How to prove a function is periodic? Given: y' = 2xy, y(1) = 1 Find y(1.2) using the Runge-Kutta method with a step size of h=0.2. Let f: Z_12 → Z_12: x → 9 x + 1 where arithmetic is done modulo 12. a) Show that f is neither injective, nor surjective. b) Now ...
A linear transformation is defined as a function that relates a one vector space from other one without disrespecting the structure of each spaces. When linear transforming from one vector space to other, it preserves the structure of the object being transformed....
In mathematics, two sets or classes A and B are equinumerous if there exists aone-to-one correspondence(or bijection) between them, that is, if there exists a function from A to B such that for every element y of B, there is exactly one element x of A with f(x) = y. Is QA co...
By this modification, we are able to prove adaptive security based on selective secure puncturable PRF, and adaptively secure fixed-access garbling. We note that, even if the address a is included in the domain of PRF, as in [9], the construction is still adaptively secure if the ...
This construction captures the design of a VIL-PRF based on a FIL primitive where the input is first hashed, then given as input to mBenes. This hashing step is what allows us to avoid the main difficulties that are encountered when one tries to prove optimal security for the mBenes ...
We prove that the asymptotic logarithmic density of copies of a graph F in the graphs of a nowhere dense class C is integral and we determine the range of its possible values. This leads to a generalization of the trichotomy theorem of Nešetřil and Ossona de Mendez (2011) [18] and...
statement of the form A implies B to prove, their method of proof is generally wholly inadequate. He jokingly said, the student assumes A, works with that for a bit, uses the fact that B is true and so concludes that A is true. How can it ...
to substitute the given data into some formula, but we need to combine and apply the known theorems. This is problematic for students and hence they have poor results in geometry even they are good in other part of mathematics. As we know since Euclid geometry is a logical system [Pól48...
For an invertible matrix A if A^ {-1} = A^T, prove that det (A) = +1 and -1. How could you check to see whether a function is invertible? How to prove a matrix is invertible with eigenvalues ? How do you determine the inverse of a 3x3 matrix? How do you determine if the ...
How to prove the countability?Question:How to prove the countability?Countable Set :A set A is countable if there exist a onto map f:N→A. Also if there exist a injective from A to N then A is countable. There are two kinds of countable sets. One is finite and another is infifinite...