Übergangsmetallkomplexe mit Schwefelliganden, LXI / Transition Metal Complexes with Sulfur Ligands, LXI

Abstract

Acta Technologica Agriculturae 1/2016Dušan Páleš et al.The most effective way for determination of curves for practical use is to use a set of control points. These control points can be accompanied by other restriction for the curve, for example boundary conditions or conditions for curve continuity (Sederberg, 2012). When a smooth curve runs only through some control points, we refer to curve approximation. The B-spline curve is one of such approximation curves and is addressed in this contribution. A special case of the B-spline curve is the Bézier curve Rédl et al., 2014). The B-spline curve is applied to a set of control points in a space, which were obtained by measurement of real vehicle movement on a slope (Rédl, 2007(Rédl, , 2008. Data were processed into the resulting trajectory (Rédl, 2012;Rédl and Kučera, 2008). Except for this, the movement of the vehicle was simulated using motion equations (Rédl, 2003;Rédl and Kročko, 2007). B-spline basis functionsBézier basis functions known as Bernstein polynomials are used in a formula as a weighting function for parametric representation of the curve (Shene, 2014). B-spline basis functions are applied similarly, although they are more complicated. They have two different properties in comparison with Bézier basis functions and these are: 1) solitary curve is divided by knots, 2) basis functions are not nonzero on the whole area. Every B-spline basis function is nonzero only on several neighbouring subintervals and thereby it is changed only locally, so the change of one control point influences only the near region around it and not the whole curve.These numbers are called knots, the set U is called the knot vector, and the half-opened interval 〈u i , u i + 1 ) is the i-th knot span. Seeing that knots u i may be equal, some knot spans may not exist, thus they are zero. If the knot u i appears p times, hence u i = u i + 1 = ... = u i + p -1 , where p >1, u i is a multiple knot of multiplicity p, written as u i (p). If u i is only a solitary knot, it is also called a simple knot. If the knots are equally spaced, i.e. (u i + 1 -u i ) = constant, for every 0 ≤ i ≤ (m -1), the knot vector or knot sequence is said uniform, otherwise it is non-uniform.Knots can be considered as division points that subdivide the interval 〈u 0 , u m 〉 into knot spans. All B-spline basis functions are supposed to have their domain on 〈u 0 , u m 〉. We will use u 0 = 0 and u m = 1.To define B-spline basis functions, we need one more parameter k, which gives the degree of these basis functions. Recursive formula is defined as follows:This definition is usually referred to as the Cox-de Boor recursion formula. If the degree is zero, i.e. k = 0, these basis functions are all step functions that follows from Eq. (1). N i, 0 (u) = 1 is only in the i-th knot span 〈u i , u i + 1 ). For example, if we have four knots u 0 = 0, u 1 = 1, u 2 = 2 and u 3 = 3, knot spans 0, 1 and 2 are 〈0, 1), 〈1, 2) and 〈2, 3), and the basis functions of degree 0 are N 0, 0 (u) = 1 on interval 〈0, 1) Acta In this co...

Stereochemistry of Transition-Metal Dinitrosyl Complexes. A Molecular Orbital Rationale for the Attracto and Repulso Conformations

“…In this study, we have not concerned ourselves with six-coordinate {M­(NO) 2 } (M = V, Cr, , Mo) complexes, the majority of which exhibit linear nitrosyls; the structures of these species are readily understood in terms of elementary back-bonding considerations. The unambiguous attracto conformation of an {Mo­(NO) 2 } porphyrin complex (CSD: DNSPMO) was analyzed in an earlier DFT study and is thought to reflect stereoelectronic constraints imposed by the porphyrin ligand .…”

Coordination and Organometallic Chemistry of Metal−NO Complexes

“…Numerous nitrosyl complexes of the group 6 metals with sulfur-dominated coordination spheres have been synthesized and characterized by Sellmann and co-workers, often in the quest for complexes modeling functional characteristics of metal sulfur oxidoreductases. Examples of such complexes include Cr(NO) x (‘S 4 ') y ( x = 2, y = 1; x =1, y = 2), [W(NO) 2 (‘S 2 ') 2 ] 2- , W(L)(NO)(‘S 4 ') (L = NO, NPMe 3 , NPEt 3 ), (μ-O)[W(NO)(‘S 4 ')] 2 , and MX(NO)(‘S 4 ') (M = Mo, W; X = Cl, SR, NHNR 2 ) in which ‘S 2 ' 2- = 1,2-benzenedithiolate(2−) and ‘S 4 ' 2- = 1,2-bis(2-mercaptophenylthio)ethane(2−). − Hydrolysis of MoX(NO)(‘S 4 ') complexes (X = Cl, Br, NMe 2 , NPMe 3 ) affords (μ-O)[Mo(NO)(‘S 4 ')] 2 in which the μ-oxo ligand acts as a σ,π donor to each metal center . Redox-substitution reactions of Mo III (SPh)(NO)(‘S 4 ') with phosphines yield the 17e complexes, Mo II (PR 3 )(NO)(‘S 4 '), which can be oxidized or reduced electrochemically .…”

Carboxy‐thioether‐thiolato titanium–graphene oxide nanocomposite as drug delivery system for targeted cancer therapy: Design, characterization, bovine serum albumin binding study, and biological evaluation

“…[4] A wide variety of transition metals can bind to the tetradentate thioether thiolate ligand [=1,2-bis(2-mercaptophenylthio)ethane], and the resulting [M('S 4 ')] complex segments can also coordinate a wide range of co ligands, resulting in six-coordinate complexes. [5][6][7][8][9][10][11][12][13] Because of their potent activity against cisplatin-resistant tumors and low toxicity, titanium (IV) complexes have shown a significant effect on cancer cells in both humans and animals. The first examples of metal-based anticancer agents with potential antitumor action on cisplatin-sensitive and resistant cells were titanocene dichloride (Cp 2 TiCl 2 ) and budotitane [(bzac) 2 Ti (OEt) 2 ] (Scheme 1a and b).…”