Multiplication formulas and isomorphism theorem of ıSchur superalgebras

We introduce the notion of ?Schur superalgebra, which can be regarded as a type B/C counterpart of the q-Schur superalgebra (of type A) formulated as centralizer algebras of certain signed q-permutation modules over Hecke algebras. Some multiplication formulas for ?Schur superalgebra are obtained to construct their canonical bases. Furthermore, we established an isomorphism theorem between the ?Scuhr superalgebras and the q-Schur superalgebras of type A, which helps us derive semisimplicity criteria of the ?Schur superalgebras.     

Quantum entanglement generation on magnons assisted with microwave cavities coupled to a superconducting qubit

We present protocols to generate quantum entanglement on nonlocal magnons in hybrid systems composed of yttrium iron garnet (YIG) spheres, microwave cavities and a superconducting (SC) qubit. In the schemes, the YIGs are coupled to respective microwave cavities in resonant way, and the SC qubit is placed at the center of the cavities, which interacts with the cavities simultaneously. By exchanging the virtual photon, the cavities can indirectly interact in the far-detuning regime. Detailed protocols are presented to establish entanglement for two, three and arbitrary N magnons with reasonable fidelities.     

Structures and Fluorescent Properties of Cadmium(II) Complexes with 1D and 2D Structures Based on Tridentate Benzimidazole Ligands

The cadmium(II) complexes [CdL1(m‐nba)₂] ( 1 ), [CdL1(p‐nba)₂] · C₂H₅OH ( 2 ), [CdL2(p‐nba)₂] · CH₃OH ( 3 ), and [CdL2(p‐nbat)₂] ( 4 ) containing the ligands L1 and L2 [L1 = 2,6‐bis(benzimidazol‐2‐yl)pyridine, L2 = bis(2‐benzimidazolylmethyl)amine] were synthesized and characterized (m‐nba, p‐nba, and p‐nbat are the anions of p‐nitrobenzoic acid, m‐nitrobenzoic acid, and p‐nitrobenzeneacetic acid, respectively). The complexes were investigated by X‐ray single crystal diffraction, elemental analysis as well as IR and fluorescence spectroscopy. Compounds 1 – 3 contain a distorted pentagonal bipyramidal coordination sphere with Cd^II coordinated by two carboxylate ligands in bidentate‐chelating mode, whereas complex 4 exhibits a distorted octahedral arrangement with one carboxylate ligand in bidentate‐chelating and the other in monodentate coordination mode. 1 and 2 form a 1D chain interplayed by hydrogen bonding and strong π–π stacking interactions. 3 and 4 vary from 1D chain into 2D single‐layer and double‐layer networks because of more extensive hydrogen bonding interactions. The complexes show emission maxima in the blue region in the solid state and emission bands are red‐shifted compared to those of the free ligands.     

Irrationally elliptic closed characteristics on symmetric compact star-shaped hypersurfaces in $$\mathbf{R}^\mathbf{4}$$

In this paper, we prove that if a symmetric compact star-shaped hypersuface in \(\mathbf{R}^4\) carries exactly two geometrically distinct closed characteristics, then both of them must be irrationally elliptic.     

Laplace Transform Method for the Ulam Stability of Linear Fractional Differential Equations with Constant Coefficients

Using the Laplace transform method, this paper deals with the Ulam stability of linear fractional differential equations with constant coefficients.     

Application of holomorphic invariants in reproducing kernel

We use holomorphic invariants to calculate the Bergman kernel for generalized quasi-homogeneous Reinhardt-Hartogs domains. In addition, we present a complete orthonormal basis for the Bergman space on bounded Reinhardt-Hartogs domains.     

Difference Cochains and Reidemeister Traces

The authors consider the difference of Reidemeister traces and difference cochain of given two self-maps,and find out a relation involving these two invariants.As an application,an inductive formula of the Reidemeister traces for self-maps on a kind of CW-complex,including spherical manifolds is obtained.     

Some new results on permutation polynomials over finite fields

Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. In this paper, four classes of monomial complete permutation polynomials and one class of trinomial complete permutation polynomials are presented, one of which confirms a conjecture proposed by Wu et al. (Sci China Math 58:2081–2094, 2015). Furthermore, we give two classes of permutation trinomial, and make some progress on a conjecture about the differential uniformity of power permutation polynomials proposed by Blondeau et al. (Int J Inf Coding Theory 1:149–170, 2010).     

Quasideterminant solutions of the extended noncommutative Kadomtsev–Petviashvili hierarchy

We construct a nonauto Darboux transformation for the extended noncommutative Kadomtsev–Petviashvili (ncKP) hierarchy and consequently derive its quasi-Wronskian solution. We also obtain the quasi-Wronskian solution of the ncKP equation with self-consistent sources (ncKPESCS) as a by-product. Finally, we use the direct verification method to prove the quasi-Wronskian solution of the ncKPESCS.