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.
We construct conjugate-linear perturbations of twisted \(\rm{spin}^{\rm c}\) Dirac operators on compact almost Hermitian manifolds of dimension congruent to \(2\) or \(6\) modulo \(8\), employing the conjugate-linear Hodge star operator rescaled by unit complex numbers depending on degree. These perturbations satisfy the concentration principle.
We prove that the polynomial entropy of the induced map F_n(f) on the n-fold symmetric product of a compact space X and its suspension are both equal to nh_pol(f), when f:X→ X is a homeomorphism with a finite non-wandering set NW(f). We also give a lower bound for the polynomial entropy on the suspension, for a homeomorphism f with at least one wandering point, under certain assumptions.
We investigate the behavior of itinerary sequence of each point of the Julia set of $z\mapsto z^2 + c$ when the parameter $c$ in the shift locus is allowed to pass through points in the bifurcation locus $\mathcal{P}_2$, which we call ``narrow", first proposed by Dierk Schleicher in \cite{schleicher2017internal}. We first show the combinatoric and geometric properties of narrow characteristic arcs. Also, we show how the itinerary sequence changes in an algorithmic way by using lamination models proposed by Keller in \cite{keller2007invariant}. Finally, we found an equivalence relation on the set of $0$-$1$ sequences so that the changing rule is a shift invariant up to the equivalence relation. This generalizes Atela's works in \cite{atela1992bifurcations}, \cite{atela1993mandelbrot}, which dealt with the special case of the generalized rabbit polynomials.
In this paper, we consider linear codes with complementary duals over the ring of integers modulo 4. These codes are defined as linear codes that intersect their duals trivially and shortly called LCD codes. We focus on some constructions of LCD codes using the adjacency matrices of two-class association schemes.
In this paper, we determine the composition series of the 1 induced representation S([v 1/2 rho, v (c)rho]) x S([v(-a)rho, v(b)rho]) & rtimes; sigma where a, b, c is an element of Z + 1/2 such that 1/2 <= a < b < c, rho is an irreducible cuspidal unitary representation of a general linear group and sigma is an irreducible cuspidal representation of a classical group such that v 1/ 2 rho & rtimes; sigma reduces.
In a recent preprint entitled "Holomorphy of Eisenstein series - a new method and applications in the case of the general linear group", the author has developed a new method for proving holomorphy of degenerate Eisenstein series, based on the Franke filtration of spaces of automorphic forms. In this paper, the method is applied in the case of degenerate Eisenstein series on the symplectic group of rank two. Although the analytic properties of Eisenstein series in that case are already known, the goal is to exhibit the method in a simple setting, in which all additional technical details are peeled off.
Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh obtained an unconditional form of Montgomery's theorem concerning pair correlation of zeros of the Riemann zeta function. They used it to prove that under certain assumptions at least 61.7% of the zeros are simple. In this paper, we obtain an analogous theorem for Dirichlet L-functions and apply it to prove a similar result regarding simple zeros of Dirichlet L-functions.
It is well known that the fixed point set of a Riemann surface of genus g under the action of a symmetry is either empty or consists of a disjoint set of at most g + 1 ovals. Bounds on the total number of fixed ovals given by a set of k non-conjugate symmetries are known. In this paper, for k >= 4, we calculate all the possible topological types of symmetries in such a maximal configuration, provided that the symmetries commute. We also find real equations for the Riemann surfaces that achieve these bounds where the symmetries are expressed as complex conjugation.
Recently, we constructed transitive homeomorphisms on the Cantor fan and the Lelek fan. In this paper, we construct a family of uncountably many pairwise non-homeomorphic smooth fans that admit transitive homeomorphisms. In order to do this, we use our recently developed techniques of combining Mahavier products of closed relations on intervals with quotients of dynamical systems. In addition, we show that the star of Cantor fans admits a transitive homeomorphism. At the end of the paper, we also construct a family of uncountably many pairwise nonhomeomorphic non-smooth fans that admit transitive homeomorphisms.
In this paper, we consider linear codes with complementary duals over the ring of integers modulo 4. These codes are defined as linear codes that intersect their duals trivially and shortly called LCD codes. We focus on some constructions of LCD codes using the adjacency matrices of two-class association schemes.
In this article, we propose a permutation test for independence in the tails of two strongly mixing and strictly stationary sequences. We establish the asymptotic validity of the test by demonstrating that both the test statistic and its permutation distribution are asymptotically normal. These results build upon and generalize findings from Basrak and Brborovic [1]. Additionally, we conduct a simulation study to evaluate the size and power properties of the proposed test.
In this paper, we show that there is no irreducible polynomial f (x) of degree 2p (p >= 5 is a prime number) over Q whose three distinct roots sum up to zero. This extends some earlier results on linear relations between three algebraic numbers. In particular, let d be the smallest positive integer not a multiple of 3, for which there exists an irreducible polynomial f (x) of degree d whose three distinct roots add up to zero. In 2015, Dubickas and Jankauskas found that 10 <= d <= 20. As a corollary, we show that it is either d = 16 or d = 20.
The main aim of this paper is to give characterizations of Datko type for the uniform dichotomy in mean with growth rates concept for reversible stochastic skew-evolution semiflows in Banach spaces. As particular cases, we obtain integral characterizations for uniform exponential dichotomy in mean. The obtained results are generalizations of well-known theorems about uniform h-dichotomy of variational systems in deterministic case.
. In this paper we analyze generalized helices lying on the non-degenerated quadric surfaces in 3-dimensional Lorentz-Minkowski space, i.e. on a pseudosphere and in a hyperbolic plane. We provide their characterizations in terms of curvature and torsion and analyze their projections onto planes orthogonal to their axes. We show that these projections appear as Euclidean or Lorentzian cycloidal curves, so we also introduce natural equations and parametrizations of Lorentzian cycloidal curves.
The class \(\mathcal{S}^{\sharp \flat }(\sigma_0, \sigma_1)\) is a very broad class of \(L\) functions that contains the Selberg class, the class of all automorphic \(L\) functions and the Rankin–Selberg \(L\) functions, as well as products of suitable shifts of those functions. In this paper, we consider generalized Euler-Stieltjes constants \(\gamma_n(F)\) attached to functions \(F(s)\) from the class \(\mathcal{S}^{\sharp \flat }(\sigma_0, \sigma_1)\). These are coefficients in Laurent series expansion of function \(F(s)\) at its pole. We derive an integral representation and an upper bound for these constants. The application of the obtained results in the case of product of suitable shifts of the Riemann zeta function is presented.
