Recent advances in Garratt-Braverman cyclization: Mechanistic and synthetic explorations

Garratt-Braverman cyclization has emerged as one of the simplest synthetic tool to construct two consecutive CC bonds leading to the formation of various important structural scaffolds having significance in the field of therapeutics and material science. The strategic design of suitable precursor for this cycloaromatization reaction involves the deep understanding of reaction pathways involving diradicals and ions. On the other hand, the reaction offers an unprecedented mechanistic paradox for the chemists to solve. This report aims at outlining the recent mechanistic and synthetic developments with special emphasis on the research outcomes from our laboratory.     

Organocatalytic mediated green approach: A versatile new L-valine promoted synthesis of diverse and densely functionalized 2-amino-3-cyano-4H-pyrans

The discovery of a new L-valine promoted facile and versatile green synthesis of diversified 2-amino-3-cyano-4H-pyrans using a one pot multicomponent-tandem reaction of aromatic aldehydes, malononitrile, and diverse electron-rich enolizable carbonyl compounds is described. To the best of our knowledge this is the first report on the use of native L-valine as a catalyst in organic synthesis. Environmental friendly, mild reaction conditions, use of easily available inexpensive starting materials, short reaction time, excellent yields, high atom economy, and recyclability of organocatalyst are the major advantages of the disclosed protocol.     

From Dislocation Motion to an Additive Velocity Gradient Decomposition, and Some Simple Models of Dislocation Dynamics

A mathematical theory of time-dependent dislocation mechanics of unrestricted geometric and material nonlinearity is reviewed. Within a ``small deformation" setting, a suite of simplified and interesting models consisting of a nonlocal Ginzburg Landau equation, a nonlocal level set equation, and a nonlocal generalized Burgers equation is derived. In the finite deformation setting, it is shown that an additive decomposition of the total velocity gradient into elastic and plastic parts emerges naturally from a micromechanical starting point that involves no notion of plastic deformation but only the elastic distortion, material velocity, dislocation density and the dislocation velocity. Moreover, a plastic spin tensor emerges naturally as well.     

Local boundedness of weak solutions to the Diffusive Wave Approximation of the Shallow Water equations

In this paper we prove that weak solutions to the Diffusive Wave Approximation of the Shallow Water equations

${?}_{t}u?\mathrm{?}?({(u?z)}^{\alpha }|\mathrm{?}u{|}^{\gamma ?1}\mathrm{?}u)=f$

are locally bounded. Here, u describes the height of the water, z is a given function that represents the land elevation and f is a source term accounting for evaporation, infiltration or rainfall.     

Toric partial density functions and stability of toric varieties

Let $(L, h)\rightarrow (X, \omega )$ denote a polarized toric Kähler manifold. Fix a toric submanifold $Y$ and denote by $\hat{\rho }_{tk}:X\rightarrow \mathbb {R}$ the partial density function corresponding to the partial Bergman kernel projecting smooth sections of $L^k$ onto holomorphic sections of $L^k$ that vanish to order at least $tk$ along $Y$ , for fixed $t>0$ such that $tk\in \mathbb {N}$ . We prove the existence of a distributional expansion of $\hat{\rho }_{tk}$ as $k\rightarrow \infty $ , including the identification of the coefficient of $k^{n-1}$ as a distribution on $X$ . This expansion is used to give a direct proof that if $\omega $ has constant scalar curvature, then $(X, L)$ must be slope semi-stable with respect to $Y$ (cf. Ross and Thomas in J Differ Geom 72(3): 429–466, 2006). Similar results are also obtained for more general partial density functions. These results have analogous applications to the study of toric K-stability of toric varieties.     

Fleet configuration subject to stochastic demand: an application in the distribution of liquefied petroleum gas

We study the problem of configuring a fleet, in which vehicles receive information on-line about the demand that they should fulfil while they are on the road. In each district it must be decided the number of vehicles and their capacity. The objective function is to minimise the operational cost subject to constraints for the minimum delivery capacity, the maximum vehicle size and the average waiting time for customers. The last constraint is modelled as a queuing system that is adjusted according to the simulation of the delivery process of a Chilean company that distributes liquefied petroleum gas in portable cylinders. We provide the analytical form of all the components of the model, so it can be solved using a standard non-linear programming package. We show that the fleet may increase its sales by 3% and reduce the waiting time of customers 10% by allowing a set of vehicles to share the buffer of orders rather than having vehicles to exclusively serve smaller sectors.     

Bessel functions and singular BVPs arising in physiology in the presence of upper and lower solutions in reverse order

In this paper, we consider the genic mutation on an impulsive population system in polluted environment. All solutions of the investigated system are proved to be uniformly bounded. Using mathematical analysis methods, the conditions of the globally asymptotically stable population-extinction solution of the investigated system are obtained. The permanent condition of the investigated system is also obtained. Finally, numerical analysis is carried out illustrate our results. Our results provide reliable tactic basis for the practical biological resource management in polluted environment.     

Residues and telescopers for bivariate rational functions

We give necessary and sufficient conditions for the existence of telescopers for rational functions of two variables in the continuous, discrete and q-discrete settings and characterize which operators can occur as telescopers. Using this latter characterization, we reprove results of Furstenberg and Zeilberger concerning diagonals of power series representing rational functions. The key concept behind these considerations is a generalization of the notion of residue in the continuous case to an analogous concept in the discrete and q-discrete cases.     

Information structuring—a new way of perceiving the content of learning

Dominating information by formation seems to be the only realistic solution to overcome the crisis generated by the higher and higher accumulation of information in each domain. The paper is proposing a model of building structured knowledge able to generate in the child's mind strategies for efficient processing of information.