Revisiting umbra-Lagrangian-Hamiltonian mechanics: Its variational foundation and extension of Noether's theorem and Poincare-Cartan integral

This paper revisits an extension of the Lagrangian-Hamiltonian mechanics that incorporates dissipative and non-potential fields, and non-integrable constraints in a compact form, such that one may obtain invariants of motion or possible invariant trajectories through an extension of Noether's theorem. A new concept of umbra-time has been introduced for this extension. This leads to a new form of equation, which is termed as the umbra-Lagrange's equation. The underlying variational principle, which is based on a recursive minimization of functionals, is presented. The introduction of the concept of umbra-time extends the classical manifold over which the system evolves. An extension of the Lagrangian-Hamiltonian mechanics over vector fields in this extended space has been presented. The idea of umbra time is then carried forward to propose the basic concept of umbra-Hamiltonian, which is used along with the extended Noether's theorem to provide an insight into the dynamics of systems with symmetries. Gauge functions for umbra-Lagrangian are also introduced. Extension of the Poincare-Cartan integral for the umbra-Lagrangian theory is also proposed, and its implications have been discussed. Several examples are presented to illustrate all these concepts.     

Catalytic Mechanism of a Heme and Tyrosyl Radical-Containing Fatty Acid α-(Di)oxygenase

The steady-state catalytic mechanism of a fatty acid α-(di)oxygenase is examined, revealing that a persistent tyrosyl radical (Tyr379(?)) effects O(2) insertion into C(α)-H bonds of fatty acids. The initiating C(α)-H homolysis step is characterized by apparent rate constants and deuterium kinetic isotope effects (KIEs) that increase hyperbolically upon raising the concentration of O(2). These results are consistent with H(?) tunneling, transitioning from a reversible to an irreversible regime. The limiting deuterium KIEs increase from ～30 to 120 as the fatty acid chain is shortened from that of the native substrate. In addition, activation barriers increase in a manner that reflects decreased fatty acid binding affinities. Anaerobic isotope exchange experiments provide compelling evidence that Tyr379(?) initiates catalysis by H(?) abstraction. C(α)-H homolysis is kinetically driven by O(2) trapping of the α-carbon radical and reduction of a putative peroxyl radical intermediate to a 2(R)-hydroperoxide product. These findings add to a body of work which establishes large-scale hydrogen tunneling in proteins. This particular example is novel because it involves a protein-derived amino acid radical.     

The spatial product of Arveson systems is intrinsic

We prove that the spatial product of two spatial Arveson systems is independent of the choice of the reference units. This also answers the same question for the minimal dilation of the Powers sum of two spatial CP-semigroups: It is independent up to cocycle conjugacy.     

<Emphasis Type="Italic">ε</Emphasis>-Uniform error estimate of hybrid numerical scheme for singularly perturbed parabolic problems with nterior layers

This article is devoted to the study of a hybrid numerical scheme for a class of singularly perturbed parabolic convection-diffusion problems with discontinuous convection coefficients. In general, the solutions of this class of problems possess strong interior layers. To solve these problems, we discretize the time derivative by the backward-Euler method and the spatial derivatives by a hybrid finite difference scheme (a proper combination of the midpoint upwind scheme in the outer regions and the classical central difference scheme in the interior layer regions) on a layer resolving piecewise-uniform Shishkin mesh. It is proved that the method converges uniformly in the discrete supremum norm with almost second-order spatial accuracy. Moreover, an optimal order of convergence (up to a logarithmic factor) is obtained inside the layer regions. Extensive numerical experiments are conducted to support the theoretical results and also, to demonstrate the accuracy of this method.     

Elastic properties of the RIV-RIII rotator phases of alkanes

A model free energy has been constructed to describe the R_IV-R_III rotator phase transition in alkanes in terms of the elastic strains and order parameter. The conditions for the R_IV-R_III phase transition are discussed. From the free energy, the order parameter and the elastic strains are determined. The model free energy describes the first or second order character of the R_IV-R_III transition depending on the strength of the coupling. The elastic properties in the vicinity of the R_IV-R_III transition are discussed on the basis of a free energy expansion. The temperature dependence of the elastic constants is calculated on both sides of the transition. The coupling between the order parameter and elastic stains is shown to have a crucial influence on the phase behavior and the order of the transition.     

A novel frequency encoded all optical logic gates exploiting polarization insesensitive four wave mixing in semiconductor optical amplifier, filtering property of ADD/DROP multiplexer and non-linearity of reflective semiconductor amplifier

All optical logic gates exploiting polarization independent four wave mixing in semiconductor optical amplifier (SOA), filtering property of ADD/DROP multiplexer (ADM) and non-linearity in reflective semiconductor optical amplifier (RSOA) have been proposed. The logic gates proposed are polarization independent which ensures hardware simplicity and greater speed. The all optical frequency encoded logic gates NOT, OR, NOR, AND, NAND, X-OR, X-NOR are implemented which are very useful in optical computing ad signal processing, cryptography, etc. The logic gates proposed have the advantages that there is no intensity loss dependent problem, and are polarization and temperature insensitive.     

Method of implementation of frequency encoded all optical half adder, half subtractor and full adder based on semiconductor optical amplifiers and add drop multiplexers

A novel frequency encoded all optical half adder, half subtractor and full adder are proposed. The implementation is ultrafast one and the frequency encoding makes it intensity loss dependent problem free. The use of polarization insensitive four-wave mixing makes the design polarization independent and the hardware simple. The frequency conversion by the reflective semiconductor optical amplifiers (RSOA) makes the design faster compared to other semiconductor optical amplifiers (SOA) based design.     

Reappraisal of the electric dipole moment enhancement factor for thallium

The electric dipole moment (EDM) enhancement factor of atomic Tl is of considerable interest as it has been used in determining the most accurate limit on the electron EDM to date. However, its value varies from -179 to -1041 in different approximations. In view of the large uncertainties associated with many of these calculations, we perform an accurate calculation employing the relativistic coupled-cluster theory and obtain -466, which in combination with the most accurate measurement of Tl EDM [Phys. Rev. Lett. 88, 071805 (2002)] yields a new limit for the electron EDM: |d(e)| < 2.0 × 10?2?e cm.     

Role of crystal orientation on the magnetic properties of CoFe2O4 thin films grown on Si (1 0 0) and Al2O3 (0 0 0 1) substrates using pulsed laser deposition

We report the influence of crystal orientation on the magnetic properties of CoFe₂O₄ (CFO) thin films grown on single crystal Si (1 0 0) and c-cut sapphire (Al₂O₃) (0 0 0 1) substrates using pulsed laser deposition technique. The thickness was varied from 200 to 50 nm for CFO films grown on Si substrates, while it was fixed at 200 nm for CFO films grown on Al₂O₃ substrates. We observed that the 200 and 100 nm thick CFO-Si films grew in both (1 1 1) and (3 1 1) directions and displayed out-of-plane anisotropy, whereas the 50 nm thick CFO-Si film showed only an (1 1 1) orientation and an in-plane anisotropy. The 200 nm thick CFO film grown on an Al₂O₃ substrate was also found to show a complete (1 1 1) orientation and a strong in-plane anisotropy. These observations pointed to a definite relation between the crystalline orientation and the observed magnetic anisotropy in the CFO thin films.     

In Situ Self Assembly of Thiolated ortho‐Quinone Capped Electrocatalysts for Bioanalytical Applications

Thiolated o‐quinone‐capped electrocatalysts modeled on the naturally occurring o‐quinone cofactor pyrroloquinoline quinone (PQQ) were designed and synthesized for the development of biosensor devices. The o‐quinone‐capped electrocatalysts self assembled on gold electrodes through a thiolated phenyleneethynylene linkage to form a monolayer less than 2 nm in thickness. Cyclic voltammetric measurements demonstrated reversible electrochemical properties between the quinone and hydroquinone forms of the head group. In an amperometric sensing mode, the modified electrodes reproducibly detected ethanethiol at micromolar levels demonstrating their robust electrocatalytic activity toward thiols. Their redox cycling and electrocatalytic properties show promise for detection of biologically important thiols and other nucleophiles.