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Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
We investigate the cosmological implications of a new class of modified gravity, where the field equations generically include higher-order derivatives of the matter fields, arising from the introduction of non-dynamical auxiliary fields in…
In recent years there has been a lot of interest in discussing frame dependences/independences of the cosmological perturbations under the conformal transformations. This problem has previously been investigated in terms of the covariant…
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it…
Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral…
Longstanding problems regarding the causality of the diffusion equation are resolved through a class of exact solutions. A universal differential solution for diffusive processes is derived that is causal and exact at any analytic point in…
We develop a general formalism for analyzing linear perturbations in multiple-field cosmological inflation based on the gauge-ready approach. Our inflationary model consists of an arbitrary number of scalar fields with non-minimal kinetic…
This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…
We examine the importance of second order corrections to linearized cosmological perturbation theory in an inflationary background, taken to be a spatially flat FRW spacetime. The full second order problem is solved in the sense that we…
The objective of this contribution is to compare two methods proposed recently in order to build efficient reduced-order models for geometrically nonlinear structures. The first method relies on the normal form theory that allows one to…
We recommended consequent discrete combinatorial research in mathematical physics. Here we show an example how discretization of partial differential equations can be done and that quickly unexpected new findings can result from research in…
This work addresses the quantization of a self-interacting higher order time derivative theory using path integrals. To quantize this system and avoid the problems of energy not bounded from below and states of negative norm, we observe the…
The linear cosmological perturbation theory of almost homogeneous and isotropic perfect fluid and scalar field universes is reconsidered and formally simplified. Using the existence of a covariant conserved quantity on large perturbation…
Cosmological perturbation theory is a key tool to study the universe. The linear or first order theory is well understood, however, developing and applying the theory beyond linear order is at the cutting edge of current research in…
Both in string field theory and in p-adic string theory the equations of motion involve infinite number of time derivatives. We argue that the initial value problem is qualitatively different from that obtained in the limit of many time…
Variable-exponent fractional models attract increasing attentions in various applications, while the rigorous analysis is far from well developed. This work provides general tools to address these models. Specifically, we first develop a…
We investigate cosmological density perturbations in a covariant and gauge-invariant formalism, incorporating relativistic causal thermodynamics to give a self-consistent description. The gradient of density inhomogeneities splits…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
Our understanding of quantum field theory rests largely on explicit and controlled calculations in perturbation theory. Because of this, much recent effort has been devoted to improve our grasp of perturbative techniques on cosmological…