Comment on "On the importance of the free energy for elasticity under pressure"

Marcus et al. (Marcus P, Ma H and Qiu S L 2002 J. Phys.: Condens. Matter 14 L525) claim that thermodynamic properties of materials under pressure must be computed using the Gibbs free energy $G$, rather than the internal energy $E$. Marcus et al. state that ``The minima of $G$, but not of $E$, give the equilibrium structure; the second derivatives of $G$, but not of $E$, with respect to strains at the equilibrium structure give the equilibrium elastic constants.'' Both statements are incorrect.Comment: Commen

Basis Independent Measures of R-parity Violation

We construct basis-independent expressions that measure the magnitude of $R$-parity breaking due to possible superpotential terms in the Minimal Supersymmetric extension of the Standard Model, in the absence of soft supersymmetry-breaking terms and spontaneous gauge symmetry breaking. We also discuss briefly their application to a consistent treatment of cosmological constraints on $R$-parity violation.Comment: 13 pages, Late

An analysis of the practical DPG method

In this work we give a complete error analysis of the Discontinuous Petrov Galerkin (DPG) method, accounting for all the approximations made in its practical implementation. Specifically, we consider the DPG method that uses a trial space consisting of polynomials of degree $p$ on each mesh element. Earlier works showed that there is a "trial-to-test" operator $T$, which when applied to the trial space, defines a test space that guarantees stability. In DPG formulations, this operator $T$ is local: it can be applied element-by-element. However, an infinite dimensional problem on each mesh element needed to be solved to apply $T$. In practical computations, $T$ is approximated using polynomials of some degree $r > p$ on each mesh element. We show that this approximation maintains optimal convergence rates, provided that $r\ge p+N$, where $N$ is the space dimension (two or more), for the Laplace equation. We also prove a similar result for the DPG method for linear elasticity. Remarks on the conditioning of the stiffness matrix in DPG methods are also included.Comment: Mathematics of Computation, 201

New records of wood inhabiting fungal species from Kondapalli reserved forest of Central Eastern Ghats, India

Wood inhabiting fungi that grow specifically on leaf litter, wood debris, humus rich soil of forest helps in biodegradation and increase soil fertility. The fruiting bodies of fungi were collected from partially dead forest trees, fallen wooden logs, leaf litter and decomposing humus rich soil of Kondapalli forest area, Central Eastern Ghats of India. Detailed macroscopic and microscopic study of collected fungal samples revealed the occurrence of wood inhabiting fungi belonging to 7 genera and 9 species; i.e. Geastrum triplex Jungh., Marasmius siccus (Schweinitz) Fries, M. fulvoferrugineus Gilliam, M. oreades (Bolt.: Fries) Fries Epicr. Lactarius piperatus (L.) Pers., Flammulina velutipes (Curtis) Singer, Artomyces microsporus (Qiu X. Wu & R. H. Petersen) Lickey, Hymenochaetopsis rigidula (Berk. & M. A. Curtis) S. H. He & Jiao Yang and Bjerkandera adusta (Willd: Fr.) Karst. For the first time, A. microsporus (Qiu X. Wu & R. H. Petersen) Lickey and H. rigidula (Berk. & M. A. Curtis) S. H. He & Jiao Yang., were reported from India. M. fulvoferrugineus Gilliam was reported second time from India. The wood inhabiting fungi were new records to Kondapalli forest area, Central Eastern Ghats of India

Norming Algebras and Automatic Complete Boundedness of Isomorphisms of Operator Algebras

We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A_1 and A_2 are operator algebras, then any bounded epimorphism of A_1 onto A_2 is completely bounded provided that A_2 contains a norming C*-subalgebra. We use this result to give some insights into Kadison's Similarity Problem: we show that every faithful bounded homomorphism of a C*-algebra on a Hilbert space has completely bounded inverse, and show that a bounded representation of a C*-algebra is similar to a *-representation precisely when the image operator algebra \lambda-norms itself. We give two applications to isometric isomorphisms of certain operator algebras. The first is an extension of a result of Davidson and Power on isometric isomorphisms of CSL algebras. Secondly, we show that an isometric isomorphism between subalgebras A_i of C*-diagonals (C_i,D_i) (i=1,2) satisfying D_i \subseteq A_i \subseteq C_i extends uniquely to a *-isomorphism of the C*-algebras generated by A_1 and A_2; this generalizes results of Muhly-Qiu-Solel and Donsig-Pitts.Comment: 9 page

Comparing Cournot and Bertrand Equilibria in a Differentiated Duopoly with Product R&D

This paper compares Bertrand and Cournot equilibria in a differentiated duopoly with substitute goods and product R&D. I find that R&D expenditure, prices and firms� net profits are always higher under quantity competition than under price competition. Furthermore, output, consumer surplus and total welfare are higher in the Bertrand equilibrium than in the Cournot equilibrium if either R&D spillovers are weak or products are sufficiently differentiated. If R&D spillovers are strong and products are not too differentiated, then output, consumer surplus and total welfare are lower in the Bertrand case than in the Cournot case. Thus a key finding of the paper is that there are circumstances where quantity competition can be more beneficial than price competition both for consumers and for firms.