Ngamiland is a melting pot of ethnicities. Over centuries, various tribal groups, originating from areas with different environmental conditions and diverse political and socio-cultural backgrounds, moved to the Okavango Delta introducing their own particular forms of land use and specialised productive skills. People gradually adapted their resource management patterns to the Delta environment...

In this paper we discuss compactness of the canonical solution operator to ∂ on weigthed L spaces on C. For this purpose we apply ideas which were used for the Witten Laplacian in the real case and various methods of spectral theory of these operators. We also point out connections to the theory of Dirac and Pauli operators.

We consider a certain second-order nonlinear delay differential equation and prove that the all solutions oscillate when proper impulse controls are imposed. An example is given. c © 2006 Elsevier Science Ltd. All rights reserved. Keywords—Delay differential equations, Second-order, Nonlinear, Oscillation, Impulses.

Given a pair of Lie algebroid structures on a vector bundle A (over M) and its dual A∗, and provided the A∗-module L = (∧A ⊗ ∧T ∗M) 1 2 exists, there exists a canonically defined differential operator D̆ on Γ(∧A ⊗ L ). We prove that the pair (A,A∗) constitutes a Lie bialgebroid if, and only if, D̆ is a Dirac generating operator as defined by Alekseev & Xu [1].

By introducing auxiliary functions, we investigate the oscillation of a class of second-order subhalf-linear neutral impulsive differential equations of the form r t φβ z′ t ′ p t φα x σ t 0, t / θk,Δφβ z′ t |t θk qkφα x σ θk 0,Δx t |t θk 0, where β > α > 0, z t x t λ t x τ t . Several oscillation criteria for the above equation are established in both the case 0 ≤ λ t ≤ 1 and the case −1 < −μ ...

It is well known that the Dirac monopole solution with the U(1) gauge group embedded into the group SU(2) is equivalent to the SU(2) Wu-Yang point monopole solution having no Dirac string singularity. We consider a multi-center configuration of m Dirac monopoles and n antimonopoles and its embedding into SU(2) gauge theory. Using geometric methods, we construct an explicit solution of the SU(2)...

Transformation properties of Dirac equation correspond to Spin(3,1) representation of Lorentz group SO(3,1), but group GL(4,R) of general relativity does not accept a similar construction with Dirac spinors. On the other hand, it is possible to look for representation of GL(4,R) in some bigger space, there Dirac spinors are formally situated as some " subsystem. " In the paper is described cons...

Transformation properties of Dirac equation correspond to Spin(3,1) representation of Lorentz group SO(3,1), but group GL(4,R) of general relativity does not accept spinor representation. On the other hand, it is possible to look for representation of GL(4,R) in some bigger space, there Dirac spinors are formally situated as some " subsystem. " In the paper is described construction of such rep...

Due to importance of the concepts of θ-closure and δ-closure, it is natural to try for their extensions to fuzzy topological spaces. So, Ganguly and Saha introduced and investigated the concept of fuzzy δ-closure by using the concept of quasicoincidence in fuzzy topological spaces. In this paper, we will introduce the concept of δ-closure in intuitionistic fuzzy topological spaces, which is a g...

1 Fourier Transform 1 1.1 Properties of the Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Schwartz space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Convergence in S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Fourier Transform in L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Fouri...