共查询到20条相似文献,搜索用时 31 毫秒
1.
E. A. Sheina 《Differential Equations》2010,46(3):415-427
In the present paper, we consider a quasilinear elliptic equation in ℝ
N
with a parameter whose values lie in a neighborhood of an eigenvalue of the linear problem. To prove the existence of a nontrivial
solution, we use a modification of the conditional mountain pass method. The difficulties related to the lack of compactness
of the Sobolev operator in the case of an unbounded domain are eliminated with the use of the Lions concentration-compactness
method. 相似文献
2.
We obtain an analog of the Poincaré-Bertrand formula for a singular Cauchy-Szegö integral in a multidimensional ball. We understand the principal value of the integral in the Cauchy sense. The obtained formula differs from that of Poincaré-Bertrand for the Cauchy integral in a complex plane. 相似文献
3.
Nitis Mukhopadhyay 《Methodology and Computing in Applied Probability》2010,12(4):609-622
In this communication, we first compare z
α
and t
ν,α
, the upper 100α% points of a standard normal and a Student’s t
ν
distributions respectively. We begin with a proof of a well-known result, namely, for every fixed
0 < a < \frac120<\alpha <\frac{1}{2} and the degree of freedom ν, one has t
ν,α
> z
α
. Next, Theorem 3.1 provides a new and explicit expression b
ν
( > 1) such that for every fixed
0 < a < \frac120<\alpha < \frac{1}{2} and ν, we can conclude t
ν,α
> b
ν
z
α
. This is clearly a significant improvement over the result that is customarily quoted in nearly every textbook and elsewhere.
A proof of Theorem 3.1 is surprisingly simple and pretty. We also extend Theorem 3.1 in the case of a non-central Student’s
t distribution (Section 3.3). In the context of Stein’s (Ann Math Stat 16:243–258, 1945; Econometrica 17:77–78, 1949) 100(1 − α)% fixed-width confidence intervals for the mean of a normal distribution having an unknown variance, we have examined the
oversampling rate on an average for a variety of choices of m, the pilot sample size. We ran simulations to investigate this issue. We have found that the oversampling rates are approximated
well by tn,a/22za/2-2t_{\nu ,\alpha /2}^{2}z_{\alpha /2}^{-2} for small and moderate values of m( ≤ 50) all across Table 2 where ν = m − 1. However, when m is chosen large (≥ 100), we find from Table 3 that the oversampling rates are not approximated by tn,a/22za/2-2t_{\nu ,\alpha /2}^{2}z_{\alpha /2}^{-2} very well anymore in some cases, and in those cases the oversampling rates either exceed the new lower bound of tn,a/22za/2-2,t_{\nu ,\alpha /2}^{2}z_{\alpha /2}^{-2}, namely bn2,b_{\nu }^{2}, or comes incredibly close to bn2b_{\nu }^{2} where ν = m − 1. That is, the new lower bound for a percentile of a Student’s t distribution may play an important role in order to come up with diagnostics in our understanding of simulated output under
Stein’s fixed-width confidence interval method. 相似文献
4.
M. Aassila 《Rendiconti del Circolo Matematico di Palermo》2002,51(1):207-212
In this note we investigate the asymptotic behavior of solutions to the wave equation:u"-Δu+g(u')=0 in ℝnxℝ+. 相似文献
5.
F. Andreu J. M. Mazón J. D. Rossi J. Toledo 《Calculus of Variations and Partial Differential Equations》2009,35(3):279-316
In this paper, we study the nonlocal ∞-Laplacian type diffusion equation obtained as the limit as p → ∞ to the nonlocal analogous to the p-Laplacian evolution,
We prove exist ence and uniqueness of a limit solution that verifies an equation governed by the subdifferential of a convex
energy functional associated to the indicator function of the set . We also find some explicit examples of solutions to the limit equation. If the kernel J is rescaled in an appropriate way, we show that the solutions to the corresponding nonlocal problems converge strongly in
L
∞(0, T; L
2 (Ω)) to the limit solution of the local evolutions of the p-Laplacian, v
t
= Δ
p
v. This last limit problem has been proposed as a model to describe the formation of a sandpile. Moreover, we also analyze
the collapse of the initial condition when it does not belong to K by means of a suitable rescale of the solution that describes the initial layer that appears for p large. Finally, we give an interpretation of the limit problem in terms of Monge–Kantorovich mass transport theory.
F. Andreu, J. M. Mazón and J. Toledo were supported by the Spanish MEC and FEDER, project MTM2005-00620, and by the project
ACOMP2007/112 from Generalitat Valenciana. J. D. Rossi was partially supported by Generalitat Valenciana under AINV2007/03
and ANPCyT PICT 5009, UBA X066 and CONICET (Argentina). 相似文献
6.
Michael Winkler 《Mathematical Methods in the Applied Sciences》2010,33(1):12-24
The parabolic–parabolic Keller–Segel system for chemotaxis phenomena, is considered under homogeneous Neumann boundary conditions in a smooth bounded domain Ω??n with n?2. It is proved that if ψ(u)/?(u) grows faster than u2/n as u→∞ and some further technical conditions are fulfilled, then there exist solutions that blow up in either finite or infinite time. Here, the total mass ∫Ωu(x, t)dx may attain arbitrarily small positive values. In particular, in the framework of chemotaxis models incorporating a volume‐filling effect in the sense of Painter and Hillen (Can. Appl. Math. Q. 2002; 10 (4):501–543), the results indicate how strongly the cellular movement must be inhibited at large cell densities in order to rule out chemotactic collapse. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
7.
8.
向量不等式|a·b|≤|a|·|b|是向量的一个重要性质,本文例谈它的应用. 相似文献
9.
《Quaestiones Mathematicae》2013,36(4):539-545
The Padé table of 2 F 1(a, 1; c; z) is normal for c > a > 0 (cf. [4]). For m ≥ n - 1 and c ? Z-, the denominator polynomial Q mn (z) in the [m/n] Padé approximant P mn (z)/Q mn (z) for 2 F 1(a, 1; c; z) and the remainder term Q mn (z)2 F 1(a, 1; c; z)-Pmn (z) were explicitly evaluated by Padé (cf. [2], [6] or [9]). We show that for c > a > 0 and m ≥ n - 1, the poles of Pmn (z)/Qmn (z) lie on the cut (1,∞). We deduce that the sequence of approximants Pmn (z)/Qmn (z) converges to 2 F 1(a, 1; c; z) as m → ∞, n/m → ρ with 0 < ρ ≤ 1, uniformly on compact subsets of the unit disc |z| < 1 for c > a > 0. 相似文献
10.
Alakes Maiti Bibek Patra G.P. Samanta 《International Journal of Mathematical Education in Science & Technology》2013,44(8):1061-1076
The present article deals with the problem of combined harvesting of a
Michaelis–Menten-type ratio-dependent predator–prey system. The
problem of determining the optimal harvest policy is solved by invoking
Pontryagin's Maximum Principle. Dynamic optimization of the harvest policy is
studied by taking the combined harvest effort as a dynamic variable. Computer
simulations are carried out to illustrate our analytical findings. Biological
and bioeconomical interpretations of the results are explained critically. 相似文献
11.
Linda Brown Westrick 《Israel Journal of Mathematics》2017,219(1):431-448
A family of sets is union-free if there are no three distinct sets in the family such that the union of two of the sets is equal to the third set. Kleitman proved that every union-free family has size at most (1+o(1))( n/2 n ). Later, Burosch–Demetrovics–Katona–Kleitman–Sapozhenko asked for the number α(n) of such families, and they proved that \({2^{\left( {\begin{array}{*{20}{c}} n \\ {n/2} \end{array}} \right)}} \leqslant \alpha \left( n \right) \leqslant {2^{2\sqrt 2 \left( {\begin{array}{*{20}{c}} n \\ {n/2} \end{array}} \right)\left( {1 + o\left( 1 \right)} \right)}}\) They conjectured that the constant \(2\sqrt 2 \) can be removed in the exponent of the right-hand side. We prove their conjecture by formulating a new container-type theorem for rooted hypergraphs. 相似文献
12.
Alois Steindl 《PAMM》2015,15(1):265-266
We investigate the bifurcating solutions at a Hopf–Hopf interaction point with an internal 1 : 3 resonance. It turns out, that the transitions from single to mixed modes can be described by Duffing or Mathieu szenarios. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
E. I. Moiseev 《Differential Equations》2008,44(5):730-733
We consider an optimal boundary control of a string with free end by a displacement of the other end in W′ p (Q, T). For p ≠ 2, we prove that the optimal control depends on the initial and terminal conditions nonlinearly. 相似文献
14.
We show that if a line ℓ is an isolated line transversal to a finite family F\mathcal{F} of (possibly intersecting) balls in ℝ3 and no two balls are externally tangent on ℓ, then there is a subfamily G í F\mathcal{G}\subseteq\mathcal{F} of size at most 12 such that ℓ is an isolated line transversal to G\mathcal{G}. We generalize this result to families of semialgebraic ovaloids. 相似文献
15.
由平面向量的数量积公式:a·b=|a|·|b|cosθ(其中θ为非零向量a与b的夹角),我们容易得到下面的结论:
-|a|·|b|≤a·b≤|a|·|b|.
当a与b共线且方面相同时,右边的不等式取等号;当a与b共线且方向相反时,左边的不等式取等号。 相似文献
16.
The dynamics of the eigenvalues of a family of Sturm–Liouville operators with complex integrable PT-symmetric potential on a finite interval is studied. In the model case of the complex Airy operator, a criterion for the similarity of operators in the family to self-adjoint and normal operators is stated and the exceptional parameter values corresponding to multiple eigenvalues are analytically calculated. 相似文献
17.
V. I. Berdyshev 《Proceedings of the Steklov Institute of Mathematics》2018,300(1):49-55
We formulate an extremal problem of constructing a trajectory of a moving object that is farthest from a group of observers with fixed visibility cones. Under some constraints on the arrangement of the observers, we give a characterization and a method of construction of an optimal trajectory. 相似文献
18.
A subgroup H of a group G is called µ-supplemented in G if there exists a subgroup K such that G = HK and H 1 K is a proper subgroup in G for every maximal subgroup H 1 in H. For the initial values of p, we establish the p-supersolubility of a finite group with a μ-supplemented Sylow p-subgroup. 相似文献
19.
A. A. Kazhymurat 《Siberian Mathematical Journal》2018,59(4):641-647
Under study is the energy functional on the set of Lagrangian tori in the complex projective plane. We prove that the value of the energy functional for a certain family of Hamiltonian minimal Lagrangian tori in the complex projective plane is strictly larger than for the Clifford torus. 相似文献
20.
Il’dar Khamitovich Musin Polina V. Yakovleva 《Central European Journal of Mathematics》2012,10(2):665-692
For some given logarithmically convex sequence M of positive numbers we construct a subspace of the space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in ? n . Due to the conditions on M each function of this space admits a holomorphic extension in ? n . In the current article, the space of holomorphic extensions is considered and Paley-Wiener type theorems are established. To prove these theorems, some auxiliary results on extensions of holomorphic functions satisfying some weighted L 2-bounds in a domain of holomorphy in ? n are obtained with the aid of L. Hörmander’s method of L 2-bounds for the \(\bar \partial\) operator. Also, some new facts on the Fourier-Laplace transform of tempered distributions complementing some well-known results of V.S. Vladimirov are employed. 相似文献