A two-step phase-retrieval method in Fourier-transform ghost imaging

A two-step phase-retrieval method, based on Fourier-transform ghost imaging, was demonstrated. For the complex objects, the phase-retrieval process was divided into two steps: first got the complex object's amplitude from the Fourier-transform patterns of the squared object function, then combining with the Fourier-transform patterns of the object function to get the phase. The theoretical basis of this technique is outlined, and the experimental results are presented. (C) 2008 Elsevier B.V. All rights reserved.

On the Cesari fixed point method in a Banach space

In a paper published in 1961, L. Cesari [1] introduces a method which extends certain earlier existence theorems of Cesari and Hale ([2] to [6]) for perturbation problems to strictly nonlinear problems. Various authors ([1], [7] to [15]) have now applied this method to nonlinear ordinary and partial differential equations. The basic idea of the method is to use the contraction principle to reduce an infinite-dimensional fixed point problem to a finite-dimensional problem which may be attacked using the methods of fixed point indexes.

The following is my formulation of the Cesari fixed point method:

Let B be a Banach space and let S be a finite-dimensional linear subspace of B. Let P be a projection of B onto S and suppose Г≤B such that pГ is compact and such that for every x in PГ, P^-1x∩Г is closed. Let W be a continuous mapping from Г into B. The Cesari method gives sufficient conditions for the existence of a fixed point of W in Г.

Let I denote the identity mapping in B. Clearly y = Wy for some y in Г if and only if both of the following conditions hold:

(i) Py = PWy.

(ii) y = (P + (I - P)W)y.

Definition. The Cesari fixed paint method applies to (Г, W, P) if and only if the following three conditions are satisfied:

(1) For each x in PГ, P + (I - P)W is a contraction from P^-1x∩Г into itself. Let y(x) be that element (uniqueness follows from the contraction principle) of P^-1x∩Г which satisfies the equation y(x) = Py(x) + (I-P)Wy(x).

(2) The function y just defined is continuous from PГ into B.

(3) There are no fixed points of PWy on the boundary of PГ, so that the (finite- dimensional) fixed point index i(PWy, int PГ) is defined.

Definition. If the Cesari fixed point method applies to (Г, W, P) then define i(Г, W, P) to be the index i(PWy, int PГ).

The three theorems of this thesis can now be easily stated.

Theorem 1 (Cesari). If i(Г, W, P) is defined and i(Г, W, P) ≠0, then there is a fixed point of W in Г.

Theorem 2. Let the Cesari fixed point method apply to both (Г, W, P₁) and (Г, W, P₂). Assume that P₂P₁=P₁P₂=P₁ and assume that either of the following two conditions holds:

(1) For every b in B and every z in the range of P₂, we have that ‖b=P₂b‖ ≤ ‖b-z‖

(2)P₂Г is convex.

Then i(Г, W, P₁) = i(Г, W, P₂).

Theorem 3. If Ω is a bounded open set and W is a compact operator defined on Ω so that the (infinite-dimensional) Leray-Schauder index i_LS(W, Ω) is defined, and if the Cesari fixed point method applies to (Ω, W, P), then i(Ω, W, P) = i_LS(W, Ω).

Theorems 2 and 3 are proved using mainly a homotopy theorem and a reduction theorem for the finite-dimensional and the Leray-Schauder indexes. These and other properties of indexes will be listed before the theorem in which they are used.

Nano-polypyrrole supercapacitor arrays prepared by layer-by-layer assembling method in anodic aluminum oxide templates

A novel method for preparing nano-supercapacitor arrays, in which each nano-supercapacitor consisted of electropolymerized Polypyrrole (PPy) electrode / porous TiO2 separator / chemical polymerized PPy electrode, was developed in this paper. The nano-supercapacitors were fabricated in the nano array pores of anodic aluminum oxide template using the bottom-up, layer-by-layer synthetic method. The nano-supercapacitor diameter was 80 nm, and length 500 nm. Based on the charge/discharge behavior of nano-supercapacitor arrays, it was found that the PPy/TiO2/PPy array supercapacitor devices performed typical electrochemical supercapacitor behavior. The method introduced here may find application in manufacturing nano-sized electrochemical power storage devices in the future for their use in the area of microelectronic devices and microelectromechanical systems.

Padal fishing - a unique fishing method in the Ashtamudi Estuary of Kerala (south India)

Bush park fishing / padal fishing is an indigenous fishing method widely employed in the Ashtamudi estuary of Kerala (south India). An artificial reef made from twigs and leaves of trees is planted in the shallow areas of the estuary. The aim is to harvest fish that find shelter in these structures for the purpose of feeding and breeding. Though the State Department of Fisheries has banned this method of fishing in the inland waters of Kerala, 400 padals are operating in this estuary. About 300 of them are anchored in the western parts of the estuary (west Kayal). Fish are harvested in the padals at monthly intervals almost round the year and this results in the destruction of a sizeable quantity of juveniles and sub-adults of the commercially important fishes, such as Pearl spot and mullets, from the estuary. These padals pose a major threat to the sustainability of the fishery resources of this estuary and, therefore, need to be phased out by providing alternative occupations for the fishermen who are dependant on the padals.

Brush shelter: a recently introduced fishing method in the Kaptai reservoir fisheries in Bangladesh

This paper describes the brush shelters in Kaptai Lake based on a field survey of four major fishing grounds undertaken in Jan-Dec 1997.