Related papers: Steiner systems $S(2,6,226)$ and $S(2,6,441)$ exis…

In this article we study extensions of Steiner triple systems by means of the associated Steiner loops. We recognize that the set of Veblen points of a Steiner triple system corresponds to the center of the Steiner loop. We investigate…

While many integrable spin systems are known to exist in (1+1) and (2+1) dimensions, the integrability property of the physically important (2+1) dimensional isotropic Heisenberg ferromagnetic spin system in the continuum limit has not been…

The finiteness problem of stationary configurations for the planar five-vortex problem is considered in this paper. The numbers of equilibria and rigidly translating configurations are shown to be at most 6 and 24 respectively. The numbers…

We discuss some families of integrable and superintegrable systems in $n$-dimensional Euclidean space which are invariant to $m\geq n-2$ rotations. The integrable invariant Hamiltonian $H=\sum p_i^2+V(q)$ commutes with $n-2$ integrals of…

We prove the existence of infinitely many non-radial positive solutions for the Schr\"{o}dinger-Newton system $$ \left\{\begin{array}{ll} \Delta u- V(|x|)u + \Psi u=0, &x\in\mathbb{R}^3,\newline \Delta \Psi+\frac12 u^2=0, &x\in\mathbb{R}^3,…

Following on from Paper I in our series (Xie 2013), we report the confirmation by Transit Timing Variations (TTVs) of a further 30 planets in 15 multiple planet systems, using the publicly available Kepler light curves (Q0-Q16). All of…

In this paper, we study the existence of positive entire large and bounded radial positive solutions for a nonlinear system. Our results give an answer of the question raised in [11].

We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and…

We investigate the set S(R) of shift-isomorphism classes of semidualizing R-complexes, ordered via the reflexivity relation, where R is a commutative noetherian local ring. Specifically, we study the question of whether S(R$ has cardinality…

Let $D(n)$ be the number of pairwise disjoint Steiner quadruple systems. A simple counting argument shows that $D(n) \leq n-3$ and a set of $n-3$ such systems is called a large set. No nontrivial large set was constructed yet, although it…

The Yang-Baxter equation for a $SU(2)\times U(1)$-symmetric $S=1/2$ spin-orbital chain was solved using the special computer algorithm developed by the author. The 8 new $R$-matrices separated on 5 groups are presented. Among the obtained…

We show that the stability problem and the problem of constructing Barabanov norms can be resolved for planar linear switching systems in an explicit form. This can be done for every compact control set of $2 \times 2$ matrices. If the…

In this study we identify 11 Kepler systems (KIC 5255552, 5653126, 5731312, 7670617, 7821010, 8023317, 10268809, 10296163, 11519226, 11558882 and 12356914) with a "flip-flop" effect in the eclipse timing variations O-C diagrams of the…

In this paper we consider periodic orbits of planar linear Filippov systems with a line of discontinuity. Unlike many publications researching only the maximum number of crossing periodic orbits, we investigate not only the number and…

In this article we construct uncountably many new homogeneous locally finite Steiner triple systems of countably infinite order as Fra\"{\i}ss\'{e} limits of classes of finite Steiner triple systems avoiding certain subsystems. The…

We consider vortex column solutions $v = V(r) e_\theta + W(r) e_z$ to the $3$D Euler equations. We give a mathematically rigorous construction of the countable family of unstable modes discovered by Liebovich and Stewartson (J. Fluid Mech.…

In this paper we analyze the existence of large positive radial solutions to some quasilinear elliptic systems. Also, a non-radially symmetric solution is obtained by using a lower and upper solution method. The equations are coupled by…

In this paper we prove the existence of infinitely many saddle-shaped positive solutions for non-cooperative nonlinear elliptic systems with bistable nonlinearities in the phase-separation regime. As an example, we prove that the system \[…

It was proved in 2009 that any partial Steiner triple system of order $u$ has an embedding of order $v$ for each admissible integer $v\geq 2u+1$. This result is best-possible in the sense that, for each $u\geq 9$, there exists a partial…

We consider a class of discontinuous piecewise linear differential systems in $\mathbb{R}^3$ with two pieces separated by a plane. In this class we show that there exist differential systems having: a unique limit cycle, a unique…