Some homological properties of commutative semitrivial ring extensions

LetR be a commutative ring with 1 andM anR-module. If:M _R MR is anR-module homomorphism satisfying(mm)=(mm) and(mm)m=m(mm), the additive abelian groupRM becomes a commutative ring, if multiplication is defined by (r,m)(r,m)=(rr+(mm),rm+rm). This ring is called the semitrivial extension ofR byM and and it is denoted byR M. This generalizes the notion of a trivial extension and leads to a more interesting variety of examples. The purpose of this paper is to studyR M; in particular, we are interested in some homological properties ofR M as that of being Cohen-Macaulay, Gorenstein or regular. A sample result: Let (R,m) be a local Noetherian ring,M a finitely generatedR-module and Im() m. ThenR M is Gorenstein if and only if eitherRM is Gorenstein orR is Gorenstein,M is a maximal Cohen-Macaulay module andMM ^*, where the isomorphism is given by the adjoint of.     

Dielectric relaxation studies of 1-hexanol and 1,2-hexanediol in heptane

Solutions of 1-hexanol and 1,2-hexanediol in heptane have been investigated tigated by means of dielectric time domain spectroscopy (TDS). The permittivity spectrum of 1-hexanol in heptane is characterized by a model function containing a sum of three elementary Debye dispersions, while 1,2-hexanediol in heptane is best described by a Cole-Davidson model function. It is shown that dilute solutions of 1-hexanol in heptane have a completely different behavior to that of 1,2-hexanediol. For the diol, the relaxation time levels off at a high value indicating an existence of higher hydrogen bonded complexes. It is possible to quantify the relative amount of monomeric 1-alcohol molecules from the dielectric spectrum. The monomerization rate for 1-hexanol upon dilution with heptane is initially low, but increases rapidly for mole fractions of heptane exceeding 0.4.     

A microwave-assisted click chemistry synthesis of 1,4-disubstituted 1,2,3-triazoles via a copper(I)-catalyzed three-component reaction

A microwave-assisted three-component reaction was used to prepare a series of 1,4-disubstituted-1,2,3-triazoles from corresponding alkyl halides, sodium azide, and alkynes. This procedure eliminates the need to handle organic azides, as they are generated in situ, making this already powerful click process even more user-friendly and safe.     

Multiple binding modes of the camptothecin family to DNA oligomers

The binding constants of camptothecin, topotecan and its lactone ring-opened carboxylate derivative to DNA octamers were measured by UV and NMR spectroscopy. The self-association of topotecan (TPT) was also measured. The carboxylate form of TPT binds in the same way as the lactone, but more weakly. Titration of TPT into d(GCGATCGC)2 shows a preferred location stacked onto the terminal G1 base. However, the intermolecular NOEs cannot be reconciled with a single conformation of the complex, and suggest a model of a limited number of conformations in fast exchange. MD calculations on four pairs of starting structures with TPT stacked onto the G1-C8 base pair in different orientations were therefore performed. The use of selected experimental "docking" restraints yielded ten MD trajectories covering a wide conformational space. From a combination of calculated free energies, NOEs and chemical shifts, some of the structures produced could be eliminated, and it is concluded that the data are consistent with two major families of conformations in fast exchange. One of these is the conformation found in a crystal of a TPT/DNA/topoisomerase I ternary complex [Proc. Natl. Acad. Sci. USA 2002, 99, 15 387-15 392].     

pH sensitivity of Si--C linked organic monolayers on crystalline silicon surfaces.

The electrochemical behavior of Si--C linked organic monolayers is studied in electrolyte-insulator-Si devices, under conditions normally encountered in potentiometric biosensors, to gain fundamental knowledge on the behavior of such Si electrodes under practical conditions. This is done via titration experiments, Mott-Schottky data analysis, and data fitting using a site-binding model. The results are compared with those of native SiO(2) layers and native SiO(2) layers modified with hexamethyldisilazane. All samples display pH sensitivity. The number of Si--OH groups on the alkylated samples is calculated to be less than 0.7 % of that of a pure SiO(2) insulator, which still causes a pH sensitivity of approximately 25 mV per pH unit in the pH range: 4-7. The alkylated samples hardly suffer from response changes during up- and down-going titrations, which indicates that very little oxide is additionally formed during the measurements. The pK(a) values of all samples with monolayers (4.0-4.4) are lower than that of native SiO(2) (6.0). The long-term drift (of approximately 1 mV h(-1)) is moderate. The results indicate that biosensors composed of alkylated Si substrates are feasible if a cross-sensitivity towards pH in the sensor signal is taken into account.     

Path integrals on finite sets

We construct an analogue of the Feynman path integral for the case of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% aaaeaacaaIXaaabaGaamyAaaaadaWcaaqaaiabgkGi2cqaaiabgkGi% 2kaadshaaaqeduuDJXwAKbYu51MyVXgaiuaacqWFvpGAcaWG0bGaey% ypa0JaamisamaaBaaaleaacaGGOaaabeaakmaaBaaaleaacaGGPaaa% beaakiab-v9aQjaadshaaaa!4A8D!\[ - \frac{1}{i}\frac{\partial }{{\partial t}}\varphi t = H_( _) \varphi t\] in which H ₍₎ is a self-adjoint operator in the space L ²(M)= % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeSOaHmkaaa!3744!\[\mathbb{C}\], where _M is a finite set, the paths being functions of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeSyhHekaaa!375D!\[\mathbb{R}\] with values in M. The path integral is a family of measures F _t,t with values in the operators on L ²(M), or equivalently, a family of complex measures corresponding to matrix coefficients.It is shown that these measures on path space are in some sense dominated by the measure of a Markov process. This implies that F _t,t is concentrated on the set of step functions S[t,t].This allows one to make sense of, and prove, the analogue of Feynman's formula for the propagator of the Hamiltonian H=H ₀+V, where V is a potential, namely the formula: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyzamaaCa% aaleqabaGaeyOeI0IaamyAaiaacIcacaWG0bGaai4jaiabgkHiTiaa% dshacaGGPaGaamisaaaakiabg2da9maapebabaGaaeyzamaaCaaale% qabaGaeyOeI0IaamyAamaapedabaGaamOvaiaacIcatCvAUfKttLea% ryqr1ngBPrgaiuGacqWF4baEcaGGOaGaam4CaiaacMcacaGGPaGaae% izaiaabohaaWqaaiaadshaaeaacaWG0bGaai4jaaGdcqGHRiI8aaaa% kiaadAeadaWgaaWcbaGaamiDaiaacEcacaGGSaGaamiDaaqabaGcca% GGOaGaaeizaiab-Hha4jaacMcaaSqaaiaadofacaGGBbGaamiDaiaa% cYcacaWG0bGaai4jaiaac2faaeqaniabgUIiYdaaaa!6410!\[{\text{e}}^{ - i(t' - t)H} = \int_{S[t,t']} {{\text{e}}^{ - i\int_t^{t'} {V(x(s)){\text{ds}}} } F_{t',t} ({\text{d}}x)} \]and the corresponding formulas for the matrix coefficients, in which the integral extends over the paths beginning and ending in the appropriate points. We show that the measures F _t,t are completely determined by these equations and by a certain multiplicative property.The path integral corresponding to a two-particle system without interaction is the direct product of the corresponding path integrals. The propagator for a two-particle system with interaction can be obtained by repeated integration.Finally, we show that the above integral formula can be generalized to the case where the potential is time dependent.     

Analysis of Open Discrete Time Queueing Networks: A Refined Decomposition Approach

This paper deals with approximate analysis methods for open queueing networks. External and internal flows from and to the nodes are characterized by renewal processes with discrete time distributions of their interarrival times. Stationary distributions of the waiting time, the queue size and the interdeparture times are obtained using efficient discrete time algorithms for single server (GI/G/1) and multi-server (GI/D/c) nodes with deterministic service. The network analysis is extended to semi-Markovian representations of each flow among the nodes, which include parameters of the autocorrelation function.     

Thioacetylacetone: structural and vibrational assignments.

Thioacetylacetone and its variously deuterated isotopomers have been investigated using electronic and vibrational spectroscopy combined with quantum chemical calculations. Thioacetylacetone is known for its photochromic properties, but the structures of the initial and final forms have been the subject of a long debate. Analysis of the IR spectra recorded in low-temperature argon and xenon matrices, room-temperature solutions, and in the gas phase has allowed us to establish the nature of the photochromic species and of its precursor. Similar to the case of another beta-thioxoketone, monothiodibenzoylmethane, the photo-product has been assigned to the nonchelated SH exo-rotamer of the (Z)-enethiol tautomeric form, whereas the dominant ground-state species corresponds to the chelated (Z)-enol tautomeric form. Detailed vibrational assignments have been proposed for both forms based on quantum chemical calculations and polarization experiments. In the case of the chelated (Z)-enol species prevailing in the ground state, a second-order perturbative anharmonic analysis at the B3LYP/cc-pVTZ level indicated strong anharmonic effects associated with the intramolecular hydrogen bond, leading to a shift of more than 600 cm-1 of the wavenumber of the OH-stretching vibration. A small fraction of the SH endo-rotameric chelated (Z)-enethiol form was also detected under unperturbed conditions. The (Z)-enethiol form can be converted into the (Z)-enol form by irradiation at 290 nm.