Structure of 5'-O-acetyl-2',3'-O-isopropylideneuridine, C14H18N2O7

M r = 326.3, monoclinic, P21, a --= 6.510 (2), b=8.432 (2), c= 15.114 (2),a, /~= 101.42 (3) ° , Z = 2, V= 813.15 A 3, D x = 1-33 Mg m -3, F(000) = 172, 2(Cu Ka) = 1.5418/~,, g(Cu Ka) = 0.906 mm -~, final R = 6.4% for 1924 observed counter reflections. The conformation about the glycosidic bond is syn [torsion angle C(6)-N(1)-C(1')-O(4')=-103.9(3)°]. The sugar pucker is C(2')-exo,C(3')-endo (3Tz). The conformation about the C(4')-C(5') bond is gauche-trans. An uncommon intermolecular hydrogen bond involving the ribose-ring oxygen O(1') and the base-nitrogen N(3) stabilizes the crystal structure.

Structure of a thionucleoside: 5'-deoxy-5',6-epithio-5,6-dihydro-2',3'-O-isopropylidene-3-methyluridine

C13HlsN205 S, M r = 314.35, orthorhombic, P212121 with a = 39.526 (4), b = 6.607 (2), c = 5.661 (2) A, Z = 4, V = 1478.36 A 3, D c = 1.412 Mg m -3, Cu Ka radiation. Final R = 0.073 for 1154 observed counter reflections. The sulphur atom is in a pseudo-equatorial position with respect to the dihydrouracil ring. The sugar pucker is predominantly O(l')-exo unlike the C(3')-exo,C(4')-endo observed for 2',3'-O-isopropylideneuridine (ISPU). The fivemembered dioxolane ring has C(7) displaced by 0.497 (7)A from the best plane through atoms 0(2'), C(2'), C(3'), 0(3'), in contrast to ISPU where 0(3') shows the maximum deviation.

Push-pull ethylenes: the structures of 3-(2-imidazolidinylidene)-2,4-pentanedione (I), C8H12N2O2, and 3-(1,3-dimethyl-2-imidazolidinylidene)-2,4-pentanedione trihydrate (II), C10H16N2O2.3H2O

(I): Mr= 168, triclinic, P1, Z=2, a= 5.596 (2), b = 6.938 (3), c = 10.852 (4) A, ~t= 75.64 (3), fl= 93.44 (3), ),= 95.47 (3) °, V= 406.0A 3, Din= 1.35 (by flotation using carbon tetrachloride and n-hexane), D x= 1.374 Mg m -3, g(Mo Kct, 2 = 0.7107 A) = 1.08 cm -l, _F(000) = 180, T= 293 K. (II): Mr= 250, triclinic, P1, Z= 2, a = 7.731(2), b=8.580(2), c=11.033(3)A, a= 97-66 (2), fl= 98.86 (2), y= 101.78 (2) °, V= 697.5 A 3, D m = 1.18 (by flotation using KI solution), Dx= 1.190Mgm -3, g(MoKa, 2=0.7107A)= 1.02 cm -1, F(000) = 272, T= 293 K. Both structures were solved by direct methods and refined to R = 4.4% for 901 reflexions for (I) and 5.7% for 2001 reflexions for (II). The C=C bond distances are 1.451 (3) A in (I) and 1.468 (3)A in (II), quite significantly longer than the C=C bond in ethylene [1.336 (2).~; Bartell, Roth, Hollowell, Kuchitsu & Young (1965). J. Chem. Phys. 42, 2683-2686]. The twist angle about the C=C bond in (II) is 72.9 (5) ° but molecule (I) is essentially planar, the twist angle being only 4.9 (5) ° .

Structure of 7-methyl-1(2)a,1(6)a,3(4)a-trihomocubane-1(6)a,3(4)a-dione,star-c12h12o2- a case of enantiomeric and rotational disorder

M r = 188.22, monoclinic, P21/n, a = 6.219 (2), b= 10.508 (2), c=7.339 (1)A, t= 107.64 (2) °, V= 457 ,/k 3, Z = 2, D m - - 1.360 (3), D x = 1.366 (2)Mgm -3, ~,(MoKa) = 0.7107/~, #= 0.053 mm -I, F(000) = 200, T= 293 K. Final R = 5.8% for 614 significant reflections. The molecule, which does not possess a centre of symmetry, occupies a crystallographic centre of symmetry because of the statistical enantiomeric and rotational disorder. Latticeenergy calculations, based on van der Waals attractive and repulsive potentials, clearly show minima at the observed disordered positions.

Structure of 2',3'-O-Isopropylidene-5'-O-tosyluridine, C19H22N 2Oas

M r = 438.45, trigonal, P32, a = b = 13.385 (4), c = 9.900 (5) A,, V = 1536.0 A 3, Z = 3, D x = 1.42, D m = 1.42 Mg m -3, 2(Cu Ka) = 1.5418 A,,g(CuKa) = .800mm -], T=290K, F(000)=690, R=6.0% for 1222 unique reflections with F o>_2o(Fo). This is the first 2',3'-O-isopropylidene pyrimidine nucleoside with the base in a syn orientation with respect to the ribose [Xcy= 116.0(7)°]. The ribose has a C(3')-endo conformation with the phase angle of pseudorotation P = 16.36 (2) °. The dioxolane ring assumes an envelope conformation with 0(2') displaced from the best four-atom plane by 0.50 (1) k. The crystal structure is possibly stabilized by a bifurcated hydrogen bond between N(3) and the 0(2) and 0(4) atoms of screw-related molecules.

Development of special fastener elements

A special finite element (FASNEL) is developed for the analysis of a neat or misfit fastener in a two-dimensional metallic/composite (orthotropic) plate subjected to biaxial loading. The misfit fasteners could be of interference or clearance type. These fasteners, which are common in engineering structures, cause stress concentrations and are potential sources of failure. Such cases of stress concentration present considerable numerical problems for analysis with conventional finite elements. In FASNEL the shape functions for displacements are derived from series stress function solutions satisfying the governing difffferential equation of the plate and some of the boundary conditions on the hole boundary. The region of the plate outside FASNEL is filled with CST or quadrilateral elements. When a plate with a fastener is gradually loaded the fastener-plate interface exhibits a state of partial contact/separation above a certain load level. In misfit fastener, the extent of contact/separation changes with applied load, leading to a nonlinear moving boundary problem and this is handled by FASNEL using an inverse formulation. The analysis is developed at present for a filled hole in a finite elastic plate providing two axes of symmetry. Numerical studies are conducted on a smooth rigid fastener in a finite elastic plate subjected to uniaxial loading to demonstrate the capability of FASNEL.

Vertical uplift capacity of two interfering horizontal anchors in sand using an upper bound limit analysis

The vertical uplift resistance of two interfering rigid rough strip anchors embedded horizontally in sand at shallow depths has been examined. The analysis is performed by using an upper bound theorem o limit analysis in combination with finite elements and linear programming. It is specified that both the anchors are loaded to failure simultaneously at the same magnitude of the failure load. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (xi(gamma)) is determined. On account of interference, the magnitude of xi(gamma) is found to reduce continuously with a decrease in the spacing between the anchors. The results from the numerical analysis were found to compare reasonably well with the available theoretical data from the literature.

Structure Of A Thionucleoside - 5'-Deoxy-5',6-Epithio-5,6-Dihydro-2',3'-Ortho-Isopropylidene-3-Methyluridine

C13HlsN205 S, M r = 314.35, orthorhombic, P212121 with a = 39.526 (4), b = 6.607 (2), c = 5.661 (2) A, Z = 4, V = 1478.36 A 3, D c = 1.412 Mg m -3, Cu Ka radiation. Final R = 0.073 for 1154 observed counter reflections. The sulphur atom is in a pseudo-equatorial position with respect to the dihydrouracil ring. The sugar pucker is predominantly O(l')-exo unlike the C(3')-exo,C(4')-endo observed for 2',3' O-isopropylideneuridine (ISPU). The fivemembered dioxolane ring has C(7) displaced by 0.497 (7)A from the best plane through atoms 0(2'), C(2'), C(3'), 0(3'), in contrast to ISPU where 0(3') shows the maximum deviation.

Polarized ethylenes: structures of (1,3-dimethyl-2-imidazolidinylidene)malononitrile and (1,3-dimethyl-2-perhydropyrimidinylidene)malononitrile

Crystal structures of the title compounds, (I) and (II), have been determined by three-dimensional diffraction methods. Crystals of CsHIoN 4 (I) are monoclinic, space group P21/a with Z = 4, Mr= 162, a = 7.965 (1), b = 16.232 (2), c = 7.343 (1) A, fl = 113.54 (1) °, V = 890.7 A 3, D,n = 1.218, D x = 1.208 gcm -3, g(Cu Ka, 2 = 1.5418/~) = 6.47 em -1, F(000) = 344. The crystals of C9H12N4 (II) are orthorhombic, space group P21en, with Z = 4, Mr = 176, a = 7.983 (3), b = 8.075 (2), c = 14.652 (3) ./k, V = 944.43/~3, Dm= 1.219, D x = 1.237 g cm -3, #(Mo Ka, ). = 0.7107 ,/k) = 0.868 cm -1, F(000) = 376. Both structures were solved by direct methods and refined to R = 5.8% for (I) and 5.3 % for (II). The C-C double-bond distances are 1.407 (3) in (I) and 1.429 (6)/~ in (II), appreciably longer than normal. The steric and push-pull effects result in rotation about the C=C bond, the rotation angles being 20.2 (3) in (I) and 31.5 (6) o in (II).

Polarized Ethylenes: Structures of (l,3-Dimethyl-2-imidazolidinylidene)malononitrile and (l,3-Dimethyl-2-perhydropyrimidinylidene)malononitrile

Crystal structures of the title compounds, (I) and (II), have been determined by three-dimensional diffraction methods. Crystals of CsHIoN 4 (I) are monoclinic, space group P21/a with Z = 4, Mr= 162, a = 7.965 (1), b = 16.232 (2), c = 7.343 (1) A, fl = 113.54 (1) °, V = 890.7 A 3, D,n = 1.218, D x = 1.208 gcm -3, g(Cu Ka, 2 = 1.5418/~) = 6.47 em -1, F(000) = 344. The crystals of C9H12N4 (II) are orthorhombic, space group P21en, with Z = 4, Mr = 176, a = 7.983 (3), b = 8.075 (2), c = 14.652 (3) ./k, V = 44.43/~3, Dm= 1.219, D x = 1.237 g cm -3, #(Mo Ka, ). = 0.7107 ,/k) = 0.868 cm -1, F(000) = 376. Both structures were solved by direct methods and refined to R = 5.8% for (I) and 5.3 % for (II). The C-C double-bond distances are 1.407 (3) in (I) and 1.429 (6)/~ in (II), appreciably longer than normal. The steric and push-pull effects result in rotation about the C=C bond, the rotation angles being 20.2 (3) in (I) and 31.5 (6) o in (II).

The structures of ethyl 1,2,2-tricyano-3,3-dimethylcyclopropane-1-carboxylate and ethyl 2',3,3'-tricyanocyclohexanespirocyclopropane-2'-carboxylate

The crystal and molecular structures of C ,,H,IN302 (I) and C14HIsN302 (II) have been determined by direct methods using three-dimensional X-ray diffractometer data. Crystals of (I) are orthorhombic, space group Pna21, with a = 14.662(6), b = 10.492(5), c = 7.375 (3)A, Z = 4, V = 1134.5 A 3, D O = 1.25 (by flotation), D e = 1.269 Mgm -a, g(MoKa) = 0.085 mm -1. Crystals of (II) are monoclinic, space group P21/a, with a = 7.886 (5), b = 22.011 (8), c = 8.100 (3) A, fl = 103.12 (5) °, Z = 4, V = 1369.2 A 3, D O = 1.23 (by flotation), D e = 1.255 Mg m -3, g(Mo Kct) = 0.080 mm -1. Least-squares full-matrix refinement based on 782 (I) and 1400 independent reflections (II) converged at R = 0.040 (I) and 0.042 (II). The effect of electron-withdrawing substituents on the geometry of the cyclopropane ring is discussed.

3,3',5,5'-Tetrabromophenolsulfonphthalein (bromphenol blue), C19H10Br4O5S

M r=670.02, monoclinic, C2/c, a= 31.003(4), b=11.037(2), c=21.183(3)A, fl= 143.7 (1) °, V= 4291.2/k 3, D,n = 2.06, D x = 2.07Mgm -3, Z=8, MoKa, 2=0.7107/k, /~=7.45 mm -1, F(000) = 2560, T= 293 K, R = 0.061 for 1697 observed reflections. The bromphenol blue molecule consists essentially of three planar groupings: the sulfonphthalein ring system and two dibromophenol rings attached to the tetrahedral C atom of the five-membered ring of the sulfonphthalein system. The dibromophenol rings are inclined with resPect to each other at 73 ° whereas they make angles of 85 and 68 ° with respect to the sulfonphthalein system. The molecules aggregate into helical columns with the non-polar regions of the molecules in the interior and the polar regions on the surface. The columns are held together by a network of hydrogen bonds.

Numerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping

This paper presents a new numerical integration technique oil arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz-Christoffel mapping and a midpoint quadrature rule defined oil this unit disk is used. This method eliminates the need for a two-level isoparametric mapping Usually required. Moreover, the positivity of the Jacobian is guaranteed. Numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results.

Vertical uplift resistance of circular plate anchors in clays under undrained condition

The vertical uplift resistance of circular plate anchors, embedded horizontally in a clayey stratum whose cohesion increases linearly with depth, has been obtained under undrained (phi = 0) condition. The axi-symmetric static limit analysis formulation in combination with finite elements proposed recently by the authors has been employed. The variation of the uplift factor (F,) with changes in the embedment ratio (H/B) has been computed for several rates of increases of soil cohesion with depth. It is noted that in all the cases, the magnitude of F-c increases continuously with depth up to a certain value of H-cr/B beyond which the uplift factor becomes essentially constant. The proposed static limit analysis formulation is seen to provide acceptable results even for the two other simple chosen axi-symmetric problems.

A new framework for solution of multidimensional population balance equations

A new framework is proposed in this work to solve multidimensional population balance equations (PBEs) using the method of discretization. A continuous PBE is considered as a statement of evolution of one evolving property of particles and conservation of their n internal attributes. Discretization must therefore preserve n + I properties of particles. Continuously distributed population is represented on discrete fixed pivots as in the fixed pivot technique of Kumar and Ramkrishna [1996a. On the solution of population balance equation by discretization-I A fixed pivot technique. Chemical Engineering Science 51(8), 1311-1332] for 1-d PBEs, but instead of the earlier extensions of this technique proposed in the literature which preserve 2(n) properties of non-pivot particles, the new framework requires n + I properties to be preserved. This opens up the use of triangular and tetrahedral elements to solve 2-d and 3-d PBEs, instead of the rectangles and cuboids that are suggested in the literature. Capabilities of computational fluid dynamics and other packages available for generating complex meshes can also be harnessed. The numerical results obtained indeed show the effectiveness of the new framework. It also brings out the hitherto unknown role of directionality of the grid in controlling the accuracy of the numerical solution of multidimensional PBEs. The numerical results obtained show that the quality of the numerical solution can be improved significantly just by altering the directionality of the grid, which does not require any increase in the number of points, or any refinement of the grid, or even redistribution of pivots in space. Directionality of a grid can be altered simply by regrouping of pivots.