Applying the extended Kalman filter to systems described by nonlinear differential-algebraic equations

This paper describes a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation models using the extended Kalman filter. The method involves the use of a time-varying linearisation of a semi-explicit index one differential-algebraic equation. The estimation technique consists of a simplified extended Kalman filter that is integrated with the differential-algebraic equation model. The paper describes a simulation study using a model of a batch chemical reactor. It also reports a study based on experimental data obtained from a mixing process, where the model of the system is solved using the sequential modular method and the estimation involves a bank of extended Kalman filters.

A synthetic route to fully substituted chiral cyclopentylamine derivatives: precursors of carbanucleosides

Removal of silyl protection from D-glucose derived substrate 6 afforded 7, which upon acetonide deprotection followed by reaction with N-benzylhydroxylamine furnished two isomeric isoxazolidinocyclopentane derivatives via spontaneous cyclization of an in situ generated nitrone. The methyl xanthate derivative of the tertiary hydroxyl group of one isomer was isolated and subjected to radical deoxygenation reaction to form epimeric products, while with the other isomer it underwent spontaneous 1,2-elimination to form a mixture of the two possible endocyclic olefins. Hydrogenolytic cleavage of the isoxazolidine rings of the purified products followed by insertion of 5-amino-4-chloropyrimidine moiety and purine ring construction smoothly afforded structurally unique carbanucleoside analogues. Various spectroscopic methods on the synthesized compounds and X-ray analysis on one important intermediate were used to assign the structures and stereochemistry of the products.

The molecular structure of propylene sulphide (methylthiirane) by gas-phase electron diffraction and theoretical calculations: a molecule used in MOCVD

Gas-phase electron-diffraction (GED) data together with results from ab initio molecular orbital calculations have been used to determine the structure of propylene sulphide. Values found for the main structural parameters for the molecule are consistent with those obtained from microwave studies and are compared here with those found for similar sulphur containing rings of general formula S(CH2)n (n = 2–5). A high ring strain enthalpy was calculated for propylene sulphide which is consistent with the small C–S–C angle (48.2(6)degrees) and the relatively long C–S bond lengths (ra = 1.831(2) Å). This is thought to account for the ease of ring opening in propylene sulphide observed in MOCVD reactions and the ready polymerisation of the molecule.

Redefining the outer boundaries of EU Law: the Zambrano, McCarthy and Dereci trilogy

In its three recent rulings in the cases of Zambrano, McCarthy, and Dereci, the Court appears to have been determined to redefine the external boundaries of EU law, in cases involving the family reunification rights of Union citizens.These three judgments can be read as an indication that for Article 20 TFEU to apply, there is no longer a requirement of a cross-border element on the facts of the case, and that it is sufficient if the contested national measure has the effect of ‘depriving citizens of the Union of the genuine enjoyment of the substance’ of their rights (the ‘Zambrano principle’).The cases can, at the same time, also be read as a confirmation that the free movement provisions do – still – require a cross-border element and, in particular, the exercise of inter-State movement, in order to apply. Though the result in these cases has not been entirely unexpected, especially in the aftermath of the Rottmann ruling, it is rather problematic in that, although it is obvious that the Court wishes to redraw the line dividing the national and EU spheres of competence, it does not make it entirely clear where this line now lies and leaves many essential questions unanswered, which will obviously require some time to be resolved. EU lawyers are consequently, once more, left with having to decipher as best as they can the real intentions of the Court in this new line of case-law, which has been further complicated by the fact that what the Court seems to have given with one hand in Zambrano (and before that in Rottmann), has taken it back to a large extent through its rulings in McCarthy and Dereci, which appear to confine the former two cases to their own exceptional facts.6 Moreover, the ‘reverse discrimination Pandora’s box’, the opening of which appears to have been the real target of these references, remains untouched: instead of providing a direct solution to this problem, the Court has chosen to – once again – broaden the scope of the Treaty provisions in order to include within it as many situations as possible and, thus, prevent the emergence of this type of differential treatment on a case-by-case basis.As will be explained, nonetheless, this is by no means an appropriate solution to the reverse discrimination conundrum.

Minimum norm regularization of descriptor systems by mixed output feedback

We study the regularization problem for linear, constant coefficient descriptor systems Ex' = Ax+Bu, y1 = Cx, y2 = Γx' by proportional and derivative mixed output feedback. Necessary and sufficient conditions are given, which guarantee that there exist output feedbacks such that the closed-loop system is regular, has index at most one and E+BGΓ has a desired rank, i.e., there is a desired number of differential and algebraic equations. To resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of E is decreased. Numerical procedures are derived to construct the desired feedback gains. These numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way.

Toeplitz operators with distributional symbols on Bergman spaces

We study the boundedness and compactness of Toeplitz operators Ta on Bergman spaces , 1 < p < ∞. The novelty is that we allow distributional symbols. It turns out that the belonging of the symbol to a weighted Sobolev space of negative order is sufficient for the boundedness of Ta. We show the natural relation of the hyperbolic geometry of the disc and the order of the distribution. A corresponding sufficient condition for the compactness is also derived.

New results and open problems on Toeplitz operators in Bergman spaces

We discuss some of the recent progress in the field of Toeplitz operators acting on Bergman spaces of the unit disk, formulate some new results, and describe a list of open problems -- concerning boundedness, compactness and Fredholm properties -- which was presented at the conference "Recent Advances in Function Related Operator Theory'' in Puerto Rico in March 2010.

Toeplitz operators on Bergman spaces with locally integrable symbols

We study the boundedness of Toeplitz operators $T_a$ with locally integrable symbols on Bergman spaces $A^p(\mathbb{D})$, $1 < p < \infty$. Our main result gives a sufficient condition for the boundedness of $T_a$ in terms of some ``averages'' (related to hyperbolic rectangles) of its symbol. If the averages satisfy an ${o}$-type condition on the boundary of $\mathbb{D}$, we show that the corresponding Toeplitz operator is compact on $A^p$. Both conditions coincide with the known necessary conditions in the case of nonnegative symbols and $p=2$. We also show that Toeplitz operators with symbols of vanishing mean oscillation are Fredholm on $A^p$ provided that the averages are bounded away from zero, and derive an index formula for these operators.

Hankel operators on Fock spaces

We study Hankel operators on the weighted Fock spaces Fp. The boundedness and compactness of these operators are characterized in terms of BMO and VMO, respectively. Along the way, we also study Berezin transform and harmonic conjugates on the plane. Our results are analogous to Zhu's characterization of bounded and compact Hankel operators on Bergman spaces of the unit disk.

Correction of atmospheric delay effects in radar interferometry using a nested mesoscale atmospheric model

The temporal variability of the atmosphere through which radio waves pass in the technique of differential radar interferometry can seriously limit the accuracy with which the method can measure surface motion. A forward, nested mesoscale model of the atmosphere can be used to simulate the variable water content along the radar path and the resultant phase delays. Using this approach we demonstrate how to correct an interferogram of Mount Etna in Sicily associated with an eruption in 2004-5. The regional mesoscale model (Unified Model) used to simulate the atmosphere at higher resolutions consists of four nested domains increasing in resolution (12, 4, 1, 0.3 km), sitting within the analysis version of a global numerical model that is used to initiate the simulation. Using the high resolution 3D model output we compute the surface pressure, temperature and the water vapour, liquid and solid water contents, enabling the dominant hydrostatic and wet delays to be calculated at specific times corresponding to the acquisition of the radar data. We can also simulate the second-order delay effects due to liquid water and ice.

Isolation and characterization of an AINTEGUMENTA-like gene in different coconut (Cocos nucifera L.) varieties from Sri Lanka

Development of an efficient tissue culture protocol in coconut is hampered by numerous technical constraints. Thus a greater understanding of the fundamental aspects of embryogenesis is essential. The role of AINTEGUMENTA-like genes in embryogenesis has been elucidated not only in model plants but also in economically important crops. A coconut gene, CnANT, that encodes two APETALA2 (AP2) domains and a conserved linker region similar to those of the BABY BOOM transcription factor was cloned, characterized, and its tissue specific expression was examined. The full-length cDNA of 1,780 bp contains a 1,425-bp open reading frame that encodes a putative peptide of 474 amino acids. The genomic DNA sequence includes 2,317 bp and consists of nine exons interrupted by eight introns. The exon/intron organization of CnANT is similar to that of homologous genes in other plant species. Analysis of differential tissue expression by real-time polymerase chain reaction indicated that CnANT is expressed more highly in in vitro grown tissues than in other vegetative tissues. Sequence comparison of the genomic sequence of CnANT in different coconut varieties revealed one single nucleotide polymorphism and one indel in the first exon and first intron, respectively, which differentiate the Tall group of trees from Dwarfs. The indel sequence, which can be considered a simple sequence repeats marker, was successfully used to distinguish the Tall and Dwarf groups as well as to develop a marker system, which may be of value in the identification of parental varieties that are used in coconut breeding programs in Sri Lanka.

Terahertz pulse imaging of stratified architectural materials for cultural heritage studies

Terahertz pulse imaging (TPI) is a novel noncontact, nondestructive technique for the examination of cultural heritage artifacts. It has the advantage of broadband spectral range, time-of-flight depth resolution, and penetration through optically opaque materials. Fiber-coupled, portable, time-domain terahertz systems have enabled this technique to move out of the laboratory and into the field. Much like the rings of a tree, stratified architectural materials give the chronology of their environmental and aesthetic history. This work concentrates on laboratory models of stratified mosaics and fresco paintings, specimens extracted from a neolithic excavation site in Catalhoyuk, Turkey, and specimens measured at the medieval Eglise de Saint Jean-Baptiste in Vif, France. Preparatory spectroscopic studies of various composite materials, including lime, gypsum and clay plasters are presented to enhance the interpretation of results and with the intent to aid future computer simulations of the TPI of stratified architectural material. The breadth of the sample range is a demonstration of the cultural demand and public interest in the life history of buildings. The results are an illustration of the potential role of TPI in providing both a chronological history of buildings and in the visualization of obscured wall paintings and mosaics.

BTBPs versus BTPhens: some reasons for their differences in properties concerning the partitioning of minor actinides and the advantages of BTPhens

Two members of the tetradentate N-donor ligand families 6,6′-bis(1,2,4-triazin-3-yl)-2,2′-bipyridine (BTBP) and 2,9-bis(1,2,4-triazin-3-yl)-1,10-phenanthroline (BTPhen) currently being developed for separating actinides from lanthanides have been studied. It has been confirmed that CyMe4-BTPhen 2 has faster complexation kinetics than CyMe4-BTBP 1. The values for the HOMO−LUMO gap of 2 are comparable with those of CyMe4-BTBP 1 for which the HOMO−LUMO gap was previously calculated to be 2.13 eV. The displacement of BTBP from its bis-lanthanum(III) complex by BTPhen was observed by NMR, and constitutes the only direct evidence for the greater thermodynamic stability of the complexes of BTPhen. NMR competition experiments suggest the following order of bis-complex stability: 1:2 bis-BTPhen complex ≥ heteroleptic BTBP/BTPhen 1:2 bis-complex > 1:2 bis-BTBP complex. Kinetics studies on some bis-triazine N-donor ligands using the stopped-flow technique showed a clear relationship between the rates of metal ion complexation and the degree to which the ligand is preorganized for metal binding. The BTBPs must overcome a significant (ca. 12 kcal mol−1) energy barrier to rotation about the central biaryl C−C axis in order to achieve the cis−cis conformation that is required to form a complex, whereas the cis−cis conformation is fixed in the BTPhens. Complexation thermodynamics and kinetics studies in acetonitrile show subtle differences between the thermodynamic stabilities of the complexes formed, with similar stability constants being found for both ligands. The first crystal structure of a 1:1 complex of CyMe4-BTPhen 2 with Y(NO3)3 is also reported. The metal ion is 10- coordinate being bonded to the tetradentate ligand 2 and three bidentate nitrate ions. The tetradentate ligand is nearly planar with angles between consecutive rings of 16.4(2)°, 6.4(2)°, 9.7(2)°, respectively.

A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.