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Kenny Pruitt 《International Journal of Mathematical Education in Science & Technology》2018,49(6):944-947
The purpose of this paper is to consider analogues of the twin-prime conjecture in various classes within modular rings. 相似文献
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Ivan Bazhov 《Journal of Pure and Applied Algebra》2019,223(6):2530-2542
We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kähler fourfold studied by Beauville and Donagi, and the hyper-Kähler fourfold constructed by Debarre and Voisin in [3]. We exhibit an analog of the notion of “triangle” for these varieties and prove that the 6-dimensional variety of “triangles” is a Lagrangian subvariety in the cube of the constructed hyper-Kähler fourfold. 相似文献
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Ludwig Hackl Dr. Alex R. Petrov Dr. Thomas Bannenberg Dr. Matthias Freytag Prof. Dr. Peter G. Jones Prof. Dr. Matthias Tamm 《Chemistry (Weinheim an der Bergstrasse, Germany)》2019,25(70):16148-16155
The reaction of 1,2-dipiperidinoacetylene ( 1 ) with 0.5 equivalents of SnCl2 or GeCl2⋅dioxane afforded the 1,2,3,4-tetrapiperidino-1,3-cyclobutadiene tin and germanium dichloride complexes 2 a and 2 b , respectively. A competing redox reaction was observed with excess amounts of SnCl2, which produced a tetrapiperidinocyclobutadiene dication with two trichlorostannate(II) counterions. Heating neat 1 to 110 °C for 16 h cleanly produced the dimer 1,3,4,4-tetrapiperidino-3-buten-1-yne ( 3 ); its reaction with stoichiometric amounts of SnCl2 or GeCl2⋅dioxane furnished the 1,3,4,4-tetrapiperidino-1,2-cyclobutadiene tin and germanium dichloride complexes 4 a and 4 b , respectively. Transition-metal complexes containing this novel four-membered cyclic bent allene (CBA) ligand were prepared by reaction of 3 with [(tht)AuCl], [RhCl(CO)2]2, and [(Me3N)W(CO)5] to form [(CBA)AuCl] ( 5 ), [(CBA)RhCl(CO)2] ( 6 ), and [(CBA)W(CO)5] ( 7 ). The molecular structures of all compounds 2 – 7 were determined by X-ray diffraction analyses, and density functional theory (DFT) calculations were carried out to rationalise the formation of 3 and 4 a . 相似文献
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Octadecanuclear Gear Wheels by Self‐Assembly of Self‐Assembled “Double Saddle”‐Type Coordination Entities: Molecular “Rangoli” 下载免费PDF全文
Hareesha Dasary Dr. Rajamony Jagan Prof. Dr. Dillip Kumar Chand 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(4):1499-1507
A series of self‐assembled “double saddle”‐type trinuclear complexes of [Pd3L′3 L 2] formulation have been synthesized by complexation of a series of cis‐protected palladium(II) components with a slightly divergent “E‐shaped” non‐chelating tridentate ligand, 1,1′‐(pyridine‐3,5‐diyl)bis(3‐(pyridin‐3‐yl)urea ( L ). The cis‐protecting agents L′ employed in the study are ethylenediamine (en), tetramethylethylenediamine (tmeda), 2,2′‐bipyridine (bpy), and 1,10‐phenanthroline (phen), for 1 , 2 , 3 , and 4 , respectively. The crystal structures of [Pd3(tmeda)3( L )2](NO3)6 ( 2 ), [Pd3(bpy)3( L )2](NO3)6 ( 3 ), and [Pd3(phen)3( L )2](NO3)6 ( 4 ) unequivocally support the new architecture. Two of the “double saddle”‐type complexes ( 3 and 4 ) are suitably crafted with π surfaces at the strategically located cis‐protecting sites to facilitate intermolecular π–π interactions in the solid state. As a consequence, six units of the 3 (or 4 ) are assembled, by means of six‐pairs of π–π stacking interactions, in a circular geometry to form an octadecanuclear molecular ring of [(Pd3L′3 L 2)6] composition. The overall arrangement of the rings in the crystal packing is equated with the traditional Indian art form rangoli. 相似文献
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We study the skew information-based coherence of quantum states and derive explicit formulas for Werner states and isotropic states in a set of autotensors of mutually unbiased bases (MUBs). We also give surfaces of skew information-based coherence for Bell-diagonal states and a special class of X states in both computational basis and in MUBs. Moreover, we depict the surfaces of the skew information-based coherence for Bell-diagonal states under various types of local nondissipative quantum channels. The results show similar as well as different features compared with relative entropy of coherence and l1 norm of coherence. 相似文献
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《Physics letters. A》2020,384(1):126037
In bosonic fields, Gaussian states, which consist of a rather wide family of states including coherent states, squeezed states, thermal states, etc., have many classical-like features, and are usually defined from the mathematical perspective in terms of characteristic functions. It is well known that some special Gaussian states, such as coherent states, are minimum uncertainty states for the conventional Heisenberg uncertainty relation involving canonical pair of position and momentum observables. A natural question arises as whether all Gaussian states can be characterized as minimum uncertainty states. In this work, we show that indeed Gaussian states coincide with minimum uncertainty states for an information-theoretic refinement of the conventional uncertainty relation established in Luo (2005) [40]. This characterization puts Gaussian states on a novel basis of physical significance. 相似文献