Accessing Spin-Crossover Behaviour In Iron(II) Complexes Of N-Confused Scorpionate Ligands

The first examples of a class of N-confused tris(pyrazolyl)methane ‘scorpionate’ ligands have been prepared. The magnetic properties of their iron(II) tetrafluoroborate complexes are dictated by changing one substituent per ligand rather than three as is typical for normal scorpionate ligands

Reaction Chemistry of Silver(I) Trifluoromethanesulfonate Complexes of Nitrogen-Confused \u3cem\u3eC\u3c/em\u3e-Scorpionates

Two new C-scorpionate ligands with a bis(3,5-dimethylpyrazol-1-yl)methyl group bound to the 3 position of either an N-tosyl (TsL*) or an N–H pyrazole (HL*) ring have been prepared. The silver(I) complexes of these new ligands and the two previously reported analogous ligands with unsubstituted bis(pyrazol-1-yl)methyl groups (TsL and HL) in both 1:1 and 2:1 ligand/metal ratios were investigated to explore the effects of ligand sterics on their physical and chemical properties. The structurally characterized derivatives of the type [Ag(L)2](OTf) are four-coordinate, where the confused pyrazolyl is not bound to the metal. On the other hand, three 1:1 complexes [Ag(L)](OTf) had all pyrazolyls bound, while the μ–κ1,κ1-TsL derivative had an unbound confused pyrazolyl. The molecularity of the latter four ranged from polymeric to dimeric to monomeric in the solid with increasing steric bulk of the ligand. The utility of these complexes in stoichiometric ligand-transfer reactions and in styrene aziridination was demonstrated. Thus, tricarbonylmanganese(I) complexes were prepared as kinetically inert models for comparative solution diffusion NMR studies. Also, [Fe(HL)2](OTf)2 was prepared for similar reasons and to compare the effects of anion on spin-crossover properties

Fr\'echet frames, general definition and expansions

We define an {\it $(X_1,\Theta, X_2)$-frame} with Banach spaces $X_2\subseteq X_1$, $|\cdot|_1 \leq |\cdot|_2$, and a $BK$-space (\Theta, \snorm[\cdot]). Then by the use of decreasing sequences of Banach spaces ${X_s}_{s=0}^\infty$ and of sequence spaces ${\Theta_s}_{s=0}^\infty$, we define a general Fr\' echet frame on the Fr\' echet space $X_F=\bigcap_{s=0}^\infty X_s$. We give frame expansions of elements of $X_F$ and its dual $X_F^*$, as well of some of the generating spaces of $X_F$ with convergence in appropriate norms. Moreover, we give necessary and sufficient conditions for a general pre-Fr\' echet frame to be a general Fr\' echet frame, as well as for the complementedness of the range of the analysis operator $U:X_F\to\Theta_F$.Comment: A new section is added and a minor revision is don

Silver(I) and Copper(I) Complexes of Semi‐Bulky Nitrogen‐Confused C‐Scorpionates

Two new sterically demanding nitrogen‐confused C‐scorpionate ligands with a bis(3,5‐diisopropylpyrazol‐1‐yl)methyl group bound to the 3‐ position of a normal pyrazole (HLiPr2) or an N‐toluenesulfonyl pyrazole (TsLiPr2) have been prepared. Reactions between the ligands (xLiPr2) and silver trifluoromethanesulfonate, AgOTf, gave four new compounds of the types [Ag(xLiPr2)](OTf) (x = Ts, 1a; x = H, 2a) or [Ag(xLiPr2)2](OTf) (x = Ts, 1b; x = H, 2b) depending on the initial metal:ligand ratio. Similarly, the reactions with [Cu(CH3CN)4](PF6) produce four new compounds of the type [Cu(xLiPr2)(CH3CN)](PF6) (x = Ts, 3a; x = H, 4a) or [Cu(xLiPr2)2](PF6) (x = Ts, 3b; x = H, 4b). The solid‐state structures of four derivatives (1a·acetone, 3a, 3b·CH2Cl2, and 4b·2THF) were determined by single‐crystal X‐ray diffraction while all complexes were characterized in CH3CN solution by NMR spectroscopy and ESI(+) MS. The eight new complexes catalyze the aziridination of styrene. The copper complexes were generally (but not exclusively) more active catalysts than their silver counterparts

Selective Isomer Formation and Crystallization-Directed Magnetic Behavior in Nitrogen-Confused C-Scorpionate Complexes of Fe(O\u3csub\u3e3\u3c/sub\u3eSCF\u3csub\u3e3\u3c/sub\u3e)\u3csub\u3e2\u3c/sub\u3e

The complex [Fe(HL*)2](OTf)2, 1, where HL* = bis(3,5-dimethylpyrazol-1-yl)(3-1H-pyrazole)methane, was prepared in order to compare its magnetic properties with those of the analogous parent complex, [Fe(HL)2](OTf)2, that lacks methyl groups on pyrazolyl rings and that undergoes spin crossover (SCO) from the low spin (LS) to the high spin (HS) form above room temperature. It was anticipated that this new semibulky derivative should favor the HS state and undergo SCO at a lower temperature range. During this study, six crystalline forms of 1 were prepared by controlling the crystallization conditions. Thus, when reagents are combined in CH3CN, an equilibrium mixture of cis and trans isomers is established that favors the latter below 311 K. The trans isomer can be isolated exclusively as a mixture of solvates, LS trans-1·2CH3CN and HS trans-1·4CH3CN, by cooling CH3CN solutions to −20 °C with the former being favored at high concentrations and short crystallization times. Subsequently, vapor diffusion of Et2O into CH3CN solutions of pure trans-1·2CH3CN gives solvate-free HS trans-1. Subjecting trans-1·2CH3CN to vacuum at room temperature gives microcrystalline trans-1·CH3CN, identified by elemental analysis and its distinct powder X-ray diffraction pattern. If an isomeric mixture of 1 is subject to room-temperature vapor diffusion, then a crystalline mixture of HS isomers cis-1 and trans-1 is obtained. Finally, slowly cooling hot acetonitrile solutions of isomeric mixtures of 1 to room temperature gives large prisms of HS co-1, a species with both cis and trans isomers in the unit cell. The complexes trans-1, trans-1·CH3CN, cis-1, and co-1 undergo SCO below 250 K while trans-1·xCH3CN (x = 2, 4) solvates do not undergo SCO before desolvation. Synopsis The complex, [Fe(HL*)2](OTf)2, 1, where HL* = bis(3,5-dimethylpyrazol-1-yl)(3-1H-pyrazole)methane, can be coerced to crystallize in one of four different forms from CH3CN solutions under normal laboratory conditions where each form has distinctive magnetic properties

Classical operators on the Hörmander algebras

We study the integration operator, the differentiation operator and more general differential operators on radial Fr´echet or (LB) H¨ormander algebras of entire functions. We analyze when these operators are power bounded, hypercyclic and (uniformly) mean ergodic.This research was partially supported by MEC and FEDER Project MTM2010-15200. The research of M. J. Beltran was also supported by grant F.P.U. AP2008-00604 and Programa de Apoyo a la Investigacion y Desarrollo de la UPV PAID-06-12, and the research of J. Bonet and C. Fernandez, by GVA under Project PROMETEOII/2013/013.Beltrán Meneu, MJ.; Bonet Solves, JA.; Fernández, C. (2015). Classical operators on the Hörmander algebras. Discrete and Continuous Dynamical Systems - Series A. 35(2):637-652. https://doi.org/10.3934/dcds.2015.35.637S63765235

Whitney’s extension theorem for ultradifferentiable functions of Beurling type

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43941/1/11512_2006_Article_BF02386123.pd

ПЕТРОХИМИЧЕСКИЕ И СТРУКТУРНЫЕ ХАРАКТЕРИСТИКИ МЕДНО-ПОРФИРОВОГО ОРУДЕНЕНИЯ В РУДОПРОЯВЛЕНИИ АСТАНЕ СРЕДНЕЙ ЧАСТИ МАГМАТИЧЕСКОЙ ДУГИ УРУМИЕ-ДОХТАР (ИРАН)

Within the Urumieh-Dokhtar Magmatic Arc in the central part of Iran, the formation of which is associated with the Neotethys closure, there are many porphyry copper deposits and ore occurrences. One of them is the Astaneh porphyry copper ore deposit, located in the central part of the Saveh-Ardestan ore region southeast of Ardestan city. The purpose of this study is to investigate the petrochemical characteristics of rocks and to determine the relationship between the distribution of porphyry copper mineralization and tectonic position of faults within the study area. To achieve the goal, there were used the structural and geological data obtained in the fieldwork, as well as the results of mineralogical and geochemical analyses. The obtained results show that rocks of different composition of the Astaneh ore deposit (andesite, andesite-basalt, basalt, trachybasalt) were formed in the suprasubduction zone, and probably in the environment prior to the collision of the of continental plates. Paragenetic relationships and mineralogical analysis show that the evolution of mineralization of the Astaneh ore deposit can be divided into three stages: pre-ore, hypogene and supergene mineralization. Geochemical research based on the study of the content of the major chemical elements in the rocks of the region shows that igneous rocks belong to calc-alkaline basalts and geodynamically can be attributed to the products of magmatism of the ensial island arc. The results concluded that the main stages of the formation of a porphyry copper ore deposit in the study area attain maximum spatio-temporal similarity with the tectonomagmatic phases of the development of the Neotethys Ocean. In addition, the Southern Ardestan fault, running through the study area and intersecting the basement structures, forms wide permeable zones favorable for the formation of porphyry copper deposits therein.В пределах магматической дуги Уромие-Дохтар в центральной части Ирана, образование которой связано с закрытием Неотетиса, расположено множество медно-порфировых месторождений и рудопроявлений. Одно из них – медно-порфировое рудопроявление Астане, которое находится в центральной части рудного района Саве-Ардестан, расположенного юго-западнее г. Ардестан. Целью данного исследования является изучение петрохимических характеристик горных пород и определение взаимосвязи между распределением меднопорфирового оруденения и положением тектонических разломов в пределах изучаемой территории. Для достижения цели были использованы структурно-геологические и минералого-геохимические данные, полученные как в ходе проведения полевых работ, так и по результатам лабораторных исследований. Результаты исследования доказывают, что разнообразные по составу горные породы рудопроявления Астане (андезит, андезибазальт, базальт, трахибазальт) сформировались в надсубдукционной зоне и, вероятно, в обстановке, предшествовавшей столкновению континентальных плит. Парагенетические связи и минералогический анализ показали, что эволюция минерализации рудопроявления Астане может быть разделена на три этапа: дорудный, рудный и гипергенный. Геохимические исследования, основанные на изучении содержания главных химических элементов в породах района, определяют, что магматические породы относятся к известково-щелочным базальтам и со стороны геодинамической обстановки могут быть отнесены к продуктам магматизма континентальной островной дуги энсиалического типа. В результате изучения был сделан вывод о том, что основные этапы формирования медно-порфирового рудопроявления на исследуемой территории демонстрируют максимальное временное и пространственное сходство с тектономагматическими фазами развития океана Неотетис. Кроме того, разлом Южный Ардестан, проходящий через изучаемую территорию и секущий структуры фундамента, образует широкие проницаемые зоны, благоприятные для формирования медно-порфировых рудопроявлений

Some results about diagonal operators on Köthe echelon spaces

[EN] Several questions about diagonal operators between Köthe echelon spaces are investigated: (1) The spectrum is characterized in terms of the Köthe matrices defining the spaces, (2) It is characterized when these operators are power bounded, mean ergodic or uniformly mean ergodic, and (3) A description of the topology in the space of diagonal operators induced by the strong topology on the space of all operators is given.This research was partially supported by MINECO Project MTM2016-76647-P and the grant PAID-01-16 of the Universitat Politècnica de València.Rodríguez-Arenas, A. (2019). Some results about diagonal operators on Köthe echelon spaces. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 113(4):2959-2968. https://doi.org/10.1007/s13398-019-00663-yS295929681134Agathen, S., Bierstedt, K.D., Bonet, J.: Projective limits of weighted (LB)-spaces of continuous functions. Arch. Math. 92, 384–398 (2009)Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. Math. 34(2), 401–436 (2009)Bennett, G.: Some elementary inequalities. Quart. J. Math. 38, 401–425 (1987)Bennett, G.: Factorizing the classical inequalities. Mem. Am. Math. Soc. (1996). https://doi.org/10.1090/memo/0576Bierstedt, K.D.: An introduction to locally convex inductive limits, Functional analysis and its applications (Nice, 1986), 35–133, ICPAM Lecture Notes. World Sci. Publishing, Singapore (1988)Bierstedt, K.D., Bonet, J.: Some aspects of the modern theory of Fréchet spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 97(2), 159–188 (2003)Bierstedt, K.D., Meise, R., Summers, W.H.: Köthe sets and Köthe sequence spaces, Functional Analysis, Holomorphy and Approximation Theory. North-Holland Math. Studies 71, 27–91 (1982)Bonet, J., Jordá, E., Rodríguez-Arenas, A.: Mean ergodic multiplication operators on weighted spaces of continuous functions. Mediterr. J. Math 15, 108 (2018)Crofts, G.: Concerning perfect Fréchet spaces and transformations. Math. Ann. 182, 67–76 (1969)Kellogg, C.N.: An extension of the Hausdorff–Young theorem. Michig. Math. J. 18, 121–127 (1971)Krengel, U.: Ergodic Theorems. de Gruyter, Berlin (1985)Meise, R., Vogt, D.: Introduction to Functional Analysis. Oxford University Press, New York (1997)Vasilescu, F.H.: Analytic Functional Calculus and Spectral Decompositions. D. Reidel Publ. Co., Dordrecht (1982)Wengenroth, J.: Derived Functors in Functional Analysis. Springer, Berlin (2003)Yosida, K.: Functional Analysis. Springer, Berlin (1980