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We give a new proof of the K-theoretic analogue of the Kirwan surjectivity theorem in symplectic geometry (see Harada–Landweber, 2007) by using the equivariant version of the Kirwan
Applying Lemma 1 we can obtain some congruence properties of some classical numbers such as the Springer numbers of even index, the median Euler numbers, the median Genocchi
Lemma 7. The first statement is trivial.. In the following Theorem we include it for sake of completeness... Theorem 9.. We also use the well-known properties of the Lambert
The following theorem proves Schur’s congruence for scaled Legendre polynomials. The proof is identical to Wahab’s for the usual
The proof uses Robin’s and Gronwall’s theorems on G(n). An alternate proof of one step depends on two properties of superabundant numbers proved using Alaoglu and Erd˝ os’s
Proposition 3.1.. The following proof is similar to that of Lemma 10.1 of [9], extended to the general Gaussian martingales. This is an extension of the simple case given in
A new proof based on local integral manifold theory and the implicit function theorem is given for the classical result that a simple periodic orbit of the equation above
The Radon Nikodym Theorem plays a key role in our proof of the Fundamen- tal Theorem of Calculus, particularly the proof given by Bradley [4], so we will outline this proof but
