BD-N is a weak principle of constructive analysis. Several interesting principles implied by BD-N have already been identified, namely the closure of the anti-Specker spaces under product, the Riemann Permutation Theorem, and the Cauchyness of all partially Cauchy sequences. Here these are shown to be strictly weaker than BD-N, yet not provable in set theory alone under constructive logic. keyw...

This is (raw) lecture notes of the course read on 6th European intensive course on Complex Analysis (Coimbra, Portugal) in 2000. Our purpose is to describe a general framework for generalizations of the complex analysis. As a consequence a classification scheme for different generalizations is obtained. The framework is based on wavelets (coherent states) in Banach spaces generated by “admissib...

We first prove some results on invariant lightlike submanifolds of indefinite Sasakian manifolds. Then, we introduce a general notion of contact Cauchy-Riemann (CR) lightlike submanifolds and study the geometry of leaves of their distributions. We also study a class, namely, contact screen Cauchy-Riemann (SCR) lightlike submanifolds which include invariant and screen real subcases. Finally, we ...

The key point in this paper is the introduction of elastic analytic functions. An elastic analytic function is a function of the form u : C ! C 2 which is diierentiable and satisses equations which are analogous to the Cauchy-Riemann equations of traditional complex analysis such that the following conditions hold: rst the real and imaginary part of the rst complex component of u satisfy the Na...

in this paper, we present recent results in integral inequality theory. our results are based on thefractional integration in the sense of riemann-liouville

This is (raw) lecture notes of the course read on 6th European intensive course on Complex Analysis (Coimbra, Portugal) in 2000. Our purpose is to describe a general framework for generalizations of the complex analysis. As a consequence a classification scheme for different generalizations is obtained. The framework is based on wavelets (coherent states) in Banach spaces generated by “admissib...

In the present paper, we discuss Monge-Ampère equations from viewpoint of differential geometry. It is known that a Monge--Ampère equation corresponds to special exterior system on 1-jet space. this generalize and prove $(k+1)$st order generalized $k$-jet space its solution naturally an integral manifold corresponding system. Moreover, show Korteweg-de Vries (KdV) Cauchy--Riemann are examples o...

The main result we obtain is that given t N M a TS-subbundle of the generalized Hopf fibration t H2+’cP over a Cauchy-Riemann product M _ cP, i.e. N _ H is a diffeomorphism on fibres and oj= ot, if s is even and N is a closed submanifold tangent to the structure vectors of the canonical 5Zstructure on H then N is a Cauchy-Riemann submanifold whose Chen class is non-vanishing.

In this article, we first give a modified Schwarz–Pompeiu formula in general sector ring with angle \(\vartheta =\frac{\pi }{\alpha },\ \alpha \ge 1/2\) by proper conformal mappings, and obtain the solution of Schwarz problem for Cauchy–Riemann equation explicit forms. Furthermore, construct some integral operators discuss their properties detail. Finally, virtue these operators, problems an in...