Synthesis and structure of dimeric bis(isothiocyanato)tris (4-methylpyridine)nickel (II)

Summary The Ni₂(NCS)₄(4-Methylpyridine)6 complex has been prepared crystalline from methanolic solutions of Ni(NCS)2(4-Methylpyridine)4. Three dimensional x-ray diffraction data were collected by means of an automated single crystal diffractometer. The structure was solved by Patterson methods and refined to a final R value of 0.075, based on 2422 observed_ reflections. The compound crystallizes in space group P1 with one dimeric molecule in a unit cell of dimensions a = 10.57(1), 6 = 14.06(1), c = 8.66(1) Å, = 105.2(1), = 114.8(1), y = 95.6(1)°. The Ni atoms have distorted octahedral coordination with one sulfur and five nitrogen atoms - two of the four thiocyanate groups form a double bridge between the neighbouring Ni atoms.4-MePy = 4-Methylpyridine     

Sampling and Reconstruction in Distinct Subspaces Using Oblique Projections

Journal of Fourier Analysis and Applications - We study reconstruction operators on a Hilbert space that are exact on a given reconstruction subspace. Among those the reconstruction operator...     

Covering the Plane with Translates of a Triangle

The minimum density of a covering of the plane with translates of a triangle is frac32frac{3}{2} .     

Weil Representations of Symplectic Groups Over Rings

We are interested in Weil representations of Sp(2n, R), whereR is the ring Z/p^lZ, p is an odd prime and l is a positive integer,or, more generally, R = O/p^l, where O is the ring of integersof a local field, p is the maximal ideal of O and O/p has oddcharacteristic. One reason for this interest is that a continuousfinite-dimensional complex representation of Sp(2n, O) has tofactor through a representation of Sp(2n, O/p^l) for some l.     

Mean-type mappings and invariant curves

The problem of invariant curves for continuous mean-type mappings is considered. The obtained results are applied in solving some functional equations.     

Limit properties of induced mappings

Given a class of mappings f between continua, near- stands for the class of uniform limits of sequences of mappings from . Let 2^f and C(f) mean the induced mappings between hyperspaces. Relations are studied between the conditions: f near-, 2^f near- and C(f) near-. A special attention is paid to the classes of open and of monotone mappings.     

Semigroups of partial transformations with kernel and image restricted by an equivalence

Semigroup Forum - For an arbitrary set X and an equivalence relation $$mu$$ on X, denote by $$P_mu (X)$$ the semigroup of partial transformations $$alpha$$ on X such that $$xmu subseteq x(ker...     

Stereochemical Behavior of Pairs of P-stereogenic Phosphanyl Groups at the Dimethylxanthene Backbone

The P-stereogenic bis(phosphanes) 7 and 9 , featuring pairs of P(Mes)-ethynyl or vinyl substituents at the dimethyl xanthene backbone show rather low barriers of stereochemical inversion at phosphorus. π-Conjugative effects are probably causing these low inversion barriers. Compound 7 reacted with B(C₆F₅)₃ to form the nine-membered heterocyclic product 10 , featuring a [P]−C≡C−B(C₆F₅)₃ substituent. Compound 7 was converted to the bis[P(Mes)vinyl] xanthene derivative 9 , which gave the zwitterionic P(H)(Mes)−CH=CH−B(C₆F₅)₃ containing product 16 upon treatment with B(C₆F₅)₃. Thermally induced epimerization barriers at phosphorus of ca. 20 to 27 kcal mol⁻¹ were calculated by DFT for the alkenyl- and alkynyl-P derived systems 6 to 9 , 15 and 16 and experimentally determined for the examples 7 and 16 .     

A New Look at Molecular and Electronic Structure of Homoleptic Diiron(II,II) Complexes with N,N-Bidentate Ligands: Combined Experimental and Theoretical Study

Paddlewheel-type binuclear complexes featuring metal−metal bonding have been the subject of widespread interest due to fundamental concern in their electronic structures and potential applications. Here, we explore the molecular and electronic structures of diiron(II,II) complexes with N,N’-diarylformamidinate ligands. While a paddlewheel-type diiron(II,II) complex with N,N’-diphenylformamidinate ligands (DPhF) exhibits the centrosymmetric [Fe₂(μ-DPhF)₄] structure, a minor alteration in the ligand system, i. e., switching from phenyl to p-tolyl N-substituted formamidinate ligand (DTolF), resulted in the isolation of an unprecedented non-centrosymmetric [Fe(μ-DTolF)₃Fe(κ²-DTolF)] complex. Both complexes were characterized using single-crystal X-ray diffraction, magnetic measurements, ⁵⁷Fe Mössbauer spectroscopy, and cyclic voltammetry along with high-level ab-initio calculations. The results provide a new view on a range of factors controlling the ground-state electronic configuration and structural diversity of homoleptic diiron(II,II) complexes. Model calculations determined that the Mayer bond orders for Fe−Fe interactions are significantly lower than 1 and equal to 0.15 and 0.28 for [Fe₂(μ-DPhF)₄] and [Fe(μ-DTolF)₃Fe(κ²-DTolF)], respectively.     

Online packing of d-dimensional boxes into the unit cube

Periodica Mathematica Hungarica - Any sequence of d-dimensional boxes of edge length smaller than or equal to 1 with total volume not greater than $$(3-2sqrt{2})cdot 3^{-d}$$ can be packed online...