Constraints on the omega pi form factor from analyticity and unitarity

Motivated by the discrepancies noted recently between the theoretical calculations of the electromagnetic omega pi form factor and certain experimental data, we investigate this form factor using analyticity and unitarity in a framework known as the method of unitarity bounds. We use a QCD correlator computed on the spacelike axis by operator product expansion and perturbative QCD as input, and exploit unitarity and the positivity of its spectral function, including the two-pion contribution that can be reliably calculated using high-precision data on the pion form factor. From this information, we derive upper and lower bounds on the modulus of the omega pi form factor in the elastic region. The results provide a significant check on those obtained with standard dispersion relations, confirming the existence of a disagreement with experimental data in the region around 0.6 GeV.

Mycobacterium tuberculosis Cell Division Protein, FtsE, is an ATPase in Dimeric Form

FtsE is one of the earliest cell division proteins that assembles along with FtsX at the mid-cell site during cell division in Escherichia coli. Both these proteins are highly conserved across diverse bacterial genera and are predicted to constitute an ABC transporter type complex, in which FtsE is predicted to bind ATP and hydrolyse it, and FtsX is predicted to be an integral membrane protein. We had earlier reported that the MtFtsE of the human pathogen, Mycobacterium tuberculosis, binds ATP and interacts with MtFtsX on the cell membrane of M. tuberculosis and E. coli. In this study, we demonstrate that MtFtsE is an ATPase, the active form of which is a dimer, wherein the participating monomers are held together by non-covalent interactions, with the Cys84 of each monomer present at the dimer interface. Under oxidising environment, the dimer gets stabilised by the formation of Cys84-Cys84 disulphide bond. While the recombinant MtFtsE forms a dimer on the membrane of E. coli, the native MtFtsE seems to be in a different conformation in the M. tuberculosis membrane. Although disulphide bridges were not observed on the cytoplasmic side (reducing environment) of the membrane, the two participating monomers could be isolated as dimers held together by non-covalent interactions. Taken together, these findings show that MtFtsE is an ATPase in the non-covalent dimer form, with the Cys84 of each monomer present in the reduced form at the dimer interface, without participating in the dimerisation or the catalytic activity of the protein.

Do carboximide-carboxylic acid combinations form co-crystals? The role of hydroxyl substitution on the formation of co-crystals and eutectics

Carboxylic acids, amides and imides are key organic systems which provide understanding of molecular recognition and binding phenomena important in biological and pharmaceutical settings. In this context, studies of their mutual interactions and compatibility through co-crystallization may pave the way for greater understanding and new applications of their combinations. Extensive co-crystallization studies are available for carboxylic acid/amide combinations, but only a few examples of carboxylic acid/imide co-crystals are currently observed in the literature. The non-formation of co-crystals for carboxylic acid/imide combinations has previously been rationalized, based on steric and computed stability factors. In the light of the growing awareness of eutectic mixtures as an alternative outcome in co-crystallization experiments, the nature of various benzoic acid/cyclic imide combinations is established in this paper. Since an additional functional group can provide sites for new intermolecular interactions and, potentially, promote supramolecular growth into a co-crystal, benzoic acids decorated with one or more hydroxyl groups have been systematically screened for co-crystallization with one unsaturated and two saturated cyclic imides. The facile formation of an abundant number of hydroxybenzoic acid/cyclic carboximide co-crystals is reported, including polymorphic and variable stoichiometry co-crystals. In the cases where co-crystals did not form, the combinations are shown invariably to result in eutectics. The presence or absence and geometric disposition of hydroxyl functionality on benzoic acid is thus found to drive the formation of co- crystals or eutectics for the studied carboxylic acid/imide combinations.

A Reliable Residual Based A Posteriori Error Estimator for a Quadratic Finite Element Method for the Elliptic Obstacle Problem

A residual based a posteriori error estimator is derived for a quadratic finite element method (FEM) for the elliptic obstacle problem. The error estimator involves various residuals consisting of the data of the problem, discrete solution and a Lagrange multiplier related to the obstacle constraint. The choice of the discrete Lagrange multiplier yields an error estimator that is comparable with the error estimator in the case of linear FEM. Further, an a priori error estimate is derived to show that the discrete Lagrange multiplier converges at the same rate as that of the discrete solution of the obstacle problem. The numerical experiments of adaptive FEM show optimal order convergence. This demonstrates that the quadratic FEM for obstacle problem exhibits optimal performance.

Alternative Formulation of the Discrete Linear Quadratic Regulator (DLQR)

In this paper, an alternative apriori and aposteriori formulation has been derived for the discrete linear quadratic regulator (DLQR) in a manner analogous to that used in the discrete Kalman filter. It has been shown that the formulation seamlessly fits into the available formulation of the DLQR and the equivalent terms in the existing formulation and the proposed formulation have been identified. Thereafter, the significance of this alternative formulation has been interpreted in terms of the sensitivity of the controller performances to any changes in the states or to changes in the control inputs. The implications of this alternative formulation to adaptive controller tuning have also been discussed.

Quantum stochastic calculus associated with quadratic quantum noises

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie dagger-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Ito formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus. (C) 2016 AIP Publishing LLC.

Style and the “Idea” of the sophist after Plato : the impact of form typology on sophistic teaching and writing on interdisciplinary scholarly work

Resumen: Después de la primera sofística, los sofistas actuaron entre el resto de los pensadores del Mediterráneo como un grupo definido. Dado que hay muchos ejemplos que muestran que los sofistas ejercían sus prácticas y que también eran personas comprometidas en otras actividades, vamos a examinar aquí diversos casos de semejanzas y diferencias entre ellos y otros grupos de pensadores. Nuestras tres preguntas fundamentales son: qué, cómo y por qué los sofistas escribían y enseñaban. Intentaremos responder haciendo un análisis diacrónico de las principales formas y géneros de escritura que produjeron (qué). El cómo lo responderemos en su desenvolvimiento como una actividad comunicativa más allá de las fronteras de las disciplinas de la época. El por qué tendrá su respuesta al enfatizar la necesidad de la actividad de los sofistas en la socialización de la época y en la educación de la antigüedad. Al aseverar que el estilo era la idea de los sofistas, ponemos la noción de idea en Platón en el contexto de idea derivado de los sofistas contemporáneos a él y de los sofistas posteriores (segunda sofística) y centramos el foco en la función de visualidad expresada en su concepto de idea desde las obras sofísticas más tempranas en la época de Platón hasta las contribuciones posteriores.

Closed form solutions of T-stress in plane elasticity crack problems

The T-stress is considered as an important parameter in linear elastic fracture mechanics. In this paper, several closed form solutions of T-stress in plane elasticity crack problems in an infinite plate are investigated using the complex potential theory. In the line crack case, if the applied loading is the remote stress or the concentrated forces, the T-stress can be derived from the basic field. Here, the basic field is defined as the field caused by the applied loading in the infinite plate without the crack. For the circular are crack, the T-stress can be abstracted from a known solution. For the cusp crack problems, the T-stress can be separated from the obtained stress solution for which the conformal mapping technique is used.

The Supercore for Normal Form Games

We study the supercore of a system derived from a normal form game. For the case of a finite game with pure strategies, we define a sequence of games and show that the supercore of that system coincides with the set of Nash equilibrium strategy profiles of the last game in the sequence. This result is illustrated with the characterization of the supercore for the n-person prisoners’ dilemma. With regard to the mixed extension of a normal form game, we show that the set of Nash equilibrium profiles coincides with the supercore for games with a finite number of Nash equilibria. For games with an infinite number of Nash equilibria this need not be no longer the case. Yet, it is not difficult to find a binary relation which guarantees the coincidence of these two sets.