Naphthalene analogues of lignans

The methodology for the synthesis of podophyllotoxin and thuriferic acid-type lignans has been applied to derivatives carrying a naphthalene moiety. Starting from the 1,3-dithiane of 2-naphthaldehyde afforded the expected analogues in the 2,1-naphthalene series. The preferred conformations of these compounds are influenced by the bulky naphthalene system. By contrast, 1,8-bridged products were obtained from the 1,3-dithiane of 1-naphthaldehyde. In this series, polycyclic naphthalene lignan analogues were isolated after deprotection and/or desulfurization reactions. The cyclizations produced in this process are due to the proximity between the 3,4,5-trimethoxyphenyl moiety and the reacting C-2 of the 1,3-dithiane ring.     

Stereodifferentiation of chiral compounds using reversed-phase liquid chromatography coupled with capillary gas chromatography

A method is described for the enantiomeric quantitation of some chiral compounds via online coupling of reversed-phase liquid chromatography-gas chromatography. The evaluation of some variables affecting the experimentation (i.e., the packing material used in the interface, volume of the transferred fraction, desorption time, initial temperature of the interface, and purge time) makes it possible to optimize the recoveries obtained for some chiral terpenes and lactones using a capillary column of beta-cyclodextrin dissolved in OV-1701. The proposed method allows the enantiomeric analysis of aqueous matrices obtaining relative standard deviations lower than 9% and detection limits ranging from 0.26-0.93 ppm for the investigated compounds.     

Multivariate Polynomial Minimization and Its Application in Signal Processing

We make a conjecture that the number of isolated local minimum points of a 2n-degree or (2n+1)-degree r-variable polynomial is not greater than n ^r when n 2. We show that this conjecture is the minimal estimate, and is true in several cases. In particular, we show that a cubic polynomial of r variables may have at most one local minimum point though it may have 2^r critical points. We then study the global minimization problem of an even-degree multivariate polynomial whose leading order coefficient tensor is positive definite. We call such a multivariate polynomial a normal multivariate polynomial. By giving a one-variable polynomial majored below a normal multivariate polynomial, we show the existence of a global minimum of a normal multivariate polynomial, and give an upper bound of the norm of the global minimum and a lower bound of the global minimization value. We show that the quartic multivariate polynomial arising from broad-band antenna array signal processing, is a normal polynomial, and give a computable upper bound of the norm of the global minimum and a computable lower bound of the global minimization value of this normal quartic multivariate polynomial. We give some sufficient and necessary conditions for an even order tensor to be positive definite. Several challenging questions remain open.     

Hermite Interpolation and Sobolev Orthogonality

In this paper, we study orthogonal polynomials with respect to the bilinear form (f, g) _S = V(f) A V(g) ^T + <u, f ^(N) g ^(N)V(f) =(f(c ₀), f "(c ₀), ..., f ^{(n – 1)} ₀(c ₀), ..., f(c _p ), f "(c _p ), ..., f ^{(n – 1)} _p(c _p )) u is a regular linear functional on the linear space P of real polynomials, c ₀, c ₁, ..., c _p are distinct real numbers, n ₀, n ₁, ..., n _p are positive integer numbers, N=n ₀+n ₁+...+n _p , and A is a N × N real matrix with all its principal submatrices nonsingular. We establish relations with the theory of interpolation and approximation.     

Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit

Classical optical lithography is diffraction limited to writing features of a size lambda/2 or greater, where lambda is the optical wavelength. Using nonclassical photon-number states, entangled N at a time, we show that it is possible to write features of minimum size lambda/(2N) in an N-photon absorbing substrate. This result allows one to write a factor of N2 more elements on a semiconductor chip. A factor of N = 2 can be achieved easily with entangled photon pairs generated from optical parametric down-conversion. It is shown how to write arbitrary 2D patterns by using this method.     

Investigation of excited states of11B and7Li by means of thermal neutron capture on10B nuclei

Theγ-radiation from the¹⁰B(n,γ) reaction is studied using an unpolarized target. More accurate values for energies of transitions in¹¹B could be determined. No new levels have been found. TheQ value of this reaction: 11,454.1 (2)keV, is in agreement with earlier experiments. Also a new value for the cross section could be derived: 0.29 (4) barn, which is a factor 5 more accurate than earlier experiments. The¹⁰B(n, α)⁷ Li reaction, leading to the 478 keV state in⁷Li, is studied by means of polarized¹⁰B nuclei and polarized neutrons. The resulting anisotropy in the directional distribution of the⁷Li particles manifests itself in the Doppler broadening of the 478 keV line. Analysis of the line shape directly yields the conclusion, that the reaction proceeds for more than 96% through theJ=7/2 channel of¹¹B in case of destructive channel interference of theJ=5/2 channel. Constructive channel interference is only possible if the reaction proceeds for more than 99.5% through theJ=7/2 channel. It appeared that the outcomingα and⁷Li particles are emitted predominantly in directions perpendicular to the nuclear orientation axis.     

2-Aryl-7,7-dimethyl-5,6,7,8-tetrahydrothieno[3,2-c]azepin-4-ones from 5,5-dimethyl-1,3-cyclohexanedione

A novel synthesis of substituted thieno[3,2-c]azepinones is described. This new approach uses 5,5-dimethyl-1,3-cyclohexanedione (dimedone) as the starting material. Oxime intermediates are obtained in three steps from the aforementioned diketone. Using these intermediates, the title compounds are synthesized in moderate yields.     

On the performance of the ICP algorithm

We present upper and lower bounds for the number of iterations performed by the Iterative Closest Point (ICP) algorithm. This algorithm has been proposed by Besl and McKay as a successful heuristic for matching of point sets in d-space under translation, but so far it seems not to have been rigorously analyzed. We consider two standard measures of resemblance that the algorithm attempts to optimize: The RMS (root mean squared distance) and the (one-sided) Hausdorff distance. We show that in both cases the number of iterations performed by the algorithm is polynomial in the number of input points. In particular, this bound is quadratic in the one-dimensional problem, under the RMS measure, for which we present a lower bound construction of Ω(nlogn) iterations, where n is the overall size of the input. Under the Hausdorff measure, this bound is only O(n) for input point sets whose spread is polynomial in n, and this is tight in the worst case.We also present several structural geometric properties of the algorithm under both measures. For the RMS measure, we show that at each iteration of the algorithm the cost function monotonically and strictly decreases along the vector Δt of the relative translation. As a result, we conclude that the polygonal path π, obtained by concatenating all the relative translations that are computed during the execution of the algorithm, does not intersect itself. In particular, in the one-dimensional problem all the relative translations of the ICP algorithm are in the same (left or right) direction. For the Hausdorff measure, some of these properties continue to hold (such as monotonicity in one dimension), whereas others do not.     

Growth rate determination of heterogeneous microbial population in swine manure

The effect of manure concentration on the growth of the heterogeneous microbial population under batch condition was studied. Four manure concentrations were used in the study. The dehydrogenase activity was used as a measure of the active biomass in the manure. The chemical oxygen demand test was used to measure the change in organic material caused by biological activities. The growth curve of the heterogeneous microbial population in swine manure was essentially similar to that of a pure culture grown batchwise in that it had the four principle phases: lag, exponential growth, stationary, and death. The exponential growth phase followed a diauxic growth pattern. High concentration of manure had an inhibitory effect on the microbial growth. Manure diluted less than 1:3 (manure:water) depressed the specific growth rate of the microbial population.