Stereospecific ion-molecule reactions of anabolic-type steroid tertiary alcohols with proton-donating cations

Isobutane and methane chemical ionization (CI) mass spectra of C-17a-epimeric, 17a-substituted 3-methoxyestra-1,3,5(10),8-tetraen-17a-ols and at C-17-epimeric 17-substituted 3-methoxyestra-1,3,5(10)-trien-17-ols, as well as of some their derivatives, have been studied. In each epimeric pair, the peak intensity ratio [MH-H(2)O](+) / [MH](+) is greater for stereoisomers having an axial (or quasi-axial) hydroxyl group. The same regularity in the peak intensity ratio [MH-CH(3)COOH](+) / [MH](+) is valid for acetates in the D-homo series. The observed quantitative differences in CI mass spectra of epimers are explained by steric hindrance of the attack of the proton-donating cation caused by the angular 18-methyl group. No differences in the ease of elimination of the silanol molecule were observed in CI mass spectra of epimeric silyl ethers.     

Diverse redox-active molecules bearing O-, S-, or Se-terminated tethers for attachment to silicon in studies of molecular information storage

A molecular approach to information storage employs redox-active molecules tethered to an electroactive surface. Attachment of the molecules to electroactive surfaces requires control over the nature of the tether (linker and surface attachment group). We have synthesized a collection of redox-active molecules bearing different linkers and surface anchor groups in free or protected form (hydroxy, mercapto, S-acetylthio, and Se-acetylseleno) for attachment to surfaces such as silicon, germanium, and gold. The molecules exhibit a number of cationic oxidation states, including one (ferrocene), two [zinc(II)porphyrin], three [cobalt(II)porphyrin], or four (lanthanide triple-decker sandwich compound). Electrochemical studies of monolayers of a variety of the redox-active molecules attached to Si(100) electrodes indicate that molecules exhibit a regular mode of attachment (via a Si-X bond, X = O, S, or Se), relatively homogeneous surface organization, and robust reversible electrochemical behavior. The acetyl protecting group undergoes cleavage during the surface deposition process, enabling attachment to silicon via thio or seleno groups without handling free thiols or selenols.     

Network manipulation algorithm based on inexact alternating minimization

In this paper, we present a network manipulation algorithm based on an alternating minimization scheme from Nesterov (Soft Comput 1–12, 2020). In our context, the alternative process mimics the natural behavior of agents and organizations operating on a network. By selecting starting distributions, the organizations determine the short-term dynamics of the network. While choosing an organization in accordance with their manipulation goals, agents are prone to errors. This rational inattentive behavior leads to discrete choice probabilities. We extend the analysis of our algorithm to the inexact case, where the corresponding subproblems can only be solved with numerical inaccuracies. The parameters reflecting the imperfect behavior of agents and the credibility of organizations, as well as the condition number of the network transition matrix have a significant impact on the convergence of our algorithm. Namely, they turn out not only to improve the rate of convergence, but also to reduce the accumulated errors. From the mathematical perspective, this is due to the induced strong convexity of an appropriate potential function.

     

On equivalence of Floer's and quantum cohomology

We show that the Floer cohomology and quantum cohomology rings of the almost Kähler manifoldM, both defined over the Novikov ring of the loop space M, are isomorphic. We do it using a BRST trivial deformation of the topological A-model. The relevant aspect of noncompactness of the moduli of pseudoholomorphic instantons is discussed. It is shown nonperturbatively that any BRST trivial deformation of A model which does not change the dimensions of BRST cohomology does not change the topological correlation functions either.     

On the Discrete Hardy Inequality

Necessary and sufficient conditions for the boundedness of thediscrete Hardy operator of the form , from to when 0 < q < 1 <p , is given.     

Integrable structure of conformal field theory,quantum KdV theory and Thermodynamic Bethe Ansatz

We construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as “T-operators,” act in highest weight Virasoro modules. TheT-operators depend on the spectral parameter λ and their expansion around λ=∞ generates an infinite set of commuting Hamiltonians of the quantum KdV system. TheT-operators can be viewed as the continuous field theory versions of the commuting transfermatrices of integrable lattice theory. In particular, we show that for the values $c = 1 - 3\frac{{3(2n + 1)^2 }}{{2n + 3}}$ ,n=1,2,3 .... of the Virasoro central charge the eigenvalues of theT-operators satisfy a closed system of functional equations sufficient for determining the spectrum. For the ground-state eigenvalue these functional equations are equivalent to those of the massless Thermodynamic Bethe Ansatz for the minimal conformal field theoryM _2,2n+3; in general they provide a way to generalize the technique of the Thermodynamic Bethe Ansatz to the excited states. We discuss a generalization of our approach to the cases of massive field theories obtained by perturbing these Conformal Field Theories with the operator Φ_1,3. The relation of theseT-operators to the boundary states is also briefly described.     

Field operators and their spectral properties in finite-dimensional quantum field theory

In Ref. 1 we have considered the finite-dimensional quantum mechanics. There the quantum mechanical space of states wasV=C ^r. It is known that the second quantization of this space is the space of square-summable functions of finite number of variables(L ²(R^r,dx)) (Segal isomorphism). Creation and annihilation operators were introduced in Ref. 1, and the former coincided with the usual position and momentum operators in the conventional quantum mechanics. In this paper we shall investigate the spectral properties of field operators. We shall show that the isomorphism between the exponential ofV andL ²(R^r,dx) can be understood as the decomposition by generalized eigenvectors of field operators (Fourier transform).     

Oxidative coupling of malononitrile with formation of 1,1,2,3,3-pentacyanopropene salts

A simple and convenient route for the synthesis of 1,1,2,3,3-pentacyanopropene salts is reported. These salts are formed by interaction of malononitrile with SeO₂ in presence of organic N-containing bases or pyridinium salts.     

SPECTROCSOPIC STUDIES OF PURINES—III. PROPERTIES OF PURINES SUBSTITUTED AT THE SIXTH AND NINTH POSITIONS*

Abstract— We have investigated the effects of solvent and pH on the absorption and emission propertied of various 6- and 9-substituted purines as a means of examining the nature of the directed not only at deteriming the relative energies of (π,π*) and (π,π*) states, but in particular, at examining the nature and energies of the two lowest-lying (π,π*) states. For examplem, the attachment of a methyl or ribosyl group to the N9 of purine does not change the relative energies of the lowest-lying (π,π*) and (π,π*) states; thus, the latter is the singlet of lowest energy. However, the lowest singles in derivatives formed by substitution at C6 are(π,π*) states—i.e. there is no long-wavelength tail in the absorption spectra and florescence is comparable in intensity to phosphorescence. Further the absence of emission from neutaral adenine at room temperature is due to temperature quenching. Both lowest (π–π*) transtions. are contained under a common envelope and cannot be resolved in the absorption spectra. The shoulder observed in some of these compounds on the long-wavelength slope of absorption envelope is vibrational in nature. Consideration of the effects of solvents on absorption and the analysis of luminescence spectra make it possible to locate the relative position of these (π–π*) transitions within the common envelope. In compounds with an -H on N9 and a free (aza) N1 (e.g. adenine, anionic hupoxanthine) the weaker, solvent-sensitive (W) band has a higher energy then the more intense, solvent-insensitive (S) band. When N1 is protonated, (e.g., in hypoxanthine or cationic adenine) and/or when methyl or ribosyl is substituted at N9, the order of these bands is inverted due ot a red shift of the W band. This shift is most apparent in the 9-substituted hypoxanthines, where in non-polar solvents the W band can be readily resolved in the absoption spectra. This inversion results in a red shift of both fluorescence and phophorescence and an increase of the P/F ratio. When chlorine or iodine is attached at C6 only phosphorescence having a very short lifetime appears due to heavy atom enhancement of single—triplet transitions.