We develop a systematic theory of symmetry fractionalization for fermionic topological phases matter in (2+1)D with general group $G_f$. In $G_f$ is central extension the bosonic $G_b$ by fermion parity, $(-1)^F$, characterized non-trivial cohomology class $[\omega_2] \in \mathcal{H}^2(G_b, \mathbb{Z}_2)$. show how presence local fermions places number constraints on algebraic data that defines...

Collective neutrino oscillations can potentially play an important role in transporting lepton flavor astrophysical scenarios where the density is large, typical examples are early universe and supernova explosions. It has been argued past that simple models of Hamiltonian designed to describe forward scattering support substantial evolution on very short time scales $t\approx\log(N)/(G_F\rho_\...

⎯ The aim of the present work is to characterize weakly efficient solution of multiobjective programming problems under the assumptions of α-invexity, using the concepts of critical point and Kuhn-Tucker stationary point for multiobjective programming problems. In this paper, we also extend the above results to the nondifferentiable multiobjective programming problems. The use of α-invex functi...

Fritz John and Kuhn-Tucker type necessary optimality conditions for a Pareto optimal (efficient) solution of a multiobjective control problem are obtained by first reducing the multiobjective control problem to a system of single objective control problems, and then using already established optimality conditions. As an application of Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir ...

Motivated by important applications, the theory of mathematical programming has been extended to the case of infinitely many restrictions. At the same time, this theory knew remarcable developments since invexity and its further generalizations have been introduced as substitute of convexity. Here, we consider the multiobjective programming with a set of restrictions indexed in a compact. We ob...

The concept of a geodesic invex subset of a Riemannian manifold is introduced. Geodesic invex and preinvex functions on a geodesic invex set with respect to particular maps are defined. The relation between geodesic invexity and preinvexity of functions on manifolds is studied. Using proximal subdifferential, certain results concerning extremum points of a non smooth geodesic preinvex function ...

In the present paper, we are concerned with a minimax fractional programming problem containing arbitrary norms and establish duality theorems for a dual model related to minimax fractional programming problem under the assumptions of second order (Φ, ρ)-invexity.