Chiral expansion and Macdonald deformation of two‐dimensional Yang‐Mills theory

We derive the analog of the large N Gross‐Taylor holomorphic string expansion for the refinement of q‐deformed Yang‐Mills theory on a compact oriented Riemann surface. The derivation combines Schur‐Weyl duality for quantum groups with the Etingof‐Kirillov theory of generalized quantum characters which are related to Macdonald polynomials. In the unrefined limit we reproduce the chiral expansion of q‐deformed Yang‐Mills theory derived by de Haro, Ramgoolam and Torrielli. In the classical limit , the expansion defines a new β‐deformation of Hurwitz theory wherein the refined partition function is a generating function for certain parameterized Euler characters, which reduce in the unrefined limit to the orbifold Euler characteristics of Hurwitz spaces of holomorphic maps. We discuss the geometrical meaning of our expansions in relation to quantum spectral curves and β‐ensembles of matrix models arising in refined topological string theory.     

In-Cell Dual Drug Synthesis by Cancer-Targeting Palladium Catalysts

Transition metals have been successfully applied to catalyze non-natural chemical transformations within living cells, with the highly efficient labeling of subcellular components and the activation of prodrugs. In vivo applications, however, have been scarce, with a need for the specific cellular targeting of the active transition metals. Here, we show the design and application of cancer-targeting palladium catalysts, with their specific uptake in brain cancer (glioblastoma) cells, while maintaining their catalytic activity. In these cells, for the first time, two different anticancer agents were synthesized simultaneously intracellularly, by two totally different mechanisms (in situ synthesis and decaging), enhancing the therapeutic effect of the drugs. Tumor specificity of the catalysts together with their ability to perform simultaneous multiple bioorthogonal transformations will empower the application of in vivo transition metals for drug activation strategies.     

Antibacterial and antioxidant constituents of Acalypha wilkesiana

This study was aimed at characterising the secondary metabolites responsible for antibacterial and antioxidant activities of Acalypha wilkesiana. Purification of the defatted methanol leaves extract was guided by the DPPH free radical scavenging assay as well as by evaluation of the antibacterial activity against four bacterial strains. As a result, geraniin, corilagin, quadrangularic acid M and shikimic acid were purified and isolated. Shikimic acid, reported for the first time from this plant, proved to be the major metabolite of the extract. All the four isolated compounds showed bactericidal activity against extended spectrum beta-lactamase-producing Klebsiella pneumoniae (700603), while corilagin was the single compound to exhibit antioxidant activity (IC₅₀ 53 μg/mL).     

On the clathrate structures of syndiotactic poly(m-methylstyrene)

The crystal structures of clathrate forms of syndiotactic poly(m-methylstyrene) containing guest molecules having different steric hindrance (CS₂, benzene and orto-dichlorobenzene) are presented. The structures are all characterized by polymer chains in s (2/1)2 helical conformation and guest molecules packed in an orthorhombic unit cell according to the space group Pcaa. All the presented clathrates belongs to β class indipendently from the dimensions of the guest molecule. In this aspect they differ both from clathrate forms of syndiotactic polystyrene, all belonging to α class, and from clathrate forms of syndiotactic poly(p-methylstyrene) that belong to α or β class according to the steric hindrance of the guest molecule.     

Clathrates with tetrahydrofuran of styrene‐p‐methyl styrene co‐syndiotactic copolymers

Clathrates with tetrahydrofuran of styrene‐p‐methyl styrene co‐syndiotactic copolymers have been characterized by wide‐angle X‐ray scattering and differential scanning calorimetry. Stable clathrate structures with THF molecules have been observed in whole range of composition. In particular, syndiotactic polystyrene like and syndiotactic poly‐p‐methylstyrene like clathrate phases are obtained for p‐methylstyrene contents lower and higher than 35% by mol, respectively.     

On the clathrate forms of syndiotactic poly(p-methylstyrene)

A classification for clathrate structures of syndiotactic poly(p-methylstyrene) in two classes (α and β), on the basis of X-ray diffraction analyses as well as of the different observed behavior with respect to the thermal and acetone treatment, is presented. A structural correlation between α and β class clathrates and forms I and II, respectively, is evidenced. It is also suggested that form I and form II could be the “emptied forms” of the α and β class clathrates, respectively. Similar steric hindrance of the molecules inducing clathrate structures, within each class has been observed.     

C ∞ regularity of solutions of an equation of Levi’s type in R 2 n +1

We study the regularity of the solutions u of a class of P.D.E., whose prototype is the prescribed Levi curvature equation in ℝ^{2 n +1}. It is a second-order quasilinear equation whose characteristic matrix is positive semidefinite and has vanishing determinant at every point and for every function u∈C ². If the Levi curvature never vanishes, we represent the operator ℒ associated with the Levi equation as a sum of squares of non-linear vector fields which are linearly independent at every point. By using a freezing method we first study the regularity properties of the solutions of a linear operator, which has the same structure as ℒ. Then we apply these results to the classical solutions of the equation, and prove their C ^∞ regularity. Received: October 10, 1998; in final form: March 5, 1999?Published online: May 10, 2001     

On the Reliability of Numerical Solutions of Brine Transport in Groundwater: Analysis of Infiltration from a Salt Lake

The density dependent flow and transport problem in groundwater is solved numerically by means of a mixed finite element scheme for the flow equation and a mixed finite element-finite volume time-splitting based technique for the transport equation. The proposed approach, spatially second order accurate, is used to address the issue of grid convergence by solving on successively refined grids the salt lake problem, a physically unstable downward convection with formation of fingers. Numerical results indicate that achievement of grid convergence is problematic due to ill-conditioning arising from the strong nonlinearities of the mathematical model.     

Molecular gas-flow over convex bodies: a physico-mathematical model for heat transfer calculation

This paper deals with a physico-mathematical model for the heat-flux over a convex body in near-free molecular flow regime. The model depends on the characteristic global physical quantity of the state of the external flux and upon two phenomenological parameters which represent the physico-chemical conditions of the gas-surface pair. The presence of these two parameters, which is due to the construction of the model by means of the theory of scattering kernels, gives the model a certain arbitrariness.To remove this limitation the model has been further identified in the sense that these parameters have been determined for a particular gas-surface pair by comparison with experimental results on a cylindrical body. The model has then been applied to a sphere in order to determine the Stanton number. Finally, these results have been approximated in terms of analytical expressions in order to simplify the model itself.