Local obstructions to projective surfaces admitting skew-symmetric Ricci tensor

The equation determining whether a projective structure admits a connection in its given projective class that has skew-symmetric Ricci tensor is an overdetermined system of semi-linear partial differential equations which we call the projective Einstein–Weyl (pEW) equation. In 2-dimensions, we give local obstructions for projective surfaces to admit such a connection in its projective class. The obstructions are the resultants of polynomial equations that have to be satisfied for there to admit any pEW solution.     

A modular spectral triple for κ-Minkowski space

We present a spectral triple for $\kappa$-Minkowski space in two dimensions. Starting from an algebra naturally associated to this space, a Hilbert space is built using a weight which is invariant under the $\kappa$-Poincaré algebra. The weight satisfies a KMS condition and its associated modular operator plays an important role in the construction. This forces us to introduce two ingredients which have a modular flavour: the first is a twisted commutator, used to obtain a boundedness condition for the Dirac operator, and the second is a weight replacing the usual operator trace, used to measure the growth of the resolvent of the Dirac operator. We show that, under some assumptions related to the symmetries and the classical limit, there is a unique Dirac operator and automorphism such that the twisted commutator is bounded. Then, using the weight mentioned above, we compute the spectral dimension associated to the spectral triple and find that is equal to the classical dimension. Finally we briefly discuss the introduction of a real structure.     

On the use of multiple interpolation series in scaled particle theory: improved predictions and limitations

We propose further modifications to recent formulations of the scaled particle theory (SPT) of hard particle fluids. In any formulation of SPT, a number of conditions are applied to the central function G. As the exact form of G is unknown, a form must be assumed. Representing G with more than one series has recently been shown (Siderius and Corti, J. Chem. Phys. 127, 144502, 2007) to lead to improved planar surface tension predictions with little change in the already accurate pressure, excess chemical potential and fluid structure predictions. Another condition on G that includes the curvature of the radial distribution at contact was not, however, invoked in this previous work. We incorporate here this additional condition into the multiple series approach, resulting in further improvements to the SPT predictions. We also consider a number of permutations of the multiple interpolation series to explore the limitations of this approach and again find that increasing the number of series will not by itself lead to better predictions of the properties of the hard sphere fluid.     

cis‐substituted tetraethynylporphyrin derivatives for small molecule organic solar cells

A 5,10‐Bis(phenylethynyl)‐15,20‐bis(triisopropylsilylethynyl)porphyrin (cis‐TIPSTEP) was synthesized by using phenylethynyl dipyrromethane and triisopropylsilylpropynal through scrambling of the ethynyl substituents. X‐ray crystallographic structures of cis‐TIPSTEP, 5‐phenylethynyl‐10,15,20‐tris(triisopropylsilylethynyl)porphyrin, and 5,10,15,20‐tetrakis(triisopropylsilylethynyl)porphyrin were determined in order to study the packing structure; cis‐TIPSTEP exhibited good π‐overlap and parallel π‐stacking structures. 5,10‐Bis(phenylethynyl)‐15,20‐bis(triisopropylsilylethynyl)porphyrinato magnesium (II) (Mg‐cis‐TIPSTEP) was synthesized for the use in small molecule organic solar cells, which gave power conversion efficiency of 1.5% with short‐circuit current density of 4.5 mA/cm², open‐circuit voltage of 0.83 V, and fill factor of 0.39. Copyright © 2013 John Wiley & Sons, Ltd.     

A wire-form emitter metal–insulator–semiconductor tunnel junction

Physical effects arising due to change of configuration of a MIS system from planar to cylindrical, are theoretically analyzed. Attention is paid to the voltage partitioning and all the components of tunneling current. A simple simulation model is developed enabling prediction of the band diagram details and calculation of the currents. The trends expected with decreasing system radius are elucidated. Cylindrical geometry can be faced with when quantum wire is used as an electron emitter. Similar form may also be roughly attributed to an edge region of conventional MIS capacitors.     

Hypersurfaces with isotropic para-Blaschke tensor

Let Mnbe an n-dimensional submanifold without umbilical points in the(n + 1)-dimensional unit sphere Sn+1.Four basic invariants of Mnunder the Moebius transformation group of Sn+1are a 1-form Φ called moebius form,a symmetric(0,2) tensor A called Blaschke tensor,a symmetric(0,2) tensor B called Moebius second fundamental form and a positive definite(0,2) tensor g called Moebius metric.A symmetric(0,2) tensor D = A + μB called para-Blaschke tensor,where μ is constant,is also an Moebius invariant.We call the para-Blaschke tensor is isotropic if there exists a function λ such that D = λg.One of the basic questions in Moebius geometry is to classify the hypersurfaces with isotropic para-Blaschke tensor.When λ is not constant,all hypersurfaces with isotropic para-Blaschke tensor are explicitly expressed in this paper.     

Analysis of diffusion process in fractured reservoirs using fractional derivative approach

The fractal geometry is used to model of a naturally fractured reservoir and the concept of fractional derivative is applied to the diffusion equation to incorporate the history of fluid flow in naturally fractured reservoirs. The resulting fractally fractional diffusion (FFD) equation is solved analytically in the Laplace space for three outer boundary conditions. The analytical solutions are used to analyze the response of a naturally fractured reservoir considering the anomalous behavior of oil production. Several synthetic examples are provided to illustrate the methodology proposed in this work and to explain the diffusion process in fractally fractured systems.     

Orlicz mixed quermassintegrals Dedicated to Professor Ren De-lin on the Occasion of his 80th Birthday

The notion of mixed quermassintegrals in the classical Brunn-Minkowski theory is extended to that of Orlicz mixed quermassintegrals in the Orlicz Brunn-Minkowski theory. The analogs of the classical CauchyKubota formula, the Minkowski isoperimetric inequality and the Brunn-Minkowski inequality are established for this new Orlicz mixed quermassintegrals.     

A Poisson manifold of strong compact type

We construct a corank one Poisson manifold which is of strong compact type, i.e., the associated Lie algebroid structure on its cotangent bundle is integrable, and the source 1-connected (symplectic) integration is compact. The construction relies on the geometry of the moduli space of marked K3 surfaces.     

Weakly conformal Finsler geometry

An extension of conformal equivalence for Finsler metrics is introduced and called weakly conformal equivalence and is used to define the weakly conformal transformations. The conformal Lichnerowicz‐Obata conjecture is refined to weakly conformal Finsler geometry. It is proved that: If X is a weakly conformal complete vector field on a connected Finsler space (M, F) of dimension , then, at least one of the following statements holds: (a) There exists a Finsler metric F₁ weakly conformally equivalent to F such that X is a Killing vector field of the Finsler metric, (b) M is diffeomorphic to the sphere and the Finsler metric is weakly conformally equivalent to the standard Riemannian metric on , and (c) M is diffeomorphic to the Euclidean space and the Finsler metric F is weakly conformally equivalent to a Minkowski metric on . The considerations invite further dynamics on Finsler manifolds.