Renormalization of potentials and generalized centers

We generalize the Riesz potential of a compact domain in Rm${\mathbb{R}}^m$ by introducing a renormalization of the rα−m$r^{\alpha -m}$-potential for α?0$\alpha ?0$. This can be considered as generalization of the dual mixed volumes of convex bodies as introduced by Lutwak. We then study the points where the extreme values of the (renormalized) potentials are attained. These points can be considered as a generalization of the center of mass. We also show that only balls give extreme values among bodied with the same volume.     

Ab initio prediction on ferrotoroidic and electronic properties of olivine Li4MnFeCoNiP4O16

First-principles calculations predict that olivine Li4MnFeCoNiP4O16 has a large toroidal moment and ferrimagnetic configuration with a magnetic moment of 1.99μB per formula unit. Density functional theory plus U (DFT+U) shows an indirect band gap of 0.65 eV in this hypothetical material. The band gap is not simply related to the electronic conductivity when it is used as cathode material in rechargeable Li-ion batteries. Based on the orbital-resolved density of states for the transition-metal ions in the hypothetical material, Co, Ni and Mn are in the high-spin configuration while Fe is in the low-spin configuration, which leads to a large resulting toroidal moment deriving from the Co and Ni ions. The spin configuration of the transition-metal ions in the system breaks the space-and time-inversion symmetry and leads to the magnetoelectric property simultaneously. The ferrotoroidic domain, the fourth form of ferroic, is observed in this new material, as in the case of LiCoPO4 reported recently.     

Structure of the Cu(Salen) molecule Cuo<Subscript>2</Subscript>N<Subscript>2</Subscript>C<Subscript>16</Subscript>H<Subscript>14</Subscript> according to gas-phase electron diffraction data and quantum chemical calculations

In the framework of synchronous gas-phase electron diffraction and mass spectrometry experiment, the saturated vapor of N,N′-ethylenebis(salicylaldiminate) copper(II) CuO₂N₂C₁₆H₁₄ is studied at a temperature T 574(5) K. It is found that evaporation is congruent and the saturated vapor consists of monomeric molecules. Electron diffraction data are proved to correspond to the geometric model for the CuO₂N₂C₁₆H₁₄ molecule of C ₂ symmetry with an almost planar structure of the CuN₂O₂ coordination fragment and internuclear distances \(r_{h_1 } \)(Cu-O) = 1.917(13) Å and \(r_{h_1 } \)(Cu-N) = 1.931(15) Å. The stuctural parameters obtained are compared to those quantum chemically calculated and molecular parameters in crystals.     

Isolation and Identification of a Newly Isolated <Emphasis Type="Italic">Alternaria</Emphasis> sp. ND-16 and Characterization of Xylanase

Alternaria sp. ND-16, a bacterium isolated from soil sample, was identified as a strain of Alternaria mali based on the morphology and comparison of internal transcribed spacer rDNA gene sequence studies. Furthermore, it is demonstrated that this strain has xylanase activity, and the activity can be optimized under suitable growing conditions where wheat bran and urea are the primary sources of carbon and nitrogen. Partially purified xylanase from Alternaria sp. ND-16 is shown to have an optimal pH of 6.0 and optimal temperature of 50 °C, making this enzyme potentially suitable for industrial applications. It is also demonstrated that Na⁺ and Mn²⁺ show strong inhibition of the xylanase while K⁺, Li⁺, Fe²⁺, Cu²⁺, and Zn²⁺ have no significant effect on the activity.     

On the Orbit of an m-Isometry

A bounded linear operator T on a Hilbert space H is called an m-isometry for a positive integer m if . We prove some properties concerning the behaviour of the orbit of an m-isometry. For example, every orbit of an m-isometry is eventually norm increasing and some m-isometries can not be N-supercyclic, that is, there does not exist an N-dimensional subspace E_N such that the orbit of T at E_N is dense in H.

---

To Professor José Rodríguez Expósito on his 60th birthday     

Algèbres et cogèbres de Gerstenhaber et cohomologie de Chevalley-Harrison

The fundamental example of Gerstenhaber algebra is the space Tpoly(Rd) of polyvector fields on Rd, equipped with the wedge product and the Schouten bracket. In this paper, we explicitely describe what is the enveloping G_∞ algebra of a Gerstenhaber algebra G. This structure gives us a definition of the Chevalley-Harrison cohomology operator for G. We finally show the nontriviality of a Chevalley-Harrison cohomology group for a natural Gerstenhaber subalgebra in Tpoly(Rd).     

The existence of regular self-complementary 3-uniform hypergraphs

A k-uniform hypergraph with vertex set V and edge set E is called t-subset-regular if every t-element subset of V lies in the same number of elements of E. In this paper we show that a 1-subset-regular self-complementary 3-uniform hypergraph with n vertices exists if and only if n≥5 and n is congruent to 1 or 2 modulo 4.     

Hydrolysis kinetics of p-nitrophenylpicolinate catalyzed by schiff base Mn(III) complexes in Gemini 16-2-16 micellar solutiony

Two mono-Schiff base Mn(III) complexes (MnL₂Cl, L=L¹ and L²) were synthesized and employed as artificial hydrolases in catalyzing the hydrolysis of p-nitrophenylpicolinate (PNPP) in Gemini 16-2-16 micellar solution. The effect of different micelles and their complex structures on the catalytic hydrolysis of PNPP is discussed in detail. The observations showed that MnL₂²Cl exhibited higher catalytic activity over MnL₁²Cl under a comparable condition, which confirmed that an open active centre is essential for modulating the activities of the two enzyme mimics. Moreover, under the conditions employed, hydrolytic rates of PNPP induced by these Mn(III) complexes were faster in Gemini 16-2-16 micelles than that in the micellar solution of cetyltrimethylammonium bromide (CTAB), a conventional analogue of Gemini 16-2-16. Electronic Supplementary Material  Supplementary material is available for this article at and is accessible for authorized users.     

A simplicial approach to factorization systems and Kurosh-Amitsur radicals

Regarding categories as simplicial sets via the nerve functor, we extend the notion of a factorization system from morphisms in a category, to 1-simplexes in an arbitrary simplicial set. Applied to what we call the simplicial set of short exact sequences, it gives the notion of Kurosh-Amitsur radical. That is, we present a unified approach to factorization systems and radicals.