A one-step fusion of 1,3-thiazine and pyrimidine cycles

The chlorotrimethylsilane-promoted Biginelli type reactions of aldehydes, thiourea, and cyanoketones led to a diverse set of tetrahydropyrimidine-2(1H)-thiones. Under similar conditions, thioureas, benzaldehyde, and cyanoacetamide reacted to give first representatives of hexahydro-5H-pyrimido[5,4-e][1,3]thiazin-5-ones in high preparative yield.     

Differences Between Consecutive Primes

Let p_n be the nth prime. Then this paper is concerned with provingthe following result on the distribution of consecutive primes. The exponent of x in this theorem improves on the work of Heath-Brownwho proved (1) with exponent . Under the Riemann hypothesisone can prove (1) with exponent .The proof of the theorem startswith the Heath-Brown–Linnik identity which leads to aformula giving the number of primes in an interval in termsof coefficients of certain Dirichlet series. I then estimatethe coefficients by using, among other things, the informationwhich can be gained from Montgomery's mean value theorem andHuxley's version of the Hal' asz lemma. Furthermore, by usingfamiliar sieve arguments I am able to discard some of the coefficientsallowing us to gain an improvement over the previous resultof Heath-Brown. 1991 Mathematics Subject Classification: 11N05.     

Aminoheterocycles as synthons for combinatorial Biginelli reactions

Chlorotrimethylsilane (TMSCl) has been utilized as an efficient promoter and water scavenger in the synthesis of diverse dihydropyrimidines via Biginelli type MCR-heterocyclization using aminoheterocycles. High yields and a simple workup of target compounds enable the facile generation of combinatorial libraries comprising more than 2,000 compounds of high structural and functional diversity. A representative set of 89 compounds is described.     

Quantum superarrivals and information transfer through a time-varying boundary

The time-dependent Schrödinger equation is solved numerically for the case of a Gaussian wave packet incident on a time-varying potential barrier. The time evolving reflection and transmission probabilities of the wave packet are computed for several different time-dependent boundary conditions obtained by reducing or increasing the height of the potential barrier. We show that in the case when the barrier height is reduced to zero, a time interval is found during which the reflection probability is larger (superarrivals) compared to the unperturbed case. We further show that the transmission probability exhibits superarrivals when the barrier is raised from zero to a finite value of its height. Superarrivals could be understood by ascribing the features of a real physical field to the Schrödinger wave function which acts as a carrier through which a disturbance, resulting from the boundary condition being perturbed, prpagates from the barrier to the detectors measuring reflected and transmitted probabilities. The speed of propagation of this effect depends upon the rate of reducing or raising the barrier height, thus suggesting an application for secure information transfer using superarrivals.     

Synthesis of quinolines from 3-formylchromone

A facile and versatile procedure for the synthesis of 3-(2-hydroxybenzoyl)quinolines and 7H-chromeno[3,2-c]quinolin-7-ones was elaborated on the basis of TMSCl-mediated recyclization of 3-formylchromone with various anilines. Limitations and scope of this methodology were established, and a possible mechanism for the heterocyclizations was proposed.     

Facile One-Pot Synthesis of 1,2,3,4-Tetrahydroquinoline-3-carboxylic Acids and Their Heterocyclic Analogs

A facile one-pot method for the synthesis of 1,2,3,4-tetrahydroquinoline-3-carboxylic acids and their heterocyclic analogs based on the tert-amino effect. A set of 1,2,3,4-tetrahydroquinoline-3-carboxylic acids was readily prepared starting from various ortho-dialkylaminoaldehydes and Meldrum's acid using Me₃SiCl in dimethylformamide (DMF) solution.     

3-haloquinolines by Friedländer reaction of α-haloketones

A general approach to 3-fluoro-, 3-chloro-, and 3-bromoquinolines which relies on organosilane-promoted Friedla?nder reaction of α-haloketones is described. The scope of the methylene component as well as influence of the organosilane component on the outcome of the reaction is studied. The method can be used under parallel synthesis conditions.