On a Jacobian Identity Associated with Real Hyperplane Arrangements

For the mapping is onto R. It was shown by G. Boole in the 1850's that We give an n-dimensional analogue of this result. The proof makes use of the Griffiths–Harris residue theorem from algebraic geometry.     

Asymptotic behavior of the partial derivatives of Laguerre kernels and some applications

The aim of this paper is to present some new results about the asymptotic behavior of the partial derivatives of the kernel polynomials associated with the Gamma distribution. We also show how these results can be used in order to obtain the inner relative asymptotics for certain Laguerre–Sobolev type polynomials.     

Derivation degree sequences of non-free arrangements

In this note, we study the logarithmic derivation module of a non-free arrangement. We prove a generalized addition theorem for all arrangements. This addition theorem allows us to find various relationships between non-free arrangements, free arrangements, and restriction counts. For graphic arrangements, we can use these results to find a lower bound for the maximal degree generator in terms of triangles in the associated graph. We also apply these results to the case of hypersolvable arrangements where we define hyperexponents and use them to find a lower bound for their maximal degree generator.     

Crystal and magnetic structure of CeVO<Subscript>3</Subscript>

The crystal structure and the magnetic ordering pattern of the electrically insulating perovskite CeVO₃ was investigated by high-resolution powder X-ray diffraction and single-crystal neutron diffraction. A structural phase transition from an orthorhombic to a monoclinic structure (with space groups Pbnm and P2₁/b, respectively) was observed upon cooling below T _s = 136 K. This transition is associated with a strong distortion of the VO₆-octahedra and can be attributed to orbital ordering. A magnetic ordering transition driven by exchange interactions between vanadium moments is observed at T _N = 124 K, and antiferromagnetic interactions between magnetic moments on vanadium and cerium ions induce a progressive magnetic polarization of the cerium sublattice at lower temperatures. The full magnetic structure is described by a superposition of the modes (C _x , F _y , −) and (F _x , C _y , −). The unit cell volume and the tilt angles of the VO₆-octahedra in the CeVO₃-crystal structure are anomalous compared to those of other members of the series RVO₃ (R = lanthanide atom), and the ordered magnetic moments on both vanadium and cerium sublattices at low temperatures are considerably smaller than the free-ion values of V³⁺ and Ce³⁺. Possible origins of this behavior are discussed.     

The study of spin ordering in FM/AFM bilayers with a mixed interface

Monte Carlo simulation is adopted to study the spin ordering in ferromagnet(FM)/antiferromagnet(AFM) bilayers with a mixed interface. We introduce the time-dependent autocorrelation function to describe the thermal stability of the spin ordering for each plane, especially the interface, in FM/AFM bilayers with uncompensated and compensated AFM surfaces. It is found that the thermal decay of spin ordering depends on the plane, the interface coupling and the interface roughness. For the uncompensated AFM surfaces, when the interface coupling is small, the thermal decay of spin ordering is faster at the interface than other planes, while the large interfae coupling makes the spin ordering at the interface become relatively stable. In the case of compensated AFM surfaces, the spin ordering at the interface is thermally disordered much before that at other planes, and the thermal decay becomes slow gradually as the interface coupling increases.     

Torsion divisors of plane curves with maximal flexes and Zariski pairs

There is a close relationship between the embedded topology of complex plane curves and the (group-theoretic) arithmetic of elliptic curves. In a recent paper, we studied the topology of some arrangements of curves that include a special smooth component, via the torsion properties induced by the divisors in the special curve associated to the remaining components, which is an arithmetic property. When this special curve has maximal flexes, there is a natural isomorphism between its Jacobian variety and the degree zero part of its Picard group. In this paper, we consider curve arrangements that contain a special smooth component with a maximal flex and exploit these properties to obtain Zariski tuples, which show the interplay between topology, geometry, and arithmetic.      

Vanishing of higher order Alexander-type invariants of plane curves

The higher order degrees are Alexander-type invariants of complements to an affine plane curve. In this paper, we characterize the vanishing of such invariants for a curve C given as a transversal union of plane curves $C^{\prime }$ and $C^{\prime \prime }$ in terms of the finiteness and the vanishing properties of the invariants of $C^{\prime }$ and $C^{\prime \prime }$, and whether or not they are irreducible. As a consequence, we prove that the multivariable Alexander polynomial ${\mathrm{\Delta }}_C^{multi}$ is a power of $(t-1)$, and we characterize when ${\mathrm{\Delta }}_C^{multi}=1$ in terms of the defining equations of $C^{\prime }$ and $C^{\prime \prime }$. Our results impose obstructions on the class of groups that can be realized as fundamental groups of complements of a transversal union of curves.     

Cohomology of moduli spaces of Del Pezzo surfaces

We compute the rational Betti cohomology groups of the coarse moduli spaces of geometrically marked Del Pezzo surfaces of degree 3 and 4 as representations of the Weyl groups of the corresponding root systems. The proof uses a blend of methods from point counting over finite fields and techniques from arrangement complements.     

Secure communication over RIS-aided underlay CR MIMO wiretap channel without Eve’s CSI

This paper investigates a reconfigurable intelligent surface (RIS)-aided underlay cognitive radio (CR) multiple-input multiple-output (MIMO) wiretap channel where the secondary transmitter (ST) communicates with primary user (PU) and secondary user (SU) in the absence of the eavesdropper’s (Eve’s) channel state information (CSI). To enhance the secrecy performance in CR MIMO wiretap channel, the power of useful signal is minimized at ST, and then the residual power is further utilized to design artificial noise (AN) based on statistical CSI at ST. Specifically, we first optimize the transmit covariance matrix at ST and the diagonal phase-shifting matrix at RIS jointly leveraging large-system approximation results. Then the power allocation for SU is optimized to obtain the minimum transmit power of useful information at ST. Besides, we further design AN with the residual power by aligning it into the null space of the SU channel and thus avert the harmful effects of AN to improve the secure communication quality of SU. Finally, through numerical simulations, we illustrate the effectiveness of the proposed algorithm and validate the existence of a trade-off between the quality-of-service (QoS) at SU and secrecy rate.