Invariant slow manifold approach for exact dynamic inversion of singularly perturbed linear mechanical systems with admissible output constraints

We propose an approach for the exact dynamic inversion of singularly perturbed second-order linear systems through asymptotic expansion in a singular parameter. We show that the inversion solution, corresponding to the invariant slow manifold, can be expressed as a converging infinite series under desired output constraints composed of exponential support functions in the complex domain. We provide systematic mathematical procedures to obtain the closed-form invariant slow manifold, along with required admissible boundary conditions. Numerical examples are given to validate the proposed approach.     

Separation and identification of volatile compounds from liquid cultures of Trichoderma harzianum by GC-MS using three different capillary columns

A simple, fast, repeatable and less laborious sample preparation protocol was developed and applied for the analysis of biocontrol fungus Trichoderma harzianum strain FA1132 by using gas chromatography-mass spectrometry. The match factors for sample spectra with respect to the mass spectra library of fungal volatile compounds were determined and used to study the complex hydrocarbons and other volatile compounds, which were separated by using different capillary columns with nonpolar, medium polar and high polar stationary phases. To date, more than 278 volatile compounds (with spectral match factor at least 90%) such as normal saturated hydrocarbons (C7-C30), cyclohexane, cyclopentane, fatty acids, alcohols, esters, sulfur-containing compounds, simple pyrane and benzene derivatives have been identified. Most of these compounds have not previously been reported. The method described in this paper is a more convenient research tool for the detection of volatile compounds from the cultures of T. harzianum.     

Stripe Order and Spin Dynamics in Nickelates

We report zero field μSR experiments on the lanthanum nickelate La_2−x Sr _x NiO_4+δ system with strontium doping level x between 0 and 0.6. In a single crystal with x=0.33 the internal field distribution shows two separated signals reflecting the antiferromagnetic domains and the non magnetic antiphase domain walls in the spin and charge ordered state below 190 K. Below 70 K a broadening of the low field line is observed. A similar behavior is observed in polycrystalline samples with 0.2≤x≤0.5. This revised version was published online in September 2006 with corrections to the Cover Date.     

Atomically dispersed Fe atoms anchored on COF-derived N-doped carbon nanospheres as efficient multi-functional catalysts

Non-noble metal isolated single atom site (ISAS) catalysts have attracted much attention due to their low cost, ultimate atom efficiency and outstanding catalytic performance. Herein, atomically dispersed Fe atoms are prepared by a covalent organic framework (COF)-absorption–pyrolysis strategy. The obtained Fe ISASs anchored on COF-derived N-doped carbon nanospheres (Fe-ISAS/CN) served as a multi-functional catalyst in electro-catalysis and organic catalysis, exhibiting better catalytic performance than commercial Pt/C for the ORR with good stability and methanol tolerance. Besides electro-catalysis, the Fe-ISAS/CN also showed outstanding catalytic performance in organic reactions, such as the selective oxidation of ethylbenzene to acetophenone and dehydrogenation of 1,2,3,4-tetrahydroquinoline with excellent reactivity, selectivity, stability and recyclability. Co and Ni ISAS materials can also be prepared by this method, suggesting that it is a general strategy to obtain metal ISAS catalysts. This work will provide new insight into the design of COF-derived metal ISAS multi-functional catalysts for electro-catalysis and organic reactions using rationally designed synthetic routes and the optimized structure of substrates.

Fe isolated single-atom sites anchored on COF-derived N-doped carbon nanospheres as efficient multi-functional catalysts.     

Inverse semigroups determined by their lattices of convex inverse subsemigroups I

Every inverse semigroup possesses a natural partial order and therefore convexity with respect to this order is of interest. We study the extent to which an inverse semigroup is determined by its lattice of convex inverse subsemigroups; that is, if the lattices of two inverse semigroups are isomorphic, how are the semigroups related? We solve this problem completely for semilattices and for inverse semigroups in general reduce it to the case where the lattice isomorphism induces an isomorphism between the semilattices of idempotents of the semigroups. For many inverse semigroups, such as the monogenic ones, this case is the only one that can occur. In Part II, a study of the reduced case enables us to prove that many inverse semigroups, such as the free ones, are strictly determined by their lattices of convex inverse subsemigroups, and to show that the answer obtained here for semilattices can be extended to a broad class of inverse semigroups, including all finite, aperiodic ones. Received September 24, 2002; accepted in final form December 15, 2002.     

Hierarchical Decompositions and Circular Ray Shooting in Simple Polygons

A hierarchical decomposition of a simple polygon is introduced. The hierarchy has logarithmic depth, linear size, and its regions have at most three neighbors. Using this hierarchy, circular ray shooting queries in a simple polygon on n vertices can be answered in O(log² n) query time and O(n log n) space. If the radius of the circle is fixed, the query time can be improved to O(log n) and the space to O(n).     

Spanning Trees Crossing Few Barriers

We consider the problem of finding low-cost spanning trees for sets of $n$ points in the plane, where the cost of a spanning tree is defined as the total number of intersections of tree edges with a given set of $m$ barriers. We obtain the following results: (i) if the barriers are possibly intersecting line segments, then there is always a spanning tree of cost $O(\min(m^2,m\sqrt{n}))$; (ii) if the barriers are disjoint line segments, then there is always a spanning tree of cost $O(m)$; (iii) ] if the barriers are disjoint convex objects, then there is always a spanning tree of cost $O(n+m)$. All our bounds are worst-case optimal, up to multiplicative constants.     

Texture dependence of capillary instabilities in nematic liquid crystalline fibres

Static and dynamic linear analyses of axisymmetric capillary instabilities in textured nematic liquid crystalline fibres are performed using the equations of nemato-statics and inviscid nemato-dynamics. Three representative textures, viz. axial, onion, and radial, are analysed to show all possible effects of Frank gradient elasticity on the wavelength selection and growth rate of peristaltic modes driven by surface area reduction. It is found that Frank elasticity may tend to stabilize or destabilize the fibre, depending on the initial fibre texture. Axial textures tend to stabilize the fibre through the director splay-bend distortions driven by surface tilting. Onion textures are destabilized by decreasing azimuthal bend elastic energy caused by surface displacement. Radial textures exhibit a stabilizing tilt mechanism due to bend modes and a destabilizing displacement mechanism due to splay modes, but the former is predicted to be dominant. The static analysis provides good estimates of the instability thresholds while the transient energy balance provides information on the fastest growing modes. The static and dynamic results are compared and shown to be fully consistent. The couplings between splay and/or bend distortions, surface tilting, and surface displacement in nematic fibres are characterized and used to explain the deviations from the classical Rayleigh instability.