On the locus formed by the maximum heights of projectile motion with air resistance

We present an analysis on the geometrical place formed by the set of maxima of the trajectories of a projectile launched in a media with linear drag. Such a place, the locus of apexes, is written in term of the Lambert $W$ function in polar coordinates, confirming the special role played by this function in the problem. In order to characterize the locus, a study of its curvature is presented in two parameterizations, in terms of the launch angle and in the polar one. The angles of maximum curvature are compared with other important angles in the projectile problem. As an addendum, we find that the synchronous curve in this problem is a circle as in the drag-free case.Comment: 7 pages, 6 color eps figures. Synchronous curve added. Typos and style corrected

Enantioselective Organocatalytic Intramolecular Diels−Alder Reactions. The Asymmetric Synthesis of Solanapyrone D

The first direct enantioselective organocatalytic intramolecular Diels−Alder reaction has been accomplished. The use of iminium catalysis has provided a new catalytic strategy for the enantioselective [4 + 2] cycloisomerization of a wide variety of tethered diene-enal systems. The use of imidazolidinones 1 and 2 as the asymmetric catalysts has been found to mediate the enantioselective construction of [4.4.0] and [4.3.0] ring systems. Application of this methodology to the highly efficient asymmetric synthesis of the marine metabolite solanpyrone D has also been accomplished. A diverse spectrum of aldehyde substrates can also be accommodated in this new organocatalytic transformation. Importantly, this technology has been utilized to execute the first enantioselective, catalytic Type II IMDA reaction

Enantioselective Organo-Cascade Catalysis

A new strategy for organocatalysis based on the biochemical blueprints of biosynthesis has enabled a new laboratory approach to cascade catalysis. Imidazolidinone-based catalytic cycles, involving iminium and enamine activation, have been successfully combined to allow a large diversity of nucleophiles (furans, thiophenes, indoles, butenolides, hydride sources, tertiary amino lactone equivalents) and electrophiles (fluorinating and chlorinating reagents) to undergo sequential addition with a wide array of α,β-unsaturated aldehydes. These new cascade catalysis protocols allow the invention of enantioselective transformations that were previously unknown, including the asymmetric catalytic addition of the elements of HF across a trisubstituted olefin. Importantly, these domino catalysis protocols can be mediated by a single imidazolidinone catalyst or using cycle-specific amine catalysts. In the latter case, cascade catalysis pathways can be readily modulated to provide a required diastereo- and enantioselective outcome via the judicious selection of the enantiomeric series of the amine catalysts. A central benefit of combining multiple asymmetric organocatalytic events into one sequence is the intrinsic requirement for enantioenrichment in the second induction cycle, as demonstrated by the enantioselectivities obtained throughout this study (≥99% ee in all cases)

Is copyright blind to the visual?

This article argues that, with respect to the copyright protection of works of visual art, the general uneasiness that has always pervaded the relationship between copyright law and concepts of creativity produces three anomalous results. One of these is that copyright lacks much in the way of a central concept of 'visual art' and, to the extent that it embraces any concept of the 'visual', it is rooted in the rhetorical discourse of the Renaissance. This means that copyright is poorly equipped to deal with modern developments in the visual arts. Secondly, the pervasive effect of rhetorical discourse appears to have made it particularly difficult for copyright law to strike a meaningful balance between protecting creativity and permitting its use in further creative works. Thirdly, just when rhetorical discourse might have been useful in identifying the significance and materiality of the unique one-off work of visual art, copyright law chooses to ignore its implications

Design of a New Cascade Reaction for the Construction of Complex Acyclic Architecture: The Tandem Acyl-Claisen Rearrangement

Tandem or domino reactions have long been established as powerful chemical tools for the rapid formation of complex cyclic and polycyclic architecture. Surprisingly, however, relatively few tandem strategies have been directed toward the production of acyclic structural motifs despite significant advances in the area of acyclic stereocontrol. In our recent study, we reported the development of the acyl-Claisen rearrangement, a catalytic [3,3]-bond reorganization that allows the stereoselective synthesis of α,β-disubstituted-γ,δ-unsaturated carbonyls. In this communication, we outline the development of the tandem acyl-Claisen reaction, a highly stereoselective three-component coupling that enables the rapid construction of complex acyclic systems in the context of 2,3,6-trisubstituted-1,7-dioxoheptane architecture (eq 1). This versatile cascade sequence is conducted by using simple allyl diamines and acid chlorides, chemicals that are widely available in a diverse range of structural formats. As such, we expect this tandem reaction to be of broad utility to a number of chemical fields that employ molecule construction including natural product and parallel medicinal agent synthesis

Liposomal delivery of p-ialB and p-omp25 DNA vaccines improves immunogenicity but fails to provide full protection against B. melitensis challenge

BACKGROUND: We have previously demonstrated protective efficacy against B. melitensis using formulations of naked DNA vaccines encoding genes ialB and omp25. The present study was undertaken to further understand the immune response generated by the protective vaccination regimens and to evaluate cationic liposome adsorption as a delivery method to improve vaccine utility. METHODS: The protective efficacy and immunogenicity of vaccines delivered as four doses of naked DNA, a single dose of naked DNA or a single dose of DNA surface adsorbed to cationic liposomes were compared using the BALB/c murine infection model of B. melitensis. Antigen-specific T cells and antibody responses were compared between the various formulations. RESULTS: The four dose vaccination strategy was confirmed to be protective against B. melitensis challenge. The immune response elicited by the various vaccines was found to be dependent upon both the antigen and the delivery strategy, with the IalB antigen favouring CD4+ T cell priming and Omp25 antigen favouring CD8+. Delivery of the p-ialB construct as a lipoplex improved antibody generation in comparison to the equivalent quantity of naked DNA. Delivery of p-omp25 as a lipoplex altered the profile of responsive T cells from CD8+ to CD4+ dominated. Under these conditions neither candidate delivered by single dose naked DNA or lipoplex vaccination methods was able to produce a robust protective effect. CONCLUSIONS: Delivery of the p-omp25 and p-ialB DNA vaccine candidates as a lipoplex was able to enhance antibody production and effect CD4+ T cell priming, but was insufficient to promote protection from a single dose of either vaccine. The enhancement of immunogenicity by lipoplex delivery is a promising step toward improving the practicality of these two candidate vaccines, and suggests that this lipoplex formulation may be of value in situations where improvements to CD4+ responses are required. However, in the case of Brucella vaccine development it is suggested that further modifications to the candidate vaccines and delivery strategies will be required in order to deliver sustained protection

The Glass Transition Temperature of Water: A Simulation Study

We report a computer simulation study of the glass transition for water. To mimic the difference between standard and hyperquenched glass, we generate glassy configurations with different cooling rates and calculate the $T$ dependence of the specific heat on heating. The absence of crystallization phenomena allows us, for properly annealed samples, to detect in the specific heat the simultaneous presence of a weak pre-peak (``shadow transition''), and an intense glass transition peak at higher temperature. We discuss the implications for the currently debated value of the glass transition temperature of water. We also compare our simulation results with the Tool-Narayanaswamy-Moynihan phenomenological model.Comment: submitted to Phys. Re