ?u/?n = 0 at the boundary. After subtracting x3 from the solution u(x1, x2, x3, ε), we get a boundary value problem for the potential ?(x1, x2, x3, ε) of the perturbed motion. Since the integral of the function ??/?n over the surface of the body is zero, we have ?(x1, x2, x3, ε) = O(r?2) as r → ∞. Hence, all the coefficients of the outer asymptotic expansion with respect to ε have the same behavior at infinity. However, these coefficients have growing singularities at the approach to the edge of the disk, which implies the bisingularity of the problem. 相似文献