Syntheses of the Stemona alkaloids (+/-)-stenine, (+/-)-neostenine, and (+/-)-13-epineostenine using a stereodivergent Diels-Alder/azido-Schmidt reaction

A tandem Diels-Alder/azido-Schmidt reaction sequence provides rapid access to the core skeleton shared by several Stemona alkaloids including stenine, neostenine, tuberostemonine, and neotuberostemonine. The discovery and evolution of inter- and intramolecular variations of this process and their applications to total syntheses of (+/-)-stenine and (+/-)-neostenine are described. The stereochemical outcome of the reaction depends on both substrate type and reaction conditions, enabling the preparation of both (+/-)-stenine and (+/-)-neostenine from the same diene/dienophile combination.     

Detection of innersphere interactions between magnesium hydrate and the phosphate backbone of the HDV ribozyme using Raman crystallography

A Raman microscope and Raman difference spectroscopy are used to detect the vibrational signature of RNA-bound magnesium hydrate in crystals of hepatitis delta virus (HDV) ribozyme and to follow the effects of magnesium hydrate binding to the nonbridging phosphate oxygens in the phosphodiester backbone. There is a correlation between the Raman intensity of the innersphere magnesium hydrate signature peak, near 322 cm-1, and the intensity of the PO2- symmetric stretch, near 1100 cm-1, perturbed by magnesium binding, demonstrating direct observation of -PO2-...Mg2+(H2O)x innersphere complexes. The complexes may be pentahydrates (x = 5) and tetrahydrates (x = 4). The assignment of the Raman feature near 322 cm-1 to a magnesium hydrate species is confirmed by isotope shifts observed in D2O and H218O that are semiquantitatively reproduced by calculations. The standardized intensity changes in the 1100 cm-1 PO2- feature seen upon magnesium hydrate binding indicates that there are approximately 5 innersphere Mg2+...-O2P contacts per HDV molecule when the crystal is exposed to a solution containing 20 mM magnesium.     

Fabrication of microfluidic hydrogels using molded gelatin as a sacrificial element

This paper describes a general procedure for the formation of hydrogels that contain microfluidic networks. In this procedure, micromolded meshes of gelatin served as sacrificial materials. Encapsulation of gelatin meshes in a hydrogel and subsequent melting and flushing of the gelatin left behind interconnected channels in the hydrogel. The channels were as narrow as approximately 6 microm, and faithfully replicated the features in the original gelatin mesh. Fifty micrometre wide microfluidic networks in collagen and fibrin readily enabled delivery of macromolecules and particles into the channels and transport of macromolecules from channels into the bulk of the gels. Microfluidic gels were also suitable as scaffolds for cell culture, and could be seeded by human microvascular endothelial cells to form rudimentary endothelial networks for potential use in tissue engineering.     

Min–Max vs. Min–Sum Vehicle Routing: A worst-case analysis

The classical objective function of the Vehicle Routing Problem (VRP) is to minimize the total distance traveled by all vehicles (Min–Sum). In several situations, such as disaster relief efforts, computer networks, and workload balance, the minimization of the longest route (Min–Max) is a better objective function. In this paper, we compare the optimal solution of several variants of the Min–Sum and the Min–Max VRP, from the worst-case point of view. Our aim is two-fold. First, we seek to motivate the design of heuristic, metaheuristic, and matheuristic algorithms for the Min–Max VRP, as even the optimal solution of the classical Min–Sum VRP can be very poor if used to solve the Min–Max VRP. Second, we aim to show that the Min–Max approach should be adopted only when it is well-justified, because the corresponding total distance can be very large with respect to the one obtained by optimally solving the classical Min–Sum VRP.     

Rapid Ti(Oi-Pr)4 facilitated synthesis of α,α,α-trisubstituted primary amines by the addition of Grignard reagents to nitriles under microwave heating conditions

A series of carbinamines (α,α,α-trisubstituted amines) have been prepared in a simple and efficient one-pot procedure by the addition of Grignard reagents to a series of aliphatic, aromatic and heteroaromatic nitriles. The resulting magnesium imines are subsequently converted to the desired amine after treatment with Ti(Oi-Pr)₄ and additional microwave heating. Key to this procedure is the use of microwave heating for both steps of the reaction protocol, which significantly improves both reaction yields and reduces reaction times. In general, the Grignard addition reaction is complete within 5-10 min at 100 °C followed by conversion with Ti(Oi-Pr)₄ and additional microwave heating to give the target amines in good yields.     

Generalizations of the Hohenberg-Kohn theorem: I. Legendre transform constructions of variational principles for density matrices and electron distribution functions

Given a general, N-particle Hamiltonian operator, analogs of the Hohenberg-Kohn theorem are derived for functions that are more general than the particle density, including density matrices and the diagonal elements thereof. The generalization of Lieb's Legendre transform ansatz to the generalized Hohenberg-Kohn functional not only solves the upsilon-representability problem for these entities, but, more importantly, also solves the N-representability problem. Restricting the range of operators explored by the Legendre transform leads to a lower bound on the true functional. If all the operators of interest are incorporated in the restricted maximization, however, the variational principle dictates that exact results are obtained for the systems of interest. This might have important implications for practical work not only for density matrices but also for density functionals. A follow-up paper will present a useful alternative approach to the upsilon- and N-representability problems based on the constrained search formalism.     

Free Energies and Minimal States for Scalar Linear Viscoelasticity

The concept of a minimal state was introduced in recent decades, based on earlier work by Noll. The property that a given quantity is a functional of the minimal state is of central interest in the present work. Using a standard representation of a free energy associated with a linear memory constitutive relation, a new condition, involving linear functionals, is derived which, if satisfied, ensures that the free energy is a functional of the minimal state. Using this result and recent work on constructing free energy functionals, it is shown that if the kernel of the rate of dissipation functional is given by sums of products, the associated free energy functional is a functional of the minimal state.     

Free energies for singleton minimal states

It is assumed that any free energy function exhibits strict periodic behavior for histories that have been periodic for all past times. This is not the case for the work function, which, however, has the usual defining properties of a free energy. Forms given in fairly recent years for the minimum and related free energies of linear materials with memory have this property. Materials for which the minimal states are all singletons are those for which at least some of the singularities of the Fourier transform of the relaxation function are not isolated. For such materials, the maximum free energy is the work function, and free energies intermediate between the minimum free energy and the work function should be given by a linear relation involving these two quantities. All such functionals, except the minimum free energy, therefore do not have strict periodic behavior for periodic histories, which contradicts our assumption. A way out of the difficulty is explored which involves approximating the relaxation function by a form for which the minimal states are no longer singletons. A representation can then be given of an arbitrary free energy as a linear combination of the minimum, maximum and intermediate free energies derived in earlier work. This representation obeys our periodicity assumption. Numerical data are presented, supporting the consistency of this approach.     

Collective Modes in Strongly Coupled Binary Liquids

We analyze the collective excitations in two‐ and three‐dimensional binary Yukawa systems, consisting of two components with different masses. Theoretical analysis reveals a profound difference between the weakly and strongly correlated limits: at weak coupling the two components interact via the mean field only and the oscillation frequency is governed by the light component. In the strongly correlated limit the mode frequency is governed by the combined mass, where the heavy component dominates. Computer simulations in the full coupling range extend and confirm the theoretical results (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)