Related papers: First-order framework and generalized global defec…
We propose a new methodology to design first-order methods for unconstrained strongly convex problems. Specifically, instead of tackling the original objective directly, we construct a shifted objective function that has the same minimizer…
In recent decades, the defect of finite extensions of valued fields has emerged as the main obstacle in several fundamental problems in algebraic geometry such as the local uniformization problem. Hence, it is important to identify…
In a coordinate free form are found the (deviation) equations satisfied by the (infinitesimal) deviation vector, relative velocity, relative momentum, relative acceleration and relative energy of two point particles in a differentiable…
Canonical analysis leading to formal quantisation of the higher derivative theories are considered. The first order formalism is adopted where all the configuration space variables along with their higher time derivatives are considered to…
In this paper we consider perturbation theory in generic two-dimensional sigma models in the so-called first-order formalism, using the coordinate regularization approach. Our goal is to analyze the first-order formalism in application to…
Scalar field theory with asymmetric potential is studied for $\phi^4$ theory with $\phi^3$ symmetry breaking. The equations of motion are solved analytically up to the second order to get the bounce-solution.
Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave…
In this work, we present a deformed solutions starting from systems of three coupled scalar fields with super-potential $W(\phi_1, \phi_2, \phi_3)$ by orbit method. First, we deform the corresponding super-potential and obtain defect…
We rewrite simplicially the standard definitions of a complete first order theory, a model of it, and various characterisations of stability of a complete first order theory. In our reformulations the simplicial language replaces the…
We discuss gravitational effects of global scalar fields and, especially, of global topological defects. We first give an introduction to the dynamics of global fields and the formation of defects. Next we investigate the induced…
In general, the system of $2$nd-order partial differential equations made of the Euler-Lagrange equations of classical field theories are not compatible for singular Lagrangians. This is the so-called second-order problem. The first aim of…
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…
The issues of quintessence and cosmic acceleration can be discussed in the framework of theories which do not include necessarily scalar fields. It is possible to define pressure and energy density for new components considering effective…
We study various aspects of codimension one defects in free scalar field theory, with particular emphasis on line defects in two-dimensions. These defects are generically non-conformal, but include conformal and topological defects as…
We use the linear scalar SDE as a test problem to show that it is possible to construct almost sure stable first-order weak balanced schemes based on the addition of stabilizing functions to the drift terms. Then, we design balanced schemes…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
Gauge-invariant treatments of general-relativistic higher-order perturbations on generic background spacetime is proposed. After reviewing the general framework of the second-order gauge-invariant perturbation theory, we show the fact that…
Symmetry in finite model finding problems of many-sorted first-order logic (MSFOL) can be exploited to reduce the number of interpretations considered during search, thereby improving solver performance. In this thesis, we situate symmetry…
We derive a second-order realizability-preserving scheme for moment models for linear kinetic equations. We apply this scheme to the first-order continuous and discontinuous models in slab and three-dimensional geometry derived in a…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…