Minkowski Length of 3D Lattice Polytopes

We study the Minkowski length L(P) of a lattice polytope P, which is defined to be the largest number of non-trivial primitive segments whose Minkowski sum lies in P. The Minkowski length represents the largest possible number of factors in a factorization of polynomials with exponent vectors in P, and shows up in lower bounds for the minimum distance of toric codes. In this paper we give a polytime algorithm for computing L(P) where P is a 3D lattice polytope. We next study 3D lattice polytopes of Minkowski length 1. In particular, we show that if Q, a subpolytope of P, is the Minkowski sum of L=L(P) lattice polytopes Q _i , each of Minkowski length 1, then the total number of interior lattice points of the polytopes Q ₁,??,Q _L is at most 4. Both results extend previously known results for lattice polygons. Our methods differ substantially from those used in the two-dimensional case.     

A robust small-molecule microarray platform for screening cell lysates

Herein we report the expanded functional group compatibility of small-molecule microarrays to include immobilization of primary alcohols, secondary alcohols, phenols, carboxylic acids, hydroxamic acids, thiols, and amines on a single slide surface. Small-molecule "diversity microarrays" containing nearly 10,000 known bioactive small molecules, natural products, and small molecules originating from several diversity-oriented syntheses were produced by using an isocyanate-mediated covalent capture strategy. Selected printed bioactive compounds were detected with antibodies against compounds of interest. The new surface of the diversity microarrays is highly compatible with approaches involving cellular lysates. This feature has enabled a robust, optimized screening methodology using cellular lysates, allowing the detection of specific interactions with a broad range of binding affinity by using epitope-tagged or chimeric fluorescent proteins without prior purification. We believe that this expanded research capability has considerable promise in biology and medicine.     

Ipso-chlorosulfonylation of calixarenes: a powerful tool for the selective functionalization of the large rim

In our quest for the elaboration of supramolecular models of metallo-enzyme active sites, we became interested in developing new methodologies for the selective functionalization of the large rim of calix[6]arenes. Here, we describe a novel reaction, i.e. the ipso-chlorosulfonylation of calixarene derivatives. The process has been found to be highly efficient, selective and versatile. The regioselectivity is controlled by the nature of the O-substituents at the small rim. Indeed, when O-alkylated by a protonable imidazole group, the aromatic rings are deactivated toward an electrophilic attack and the anisol units can be selectively ipso-chlorosulfonylated under mild conditions (rt). Performing the reaction at a higher temperature allowed the per-chlorosulfonylation to take place. Hence, the synthesis of various sulfonate and sulfonamide derivatives is reported. Finally, a combination of ipso-nitration and chlorosulfonylation allows the per-functionalization of the aromatic units at the large rim in selective alternate positions. Overall, this novel methodology opens new routes to a variety of calixarenes, allowing the tuning of their physical properties without drastically altering their hydrophobic conic cavities.     

Dual solutions in mixed convection boundary layer flow of micropolar fluids

The steady mixed convection boundary layer flow over a vertical surface immersed in an incompressible micropolar fluid is considered in this paper. Employing suitable similarity transformations, the governing partial differential equations are transformed into ordinary differential equations, and the transformed equations are solved numerically by the Keller-box method. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity, angular velocity and temperature profiles. Both cases of assisting and opposing buoyant flows are considered. It is found that dual solutions exist for the assisting flow, besides that usually reported in the literature for the opposing flow. Moreover, in contrast to the classical boundary layer theory, the separation point of the boundary layer is found to be distinct from the point of vanishing skin friction.     

Development of a biomechanical model to study the horizontal vibration transmitted from shoulder to head

On daily activity a human operator is exposed to vibration in working environment. So, the human body will react in different way. The problem is how much from the initial signal will be sent to the other parts of the body and how much that motion will be damped along the studied parts. The vibrations in horizontal plane are some unexpected, so the human operator will not take any position to prevent them. In this condition the horizontal vibrations will have the higher effect possible. In this paper, the shoulder, neck and the head are modeled together like a mechanical system with four degree of freedom. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Reynolds analogy for the mixed convection over a vertical surface with prescribed heat flux

The steady mixed convection boundary layer flow over a vertical surface with prescribed heat flux is revisited in this Note. The subset of solutions which can be obtained with the aid of the Reynolds analogy is discussed in a close relationship with the dual solutions reported by Merkin and Mahmood [1] for impermeable, and more recently by Ishak et al. [2], for permeable surfaces.      

PdGa intermetallic hydrogenation catalyst: an NMR and physical property study

The PdGa intermetallic compound is a highly selective and stable heterogeneous hydrogenation catalyst for the semi-hydrogenation of acetylene. We have studied single crystals of PdGa grown by the Czochralski technique. The (69)Ga electric-field-gradient (EFG) tensor was determined by means of NMR spectroscopy, giving experimental confirmation of both the recently refined structural model of PdGa and the theoretically predicted Pd-Ga covalent bonding scheme. The hydrogenation experiment has detected no hydrogen uptake in the PdGa, thus preventing in situ hydride formation that leads to a reduction of the catalytic selectivity. We have also determined bulk physical properties (the magnetic susceptibility, the electrical resistivity, the thermoelectric power, the Hall coefficient, the thermal conductivity and the specific heat) of single-crystalline PdGa. The results show that PdGa is a diamagnet with metallic electrical resistivity and moderately high thermal conductivity. The thermoelectric power is negative with complicated temperature dependence, whereas the Hall coefficient is positive and temperature-dependent, indicating complexity of the Fermi surface. Partial fulfillment of the NMR Korringa relation reveals that the charge carriers are weakly correlated. Specific heat measurements show that the density of electronic states (DOS) at the Fermi energy of PdGa is reduced to 15% of the DOS of the elemental Pd metal.     

Chiral Bis(tetrathiafulvalene)-1,2-cyclohexane-diamides

Chiral bis(TTF) diamides have been obtained in good yields (54–74%) from 1,2-cyclohexane-diamine and the corresponding TTF acyl chlorides. The (R,R)-1 and (S,S)-1 enantiomers have been characterized by circular dichroism and the racemic form by single-crystal X-ray diffraction. The neutral racemic bis(TTF)-diamide shows the formation of a pincer-like framework in the solid state, thanks to the intramolecular S···S interactions. The chemical oxidation in a solution using FeCl₃ provides stable oxidized species, while the electrocrystallization experiments provided radical cation salts. In particular, single-crystal resistivity measurements on the racemic donor with AsF₆⁻ as a counterion demonstrate semiconductor behavior in this material. The DFT and TD-DFT calculations support the structural and chiroptical features of these new chiral TTF donors.