Hilbert phase microscopy for investigating fast dynamics in transparent systems

We introduce Hilbert phase microscopy (HPM) as a novel optical technique for measuring high transverse resolution quantitative phase images associated with optically transparent objects. Because of its single-shot nature, HPM is suitable for investigating rapid phenomena that take place in transparent structures such as biological cells. The potential of this technique for studying biological systems is demonstrated with measurements of red blood cells, and its ability to quantify dynamic processes on a millisecond scale is exemplified with measurements of evaporating micrometer-sized water droplets.     

Exactly solvable model of monomer-monomer reactions on a two-dimensional random catalytic substrate

We study the equilibrium properties of a monomer-monomer A+B--> reaction on a two-dimensional substrate containing randomly placed catalytic bonds. Interacting A and B species undergo continuous exchanges with particle reservoirs and react as soon as a pair of unlike particles appears on sites connected by a catalytic bond. For annealed disorder in the placement of catalytic bonds the model is mapped onto a general spin S=1 model and solved exactly for the pressure in a particular case. At equal activities of the two species a second order phase transition is revealed.     

Non-dual fuzzy connections

The lack of double negation and de Morgan properties makes fuzzy logic unsymmetrical. This is the reason why fuzzy versions of notions like closure operator or Galois connection deserve attention for both antiotone and isotone cases, these two cases not being dual. This paper offers them attention, comming to the following conclusions: – some kind of hardly describable local preduality still makes possible important parallel results; – interesting new concepts besides antitone and isotone ones (like, for instance, conjugated pair), that were classically reducible to the first, gain independency in fuzzy setting.     

Fast light, slow light, and phase singularities: a connection to generalized weak values

We demonstrate that Aharonov-Albert-Vaidman weak values have a direct relationship with the response function of a system, and have a much wider range of applicability in both the classical and quantum domains than previously thought. Using this idea, we have built an optical system, based on a birefringent photonic crystal, with an infinite number of weak values. In this system, the propagation speed of a polarized light pulse displays both superluminal and slow light behavior with a sharp transition between the two regimes. We show that this system's response possesses two-dimensional, vortex-antivortex phase singularities. Important consequences for optical signal processing are discussed.     

Biosensors for phenol derivatives using biochemical signal amplification

Two different approaches, both exploiting two enzymes cooperative functioning, to enhance the sensitivity of tyrosinase (PPO) based biosensor for amperometric detection of phenols have been compared. For this purpose, one monoenzyme electrode (PPO) and two bienzyme electrodes (PPO and d-glucose dehydrogenase, GDH; PPO and horseradish peroxidase, HRP) were constructed using agar-agar gel as enzyme immobilization matrix. The biosensors responses for l-tyrosine detection were recorded at −50 mV versus saturated calomel electrode (SCE). The highest sensitivity (74 mA M⁻¹) was observed for the PPO-GDH couple, while that recorded for PPO-HRP couple system was only 32 times higher than that measured for monoenzyme electrode (0.01 mA M⁻¹). The ability of the PPO-, PPO-GDH-, PPO-HRP-based biosensors to assay phenols was demonstrated by quantitative determination of phenol, 1,2-dihydroxybenzene, 1,3-dihydroxybenzene, 1,4-dihydroxybenzene, 2-amino-3 (4-hydroxyphenyl) propanoic acid, 2-hydroxytoluene, 3-hydroxytoluene, 4-hydroxytoluene, 4-clorophenol, 3-clorophenol, 2-clorophenol, 4-hydroxybenzoic acid.     

Hyperplane arrangement cohomology and monomials in the exterior algebra

We show that if is the complement of a complex hyperplane arrangement, then the homology of has linear free resolution as a module over the exterior algebra on the first cohomology of . We study invariants of that can be deduced from this resolution. A key ingredient is a result of Aramova, Avramov, and Herzog (2000) on resolutions of monomial ideals in the exterior algebra. We give a new conceptual proof of this result.

     

Total Valuation Rings of Ore Extensions

We consider extensions of a total valuation ring V of a skew field K to the Ore extension K(X;σ, δ) for an endomorphism σ of K and a σ-derivation δ. It is shown that there exists an extension R of V with X ∈ R, such that ${\overline X}$ is transcendental over V/J(V) if and only if (σ,δ) is compatible with V, where ${\overline X} = X + J(R^(1))$ . In the case V is invariant, it is established that there is an invariant extension R of V in K(X;σ,δ) such that ${\overline X}$ is transcendental if and only if σ(a)V = aV and δ(a) ∈ aV for all a ∈ K.     

Spectral lifting in Banach algebras and interpolation in several variables

Let be a unital Banach algebra and let be a closed two-sided ideal of . We prove that if any invertible element of has an invertible lifting in , then the quotient homomorphism is a spectral interpolant. This result is used to obtain a noncommutative multivariable analogue of the spectral commutant lifting theorem of Bercovici, Foias, and Tannenbaum. This yields spectral versions of Sarason, Nevanlinna-Pick, and Carathéodory type interpolation for , the WOT-closed algebra generated by the spatial tensor product of the noncommutative analytic Toeplitz algebra and , the algebra of bounded operators on a finite dimensional Hilbert space . A spectral tangential commutant lifting theorem in several variables is considered and used to obtain a spectral tangential version of the Nevanlinna-Pick interpolation for .

In particular, we obtain interpolation theorems for matrix-valued bounded analytic functions on the open unit ball of , in which one bounds the spectral radius of the interpolant and not the norm.

     

Synthesis of Iron Oxides by Co2 Laser vs. Thermally Induced Decomposition of Inorganic Salts

This paper reports on the synthesis of various iron oxides by the IR laser processing of different iron salts. X-ray diffraction techniques were used to characterize the reaction products. Some differences in terms of crystallite size and isotropy between these oxides and those obtained from the same salt by thermal means are described and explained. This revised version was published online in July 2006 with corrections to the Cover Date.