Two natural products from the algae Laurencia scoparia

The structures and absolute stereochemistries of two chamigrene-type metabolites (spiro­[5.5]­un­decane derivatives) isolated from the red algae Laurencia scoparia are described. One, a non-sesquiterpene named ma?lione (8-bromo-9-hydroxy-7,7-di­methyl-11-methyl­ene­spiro­[5.5]­undec-1-en-3-one), C₁₄H₁₉BrO₂, was detected previously in Laurencia cartilaginea, while the other, the sesquiterpene isorigidol (8-bromo-3,7,7-tri­methyl-11-methyl­ene­spiro­[5.5]-undec-1-ene-3,9-diol), C₁₅H₂₃BrO₂, is a new isomer of rigidol, first isolated from Laurencia rigida. The A rings of these spiro­cyclic compounds show the same carbon skeleton. However, the relative stereochemistry of the 8-Br and 9-OH substituents is different. While ma?lione displays the usual syn (or cis) relative stereochemistry of the bromo­hydroxy vicinal group, isorigidol shows an anti (or trans) arrangement. The 8-Br and 9-OH groups are both in equatorial positions in isorigidol, while the 9-OH group is axial in ma?lione, as in most chamigrenes. The absolute configurations of the chiral centers were determined as 6S, 8S and 9R in ma?lione, and 3R, 6S, 8S and 9S in isorigidol.     

Studies in organic mass spectrometry. Part 9—mass spectra of 9,10-disubstituted 2,3,6,7-tetraalkoxy-9,10-dihydroanthracenes: A remarkable loss of radicals from even-electron ions

The electron impact-induced fragmentations of 23 9,10-disubstituted 2,3,6,7-tetraalkoxy-9,10-dihydroanthracenes, including six stereoisomeric pairs, were studied. The loss of the 9-(or 10-)substituent constitutes the main fragmentation route. The resulting ions give rise to a remarkable violation of the so-called ‘even-electron rule’ as they eject the second substituent at the 10-(or 9-)position as a radical. The latter aspect was particularly investigated with the aid of low-energy (nominal value 15 eV) and mass-analysed ion kinetic energy spectra.     

Towards measuring variations of Casimir energy by a superconducting cavity

We consider a Casimir cavity, one plate of which is a thin superconducting film. We show that when the cavity is cooled below the critical temperature for the onset of superconductivity, the sharp variation (in the far infrared) of the reflection coefficient of the film engenders a variation in the value of the Casimir energy. Even though the relative variation in the Casimir energy is very small, its magnitude can be comparable to the condensation energy of the superconducting film, and this gives rise to a number of testable effects, including a significant increase in the value of the critical magnetic field, required to destroy the superconductivity of the film. The theoretical ground is therefore prepared for the first experiment ever aimed at measuring variations of the Casimir energy itself.     

Comprehensive determination of trace elements in human saliva by ETA-AAS

A method is described for the comprehensive determination of a series of trace and ultratrace elements (Fe, Mn, Zn, Cu, Sr, Cr, Al and Si) in human saliva by atomic absorption spectrometry with electrothermal atomization and Zeeman-effect background correction. Procedures for sampling of total mixed saliva and its treatment including centrifugation and mineralization by HNO₃ are described in detail. To avoid the use of matrix modifiers, element standards with an artificial saliva matrix were used to construct calibration curves. Instrumental precision, tested by repeated analyses of natural salivas, is good (error less than 5%) for most elements. Lower precision was obtained for elements like Al and Si present in concentrations close to the detection limit. The analysis of some natural salivas clearly shows the influence of the sampling and treatment procedures on the reliability of the data. An accurate standardization of these procedures is thus recommended.     

Entire functions of exponential type bounded on the real axis and fourier transforms of distributions with bounded supports

On the complexification of the dual spaceE′ of a real Banach spaceE′ of infinite dimension, there is an entire complex valued function of exponential type, bounded onE′, hence slowly increasing onE′, which is not the Fourier transform of any distribution with bounded support onE. Partially supported by the Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, GB, Brasil and by the National Science Foundation, Washington, DC, USA. Attendance at the International Symposium on Partial Differential Equations and the Geometry of Normed Spaces was possible in part thanks to a grant from CAPES, Brasil.     

Stability of the residual free bubble method for bilinear finite elements on rectangular grids

We consider the nature of the stabilizing term arising in theresidual free bubble approach for piecewise bilinear functionson rectangular grids. We show, that on the subspace of piecewiselinear functions the stabilizing term is identical to that inthe streamline diffusion approach. However, on the space ofpiecewise bilinear functions there is a case in which the stabilizingterm is weaker compared to the term used in the streamline diffusionmethod. In the particular case when the direction of the convectionis parallel to a diagonal of the quadrilateral, control is lostover the mixed derivatives in the convection-dominated limit.     

Partitioning study of polycyclic aromatic hydrocarbons between water and some selected water-insoluble phases

An investigation on the partitioning of naphthalene and phenanthrene between water and some water-insoluble phases has been carried out by Uv-vis-NIR spectrophotometry. The analysis of the experimental results emphasized the role of intermolecular interactions and structural features of the hosting phases as driving forces of the partitioning of these polycyclic aromatic hydrocarbons. The critical comparison of the resulting distribution constants allowed to evaluate the potentials of some extracting phases to set up sensitive analytical methods and/or effective environment remediation technologies.     

Supply chain models for an assembly system with preprocessing of raw materials: A simple and better algorithm

Recently, Rahman and Sarker [1] formulated a nonlinear cost function to include the costs of inventories, ordering, shipping and deliveries for a manufacturing system where raw materials enter into the assembly line from two different channels. In order to find the best integer solutions to the variables, they proposed an algorithm that uses the branch and bound concept. The authors claim that their algorithm finds an optimal solution. In this paper, we present a simple and better heuristic algorithm that provides better solutions with a lower number of evaluations than Rahman and Sarker’s algorithm.     

A complement to “A comprehensive note on: An economic order quantity with imperfect quality and quantity discounts”

Chang [1] [H.-C. Chang, A comprehensive note on: an economic order quantity with imperfect quality and quantity discounts, Appl. Math. Model. 35 (10) (2011) 5208-5216] corrects a flaw in Lin’s inventory model [T.Y. Lin, An economic order quantity with imperfect quality and quantity discounts, Appl. Math. Model. 34 (10) (2010) 3158–3165]. Then, he develops an algorithm to find the optimal solution for the corrected Lin’s inventory model and furthermore derives close form expressions to determining the optimal solution to an EOQ inventory model considering items with imperfect quality with different holding costs for good and defective items. In both models there is a discrete variable and he presents some inequalities in order to find the integer value. This paper provides some simple formulas to obtain, in an easy way, the integral value for the discrete variable.     

Hadronic density of states from string theory

We present an exact calculation of the finite temperature partition function for the hadronic states corresponding to a Penrose-Güven limit of the Maldacena-Nù?ez embedding of the N=1 super Yang-Mills (SYM) into string theory. It is established that the theory exhibits a Hagedorn density of states. We propose a semiclassical string approximation to the finite temperature partition function for confining gauge theories admitting a supergravity dual, by performing an expansion around classical solutions characterized by temporal windings. This semiclassical approximation reveals a hadronic energy density of states of a Hagedorn type, with the coefficient determined by the gauge theory string tension as expected for confining theories. We argue that our proposal captures primarily information about states of pure N=1 SYM theory, given that this semiclassical approximation does not entail a projection onto states of large U(1) charge.