Gold-Catalyzed Cycloisomerization of Sulfur Ylides to Dihydrobenzothiepines

The metal-promoted nucleophilic addition of sulfur ylides to π-systems is a well-established reactivity. However, the driving force of such transformations, elimination of a sulfide moiety, entails stoichiometric byproducts making them unfavorable in terms of atom economy. In this work, a new take on sulfur ylide chemistry is reported, an atom-economical gold(I)-catalyzed synthesis of dihydrobenzo[b]thiepines. The reaction proceeds under mild conditions at room temperature.     

Domains of divergence of the USSOR method applied onp-cyclic matrices

Summary Using a recently derived classical type general functional equation, relating the eigenvalues of a weakly cyclic Jacobi iteration matrix to the eigenvalues of its associated Unsymmetric Successive Overrelaxation (USSOR) iteration matrix, we obtain bounds for the convergence of the USSOR method, when applied to systems with ap-cyclic coefficient matrix.     

Inflation in entropic cosmology: Primordial perturbations and non-Gaussianities

We investigate thermal inflation in double-screen entropic cosmology. We find that its realization is general, resulting from the system evolution from non-equilibrium to equilibrium. Furthermore, going beyond the background evolution, we study the primordial curvature perturbations arising from the universe interior, as well as from the thermal fluctuations generated on the holographic screens. We show that the power spectrum is nearly scale-invariant with a red tilt, while the tensor-to-scalar ratio is in agreement with observations. Finally, we examine the non-Gaussianities of primordial curvature perturbations, and we find that a sizable value of the non-linearity parameter is possible due to holographic statistics on the outer screen.     

A generalized expression for the ratio of the critical temperature to the critical pressure with the van der Waals surface area

Using an extensive database of experimental critical properties for heavy compounds, which have been compiled mostly from recent literature sources, it is shown that the ratio T_c: P_c (critical temperature over critical pressure) can be expressed in terms of the van der Waals surface area (Q_w), which is readily available for any compound from the group contributions of Bondi (given also in UNIFAC tables). The proposed correlation is based on the hole theory of Kurata and Isida for n-paraffin liquids, which is mathematically equivalent to Flory's theory of polymer solutions. The method is suitable for medium to high molecular weight compounds with unknown critical constants. For example, if only one of the two critical constants is available, then the proposed generalized equation offers a useful rapid procedure for the estimation of the other critical property for use in corresponding states, and other relevant applications where knowledge of the critical properties is required. Furthermore, the T_c: P_c method can be used in many cases for identifying the most suitable among the existing group contribution methods for estimating the critical properties of heavy and complex compounds for which experimental values are, very often, not available.     

Regions of exact convergence of the USSOR method applied on generalized consistently ordered matrices

Summary. Using the theory of nonnegative matrices and regular splittings, exact convergence and divergence domains of the Unsymmetric Successive Overrelaxation (USSOR) method, as it pertains to the class of Generalized Consistently Ordered (GCO) matrices, are determined. Our recently derived upper bounds, for the convergence of the USSOR method, re also used as effective tools. Received October 17, 1993 / Revised version received December 19, 1994     

Hořava–Lifshitz dark energy

We formulate Ho?ava–Lifshitz cosmology with an additional scalar field that leads to an effective dark energy sector. We find that, due to the inherited features from the gravitational background, Ho?ava–Lifshitz dark energy naturally presents very interesting behaviors, possessing a varying equation-of-state parameter, exhibiting phantom behavior and allowing for a realization of the phantom divide crossing. In addition, Ho?ava–Lifshitz dark energy guarantees for a bounce at small scale factors and it may trigger the turnaround at large scale factors, leading naturally to cyclic cosmology.     

Smoothness of holonomy covers for singular foliations and essential isotropy

Given a singular foliation, we attach an “essential isotropy” group to each of its leaves, and show that its discreteness is the integrability obstruction of a natural Lie algebroid over the leaf. We show that a condition ensuring discreteness is the local surjectivity of a transversal exponential map associated with the maximal ideal of vector fields prescribed to be tangent to the foliation. The essential isotropy group is also shown to control the smoothness of the holonomy cover of the leaf (the associated fiber of the holonomy groupoid), as well as the smoothness of the associated isotropy group. Namely, the (topological) closeness of the essential isotropy group is a necessary and sufficient condition for the holonomy cover to be a smooth (finite-dimensional) manifold and the isotropy group to be a Lie group. These results are useful towards understanding the normal form of a singular foliation around a compact leaf. At the end of this article we briefly outline work of ours on this normal form, to be presented in a subsequent paper.     

The Transient Acceleration from Time-Dependent Interacting Dark Energy Models

The transient acceleration which the current cosmic acceleration is not eternal is possible by introducing the interaction between dark matter and dark energy. If the energy transfer is from dark energy to dark matter, then it is possible to realize the transient acceleration. We study the possibility of transient acceleration by considering two time-dependent phenomenological interaction forms so that the energy transfer increases as the universe evolves. Starting from a simple and extending to a more complicated ansatz, we obtain analytical expressions for the evolutions of the deceleration and the various energy density parameters. We find the ranges of the parameters in the models for a transient acceleration.     

Coordination-driven self assembly of a brilliantly fluorescent rhomboid cavitand composed of bodipy-dye subunits

The two sp(3) hybridized fluorine atoms of a Bodipy dye have been synthetically replaced with the linear donor ligand 4-ethynylpyridine (-C≡C-Py) to form a rigid and highly symmetrical 109.5° building block in which the fluorophore subunit is vertically aligned to the plane formed by the -C≡C-Py donors. Upon reaction of the above tecton with a 90° organoplatinum acceptor unit, an intensely fluorescent rhomboid cavitand was manifested in solution. In contrast to the vast majority of coordination-driven self-assembled chromophoric systems, the present one fully conserves the excellent photophysical properties of the parent Bodipy dye. These unique features of the present metallosupramolecular entity constitute a fascinating metal-to-ligand self-assembled prototype for building compact and intensely luminescent materials with host-guest capabilities.     

Direct and iterative solution of the generalized Dirichlet–Neumann map for elliptic PDEs on square domains

In this work we derive the structural properties of the Collocation coefficient matrix associated with the Dirichlet–Neumann map for Laplace’s equation on a square domain. The analysis is independent of the choice of basis functions and includes the case involving the same type of boundary conditions on all sides, as well as the case where different boundary conditions are used on each side of the square domain. Taking advantage of said properties, we present efficient implementations of direct factorization and iterative methods, including classical SOR-type and Krylov subspace (Bi-CGSTAB and GMRES) methods appropriately preconditioned, for both Sine and Chebyshev basis functions. Numerical experimentation, to verify our results, is also included.