Solitary wave solutions to nonlinear evolution equations in mathematical physics

This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions.     

Studies on the synthesis of bafilomycin A(1): stereochemical aspects of the fragment assembly aldol reaction for construction of the C(13)-C25) segment

Highly stereoselective syntheses of aldols 8a-c corresponding to the C(13)-C(25) segment of bafilomycin A(1) were developed by routes involving fragment assembly aldol reactions of chiral aldehyde 6a and the chiral methyl ketones 7. A remote chelation effect plays a critical role in determining the stereoselectivity of the key aldol coupling of 6a and the lithium enolate of 7b. The protecting group for C(23)-OH of the chiral aldehyde fragment also influences the selectivity of the lithium enolate aldol reaction. In contrast, the aldol reaction of 6a and the chlorotitanium enolates of 7a,c were much less sensitive to the nature of the C(15)-hydroxyl protecting group. Studies of the reactions of chiral aldehydes with Takai's (gamma-methoxyallyl)chromium reagent 40 are also described. The stereoselectivity of these reactions is also highly dependent on the protecting groups and stereochemistry of the chiral aldehyde substrates.     

Peroxycarbenium-mediated C-C bond formation: applications to the synthesis of hydroperoxides and peroxides

The Lewis acid-mediated reaction of alkene nucleophiles with peroxyacetals provides an effective route for the synthesis of homologated peroxides and hydroperoxides. In the presence of Lewis acids such as TiCl(4), SnCl(4), and trimethylsilyl triflate, peroxyacetals and peroxyketals undergo reaction with allyltrimethylsilane, silyl enol ethers, and silyl ketene acetals to afford homoallyl peroxides, 3-peroxyketones, and 3-peroxyalkanoates, respectively. Reactions of peroxyacetals are Lewis acid dependent; TiCl(4) promotes formation of ethers while SnCl(4) and trimethylsilyl triflate promote formation of peroxides. Lewis acid-promoted reactions of silylated hydroperoxyacetals furnish silylated hydroperoxides, which can be deprotected to homologated hydroperoxides. Hydroperoxyketals undergo Lewis acid-mediated allylation to furnish 1,2-dioxolanes via attack of hydroperoxide on the intermediate carbocation. Lewis acid-mediated cyclization of unsaturated peroxyacetals furnishes 1,2-dioxanes, 1,2-dioxepanes, and 1,2-dioxacanes through 6-endo/exo, 7-endo/endo, and 8-endo/endo pathways. The corresponding reactions involving 6-endo/endo and 5-endo/exo pathways were unsuccessful.     

Neural correlates of semantic and syntactic processes in the comprehension of case marked pronouns: Evidence from German and Dutch

Background  

It is well known that both semantic and syntactic information play a role in pronoun resolution in sentences. However, it is unclear what the relative contribution of these sources of information is for the establishment of a coreferential relationship between the pronoun and the antecedent in combination with a local structural case constraint on the pronoun (i.e. case assignment of a pronoun under preposition governing). In a prepositional phrase in German and Dutch, it is the preposition that assigns case to the pronoun. Furthermore, in these languages different overtly case-marked pronouns are used to refer to male and female persons. Thus, one can manipulate biological/syntactic gender features separately from case marking features.     

Microwave heating of ceramic composites

The microwave heating of a ceramic composite is modelled andanalysed. The composite consists of many small ceramic particlesembedded in a ceramic cement. The composite is assumed to bewell insulated, and each particle is assumed to be in imperfectthermal contact with the surrounding cement. Based on thesetwo assumptions an asymptotic theory exploiting the small Biotnumber and small non-dimensional contact conductance is developed.Our asymptotic theory yields a set of nonlinear partial differentialequations which govern the temperature in the composite. Theseare reduced to a set of coupled nonlinear ordinary differentialequations in which the surface area of each particle entersas a parameter. Recent experiments with such composites haveshown that the steady-state temperature of the composite isstrongly dependent upon the radii of the embedded particles.Our model captures this effect. In fact, our analysis showsthat the assumption of imperfect thermal contact between theparticles and the ceramic cement is essential for this trendto be established.