We shall study smooth maps ~ u : _ S ! RM of nite energy deened on the punctured Riemann surface _ S = S n? and satisfying a Cauchy-Riemann type equation T ~ u j = J(~ u) T ~ u for special almost complex structures J, related to contact forms on the compact three manifold M. Neither the domain nor the target space are compact. This diiculty leads to an asymptotic analysis near the punctures. A ...

It has been shown by Strahov and Fyodorov that averages of products and ratios of characteristic polynomials corresponding to Hermitian matrices of a unitary ensemble, involve kernels related to orthogonal polynomials and their Cauchy transforms. We will show that, for the unitary ensemble 1 Ẑn | detM |2αe−nV dM of n×n Hermitian matrices, these kernels have universal behavior at the origin of t...

We prove the algebraicity of smooth CR-mappings between algebraic Cauchy–Riemann manifolds. A generalization of separate algebraicity principle is established.

In this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional Cauchy problem with an integral initial condition in Banach spaces.

where we use the notation dxI for (1.4) dxI = dxi1 ∧ dxi2 ∧ ... ∧ dxik for I = {i1, i2, ..., ik} with i1 < i2 < ... < ik. So ΩX is a free module over C ∞(X) generated by dxI . Obviously, Ω k X = 0 for k > n and ⊕ΩX is a graded ring (noncommutative without multiplicative identity) with multiplication defined by the wedge product (1.5) ∧ : (ω1, ω2)→ ω1 ∧ ω2. Note that (1.6) ω1 ∧ ω2 = (−1)12ω2 ∧ ω...

In this paper, we establish the new forms of Riemann-type fractional integral and derivative operators. The novel operator is proved to be bounded in Lebesgue space some classical differential operators are obtained as special cases. properties like semi-group, inverse certain others discussed its weighted Laplace transform evaluated. Fractional integro-differential free-electron laser (FEL) ki...