共查询到20条相似文献,搜索用时 46 毫秒
1.
R. N. Boyarinov 《Moscow University Mathematics Bulletin》2010,65(3):132-134
A theorem for the sign variation of the argument of the Riemann zeta function S(t) in the interval (t − A, t + A) with A = 4.39 ln ln ln ln T for each t, T ≤ t ≤ T + H excluding values from the set E with the measure mes(E) = O(H(ln ln T)−1(ln ln ln T)−0,5) is proved. 相似文献
2.
We study the Navier-Stokes equations for compressible barotropic fluids in a bounded or unbounded domain Ω of R3. We first prove the local existence of solutions (ρ,u) in C([0,T*]; (ρ∞ +H3(Ω)) × under the assumption that the data satisfies a natural compatibility condition. Then deriving the smoothing effect of the
velocity u in t>0, we conclude that (ρ,u) is a classical solution in (0,T**)×Ω for some T** ∈ (0,T*]. For these results, the initial density needs not be bounded below away from zero and may vanish in an open subset (vacuum) of Ω. 相似文献
3.
M. N. Mishra B. L. S. Prakasa Rao 《Statistical Inference for Stochastic Processes》2011,14(2):101-109
Consider a stochastic process {X
t
, 0 ≤ t ≤ T} governed by a stochastic differential equation given by
dXt = S(Xt) dt + e dWtH, X0=x0, 0 £ t £ T dX_t= S(X_t) \;dt + \epsilon \; dW_t^H,\quad X_0=x_0,\quad 0 \leq t \leq T 相似文献
4.
IfG andH are graphs, let us writeG→(H)2 ifG contains a monochromatic copy ofH in any 2-colouring of the edges ofG. Thesize-Ramsey number
r
e(H) of a graphH is the smallest possible number of edges a graphG may have ifG→(H)2. SupposeT is a tree of order |T|≥2, and lett
0,t
1 be the cardinalities of the vertex classes ofT as a bipartite graph, and let Δ(T) be the maximal degree ofT. Moreover, let Δ0, Δ1 be the maxima of the degrees of the vertices in the respective vertex classes, and letβ(T)=T
0Δ0+t
1Δ1. Beck [7] proved thatβ(T)/4≤r
e(T)=O{β(T)(log|T|)12}, improving on a previous result of his [6] stating thatr
e(T)≤Δ(T)|T|(log|T|)12. In [6], Beck conjectures thatr
e(T)=O{Δ(T)|T|}, and in [7] he puts forward the stronger conjecture thatr
e(T)=O{β(T)}. Here, we prove the first of these conjectures, and come quite close to proving the second by showing thatr
e(T)=O{β(T)logΔ(T)}. 相似文献
5.
Piernicola Bettiol 《Journal of Mathematical Sciences》2007,144(1):3760-3774
Consider an initial Lagrangian submanifold Λ0 ⊂ T* ℝ
n
that admits a global generating function and a Hamiltonian isotopy Φ
H
t
. Then, we provide a global generating function for the Lagrangian submanifold Λ
t
= Φ
H
t
(Λ0) realized by applying the so-called Amann-Conley-Zehnder reduction. When Λ0 is the zero-section, we study in some detail the asymptotic behavior of such generating functions and give an approximation
result.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal
Conference-2004, Part 1, 2005. 相似文献
6.
Yu. N. Skiba 《Journal of Mathematical Sciences》2008,149(6):1708-1725
The dynamics of perturbations to the Rossby-Haurwitz (RH) wave is analytically analyzed. These waves, being of great meteorological
importance, are exact solutions to the nonlinear vorticity equation describing the motion of an ideal incompressible fluid
on a rotating sphere. Each RH wave belongs to a space H
1 ⊕ H
n
, where H
n
is the subspace of homogeneous spherical polynomials of degree n. It is shown that any perturbation of the RH wave evolves in such a way that its energy K(t) and enstrophy η(t) decrease, remain constant, or increase simultaneously. A geometric interpretation of variations in the perturbation energy
is given. A conservation law for arbitrary perturbations is obtained and used to classify all the RH-wave perturbations in
four invariant sets, M
−
n
, M
+
n
, H
n
, and M
0
n
− H
n
, depending on the value of their mean spectral number χ(t) = η(t)/K(t). The energy cascade of growing (or decaying) perturbations has opposite directions in the sets M
−
n
and M
+
n
due to the hyperbolic dependence between K(t) and χ(t). A factor space with a factor norm of the perturbations is introduced, using the invariant subspace H
n
of neutral perturbations as the zero factor class. While the energy norm controls the perturbation part belonging to H
n
, the factor norm controls the perturbation part orthogonal to H
n
. It is shown that in the set M
−
n
(χ(t) < n(n + 1)), any nonzonal RH wave of subspace H
1 ⊕ H
n
(n ≥ 2) is Lyapunov unstable in the energy norm. This instability has nothing in common with the orbital (Poincaré) instability
and is caused by asynchronous oscillations of two almost coinciding RH-wave solutions. It is also shown that the exponential
instability is possible only in the invariant set M
0
n
− H
n
. A necessary condition for this instability is given. The condition states that the spectral number η(t) of the amplitude of each unstable mode must be equal to n(n + 1), where n is the RH wave degree. The growth rate is estimated and the orthogonality of the unstable normal modes to the RH wave are
shown in two Hilbert spaces. The instability in the invariant set M
+
n
of small-scale perturbations (χ(t) > n(n + 1)) is still an open problem.
__________
Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 17, Differential and Functional Differential Equations. Part 3, 2006. 相似文献
7.
R. Norvaiša 《Lithuanian Mathematical Journal》2008,48(4):418-426
Let B
H,K
= {B
H,K
(t)}
t⩾0 be a bifractional Brownian motion with parameters H ∈ (0, 1) and K ∈ (0, 1]. For a function Φ: [0, ∞) → [0, ∞) and for a partition κ = {t
i
}n
i=0 of an interval [0, T] with T > 0, let {ie418-01}. We prove that, for a suitable Φ depending on H and K, {ie418-02} almost surely.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-16/08 相似文献
8.
For a triple {V, H, V*} of Hilbert spaces, we consider an evolution inclusion of the form u′(t)+A(t)u(t)+δϕ(t, u(t)) ∋
f(t), u(0) = u0, t ∈ (0, T ], where A(t) and ϕ(t, ·), t ∈ [0, T], are a family of nonlinear operators from V to V * and a family of convex lower semicontinuous functionals with common effective domain D(ϕ) ⊂ V. We indicate conditions on the data under which there exists a unique solution of the problem in the space H
1(0, T; V)∩W
∞1 (0, T;H) and the implicit Euler method has first-order accuracy in the energy norm. 相似文献
9.
Werner Georg Nowak 《Monatshefte für Mathematik》2002,137(3):227-238
This article is concerned with sums 𝒮(t) = ∑
n
ψ(tf(n/t)) where ψ denotes, essentially, the fractional part minus ?, f is a C
4-function with f″ ≠ 0 throughout, summation being extended over an interval of order t. We establish an asymptotic formula for ∫
T−Λ
T+Λ
(𝒮(t))2dt for any Λ = Λ(T) growing faster than log T.
Received April 30, 2001; in revised form February 15, 2002
RID="a"
ID="a" Dedicated to Professor Edmund Hlawka on the occasion of his 85th birthday 相似文献
10.
LetX be a Banach space and letA be the infinitesimal generator of a differentiable semigroup {T(t) |t ≥ 0}, i.e. aC
0-semigroup such thatt ↦T(t)x is differentiable on (0, ∞) for everyx εX. LetB be a bounded linear operator onX and let {S(t) |t ≥ 0} be the semigroup generated byA +B. Renardy recently gave an example which shows that {S(t) |t ≥ 0} need not be differentiable. In this paper we give a condition on the growth of ‖T′(t)‖ ast ↓ 0 which is sufficient to ensure that {S(t) |t ≥ 0} is differentiable. Moreover, we use Renardy’s example to study the optimality of our growth condition. Our results can
be summarized roughly as follows:
11.
We obtain an existence result for global solutions to initial-value problems for Riccati equations of the form R′(t) + TR(t) + R(t)T = Tρ A(t)T1?ρ + Tρ B(t)T1?ρ R(t) + R(t)TρC(t) T1?ρ + R(t)TρD(t)T1?ρ R(t), R(0)=R0, where 0 ? ρ ? 1 and where the functions R and A through D take on values in the cone of non-negative bounded linear operators on L1 (0, W; μ). T is an unbounded multiplication operator. This problem is of particular interest in case ρ = 1 since it arisess in the theories of particle transport and radiative transfer in a slab. However, in this case there are some serious difficulties associated with this equation, which lead us to define a solution for the case ρ = 1 as the limit of solutions for the cases 0 < ρ < 1. 相似文献
12.
G. A. Seregin 《Journal of Mathematical Sciences》2011,178(3):345-352
Assuming that T is a potential blow-up time, it is shown that the
H\frac12 {H^{\frac{1}{2}}} -norm of the velocity field goes to ∞ as the time t approaches T. Bibliography: 9 titles. 相似文献
13.
Let M^n be a smooth, compact manifold without boundary, and F0 : M^n→ R^n+1 a smooth immersion which is convex. The one-parameter families F(·, t) : M^n× [0, T) → R^n+1 of hypersurfaces Mt^n= F(·,t)(M^n) satisfy an initial value problem dF/dt (·,t) = -H^k(· ,t)v(· ,t), F(· ,0) = F0(· ), where H is the mean curvature and u(·,t) is the outer unit normal at F(·, t), such that -Hu = H is the mean curvature vector, and k 〉 0 is a constant. This problem is called H^k-fiow. Such flow will develop singularities after finite time. According to the blow-up rate of the square norm of the second fundamental forms, the authors analyze the structure of the rescaled limit by classifying the singularities as two types, i.e., Type Ⅰ and Type Ⅱ. It is proved that for Type Ⅰ singularity, the limiting hypersurface satisfies an elliptic equation; for Type Ⅱ singularity, the limiting hypersurface must be a translating soliton. 相似文献
14.
Mustapha Mokhtar-Kharroubi 《Journal of Evolution Equations》2008,8(2):327-352
We deal with streaming operators T
H
defined in L
1 spaces by the directional derivative with positive boundary operator H of norm 1 relating the incoming and outgoing fluxes. It is known that T
H
need not be a generator but there exists a contraction semigroup generated by an extension A of T
H
. This paper deals with the total mass carried by individual trajectories {e
tA
f; t ≥ 0} for nonnegative initial data f and related topics. In particular, our analysis covers the problem of (the lack of) stochasticity of {e
tA
; t ≥ 0} for conservative boundary operator H.
相似文献
15.
A semigroup [T(t)] on a Hilbert space is exponentially stable if there exist real constants M≥1 and α>0 such that ∥T(t)∥≤Me
−αt
for every t≥0. If [T(t)] is a strongly continuous contraction semigroup, then it is proved that we can set M=1 in the definition of exponential stability if and only if the generator A of [T(t)] is boundedly strict dissipative (just a strict dissipative A is not enough). 相似文献
16.
Nam Q. Le 《Geometriae Dedicata》2011,151(1):361-371
Consider a family of smooth immersions
F(·,t) : Mn? \mathbbRn+1{F(\cdot,t)\,:\,{M^n\to \mathbb{R}^{n+1}}} of closed hypersurfaces in
\mathbbRn+1{\mathbb{R}^{n+1}} moving by the mean curvature flow
\frac?F(p,t)?t = -H(p,t)·n(p,t){\frac{\partial F(p,t)}{\partial t} = -H(p,t)\cdot \nu(p,t)}, for t ? [0,T){t\in [0,T)}. We show that at the first singular time of the mean curvature flow, certain subcritical quantities concerning the second
fundamental form, for example
ò0tòMs\frac|A|n + 2 log (2 + |A|) dmds,{\int_{0}^{t}\int_{M_{s}}\frac{{\vert{\it A}\vert}^{n + 2}}{ log (2 + {\vert{\it A}\vert})}} d\mu ds, blow up. Our result is a log improvement of recent results of Le-Sesum, Xu-Ye-Zhao where the scaling invariant quantities
were considered. 相似文献
17.
Let T(t), t ≥ 0, be a C
0-semigroup of linear operators acting in a Hilbert space H with norm ‖·‖. We prove that T(t) is uniformly bounded, i.e., ‖T(t)‖ ≤ M, t ≥ 0, if and only if the following condition is satisfied:
18.
V. I. Borzdyko 《Ukrainian Mathematical Journal》2008,60(3):339-356
We consider an operator (variable hysteron) used to describe a nonstationary hysteresis nonlinearity (whose characteristics
vary under the action of external forces) according to the Krasnosel’skii-Pokrovskii scheme. Sufficient conditions under which
the operator is defined for the inputs from the class of functions H
1[t
0, T] satisfying the Lipschitz condition in the segment [t
0, T] are established.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 3, pp. 295–309, March, 2008. 相似文献
19.
Fritz Gesztesy Alexander Gomilko Fedor Sukochev Yuri Tomilov 《Israel Journal of Mathematics》2012,188(1):195-219
The purpose of this note is to answer a question A. E. Nussbaum formulated in 1964 about the possible equivalence between
weak measurability of a family of densely defined, closed operators {T(t)}
t∈ℝ in a separable complex Hilbert space H\mathcal{H} on one hand, and the notion of measurability of the 2 × 2 operator-valued matrix of projections {(P(Γ(T(t)))
j,k
)1⩽j,k⩽2}
t∈ℝ onto the graph Γ(T(t)) of T(t) on the other, in the negative. 相似文献
20.
We show that if the pseudodifferential operator −q(x,D) generates a Feller semigroup (Tt)t≥0 then the Feller semigroups (Tt(v))t≥0 generated by the pseudodifferential operators with symbol will converge strongly to (Tt)t≥0 as ν →∞. 相似文献
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