Group divisible 3‐designs with block size four and group type 1ns1

In this article, we mainly consider the existence problem of a group divisible design GDD $\left(3,4,n+s\right)$ of type $1^n{s}^1$. We present two recursive constructions for this configuration using candelabra systems and construct explicitly a few small examples admitting given automorphism groups. As an application, several new infinite classes of GDD $\left(3,4,n+s\right)$s of type $1^n{s}^1$ are produced. Meanwhile a few new infinite families on candelabra quadruple systems with group sizes being odd and stem size greater than one are also obtained.     

Synthesis of heterobiaryls via Suzuki‐Miyaura coupling reaction of potassium aryltrifluoroborates with heteroaryl halides in aqueous systems

A variety of heterobiaryl compounds have been synthesized by the Suzuki‐Miyaura coupling reactions of heteroaryl halides with potassium aryltrifluoroborates. Pd (OAc)₂ was found to be highly efficient for the Suzuki‐Miyaura coupling reactions of various heteroaryl halides with potassium aryltrifluoroborates in aqueous systems, delivering the corresponding heterobiaryl compounds in good to excellent yields.     

‐Theory for Schrödinger systems

In this article, we study for the ‐realization of the vector‐valued Schrödinger operator . Using a noncommutative version of the Dore–Venni theorem due to Monniaux and Prüss, we prove that the ‐realization of , defined on the intersection of the natural domains of the differential and multiplication operators which form , generates a strongly continuous contraction semigroup on . We also study additional properties of the semigroup such as extension to L¹, positivity, ultracontractivity and prove that the generator has compact resolvent.     

Multiple positive solutions for Schrödinger‐Poisson system involving singularity and critical exponent

In this paper, the existence and multiplicity of positive solutions is established for Schrödinger‐Poisson system of the form where 0 ∈ Ω is a smooth bounded domain in , , and λ > 0 is a real parameter. Combining with the variational method and Nehari manifold method, two positive solutions of the system are obtained.     

Relaxation oscillations in a slow–fast modified Leslie–Gower model

In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result.     

Geometrically distinct solutions for Klein–Gordon–Maxwell systems with super-linear nonlinearities

This paper is concerned with the following Klein–Gordon–Maxwell system $\left\{\begin{array}{c}-△u+V\left(x\right)u-(2\omega +\varphi )\varphi u=f(x,u),x\in {\mathbb{R}}^3,\hfill \\ △\varphi =(\omega +\varphi )u^2,x\in {\mathbb{R}}^3,\hfill \end{array}\right.$where $\omega >0$ is a constant, $V$ and $f$ are periodic with respect to $x$. By combining deformation type arguments, Lusternik–Schnirelmann theory and some new tricks, we prove that the above system admits infinitely many geometrically distinct solutions under weaker superlinear conditions instead of the common super-cubic conditions on $f$. Our result seems new and extends the previous results in the literature.     

An improved generalized predictive control algorithm based on the difference equation CARIMA model for the SISO system with known strong interference

ABSTRACT

The single input single output (SISO) system with known strong interference is widely used in various occasions. Due to its strong interference, the control accuracy is hard to guarantee. To solve this problem, an improved generalized predictive control (IGPC) algorithm is developed. The IGPC firstly builds the difference equation CARIMA (Controlled Auto-Regressive Integrated Moving-Average) model of the SISO system and then treats the system as a two input single output (TISO) system and calculates its predictive vector, then transforms it into a SISO system and uses the TISO system predictive vector to calculate the SISO system control increment. A new parameter called phase coefficient is added to inhibit the control lag. Simulations are performed to make the comparison among the traditional GPC, PID control, velocity synchronization control (VSC), fuzzy adaptive PID control (FAPID), model-based robust PID control (BPID) and the IGPC. Results show that IGPC has best performance compared to the others. Finally, experiments are developed which proved that the IGPC algorithm has a higher accuracy in the SISO system with known strong interference than that of VSC.     

Anti‐Pasch optimal packings with triples

It is shown that for , there exists an optimal packing with triples on points that contains no Pasch configurations. Furthermore, for all (mod 6), there exists a pairwise balanced design of order , whose blocks are all triples apart from a single quintuple, and that has no Pasch configurations amongst its triples.