Statistical properties of random environment of 1<Emphasis Type="Italic">D</Emphasis> quantum <Emphasis Type="Italic">N</Emphasis>-particles system in external field

The investigation of 1D quantum N-particle system (PS) with relaxation in the random environment under the influence of external field is conducted within the framework of the stochastic differential equation of the Langevin—Schrödinger (L—Sch) type. Using L—Sch equation, the 2D second-order nonstationary partial differential equation is found, which describes the quantum distribution in the environment, depending on the energy of nonperturbed 1D quantum N-PS and on the external field parameters. It is shown that the average value of the interaction potential between 1D disordered quantum N-PS and the external field, has the ultraviolet divergence. This problem is solved by the renormalization of the equation for the function of quantum distribution. It is shown that it has a sense of dimensional renormalization which is characteristic for the quantum field theory. Critical properties of the environment are investigated in detail. The possibility of the first-order phase transition in the environment distribution depending on amplitude of an external field is been shown.     

Alternative Proof of Mironov’s Results on Commuting Self-Adjoint Operators of Rank 2

We give an alternative proof of Mironov’s results on commuting self-adjoint operators of rank 2. Mironov’s proof is based on Krichever’s complicated theory of the existence of a high-rank Baker–Akhiezer function. In contrast to Mironov’s proof, our proof is simpler but the results are slightly weaker. Note that the method of this article can be extended to matrix operators. Using the method, we can construct the first explicit examples of matrix commuting differential operators of rank 2 and arbitrary genus.     

Generalized Double Fourier Sine Series

The paper is focused on studies of connections between the integrability of a two-variable function near the origin and the behavior of its generalized Fourier sine series. This problem has direct relevance to issues of asymptotic behavior of Fourier series with monotone coefficients in a neighborhood of the origin.     

Nitrosylation of Nitric‐Oxide‐Sensing Regulatory Proteins Containing [4Fe‐4S] Clusters Gives Rise to Multiple Iron–Nitrosyl Complexes

The reaction of protein‐bound iron–sulfur (Fe‐S) clusters with nitric oxide (NO) plays key roles in NO‐mediated toxicity and signaling. Elucidation of the mechanism of the reaction of NO with DNA regulatory proteins that contain Fe‐S clusters has been hampered by a lack of information about the nature of the iron‐nitrosyl products formed. Herein, we report nuclear resonance vibrational spectroscopy (NRVS) and density functional theory (DFT) calculations that identify NO reaction products in WhiD and NsrR, regulatory proteins that use a [4Fe‐4S] cluster to sense NO. This work reveals that nitrosylation yields multiple products structurally related to Roussin's Red Ester (RRE, [Fe₂(NO)₄(Cys)₂]) and Roussin's Black Salt (RBS, [Fe₄(NO)₇S₃]. In the latter case, the absence of ³²S/³⁴S shifts in the Fe?S region of the NRVS spectra suggest that a new species, Roussin's Black Ester (RBE), may be formed, in which one or more of the sulfide ligands is replaced by Cys thiolates.     

Common eigenfunctions of commuting differential operators of rank 2

Commuting differential operators of rank 2 are considered. With each pair of commuting operators a complex curve called the spectral curve is associated. The genus of this curve is called the genus of the commuting pair. The dimension of the space of common eigenfunctions is called the rank of the commuting operators. The case of rank 1 was studied by I. M. Krichever; there exist explicit expressions for the coefficients of commuting operators in terms of Riemann theta-functions. The case of rank 2 and genus 1 was considered and studied by S. P. Novikov and I.M. Krichever. All commuting operators of rank 3 and genus 1 were found by O. I. Mokhov. A. E. Mironov invented an effective method for constructing operators of rank 2 and genus greater than 1; by using this method, many diverse examples were constructed. Of special interest are commuting operators with polynomial coefficients, which are closely related to the Jacobian problem and many other problems. Common eigenfunctions of commuting operators with polynomial coefficients and smooth spectral curve are found explicitly in the present paper. This has not been done so far.     

Zolotarev polynomials and reduction of Shabat polynomials into a positive characteristic

The paper is focused on the study of Shabat polynomials over fields of different characteristics and their deformation into polynomials with three critical values. Using this deformation, we obtain prime numbers of bad reduction for Shabat polynomials corresponding to trees of diameter 4.     

Synthesis of Conjugated Systems Based on 3-(5-Methylfur-2-yl)-2-(3-oxobutyl)benzofurans

Methods were developed for the synthesis of 3-butyl-2-(3-oxobutenyl)benzofurans and 3-(3-furylbenzofuran-2-yl)acrylic acids on the basis of 3-furyl-2-(3-oxobutyl)benzofurans.     

A Functional Inequality for Sine Series

Mathematical Notes -     

Superconductors are topologically ordered

We revisit a venerable question: what is the nature of the ordering in a superconductor? We find that the answer is properly that the superconducting state exhibits topological order in the sense of Wen, i.e., that while it lacks a local order parameter, it is sensitive to the global topology of the underlying manifold and exhibits an associated fractionalization of quantum numbers. We show that this perspective unifies a number of previous observations on superconductors and their low lying excitations and that this complex can be elegantly summarized in a purely topological action of the “BF” type and its elementary quantization. On manifolds with boundaries, the BF action correctly predicts non-chiral edge states, gapped in general, but crucial for fractionalization and establishing the ground state degeneracy. In all of this the role of the physical electromagnetic fields is central. We also observe that the BF action describes the topological order in several other physically distinct systems thus providing an example of topological universality.     

Phenylpropanoid glycosides of Teucrium polium

Together with poliumoside we have isolated for the first time from golden germander verbascoside and a new phenylpropanoid glycoside (teupolioside) for which the structure of 2-(3,4-dihydroxyphenyl)ethyl O--D-galactopyranosyl-(12)-O--L-rhamnopyranosyl-(13)-4-O-caffeoyl--D-glucopyranoside is proposed. A mixture of poliumoside and teupolioside revealed a moderate antibacterial activity.A. L. Mnadzhoyan Institute of Fine Organic Chemistry, Armenian Academy of Sciences, Erevan. Translated from Khimiya Prirodnykh Soedinenii, No. 5, pp. 630–634, September–October, 1991.