Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

Self-affine crossover length in a layered silicate deposit

Self-affine dehydrated colloidal deposits on fresh mica surfaces of the synthetic layered silicate 2:1 smectite clay laponite have been studied by means of atomic force microscopy (AFM). AFM images of these prepared assemblies of sol and gel aggregates have been analyzed both by means of standard AFM Fourier software and a wavelet method. The deposited surfaces show a persistence to antipersistent crossover with a clay concentration dependent crossover length. It is concluded that the crossover length is associated with aggregate size, and further that the persistent roughness at small length scales signals near compact clusters of fractal dimension three, whereas the antipersistent roughness at large length scales signals a sedimentation process.

Observation of stable phase jump lines in convection of a twisted nematic liquid crystal

We report observations of stable, localized, linelike structures in the spatially periodic pattern formed by nematic electroconvection, along which the phase of the pattern jumps by pi. With increasing electric voltage, these lines form a gridlike structure that goes over into a structure indistinguishable from the well-known grid pattern. We present theoretical arguments that suggest that the twisted cell geometry we are using is indirectly stabilizing the phase jump lines, and that the phase jump lines lattice is caused by an interaction of phase jump lines and a zig-zag instability of the surrounding pattern.

Equivalent Circuit Model of Twisted Split Ring Frequency Selective Surfaces

This paper proposes a wideband equivalent circuit model for a twisted split ring frequency selective surface (FSS). Such surfaces can be used for modelling and design of polarisation sensitive surfaces such as circularly polarized selective surfaces as well as structures with asymmetric transmission. The proposed model is based extraction of equivalent circuit parameters from a single split ring (SRR) FSS and magnetic coupling from periodic eigenmode analysis of the coupled SRR. The resulting equivalent circuit model demonstrates excellent agreement with full-wave simulations.

Self-assembled triple helicates with preferential helicity

The enantiomerically pure ligands LRR and LSS (N,N'-bis(-2,2'-bipyridyl-5-yl)carbonyl-(1S/R,2S/R)-(+/-)-1,2-diaminocyclohexane) have been synthesised by linking two 2,2'-bipyridine units by (R,R)- and (S,S)-1,2-diaminocyclohexane respectively. The crystal structure confirmed that the ligand had a twisted orientation between the two chelating units. The reaction of LRR and LSS with Fe(II), Co(III), Cd(II) and Zn(II) afforded dinuclear complexes confirmed by ES mass spectroscopy. CD spectroscopy indicated that the chiral diaminocyclohexane conferred helicity to the metal centre giving a dominant triple helicate diastereoisomer, with the LRR ligand giving a delta-configuration of each metal centre (P helicate) and the LSS ligand a lambda configuration (M helicate). 1H NMR spectroscopy confirmed a dominant major diastereoisomer with cadmium. The Zn(II) and Cd(II) complexes however were observed to undergo rapid ligand dissociation in solution.

Brief review of invariant texture analysis methods

This paper considers invariant texture analysis. Texture analysis approaches whose performances are not affected by translation, rotation, affine, and perspective transform are addressed. Existing invariant texture analysis algorithms are carefully studied and classified into three categories: statistical methods, model based methods, and structural methods. The importance of invariant texture analysis is presented first. Each approach is reviewed according to its classification, and its merits and drawbacks are outlined. The focus of possible future work is also suggested.

On velocity-based local model networks for nonlinear identification

This paper exposes the strengths and weaknesses of the recently proposed velocity-based local model (LM) network. The global dynamics of the velocity-based blended representation are directly related to the dynamics of the underlying local models, an important property in the design of local controller networks. Furthermore, the sub-models are continuous-time and linear providing continuity with established linear theory and methods. This is not true for the conventional LM framework, where the global dynamics are only weakly related to the affine sub-models. In this paper, a velocity-based multiple model network is identified for a highly nonlinear dynamical system. The results show excellent dynamical modelling performances, highlighting the value of the velocity-based approach for the design and analysis of LM based control. Three important practical issues are also addressed. These relate to the blending of the velocity-based local models, the use of normalised Gaussian basis functions and the requirement of an input derivative.

Constructing networks of continuous-time velocity-based models

A conventional local model (LM) network consists of a set of affine local models blended together using appropriate weighting functions. Such networks have poor interpretability since the dynamics of the blended network are only weakly related to the underlying local models. In contrast, velocity-based LM networks employ strictly linear local models to provide a transparent framework for nonlinear modelling in which the global dynamics are a simple linear combination of the local model dynamics. A novel approach for constructing continuous-time velocity-based networks from plant data is presented. Key issues including continuous-time parameter estimation, correct realisation of the velocity-based local models and avoidance of the input derivative are all addressed. Application results are reported for the highly nonlinear simulated continuous stirred tank reactor process.

Molecular systematics of Ceramium and Centroceras (Ceramiaceae, Rhodophyta) from Brazil

Morphological investigations identified 11 Ceramium Roth species, of the 18 previously reported from Brazil. Phylogenetic analyses of sequences of the chloroplast-encoded rbcL gene confirmed the presence of seven of these species. Three other species are reported from Brazil for the first time. Ceramium affine Setchell & Gardner and C. filicula Harvey ex Womersley were previously known only from the Pacific Ocean (Mexico and Australia, respectively). A new species, C. fujianum Barros-Barreto et Maggs sp. nov., is described here. Its general habit is similar to that of C. strictum sensu Harvey from Europe but it has one less periaxial cell than C. strictum; its cortical filament arrangement is closest to C. deslongchampsii Chauvin ex Duby, also from Europe, but whorled tetrasporangia partially covered by cortical cells differ strikingly from the naked protruding tetrasporangia of C. deslongchampsii. Ceramium species in which each periaxial cell cuts off transversely only a single basipetal cell formed a robust clade. The genus Ceramium as represented in Brazil is not monophyletic with respect to Centroceras Kutzing and Corallophila Weber-van Bosse; Ceramium nitens, which has axial cells completely covered by rounded cortical cells formed by acropetal and basipetal filaments, did not group with any Ceramium clade but was weakly allied to a species of Corallophila. All three Brazilian Centroceras sequences were attributed to a single species, C. clavulatum.

Crystal structures of imidazolium bis(trifluoromethanesulfonyl)imide 'ionic liquid' salts: the first organic salt with a cis-TFSI anion conformation

Crystal structures of two examples of an important class of ionic liquids, 1,3-dimethylimidazolium and 1,2,3-triethylimidazolium bis(trifluoromethanesulfonyl)imide have been characterized by single crystal X-ray diffraction. The anion in the 1,3-dimethylimidazolium example (mp 22 degreesC), adopts an unusual cis-geometry constrained by bifurcated cation-anion C-H...O hydrogen-bonds from the imidazolium cation to the anion resulting in the formation of fluorous layers within the solid-state structure. In contrast, in the 1,2,3-triethylimidazolium salt (mp 57 degreesC), the ions are discretely packed with only weak C-H...O contacts between the ions close to the van der Waals separation distances, and with the anion adopting the twisted conformation observed for all other examples from the limited set of organic bis( trifluoromethanesulfonyl) imide crystal structures. The structures are discussed in terms of the favorable physical properties that bis(trifluoromethanesulfonyl) imide anions impart in ionic liquids.

Structural changes in quasi-one-dimensional many-electron systems: From linear to zigzag and beyond

Many-electron systems confined to a quasi-one-dimensional geometry by a cylindrical distribution of positive charge have been investigated by density functional computations in the unrestricted local spin density approximation. Our investigations have been focused on the low-density regime, in which electrons are localized. The results reveal a wide variety of different charge and spin configurations, including linear and zig-zag chains, single-and double-strand helices, and twisted chains of dimers. The spin-spin coupling turns from weakly antiferromagnetic at relatively high density, to weakly ferromagnetic at the lowest densities considered in our computations. The stability of linear chains of localized charge has been investigated by analyzing the radial dependence of the self-consistent potential and by computing the dispersion relation of low-energy harmonic excitations.

On the derived category of a regular toric scheme

Let X be a quasi-compact scheme, equipped with an open covering by affine schemes U s = Spec A s . A quasi-coherent sheaf on X gives rise, by taking sections over the U s , to a diagram of modules over the coordinate rings A s , indexed by the intersection poset S of the covering. If X is a regular toric scheme over an arbitrary commutative ring, we prove that the unbounded derived category of quasi-coherent sheaves on X can be obtained from a category of Sop-diagrams of chain complexes of modules by inverting maps which induce homology isomorphisms on hyper-derived inverse limits. Moreover, we show that there is a finite set of weak generators, one for each cone in the fan S. The approach taken uses the machinery of Bousfield–Hirschhorn colocalisation of model categories. The first step is to characterise colocal objects; these turn out to be homotopy sheaves in the sense that chain complexes over different open sets U s agree on intersections up to quasi-isomorphism. In a second step it is shown that the homotopy category of homotopy sheaves is equivalent to the derived category of X.

Twist localizes three-dimensional patterns

A mechanism or the localization of spatially periodic,self-oganized patterns in anisotropic media which requires systems extended in all three spatial dimensions is presented: When the anisotropy axis is twisted, the pattern becomes localized in planes parallel to the anisotropy axis. An analytical description of the effect is developed, and used to interpret recent experiments in the high-frequency regime of electroconvection by Bohatsch and Stannarius [Phys. Rev. E 60, 5591 (1999)]. The localization width is found to be of the order of magnitude of the geometrical average of the pattern wavelength and the inverse twist.

Raman spectroelectrochemical studies and crystal structure of a binuclear copper(I) complex with a bridging diimine ligand

Raman spectroelectrochemical and X-ray crystallographic studies have been made for the binuclear copper(I) complex, [(Ph(3)P)(2)Cu(dpq)Cu(PPh(3))(2)][BF4](2), where dpq is the bridging ligand 2,3-di(2-pyridyl)quinoxaline. The X-ray data show that the pyridine rings are twisted out of plane with respect to the quinoxaline ring which is itself non-planar. The UV/VIS spectra of the metal-to-ligand charge-transfer excited state and those of the electrochemically reduced complex are similar. The resonance-Raman spectrum of the latter species exhibits little change in the frequency of the pyridinylquinoxaline inter-ring C-C bond stretching mode, compared to the ground electronic state. This suggests minimum change in the inter-ring C-C bond order in the electrochemically or charge-transfer generated radical anion. Semiempirical molecular-orbital calculations on both the neutral dpq and radical anion show two near-degenerate lowest unoccupied orbitals in the neutral species. One is strongly bonding across the inter-ring C-C bond while the other is almost nun-bonding. The Raman data suggest that it is this latter orbital which is populated in the transient and electrochemical experiments.