self-consistent methodnonMarkovian treatmentatom-field interactionsconsistency conditionborn approximationIn this paper it is pointed out, for the first time to the author's knowledge, that the application of the projection-operator method leads to the violation of a consistency condition if the so-...
A quadratic equation is any equation that can be formed to this standard form, {eq}\displaystyle ax^{2}+bx+c=0 {/eq}, where a, b, c are known numbers and x is the unknown. There are several methods to solve for the value of x, such as factorin...
The general form of a linear approximation for a function f(x) with a derivative f′(x) is: L(x)=f(a)+f′(a)(x−a) Here, x=a is the reference point. Answer and Explanation: Given: f(x)=sin x a=π2 is the reference point First, we differentiate ...
Know about Interpolation, its formula, differences, and its types. Get more details about interpolation, why it is used, and its role in data science.
is a decimal approximation. Another example comes from geometry, where π is the exact form of the number which is often approximated as 3.14159 or 227722.You can always find the exact zeroes of a quadratic equation, because you have a formula; namely, the Quadratic Formula. This formula all...
A basic type of problem that occurs throughout mathematics is the lifting problem: given some space that “sits above” some other “base” space due to a projection map , and some map from a third space into the base space , find a “lift” of to , that is to say a map such tha...
The term "nature" may refer to living plants and animals, geological processes, weather, and physics, such as matter and energy. The term is often refers to the "natural environment" or wilderness—wild animals, rocks, forest, beaches, and in general areas that have not been substantially al...
A basic type of problem that occurs throughout mathematics is the lifting problem: given some space that “sits above” some other “base” space due to a projection map , and some map from a third space into the base space , find a “lift” of to , that is to say a map such tha...
Another alternative is to use the Mantel-Haenszel method,4 which can adjust for 1 or 2 confounders and still provide a risk ratio in a cohort study. However, this method becomes inefficient when several factors, especially continuous variables, are being adjusted for simultaneously. We herein ...
Prime uses involve any process that operates according to strict rules or patterns and has large amounts of data. If the data involved is too large for a human to make sense of in a reasonable amount of time, the process is likely a prime candidate for automation through artificial neural ...