Related papers: Understanding Preservation Theorems, Chapter VI of…
Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficult to identify,…
Certain transformations of isolated physical systems underlying various conservation laws in physics are noted. As regards each of these transformations, there is a theoretical action that is equivalent to a matched physical action on the…
The present work introduces a simple, yet effective particle coalescing procedure for two-dimensional SPH simulations with spatially varying resolution. In addition to the regular conservation properties of former algorithms concerning the…
We prove a compactness theorem for pseudopower operations of the form $pp_{\Gamma(\mu,\sigma)}(\mu)$ where $\aleph_0<\sigma=cf(\sigma)\leq cf(\mu)$. Our main tool is a result that has Shelah's cov vs. pp Theorem as a consequence. We also…
Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…
Using the theory of almost conserved energies and the ``I-method'' developed by Colliander, Keel, Staffilani, Takaoka and Tao, we prove that the initial value problem for a higher order Schr\"odinger equation is globally well-posed in…
This paper introduces and reviews light forces, atom cooling and atom trapping. The emphasis is on the physics of the basic processes. In discussing conservative forces the semi-classical dressed states are used rather than the usual…
In Chapter 1 we start with general Landau scheme of the conservation laws for the hydrodynamics of classical liquids and superfluids. On the basis of Landau scheme we consider hydrodynamics of rotating superfluids with large number of…
In the present paper we are interested in simple forcing notions and Forcing Axioms. A starting point for our investigations was the article [JR1] in which several problems were posed. We answer some of those problems here.
We study a class of variational problems for regularized conservation laws with Lax's entropy-entropy flux pairs. We first introduce a modified optimal transport space based on conservation laws with diffusion. Using this space, we…
The objective of this paper is, in the main, twofold: Firstly, to develop an algebraic setting for dealing with Bell polynomials and related extensions. Secondly, based on the author's previous work on multivariate Stirling polynomials…
When considering how self-interaction affects an object's motion, it can be convenient to decompose the self-force into conservative and dissipative pieces. As a toy model for understanding such decompositions of the gravitational…
A strong antidiamond principle (*c) is shown to be consistent with CH. This principle can be stated as a "P-ideal dichotomy": every P-ideal on omega-1 (i.e. an ideal that is sigma-directed under inclusion modulo finite) either has a closed…
This paper extends the foundational concept to second-order quantum correlation tensors, representing intensity-intensity correlations.As their application in diverse optical field experiments gaining importance, we investigate conserved…
The Szekeres system is studied with two methods for the determination of conservation laws. Specifically we apply the theory of group invariant transformations and the method of singularity analysis. We show that the Szekeres system admits…
This paper gives a general treatment and proof of the direct conservation law method presented in Part I. In particular, the treatment here applies to finding the local conservation laws of any system of one or more partial differential…
We show that in the new description, Dirac's ``current vector'' is not related to a vector but to a tensor: the ``stress-energy tensor.'' Corresponding to Dirac's conservation law, we have the conservation laws of momentum and energy. The…
Predicting when a chaotic trajectory will switch between the lobes of the Lorenz attractor is a long-standing challenge in nonlinear dynamics. This work shows that algebraic conservation laws, constructed by augmenting phase space with…
Generalizing the proof for Sacks forcing, we show that the $h$-perfect tree forcing notions introduced by Goldstern, Judah and Shelah preserve selective independent families even when iterated. As a result we obtain new proofs of the…
We investigate properties of trees of height $\omega_1$ and their preservation under subcomplete forcing. We show that subcomplete forcing cannot add a new branch to an $\omega_1$-tree. We introduce fragments of subcompleteness which are…