共查询到20条相似文献,搜索用时 46 毫秒
1.
Alessio Porretta 《Annali di Matematica Pura ed Applicata》1999,177(1):143-172
Summary We prove existence results for the initial-boundary value problem for parabolic equations of the type
where ω is a bounded open subset ofR
N and T>0, A is a pseudomonotone operator of Leray-Lions type defined in L2(), T; H
0
1
(ω), u0 is in L1 (ω) and g(x, t, s) is only assumed to be a Carathéodory function satisfying a sign condition. The result is achieved by proving
the strong convergence in L2 (0, T; H
0
1
(ω)) of trucations of solutions of approximating problems with L1 converging data. To underline the importance of this tool, we show how it can be used for getting other existence theorems,
dealing in particular with the following class of Cauchy-Dirichlet problems:
where ΦεC0 (R, R
N) and the data f and u0 are still taken in L1(Q) and L1(ω) respectively.
Entrata in Redazione il 2 aprile 1998. 相似文献
2.
Michel WEBER 《数学学报(英文版)》2006,22(2):377-382
Let D be an increasing sequence of positive integers, and consider the divisor functions:
d(n, D) =∑d|n,d∈D,d≤√n1, d2(n,D)=∑[d,δ]|n,d,δ∈D,[d,δ]≤√n1,
where [d,δ]=1.c.m.(d,δ). A probabilistic argument is introduced to evaluate the series ∑n=1^∞and(n,D) and ∑n=1^∞and2(n,D). 相似文献
3.
A. B. Khasanov 《Theoretical and Mathematical Physics》1994,99(1):396-401
Functionsp(x) andq(x) for which the Dirac operator $$Dy = \left( {\begin{array}{*{20}c} {\begin{array}{*{20}c} 0 \\ { - 1} \\ \end{array} } & {\begin{array}{*{20}c} 1 \\ 0 \\ \end{array} } \\ \end{array} } \right)\frac{{dy}}{{dx}} + \left( {\begin{array}{*{20}c} {p(x) q(x)} \\ {q(x) - p(x)} \\ \end{array} } \right)y = \lambda y, y = \left( {\begin{array}{*{20}c} {y_1 } \\ {y_2 } \\ \end{array} } \right), y_1 (0) = 0,$$ has a countable number of eigenvalues in the continuous spectrum are constructed. 相似文献
4.
This paper is a continuation of [3]. Suppose f∈Hp(T), 0σ r σ f,σ=1/p?1. When p=1, it is just the partial Fourier sums Skf. In this paper we establish the sharp estimations on the degree of approximation: $$\left\{ { - \frac{1}{{logR}}\int\limits_1^R {\left\| {\sigma _r^\delta f - f} \right\|_{H^p (T)}^p \frac{{dr}}{r}} } \right\}^{1/p} \leqq C{\mathbf{ }}{}_p\omega \left( {f,{\mathbf{ }}( - \frac{1}{{logR}})^{1/p} } \right)_{H^p (T)} ,0< p< 1,$$ and \(\frac{1}{{\log L}}\sum\limits_{k - 1}^L {\frac{{\left\| {S_k f - f} \right\|_H 1_{(T)} }}{k} \leqq Cp\omega (f; - \frac{1}{{\log L}})_H 1_{(T)} } \) Where $$\omega (f,{\mathbf{ }}h)_{H^p (T)} \begin{array}{*{20}c} { = Sup} \\ {0 \leqq \left| u \right| \leqq h} \\ \end{array} \left\| {f( \cdot + u) - f( \cdot )} \right\|_{H^p (T).} $$ . 相似文献
5.
Adimurthi Jacques Giacomoni 《NoDEA : Nonlinear Differential Equations and Applications》2005,12(1):1-20
This paper deals with the existence and the behaviour of global connected branches of positive solutions of the problem
We consider a function h which is smooth and changes sign. 相似文献
6.
Cao Jiading 《分析论及其应用》1989,5(2):99-109
Let an≥0 and F(u)∈C [0,1], Sikkema constructed polynomials:
, ifα
n
≡0, then Bn (0, F, x) are Bernstein polynomials.
Let
, we constructe new polynomials in this paper:
Q
n
(k)
(α
n
,f(t))=d
k
/dx
k
B
n+k
(α
n
,F
k
(u),x), which are called Sikkema-Kantorovic polynomials of order k. Ifα
n
≡0, k=1, then Qn
(1) (0, f(t), x) are Kantorovič polynomials Pn(f). Ifα
n
=0, k=2, then Qn
(2), (0, f(t), x) are Kantorovič polynomials of second order (see Nagel). The main result is:
Theorem 2. Let 1≤p≤∞, in order that for every f∈LP [0, 1],
, it is sufficient and necessary that
,
§ 1. Let f(t) de a continuous function on [a, b], i. e., f∈C [a, b], we define[1–2],[8–10]:
.
As usual, for the space Lp [a,b](1≤p<∞), we have
and L[a, b]=l1[a, b].
Letα
n
⩾0and F(u)∈C[0,1],Sikkema-Bernstein polynomials
[3] [4].
The author expresses his thanks to Professor M. W. Müller of Dortmund University at West Germany for his supports. 相似文献
7.
Let τ(n) be the Ramanujan τ-function, x ≥ 10 be an integer parameter. We prove that
We also show that
where ω(n) is the number of distinct prime divisors of n and p denotes prime numbers. These estimates improve several results from [6, 9].
Received: 23 November 2006 相似文献
8.
IfK is a field of characteristic 0 then the following is shown. Iff, g, h: M
n
(K) K are non-constant solutions of the Binet—Pexider functional equation
相似文献
9.
In this paper, we consider the stochastic Dirac operatoron a polish space (Ω,β, P). The relation between the Lyapunov index, rotation number andthe spectrum of L_ω is discussed. The existence of the Lyapunov index and rotation number isshown. By using the W-T functions and W-function we prove the theorems for L_ω as in Kotani[1], [2] for Schrodinger operatorB, and in Johnson [5] for Dirac operators on compact space. 相似文献
10.
We consider an eigenvalue problem for a system on [0, 1]:
$$\left\{ {\begin{array}{*{20}l} {\left[ {\left( {\begin{array}{*{20}c} 0 & 1 \\ 1 & 0 \\ \end{array} } \right)\frac{{\text{d}}}
{{{\text{d}}x}} + \left( {\begin{array}{*{20}c} {p_{11} (x)} & {p_{12} (x)} \\ {p_{21} (x)} & {p_{22} (x)} \\ \end{array}
} \right)} \right]\left( {\begin{array}{*{20}c} {\varphi ^{(1)} (x)} \\ {\varphi ^{(2)} (x)} \\ \end{array} } \right) =
\lambda \left( {\begin{array}{*{20}c} {\varphi ^{(1)} (x)} \\ {\varphi ^{(1)} (x)} \\ \end{array} } \right)} \\ {\varphi
^{(2)} (0)\cosh \mu - \varphi ^{(1)} (0)\sinh \mu = \varphi ^{(2)} (1)\cosh \nu + \varphi ^{(1)} (1)\sinh \nu = 0} \\ \end{array}
} \right.$$ with constants
$$\mu ,\nu \in \mathbb{C}.$$ Under the assumption that p21, p22 are known, we prove a uniqueness theorem and provide a reconstruction formula for p11 and p12 from the spectral characteristics consisting of one spectrum and the associated norming constants. 相似文献
11.
Richard P. Stanley 《Graphs and Combinatorics》1987,3(1):55-66
I. Bárány and L. Lovász [Acta Math. Acad. Sci. Hung.40, 323–329 (1982)] showed that ad-dimensional centrally-symmetric simplicial polytopeP has at least 2
d
facets, and conjectured a lower bound for the numberf
i
ofi-dimensional faces ofP in terms ofd and the numberf
0 =2n of vertices. Define integers
A. Björner conjectured (unpublished) that
(which generalizes the result of Bárány-Lovász sincef
d–1
= h
i
), and more strongly that
, which is easily seen to imply the conjecture of Bárány-Lovász. In this paper the conjectures of Björner are proved.Partially supported by NSF grant MCS-8104855. The research was performed when the author was a Sherman Fairchild Distinguished Scholar at Caltech. 相似文献
12.
Wavelengths and wavenumbers of the band heads in the region 3915–3540 Å are recorded as obtained from the measurements of the plates taken on a first order 21-feet grating spectrograph. Earlier workers recently reported 40 bands of this system covering the region 3900–3800 Å. All the bands of this system obtained in the present experiments are analysed as involving the3 Π (1) state for lower state. The constants for the lower state are such that they represent well the ΔG (v+1/2) values obtained in the present experiments fromv=0 tov=26 as well as those obtained by Brown fromv=9 tov=43. The vibrational constants of the two states involved are:
$$\begin{gathered} \begin{array}{*{20}c} {\omega _e ^{\prime \prime } } \\ {137 \cdot 8 cm.^{ - 1} ,} \\ \end{array} \begin{array}{*{20}c} {\omega _e ^{\prime \prime } x_e ^{\prime \prime } } \\ {0 \cdot 571 cm.^{ - 1} } \\ \end{array} \begin{array}{*{20}c} {\omega _e ^{\prime \prime } y_e ^{\prime \prime } } \\ { - 0 \cdot 1156 cm.^{ - 1} } \\ \end{array} \begin{array}{*{20}c} {\omega _e z_e ^{\prime \prime } } \\ {3 \cdot 09 \times 10^{ - 3} cm.^{ - 1} } \\ \end{array} \hfill \\ \begin{array}{*{20}c} {\omega _e ^{\prime \prime } t_e ^{\prime \prime } } \\ { - 2 \cdot 5 \times 10^{ - 5} cm.^{ - 1} ,} \\ \end{array} \begin{array}{*{20}c} {\omega _e ^\prime } \\ {90 \cdot 1 cm.^{ - 1} ,} \\ \end{array} \begin{array}{*{20}c} {\omega _e ^\prime x_e ^\prime } \\ {0 \cdot 15 cm.^{ - 1} } \\ \end{array} \hfill \\ \end{gathered} $$ 相似文献
13.
In the present paper, the following Dirichlet problem and Neumann problem involving the p-Laplacian
14.
We consider the question of evaluating the normalizing multiplier $$\gamma _{n,k} = \frac{1}{\pi }\int_{ - \pi }^\pi {\left( {\frac{{sin\tfrac{{nt}}{2}}}{{sin\tfrac{t}{2}}}} \right)^{2k} dt} $$ for the generalized Jackson kernel J n,k (t). We obtain the explicit formula $$\gamma _{n,k} = 2\sum\limits_{p = 0}^{\left[ {k - \tfrac{k}{n}} \right]} {( - 1)\left( {\begin{array}{*{20}c} {2k} \\ p \\ \end{array} } \right)\left( {\begin{array}{*{20}c} {k(n + 1) - np - 1} \\ {k(n - 1) - np} \\ \end{array} } \right)} $$ and the representation $$\gamma _{n,k} = \sqrt {\frac{{24}}{\pi }} \cdot \frac{{(n - 1)^{2k - 1} }}{{\sqrt {2k - 1} }}\left[ {1\frac{1}{8} \cdot \frac{1}{{2k - 1}} + \omega (n,k)} \right],$$ , where $$\left| {\omega (n,k)} \right| < \frac{4}{{(2k - 1)\sqrt {ln(2k - 1)} }} + \sqrt {12\pi } \cdot \frac{{k^{\tfrac{3}{2}} }}{{n - 1}}\left( {1 + \frac{1}{{n - 1}}} \right)^{2k - 2} .$$ . 相似文献
15.
We investigate here a new numerical method, base on the Laguerre inequalities, for determining lower bounds for the de Bruijn-Newman constant ∧, which is related to the Riemann Hypothesis. (Specifically, the truth of the Riemann Hypothesis would imply that ∧≦0.) Unlike previous methods which involved either finding nonreal zeros of associated Jensen polynomials or finding nonreal zeros of a certain real entire function, this new method depends only on evaluating, in real arithmetic, the Laguerre difference $$L_1 (H_\lambda (x))\begin{array}{*{20}c} {\text{.}} \\ {\text{.}} \\ \end{array} = (H'_\lambda (x))^2 - H_\lambda (x) \cdot H''_{_\lambda } (x){\text{ (}}x,{\text{ }}\lambda \in \mathbb{R}{\text{)}}$$ where \((H_\lambda (z)\begin{array}{*{20}c} {\text{.}} \\ {\text{.}} \\ \end{array} = \int_0^\infty {e^{\lambda t^2 } \Phi (t)}\) cos(tz)dt is a real entire function. We apply this method to obtain the new lower bound for ∧, -0.0991 < ∧ which improves all previously published lower bounds for ∧. 相似文献
16.
Letn>1. The number of all strictly increasing selfmappings of a 2n-element crown is
. The number of all order-preserving selfmappings of a 2n-element crown is
|
设为首页 | 免责声明 | 关于勤云 | 加入收藏 |
Copyright©北京勤云科技发展有限公司 京ICP备09084417号 |