On the Characterization of the Dynamic Performances of Planar Manipulators

The characterization of the dynamic performances of a manipulator is important both to compare different manipulators and to improve the dynamic performances of a manipulator during the design stage. In a previous paper the concepts of swiftness and of dynamic isotropy were used to characterize some dynamic performances of 3-dof manipulators. This paper analyzes the usefulness of these concepts for three-dof planar manipulators and shows that the concept of swiftness is still significant, whereas the concept of dynamic isotropy has no practical interest. Moreover, it introduces three new dynamic properties that are useful in the design of a 3-dof planar manipulator. Finally, it proposes some indices that measure both the swiftness and the three new dynamic properties and shows how to use them, both for evaluating the dynamic performances of a given 3-dof planar manipulator and for improving the dynamic performances during its design.     

Smooth and discontinuous junctions in the p-system

Consider the p-system describing the subsonic flow of a fluid in a pipe with section a=a(x). We prove that the resulting Cauchy problem generates a Lipschitz semigroup, provided the total variation of the initial datum and the oscillation of a are small. An explicit estimate on the bound of the total variation of a is provided, showing that at lower fluid speeds, higher total variations of a are acceptable. An example shows that the bound on TV(a) is mandatory, for otherwise the total variation of the solution may grow arbitrarily.     

Convergence of the Law of the Environment Seen by the Particle for Directed Polymers in Random Media in the <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> Region

We consider the model of directed polymers in an i.i.d. Gaussian or bounded environment (Imbrie and Spencer in J. Stat. Phys. 52(3/4), 609–626, 1988; Carmona and Hu in Probab. Theory Relat. Fields 124(3), 431–457, 2002; Comets et al. in Adv. Stud. Pure Math. 39, 115–142, 2004) in the L ² region. We prove the convergence of the law of the environment seen by the particle.     

Arithmetical Rank of Squarefree Monomial Ideals Generated by Five Elements or with Arithmetic Degree Four

Let I be a squarefree monomial ideal of a polynomial ring S. In this article, we prove that the arithmetical rank of I is equal to the projective dimension of S/I when one of the following conditions is satisfied: (1) μ(I) ≤5; (2) arithdeg I ≤ 4.     

Reflecting diffusions and hyperbolic Brownian motions in multidimensional spheres

We consider diffusion processes $ {{\left( {{{{\underline{\mathrm{X}}}}_d}(t)} \right)}_{{t\geqslant 0}}} $ moving inside spheres $ S_R^d $ ? ? ^d and reflecting orthogonally on their surfaces. We present stochastic differential equations governing the reflecting diffusions and explicitly derive their kernels and distributions. Reflection is obtained by means of the inversion with respect to the sphere $ S_R^d $ . The particular cases of Ornstein–Uhlenbeck process and Brownian motion are examined in detail. The hyperbolic Brownian motion on the Poincaré half-space ? _d is examined in the last part of the paper, and its reflecting counterpart within hyperbolic spheres is studied. Finally, a section is devoted to reflecting hyperbolic Brownian motion in the Poincaré disc D within spheres concentric with D.     

A Size‐Flexible Organometallic Box for the Encapsulation of Fullerenes

A palladium‐cornered molecular square with four pyrene‐bis(imidazolylidene) bridging ligands is reported. This metallo‐polygon can encapsulate C₆₀ and C₇₀. The X‐ray diffraction structures of the empty cage as well as the cages complexed with both fullerenes are described. The fullerene encapsulation produces perturbations in the structural parameters of the metallo‐square, showing that it can adjust the shape of its cavity to the size of each fullerene.     

Oxygen‐Triggered Switchable Polymerization for the One‐Pot Synthesis of CO2‐Based Block Copolymers from Monomer Mixtures

Switchable polymerization provides the opportunity to regulate polymer sequence and structure in a one‐pot process from mixtures of monomers. Herein we report the use of O₂ as an external stimulus to switch the polymerization mechanism from the radical polymerization of vinyl monomers mediated by (Salen)Co^III?R [Salen=N,N′‐bis(3,5‐di‐tert‐butylsalicylidene)‐1,2‐cyclohexanediamine; R=alkyl] to the ring‐opening copolymerization (ROCOP) of CO₂/epoxides. Critical to this process is unprecedented monooxygen insertion into the Co?C bond, as rationalized by DFT calculations, leading to the formation of (Salen)Co^III?O?R as an active species to initiate ROCOP. Diblock poly(vinyl acetate)‐b‐polycarbonate could be obtained by ROCOP of CO₂/epoxides with preactivation of (Salen)Co end‐capped poly(vinyl acetate). Furthermore, a poly(vinyl acetate)‐b‐poly(methyl acrylate)‐b‐polycarbonate triblock copolymer was successfully synthesized by a (Salen)cobalt‐mediated sequential polymerization with an O₂‐triggered switch in a one‐pot process.     

Mirror fibrations and root stacks of weighted projective spaces

We show that the orbifold Chow ring of a root stack over a well-formed weighted projective space can be naturally seen as the Jacobian algebra of a function on a singular variety.     

Determination of zearalenone and its metabolites in urine samples by liquid chromatography with electrochemical detection using a carbon nanotube-modified electrode

A simple and sensitive method for the separation and determination of zearalenone (ZON) and its secondary metabolites, namely beta-zearalenol (beta-ZAL), beta-zearalanol (beta-ZOL), alpha-zearalenol (alpha-ZAL), alpha-zearalanol (alpha-ZOL) and zearalanone (ZAN) in urine (human, bovine and swine) samples is proposed. The method comprises previous clean-up and pre-concentration on C(18) adsorption cartridges of the analytes followed by liquid chromatographic separation and direct electrochemical detection at +0.85mV using a carbon nanotube-modified glassy carbon electrode (CNT-GCE). This method allows the determination of beta-ZAL, beta-ZOL, alpha-ZAL, alpha-ZOL, ZAN and ZON in a linear range between 5 and 50ngmL(-1), with relative standard deviation values lower than 6.9% (intra-day) and 7.1% (inter-day), in all cases. Detection limits ranging between 1.3ngmL(-1) (beta-ZOL, alpha-ZAL, alpha-ZOL) and 1.4ngmL(-1) (beta-ZAL, ZAN, ZON) were achieved. The usefulness of the proposed method was demonstrated by the analysis of spiked and natural samples of human, bovine and swine urine samples.