Statistical procedures of estimation and inference are most frequently justified in econometric work on the basis of certain desirable asymptotic properties. One estimation procedure may, for example, be selected over another because it is known to provide consistent and asymptotically efficient parameter estimates
under certain stochastic environments.
Nonhomogeneous ordinary differential equations can be solved if the general solution to the homogenous version is known, in which case the undetermined coefficients method or variation of parameters can be used to find the particular solution.
Knowledge of thermodynamic data of copolymer solutions is a necessity for industrial and
laboratory processes. Furthermore, such data serve as essential tools for understanding the physical
behavior of copolymer solutions, for studying intermolecular interactions, and for gaining insights into the
molecular nature of mixtures. They also provide the necessary basis for any developments of theoretical
thermodynamic models. Scientists and engineers in academic and industrial research need such data and
will benefit from a careful collection of existing data.
standard tridiagonal algorithm. Given un , one solves (19.5.36) for un+1/2 , substitutes on the right-hand side of (19.5.37), and then solves for un+1 . The key question is how to choose the iteration parameter r
As Carlo (2001) comments in a recent review, “research on cross-language
transfer has made some progress with regard to the issue of identifying particular skills
that appear susceptible to transfer from first- to second-language reading. However,
questions remain concerning the specification of the cognitive mechanisms responsible
for transfer as well as the developmental parameters that constrain transfer effects.
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article A Parameter Robust Method for Singularly Perturbed Delay Differential Equations
This work is intended to survey the basic theory that underlies the multitude of
parameter-rich models that dominate the hydrological literature today. It is concerned
with the application of the equation of continuity (which is the fundamental theorem of
hydrology) in its complete form combined with a simplified representation of the
principle of conservation of momentum. Since the equation of continuity can be
expressed in linear form by a suitable choice of state variables and is also parameterfree,
it can be readily formulated at all scales of interest.
For the complex parabolic Ginzburg-Landau equation, we prove that, asymptotically, vorticity evolves according to motion by mean curvature in Brakke’s weak formulation. The only assumption is a natural energy bound on the initial data. In some cases, we also prove convergence to enhanced motion in the sense of Ilmanen. Introduction In this paper we study the asymptotic analysis, as the parameter ε goes to zero, of the complex-valued parabolic Ginzburg-Landau equation for functions uε :
Part I discussed the basics of industrial servo drives from a hardware point of view. Physical parameters and practical applications were discussed. Part II repeats some of the things in Part I but from a mathematical point of view. The advanced application of industrial servo drives requires the use of differential equations to describe mechanical, electrical, and ﬂuid systems. As applied to servo drives there are numerous academic techniques to analyze these systems (e.g., root locus, Nyquist diagrams, etc.).
EES is particularly useful for design problems in which the effects of one or more parameters need to be determined. The program provides this capability with its Parametric Table, which is similar to a spreadsheet. The user identifies the variables that are independent by entering their values in the table cells. EES will calculate the values of the dependent variables in the table. The relationship of the variables in the table can then be in publication-quality plots.
Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article On an Inverse Scattering Problem for a Discontinuous Sturm-Liouville Equation with a Spectral Parameter in the Boundary Condition
OF INVARIANT FIBER BUNDLES FOR DYNAMIC EQUATIONS ON MEASURE CHAINS
¨ CHRISTIAN POTZSCHE AND STEFAN SIEGMUND Received 8 August 2003
We present a new self-contained and rigorous proof of the smoothness of invariant ﬁber bundles for dynamic equations on measure chains or time scales. Here, an invariant ﬁber bundle is the generalization of an invariant manifold to the nonautonomous case.
RATE OF CONVERGENCE OF SOLUTIONS OF RATIONAL DIFFERENCE EQUATION OF SECOND ORDER
ˇ ´ ´ S. KALABUSIC AND M. R. S. KULENOVIC Received 13 August 2003 and in revised form 7 October 2003
We investigate the rate of convergence of solutions of some special cases of the equation xn+1 = (α + βxn + γxn−1 )/(A + Bxn + Cxn−1 ), n = 0,1,..., with positive parameters and nonnegative initial conditions. We give precise results about the rate of convergence of the solutions that converge to the equilibrium or period-two solution by using Poincar´ ’s e theorem and an improvement of Perron’s...
POWER SERIES TECHNIQUES FOR A SPECIAL SCHRÖDINGER OPERATOR AND RELATED DIFFERENCE EQUATIONS
MORITZ SIMON AND ANDREAS RUFFING Received 27 July 2004 and in revised form 16 February 2005
We address ﬁnding solutions y ∈ 2 (R+ ) of the special (linear) ordinary diﬀerential equation xy (x) + (ax2 + b)y (x) + (cx + d)y(x) = 0 for all x ∈ R+ , where a,b,c,d ∈ R are constant parameters. This will be achieved in three special cases via separation and a power series method which is speciﬁed using diﬀerence equation techniques.
ONE PARAMETER FAMILY OF LINEAR DIFFERENCE EQUATIONS AND THE STABILITY PROBLEM FOR THE NUMERICAL SOLUTION OF ODEs
L. ACETO, R. PANDOLFI, AND D. TRIGIANTE Received 21 July 2004; Accepted 4 October 2004
The study of the stability properties of numerical methods leads to considering linear difference equations depending on a complex parameter q. Essentially, the associated characteristic polynomial must have constant type for q ∈ C− . Usually such request is proved with the help of computers.
Discussion of nanotechnology can quickly become complex as a full
analysis involves advanced chemistry, biology, physics, computer science,
and engineering. The properties of nano-scale materials are governed by laws
of quantum physics, causing materials to display properties and characteristics
that would be considered by the laws of classic Newtonian physics. It is these
intermolecular forces which cause nanotechnology to be both a vexing
research problem, and yet have enormous potential.
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Critical parameter equations for degenerate parabolic equations coupled via nonlinear boundary flux
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài:
Research Article Multiple Positive Solutions for Nonlinear First-Order Impulsive Dynamic Equations on Time Scales with Parameter
The theory of one-parameter semigroups of linear operators on Banach
spaces started in the first half of this century, acquired its core in 1948
with the Hille–Yosida generation theorem, and attained its first apex with
the 1957 edition of Semigroups and Functional Analysis by E. Hille and
R.S. Phillips. In the 1970s and 80s, thanks to the efforts of many different
schools, the theory reached a certain state of perfection, which is well represented
in the monographs by E.B. Davies [Dav80], J.A. Goldstein [Gol85],
A. Pazy [Paz83], and others.