Proton chemical shifts and pi-electron densities in substituted benzenes

The relation between proton chemical shifts and pi-electron densities in aromatic systems suggested by Schug and Dech has been modified so as to include contributions due to steric effects. The proton chemical shifts inmeta disubstituted benzenes calculated from the modified relation are in good agreement with the observed data. The relation enables one to assess the steric effects of the substituents.     

Thermodynamics of the model of equal spin-spin interactions

We consider the thermodynamics of the model of equal spin-spin interactions. We obtain exact expressions for the correlation functions and heat capacity of finite clusters applicable in the entire range of temperature and external fields. We analyze the obtained thermodynamic characteristics depending on the interaction parameters, the external magnetic field, and the number of particles in the cluster. We find an anomalous behavior of the heat capacity and other thermodynamic quantities due to elementary spin gap excitations occurring in the spectrum. The absence of a long-range order in the system is ensured by the presence of topological excitations (solitons). We study the effect of an anisotropic interaction parameter on the soliton structure.     

Proton emission from nuclei due to neutron interactions

The energy spectra of protons emitted in neutron bombardment of Al²⁷ is analysed in terms of the statistical model and volume direct interaction. It is found that the diffuseness of the nuclear potential or the form of level density used does not alter the shape of the energy spectra very much. The available experimental data agree fairly well with theory. The contribution of direct interaction is seen to be small and hence does not alter the general shape of the spectra. The direct interaction cross-section obtained from the measurements of the angular distribution in the case of iron and copper agree reasonably well with theory.     

Aromaticities of monosubstituted benzenes and thiophenes

The aromaticities of monosubstituted benzenes and thiophenes have been estimated using a method based on dilution shifts proposed earlier. As a result of such studies, a novel method for the study of molecular association in aromatic compounds has been proposed and utilised to study association in phenol and aniline.     

High resolution NMR spectra of some tri-substituted benzenes

This paper presents the analysis of the proton magnetic resonance spectra of 2:4 dinitro phenol, 1-chloro 2:4 dinitro benzene, 1-nitro, 2-methyl, 3-chloro benzene (2-chloro, 6-nitro toluene) and 5-sulpho, 3-nitro benzoic acid based on the exact solution obtained by Jha for the splitting of NMR lines of a three nuclei system of the ABC type.     

Quasiclassical approximation for models of spin-spin interaction on a one-dimensional lattice

The one-dimensional anisotropic Heisenberg model in an external field is considered. For the corresponding energy operator with parameter, the quasiclassical (h0) spectral series are constructed using the method of the canonical operator. In the integrable case (in the absence of the external field) the results obtained coincide with the exact ones.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 133, pp. 63–76, 1984.     

Experimental bounds on parameters of spin-spin interaction in gauge theory of gravitation

The contribution of the pseudovector component of the torsion for the hyperfine splitting of the hydrogen atom is considered. The calculations are made in the framework of a Poincaré gauge theory of gravitation with the most general Lagrangian quadratic in the curvature and torsion and containing a term of Hilbert-Einstein type. Some estimates of the model are obtained.Section of Theoretical Problems, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 2, pp. 307–312, February, 1992.     

Proton magnetic resonance in coumarins

The high resolution proton magnetic resonance spectra of AB, ABC and ABCD systems in fourteen coumarins have been studied. Chemical shifts and spin coupling constants for the protons in various positions in the benzo-α-pyrone ring have been obtained. The spectrum of coumarin confirms the ethylenic nature of double bond between carbon atoms in positions 3 and 4. The chemical shifts for the phenyl protons are in conformity with the reactivities of the coumarins at various positions in the ring. A linear relation has been observed between the chemical shift for proton in 8 position in various 6 substituted coumarins and the Hammett’s constants (σ) for substituents in themeta position. The NMR spectra offer a very convenient method for distinguishing between 3 and 4 substituted coumarins on account of the large chemical shift for the protons in positions 3 and 4. The results do not substantiate resonance of the naphthalene type in coumarin as suggested to explain its dipole moment.     

Aromatic nucleophilic substitutions. Reactions of halogeno and nitro-substituted benzenes—part II

The kinetics of the reaction of 2, 4-dinitro-1-bromo benzene and 2, 4-dinitro-1-iodo benzene with various aromatic bases has been studied in alcohol, alcohol-acetonitrile, alcohol-dimethylformamide and alcohol-dimethyl sulfoxide mixtures. The halogen order observed is Br > Cl > I. No base catalysis has been observed under these conditions. ρ values have been computed. Mechanism of the aromatic nucleophilic substitution is discussed.     

Influence of spin-spin interaction and magnetic field in the collective excitations in superfluid He3

Journal of Mathematical Sciences - The model of He3 is generalized with due regard to spin-spin interaction (SSI). The hydrodynamic action functional describing, in particular, all NMR phenomenon...     

The NMR line shape of a system of nuclear spins with equal spin-spin coupling constants

We obtain an expression for the NMR line at low temperatures for a system of nuclear spins described by a Hamiltonian with equal spin-spin coupling constants. We show that in the case of “easy axis” anisotropy, the line has a logarithmic low-frequency singularity and an exponentially decreasing high-frequency asymptotic behavior at the temperature of an anomalous peak of heat capacity. In the case of “easy plane” anisotropy, the line has the traditional Gaussian form. We discuss the possibility of using NMR data to discover specific thermodynamic and magnetic properties of the considered model system.     

Modelling energy-economy interactions

A model is developed to enable policy analysis for coping with changes in the price and/or availability of energy. A simulation approach is used and the model is validated for the Turkish economy. The model allows the evaluation of tax/subsidy policies, effects of foreign borrowing, etc. on near and medium term macroeconomic factors such as GNP, consumption, capital stock, energy, and non-energy imports.     

Nonlinear radion interactions

Theoretical and Mathematical Physics - We consider the Randall–Sundrum model with two branes in which the fields of the Standard Model are localized on the brane with negative tension and the...     

Finite-range interactions and phases

Summary We consider a one-dimensional system of hard balls on the positive half-line with a general finite-range interaction in thermodynamical equilibrium. We show that, under the action of a weak gravitational field, one can distinguish two spatially separated subsystems: a dense one, which we call the condensate, and a dilute one which we call the gas; between these two, there is a narrow interface where both subsystems mix.     

Micro-swimmers with hydrodynamic interactions

The low-Reynolds-number motions of Purcell’s three-link swimmer, and of a closely related two-paddle swimmer, are investigated and compared using slender-body theory and resistive-force theory. The results are compared (in the case of the three-link swimmer) with the resistive-force calculations of Becker, Koehler and Stone (BKS). In particular, we examine the effect of hydrodynamic interaction and slenderness on the displacement and efficiency of the swimmers. The BKS analysis is, for the most part, confirmed and extended. However, deviations of up to 43% are found in cases where the swimmer propels itself with large stroke angles. Finally, we discuss recent experimental data in light of our numerical results.     

Proton magnetic resonance studies of the association of amino methyl pyridines

Proton magnetic resonance studies of the solutions of (a) 2-amino, 3-methyl pyridine and (b) 2-amino, 6-methyl pyridine in carbontetrachloride show that in these molecules there is an equilibrium between monomers and hydrogen-bonded dimers. The equilibrium constants for the two cases have been obtained. Evidence has also been obtained to show that chloroform forms hydrogen bond with the ring nitrogen of these compounds. These NMR results have been compared with those obtained earlier from infra-red studies.     

Nuclear interactions of K-mesons

Fast K-mesons (τ- as well as K_w-mesons) with energies between 150 and 250 MeV can cause nuclear disintegrations and lose a substantial fraction of their kinetic energy without losing their identity. The character of the interaction in three of the four cases discussed here exhibit a remarkable degree of similarity. The nuclear capture of a K-meson at rest is discussed. The nature and distribution of prongs in the capture star suggest that a Λ°-hyperon may have been formed during the capture process.     

Point interactions inL p

An interpretation is given to point interactions of the form −Δ+d inL ^p (ℝ ^N ), where Δ is the Laplacian operator andd is a pseudopotential related to the ‘Dirac measure at 0', depending on the dimension. They are described as extensions of −Δ, defined on the space {u∈C ₀ ^∞ (ℝ ^N )|u(0)=0} that are negative generators of analytic semigroups. This is done forN=1,2 and 1<p<∞ and forN=3 and 3/2<p<3.