Nonholonomic Mapping Principle for Classical and Quantum Mechanics in Spaces with Curvature and Torsion

I explain the geometric basis for the recently-discovered nonholonomic mapping principle which permits deriving laws of nature in spacetimes with curvature and torsion from those in flat spacetime, thus replacing and extending Einstein's equivalence principle. As an important consequence, it yields a new action principle for determining the equation of motion of a free spinless point particle in such spacetimes. Surprisingly, this equation contains a torsion force, although the action involves only the metric. This force makes trajectories autoparallel rather than geodesic, as a manifestation of inertia. A generalization of the mapping principle transforms path integrals from flat spacetimes to those with curvature and torsion, thus playing the role of a quantum equivalence principle. This generalization yields consistent results only for completely antisymmetric or for gradient torsion.     

Mathematics in engineering programs: what teachers with different academic and professional backgrounds bring to the table. An institutional analysis

ABSTRACT

In this paper, we examine how differences in the academic and professional backgrounds of engineering teachers shape their personal relationship to the use of mathematics in engineering practices, and whether these differences affect some of their practices. The analyses herein are based on an institutional perspective and employ Chevallard's anthropological theory of the didactic (ATD). We interviewed two teachers in an engineering programme to identify specific elements of their practice that could be attributable to the mobilisation of knowledge and skills derived from their distinct academic backgrounds and experience. The results indicate that the teachers mobilise different tasks, techniques, and technologies in many of their practices, and that they take different approaches to using mathematics and applying rigour.     

Adsorptive Stripping Voltammetric Determination of 2,4-Dichlorophenol by Laponite Modified Carbon Paste Electrode

A laponite modified carbon paste electrode was prepared, characterized and applied for the 2,4-dichlorophenol (2,4-DCP) voltammetric determination. It takes advantage of the ability of laponite to adsorb phenols, as well as of its availability and very low cost. Kinetic and equilibrium data for 2,4-DCP adsorption by laponite in aqueous dispersions demonstrated that the adsorption process obeyed a pseudo first order kinetic model and was consistent with the formation of adsorbed multilayers on a surface with heterogeneous pore distribution. The composite paste electrode exhibited a heterogeneous surface with 65 % increased surface area and 27 % enhanced catalytic activity compared to the unmodified one. The adsorptive stripping voltammetric determination of 2,4-DCP at an electrode with an optimized graphite:laponite ratio of 55 : 15 w% using a 3 min accumulation time at pH 5.5 was found to be suitable for its quantification in the linear concentration range extended up to 50 μmol L⁻¹ with a sensitivity of 0.56 μA L μmol⁻¹ and a LOD of 0.2 μmol L⁻¹ (S/N=3).The 2,4-DCP electrochemical response was not affected by the presence of some structurally similar phenols, like catechol and p-nitrophenol, while resorcinol, 2-chlorophenol, and 4-chlorophenol presented interferences. The results were validated by 2,4-DCP determination in spiked tap water.     

Jeffreys fluids in forced elongation

In this paper we study existence, uniqueness and regularity of solutions for the equations governing the forced elongation of fluids with differential constitutive law of Jeffreys type. These equations consist of nonlinear first-order hyperbolic equations in one spatial dimension. Forced elongation is imposed through velocity boundary conditions at the domain entry and exit. The existence result is based on the Schauder fixed point theorem and energy methods in the space of boundary-regular functions.     

Standard single-mode fibers as convenient means for the generation of ultrafast high-pulse-energy super-continua

High-pulse-energy super-continua featuring an M² of one were generated in standard single-mode fibers. The highest pulse energy achieved was ∼600 nJ and the pulse duration was ∼1 ps. The spectral width of the generated continua extended over up to 35% of the pump wavelength. PACS 42.65.-k; 42.81.-i; 42.79.Nv     

Classical solutions of quasilinear parabolic systems on two dimensional domains

Using results on abstract evolutions equations and recently obtained results on elliptic operators with discontinuous coefficients including mixed boundary conditions we prove that quasilinear parabolic systems admit a local, classical solution in the space of p–integrable functions, for some p greater than 1, over a bounded two dimensional space domain. The treatment of such equations in a space of integrable functions enables us to define the normal component of the current across the boundary of any Lipschitz subset. As applications we have in mind systems of reaction diffusion equations, e.g. van Roosbroeck’s system.     

Synthesis of analogs of D-Ala-D-Ala as potential inhibitors of bacterial cell wall biosynthesis

The syntheses of the L,L- and D,D-stereoisomers of N- phenoxyacetyl -X-alanine in which X = Ser, Ala( beta Cl ) or Arg, are described. The antibacterial activity of these peptides and some of their synthetic intermediates has been examined. Four of the intermediates in which X = Ala( beta Cl ) and Arg(NO2), which possess C-terminal benzyl ester groups, were active against viridans streptococci and Streptococcus agalactiae. The D,D-enantiomers were more active than the corresponding L,L-isomers. None of the compounds were active against beta-lactamase producing bacteria or acted as beta-lactamase inhibitors.     

Ueber die Best?ndigkeit einiger Explosivstoffe

Ohne Zusammenfassung     

Exceptional Modules for Tubular Canonical Algebras

Let Λ be a tubular canonical algebra of quiver type over a field. We show that each exceptional Λ-module can be exhibited by matrices involving as coefficients 0, 1 and –1 if Λ is of type (3,3,3), (2,4,4) or (2,3,6) and by matrices involving as coefficients 0, 1, –1, λ, –λ and λ–1 if Λ is of type (2,2,2,2) and defined by a parameter λ. Presented by Claus M. Ringel.