In this paper, we consider some sufficient conditions for the breakdown of local smooth solutions to the Cauchy problem of the 3D Navier–Stokes/Poisson–Nernst–Planck system modeling electro-diffusion in terms of the horizontal velocity (or vorticity, or the positive part of the second eigenvalue of the strain matrix, or pressure) in scale-critical mixed Lebesgue sum spaces.

In this paper, we provide partial solutions to a problem raised by Väisälä on local properties of free quasiconformal mappings. In particular, we show that a locally free quasiconformal mapping is a globally free quasiconformal mapping under the condition of locally relative quasisymmetry.

In this paper, we study the standard problem of the wind in the steady atmospheric Ekman layer with classical boundary conditions. We consider the system with varying eddy viscosity coefficients that are small perturbation of a constant. We derive the explicit solution by using a different argument in the previous works. For two layers, the eddy viscosity is constant in the upper layer, while is only

We investigate the boundary-value problem that models wind-induced equatorial flows, establishing the existence and uniqueness of solutions. We also discuss some special cases that were studied in recent geophysical research.

We give an elementary proof of a Landesman-Lazer type result for systems by means of a shooting argument and explore its connection with the fundamental theorem of algebra.

We prove a two-parameter family of second order geometric Rellich type equalities on the half-space \( \mathbb {R} _{+}^{n}\). We then use it to derive several refined geometric Rellich type inequalities. We also prove an improved version of the Rellich–Sobolev–Maz’ya type inequality.

A correction to this paper has been published: https://doi.org/10.1007/s00605-020-01422-7

In this paper, we study a new model for a jet component of the Antarctic Circumpolar Current. In the case of vorticity with perturbation, we present the existence results for positive solutions to periodic boundary value problems for general nonlinear, weak nonlinearity and semilinear terms. A computational method is established and an approximate scheme of solution is also given.

In Rao et al. (Comptes Rendus Acad Sci Paris Ser I(342):191–196, 2006), Rao–Ruan–Xi solved an open question posed by David and Semmes and gave a complete Lipschitz classification of self-similar sets on \(\mathbb R\) with touching structure. In this short note, by applying a matrix rearrangeable condition introduced in Luo (J Lond Math Soc 99(2):428–446, 2019), we generalize their result onto the self-similar

A correction to this paper has been published: https://doi.org/10.1007/s00605-021-01543-7

Let F be a non-singular homogeneous polynomial of degree d in n variables. We give an asymptotic formula of the pairs of integer points \((\mathbf {x}, \mathbf {y})\) with \(|\mathbf {x}| \leqslant X\) and \(|\mathbf {y}| \leqslant Y\) which generate a line lying in the hypersurface defined by F, provided that \(n > 2^{d-1}d^4(d+1)(d+2)\). In particular, by restricting to Zariski-open subsets we are

We extend the notion of jittered sampling to arbitrary partitions and study the discrepancy of the related point sets. Let \({\varvec{\Omega }}=(\Omega _1,\ldots ,\Omega _N)\) be a partition of \([0,1]^d\) and let the ith point in \({{\mathcal {P}}}\) be chosen uniformly in the ith set of the partition (and stochastically independent of the other points), \(i=1,\ldots ,N\). For the study of such sets

To describe the geometry of normed space, many geometric constants have been investigated. Among them, the von Neumann–Jordan constant has been treated by a lot of mathematicians. Here we also consider Birkhoff orthogonality and isosceles orthogonality. The usual orthogonality in inner product spaces and isosceles orthogonality in normed spaces are symmetric. However, Birkhoff orthogonality is not

We consider the Fourier expansion of a Hecke (resp. Hecke–Maaß) cusp form of general level N at the various cusps of \(\Gamma _{0}(N)\backslash \mathbb {H}\). We explain how to compute these coefficients via the local theory of p-adic Whittaker functions and establish a classical Voronoï summation formula allowing an arbitrary additive twist. Our discussion has applications to bounding sums of Fourier

In this note we correct errors in [1] as pointed out to us by V. V. Lebedev.

We consider two discrete completely integrable evolutions: the Toda Lattice and the Ablowitz–Ladik system. The principal thrust of the paper is the development of microscopic conservation laws that witness the conservation of the perturbation determinant under these dynamics. In this way, we obtain discrete analogues of objects that we found essential in our recent analyses of KdV, NLS, and mKdV. In

We present Hausdorff versions for Lie Integration Theorems 1 and 2 and apply them to study Hausdorff symplectic groupoids arising from Poisson manifolds. To prepare for these results we include a discussion on Lie equivalences and propose an algebraic approach to holonomy. We also include subsidiary results, such as a generalization of the integration of subalgebroids to the non-wide case, and explore

Tropical climate model derived by Frierson et al. (Commun Math Sci 2:591–626, 2004) and its modified versions have been investigated in a number of papers [see, e.g., Li and Titi (Discrete Contin Dyn Syst Series A 36(8):4495–4516, 2016), Wan (J Math Phys 57(2):021507, 2016), Ye (J Math Anal Appl 446:307–321, 2017) and more recently Dong et al. (Discrete Contin Dyn Syst Ser B 24(1):211–229, 2019)].

Niederreiter and Halton sequences are two prominent classes of higher-dimensional sequences which are widely used in practice for numerical integration methods because of their excellent distribution qualities. In this paper we show that these sequences—even though they are uniformly distributed—fail to satisfy the stronger property of Poissonian pair correlations. This extends already established

Let \(S=\{p_{1},\ldots ,p_{t}\}\) be a fixed finite set of prime numbers listed in increasing order. In this paper, we prove that the Diophantine equation \((F_n^{(k)})^s=p_{1}^{a_{1}}+\cdots +p_{t}^{a_{t}}\), in integer unknowns \(n\ge 1\), \(s\ge 1,~k\ge 2\) and \(a_i\ge 0\) for \(i=1,\ldots ,t\) such that \(\max \left\{ a_{i}: 1\le i\le t\right\} =a_t\) has only finitely many effectively computable

We study logarithmic integrals of the form \(\int _0^1 x^i\ln ^n(x)\ln ^m(1-x)dx\). They are expressed as a rational linear combination of certain rational numbers \((n,m)_{i}\), which we call tiered binomial coefficients, and products of the zeta values \(\zeta (2)\), \(\zeta (3)\),.... Various properties of the tiered binomial coefficients are established. They involve, amongst others, the binomial

Let \(\pi \) be a set of prime numbers and G be a \(\pi \)-separable group. If \(\varphi (1)_{\pi '}^{2}\) divides \(|G: \ker \varphi |_{\pi '}\) for every \(\pi \)-partial character \(\varphi \in \mathrm{I}_{\pi }(G)\), then G has a normal Hall \(\pi '\)-subgroup, where \(\varphi (1)_{\pi '}\) denotes the \(\pi '\)-part of \(\varphi (1)\) and \(\mathrm{I}_{\pi }(G)\) is the set of irreducible \(\pi

In this paper we prove that all pure Artin braid groups \(P_n\) (\(n\ge 3\)) have the \(R_\infty \) property. In order to obtain this result, we analyse the naturally induced morphism \({\text {Aut}}\left( {P_n}\right) \longrightarrow {\text {Aut}}\left( {\Gamma _2 (P_n)/\Gamma _3(P_n)}\right) \) which turns out to factor through a representation \(\rho :S_{{n+1}} \longrightarrow {\text {Aut}}\left(

We study the dispersion of digital (0, m, 2)-nets; i.e. the size of the largest axes-parallel box within such point sets. Digital nets are an important class of low-discrepancy point sets. We prove tight lower and upper bounds for certain subclasses of digital nets where the generating matrices are of triangular form and compute the dispersion of special nets such as the Hammersley point set exactly

We introduce a new strategy to prove simplicity of the spectrum of Lyapunov exponents that can be applied to a wide class of Markovian multidimensional continued fraction algorithms. As an application we use it for Selmer algorithm in dimension 2 and for the Triangle sequence algorithm and show that these algorithms are not optimal.

In this paper, we consider an asymptotic model for wave propagation in shallow water with the effect of the Coriolis force is derived from the governing equation in two dimensional flows. Motivated by the eariler works (Brandolese in Int Math Res Not 22:5161–5181, 2012; Escauriaza et al. in J Funct Anal 244:504–535, 2007; Himonas et al. in Commun Math Phys 271:511–522, 2007; Himonas and Misiolek in

We prove that if X is a regular space with no uncountable free sequences, then the tightness of its \(G_\delta \) topology is at most the continuum and if X is, in addition, assumed to be Lindelöf then its \(G_\delta \) topology contains no free sequences of length larger then the continuum. We also show that, surprisingly, the higher cardinal generalization of our theorem does not hold, by constructing

A locally compact group G is said to be approximable by totally disconnected subgroups if there is a sequence of closed totally disconnected subgroups \((\Gamma _n)_{n\in {\mathbb N}}\) of G such that for any non-empty open set O of G, there exists an integer k such that \(O\cap \Gamma _n \ne \varnothing \), for every \(n\ge k\). In this paper, we prove that every pro-torus is approximable by profinite

Some global solvability criteria for the scalar Riccati equations are used to establish new reducibility criteria for systems of two linear first-order ordinary differential equations. Some examples are presented.

In this work, the mechanism for the formation of the delta shock wave is analyzed to deal with interaction of delta shock waves and contact discontinuities for a system of Keyfitz–Kranzer type by means of analysis and solutions of Riemann problems. A set of numerical experiments are provided, illustrating the theoretical findings numerically. A brief survey of the Keyfitz–Kranzer systems as a base

We prove that the \(\mathbb {F}_p[[t]]\)-standard Hausdorff spectrum of a compact \(\mathbb {F}_p[[t]]\)-analytic group contains a real interval and that it coincides with the full unit interval when the group is soluble. Moreover, we show that the \(\mathbb {F}_p[[t]]\)-standard Hausdorff spectrum of classical Chevalley groups over \(\mathbb {F}_p[[t]]\) is not full, since 1 is an isolated point thereof

With the help of operator-theoretic methods, we derive new and powerful criteria for finiteness of the uniton number for a harmonic map from a Riemann surface to the unitary group \({{\,\mathrm{U}\,}}(n)\). These use the Grassmannian model where harmonic maps are represented by families of shift-invariant subspaces of \(L^2(S^1,{{\mathbb {C}}}^n)\); we give a new description of that model.

The properties of the intersection of Rauzy fractals associated with substitutions having the same incidence matrix have been studied by several authors. Different techniques have been introduced and used for this purpose, one of them is the balanced pair algorithm. In the present paper we explore the actual limitations of this algorithm. We show that the balanced pair algorithm is defined and terminates

Taking the hint from usual parametrization of circle and hyperbola, and inspired by the pathwork initiated by Cayley and Dixon for the parametrization of the “Fermat” elliptic curve \(x^3+y^3=1\), we develop an axiomatic study of what we call “Keplerian maps”, that is, functions \({{\,\mathrm{{\mathbf {m}}}\,}}(\kappa )\) mapping a real interval to a planar curve, whose variable \(\kappa \) measures

In this note we obtain estimates on the relative growth of normal subgroups of non-elementary hyperbolic groups, particularly those with free abelian quotient. As a corollary, we deduce that the associated relative growth series fail to be rational.

Some global solvability criteria for the scalar Riccati equations are used to establish new reducibility criteria for systems of two linear first-order ordinary differential equations. Some examples are presented.

Dimension groups are complete invariants of strong orbit equivalence for minimal Cantor systems. This paper studies a natural family of minimal Cantor systems having a finitely generated dimension group, namely the primitive unimodular proper \({\mathcal {S}}\)-adic subshifts. They are generated by iterating sequences of substitutions. Proper substitutions are such that the images of letters start

This paper investigates the following critical elliptic problem with singularity $$\begin{aligned} \left\{ \begin{array}{lll} -\Delta u=\lambda f(x)|u|^{-\gamma }+Q(x)|u|^{4}u, &{}&{}\quad x\in {\mathbb {R}}^3,\\ u>0,&{}&{}\quad x\in {\mathbb {R}}^3, \end{array}\right. \end{aligned}$$ where \(0<\gamma <1\), \(\lambda >0\), \(f\in L^{\frac{6}{5+\gamma }}({\mathbb {R}}^3)\) is a positive function and

Consideration in this paper is the generalized fractional Camassa–Holm equation. The local well-posedness is established in Besov space \(B^{s_0}_{2,1}\) with \(s_0=2\nu -\frac{1}{2}\) for \(\nu >\frac{3}{2} \) and \(s_0=\frac{5}{2}\) for \(1<\nu \le \frac{3}{2} \). Then, with a given analytic initial data, the analyticity of the solutions in both variables, globally in space and locally in time, is

The notion of rigid commutators is introduced to determine the sequence of the logarithms of the indices of a certain normalizer chain in the Sylow 2-subgroup of the symmetric group on \(2^n\) letters. The terms of this sequence are proved to be those of the partial sums of the partitions of an integer into at least two distinct parts, that relates to a famous Euler’s partition theorem.

We generalize the universal power series of Seleznev to several variables and we allow the coefficients to depend on parameters. Then, the approximable functions may depend on the same parameters. The universal approximation holds on products \(K = \displaystyle \prod \nolimits _{i = 1}^d K_i\), where \(K_i \subseteq \mathbb {C}\) are compact sets and \(\mathbb {C} {\setminus } K_i\) are connected

We study the Wasserstein metric \(W_p\), a notion of distance between two probability distributions, from the perspective of Fourier Analysis and discuss applications. In particular, we bound the Earth Mover Distance \(W_1\) between the distribution of quadratic residues in a finite field \({\mathbb {F}}_p\) and uniform distribution by \(\lesssim p^{-1/2}\) (the Polya–Vinogradov inequality implies

In this note we point out an error in a recent paper on flag-transitive block designs with gcd\((r,\lambda )=1\), and we prove a result correcting the error.

We prove that every finite abelian group G occurs as a subgroup of the class group of infinitely many real cyclotomic fields.

An odd Coxeter group W is one which admits a Coxeter system (W, S) for which all the exponents \(m_{ij}\) are either odd or infinity. The paper investigates the family of odd Coxeter groups whose associated labeled graphs \({\mathcal {V}}_{(W,S)}\) are trees. It is known that two Coxeter groups in this family are isomorphic if and only if they admit Coxeter systems having the same rank and the same

This paper deals with the half-liner difference equation $$\begin{aligned} \varDelta (r_n\phi _p(\varDelta x_n))+c_n\phi _p(x_{n+1})=0, \end{aligned}$$ where \(r_n\), \(c_n\) are real-valued sequences, \(r_n>0\) for \(n \in \mathbb {N} \cup \{0\}\), and \(\phi _p(z)=|z|^{p-2}z\) with \(p>1\) and \(\mathbb {N}\) is the set of natural numbers. The purpose of this paper is to use the function transformation

In this paper we provide an improved BMO version of the Mikhlin–Hörmander multiplier theorem for multilinear operators.

We study 3-dimensional Poincaré duality pro-p groups in the spirit of the work by Robert Bieri and Jonathan Hillmann, and show that if such a pro-p group G has a nontrivial finitely presented subnormal subgroup of infinite index, then either the subgroup is cyclic and normal or the subgroup is cyclic and the group is polycyclic or the subgroup is Demushkin and normal in an open subgroup of G. Also

For each \(m\ge 1\), there exists \(H=H(m)>0\) such that the set $$\begin{aligned} \bigg \{\frac{\phi (p+1)}{\phi (p-1)}:\,p\text { is prime and }[p+1,p+H]\text { contains at least }m\text { primes}\bigg \} \end{aligned}$$ is dense in \([0,+\infty )\), where \(\phi \) denotes the Euler totient function. This gives a unconditional weak form of a recent result of Garcia, Luca, Shi and Udell, which was

We study the two-dimensional continued fraction algorithm introduced in Garrity (J Number Theory 88(1):86–103, 2001) and the associated triangle map T, defined on a triangle \(\triangle \subseteq \mathbb {R}^2\). We introduce a slow version of the triangle map, the map S, which is ergodic with respect to the Lebesgue measure and preserves an infinite Lebesgue-absolutely continuous invariant measure

This work has been motivated by recent papers that quantify the density of values of generic quadratic forms and other polynomials at integer points, in particular ones that use Rogers’ second moment estimates. In this paper, we establish such results in a very general framework. Given any subhomogeneous function (a notion to be defined) \(f: \mathbb {R}^n \rightarrow \mathbb {R}\), we derive a necessary

In this paper we are concerned with the analysis of a mathematical model, a two point boundary value problem for a second-order differential equation, that is used to deal with the jet flow of the antarctic circumpolar current. We present some new existence and uniqueness results when the vorticity function satisfies either a Lipschitz condition or is continuous.

We study finite groups G with the property that for any subgroup M maximal in G whose order is divisible by all the prime divisors of |G|, M is supersolvable. We show that any nonabelian simple group can occur as a composition factor of such a group and that, if G is solvable, then the nilpotency length and the rank are arbitrarily large. On the other hand, for every prime p, the p-length of such a

Normalized exponential sums are entire functions of the form $$\begin{aligned} f(z)=1+H_1e^{w_1z}+\cdots +H_ne^{w_nz}, \end{aligned}$$ where \(H_1,\ldots , H_n\in {{\mathbb {C}}}\) and \(0

In homogeneous space (\(\mathbb {R}^N, d, \mu \)) we explore Poincare’s type inequality $$\begin{aligned} \Vert f-\overline{f}_{\Omega , v}\Vert _{q, v}\le C \Vert \nabla _\lambda f \Vert _{p}, \,\,\,\, q \ge p\ge 1 \end{aligned}$$ on estimation of weighted Lebesgue norm of a Lipschitz continuous function \(f: \Omega \rightarrow \mathbb {R}\) over the bounded convex domain \(\Omega \subset \mathbb

The article Construction of some Chowla sequences, written by Ruxi Shi was originally published electronically on the publisher’s internet portal on October 10, 2020 without open access. With the author(s)’ decision to opt for Open Choice the copyright of the article changed on November 25, 2020 to © [The author(s)] [2020] and the article is forthwith distributed under a Creative Commons Attribution

In this paper we present an analytical framework for the following system of multivalued parabolic variational inequalities in a cylindrical domain \(Q=\varOmega \times (0,\tau )\): For \(k=1,\dots , m\), find \(u_k\in K_k\) and \(\eta _k\in L^{p'_k}(Q)\) such that $$\begin{aligned}&u_k(\cdot ,0)=0\ \text{ in } \varOmega ,\ \ \eta _k(x,t)\in f_k(x,t,u_1(x,t), \dots , u_m(x,t)), \\&\langle u_{kt}+A_k

We discuss concepts and review results about the Cauchy problem for the Fornberg–Whitham equation, which has also been called Burgers–Poisson equation in the literature. Our focus is on a comparison of various strong and weak solution concepts as well as on blow-up of strong solutions in the form of wave breaking. Along the way we add aspects regarding semiboundedness at blow-up, from semigroups of

Given an integer \(q\ge 2\) and \(\theta _1,\ldots ,\theta _{q-1}\in \{0,1\}\), let \((\theta _n)_{n\ge 0}\) be the generalized Thue–Morse sequence, defined to be the unique fixed point of the morphism $$\begin{aligned} 0\mapsto & {} 0\theta _1\cdots \theta _{q-1}\\ 1\mapsto & {} 1\overline{\theta }_1\cdots \overline{\theta }_{q-1} \end{aligned}$$ beginning with \(\theta _0:=0\), where \(\overline{0}:=1\)

Let A be the direct product of a cyclic group of order \(2^u\) with \(u\ge 1\) and a cyclic group of order \(2^v\) with \(u\ge v\ge 0\). There are some 2-adic properties of the number \(h(A,A_n)\) of homomorphisms from A to the alternating group \(A_n\) on n-letters, which are similar to those of the number of homomorphisms from A to the symmetric group on n-letters. The exponent of 2 in the decomposition