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31.
1IntroductionInthispaper,weconsidertheexistence,uniqueuessandnonexistenceoftheradialgroundstatetothefollowingp-Laplacianequation:whereApu=div(IDttl)Du),n>p22,qissubcriticalexponents,i.e.,q
o.Bydefinition,afunctionu(x)issaidtobetheradialgroundstateto(1.1),ifu(x)=u(r)satisfies:1)u(r),Iu'Ip-'U'eC'([o, oo));2)u(r)isthesolutionofthefollowingCauchyproblem:3)u(r)satisfiesIn0urf0rmerpaper[1],westlldiedtheexistenceanduniqueness0fradialgroundstatetoproblem(1-1)inthecasewhereq… 相似文献
32.
To investigate the viscoelastic behavior of fluid dispersions under steady shear flow conditions, an apparatus for parallel superimposed oscillations has been constructed which consists of a rotating cup containing the liquid under investigation in which a torsional pendulum is immersed. By measuring the resonance frequency and bandwidth of the resonator in both liquid and in air, the frequency and steady-shear-rate-dependent complex shear modulus can be obtained. By exchange of the resonator lumps it is possible to use the instrument at four different frequencies: 85, 284, 740, and 2440 Hz while the steady shear rate can be varied from 1 to 55 s–1. After treatment of the theoretical background, design, and measuring procedure, the calibration with a number of Newtonian liquids is described and the accuracy of the instrument is discussed.Notation
a
radius of the lump
-
A
geometrical constant
-
b
inner radius of the sample holder
-
c
constant
-
C
1, C
2
apparatus constants
-
D
damping of the pendulum
-
e
x
, e
y
, e
z
Cartesian basis
-
e
r
, e
, e
z
orthonormal cylindrical basis
-
E
geometrical constant
-
E
t
, 0
E
t
,
t
relative strain tensor
-
f
function of shear rate
-
F
t
relative deformation tensor
-
G
(t)
memory function
-
G
*
complex shear modulus
-
G
Re(G
*
)
-
G
Im(G
*
)
-
h
distance between plates
-
H
*
transfer function
-
,
functional
-
i
imaginary unit: i
2= – 1
-
I
moment of inertia
-
J
exc
excitation current
-
J
0
amplitude of J
exc
-
k
* = k – ik
complex wave number
-
K
torsional constant
-
K
fourth order tensor
-
l
length of the lump
-
L
mutual inductance
-
M
dr
driving torque
-
M
liq
torque exerted by the liquid
-
0
M
liq,
liq
steady state and dynamic part of Mliq
-
n
power of the shear rate
-
p
isotropic pressure
-
Q
quality factor
-
r
radial position
-
R,R
0, R
c
Re(Z
*, Z
0
*
, Z
c
*
)
-
s
time
-
t, t
time
-
T
temperature
-
T, 0
T,
stress tensor
-
u
velocity
-
U
lock-in output
- 0
velocity
-
V
det
detector output voltage
-
V
sig, V
cr
signal and cross-talk part of V
det
-
x
Cartesian coordinate
-
X , X
0, X
c
Im(Z
*, Z
0
*
, Z
c
*
)
-
y
Cartesian coordinate
-
z
Cartesian coordinate, axial position 相似文献
33.
Erdoğan Şen Serkan Araci Mehmet Acikgoz 《Mathematical Methods in the Applied Sciences》2014,37(17):2619-2625
In this work, we study the asymptotic properties of a new Sturm–Liouville problem with retarded argument. Contrary to previous works, differential equation includes eigenparameter as a quadratic function. In the considered problem arise new difficulties. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
34.
An analytic function f in the unit disk
D :={z ∈ ? : |z| < 1}, standardly normalized, is called close-to-convex with respect to the Koebe function
k(z) := z/(1−z)2, z ∈ D if there exists δ∈(-π/2,π/2) such that
Re{eiδ(1−z)2f′(z)} > 0, ∈ D. For the class C(k) of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szegö problem is studied. 相似文献
35.
36.
The menace of insect pests is a topic of major concern throughout the world. Chemical pesticides are conventionally used to control these insect pests. However, the adverse effects of these synthetic pesticides, such as high toxicity from residues in food, contamination of water and the environment resulting in human health hazard and resistance of the pest to the pesticides have necessitated development of some nonconventional approaches of biological pest control. In this research, we have focused on a mathematical model of biological pest control using the sterile insect release technique. Unlike most of the existing modeling studies in this field that mainly deal with the pest population only, we have incorporated the crop population as a distinct dynamical equation together with the fertile and sterile insect pests. Local stability analysis is performed around the crop and fertile insect free axial equilibrium, the fertile‐insect‐free boundary equilibrium, the crop‐free boundary equilibrium and the equilibrium point of coexistence. From the study we have derived a number of thresholds for the SIRR (the main parameter for our study) that cause existence and or extinction of the crop population as well as the fertile insect pests. A global study of the model system using comparison arguments revealed existence of a global attractor for the system. Numerical simulations are done to support and augment analytical results. 相似文献
37.
This paper studies a discrete-time queueing system in which the traffic regulation places an upper bound on the number of arrivals in each of the non-overlapping time windows (virtual frames) of a fixed length. The worst traffic passing through this traffic regulation is characterized. As a criterion for traffic comparison, this paper employs the weighted sum of queueing delays with the weighting factors decaying geometrically over the time horizon. This paper uses dynamic programming techniques and convexity argument to characterize the worst traffic. 相似文献
38.
WANGYOUBIN ZHAOAIMIN YANJURANG 《高校应用数学学报(英文版)》1998,13(4):391-396
The necessary and sufficient conditions for the oscillations of every solution of the nonlinear delay equation x(t) f(x(t l)) g(x([t-k]))=0 are oblained. 相似文献
39.
一类多偏差变元的二阶微分方程周期解 总被引:1,自引:0,他引:1
本文利用重合度理论研究了一类二阶多偏差变元的微分方程
x"(t)+f(t,x(t),x(t-τ0(t)),x'(t))+∑nj=1g(x(t-τj(t)))=p(t)
的周期解问题,得到了存在周期解的新的结果. 相似文献
40.
We consider the problem of discriminating between two independent multivariate normal populations, Np(μ1, Σ1) and Np(μ2, Σ2), having distinct mean vectors μ1 and μ2 and distinct covariance matrices Σ1 and Σ2. The parameters μ1, μ2, Σ1, and Σ2 are unknown and are estimated by means of independent random training samples from each population. We derive a stochastic representation for the exact distribution of the “plug-in” quadratic discriminant function for classifying a new observation between the two populations. The stochastic representation involves only the classical standard normal, chi-square, and F distributions and is easily implemented for simulation purposes. Using Monte Carlo simulation of the stochastic representation we provide applications to the estimation of misclassification probabilities for the well-known iris data studied by Fisher (Ann. Eugen.7 (1936), 179–188); a data set on corporate financial ratios provided by Johnson and Wichern (Applied Multivariate Statistical Analysis, 4th ed., Prentice–Hall, Englewood Cliffs, NJ, 1998); and a data set analyzed by Reaven and Miller (Diabetologia16 (1979), 17–24) in a classification of diabetic status. 相似文献