Backward bifurcations in simple vaccination models

We describe and analyze by elementary means some simple models for disease transmission with vaccination. In particular, we give conditions for the existence of multiple endemic equilibria and backward bifurcations. We extend the results to include models in which the parameters may depend on the level of infection.     

Preparation and Structure of [Me3N(CF3)2BCCB(CF3)2NMe3]

Bis‐trimethylamine‐ethynyl‐di‐bis(trifluoromethyl)borane [Me₃N(CF₃)₂BCCB(CF₃)₂NMe₃] ( 1 ) has been prepared from trimethylamine‐ethynyl‐bis(trifluoromethyl)borane, [HCCB(CF₃)₂NMe₃], and dimethylamino‐bis(trifluoromethyl)borane, (CF₃)₂BNMe₂. The structure of 1 has been determined by x‐ray crystallography. In the solid state the molecule possesses crystallographic C_i symmetry. The acetylenic attachment to the boron atom is characterized by a short B–C bond length of 1.565(4) Å and an essentially linear B–C–C′ bond angle of 178.1(4)°.     

Potential photosensitizers for photodynamic therapy. III. Photophysical properties of a lipophilic chlorin and its zinc and tin chelates.

Photophysical properties of a lipophilic chlorin derivative and its zinc and tin chelates were investigated in chloroform. The quantum yields of the fluorescence phi F, of the S1----T1 intersystem crossing phi T and of singlet oxygen (1 delta g) formation phi delta, as well as the Stern-Volmer constants for the quenching of the S1 states by oxygen and the rate constants of quenching of O2(1 delta g) by the chlorins were measured. In comparison to the metal-free chlorin an increase of phi T and a decrease of phi F have been observed for the metal-containing derivatives, whereas the phi delta values remain constant.     

Chromium(VI) Forms Thiolate Complexes with gamma-Glutamylcysteine, N-Acetylcysteine, Cysteine, and the Methyl Ester of N-Acetylcysteine

Reaction of potassium dichromate with gamma-glutamylcysteine, N-acetylcysteine, and cysteine in aqueous solution resulted in the formation of 1:1 complexes of Cr(VI) with the cysteinyl thiolate ligand. The brownish red Cr(VI)-amino acid/peptide complexes exhibited differential stability in aqueous solutions at 4 degrees C and ionic strength = 1.5 M, decreasing in stability in the order: gamma-glutamylcysteine > N-acetylcysteine > cysteine. (1)H, (13)C, and (17)O NMR studies showed that the amino acids act as monodentate ligands and bind to Cr(VI) through the cysteinyl thiolate group, forming RS-Cr(VI)O(3)(-) complexes. No evidence was obtained for involvement of any other possible ligating groups, e.g., amine or carboxylate, of the amino acid/peptide in binding to Cr(VI). EPR studies showed that chromium(V) species at g = 1.973-4 were formed upon reaction of potassium dichromate with gamma-glutamylcysteine and N-acetylcysteine. Reaction of potassium dichromate or sodium dichromate with N-acetylcysteine and the methyl ester of N-acetylcysteine in N,N-dimethylformamide (DMF) also led to the formation of RS-Cr(VI)O(3)(-) complexes as determined by UV/vis, IR, and (1)H NMR spectroscopy. Thus, an early step in the reaction of Cr(VI) with cysteine and cysteine derviatives in aqueous and DMF solutions involves the formation of RS-CrO(3)(-) complexes. The Cr(VI)-thiolate complexes are more stable in DMF than in aqueous solution, and their stability towards reduction in aqueous solution follows the order cysteine < N-acetylcysteine < gamma-glutamylcysteine < glutathione.     

Vibrational spectroscopy of the G...C base pair: experiment, harmonic and anharmonic calculations, and the nature of the anharmonic couplings

The results of harmonic and anharmonic frequency calculations on a guanine-cytosine complex with an enolic structure (a tautomeric form with cytosine in the enol form and with a hydrogen at the 7-position on guanine) are presented and compared to gas-phase IR-UV double resonance spectral data. Harmonic frequencies were obtained at the RI-MP2/cc-pVDZ, RI-MP2/TZVPP, and semiempirical PM3 levels of electronic structure theory. Anharmonic frequencies were obtained by the CC-VSCF method with improved PM3 potential surfaces; the improved PM3 potential surfaces are obtained from standard PM3 theory by coordinate scaling such that the improved PM3 harmonic frequencies are the same as those computed at the RI-MP2/cc-pVDZ level. Comparison of the data with experimental results indicates that the average absolute percentage deviation for the methods is 2.6% for harmonic RI-MP2/cc-pVDZ (3.0% with the inclusion of a 0.956 scaling factor that compensates for anharmonicity), 2.5% for harmonic RI-MP2/TZVPP (2.9% with a 0.956 anharmonicity factor included), and 2.3% for adapted PM3 CC-VSCF; the empirical scaling factor for the ab initio harmonic calculations improves the stretching frequencies but decreases the accuracy of the other mode frequencies. The agreement with experiment supports the adequacy of the improved PM3 potentials for describing the anharmonic force field of the G...C base pair in the spectroscopically probed region. These results may be useful for the prediction of the pathways of vibrational energy flow upon excitation of this system. The anharmonic calculations indicate that anharmonicity along single mode coordinates can be significant for simple stretching modes. For several other cases, coupling between different vibrational modes provides the main contribution to anharmonicity. Examples of strongly anharmonically coupled modes are the symmetric stretch and group torsion of the hydrogen-bonded NH2 group on guanine, the OH stretch and torsion of the enol group on cytosine, and the NH stretch and NH out-of-plane bend of the non-hydrogen-bonded NH group on guanine.     

Heterocyclization of compounds containing diazo and cyano groups. 6. Theoretical and experimental investigations of cyclization of 2-cyano-2-diazoacetamides to 5-hydroxy-1,2,3-triazole-4-carbonitriles

A series of N-alkyl- and N-aryl-2-cyano-2-diazoacetamides was synthesized by the reaction of 2-amino-2-cyanoacetamides with sodium nitrite in hydrochloric acid. The mechanism of their heteroclectrocyclization to 5-hydroxy-1,2,3-triazoles was investigated kinetically and theoretically by the B3LYP/6-31+G^* method. The conclusion was made on the basis of the determined activation energy of the cyclization process. reaction parameters , and kinetic isotope effects, that there is a difference between the mechanisms of cyclization of the N-alkyl and N-aryl derivatives of 2-cyano-2-diazoacetamide; cyclization of the N-alkyl derivatives takes place by a monorotatory mechanism, while cyclization of the N-aryl derivatives takes place by a mechanism where one of the stages is heteroelectrocyclization of 2-diazoacetimidates.For Communication 5, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 26–41, January, 2000.