What is a finite function?
A function is finite if it never asigns infinity to any element in its domain. Note that this is different than bounded as f(x):R→R∪{∞}:f(x)=x2 is not bounded since limx→∞=∞.
What is Holonomic sequence?
Holonomic sequences are also called P-recursive sequences: they are defined recursively by multivariate recurrences satisfied by the whole sequence and by suitable specializations of it. …
What is finite set example?
In the set theory of mathematics, a finite set is defined as a set that has a finite number of elements. For example, {1,3,5,7} is a finite set with four elements. The element in the finite set is a natural number, i.e. non-negative integer.
What is finite number?
A number that is not infinite. In other words it could be measured, or given a value. There are a finite number of people at this beach. And the length of the beach is also a finite number.
Is zero a finite number?
Zero is a finite number. When we say that a number is infinite, it means that it is uncountable, limitless, or endless.
What is holonomic?
Holonomic (robotics), when controllable degrees of freedom are equal to the total degrees of freedom. Holonomic brain theory, model of cognitive function as being guided by a matrix of neurological wave interference patterns.
How do you check if a constraint is holonomic?
If every test equation is true for the entire set of combinations for all constraint equations, the system is holonomic. If it is untrue for even one test combination, the system is nonholonomic.
What is holonomic and nonholonomic?
Holonomic system are systems for which all constraints are integrable into positional constraints. Nonholonomic systems are systems which have constraints that are nonintegrable into positional constraints.
Which is the bigger class of D finite functions?
The bigger class that we introduce are functions satisfying linear differential equations with D-finite coefficients and we refer to this class as DD-finite functions. As we stressed earlier, D-finite functions form a large class of useful functions – hence DD-finite functions are a considerable extension.
Can a D finite function be computed automatically?
In order to specify a D-finite function only the order of the equation, the polynomial coefficients, and sufficiently many initial values need to be stored. Given functions in this form, a defining differential equation of the same type (plus initial values) for their sum, product, etc., can be computed from this input automatically.
What is the property of a definite function?
Assume lim ‖ x ‖ → ∞ V ( ‖ x ‖) = ∞, then the positive definite function V ( x) has the property of infinity. 1. V ( x) = x 1 2 + x 2 2 For all the components of a vector x, there is a continuous partial derivative of V ( x ); when x = 0, V (0) = 0 for any x ≠ 0, we have V ( x) > 0, so V ( x) is positive definite function.
When is v ( x ) a negative definite function?
V ( x) = x 1 x 2 + x 2 2 For all the components of a vector x, there is a continuous partial derivative of V ( x ); when x = 0, V (0) = 0, but for any x ≠0, the symbols of V ( x) cannot be determined, so V ( x) is not positive definite function or negative definite function, it can be called indeterminate function.