Three-dimensional Schwarzschild spacetimes

In the following we find all of the three-dimensional flat spacetimes which are static and rotationally symmetric.     

Particle ratios from a chiral SU(3) model

The measured particle ratios in central heavy-ion collisions are investigated within a chemical and thermal equilibrium chiral SU(3) σ?ω approach. Contrary to the commonly adopted non-interacting gas calculations, the chiral SU(3) model predicts modified effective hadron masses and effective chemical potentials in the medium and a transition to a chirally restored phase at high temperatures or chemical potentials. the influence of three different types of phase transitions is investigated. We show that the deduced freeze-out values considerably depend on the underlying model while the quality of the fit is approximately the same.     

Transverse susceptibility as the low-frequency limit of ferromagnetic resonance

A new theory of transverse susceptibility (TS) based on magnetization vector dynamics, as described by the Landau–Lifshitz equation of motion, is given. It is shown that the traditional TS experiment is, in fact, the zero-frequency limit of the ferromagnetic resonance (FMR). The importance of these results resides in the generality of the approach which allows one to find the TS for virtually any magnetic system if an expression for the magnetic free-energy density is known. Moreover, the effect of the frequency of excitatory AC field on the TS experiments and the effect of energy dissipation through the imaginary part of TS emerge coherently from the new TS model.     

2,4,6‐Trifluoropyrimidine. Reactions with nitrogen nucleophiles

In a continuation of our studies involving the nucleophilic displacement of one of the chlorines from 2,4,6‐trichloropyrimidine, we now report the initial displacement of one of the fluorine atoms from 2,4,6‐trifluoropyrimidine using both aliphatic and aromatic amines. The monosubstitution products favor 2‐substitution with ammonia and ethanolamine while aniline gave the 4‐substituted derivative as the preferred product.     

Pyrimidine N-oxides. Preparation of 6-chloro-2,4-diaminopyrimidine 3-N-oxide and its reactions

The peroxyacid oxidation of 6-chloro-2,4-diaminopyrimidine ( 1 ) led to two products, 6-chloro-2,4-diaminopyrimidine 3-N-oxide ( 2 ) and 2,4-diamino-5,6-dichloropyrimidine 3-N-oxide ( 3 ). The assignment of structure of both of these compounds was made on the basis of ir, uv, nmr, and mass spectral data. A discussion of the pathways involved in the formation of 3 is presented.     

Evolutionary Quasi-Variational-Hemivariational Inequalities I: Existence and Optimal Control

Journal of Optimization Theory and Applications - We study a nonlinear evolutionary quasi–variational–hemivariational inequality (in short, (QVHVI)) involving a set-valued...     

An exact homology sequences approach to the controllability of systems

Some results are given on the homology groups of the abstract simplicial complex associated to a multivariable control system, as an extension of the central result of J. Casti (J. Math. Anal. Appl.68 (1979), 347–370) to the multivariable case. The method used is “polyhedral dynamics” as termed by J. Casti, who introduced it. A given control system is mapped into a simplicial complex and then its homological structure is studied. These results, obtained in the multivariable case by the use of the Mayer-Vietoris homology sequence and of the relative homology sequence, present topological invariants for control systems thus creating the possibility of a new topological classification of multivariable systems. An example is given to clarify the approach.     

Multicomponent quantitative resolution of binary mixtures by using continuous wavelet transform

Continuous 1-dimensional wavelet transform (WT) was applied to the quantitative analysis of a vitamin combination of thiamine hydrochloride (THI) and pyridoxine hydrochloride (PYR) with strongly overlapping signals. Absorbance data from the UV-Vis absorption spectrum of width 1150 were subjected to Gauss1 and Gauss2 WTs. Because of its flexibility, data processing, and its high signal amplitude, the continuous WT method is a powerful tool for analysis of multicomponent mixtures. By measuring the amplitude signals corresponding to the selected zero-crossing points of the transformed signal, we obtained the calibration curve. The validation of the calibration graphs was confirmed with different mixtures of THI and PYR at various concentration ratios. A brief explanation of the continuous wavelet method is given. MATLAB 6.5 software was used to perform the calculations. The results of our study were compared with those obtained by spectroscopic, chemometric, and liquid chromatographic methods, and good agreement was found.     

(Fluoren-9-ylidene)methanedithiolato complexes of platinum: synthesis, reactivity, and luminescence

Platinum(II) complexes with (fluoren-9-ylidene)methanedithiolato and its 2,7-di-tert-butyl- and 2,7-dimethoxy-substituted analogues were obtained by reacting different chloroplatinum(II) precursors with the piperidinium dithioates (pipH)[(2,7-R2C12H6)CHCS2] [R = H (1a), t-Bu (1b), or OMe (1c)] in the presence of piperidine. The anionic complexes Q2[Pt{S(2)C=C(C12H6R(2)-2,7)}2] [R = H, (Pr(4)N)(2)2a; R = t-Bu, (Pr4N)(2)2b, (Et4N)(2)2b; R = OMe, (Pr4N)(2)2c] were prepared from PtCl(2), piperidine, the corresponding QCl salt, and 1a-c in molar ratio 1:2:2:2. In the absence of QCl, the complexes (pipH)(2)2b and [Pt(pip)(4)]2b were isolated depending on the PtCl(2):pip molar ratio. The neutral complexes [Pt{S2C=C(C12H6R(2)-2,7)L(2)] [L = PPh(3), R = H (3a), t-Bu (3b), OMe (3c); L = PEt(3), R = H (4a), t-Bu (4b), OMe (4c); L(2) = dbbpy, R = H (5a), t-Bu (5b), OMe (5c) (dbbpy = 4,4'-di-tert-butyl-2,2'-bipyridyl)] were similarly prepared from the corresponding precursors [PtCl2L2] and 1a-c in the presence of piperidine. Oxidation of Q(2)2b with [FeCp2]PF6 afforded the mixed Pt(II)-Pt(IV) complex Q2[Pt2{S2C=C[C12H6(t-Bu)(2)-2,7]}4] (Q(2)6, Q = Et4N+, Pr4N+). The protonation of (Pr4N)(2)2b with 2 equiv of triflic acid gave the neutral dithioato complex [Pt2{S2CCH[C12H6(t-Bu)(2)-2,7]}4] (7). The same reaction in 1:1 molar ratio gave the mixed dithiolato/dithioato complex Pr4N[Pt{S2C=C[C12H6(t-Bu)(2)-2,7]}{S2CCH[C12H6(t-Bu)(2)-2,7]}] (Pr(4)N8) while the corresponding DMANH+ salt was obtained by treating 7 with 2 equiv of 1,8-bis(dimethylamino)naphthalene (DMAN). The crystal structures of 3b and 5c.CH2Cl2 have been solved by X-ray crystallography. All the platinum complexes are photoluminescent at 77 K in CH2Cl2 or KBr matrix, except for Q(2)6. Compounds 5a-c and Q8 show room-temperature luminescence in fluid solution. The electronic absorption and emission spectra of the dithiolato complexes reveal charge-transfer absorption and emission energies which are significantly lower than those of analogous platinum complexes with previously described 1,1-ethylenedithiolato ligands and in most cases compare well to those of 1,2-dithiolene complexes.     

An application of the mannich reaction using hydroxylamine and some of its derivatives. 6-Substituted-2,4-diamino-5,6,7,8-tetrahydropyrimido[4,5-dpyrimidines

Hydroxylamine and some of its O -substituted derivatives ( 2 ) have been used as the amine component in Mannich reactions with 2,4,6-triaminopyrimidine ( 1 ). The resulting 6-substituted tetrahydropyrimido[4,5-d]-pyrimidines ( 3 ) contain an N-0 bond linking the substituent to the ring. These results extend the utility of this modified Mannich reaction to otherwise inaccessible substituents. Reaction conditions, spectral data and certain limitations of the reaction are discussed.