Deligne categories and reduced Kronecker coefficients

The Kronecker coefficients are the structural constants for the tensor categories of representations of the symmetric groups, namely, given three partitions λ,μ,τ of n, the multiplicity of λ in μ⊗τ is called the Kronecker coefficient g[superscript λ][subscript μ,τ]. When the first part of each of the partitions is taken to be very large (the remaining parts being fixed), the values of the appropriate Kronecker coefficients stabilize; the stable value is called the reduced (or stable) Kronecker coefficient. These coefficients also generalize the Littlewood–Richardson coefficients and have been studied quite extensively. In this paper, we show that reduced Kronecker coefficients appear naturally as structure constants of Deligne categories [bar under Rep](S[subscript t]). This allows us to interpret various properties of the reduced Kronecker coefficients as categorical properties of Deligne categories [bar under Rep](S[subscript t]) and derive new combinatorial identities

A comprehensive evaluation of the EU's biofuel policy: From biofuels to agrofuels

During a time in which the subject of climate change is deemed high on the list of priorities of many governments, it is important to assess to what extent policies in this field are achieving meaningful results. The link between energy usage and global warming is clear and today in the European Union the use of renewable resources is being promoted more than ever before. The move towards a renewables based economy has clear benefits over a fossil fuel based one with regards to climate change and the environment, however if the implementation of renewables is not monitored and regulated then this is not a given by any means. Of the renewable resources, bioenergy has a high level of importance in the EU. For this reason, this paper will make a comprehensive evaluation of the EU's biofuel policy in order to assess what the driving forces behind the regulation of this resource are, and how they affect to what extent it is successful or not. In order to do this, firstly the impacts of current EU bioenergy consumption will be assessed, to determine whether it is achieving the stated and desired climate goals or not. Findings will show that in fact the current formulation of Europe's Renewable Strategy creates pressure to meet binding targets for renewable usage and the resultant rapid increase in the demand for bioenergy has caused a number of negative social and ecological impacts to arise. Therefore in light of this, the current systems in place at the EU level meant to regulate the use of bioenergy and ensure it is implemented in a sustainable way will be critically analysed in order to find out how such negative impacts have been able to occur. The final section will then look into the driving forces responsible for regulation of this kind through a case study of Germany and Indonesia

Orthogonality relations in Quantum Tomography

Quantum estimation of the operators of a system is investigated by analyzing its Liouville space of operators. In this way it is possible to easily derive some general characterization for the sets of observables (i.e. the possible quorums) that are measured for the quantum estimation. In particular we analyze the reconstruction of operators of spin systems.Comment: 10 pages, 2 figure

An electric charge has no screw sense--a comment on the twistfree formulation of electrodynamics by da Rocha & Rodrigues

Da Rocha and Rodigues (RR) claim (i) that in classical electrodynamics in vector calculus the distinction between polar and axial vectors and in exterior calculus between twisted and untwisted forms is inappropriate and superfluous, and (ii) that they can derive the Lorentz force equation from Maxwell's equations. As to (i), we point out that the distinction of polar/axial and twisted/untwisted derives from the property of the electric charge of being a pure scalar, that is, not carrying any screw sense. Therefore, the mentioned distinctions are necessary ingredients in any fundamental theory of electrodynamics. If one restricted the allowed coordinate transformations to those with positive Jacobian determinants (or prescribed an equivalent constraint), then the RR scheme could be accommodated; however, such a restriction is illegal since electrodynamics is, in fact, also covariant under transformations with negative Jacobians. As to (ii), the "derivation" of the Lorentz force from Maxwell's equations, we point out that RR forgot to give the symbol F (the field strength) in Maxwell's equations an operational meaning in the first place. Thus, their proof is empty. Summing up: the approach of RR does not bring in any new insight into the structure of electrodynamics.Comment: Added answer to da Rocha & Rodrigues arXiv:0912.212

Physical Activity in Intermediate Schools: The Interplay of School Culture, Adolescent Challenges, and Athletic Elitism

The intervention potential of physical activity programs for intermediate schools (grades 7–9), could be enhanced by an understanding of how students engage with and disengage from physical activity. This study provides an interpretation of how adolescents, parents, teachers, and principals perceive students’ involvement in physical activity within their intermediate school environment. Thematic analyses of eighteen interview transcripts resulted in an interpretation of students’ continuum of engagement with or disengagement from physical activity. The continuum is reflective of a social process that is grounded in three key themes: school culture, social valuing of athletic elitism, and adolescent challeng

Tight-Binding study of the electronic and magnetic properties of an L1_0 ordered FeCu alloy

We have calculated the electronic structure of the tetragonal L1$_0$ ordered FeCu by solving self-consistently a tight-binding Hamiltonian for s, p and d electrons. We have found by total energy calculation that this structure is ferromagnetic. In addition, we have determined that the equilibrium ratio between the interlayer and the intralayer lattice parameters is 0.947.Comment: 7 pages latex, 4 postscript figures included. To appear in Phys. Lett.

Photoelasticity of sodium silicate glass from first principles

Based on density-functional perturbation theory we have computed the photoelastic tensor of a model of sodium silicate glass of composition (Na$_2$O)$_{0.25}$(SiO$_2$)$_{0.75}$ (NS3). The model (containig 84 atoms) is obtained by quenching from the melt in combined classical and Car-Parrinello molecular dynamics simulations. The calculated photoelastic coefficients are in good agreement with experimental data. In particular, the calculation reproduces quantitatively the decrease of the photoelastic response induced by the insertion of Na, as measured experimentally. The extension to NS3 of a phenomenological model developed in a previous work for pure a-SiO$_2$ indicates that the modulation upon strain of other structural parameters besides the SiOSi angles must be invoked to explain the change in the photoelstic response induced by Na

Maximizing nearest neighbour entanglement in finitely correlated qubit--chains

We consider translationally invariant states of an infinite one dimensional chain of qubits or spin-1/2 particles. We maximize the entanglement shared by nearest neighbours via a variational approach based on finitely correlated states. We find an upper bound of nearest neighbour concurrence equal to C=0.434095 which is 0.09% away from the bound C_W=0.434467 obtained by a completely different procedure. The obtained state maximizing nearest neighbour entanglement seems to approximate the maximally entangled mixed states (MEMS). Further we investigate in detail several other properties of the so obtained optimal state.Comment: 12 pages, 4 figures, 2nd version minor change