C—H⃛π interactions in 9‐(n‐do­decylamino­methyl)­anthracene

The title compound, C₂₇H₃₇N, which is intended to be included in the structure of a sulfon­amide porphyrin for the preparation of Langmuir–Blodgett films, consists of a do­decyl chain linked to an anthracene mol­ecule through an amino­methyl group. The angle between the least‐squares plane of the anthracene and the do­decyl chain is 11.44 (8)°. The mol­ecules are arranged in zigzag layers head‐to‐head, with the hydro­carbon chains side‐by‐side. The structure is stabilized by C—H?π interactions, the strongest having an H?centroid distance of 2.63 Å.     

Benzyl 5‐carboxy‐4‐ethyl‐3‐methyl­pyrrole‐2‐carboxyl­ate

In the title compound, C₁₆H₁₇NO₄, the benzyl­oxy­carbonyl group is anti to the pyrrolic N atom. The mol­ecules are joined into head‐to‐head dimers by hydrogen bonds involving the carboxyl­ic acid groups. There is orientational disorder of these groups over two positions with approximately equal occupancy. A weaker hydrogen bond between the pyrrolic N atom and the carbonyl O atom of the benzyl­oxy­carbonyl group joins the dimers into chains running parallel to the [110] direction.     

2,4‐Dibromo‐3‐methoxy‐6‐nitrobenz­aldeyde: effect of substituents on ring geometry

In the title compound, C₈H₅Br₂NO₄, the endocyclic angles of the ring deviate significantly from the ideal value of 120°. The substituents deviate from the plane of the ring, with large twist angles for the aldehyde, nitro and methoxy groups. The geometry of the mol­ecule in the crystal is compared with that of the isolated mol­ecule, as given by a self‐consistent field molecular‐orbital Hartree–Fock calculation. Only weak hydrogen bonds of the C—H?Br and C—H?O types are present in the crystal structure.     

Heuristics for Distribution Network Design in Telecommunication

A distribution network problem arises in a lower level of an hierarchical modeling approach for telecommunication network planning. This paper describes a model and proposes a lagrangian heuristic for designing a distribution network. Our model is a complex extension of a capacitated single commodity network design problem. We are given a network containing a set of sources with maximum available supply, a set of sinks with required demands, and a set of transshipment points. We need to install adequate capacities on the arcs to route the required flow to each sink, that may be an intermediate or a terminal node of an arborescence. Capacity can only be installed in discrete levels, i.e., cables are available only in certain standard capacities. Economies of scale induce the use of a unique higher capacity cable instead of an equivalent set of lower capacity cables to cover the flow requirements of any link. A path from a source to a terminal node requires a lower flow in the measure that we are closer to the terminal node, since many nodes in the path may be intermediate sinks. On the other hand, the reduction of cable capacity levels across any path is inhibited by splicing costs. The objective is to minimize the total cost of the network, given by the sum of the arc capacity (cables) costs plus the splicing costs along the nodes. In addition to the limited supply and the node demand requirements, the model incorporates constraints on the number of cables installed on each edge and the maximum number of splices at each node. The model is a NP-hard combinatorial optimization problem because it is an extension of the Steiner problem in graphs. Moreover, the discrete levels of cable capacity and the need to consider splicing costs increase the complexity of the problem. We include some computational results of the lagrangian heuristics that works well in the practice of computer aided distribution network design.     

Di­bromo{N-[2-(di­phenyl­phosphino)­benzyl­idene]-2,6-diiso­propyl­aniline-κ2N,P}nickel

In the title compound, [NiBr₂(C₃₁H₃₂NP)], (I), the second reported example of a nickel–imino­phosphine N,P-chelate in which the Ni atom has tetrahedral coordination, the Ni coordination is distorted as a consequence of the N—Ni—P chelate bite angle of 91.07 (6)° compensated by the Br—­Ni—­Br angle of 126.385 (18)°. In (I) and its analogue, viz. dichloro{[2-(4-isobutyloxazol-2-yl)phenyl]diphenylphos­phine-N,P}nickel(II), the Ni—N and Ni—P distances are greater and the N—Ni—P ligand bite angles smaller than those observed in a series of related complexes with square-planar nickel.     

13C NMR determination of the microstructure of polypropylene obtained with the DADNi(NCS)2/methylaluminoxane catalyst system

A complete ¹³C NMR characterization of a polymer synthesized with a new Ni‐diimine complex [DADNi(NCS)₂, where DAD = 2,6‐iPr? C₆H₃? N?C(Me)? C(Me)? N? 2,6‐iPr? C₆H₃] activated by methylaluminoxane by homopolymerization of propylene is presented. The amorphous material was made up mainly of blocks of syndiotactic polypropylene and ethylene–propylene copolymer. Some degree of propylene inversion (<1.2 mol %) and of long isobutyl and 2‐methyl hexyl branching (<1 mol %) were assigned and quantified. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2171–2178, 2004     

A NEW REGULARITY CLASS FOR THE NAVIER-STOKES EQUATIONS IN IR~n

ＡＮＥＷＲＥＧＵＬＡＲＩＴＹＣＬＡＳＳＦＯＲＴＨＥＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮＳＩＮＩＲ~ｎ￥Ｈ．ＢＥＩＲａＯＤＡＶＥＩＧＡ（ＤｅｐｏｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＰｉｓａＵｎｉｖｅｒｓｉｔｙ，Ｐｉｓａ，Ｉｔａｌｙ）Ａｂｓｔｒａ?..     

On the solutions in the large of the two-dimensional flow of a nonviscous incompressible fluid

The Euler equations (1.1) for the motion of a nonviscous imcompressible fluid in a plane domain Ω are studied. Let E be the Banach space defined in (1.4), let the initial data v₀ belong to E, and let the external forces f(t) belong to L_loc¹(R; E). In Theorem 1.1 the strong continuity and the global boundedness of the (unique) solution v(t) are proved, and in Theorem 1.2 the strong-continuous dependence of v on the data v₀ and f is proved. In particular the vorticity rot v(t) is a continuous function in $\text{}\text{?}$gW, for every t ? R, if and only if this property holds for one value of t. In Theorem 1.3 some properties for the associated group of nonlinear operators S(t). are stated. Finally, in Theorem 1.4 a quite general sufficient condition is given on the data in order to get classical solutions.