His topics include the q-binomial theorem, Heine's transformation, the Jacobi triple product identity, the Rogers-Fine identity, Bailey chains, WP-Bailey pairs and chains, further results on Bailey/WP-Bailey pairs and chains, bijective
proofs of basic hypergeometric identities, q-continued fractions, Lambert series, and mock theta functions.
A mapping f : X [right arrow] Y is said to be a neutrosophic homeomorphism if f is bijective
, neutrosophic continuous and neutrosophic open.
mapping between nodes on the receiver end and units on the sender end are applied in interpolation method.
Indeed, it is easy to see that the family of bijective
linear functions [R.
is knows as a fuzzy magic graph if there exist two bijective
Then we shall give a bijective
proof the following theorem.
In order to prove the map is bijective
, we only need to prove the map f is injective.
A weak isomorphism f: H [right arrow] K between two SVNHGs H = (X, E, R) and K = (Y, F, S) is a bijective
mapping f: X [right arrow] Y, which satisfies f is homomorphism, such that:
The first part uses arguments with generating functions while the second part presents bijective
proofs for the sets of permutations counted by Motzkin numbers.
In Section 3, we look at bijective
linear preservers of ([epsilon], I)-rank for all matrices over commutative antinegative semirings.
Then, f is called an orthomorphism if both f (x) and g(x) = f (x) [direct sum] x are bijective
Conversion from color to grayscale is a lossy image procedure, as there is usually no way of having a bijective
mapping between three channel values and single channel ones (of course there is also the case of images with low number of colors but these are an exception).