Fractional Order Disturbance Observer for Robust Vibration Suppression

For the first time, the fractional order disturbance observer (FO-DOB) is proposed for vibration suppression applications such as hard disk drive servo control. It has been discovered in a recently published US patent application (US20010036026) that there is a tradeoff between phase margin loss and strength of the low frequency vibration suppression. Given the required cutoff frequency of the low pass filter, also known as the Q-filter, it turns out that the relative degree of the Q-filter is the major tuning knob for this tradeoff. The solution in US20010036026 was based on an integer order Q-filter with a variable relative degree. This actually motivated the use of a fractional order Q-filter. The fractional order disturbance observer is based on the fractional order Q-filter. The implementation issue is also discussed. The nice point of this paper is that the traditional DOB is extended to the fractional order DOB with the advantage that the FO-DOB design is now no longer conservative nor aggressive, i.e., given the cutoff frequency and the desired phase margin, we can uniquely determine the fractional order of the low pass filter.     

Certain graphs with exactly one irreducible T-module with endpoint 1, which is thin

Journal of Algebraic Combinatorics - Let $$\Gamma $$ denote a finite, simple and connected graph. Fix a vertex x of $$\Gamma $$ and let $$T=T(x)$$ denote the Terwilliger algebra of $$\Gamma $$ with...     

Lead(II) thiocyanate complexes with bibracchial lariat ethers: an X-ray and DFT study

Compounds of formula [Pb(L2)(NCS)2] (1) and [Pb(L4)(SCN)2] (2) (where L2 is the lariat crown ether N,N'-bis(3-aminobenzyl)-4,13-diaza-18-crown-6 and L4 is the Schiff-base lariat crown ether N,N'-bis(3-(salicylaldimino)benzyl)-4,13-diaza-18-crown-6) were isolated and structurally characterized by X-ray diffraction analyses. The X-ray crystal structures of both compounds show the metal ion coordinated to the six donor atoms of the crown moiety, leaving the corresponding pendant arms uncoordinated. The coordination sphere of lead(II) is completed by two thiocyanate groups that coordinate either through their nitrogen (1) or sulfur (2) atoms. The organic receptor adopts a syn conformation in 1, while in 2 it shows an anti conformation. To rationalize these unexpected different conformations of the L2 and L4 receptors in compounds 1 and 2, as well as the different binding modes found for the thiocyanate ligands, we have carried out theoretical calculations at the DFT (B3LYP) level. These calculations predict the syn conformation being the most stable in both 1 and 2 complexes. So, the anti conformation found for 2 in the solid state is tentatively attributed to the presence of intermolecular pi-pi interactions between phenol rings, for which the dihedral angle between the least-squares planes of both rings amounts to 2.6 degrees and the distance between the center of both rings is 3.766 A. On the other hand, the analysis of the electronic structure has revealed that the Pb-ligand bonds present highly ionic character in this family of compounds. They also suggest a greater transfer of electron density from the NCS- ligands when they coordinate through the less electronegative S atom. The Pb-SCN covalent bond formation mainly occurs due to an effective overlap of the occupied 3p z orbitals of the S atoms and the unoccupied 6p z AO of the Pb atom, while the Pb-NCS bonding interaction is primarily due to the overlap of the 6s and 7s AO of Pb with sp(1.10) hybrids of the N donor atoms. Our electronic structure calculations can rationalize the different coordination of the thiocyanate groups in compounds 1 and 2: the simultaneous formation of two Pb-SCN bonds is more favorable for S-Pb-S angles close to 180 degrees , for which the overlap between the occupied 3p z orbitals of the S atoms and the unoccupied 6 pz AO of the Pb atom is maximized.     

Synthesis and crystallographic studies of two new 1,3,5‐triazines

The synthesis and characterization of two new 1,3,5‐triazines containing 2‐(aminomethyl)‐1H‐benzimidazole hydrochloride as a substituent are reported, namely, 2‐{[(4,6‐dichloro‐1,3,5‐triazin‐2‐yl)amino]methyl}‐1H‐benzimidazol‐3‐ium chloride, C₁₁H₉Cl₂N₆⁺·Cl^? ( 1 ), and bis(2,2′‐{[(6‐chloro‐1,3,5‐triazine‐2,4‐diyl)bis(azanediyl)]bis(methylene)}bis(1H‐benzimidazol‐3‐ium)) tetrachloride heptahydrate, 2C₁₉H₁₈ClN₉²⁺·4Cl^?·7H₂O ( 2 ). Both salts were characterized using single‐crystal X‐ray diffraction analysis and IR spectroscopy. Moreover, the NMR (¹H and ¹³C) spectra of 1 were obtained. Salts 1 and 2 have triclinic symmetry (space group P) and their supramolecular structures are stabilized by hydrogen bonding and offset π–π interactions. In hydrated salt 2 , the noncovalent interactions yield pseudo‐nanotubes filled with chloride anions and water molecules, which were modelled in the refinement with substitutional and positional disorder.     

Understanding Stability Trends along the Lanthanide Series

The stability trends across the lanthanide series of complexes with the polyaminocarboxylate ligands TETA^4? (H₄TETA=2,2′,2′′,2′′′‐(1,4,8,11‐tetraazacyclotetradecane‐1,4,8,11‐tetrayl)tetraacetic acid), BCAED^4? (H₄BCAED=2,2′,2′′,2′′′‐{[(1,4‐diazepane‐1,4‐diyl)bis(ethane‐2,1‐diyl)]bis(azanetriyl)}tetraacetic acid), and BP18C6^2? (H₂BP18C6=6,6′‐[(1,4,10,13‐tetraoxa‐7,16‐diazacyclooctadecane‐7,16‐diyl)bis(methylene)]dipicolinic acid) were investigated using DFT calculations. Geometry optimizations performed at the TPSSh/6‐31G(d,p) level, and using a 46+4fⁿ ECP for lanthanides, provide bond lengths of the metal coordination environments in good agreement with the experimental values observed in the X‐ray structures. The contractions of the Ln³⁺ coordination spheres follow quadratic trends, as observed previously for different isostructural series of complexes. We show here that the parameters obtained from the quantitative analysis of these data can be used to rationalize the observed stability trends across the 4f period. The stability trends along the lanthanide series were also evaluated by calculating the free energy for the reaction [La( L )]^n+/?_(sol)+Ln³⁺_(sol)→[Ln( L )]^n+/?_(sol)+La³⁺_(sol). A parameterization of the Ln³⁺ radii was performed by minimizing the differences between experimental and calculated standard hydration free energies. The calculated stability trends are in good agreement with the experimental stability constants, which increase markedly across the series for BCAED^4? complexes, increase smoothly for the TETA^4? analogues, and decrease in the case of BP18C6^2? complexes. The resulting stability trend is the result of a subtle balance between the increased binding energies of the ligand across the lanthanide series, which contribute to an increasing complex stability, and the increase in the absolute values of hydration energies along the 4f period.     

Multiobjective routing problems

Summary Many network routing problems, particularly where the transportation of hazardous materials is involved, are multiobjective in nature; that is, it is desired to optimise not only physical path length but other features as well. Several such problems are defined here and a general framework for multiobjective routing problems is proposed. The notion of “efficient solution” is defined and it is demonstrated, by means of an example, that a problem may have very many solutions which are efficient. Next, potentially useful solution methods for multiobjective routing problems are discussed with emphasis being placed on the use of shortest/k-shortest path techniques. Finally, some directions for possible further research are indicated. Invited by B. Pelegrin     

Twisted Smash Products and L-R Smash Products for Biquasimodule Hopf Quasigroups

We consider two new algebras from an H-biquasimodule algebra A and a Hopf quasigroup H: twisted smash product A ? H and L-R smash product A?H, and find necessary and sufficient conditions for making them Hopf quasigroups. We generalize the main results in Brzeziński and Jiao [5] and Klim and Majid [9]. Moreover, if H is a cocommutative Hopf quasigroup, we prove that A ? H is isomorphic to A?H as Hopf quasigroups.     

Simultaneous analysis of multiple PCR amplicons enhances capillary SSCP discrimination of MHC alleles

Major histocompatibility complex (MHC) genotyping still remains one of the most challenging issues for evolutionary ecologists. To date, none of the proposed methods have proven to be perfect, and all provide both important pros and cons. Although denaturing capillary electrophoresis has become a popular alternative, allele identification commonly relies upon conformational polymorphisms of two single‐stranded DNA molecules at the most. Using the MHC class II (β chain, exon 2) of the black kite (Aves: Accipitridae) as our model system, we show that the simultaneous analysis of overlapping PCR amplicons from the same target region substantially enhances allele discrimination. To cover this aim, we designed a multiplex PCR capable to generate four differentially sized and labeled amplicons from the same allele. Informative peaks to assist allele calling then fourfold those generated by the analysis of single PCR amplicons. Our approach proved successful to differentiate all the alleles (N=13) isolated from eight unrelated birds at a single optimal run temperature and electrophoretic conditions. In particular, we emphasize that this approach may constitute a straightforward and cost‐effective alternative for the genotyping of single or duplicated MHC genes displaying low to moderate sets of divergent alleles.     

A practical algorithm for decomposing polygonal domains into convex polygons by diagonals

We present algorithms for decomposing a polygon (with holes) into convex polygons by diagonals. The methods are computationally quick, and although the partitions that they produce may not have minimal cardinality they usually have a low number of convex pieces. Thus, the methods are suitable for being used when achieving a modest load on the CPU time is more important than finding optimal decompositions as, for instance, in location problems. Part of the results in this paper are from Fernández (1999), and were presented in Fernández et al. (1998). This work has been supported by the Ministry of Science and Technology of Spain under the research projects BEC2002-01026, SEJ2005-06273/ECON (J. Fernández, B. Tóth and B. Pelegrín) and TIC2003-05982-C05-03 (L. Cánovas), in part financed by the European Regional Development Fund (ERDF).