Renormalization point invariance,twisted fans,and critical exponents at finite ϵ in the reggeon calculus.

A procedure for calculating critical exponents directly at finite ? is proposed. It relies on the invariance of the critical exponents at the critical coupling g^c of the full theory with respect to finite changes in the renormalization point. This is expressed as the coincidence of curves at the point β = 0 in the plane of β versus a critical exponent parametrically described by the renormalized coupling for various values of the renormalization point (the “twisted fan”). If more than one critical exponent is present the fan is a set of curves in a multidimensional space with the twist at β = 0 and the exact values of the critical exponents. In perturbative approximations, an approximate invariance may result whether or not a zero of β exists to that order. We show that in the one and two loop approximations to the Reggeon calculus this approximate invariance does occur. The values of the critical exponents at the approximate twists show remarkable stability properties. We obtain σ_tot ≈ (lns)^?γ where ?γ ≈ 0.11 and 0.17 for one and two loops respectively.     

The n-loop expansion of the Reggeon calculus

We apply the technique known in solid state physics as the n-loop expansion to calculate the critical indices of the φ³ Gribov Reggeon calculus directly in two transverse dimensions. Infrared pathologies of the massless theory require the calculation to be done in the infinite momentum limit of the massive theory. For n = 1 the results are close to those of the ε-expansion in O(ε). For n = 2 the β function has no zero, analogously to the case in solid state physics. Use of a Padé approximant for β yields σ_tot ≈ (1n s)^0.27 at infinity, close to the O(ε²) result.     

Tetrameric zirconium(IV) compounds derived from oxozirconium(IV) chloride and heterocyclic aldimines and ketimines

Summary Interaction of ZrOCl₂:8H₂O, [Zr₄(OH)₈(H₂O)₁₆]Cl₈ 12H₂O, with the heterocyclic, aldimines (PyAlA) and heterocyclic ketimines (AcPyA) in Me₂CO in the presence of HC(OEt)₃ yields white amorphous compounds of the type [Zr₄(OH)₁₂(H₂O)₈(PyAlA)₂]Cl₄ and [Zr₄(OH)₁₂(H₂O)₁₀(AcPyA)]Cl₄. Presumably these compounds have a tetrameric dodecahedral structure, derived from the parent. The analytical data, i.r., electrical conductance and t.g. measurements all favour the tetrameric formulation. The t.g. studies also indicate the intermediacy of complex species, which lose water and the Schiff base ligands, with increase in temperature.     

A model for πp,Kp and ψp total cross section ratios

We calculate the ratios of πp, Kp and ψp total cross sections utilizing coupled homogeneous linear integral equations supplemented with SU(4) symmetry for the couplings. Kinematic effects arising from mass splitting and t_min effects are crucial. We obtain $\text{σ}{}_{\mathrm{<mtext>\pi </mtext><mtext>p</mtext>}}\text{σ}{}_{\mathrm{<mtext>Kp</mtext>}}\text{≈ 1.7}\text{and}\text{σ}{}_{\mathrm{<mtext>\psi </mtext><mtext>p</mtext>}}\text{σ}{}_{\mathrm{<mtext>\pi </mtext><mtext>p</mtext>}}\text{≈}\text{1}\text{50}$.     

C3-bonded hetero-β-diketonates of palladium(II)

Reactions of PdL₂ complexes, where LH = benzoylacetone, dibenzoyl methane, or dipivaloyl methane, with pyridine and neat β-diketones (L ¹H trifluoroacetylacetone, hexafluoroacetylacetone, thenoyltrifluoroacetone and pivaloyltrifluoroacetone) in toluene resulted in the formation of central carbon (C³) bonded hetero-β-diketonate complexes of the formula [Pd(L)(C³-L′)py]. These were characterized by microanalyses, IR and ¹H NMR spectral data.     

N2 Monolayers on graphite: Specific heat and vapor pressure measurements — thermodynamics of size effects and steric factors

Calorimetric and vapor pressure measurements of N₂ monolayers on Grafoil have been made in the regions recently explored by neutron scattering. The phase transition at T = 48 K involves approximately symmetric specific heat anomalies of 2&#x0303; K FWHM, and the peak position shifts about 1 K from $\text{1}\text{3}$ to $\text{2}\text{3}$ of one monolayer. In spite of the peak width and temperature shift the transition is intrinsically first order, due to melting of the √3 registered structure into a disordered phase in the presence of 2D vapor. The shift and broadening are shown to be a consequence of size effects primarily due to large edge-to-area ratios of the ordered phase domains. A formula relating the domain size to the shift in transition temperature gives r = 50' A for the mean radius of the domains. At film densities above $\text{2}\text{3}$ monolayer the peak broadens and shifts to a higher temperature until a critical region is reached near T= 85 K. The combined heat capacity and vapor pressure data indicate that there is no two phase region at coverages near monolayer completion and that the transition near T = 85 K is higher than first order. Effects of molecular orientation and surface-normal vibration appear in certain regions of temperature and density. A phase diagram is constructed which is consistent with both calorimetric and neutron scattering results.     

Ultrasound-assisted analyte extraction for the determination of sulfate and elemental sulfur in zinc sulfide by different liquid chromatography techniques

The speciation and determination of sulfate (SO4(2-)) and elemental sulfur (S degree) in zinc sulfide (ZnS) using ion-chromatography (IC) and reversed-phase liquid chromatography (RPLC) respectively is described. Three sample pretreatment approaches were employed with the aim of determining sulfate: (i) conventional water extraction of the analyte; (ii) solid-liquid aqueous extraction with an ultrasonic probe; and (iii) elimination of the zinc sulfide matrix via ion-exchange dissolution (IED). The separation of sulfate was carried out by an anion-exchange column (IonPac AS17), followed by suppressed conductivity detection. Elemental sulfur was extracted ultrasonically from the acid treated sample solution into chloroform and separated on a reversed phase HPLC column equipped with a diode array detector (DAD) at 264 nm. The achievable solid detection limits for sulfate and sulfur were 35 and 10 microg g(-1) respectively.     

Random vibration analysis of stochastic time-varying systems

The analysis of the free and forced vibration of a randomly time-varying system is the subject matter of this paper. This is a complicated problem which has received relatively little discussion in the literature. Herein two methods are presented, apart from the digital simulation technique, of finding the response moments. The first one is a series technique which can be considered as a generalization of the well known Galerkin method. The second method belongs to the class of closure techniques. Upon presuming some of the joint distributions to be Gaussian, equations are derived for the first two response moments. It is shown further that the non-Gaussian output density can be approximately predicted by a simple transformation. Detailed numerical results are obtained and compared with computer simulated response statistics. It is demonstrated that the methods developed here are highly efficient. In particular it is found that the Gaussian closure approximation has a wide range of application.     

Spectral studies on mixed ligand complexes of sodium dinitro-bis(acetylacetonato) cobaltate(iii) with imida-zole ligands

A number of mixed ligand complexes, nitro(imidazole) bis(acetylacetonato) cobaltate(III), [Co(acac)₂ (NO₂ )₂ (L)] (L = imidazole or substituted imidazole) have been synthesised and characterised on the basis of chemical analyses, IR, electronic, mass and nuclear (¹H and ¹³C) magnetic resonance spectra as well as TGA and DTA data. All complexes are non-electrolytic and possess a trans octahedral structure. The NO₂^? group is coordinated through the N atom. Though the ¹H NMR data of fresh CDCl₃ solutions of complexes confirm the trans structure, slow isomerisation to the cis configuration is observed at room temperature.