Chemical modification of poly(acrylonitrile) with amines

The chemical modification of poly(acrylonitrile) was carried out using monoethanolamine and 1,2-ethylenediamine. The effect of the reaction conditions on the content of basic groups was studied. Polymer analogous reactions were carried out by varying the amount of the starting reagents and the temperature. The amino-containing polymers were characterized by elemental analysis. The obtained water-soluble polymers were used as carriers of low-molecular substances. © 1996 John Wiley & Sons, Inc.     

Thermodynamics of the 3D Hubbard model on approaching the Néel transition

We study the thermodynamic properties of the 3D Hubbard model for temperatures down to the Néel temperature by using cluster dynamical mean-field theory. In particular, we calculate the energy, entropy, density, double occupancy, and nearest-neighbor spin correlations as a function of chemical potential, temperature, and repulsion strength. To make contact with cold-gas experiments, we also compute properties of the system subject to an external trap in the local density approximation. We find that an entropy per particle S/N ≈ 0.65(6) at U/t = 8 is sufficient to achieve a Néel state in the center of the trap, substantially higher than the entropy required in a homogeneous system. Precursors to antiferromagnetism can clearly be observed in nearest-neighbor spin correlators.     

Fourier treatment of near-field synchrotron radiation theory

In this paper, we couple synchrotron radiation (SR) theory with a branch of physical optics, namely laser beam optics. We show that the theory of laser beams is successful in characterizing radiation fields associated with any SR source. Both radiation beam generated by an ultra-relativistic electron in a magnetic device and laser beam are solutions of the wave equation based on paraxial approximation. It follows that they are similar in all aspects. In the space-frequency domain SR beams appear as laser beams whose transverse extents are large compared with the wavelength. In practical situations (e.g. undulator, bending magnet sources), radiation beams exhibit a virtual “waist” where the wavefront is often plane. Remarkably, the field distribution of a SR beam across the waist turns out to be strictly related with the inverse Fourier transform of the far-field angle distribution. Then, we take advantage of standard Fourier Optics techniques and apply the Fresnel propagation formula to characterize the SR beam. Altogether, we show that it is possible to reconstruct the near-field distribution of the SR beam outside the magnetic setup from the knowledge of the far-field pattern. The general theory of SR in the near-zone developed in this paper is illustrated for the special cases of undulator radiation. Using known analytical formulas for the far-field pattern and its inverse Fourier transform we find analytical expressions for near-field distributions in terms of far-field distributions.     

Effects of energy spread on brightness and coherence of undulator sources

The (spectral) brightness for partially transverse coherent sources such as synchrotron radiation and free‐electron laser sources can be defined as the maximum of the Wigner distribution. Then, the brightness includes information on both coherence and wavefront characteristics of the radiation field. For undulator sources, it is customary to approximate the single‐electron electric field at resonance with a Gaussian beam, leading to great simplifications. Attempts to account for the modified spatial and angular profile of the undulator radiation in the presence of detuning due to energy spread, currently build on the simplified brightness expression derived under the assumption of Gaussian beams. The influence of energy spread on undulator radiation properties is becoming important in view of diffraction‐limited rings with ultralow emittance coming on‐line. Here the effects of energy spread on the brightness of undulator radiation at resonance are discussed, as well as relevant relations with coherence properties.     

Cooperative C≡C-H⋯O-H⋯O hydrogen bonding in a crystalline alkynol

In the X-ray crystal structure of the alkynol 5-hydroxy-5-(prop-2-ynyl)-10-methyl-¹⁽⁹⁾-octalin-2-one [C₁₄H₁₈O₂, Pca2 ₁, a = 13.559(1), b = 7.960(2), c = 21.748(3) Å], the hydroxyl and propynyl groups form a hydrogen bond chain C---C-HO-HO which is supposed to be a cooperative arrangement. Quantum chemical calculations estimate cooperativity enhancement within the array to be 0.4 kcal/mol, which is only a small (but recognizable) effect.     

On bands in which every finitely generated subband is an endomorphic image

A semigroup S is calledE-semigroup ( -semigroup) if every (finitely generated) subsemigroup of S is an endomorphic image of S and Ē-semigroup ( -semigroup) if every subsemigroup of S is an E-semigroup -semigroup. All classes X ε {Ē, , E, } are distinct even in the case of semilattices. It is established when a free band (semilattice) is an X-semigroup. -, - and Ē-chains and E-chains with identity or zero, Ē-and , X-bands with identity and X-semigroups with identity and zero are found.     

Synthesis and crystal structure of dimeric 2,4,6-triphenylphenylbismuthdichloride

Reaction of BiCl₃ with one equivalent of 2,4,6-triphenylphenyllithium in toluene results in the formation of crystalline 2,4,6-triphenyl-phenylbismuthdichloride toluene disolvate (1). The crystal structure of 1 has been determined by X-ray diffraction. In spite of the extremely bulky substituents at the bismuth atom, complex 1 is dimeric in the solid state with intramolecular Bi-Cl bond lengths of 2.530(1) Å and bridging Bi-Cl of 3.074(1) Å.