In this paper we introduce the notion of an approximately lower pre-oscillatory (app LPO, for brevity) sequence of functions. When the domain is a compact interval and the sequence consists of absolutely continuous functions, a similar notion is introduced in the paper [26]. The generalization considered herein is twofold. On the one hand, we consider the case of a domain which is a measurable set of possibly infinite measure, and, on the other, we consider the case of a sequence of measurable functions. We adapt the definition accordingly, and we present some properties of the aforementioned notion of an app LPO sequence of functions. In particular, we study the cases when such an app LPO property is preserved under the outer or the inner composition with a suitable class of functions.
The objective of this paper is to prove a broader, generalized version of the Hitchin–Kobayashi correspondence for the twisted quiver bundle \(\mathcal{R}\) over the non-compact special affine Gauduchon manifold \((M, D, g, \nu)\). On the one hand, we prove that the analytic \((\sigma,\tau)\)-stability on \(\mathcal{R}\) implies the existence of an affine \((\sigma,\tau)\)-Hermite–Einstein metric. On the other hand, we prove that the analytic \((\sigma,\tau)\)-semi-stability on \(\mathcal{R}\) implies the existence of approximate affine \((\sigma,\tau)\)-Hermite–Einstein structure. The proof of the theorems relies on the heat flow method, alongside the continuity approach by Uhlenbeck and Yau. To overcome the analytical obstacles brought by the structure of the quiver, we use the maximum and minimum values of some eigenvalues to define a new quantity \(\chi\). Based on the method of proof by contradiction, the quantity \(\chi\) can be used in the discussion of constructing weak quiver subbundles that contradict stability or semi-stability.
This paper concerns the initial-boundary value problem for a compressible two-fluid model with density-dependent viscosities (possibly degenerating in vacuum), subject to Dirichlet boundary conditions. We prove that the two-fluid system with non-monotone pressure will blow up in finite time under the assumption that the initial densities include an isolated mass group.
In this paper, we present a construction of LDPC codes obtained from Deza digraphs with parameters \((n,k,0,1)\). The obtained LDPC codes have no cycles of length four in the Tanner graphs corresponding to the adjacency matrices of the Deza digraphs as parity-check matrices. We describe how LDPC codes can be obtained by applying the Cartesian product of certain Deza digraphs, and the Kronecker product of an adjacency matrix of a Deza digraph with parameters \((n,k,0,1)\) or \((n,k,1,1)\) and a permutation matrix. We also use several other combinatorial objects in the construction of LDPC codes.
We determine the Aubert duals of strongly positive representations of the metaplectic group Sp(n) over a non-Archimedean local field F of characteristic different from two. Using the classification of Matić and an explicit analysis of Jacquet modules, we describe these duals in terms of precise inducing data. Our results extend known descriptions for classical groups to the metaplectic groups case and clarify the role of Aubert duality for non-linear covering groups, providing a foundation for future applications to the study of unitary representations for those cases. Furthermore, We are able to show that the same method applies to odd general spin groups GSpin(2n+1), yielding an explicit description of Aubert duals in that setting as well.
