Some Functions of Points in Projective Spaces

Extending earlier results in the plane, we prove that every n-polygon in sufficiently general position in d-dimensional projective space, n d + 2, gives rise to a derived n-polygon, which preserves a few functions; these functions are the cyclial product of (actually affine) ratios of various points, obtained by proper projections on suitable lines.     

Frobenius morphisms and stable module categories of repetitive algebras

Let k be the algebraic closure of a finite field F_q and A be a finite dimensional k-algebra with a Frobenius morphism F.In the present paper we establish a relation between the stable module category of the repetitive algebra  of A and that of the repetitive algebra of the fixed-point algebra A~F.As an application,it is shown that the derived category of A~F is equivalent to the subcategory of F-stable objects in the derived category of A when A has a finite global dimension.     

Groups which do not admit ghosts

A ghost in the stable module category of a group is a map between representations of that is invisible to Tate cohomology. We show that the only non-trivial finite -groups whose stable module categories have no non-trivial ghosts are the cyclic groups and . We compare this to the situation in the derived category of a commutative ring. We also determine for which groups the second power of the Jacobson radical of is stably isomorphic to a suspension of .

     

Rigid complexes via DG algebras

Let be a commutative ring, a commutative -algebra and a complex of -modules. We begin by constructing the square , which is also a complex of -modules. The squaring operation is a quadratic functor, and its construction requires differential graded (DG) algebras. If there exists an isomorphism , then the pair is called a rigid complex over relative to (there are some finiteness conditions). There is an obvious notion of rigid morphism between rigid complexes.

We establish several properties of rigid complexes, including their uniqueness, existence (under some extra hypothesis), and formation of pullbacks (resp. ) along a finite (resp. essentially smooth) ring homomorphism .

In the subsequent paper, Rigid Dualizing Complexes over Commutative Rings, we consider rigid dualizing complexes over commutative rings, building on the results of the present paper. The project culminates in our paper Rigid Dualizing Complexes and Perverse Sheaves on Schemes, where we give a comprehensive version of Grothendieck duality for schemes.

The idea of rigid complexes originates in noncommutative algebraic geometry, and is due to Van den Bergh (1997).

     

金属-有机框架衍生的多功能光催化剂

在光催化过程中,光催化剂被太阳能激发产生光生电子和空穴,来实现环境净化或能量转换,是应对全球变暖和能源短缺的有效途径之一.然而,光催化技术面临的主要瓶颈问题是光生载流子的低分离效率和高反应能垒.而催化剂本身的特性对这一点起到了决定性的作用.因此,催化剂的合理设计和改性是提高光催化效率的关键.金属有机框架(MOFs)是一...     

Suitability of density functional methods for calculation of electrostatic properties

A systematic analysis was performed on the suitability of the molecular electrostatic potential (MEP) and MEP-derived properties determined by means of density functional (DFT) methods. Attention was paid to the electrostatic potential (ESP) derived charges, the ESP and exact quantum mechanical dipole moments, the depth of MEP minima, and the MEP distribution in layers around the molecule for a large series of molecules. The electrostatic properties were determined at either local or nonlocal DFT levels using different functionals. The results were compared with the values estimated from quantum mechanical calculations performed at Hartree–Fock, Møller–Plesset up to fourth order, and CIPSI levels. The suitability of the MEP-derived properties estimated from DFT methods is discussed for application in different areas of chemical interest. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 980–991, 1997     

Resin‐Derived Ni3S2/Carbon Nanocomposite for Advanced Rechargeable Aqueous Zn‐Based Batteries

The exploration of high‐energy and stable cathode materials is highly desirable and challenging for the development of advanced Zn‐based batteries. In this work, a facile pyrolysis method is reported to synthetize Ni₃S₂/carbon nanocomposite as high‐performance cathode by employing ion exchange resin as a precursor. Attributing to the abundant active sites and enhanced conductivity from well binding between Ni₃S₂ and carbon, a markedly high capacity of 234.3 mA h g^?1 is obtained for this Ni₃S₂/carbon at a high current density of 6.9 A g^?1. Moreover, a Zn‐based battery is demonstrated by using the Ni₃S₂/carbon as a cathode and Zn plate as an anode, which delivers a maximum power density of 58.6 kW kg^?1, together with a peak energy density of 356 W h kg^?1 and 93.7% capacity retention after 5000 charging–discharging cycles. This simple synthetic strategy to achieve robust Ni‐based composite electrodes may open up new opportunities to design other transition metal–based electrodes for energy storage applications.     

A recollement construction of Gorenstein derived categories

We first give an equivalence between the derived category of a locally finitely presented category and the derived category of contravariant functors from its finitely presented subcategory to the category of abelian groups, in the spirit of Krause’s work [Math. Ann., 2012, 353: 765–781]. Then we provide a criterion for the existence of recollement of derived categories of functor categories, which shows that the recollement structure may be induced by a proper morphism defined in finitely presented subcategories. This criterion is then used to construct a recollement of derived category of Gorenstein injective modules over CM-finite 2-Gorenstein artin algebras.     

One-Side Derived Categories of Pre-Strict $P$-Semi-Abelian Categories

In this paper, we study a class of $P$-semi-abelian categories, as well as left and right cohomological functors. Then we establish the corresponding one-side derived categories.     

Nonlinear approximation with general wave packets

We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete characterization of the approximation spaces is derived.