Crystal structure of a liquid crystal non‐symmetric dimer: cholesteryl 4‐[4‐(4‐n‐butylphenylethynyl)phenoxy]butanoate

The crystal structure of cholesteryl 4‐[4‐(4‐n‐butylphenylethynyl)phenoxy]butanoate [phase sequence: Cr 155°C (46.1?J?g^?1) SmA 186.8°C (1.5?J?g^?1) TGB‐N* 204.7 (6?J?g^?1) I] has been solved from single crystal X‐ray diffraction data. The compound crystallizes in the monoclinic space group P2₁ with unit cell parameters: a?=?13.129(2), b?=?9.3904(10), c?=?17.4121(8)?Å, β?=?92.790(7)°, Z?=?2. The structure has been solved by direct methods and refined to R?=?0.0606 for 3?250 observed reflections. The bond distances and angles are in good agreement with the corresponding values for compounds containing phenyl and cholesterol moieties. The phenyl rings A and B are planar. The dihedral angle between the least‐squares planes of the two phenyl rings is 28°. The cholesterol moiety has the usual structure: the C and E rings have chair conformations, and the D and F rings adopt half‐chair conformations. The molecules in the unit cell are arranged in an antiparallel manner. The crystal structure is stabilized by an intermolecular C–H…O contact of 2.989(10)?Å.     

Electron-impact total cross sections for inelastic processes for furan,tetrahydrofuran and 2,5-dimethylfuran

We report total inelastic, total ionisation and summed total excitation cross sections for electron scattering on furan, tetrahydrofuran (THF) and 2,5-dimethylfuran at energies between the ionisation threshold and 5 keV. We have employed the spherical complex optical potential formalism (SCOP) to calculate the total inelastic cross sections (Q_inel) and have used complex scattering potential-ionisation contribution (CSP-ic) method to derive total ionisation cross sections (Q_ion) and summed total excitation cross sections (∑Q_exc) from the calculated Q_inel. We have also computed Q_ion for these molecules using binary-encounter-Bethe (BEB) approach. We have compared our total cross sections (TCS) with available experimental as well as previous theoretical results and have found good agreement. The results are presented graphically as well as numerically.     

Measuring randomness with periodic media

We show that the sensitivity to disorder of certain physical properties of periodic media depends on whether the disorder is truly random or not. This allows to utilize periodic media for testing sequences of random numbers and to quantify their departure from true randomness via simple transmission and/or reflection data analysis. This physics-based model shows promises for device applications to test random data.     

A polyhedral branch-and-cut approach to global optimization

A variety of nonlinear, including semidefinite, relaxations have been developed in recent years for nonconvex optimization problems. Their potential can be realized only if they can be solved with sufficient speed and reliability. Unfortunately, state-of-the-art nonlinear programming codes are significantly slower and numerically unstable compared to linear programming software.In this paper, we facilitate the reliable use of nonlinear convex relaxations in global optimization via a polyhedral branch-and-cut approach. Our algorithm exploits convexity, either identified automatically or supplied through a suitable modeling language construct, in order to generate polyhedral cutting planes and relaxations for multivariate nonconvex problems. We prove that, if the convexity of a univariate or multivariate function is apparent by decomposing it into convex subexpressions, our relaxation constructor automatically exploits this convexity in a manner that is much superior to developing polyhedral outer approximators for the original function. The convexity of functional expressions that are composed to form nonconvex expressions is also automatically exploited.Root-node relaxations are computed for 87 problems from globallib and minlplib, and detailed computational results are presented for globally solving 26 of these problems with BARON 7.2, which implements the proposed techniques. The use of cutting planes for these problems reduces root-node relaxation gaps by up to 100% and expedites the solution process, often by several orders of magnitude.The research was supported in part by ExxonMobil Upstream Research Company, the National Science Foundation under awards DMII 0115166 and CTS 0124751, and the Joint NSF/NIGMS Initiative to Support Research in the Area of Mathematical Biology under NIH award GM072023.     

Convex extensions and envelopes of lower semi-continuous functions

 We define a convex extension of a lower semi-continuous function to be a convex function that is identical to the given function over a pre-specified subset of its domain. Convex extensions are not necessarily constructible or unique. We identify conditions under which a convex extension can be constructed. When multiple convex extensions exist, we characterize the tightest convex extension in a well-defined sense. Using the notion of a generating set, we establish conditions under which the tightest convex extension is the convex envelope. Then, we employ convex extensions to develop a constructive technique for deriving convex envelopes of nonlinear functions. Finally, using the theory of convex extensions we characterize the precise gaps exhibited by various underestimators of $x/y$ over a rectangle and prove that the extensions theory provides convex relaxations that are much tighter than the relaxation provided by the classical outer-linearization of bilinear terms. Received: December 2000 / Accepted: May 2002 Published online: September 5, 2002 RID="*" ID="*" The research was funded in part by a Computational Science and Engineering Fellowship to M.T., and NSF CAREER award (DMI 95-02722) and NSF/Lucent Technologies Industrial Ecology Fellowship (NSF award BES 98-73586) to N.V.S. Key words. convex hulls and envelopes – multilinear functions – disjunctive programming – global optimization     

A new framework to relax composite functions in nonlinear programs

Mathematical Programming - In this paper, we devise new relaxations for composite functions, which improve the prevalent factorable relaxations, without introducing additional variables, by...     

Performance studies of compact GGAG:Ce,B thermal neutron detector coupled to Si-based photosensors

Pramana - This work concerns the modelling of the dynamics of polarisation of a centrosymmetric material subjected to an amplitude-modulated excitation (AME). The dynamic equation obtained for the...     

Uncatalyzed Michael addition of indoles: synthesis of some novel 3-alkylated indoles via a three-component reaction in solvent-free conditions

Synthesis of some novel 3-alkylated indoles via an uncatalyzed Michael addition of indoles using three components in one-pot solvent-free conditions is reported. The mechanism was established by performing the reaction in two steps. The reaction was also studied in different solvents and an important solvent effect was noticed.