A nonlinear parabolic-Sobolev equation

Let M and L be (nonlinear) operators in a reflexive Banach space B for which Rg(M + L) = B and $\text{¦(Mx ? My) + α(Lx ? Ly)¦ ? | mx ? My |}$ for all α > 0 and pairs x, y in D(M) ∩ D(L). Then there is a unique solution of the Cauchy problem (Mu(t))′ + Lu(t) = 0, Mu(0) = v₀. When M and L are realizations of elliptic partial differential operators in space variables, this gives existence and uniqueness of generalized solutions of boundary value problems for nonlinear partial differential equations of mixed parabolic-Sobolev type.     

Topographic organization of Hebbian neural connections by synchronous wave activity

Experimental studies have revealed that the refinement of early, imprecise connections in the developing visual system involves activity in the retina before the onset of vision. We study the evolution of initially random unidirectional connections between two excitable layers of FitzHugh-Nagumo neurons with simulated spontaneous activity in the input layer. Lateral coupling within the layers yields synchronous neural wave activity that serves as a template for the Hebbian learning process, which establishes topographically precise interlayer connections. (c) 2001 American Institute of Physics.     

Synthesis of 3,4‐dihydro‐1(2H)‐isoquinolinonesxs

Approaches toward the preparative‐scale synthesis of target 3,4‐dihydro‐1(2H)‐isoquinolinones 1–3 are presented. Compounds 1 and 2 were prepared via a Schmidt rearrangement on easily obtained indanone precursors, but in low overall yield. A better method to make this class of compounds is exemplified by the large‐scale synthesis of 2 via a Curtius rearrangement sequence. Thus, high‐temperature thermal cyclization of an in situ formed styryl isocyanate from precursor 8 in the presence of tributylamine gave the corresponding 1(2H)‐isoquinolinone ( 9 ). Catalytic hydrogenation of 9 provided the desired 3,4‐dihydro‐5‐methyl‐1(2H)‐isoquinolinone ( 2 ) in 65 % overall yield. Similar reduction of a commercially available 5‐hydroxy‐1(2H)‐isoquinolinone precursor 10 followed by an O ‐alkylation/amination sequence gave target 3 in good overall yield. The route proceeding via the Curtius rearrangement is recommended for large scale synthesis of other 3,4‐dihydro‐1(2H)‐isoquinolinones. Only when deactivating substituents or sensitive functionality within the benzenoid ring render the high temperature ring closure of the intermediate isocyanate inefficient might a Schmidt rearrangement protocol be the method of choice.     

Evolution of phase transitions in methane hydrate

We consider a simplified model of methane hydrates which we cast as a nonlinear evolution problem. For its well-posedness we extend the existing theory to cover the case in which the problem involves a measurable family of graphs. We represent the nonlinearity as a subgradient and prove a useful comparison principle, thus optimal regularity results follow. For the numerical solution we apply a fully implicit scheme without regularization and use the semismooth Newton algorithm for a solver, and the graph is realized as a complementarity constraint (CC). The algorithm is very robust and we extend it to define an easy and superlinearly convergent fully implicit scheme for the Stefan problem and other multivalued examples.     

Anticancer anilinoacridines. A process synthesis of the disubstituted amsacrine analog CI-921

An improved process for the synthesis of bulk quantities of the clinical amsacrine analog CI-921 is reported. Described also are detailed analytical and spectroscopic data for this agent.     

Functionalization of substituted 2-(1H)pyridones. I. A novel synthesis of a-arylgyloxylates and related systems

A novel synthetic strategy is presented in which the heteroaryl[(trimethylsilyl)oxy]acetonitrile intermediate 3 is utilized either as a homologation or reverse-polarity synthon for convenient entry into its corresponding α-hydroxy- and α-ketoarylalkanoate 4 and 6 , respectively. Further functionalization, including a stereo-selective oximation procedure, is described.     

Studies related to the total synthesis of pentostatin. Approaches to the synthesis of (8R)-3,6,7,8-tetrahydroimidazo-[4,5-d][1,3]diazepin-8-ol and N-3 alkyl congeners

A number of synthetic approaches to the (8R)-3,6,7,8-tetrahydroimidazo[4,5-d][1,3]diazepin-8-ol ring system ( 3 ) of pentostatin ( 1 ) are reported. These involve the synthesis of a number of 4-C-derivatives of N-alkyl-5-amino- and 5-nitro-1H-imidazoles derived from 4-methyl-5-nitro-1H-imidazole.