The geometry of a collector is one of the important factors that can increase the incident radiation on the collector surface. In the present study, the incident radiation for a stationary collector with cone geometry, i.e. a conical collector, is theoretically and experimentally investigated. This type of collector is always stable and does not need a fixture to install. Moreover, it has a...

We compute the spectra of Laplace-Beltrami operator, connection Laplacian on 1-forms and Einstein operator symmetric 2-tensors sine-cone over a positive manifold $(M, g)$. conclude under which conditions $(M,g)$, is dynamically stable singular Ricci-de Turck flow rigid as

Abstract A new primal-dual interior-point algorithm applicable to nonsymmetric conic optimization is proposed. It a generalization of the famous suggested by Nesterov and Todd for symmetric case, uses scalings cones proposed Tunçel. We specialize Tunçel’s important case 3 dimensional exponential-cones, resulting in practical with good numerical performance, on level standard cone ( e.g. , quadr...

We investigate the phenomenon of “faster than light” photons in a family of dilaton black hole spacetimes. For radially directed photons, we find that their light-cone condition is modified even though the spacetimes are spherically symmetric. They also satisfy the “horizon theorem” and the “polarization sum rule” of Shore. For orbital photons, the dilatonic effect on the modification of the li...

The symmetric cone complementarity problem (denoted by SCCP) is a class of equilibrium optimization problems, and it contains the standard linear/nonlinear complementarity problem (LCP/NCP), the second-order cone complementarity problem (SOCCP) and the semidefinite complementarity problem (SDCP) as special cases. In this paper, we present a regularized smoothing Newton algorithm for SCCP by mak...

In a recent paper, Chua and Yi introduced the so-called uniform nonsingularity property for a nonlinear transformation on a Euclidean Jordan algebra and showed that it implies the global uniqueness property in the context of symmetric cone complementarity problems. In a related paper, Chua, Lin, and Yi raise the question of converse. In this paper, we show that, for linear transformations, the ...

We define an equivalence relation on integer compositions and show that two ribbon Schur functions are identical if and only if their defining compositions are equivalent in this sense. This equivalence is completely determined by means of a factorization for compositions: equivalent compositions have factorizations that differ only by reversing some of the terms. As an application, we can deri...

We define an equivalence relation on integer compositions and show that two ribbon Schur functions are identical if and only if their defining compositions are equivalent in this sense. This equivalence is completely determined by means of a factorization for compositions: equivalent compositions have factorizations that differ only by reversing some of the terms. As an application, we can deri...

We consider quasiparticles of a clean d-wave superconductor in the vortex lattice state. For vortex lattices that are inversion symmetric, the quasiparticle bands are found to have a Dirac cone dispersion at zero energy, within the linearized approximation. Upon going beyond the linearized approximation by including the effect of the smaller curvature terms, the Dirac cone dispersions acquire a...

A symmetric matrix is defined to be completely positive if it allows a factorisation BB , where B is an entrywise nonnegative matrix. This set is useful in certain optimisation problems. The interior of the completely positive cone has previously been characterised by Dür and Still [7]. In this paper we introduce the concept of the set of zeros in the nonnegative orthant for a quadratic form an...