About integrated invariance, arising at resonance of oscillations in some types non-conservative mechanical systems

Locality and modular invariance in 2D conformal QFT

The relations and differences between various classification problems arising in the context of local two-dimensional conformal QFT, modular invariants, and subfactors are discussed. The extent to which locality implies modular invariance, is exhibited.

Temparature as Order Parameter of Broken Scale Invariance

In algebraic quantum field theory the (inverse) temperature is shown to be a macroscopic \textit{order parameter} to parametrize mutually disjoint thermal \textit{sectors} arising from the \textit{broken scale invariance} under renormalization-group transformations. This is accomplished in a mathematical formalism for the consistent treatment of \textit{explicitly broken symmetries} such as broken scale invariance, on the basis of a clear-cut criterion for the symmetry breakdown in a unified scheme for sectors proposed recently by the author.

Fractional Noether's Theorem with Classical and Caputo Derivatives: constants of motion for non-conservative systems

Since the seminal work of Emmy Noether it is well know that all conservations laws in physics, \textrm{e.g.}, conservation of energy or conservation of momentum, are directly related to the invariance of the action under a family of transformations. However, the classical Noether's theorem can not yields informations about constants of motion for non-conservative systems since it is not possible to formulate physically meaningful Lagragians for this kind of systems in classical calculus of variation. On the other hand, in recent years the fractional calculus of variation within Lagrangians dep…

Noether theorem for action-dependent Lagrangian functions: conservation laws for non-conservative systems

In the present work, we formulate a generalization of the Noether Theorem for action-dependent Lagrangian functions. The Noether's theorem is one of the most important theorems for physics. It is well known that all conservation laws, \textrm{e.g.}, conservation of energy and momentum, are directly related to the invariance of the action under a family of transformations. However, the classical Noether theorem cannot be applied to study non-conservative systems because it is not possible to formulate physically meaningful Lagrangian functions for this kind of systems in the classical calculus …

Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials

The existence of a novel enlarged shape invariance property valid for some rational extensions of shape-invariant conventional potentials, first pointed out in the case of the Morse potential, is confirmed by deriving all rational extensions of the Rosen-Morse II and Eckart potentials that can be obtained in first-order supersymmetric quantum mechanics. Such extensions are shown to belong to three different types, the first two strictly isospectral to some starting conventional potential with different parameters and the third with an extra bound state below the spectrum of the latter. In the …

配对显式松弛龙格-库塔方法：熵守恒与熵稳定的高阶优化多速率时间积分

Paired Explicit Relaxation Runge-Kutta Methods: Entropy-Conservative and Entropy-Stable High-Order Optimized Multirate Time Integration

提出基于配对显式松弛龙格-库塔的熵守恒/稳定多速率时间积分方法，达四阶精度，在多种流体与磁流体问题中较独立松弛方法提速达四倍。