Nearest-neighbor two-point correlation function of the Z-invariant eight-vertex model

The nearest-neighbor two-point correlation function of the Z-invariant inhomogeneous eight-vertex model in the thermodynamic limit is computed using the free-field representation. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 3, 243–247 (10 August 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Cauchy problem and averaging in Fock space

We investigate a Cauchy problem in the Fock space for a system consisting of a two-level atom, a quantum field, and a classical field. A solution estimate is obtained for the Cauchy problem with initial data from a special class. This class is invariant with respect to the dynamic semigroup of the system. We propose an averaging method for solving the Cauchy problem in the case where the Hamiltonian parameters differ greatly in the order of magnitude. An estimate of the averaging error is obtained. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 1, pp. 92–106, October, 1998.     

Synthesis of ω-amino- and ω-carboxyalkylamides of N-acetylmuramoyl-L-alanyl-D-isoglutamine

The synthesis has been effected of derivatives of MDP having a spacer with an amino or carboxy group. The final stage of the synthesis was the condensation of Boc-L-Ala-D-iGln with 6-aminohexanol (followed by the two-stage replacement of the hydroxy by an azido group) or with benzyl 6-aminohexanoate.Simferopol' State University. Translated from Khimiya Prirodnykh Soedinenii, No. 1, pp. 122–125, January–February, 1993.     

Noncoercive Boundary Value Problems for Elliptic Partial Differential and Differential-Operator Equations

In this paper we find conditions guarantee that irregular boundary value problems for elliptic differential-operator equations of the second order in an interval are fredholm. We apply this result to find some algebraic conditions guarantee that irregular boundary value problems for elliptic partial differential equations of the second order in cylindrical domains are fredholm. Apparently this is the first paper where the regularity of an elliptic boundary value problem is not satisfied on a manifold of the dimension equal to dimension of the boundary. Nevertheless the problem is fredholm and the resolvent is compact. It is interesting to note that the considered boundary value problems for elliptic equations in a cylinder being with separating variables are noncoercive.     

Efficient synthesis of an aldehyde‐capped polythiophene containing fluorinated electron‐withdrawing groups

To incorporate an acceptor type polythiophene segment onto a supramolecular block copolymer for potential light harvesting applications, effective synthetic routes for the end‐functionalized and acceptor‐substituted polythiophenes are critical. The Ullmann coupling reaction can be utilized to obtain electron‐deficient polythiophenes and to attach terminal thiophene units that carry functional groups. In this article, the reactions involving a 2,5‐dibromothiophene monomer containing an electron‐withdrawing fluorinated ester and 5‐bromo‐2‐thiophenecarboxaldehyde (the end‐capper) were studied in detail. It was found that the Ullmann coupling reaction of the dibromide is very fast (completed in a few minutes) and the terminal bromine group does not survive long under the reaction condition. These findings lead to the development of an effective procedure for aldehyde end‐capping of electron‐deficient polythiophenes. Polymers with molecular weights around 4000 Da are routinely obtained. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 41–47, 2007     

Subthreshold ϕ-meson production and medium effects in proton-nucleus reactions

Within the spectral function approach, we study the direct production and decay via the dikaon (dimuon) channel of ϕ mesons in the interactions of 2.4-and 2.7-GeV protons with light and medium target nuclei. It is shown that the K ⁺ K ⁻ (μ⁺ μ⁻) invariant-mass distribution consists of the two components, which correspond to the ϕ decay “outside” and “inside” the target nucleus. The first (narrow) component has the free ϕ width, while the second (broad) component is distorted by the nuclear matter owing to resonance-nucleon scattering and a possible in-medium modification of the kaons and ρ meson at finite baryon density. The relative strength of the “inside” and “outside” components is analyzed in different scenarios for the ϕ width and momentum cut. It is demonstrated that the width of the resulting dimuon invariant-mass distribution on medium nuclei is larger than the free ϕ width by a factor of about 2 if the total ϕ in-medium width is used and the respective cutoff for the ϕ three-momentum is applied, whereas the resulting dikaon invariant-mass distribution has an insignificant sensitivity to the ϕ in-medium properties owing to the strong absorption of the K ⁻ in the surrounding nuclear matter. On the other hand, because of the distortion of the K ⁺ and K ⁻ on their way out of the target nucleus mainly due to the hadronic kaon potentials, the latter distribution is broadened and shifted to higher invariant masses, which means that the measurement of such broadening would give additional evidence for the modification of the kaon and antikaon properties in the nuclear medium. The text was submitted by the author in English.     

Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007