Search
Search Results
-
Change of Variables
This short chapter is devoted to the change of variables formula, which identifies the pushforward of Lebesgue measure on an open set of...
-
On paracomposition and change of variables in paradifferential operators
In this paper we revisit the hypothesis needed to define the “paracomposition” operator, an analogue to the classic pull-back operation in the low...
-
Random Variables
Random variables are the central objects of study in probability. The name ‘random variables’ is somewhat of a misnomer since they are neither random...
-
Invariance Under Change of Variables
In this chapter, we show that some of the notions introduced in Chap. 3 are independent of the...
-
Derivatives of Functions of Two Variables
The idea of the derivative generalizes to functions of more than one variable where can capture the rate of change relative to one of the variables....
-
Separation of Variables
We are now ready to resume our work on solving the three main equations: the heat equation, Laplace’s equation, and the wave equation, using the...
-
Weak convergence of sequences of random variables
The chapter four is devoted in a systematic study of a weak convergence of sequences of random variables. It is shown the equivalence between a weak...
-
Random Variables and Their Probability Distributions
Chapter 5 defines the random variables and their probability distributions. Many properties such as mean,...
-
Separation of Variables
Covers separable equations and Newton’s equation, both of which are solved by quadratures. Includes the Kepler problem and an introduction to...
-
On Normalization of Integer-Valued Random Variables
The notion of general families of thinning operators is proposed. The main goal of such notion is to allow normalization of integer-valued random...
-
Multicovariance and Multicorrelation for p-variables
The covariance and correlation are important indicators to measure the linear dependence between two variables. The multivariables as p-variables in...
-
Modes of convergence of random variables and algebraic genericity
Important probabilistic problems require to find the limit of a sequence of random variables. However, this limit can be understood in different ways...
-
Singularly Perturbed Problems with Multi-Tempo Fast Variables
AbstractThe article contains a survey of publications studying problems characterized by the presence of fast variables with various rates of change...
-
Discrete Random Variables
The number of heads in a sequence of 10,000 coin tosses, the number of days it takes until the next rain and the size of a genealogical tree are...
-
Random variables and their quantitative characteristics
In the second chapter random variables are introduced and investigated in the framework of axiomatic of Kolmogorov. It is shown a connection of...
-
Properties of complex-valued power means of random variables and their applications
We consider power means of independent and identically distributed (i.i.d.) non-integrable random variables. The power mean is an example of a...
-
Change Point Analysis of the Mean
We have seen that under the no change in the mean null hypothesis...
-
Coprime values of polynomials in several variables
Given two polynomials P (
x ), Q (x ) in one or more variables and with integer coefficients, how does the property that they are coprime relate to their... -
Predictive modelling of critical variables for improving HVOF coating using gamma regression models
Thermal spray coating is a critical process in many industries, involving the application of coatings to surfaces to enhance their functionality....
