Correlation functions for n species of one-dimensional impenetrable bosons

The correlation functions for n species of one-dimensional impenetrable bosons are expanded in terms of correlation functions for identical free fermions. The expansion is obtained by exploiting the quantum inverse method for the n-component nonlinear Schrödinger model.     

Special networks in the hypersurfaces of generalised recurrent and birecurrent Weyl spaces

In this paper, we study some properties of the Chebyshev nets and geodesic nets in the hypersurfaces of the generalised recurrent and birecurrent Weyl spaces. Received 4. Dezember 1998.     

Is MFM really useful?

The ill-posed linear inverse problems, characterised by Fredholm integral equations of the first kind, are encountered in many areas of science and technology. This type of problems present some loss of information under the inversion process. The loss of information often makes the inversion process very difficult. Magnetic force microscopy (MFM) is a technique where problems related to loss of information occur. Work is presented here to understand what can be measured by the magnetic force microscope. A simple model is constructed, where the magnetic tip is approximated by a point dipole. Given the force F() acting on the dipole tip, we attempt to determine the magnetization distributlon in a thin ferromagnetic film, M(). This calculation should be interesting due to the rapidiy growing interest in magnetic thin films and magnetic multilayers. Received 3 December 2001 and Received in final form 11 March 2002     

Influence of gel composition on the solubility parameter of poly(2‐hydroxyethyl methacrylate‐itaconic acid) hydrogels

The solubility parameters of pure poly(2‐hydroxyethyl methacrylate) (PHEMA) and poly(2‐hydroxyethyl methacrylate/itaconic acid) [P(HEMA/IA)] hydrogels were determined by 20 solvents with various solubility parameters in swelling experiments. The solubility parameter of pure PHEMA was 26.93 ± 0.46 (MPa)^1/2. The effect of mole percentages of itaconic acid (IA) in P(HEMA/IA) hydrogels on the solubility parameter was investigated. The measured values were compared to literature and solubility values theoretically determined by group contribution values of van Krevelen and Hoy. The incorporation of IA into the hydrogel system slightly increased the solubility parameter. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1995–2003, 2002     

A note on W-I-continuous functions

In [1], Aç?kgöz et al. introduced and investigated the notions of w-I-continuous and w*-I-continuous functions in ideal topological spaces. In this paper, we investigate their relationships with continuous and θ-continuous functions.     

Enzymatic Oxy- and Amino-Functionalization in Biocatalytic Cascade Synthesis: Recent Advances and Future Perspectives

Biocatalytic cascades are a powerful tool for building complex molecules containing oxygen and nitrogen functionalities. Moreover, the combination of multiple enzymes in one pot offers the possibility to minimize downstream processing and waste production. In this review, we illustrate various recent efforts in the development of multi-step syntheses involving C−O and C−N bond-forming enzymes to produce high value-added compounds, such as pharmaceuticals and polymer precursors. Both in vitro and in vivo examples are discussed, revealing the respective advantages and drawbacks. The use of engineered enzymes to boost the cascades outcome is also addressed and current co-substrate and cofactor recycling strategies are presented, highlighting the importance of atom economy. Finally, tools to overcome current challenges for multi-enzymatic oxy- and amino-functionalization reactions are discussed, including flow systems with immobilized biocatalysts and cascades in confined nanomaterials.     

Disjoint Supercyclic Weighted Shifts

Complementing the existing literature in d-hypercyclicity, we characterize disjoint supercyclicity for a finite family of weighted shift operators. Using this characterization, we answer Question 2 in a recent paper by Bès, Martin and Peris in the negative by constructing examples of disjoint supercyclic weighted shifts whose direct sum operator is hypercyclic, but the same shifts operators fail to be disjoint hypercyclic. We also show the Disjoint Blow-Up/Collapse Property and the Strong Disjoint Blow-Up/Collapse Property for disjoint supercyclicity are equivalent when dealing with a finite family with two or more weighted shifts. However, those weighted shifts operators will never satisfy the Disjoint Supercyclicity Criterion. This provides a sharp distinction between disjoint supercyclicity and supercyclicity for a single operator. We provide a partial answer to disjoint supercyclic version of Question 3 in a recent paper by Salas by showing that we can always select an additional operator to add to an family of d-supercyclic weighted shift operators while maintaining the d-supercyclicity. We also show that, in general, this additional operator cannot be another weighted shift.     

Characteristic classes and Hilbert–Poincaré series for perverse sheaves on abelian varieties

The convolution powers of a perverse sheaf on an abelian variety define an interesting family of branched local systems whose geometry is still poorly understood. We show that the generating series for their generic rank is a rational function of a very simple shape and that a similar result holds for the symmetric convolution powers. We also give formulae for other Schur functors in terms of characteristic classes on the dual abelian variety, and as an example we discuss the case of Prym–Tjurin varieties.