Related papers: Semi-equational theories
It is shown that in the weak field approximation the new geometrical approach can lead to the linear field equations for the several independent fields. For the stronger fields and in the second order approximation the field equations…
We define weaker forms of topological and measure theoretical equicontinuity for topological dynamical systems and we study their relationships with systems with discrete spectrum and zero sequence entropy. In the topological category we…
We review the status of duality symmetries in superstring theories. These discrete symmetries mark the striking differences between theories of pointlike objects and theories of extended objects. They prove to be very helpful in…
In this paper, we give a new approach for the study of Weyl-type theorems. Precisely we introduce the concepts of spectral valued and spectral partitioning functions. Using two natural order relations on the set of spectral valued…
We present a general definition of entropy in the setting of pre-ordered semigroups, extending the notion of topological entropy. From our definition, we obtain the basic properties exhibited by various entropy-like theories encountered in…
We give a geometrical interpretation of the notion of $\mu$-prolongations of vector fields and of the related concept of $\mu$-symmetry for partial differential equations (extending to PDEs the notion of $\lambda$-symmetry for ODEs). We…
Semi-classical gravity attempts to define a hybrid theory in which a classical gravitational field is coupled to a unitarily evolving quantum state. Although semi-classical gravity is inconsistent with observation, a viable theory of this…
This note presents a uniform treatment of normality and three of its variants---topological, weak and seminormality---for Noetherian schemes. The key is to define these notions for pairs $(Z, X)$ consisting of a (not necessarily reduced)…
A simple example is given of the implementation of the usual method of asymptotic expansions for weak gravitational fields. A scalar, preferred-frame theory of gravitation is considered, but the method is general. Two kinds of asymptotic…
We study the theory of equations in one variable over polyhedral semirings. The article revolves around a notion of solution to a polynomial equation over a polyhedral semiring. Our main results are a characterisation of local solutions in…
A linear system of difference equations and a nonlinear perturbation are considered, we obtain sufficient conditions to ensure the topological equivalence between them, namely, the linear part satisfies a property of dichotomy on the…
A class of two-dimensional globally scale-invariant, but not conformally invariant, theories is obtained. These systems are identified in the process of discussing global and local scaling properties of models related by duality…
In this short review main issues related to the non-Abelian Stokes theorem have been addressed. The two principal approaches to the non-Abelian Stokes theorem, operator and two variants (coherent-state and holomorphic) of the path-integral…
We study the evolution of the non-equilibrium quantum fields from a highly excited initial state in two approaches: the standard Keldysh-Schwinger diagram technique and the semiclassical expansion. We demonstrate explicitly that these two…
Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…
We prove well-posedness and rough path stability of a class of linear and semi-linear rough PDE's on $\mathbb{R}^d$ using the variational approach. This includes well-posedness of (possibly degenerate) linear rough PDE's in…
We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolution equations with compact nonlinearities. We show, in particular, that compact nonlinear perturbations of a linear evolution equation can be…
The problem of renormalization of the semiclassical one-loop equations used in the non-equilibrium field theory is considered. Recently, the renormalizability of such equations has been justified for some special cases of classical field…
We relate the local specification and periodic shadowing properties. We also clarify the relation between local weak specification and local specification if the system is measure expansive. The notion of strong measure expansiveness is…
We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the Quantum Energy Inequalities satisfied by…