Comparison theorems forL-monosplines of minimal norm

Summary LetLM _N be the set of allL-monosplines withN free knots, prescribed by a pair (x;E) of pointsx = {x _i } ₁ ⁿ ,a <x ₁ < ... <x _n <b and an incidence matrixE = (e _ij ) _i=1 ⁿ , _r-1 ^j=0 with Denote byLM _N ^O the subset ofLM _N consisting of theL-monosplines withN simple knots (n=N). We prove that theL-monosplines of minimalL _p-norms inLM _N belong toLM _N ^O .The results are reformulated as comparison theorems for quadrature formulae.     

Multipole induced splitting of metal-cage vibrations in crystalline endohedral D2d-M2@C84 dimetallofullerenes

Metal-carbon cage vibrations of crystalline endohedral D2d-M2@C84 (M=Sc,Y,Dy) dimetallofullerenes were analyzed by temperature dependent Raman scattering and a dynamical force field model. Three groups of metal-carbon cage modes were found at energies of 35-200 cm(-1) and assigned to metal-cage stretching and deformation vibrations. They exhibit a textbook example for the splitting of molecular vibrations in a crystal field. Induced dipole-dipole and quadrupole-quadrupole interactions account quantitatively for the observed mode splitting. Based on the metal-cage vibrational structure it is demonstrated that D2d-Y2@C84 dimetallofullerene retains a monoclinic crystal structure up to 550 K and undergoes a transition from a disordered to an ordered orientational state at a temperature of approximately 150 K.     

Ab initio Study of the Keto-Enol Equilibriumof Malonaldehyde

 The mechanism of the keto-enol tautomerism of malonaldehyde was studied by ab initio methods using 6-21G^** and 6-311G^** basis functions at the HF level. Two separate mechanisms were examined: through-space proton transfer in the ω-shaped form and through-space proton transfer in a sickle-shaped form obtained from the ω form by rotation. The transition state structure of the ω form is non-planar, whereas that of the sickle form is planar. The sickle form is connected with a 2^nd order saddle, indicating that there should exist a lower energy barrier, i.e. that the through-bond mechanism may be preferred. The calculated energy barriers of keto-enol tautomerism for the sickle form is twice as high as those for the omega form.     

Benzthiazolderivate, 5. Mitt.: Dequartärisierung und nucleophile Substitution von Benzthiazoliumsalzen

Zusammenfassung Benzthiazoliumsalze (I) reagieren, wie an 20 Beispielen gezeigt wird, mit nucleophilen Partnern unter gleichzeitiger Labilisierung des Oniumsystems zu 2-substituierten 2,3-Dihydro-benzthiazolen (dequartärisierende nucleophile Substitution). Der Reaktionsverlauf wird von der Art der nucleophilen Komponente bestimmt: Freie Amino-(Hydrazino)-Verbindungen und I lassen sich im Molverhältnis 21, die Alkalisalze von Aminocarbonsäuren und-sulfosäuren im Molverhältnis 11 umsetzen. Verbindungen mit reaktiver Methylengruppierung reagieren glatt mit der äquivalenten Menge I, wenn in Gegenwart einer Base gearbeitet wird. Die verwendeten I-Verbindungen sind: 2-Äthoxy-3-methyl-benzthiazolium-tetrafluoroborat (VII) und 2-Methylmercapto-3-methylbenzthiazolium-methylsulfat (VIII).     

Multidimensional On-Line SPE for Undisturbed LC-MS-MS Analysis of Basic Drugs in Biofluids

In bioanalytical LC-MS-MS matrix effects influencing the ionization process are a major concern with respect to the quality of the results obtained. In general such matrix effects are directly related to an insufficient sample clean-up of the biofluids. In order to establish a MS-adequate clean-up procedure for basic analytes present in biofluids (e.g. urine, plasma) which is based on solid-phase extraction (SPE) principles a combination of tailor-made SPE column packings and automated column-switching was developed. This novel, multidimensional (MD) SPE platform relies on the combination of a SPE column packed with a restricted access material (RAM) allowing size-exclusion and reversed phase chromatography (SEC-RPC) and a second SPE column packed with a mixed-mode phase (MMP) allowing ion exchange and reversed phase chromatography (IEX-RPC). For the evaluation of this MD-SPE platform 8 tricyclic antidepressants and two metabolites were chosen as model analytes. In order to monitor matrix effects, i.e. ion suppression, postcolumn infusion experiments were performed and compared with a two-dimensional SPE column mode (SEC-RPC). The MD-SPE platform is highly efficient for removal of low and high molecular weight sample components which suppress ionization to varying extend. In addition electrospray ionization of the model analytes is not affected by inter- or intra-individual variations in the composition of the matrix investigated. It is also independent of the species the biofluids originate from. It was demonstrated that the MD-SPE platform has a generic potential with respect to on-line SPE of basic drugs having a pKa > 6.5 and a moderate to low polarity and being present in different biofluids.     

A semiempirical and ab initio MO study of the tautomers ofN-unsubstituted pyrazolones [hydroxy pyrazoles]

Semiempirical (MNDOC, MINDO/3, AM1, and MNDO) and ab initio (STO-3G and 4-31G basis sets) calculations on the relative stabilities, structures, and dipole moments of the 8 theoretically possible tautomeric forms of pyrazolone are reported. It is shown that MNDO + CI and MINDO/3 predict that 5-hydroxy pyrazole, 3-hydroxy pyrazole, and 2-pyrazolin-5-on are the most stable. These results correspond to the known experimental data. Of all used quantum chemical methods, the MINDO/3 results for the dipole moments of the investigated tautomers are in best agreement with the known experimental data. The electronic excitation energies were calculated using the CNDO/S-CI method. The results are in good agreement with the experimental UV spectra.     

Sharp bounds on the number of scattering poles for perturbations of the Laplacian

Sharp bounds on the numberN(r) of the scattering poles in the disc |z|r for a large class of compactly supported perturbations (not necessarily selfadjoint) of the Laplacian in ⁿ ,n3, odd, are obtained. In particular, in the elliptic case the estimateN(r)Cr ⁿ+C is proved.Partially supported by Bulgarian Scientific Fondation under grant no. MM8/91