We briefly review analytic approximations of thermodynamic functions of fully ionized nonideal electronion plasmas, applicable in a wide range of plasma parameters, including the domains of nondegenerate and degenerate, nonrelativistic and relativistic electrons, weakly and strongly coupled Coulomb liquids, classical and quantum Coulomb crystals. We present improvements to previously published ...

Hyperplane codes are a class of convex codes that arise as the output of a one layer feed-forward neural network. Here we establish several natural properties of nondegenerate hyperplane codes, in terms of the polar complex of the code, a simplicial complex associated to any combinatorial code. We prove that the polar complex of a non-degenerate hyperplane code is shellable and show that all cu...

In this paper, we consider operator realizations of quadratic algebras generated by second-order superintegrable systems in 2D. At least one such realization is given for each set of Stäckel equivalent systems for both degenerate and nondegenerate systems. In almost all cases, the models can be used to determine the quantization of energy and eigenvalues for integrals associated with separation...

The symmetry of an optical waveguide determines its modal degeneracies. A fiber with rotational symmetry of order higher than 2 has modes that either are nondegenerate and support the complete fiber symmetry or are twofold degenerate pairs of lower symmetry. The latter case applies to the fundamental modes of perfect microstructured optical fibers, guaranteeing that such fibers are not birefrin...

We use a white-light continuum (WLC) Z-scan technique to measure the degenerate two-photon absorption spectrum and associated dispersion of the nonlinear refraction in ZnSe. The spectral components of the WLC source are separated by using a narrow band variable filter to minimize nondegenerate nonlinearities. We observe a change in sign of the ultrafast nonlinear refractive index around 0.7 of ...

Although it is NP complete to decide whether a linear program ming problemis degenerate the perturbation method can be used to reduce in polynomial time any linear programming problemwith rational coe cients to a nondegenerate problem The perturbed problem has the same status as the given one in terms of feasibility and unboundedness and optimal bases of the perturbed problem are optimal in the...

We will deal with a new geometrical interpretation of the classical Legendre and Jacobi conditions: they are represented by the rate and the magnitude of rotation of certain linear subspaces of the tangent space around the tangents to the extremals. (The linear subspaces can be replaced by conical subsets of the tangent space.) This interpretation can be carried over to nondegenerate Lagrange p...

We give a new geometric construction of the big projective module in the principal block of the BGG category O, or rather the corresponding D-module on the flag variety. Namely, given a one-parameter family of nondegenerate additive characters of the unipotent radical of a Borel subgroup which degenerate to the trivial character, there is a corresponding one-parameter family of Whittaker sheave...

We consider the interior-point approach to sensitivity analysis in linear programming developed by the authors. We investigate the quality of the interior-point bounds under degeneracy. In the case of a special degeneracy, we show that these bounds have the same nice asymptotic relationship with the optimal partition bounds as in the nondegenerate case. We prove a weaker relationship for genera...

A single-photon-sensitive intensified charge-coupled-device (ICCD) camera has been used to simultaneously detect, over a broad area, degenerate and nondegenerate photon pairs generated by the quantum-optical process of spontaneous parametric down-conversion. We have developed a new method for determining the quantum fourth- order correlations in spatially extended detection systems such as this...