Mathematics, Volume 11, Issue 8

In this paper, we study the D- and A-optimal assignment problems for regression models with experimental cost constraints. To solve these two problems, we propose two multiplicative algorithms for obtaining optimal designs and establishing extended D...

Seaweeds or seaweed Lie algebras are subalgebras of the full-matrix algebra Mat(n) introduced by Dergachev and Kirillov to give an example of algebras for which it is possible to compute the Dixmier index via combinatorial methods. It is worth noting...

With the wide application of the artificial ground freezing method in municipal underground engineering, the annular layout of freezing pipes is often adopted to form a frozen soil cylinder. However, there is still no analytical solution that can cal...

In this paper, we utilize the Ramsey theory to investigate the geometrical characteristics of closed contours. We begin by examining a set of six points arranged on a closed contour and connected as a complete graph. We assign the downward-pointing e...

In construction engineering, rock is an important building material. During the construction process, layered rock masses are typically subjected to varying dynamic load disturbances under triaxial loads. It is thus essential to investigate the mecha...

We studied the random variable Vt=volS2(gtB∩B), where B is a disc on the sphere S2 centered at the north pole and (gt)t≥0 is the Brownian motion on the special orthogonal group SO(3) starting at the identity. We applied the results of the theo...

The main purpose of this manuscript is to present some new estimations of the Jensen gap in a discrete sense along with their applications. The proposed estimations for the Jensen gap are provided with the help of the notion of 6-convex functions. So...

We study the sequence of polynomials {Sn}n≥0 that are orthogonal with respect to the general discrete Sobolev-type inner product ⟨f,g⟩s=∫f(x)g(x)dμ(x)+∑j=1N∑k=0djλj,kf(k)(cj)g(k)(cj), where μ is a finite Bore...

We consider a nonlinear variational elliptic problem with critical nonlinearity on a bounded domain of Rn,n≥3 and mixed Dirichlet–Neumann boundary conditions. We study the effect of the domain’s topology on the existence of solutions a...

Wind farms have gained wide attention due to unlimited resources and clean energy. Considering that wind turbine systems are always in harsh conditions, subsystem failures could reduce the reliability of wind turbine systems. At present, the maintena...