A monadic formula (Y ) is a selector for a formula '(Y ) in a structure M if there exists a unique subset P of M which satis es and this P also satis es '. We show that for every ordinal ! there are formulas having no selector in the structure ( ;<). For !1, we decide which formulas have a selector in ( ;<), and construct selectors for them. We deduce the impossibility of a full generalization ...

Let H be a bialgebra and let A be an associative algebra. The algebra A is said to be an H-module-algebra if there is an H-module structure on A such that the multiplication on A becomes an H-module morphism. For example, if S denotes the Landweber-Novikov algebra [15, 21], then the complex cobordism MU(X) of a topological space X is an S module-algebra. Likewise, the singular mod p cohomology ...

For a two-variable formula B(X,Y) of Monadic Logic of Order (MLO) the Church Synthesis Problem concerns the existence and construction of a finite-state operator Y=F(X) such that B(X,F(X)) is universally valid over Nat. Büchi and Landweber (1969) proved that the Church synthesis problem is decidable. We investigate a parameterized version of the Church synthesis problem. In this extended versio...

Simultaneous algebraic reconstruction technique (SART) [1, 2] is an iterative method for solving inverse problems of form Ax(+n) = b. This type of problems arises for example in computed tomography reconstruction, in which case A is obtained from discrete Radon transform. In this paper, we provide several methods for derivation of SART and connections between SART and other methods. Using these...

Electrical capacitance tomography (ECT) technique is a new technique for two-phase flow measurement. ECT is a complex nonlinear problem. To solve the ill-posed image reconstruction problem, image reconstruction algorithm based on wavelet neural networks (WNN) was presented. The principal component analysis (PCA) method was used to reduce the dimension of the input vectors. The transfer function...

This paper presents a novel multi-channel image restoration algorithm. The main idea is to develop practical approaches to reduce optical blur from noisy observations produced by the sensor of a camera phone. An iterative deconvolution is applied separately to each color channel directly on the raw data. We use a modified iterative Landweber algorithm combined with an adaptive denoising techniq...

We describe the author’s research with Neil Strickland on the global algebra and global homological algebra of the category of BP∗BP comodules. We show, following [HS02a], that the category of E(n)∗E(n)comodules is a localization, in the abelian sense, of the category of BP∗BP comodules. This gives analogues of the usual structure theorems, such as the Landweber filtration theorem, for E(n)∗E(n...

We study the existence of eeective winning strategies in certain innnite games, so called enumeration games. Originally, these were introduced by Lachlan (1970) in his study of the lattice of recursively enumerable sets. We argue that they provide a general and interesting framework for computable games and may also be well suited for modelling reactive systems. Our results are obtained by redu...

Let H be a bialgebra. An H-module-algebra is an associative algebra A that is also an H-module such that the multiplication map on A becomes an H-module morphism. This algebraic structure arises often in algebraic topology, quantum groups [11, Chapter V.6], Lie and Hopf algebras theory [3, 16, 19], and group representations [1, Chapter 3]. For example, in algebraic topology, the complex cobordi...

For a two-variable formula B(X,Y) of Monadic Logic of Order (MLO) the Church Synthesis Problem concerns the existence and construction of a finite-state operator Y=F(X) such that B(X,F(X)) is universally valid over Nat. Büchi and Landweber (1969) proved that the Church synthesis problem is decidable. We investigate a parameterized version of the Church synthesis problem. In this extended versio...