Light beams with minimum phase space product

We derive a reciprocity inequality involving the product of the effective size of a statistically stationary, planar, secondary source of any state of coherence and of the angular spread of the far-zone intensity generated by the source. We show that of all possible such sources, the fully spatially coherent lowest-order Hermite-Gaussian laser mode has the smallest possible reciprocity product.     

Accepted Elasticity in Local Arithmetic Congruence Monoids

For certain \({a,b \in \mathbb{N}}\) , an Arithmetic Congruence Monoid M(a, b) is a multiplicatively closed subset of \({\mathbb{N}}\) given by \({\{x\in\mathbb{N}:x \equiv a \pmod{b}\} \cup\{1\}}\) . An irreducible in this monoid is any element that cannot be factored into two elements, each greater than 1. Each monoid element (apart from 1) may be factored into irreducibles in at least one way. The elasticity of a monoid element (apart from 1) is the longest length of a factorization into irreducibles, divided by the shortest length of a factorization into irreducibles. The elasticity of the monoid is the supremum of the elasticities of the monoid elements. A monoid has accepted elasticity if there is some monoid element that has the same elasticity as the monoid. An Arithmetic Congruence Monoid is local if gcd(a, b) is a prime power (apart from 1). It has already been determined whether Arithmetic Congruence Monoids have accepted elasticity in the non-local case; we make make significant progress in the local case, i.e. for many values of a, b.     

Determination of three-photon ionization cross sections of xenon atoms from comparison with electron ionization

Multiphoton and electron-impact ionization of a gas-dynamic beam of xenon atoms are compared in order to determine the effective multiphoton ionization cross sections. The three-photon ionization cross section of the xenon atom is determined.     

Optical and electro-optical properties of silicon-contaning thiophene derivatives of star-shaped and dendritic structure

Star-thiophene derivatives with a silicon atom as the branching center were investigated by absorption spectroscopy and electro-optical Kerr effect in solutions at variations in a number and chemical structure of branches. The star-shaped oligomers were compared with dendritic analogues containing silicon atoms at the points of branching. It is shown that thiophene-containing moieties determine both spectral and electrooptical properties of the molecules. Molecular parameters of the star-shaped oligomers of various structure vary identically with increasing the number of branches. The absorption of star-shaped oligomers is additive due to the autonomy of the absorption of radiation by the separate branches. For dendritic molecules the additive nature of the absorption is kept, but their electro-optical properties are independent of a generation number. It was shown that the latter is a consequence of the manifestation by dendrimers of deformation flexibility, which is not peculiar to the starshaped derivatives.     

Fluorolactonization of unsaturated carboxylic acids with F-TEDA-BF4 in ionic liquids

Fluorolactonization of unsaturated carboxylic acids under action of the electrophilic reagent F-TEDA-BF₄ in ionic liquids (ILs) has been studied. This reaction proceeds in ILs faster and provides a better stereoselectivity in comparison to acetonitrile as reaction media. Gem-difluorinated γ-lactones have been synthesized by interaction of unsaturated carboxylic acids with F-TEDA-BF₄ in ILs.     

Structure and phase transitions of lead zirconate hafnate solid solutions

Solid solutions of two antiferroelectrics, namely, lead zirconate and lead hafnate, i.e., PbZr_{1 − x} Hf _x O₃ (x = 0, 0.3, 0.5, 0.7, 1.0), have been prepared by solid-phase synthesis from simple oxides. The elemental composition of the samples and their structure have been studied using X-ray fluorescence and X-ray diffraction analyses. The phase transformations of the solid solutions have been determined in the temperature range 20°C < T < 300°C.     

Phase-space quality factor for ultrashort pulsed beams

We derive an expression for the lower bound of the phase-space beam quality factor M(2) of an ultrashort pulse. We show that the condition M(2)>or=1 does not, in general, hold for such pulsed beams. Rather, the minimum value of M(2) depends on the pulse spectrum. We also show that M(2) attains minimum only for pulsed beams whose spot size varies with frequency as omega(-1/2), and that the radial intensity profile of the best-quality pulsed beam can be non-Gaussian.     

Multi-stage work hardening in soft KCl crystals

In order to verify notions about the nature of the stage behaviour in KCl crystals the influence of purity and dimensions of KCl crystals on the stage behaviour of the workhardening curve τ(ϵ) has been studied. It is shown that in soft KCl crystals up to six stages of work hardening are observed. With increasing rigidity and decreasing sample dimensions (less than 2 mm² cross section) the number of observable stages is reduced to three. As work hardening builds up the extent of odd stages (I, III, V) grows and that of even stages (II, IV) falls. The dependence of 1/γ on strain ϵ (γ-activation “volume” of dislocation motion) for all the crystals studied is shown to replicate the τ(ϵ) curve. The rule of increasing the linear density of thermally surmountable obstacles on dislocations is the same for every pair of stages. This indicates that the nature of stages III and V is the same and caused by the activity of new slip systems oblique to the primarily active in stages II and IV, respectively.