Related papers: First-order framework and generalized global defec…

In this work we study the problem of first order perturbations of a general hypersurface, i.e. with arbitrary causal character at each point. We extend the framework by Mars (Class. Quantum Grav. 22 3325 (2005)) where this problem was…

This work offers an extension of the deformation procedure introduced in field theory to the case of standard cosmology in the presence of real scalar field in flat space-time. The procedure is shown to work for many models, which give rise…

We develop an augmented characteristic, first-order formulation of the field equations in f(R) gravity governing the global evolution of a (possibly) massive scalar field phi under spherical symmetry. This formulation is designed to isolate…

Here we present a new approach to deal with first order ordinary differential equations (1ODEs), presenting functions. This method is an alternative to the one we have presented in [1]. In [2], we have establish the theoretical background…

A covariant, global, variational framework for perturbations in field theories is presented. Perturbations are obtained as vertical vector fields on the configuration bundle and they drag, exactly, solution into solutions. The flow of a…

Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…

This work deals with an Abelian gauge field in the presence of an electric charge immersed in a medium controlled by neutral scalar fields, which interact with the gauge field through a generalized dielectric function. We develop an…

This work contains a set of lectures on defect structures, mainly in models described by scalar fields in diverse dimensions.

The higher order symmetries are investigated in a covariant Hamiltonian formulation. The covariant phase-space approach is extended to include the presence of external gauge fields and scalar potentials. The special role of the Killing-Yano…

We consider the renormalization group flow equation for the two-dimensional sigma models with the K\"ahler target space. The first-order formulation allows us to treat perturbations in these models as current-current deformations. We…

A framework is developed for applying accelerated methods to general hyperbolic programming, including linear, second-order cone, and semidefinite programming as special cases. The approach replaces a hyperbolic program with a convex…

We demonstrate that the complete factorization of equations of motion into first-order differential equations can be obtained for real and complex scalar field theories with non-canonical dynamics.

This work discuss the construction of braneworld solutions in modified gravity with Lagrange multipliers. We examine the general aspects of the model and present a first order formalism that help us to find analytic solutions of the…

We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent conditions. We show that global fields belong to this class, and…

Let $k$ be a differential field of characteristic zero with an algebraically closed field of constants. In this article, we provide a classification of first order differential equations over $k$ and study the algebraic dependence of…

We describe a framework for reformulating and solving optimization problems that generalizes the well-known framework originally introduced by Benders. We discuss details of the application of the procedures to several classes of…

A general discussion of equations with universal invariance for a scalar field is provided in the framework of Lagrangian theory of first-order systems.

Second-order self-force computations, which will be essential in modeling extreme-mass-ratio inspirals, involve two major new difficulties that were not present at first order. One is the problem of large scales, discussed in [Phys. Rev. D…

We develop a first order formalism for constructing gravitational duals of conformal defects in a bottom up approach. Similarly as for the flat domain walls a single function specifies the solution completely. Using this formalism we…

This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…