The cyclodimerisation of 3-methyl-2-butenenitrile

3-Methyl-2-butenenitrile (1) cyclodimerised on treatment with lithium diisopropylamide in dimethoxyethane at temperatures between ?78°C and 0°C to 3-amino-4-cyano-1,5,5-trimethyl-1,3-cyclohexadiene (2) the structure of which was established by acid hydrolysis to the known 4-cyano-1,5,5-trimethyl-1-cyclohexene-3-one (3).     

Kinetic theory of granular shear flow: Constitutive relations for the hard-disk model

A kinetic theory for the constitutive Theological relations of rapid granular shear flow of hard circular disks, characterized by a coefficient of restitutione and a surface roughness coefficient, is formulated. From a set of general constitutive equations for single-particle dynamical variables, the approximate expressions for the limit of small and large dimensionless dissipative parameterR _t are obtained. HereR _t is defined as the ratio /, where is the fluctuation of translational velocity from the mean flow velocity, is the diameter of a disk, and is the shear rate. At smallR _t the theoretical predictions can be compared with exact computer simulation results of granular dynamics that are also reported. The agreement between theory and simulation is better than expected; the present theory is accurate up to high packing density in this region ofR _t .     

Effect of ether versus ester tethering on Heck cyclizations

Ether tethers allow Heck cyclizations to proceed in high yields. Ester tethers lead to low yields. Styrene trapping experiments indicate that ester reactions form viable organopalladium intermediates that cannot cyclize efficiently.     

On the viability of small endohedral hydrocarbon cage complexes: X@C4H4, X@C8H8, X@C8H14, X@C10H16, X@C12H12, AND X@C16H16

Small hydrocarbon complexes (X@cage) incorporating cage-centered endohedral atoms and ions (X = H(+), H, He, Ne, Ar, Li(0,+), Be(0,+,2+), Na(0,+), Mg(0,+,2+)) have been studied at the B3LYP/6-31G(d) hybrid HF/DFT level of theory. No tetrahedrane (C(4)H(4), T(d)()) endohedral complexes are minima, not even with the very small hydrogen atom or beryllium dication. Cubane (C(8)H(8), O(h)()) and bicyclo[2.2.2]octane (C(8)H(14), D(3)(h)()) minima are limited to encapsulating species smaller than Ne and Na(+). Despite its intermediate size, adamantane (C(10)H(16), T(d)()) can enclose a wide variety of endohedral atoms and ions including H, He, Ne, Li(0,+), Be(0,+,2+), Na(0,+), and Mg(2+). In contrast, the truncated tetrahedrane (C(12)H(12), T(d)()) encapsulates fewer species, while the D(4)(d)() symmetric C(16)H(16) hydrocarbon cage (see Table of Contents graphic) encapsulates all but the larger Be, Mg, and Mg(+) species. The host cages have more compact geometries when metal atoms, rather than cations, are inside. This is due to electron donation from the endohedral metals into C-C bonding and C-H antibonding cage molecular orbitals. The relative stabilities of endohedral minima are evaluated by comparing their energies (E(endo)) to the sum of their isolated components (E(inc) = E(endo) - E(cage) - E(x)) and to their exohedral isomer energies (E(isom) = E(endo) - E(exo)). Although exohedral binding is preferred to endohedral encapsulation without exception (i.e., E(isom) is always exothermic), Be(2+)@C(10)H(16) (T(d)(); -235.5 kcal/mol), Li(+)@C(12)H(12) (T(d)(); 50.2 kcal/mol), Be(2+)@C(12)H(12) (T(d)(); -181.2 kcal/mol), Mg(2+)@C(12)H(12) (T(d)(); -45.0 kcal/mol), Li(+)@C(16)H(16) (D(4)(d)(); 13.3 kcal/mol), Be(+)@C(16)H(16) (C(4)(v)(); 31.8 kcal/mol), Be(2+)@C(16)H(16) (D(4)(d)(); -239.2 kcal/mol), and Mg(2+)@C(16)H(16) (D(4)(d)(); -37.7 kcal/mol) are relatively stable as compared to experimentally known He@C(20)H(20) (I(h)()), which has an E(inc) = 37.9 kcal/mol and E(isom) = -35.4 kcal/mol. Overall, endohedral cage complexes with low parent cage strain energies, large cage internal cavity volumes, and a small, highly charged guest species are the most viable synthetic targets.     

Conical parametric scattering of a single extraordinary beam in BaTiO3 crystal

In this paper, the parametric scattering of a single extraordinary polarized beam of laser in BaTiO₃ photorefractive crystal has been investigated experimentally and theoretically. The resulting pattern consists of beam fanning, isotropic ring, and anisotropic one. Among all parts of scattering pattern, isotropic ring has not been studied as much as beam fanning and anisotropic ring, and there still are some differences in reports about it. Therefore, the study has mainly focused on this part. In this experimental configuration, isotropic ring is just visible in positive angles although the other parts of parametric scattering pattern can be visible from behind and in front of the crystal. In addition to steady state pattern in forward and backward directions, its transient behavior with the rotation of crystal has been studied. The results of experiments have been analyzed carefully, and their theoretical explanations have been presented based on the standard theory of parametric scattering in photorefractive crystals. It has been shown that this configuration corresponds to the so called parametric B-process scattering.     

A commutative analogue of the group ring

Throughout, all rings R will be commutative with identity element. In this paper we introduce, for each finite group G, a commutative graded Z-algebra R_G. This classifies the G-invariant commutative R-algebra multiplications on the group algebra R[G] which are cocycles (in fact coboundaries) with respect to the standard “direct sum” multiplication and have the same identity element.In the case when G is an elementary Abelian p-group it turns out that R_G is closely related to the symmetric algebra over F_p of the dual of G. We intend in subsequent papers to explore the close relationship between G and R_G in the case of a general (possibly non-Abelian) group G.Here we show that the Krull dimension of R_G is the maximal rank r of an elementary Abelian subgroup E of G unless either E is cyclic or for some such E its normalizer in G contains a non-trivial cyclic group which acts faithfully on E via “scalar multiplication” in which case it is r+1.     

Catalytic asymmetric aza-Darzens reaction with a vaulted biphenanthrol magnesium phosphate salt

Conditions for a catalytic asymmetric aza-Darzens aziridine synthesis mediated by a vaulted biphenanthrol (VAPOL) magnesium phosphate salt is described. Using simple substrates, this methodology explores the scope and reactivity of a new magnesium catalyst for an aziridination reaction capable of building chirality and complexity simultaneously.     

Tumour detection by ultrasonic Doppler blood-flow signals

Ultrasonic Doppler blood-flow signals which seem to be associated with malignant tumour neovascularization have been detected in the female breast. No such signals have been detected from cysts. This discovery may lead to the development of a high-speed ultrasonic Doppler scanner which might make breast screening for cancer practicable.