In the above letter 1 , the second author’s affiliation was listed incorrectly. The correct affiliation is as follows: Javier Tejedor is with the Institute of Technology, Universidad San Pablo-CEU, ...CEU Universities, Urbanización Montepríncipe, 28668 Boadilla del Monte, Spain (e-mail: javier.tejedornoguerales@ceu.es).
A family of perturbative Lagrangians that describe approximate and multidimensional Klein-Gordon equations are studied. We probe the existence of approximate Noether symmetries via generalized ...geometric conditions for a perturbation of any order. The knowledge of the geometric conditions uncovers that unlike exact symmetries, the approximate Noether symmetries of the Lagrangian which describes the motion of a particle in n-dimensional space under the action of an autonomous force, is inequivalent to the Noether symmetries admitted by the Klein-Gordon Lagrangian in general.
If the very early Universe is dominated by the nonminimally coupled Higgs field and Starobinsky’s curvature-squared term together, the potential diagram would mimic the landscape of a valley, serving ...as a cosmological attractor. The inflationary dynamics along this valley is studied, model parameters are constrained against observational data, and the effect of isocurvature perturbation is estimated.
In the present paper we deal with the existence of multiple solutions for a quasilinear elliptic problem involving an arbitrary perturbation. Our approach, based on an abstract result of Ricceri, ...combines truncation arguments with Moser-type iteration technique.
During the past two decades the gravitational asymptotic safety scenario has undergone a major transition from an exotic possibility to a serious contender for a realistic theory of quantum gravity. ...It aims at a mathematically consistent quantum description of the gravitational interaction and the geometry of spacetime within the realm of quantum field theory, which keeps its predictive power at the highest energies. This volume provides a self-contained pedagogical introduction to asymptotic safety, and introduces the functional renormalization group techniques used in its investigation, along with the requisite computational techniques. The foundational chapters are followed by an accessible summary of the results obtained so far. It is the first detailed exposition of asymptotic safety, providing a unique introduction to quantum gravity and it assumes no previous familiarity with the renormalization group. It serves as an important resource for both practising researchers and graduate students entering this maturing field.
The slow state variables feedback stabilization problem for semi-Markov jump discrete-time systems with slow sampling singular perturbations is discussed in this work. A new fairly comprehensive ...system model, semi-Markov jump system with singular perturbations, which is more general than Markov jump model, is employed to describe the phenomena of random abrupt changes in structure and parameters of the systems. Based on a slow state variables feedback control scheme, a novel technique to design the desired controller is presented and the allowed maximum of singular perturbation parameter can be calculated. With the help of the discrete-time semi-Markov kernel approach, some sojourn-time-dependent and less-conservative sufficient conditions are established via a novel matrix decoupling technique to ensure the solvability of the problem to be addressed. Finally, an illustrative example is given to show the superiority and usefulness of the proposed method.
Recently it was shown that the scaling dimension of the operator ϕn in scale invariant d = 3 theory may be computed semiclassically, and this was verified to leading order (two loops) in perturbation ...theory at leading and subleading n. Here we extend this verification to six loops, once again at leading and subleading n. We then perform a similar exercise for a theory with a multiplet of real scalars and an O(N) invariant hexic interaction. We also investigate the strong-coupling regime for this example.
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