Normal Transversality and Uniform Bounds

Let A be a commutative ring. A graded A-algebra U = _n0 U_n isa standard A-algebra if U₀ = A and U = A[U₁] is generated asan A-algebra by the elements of U₁. A graded U-module F = _n0F_nis a standard U-module if F is generated as a U-module by theelements of F₀, that is, F_n = U_nF₀ for all n 0. In particular,F_n = U₁F_n–1 for all n 1. Given I, J, two ideals of A,we consider the following standard algebras: the Rees algebraof I, R(I) = _n0Iⁿtⁿ = A[It] A[t], and the multi-Rees algebraof I and J, R(I, J) = _n0(_p+q=nI^pJ^qu^pv^q) = A[Iu, Jv] A[u, v].Consider the associated graded ring of I, G(I) = R(I) A/I =_n0Iⁿ/Iⁿ⁺¹, and the multi-associated graded ring of I and J,G(I, J) = R(I, J) A/(I+J) = _n0(_p+q=nI^pJ^q/(I+J)I^pJ^q). We canalways consider the tensor product of two standard A-algebrasU = _p0U_p and V = _q0V_q as a standard A-algebra with the naturalgrading U V = _n0(_p+q=nU_p V_q). If M is an A-module, we havethe standard modules: the Rees module of I with respect to M,R(I; M) = _n0IⁿMtⁿ = M[It] M[t] (a standard R(I)-module), andthe multi-Rees module of I and J with respect to M, R(I, J;M) = _n0(_p+q=nI^pJ^qMu^pv^q) = M[Iu, Jv] M[u, v] (a standard R(I,J)-module). Consider the associated graded module of M withrespect to I, G(I; M) = R(I; M) A/I = _n0IⁿM/Iⁿ⁺¹M (a standardG(I)-module), and the multi-associated graded module of M withrespect to I and J, G(I, J; M) = R(I, J; M) A/(I+J) = _n0(_p+q=nI^pJ^qM/(I+J)I^pJ^qM)(a standard G(I, J)-module). If U, V are two standard A-algebras,F is a standard U-module and G is a standard V-module, thenF G = _n0(_p+q=nF_p G_q) is a standard U V-module. Denote by :R(I) R(J; M) R(I, J; M) and :R(I, J; M) R(I+J;M) the natural surjective graded morphisms of standard RI) R(J)-modules. Let :R(I) R(J; M) R(I+J; M) be . Denote by :G(I) G(J; M) G(I, J; M) and :G(I, J; M) G(I+J; M) the tensor productof and by A/(I+J); these are two natural surjective gradedmorphisms of standard G(I) G(J)-modules. Let :G(I) G(J; M) G(I+J; M) be . The first purpose of this paper is to prove the following theorem.     

Possible evidence for MeV dark matter in dwarf spheroidals

The observed 511 keV emission from the galactic bulge could be due to very light (MeV) annihilating dark matter particles. To distinguish this hypothesis from conventional astrophysical sources, we study dwarf spheroidals in the region observed by the International Gamma-Ray Astrophysics Laboratory/SPI such as Sagittarius. As these galaxies have comparatively few stars, the prospects for 511 keV emission from standard astrophysical scenarios are minimal. The dwarf spheroidals do, however, contain copious amounts of dark matter. The observation of 511 keV emission from Sagittarius should be a "smoking gun" for MeV dark matter.     

Aurophilicity as a cofactor in crystal engineering. Dicyanoaurate(I) anion as a building block in a novel Co(II)-Au(I) bimetallic assembly

A 2D grid-shaped cyanide-bridged Co(II)-Au(I) bimetallic coordination polymer, [Co(DMF)2(Au(CN)2)2], has been prepared from the [Au(CN)2]- building block; sheets associate pair-wise by aurophilic interactions and the compound exhibits zeolite-like properties.     

Recovery stress and work output in hyperbranched poly(ethyleneimine)‐modified shape‐memory epoxy polymers

In this study a series of hyperbranched modified shape‐memory polymers were subjected to constrained shape recoveries in order to determine their potential use as thermomechanical actuators. Materials were synthesized from a diglycidyl ether of bisphenol A as base epoxy and a polyetheramine and a commercial hyperbranched poly(ethyleneimine) as crosslinker agents. Hyperbranched polymers within the structure of the shape‐memory epoxy polymers led to a more heterogeneous network that can substantially modify mechanical properties. Thermomechanical and mechanical properties were analyzed and discussed in terms of the content of hyperbranched polymer. Shape‐memory effect was analyzed under fully and partially constrained conditions. When shape recovery was carried out with fixed strain a recovery stress was obtained whereas when it was carried out with a constraining stress the material performs mechanical work. Tensile tests at Tg^E′ showed excellent values of stress and strain at break (up to 15 MPa and almost 60%, respectively). Constrained recovery performances revealed rapid recovery stress generation and unusually high recovery stresses (up to 7 MPa) and extremely high work densities (up to 750 kJ/m³). The network structure of shape‐memory polymers was found to be a key factor for actuator‐like applications. Results confirm that hyperbranched modified‐epoxy shape memory polymers are good candidates for actuator‐like shape‐memory applications. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1002–1013     

Heterotrimetallic Coordination Polymers: {CuIILnIIIFeIII} Chains and {NiIILnIIIFeIII} Layers: Synthesis,Crystal Structures,and Magnetic Properties

The use of the [Fe^III(AA)(CN)₄]^? complex anion as metalloligand towards the preformed [Cu^II(valpn)Ln^III]³⁺ or [Ni^II(valpn)Ln^III]³⁺ heterometallic complex cations (AA=2,2′‐bipyridine (bipy) and 1,10‐phenathroline (phen); H₂valpn=1,3‐propanediyl‐bis(2‐iminomethylene‐6‐methoxyphenol)) allowed the preparation of two families of heterotrimetallic complexes: three isostructural 1D coordination polymers of general formula {[Cu^II(valpn)Ln^III(H₂O)₃(μ‐NC)₂Fe^III(phen)(CN)₂ {(μ‐NC)Fe^III(phen)(CN)₃}]NO₃ ? 7 H₂O}_n (Ln=Gd ( 1 ), Tb ( 2 ), and Dy ( 3 )) and the trinuclear complex [Cu^II(valpn)La^III(OH₂)₃(O₂NO)(μ‐NC)Fe^III(phen)(CN)₃] ? NO₃ ? H₂O ? CH₃CN ( 4 ) were obtained with the [Cu^II(valpn)Ln^III]³⁺ assembling unit, whereas three isostructural heterotrimetallic 2D networks, {[Ni^II(valpn)Ln^III(ONO₂)₂(H₂O)(μ‐NC)₃Fe^III(bipy)(CN)] ? 2 H₂O ? 2 CH₃CN}_n (Ln=Gd ( 5 ), Tb ( 6 ), and Dy ( 7 )) resulted with the related [Ni^II(valpn)Ln^III]³⁺ precursor. The crystal structure of compound 4 consists of discrete heterotrimetallic complex cations, [Cu^II(valpn)La^III(OH₂)₃(O₂NO)(μ‐NC)Fe^III(phen)(CN)₃]⁺, nitrate counterions, and non‐coordinate water and acetonitrile molecules. The heteroleptic {Fe^III(bipy)(CN)₄} moiety in 5 – 7 acts as a tris‐monodentate ligand towards three {Ni^II(valpn)Ln^III} binuclear nodes leading to heterotrimetallic 2D networks. The ferromagnetic interaction through the diphenoxo bridge in the Cu^II?Ln^III ( 1 – 3 ) and Ni^II?Ln^III ( 5 – 7 ) units, as well as through the single cyanide bridge between the Fe^III and either Ni^II ( 5 – 7 ) or Cu^II ( 4 ) account for the overall ferromagnetic behavior observed in 1 – 7 . DFT‐type calculations were performed to substantiate the magnetic interactions in 1 , 4 , and 5 . Interestingly, compound 6 exhibits slow relaxation of the magnetization with maxima of the out‐of‐phase ac signals below 4.0 K in the lack of a dc field, the values of the pre‐exponential factor (τ_o) and energy barrier (E_a) through the Arrhenius equation being 2.0×10^?12 s and 29.1 cm^?1, respectively. In the case of 7 , the ferromagnetic interactions through the double phenoxo (Ni^II–Dy^III) and single cyanide (Fe^III–Ni^II) pathways are masked by the depopulation of the Stark levels of the Dy^III ion, this feature most likely accounting for the continuous decrease of χ_M T upon cooling observed for this last compound.     

How carbo-benzenes fit molecules in their inner core as do biologic ion carriers?

Structural Chemistry - The present computational study complements experimental efforts to describe and characterize carbo-benzene derivatives as paradigms of aromatic carbo-mers. A long-lasting...