On a Conjecture of Cai-Zhang-Shen for Figurate Primes

A conjecture of Cai-Zhang-Shen for figurate primes says that every integer n > 1 is the sum of two figurate primes. In this paper we give respectively equivalent propositions to the conjecture in the cases of even and odd integers and then confirm the conjecture by considering functions with several variables.Comment: 12page

Antiferromagnetic order and spin dynamics in iron-based superconductors

High-transition temperature (high-$T_c$) superconductivity in the iron pnictides/chalcogenides emerges from the suppression of the static antiferromagnetic order in their parent compounds, similar to copper oxides superconductors. This raises a fundamental question concerning the role of magnetism in the superconductivity of these materials. Neutron scattering, a powerful probe to study the magnetic order and spin dynamics, plays an essential role in determining the relationship between magnetism and superconductivity in high-$T_c$ superconductors. The rapid development of modern neutron time-of-flight spectrometers allows a direct determination of the spin dynamical properties of iron-based superconductors throughout the entire Brillouin zone. In this review, we present an overview of the neutron scattering results on iron-based superconductors, focusing on the evolution of spin excitation spectra as a function of electron/hole-doping and isoelectronic substitution. We compare spin dynamical properties of iron-based superconductors with those of copper oxide and heavy fermion superconductors, and discuss the common features of spin excitations in these three families of unconventional superconductors and their relationship with superconductivity.Comment: 48 pages, 41 figures. Accepted by Reviews of Modern Physic

Distinct stages in the recognition, sorting, and packaging of proTGFα into COPII-coated transport vesicles.

In addition to its role in forming vesicles from the endoplasmic reticulum (ER), the coat protein complex II (COPII) is also responsible for selecting specific cargo proteins to be packaged into COPII transport vesicles. Comparison of COPII vesicle formation in mammalian systems and in yeast suggested that the former uses more elaborate mechanisms for cargo recognition, presumably to cope with a significantly expanded repertoire of cargo that transits the secretory pathway. Using proTGFα, the transmembrane precursor of transforming growth factor α (TGFα), as a model cargo protein, we demonstrate in cell-free assays that at least one auxiliary cytosolic factor is specifically required for the efficient packaging of proTGFα into COPII vesicles. Using a knockout HeLa cell line generated by CRISPR/Cas9, we provide functional evidence showing that a transmembrane protein, Cornichon-1 (CNIH), acts as a cargo receptor of proTGFα. We show that both CNIH and the auxiliary cytosolic factor(s) are required for efficient recruitment of proTGFα to the COPII coat in vitro. Moreover, we provide evidence that the recruitment of cargo protein by the COPII coat precedes and may be distinct from subsequent cargo packaging into COPII vesicles

Some New Inequalities of Dirichlet Eigenvalues for Laplace Operator with any Order

In this paper, we establish several inequalities of Dirichlet eigenvalues for Laplace operator $\Delta$ with any order on \emph{n}-dimensional Euclidean space. These inequalities are more general than known Yang's inequalities and contain new consequences. To obtain them, we borrow the approach of Illias and Makhoul, and use a generalized Chebyshev's inequality