Rolling Against a Sphere: The Non-transitive Case

We study the control system of a Riemannian manifold M of dimension n rolling on the sphere \(S^n\). The controllability of this system is described in terms of the holonomy of a vector bundle connection which, we prove, is isomorphic to the Riemannian holonomy group of the cone C(M) of M. Using Berger’s list, we reduce the possible holonomies to a few families. In particular, we focus on the cases where the holonomy is the unitary and the symplectic group. In the first case, using the rolling formalism, we construct explicitly a Sasakian structure on M; and in the second case, we construct a 3-Sasakian structure on M.     

Fast and Simple Preparation of a Sensor Based on Electrochemically Reduced Graphene Oxide (rGO) for the Determination of Zopiclone in Pharmaceutical Dosage by Square Wave Adsorptive Stripping Voltammetry (SWAdSV)

The interactions of zopiclone with electrochemically reduced graphene oxide (rGO) modified electrode were examined. A comparison of GC/rGO and glassy carbon electrode (GC) by electrochemical impedance spectroscopy and scanning electrochemical microscopy (SECM) shows that the modified surface is much less conductive than GC. The role of rGO is to act as a site of specific adsorption of the analyte. Molecular dynamics showed that the monoanionic form of zopiclone presents more interactions with defects of rGO. The analytical methodology allowed obtaining a linearity of 10–130 μg L⁻¹, with a limit of detection of 2.14 μg L⁻¹ using SWAdSV at pH 10.0.     

Multivariate generalized Bernstein polynomials: identities for orthogonal polynomials of two variables

We introduce polynomials $B^n_{k}(\boldmath{x};\omega|q)$ of total degree n, where $\boldmath{k} = (k_1,\ldots,k_d)\in\mathbb N_0^d, \; 0\le k_1+\ldots+k_d\le n$ , and $\boldmath{x}=(x_1,x_2,\ldots,x_d)\in\mathbb R^d$ , depending on two parameters q and ω, which generalize the multivariate classical and discrete Bernstein polynomials. For ω=0, we obtain an extension of univariate q-Bernstein polynomials, introduced by Phillips (Ann Numer Math 4:511–518, 1997). Basic properties of the new polynomials are given, including recurrence relations, q-differentiation rules and de Casteljau algorithm. For the case d=2, connections between $B^n_{k}(\boldmath{x};\omega|q)$ and bivariate orthogonal big q-Jacobi polynomials—introduced recently by the first two authors—are given, with the connection coefficients being expressed in terms of bivariate q-Hahn polynomials. As limiting forms of these relations, we give connections between bivariate q-Bernstein and Dunkl’s (little) q-Jacobi polynomials (SIAM J Algebr Discrete Methods 1:137–151, 1980), as well as between bivariate discrete Bernstein and Hahn polynomials.     

Synthesis, structure and magnetic properties of a decametallic Ni single-molecule magnet

Ferromagnetic exchange between the ten Ni2+ ions in the complex [Ni10(tmp)2(N3)8(acac)6(MeOH)6] leads to a spin ground state of S = 10; single crystal M vs. H studies reveal the temperature and sweep rate dependent hysteresis loops expected for a single-molecule magnet.     

Comparative study of two analytical methods to the determination of boron in leachate samples from sanitary landfills and groundwater for routine analysis and feasible on-site environmental monitoring

Two analytical methods as inductively coupled plasma optical emission spectrometry (inductively coupled plasma optical emission spectroscopy (ICP-OES)) and azomethine-H UV-Vis-based method were compared statistically, to evaluate their analytical characteristics and applicability to the determination of boron in leachates (complex matrix) from sanitary landfills (SLs) and groundwater (simple matrix) from different sampling points near SLs. Calibration curves and standard addition methods were used for this purpose. Azomethine-H UV-Vis-based procedure has proven better precision and accuracy than ICP-OES. However, statistical analysis (F-test and t-test) does not show significant differences between these two methods, achieving concentration range of up to 10 mg L^?1 of the boron in both simple and complex matrices. Due to low cost and gentle-to-operate easy-accessible system, the azomethine-H UV-Vis-based method was therefore proposed (rather than ICP-OES) for routine analysis and for feasible on-site monitoring of boron in SLs, with respect to satisfy Chilean Standard 409 (NCh409) related to drinking water policy.     

Guest‐, Light‐ and Thermally‐Modulated Spin Crossover in [FeII2] Supramolecular Helicates

A new bis(pyrazolylpyridine) ligand (H₂L) has been prepared to form functional [Fe₂(H₂L)₃]⁴⁺ metallohelicates. Changes to the synthesis yield six derivatives, X@[Fe₂(H₂L)₃]X(PF₆)₂?xCH₃OH ( 1 , x=5.7 and X=Cl; 2 , x=4 and X=Br), X@[Fe₂(H₂L)₃]X(PF₆)₂?yCH₃OH?H₂O ( 1 a , y=3 and X=Cl; 2 a , y=1 and X=Br) and X@[Fe₂(H₂L)₃](I₃)₂?3 Et₂O ( 1 b , X=Cl; 2 b , X=Br). Their structure and functional properties are described in detail by single‐crystal X‐ray diffraction experiments at several temperatures. Helicates 1 a and 2 a are obtained from 1 and 2 , respectively, by a single‐crystal‐to‐single‐crystal mechanism. The three possible magnetic states, [LS–LS], [LS–HS], and [HS–HS] can be accessed over large temperature ranges as a result of the structural nonequivalence of the Fe^II centers. The nature of the guest (Cl^? vs. Br^?) shifts the spin crossover (SCO) temperature by roughly 40 K. Also, metastable [LS–HS] or [HS–HS] states are generated through irradiation. All helicates (X@[Fe₂(H₂L)₃])³⁺ persist in solution.     

Structural and Magnetic Diversity in Alkali‐Metal Manganate Chemistry: Evaluating Donor and Alkali‐Metal Effects in Co‐complexation Processes

By exploring co‐complexation reactions between the manganese alkyl Mn(CH₂SiMe₃)₂ and the heavier alkali‐metal alkyls M(CH₂SiMe₃) (M=Na, K) in a benzene/hexane solvent mixture and in some cases adding Lewis donors (bidentate TMEDA, 1,4‐dioxane, and 1,4‐diazabicyclo[2,2,2] octane (DABCO)) has produced a new family of alkali‐metal tris(alkyl) manganates. The influences that the alkali metal and the donor solvent impose on the structures and magnetic properties of these ates have been assessed by a combination of X‐ray, SQUID magnetization measurements, and EPR spectroscopy. These studies uncover a diverse structural chemistry ranging from discrete monomers [(TMEDA)₂MMn(CH₂SiMe₃)₃] (M=Na, 3 ; M=K, 4 ) to dimers [{KMn(CH₂SiMe₃)₃?C₆H₆}₂] ( 2 ) and [{NaMn(CH₂SiMe₃)₃}₂(dioxane)₇] ( 5 ); and to more complex supramolecular networks [{NaMn(CH₂SiMe₃)₃}_∞] ( 1 ) and [{Na₂Mn₂(CH₂SiMe₃)₆(DABCO)₂}_∞] ( 7 )). Interestingly, the identity of the alkali metal exerts a significant effect in the reactions of 1 and 2 with 1,4‐dioxane, as 1 produces coordination adduct 5 , while 2 forms heteroleptic [{(dioxane)₆K₂Mn₂(CH₂SiMe₃)₄(O(CH₂)₂OCH=CH₂)₂}_∞] ( 6 ) containing two alkoxide–vinyl anions resulting from α‐metalation and ring opening of dioxane. Compounds 6 and 7 , containing two spin carriers, exhibit antiferromagnetic coupling of their S=5/2 moments with varying intensity depending on the nature of the exchange pathways.     

Permanence of stability for a class of system of differential equations with two delays

The paper studies a class of a system of linear retarded differential difference equations with several parameters. It presents some sufficient conditions under which no stability changes for an equilibrium point occurs. Application of these results is given.     

Quantification of Lamotrigine in Human Serum by High-Performance Thin-Layer Chromatography

JPC – Journal of Planar Chromatography – Modern TLC - An HPTLC method with densitometric detection at 280 nm has been established for quantification of lamotrigine in human serum....     

Highly enantioselective organocatalytic synthesis of piperidines. Formal synthesis of (−)-Paroxetine

A highly enantioselective organocatalytic synthesis of piperidines is reported. The reaction is catalyzed by simple and commercially available secondary amines, affording the corresponding adducts with high yields and enantioselectivities. Moreover, this reaction is used for the formal synthesis of (−)-Paroxetine, a blockbuster drug, in only three steps.