Modular class primes in the Sundaram sieve

The purpose of this paper is to consider analogues of the twin-prime conjecture in various classes within modular rings.     

Commuting traces of multilinear maps on invertible elements

Let R be a unital simple ring. Under some technical restrictions, we characterize m-linear mappings G:R^m→R satisfying [G(u,…,u),u]?=?0 for all unit u∈R.     

Laser control of magneto-polaron in transition metal dichalcogenides triangular quantum well

We study the dynamic of magneto-polaron condensate in monolayer two dimensional (2D) transition metal dichalcogenides (TMDs) materials of 2H types in triangular quantum well potential. Within both the quantum mechanical Schrödinger approach (QMSA) and the improved Wigner-Brillouin theory (IWBT), Landau energies levels (LELs) are derived. We have shown that the magneto-polaron condensation is enhanced in monolayer MoSe₂ compared to MoS₂, WS₂ and WSe₂. We derive various levels by increasing a magnetic field and laser parameter. We show that the quantum confinement lifts the degeneracy of the Landau levels (LLs) resulting in an anticrossing and crossing. The dephasing effect due to the quantum well potential's parameter plays an important role in the magneto-polaron energy corrections, which are also affected by the amplitude of the laser field. The system presents Stückelberg oscillations which is important for practical applications.     

On ω-limit Sets of Triangular Maps on the Unit Cube

We consider Sturm–Liouville eigenvalue problems of second order with arbitary seperated boundary conditions and perform a suitabl discretization of them. The obtained discrete Sturm–Liouville eigenvalue problems are examined and the asymptotic behavior of their eigenvalue as the norm of the partition tends to zero is investigated.     

The Conformation of Sterically Congested Seven-Membered Rings Containing Tetracoordinate Germanium(IV): A First X-Ray Crystallographic Structure Determination

The X-ray crystallographic analysis of 6,6-dimethyl-2,4,8,10-tetra-tert-octyl-dibenzo[d,f][1,3,2]dioxagermepin, 1 is reported. In the solid-state conformation of 1, the dihedral angle about the C─C sp²-sp ² σ bond connecting the two aryl rings is 50.1°. The observed C₂ symmetry in the solid-state conformation of 1 is consistent with the previously suggested solution conformation.     

Practical synthesis of bicyclic pyrazol-5-one derivatives

This communication describes a convenient synthesis of fused bicyclic pyrazolones in a one-pot reaction procedure. Modified protocols are also developed to access 5,5-bicyclic and bulky pyrazolones in good yields. The method reported herein represents a practical approach to structurally diversified bicyclic pyrazolones.