Related papers: On the conservation results for local reflection p…
The Local Converse Problem is to determine how the family of the local gamma factors $\gamma(s,\pi\times\tau,\psi)$ characterizes the isomorphism class of an irreducible admissible generic representation $\pi$ of $\mathrm{GL}_n(F)$, with…
We investigate sentences which are simultaneously partially conservative over several theories. First, we generalize Bennet's results on this topic to the case of more than two theories. In particular, for any finite family $\{T_i\}_{i \leq…
The principle of open class determinacy is preserved by pre-tame class forcing, and after such forcing, every new class well-order is isomorphic to a ground-model class well-order. Similarly, the principle of elementary transfinite…
We present a decomposition principle for general regular Dirichlet forms satisfying a spatial local compactness condition. We use the decomposition principle to derive a Persson type theorem for the corresponding Dirichlet forms. In…
We establish a version of the first Noether Theorem, according to which the (equivalence classes of) conserved quantities of given Euler-Lagrange equations in several independent variables are in one-to-one correspondence with the…
[Note: Currently the proof is incomplete as we are using the lemma 3.2 which is not true in general]. We offer a complete resolution of a conjecture by Lions-Perthame-Tadmor mentioned in their celebrated work (1994, [34]). We prove the…
A group $\Gamma$ is said to be uniformly HS stable if any map $\varphi : \Gamma \to U(n)$ that is almost a unitary representation (w.r.t. the Hilbert Schmidt norm) is close to a genuine unitary representation of the same dimension. We…
There is a widely-held belief amongst theoreticians that the Gilbert damping parameter {\alpha} in magnetization dynamics is infinite for a pure metal at T=0. The basic error leading to this belief is pointed out explicitly and the various…
Consider a stochastic process $\mathfrak{X}$, regenerative at a state $x$ which is instantaneous and regular. Let $L$ be a regenerative local time for $\mathfrak{X}$ at $x$. Suppose furthermore that $\mathfrak{X}$ can be approximated by…
We establish a framework with reflection positivity as the first principle for establishing the boundary theory of topologically ordered quantum spin systems. For any reflection positive frustration-free Hamiltonian, We proved that the…
We prove several preservation theorems for NATP and furnish several examples of NATP. First, we prove preservation of NATP for the parametrization and sum of the theories of Fra\"{i}ss\'{e} limits of Fra\"{i}ss\'{e} classes satisfying…
Let $\Gamma$ be a finitely generated group acting by probability measure preserving maps on the standard Borel space $(X,\mu)$. We show that if $H\leq\Gamma$ is a subgroup with relative spectral radius greater than the global spectral…
We study the conditions under which one can conserve local translationally invariant operators by local translationally invariant Lindblad equations in one-dimensional rings of spin-1/2 particles. We prove that for any 1-local operator…
The higher derivative field theories are notorious for the stability problems both at classical and quantum level. Classical instability is connected with unboundedness of the canonical energy, while the unbounded energy spectrum leads to…
We consider transport through a non-Hermitian conductor connected to a pair of Hermitian leads and analyze the underlying non-Hermitian scattering problem. In a typical non-Hermitian system, such as a Hatano--Nelson-type asymmetric hopping…
Rutenberg [cond-mat/9411016] claimed erroneously that I incorrectly apply only global conservation constraint to systems with local conservation embodied by continuity equation [PRL vol.72, p.1850 (1994)]. I reply that my theory describes…
In this article we proved so-called strong reflection principles corresponding to formal theories Th which has omega-models. An posible generalization of the Lob's theorem is considered.Main results is: (1) let $k$ be an inaccessible…
Semimartingale reflecting Brownian motions (SRBMs) living in the closures of domains with piecewise smooth boundaries are of interest in applied probability because of their role as heavy traffic approximations for some stochastic networks.…
The Free Energy Principle (FEP) states that self-organizing systems must minimize variational free energy to persist, but the path from principle to implementable algorithm has remained unclear. We present a constructive proof that the FEP…
Let $Z=\{Z(t): t\in \mathbb R\}$ be a stochastic process with trajectories in space $\mathbb D (\mathbb R)$. It is assumed that there exists an essentially smooth function $A:\mathbb R\to (-\infty, \infty] $ such that, for all $\alpha \in…