Fixed-Size Quadruples for a New, Hardware-Oriented Representation of the 4D Clifford Algebra

Clifford algebra (geometric algebra) offers a natural and intuitive way to model geometry in fields as robotics, machine vision and computer graphics. This paper proposes a new representation based on fixed-size elements (quadruples) of 4D Clifford algebra and demonstrates that this choice leads to an algorithmic simplification which in turn leads to a simpler and more compact hardware implementation of the algebraic operations. In order to prove the advantages of the new, quadruple-based representation over the classical representation based on homogeneous elements, a coprocessing core supporting the new fixed-size Clifford operands, namely Quad-CliffoSor (Quadruple-based Clifford coprocesSor) was designed and prototyped on an FPGA board. Test results show the potential to achieve a 23× speedup for Clifford products and a 33× speedup for Clifford sums and differences compared to the same operations executed by a software library running on a general-purpose processor.     

Lie point symmetries and some group invariant solutions of the quasilinear equation involving the infinity Laplacian

Using the classical Lie method we obtain the full Lie point symmetry group of the Aronsson equation in two independent variables. Some group invariant solutions of this equation are found and a conjecture on the Lie point symmetry group of the Aronsson equation in Rⁿ is presented.     

Metric techniques for convex stationary ergodic Hamiltonians

We adapt the metric approach to the study of stationary ergodic Hamilton?CJacobi equations, for which a notion of admissible random (sub)solution is defined. For any level of the Hamiltonian greater than or equal to a distinguished critical value, we define an intrinsic random semidistance and prove that an asymptotic norm does exist. Taking as source region a suitable class of closed random sets, we show that the Lax formula provides admissible subsolutions. This enables us to relate the degeneracies of the critical stable norm to the existence/nonexistence of exact or approximate critical admissible solutions.     

Cascades-based synchronization of hyperchaotic systems: Application to Chen systems

We discuss the cascaded-based controlled synchronization method for hyperchaotic systems. The control approach is based on analysis tools for cascaded time-varying systems. That is, the closed-loop system takes the form of two subsystems which are interconnected in a manner that the state of one system enters into another but without feedback loop. The advantage of such construction is that the controller is largely simplified relative to other design methods such as backstepping. We apply the method to Chen’s hyperchaotic system and show that global synchronization is achieved via linear control. Also, we assume that only three instead of four control inputs are available. The method is tested in numerical simulations.     

Cyclopropanation with gold(I) carbenes by retro-Buchner reaction from cycloheptatrienes

Cationic gold(I) promotes the retro-Buchner reaction of 7-substituted 1,3,5-cycloheptatrienes, leading to gold(I) carbenes that cyclopropanate alkenes.     

Synthesis of caffeic acid molecularly imprinted polymer microspheres and high-performance liquid chromatography evaluation of their sorption properties

In the current work, a molecularly imprinted polymer (MIP) has been synthesised and used to enable the extraction of a naturally-occurring antioxidant from complex media. More specifically, we describe the first example of a caffeic acid (CA) MIP which has been synthesised in the form of well-defined polymer microspheres, and its use for the extraction of CA from fruit juice sample. The CA MIP was synthesised by precipitation polymerisation using 4-vinylpyridine as functional monomer, divinylbenzene-80 as crosslinker and acetonitrile:toluene (75/25, v/v) as porogen. The particle sizing and morphological characterisation of the polymers was carried out by means of scanning electron microscopy (narrow particle size distribution; ～5 and 1.5 μm particle diameters for the MIP and NIP [non-imprinted polymer], respectively) and nitrogen sorption porosimetry (specific surface areas of 340 and 350 m(2)g(-1), and specific pore volumes of 0.17 and 0.19 cm(3)g(-1) for the MIP and NIP, respectively). The polymers were evaluated further by batch rebinding experiments, and from the derived isotherms their binding capacity and binding strength were determined (number of binding sites (N(K))=0.6 and 0.3 mmol g(-1) for the MIP and NIP, respectively, and apparent average adsorption constant (K(N))=10.0 and 1.6L mmol(-1) for the MIP and NIP, respectively). To evaluate the molecular recognition character of the MIP it was packed into a stainless steel column (50 mm × 4.6 mm i.d.) and evaluated as an HPLC-stationary phase. The mobile phase composition, flow rate, and the elution profile were then optimised in order to improve the peak shape without negatively affecting the imprinting factor (IF). Very interesting, promising properties were revealed. The imprinting factor (IF) under the optimised conditions was 11.9. Finally, when the imprinted LC column was used for the selective recognition of CA over eight related compounds, very good selectivity was obtained. This outcome enabled the direct extraction of CA in commercial apple juice samples with recoveries in excess of 81% and, rather significantly, without any need for a clean-up step prior to the extraction.     

Fast determination of the functional peptide soymetide in different soybean derived foods by capillary-high performance liquid chromatography

The determination of bioactive peptides derived from food sources is gaining special attention in last years, due to their ability to promote health and their potential to reduce the risk of chronic diseases. In this work, a new analytical methodology has been developed enabling for the first time the determination of soymetide, a new immunostimulating peptide derived from soybean, in different soybean derived foodstuffs. Capillary-HPLC was employed for peptide separation after accelerated tryptic digestion of soybean proteins. Two different capillary-HPLC columns were tested and chromatographic separation was optimized in each case. The use of a 300 μm fused-core technology C18 column enabled a suitable separation of soymetide from the other peptides in less than 18 min. Different analytical characteristics of the method were evaluated: selectivity, linearity, accuracy, precision, limit of detection and quantitation, and stability. The developed method was applied to the determination of soymetide content in different soybean dairy-like products for human consumption (powdered milks and infant formulas).     

Optical, morphological and structural characterization of Langmuir-Schaefer films of a functionalized copper phthalocyanine

Langmuir-Schaefer (LS) films of copper(II) tetrakis-(isoprpoxy-carbonyl)-phthalocyanine (TiPCuPc) have been deposited onto various solid supports. Its floating film have been characterized at the air-water interface by means of Brewster Angle Microscopy and Langmuir curves. Vibrational modes of multilayer transferred LS film have been studied by Raman spectroscopy and the optical parameters (refractive index n and extinction coefficient k) have been determined in the visible range of the electromagnetic spectrum. Linearly polarized light absorbance measurements have been performed at room temperature in the 400-800 nm spectral range and the average orientation of the phthalocyanine rings have been estimated. Transmission electron microscopy has been also used to characterize the morphological properties of the LS film and a close packed arrangement of the deposited molecules has been observed.     

Molecular aspects of the interaction between plants sterols and DPPC bilayers: an experimental and theoretical approach

The effect of sterols composition in a lipid bilayer was investigated on membranes of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and mixtures with the plant sterols β-sitosterol and stigmasterol. Differential scanning calorimetry, 1,6-diphenyl-1,3,5-hexatriene (DPH) fluorescence polarization and infrared spectroscopy studies showed that both sterols changed the packing of the membrane and the hydration of the polar headgroup of the phospholipids, disordering the gel phase and, vice versa, ordering the membrane in the liquid crystalline phase. In all cases some differences among β-sitosterol and stigmasterol could be observed, being β-sitosterol slightly more efficient than stigmasterol in ordering a fluid membrane, bringing the membrane to a more packed liquid ordered phase. Molecular dynamic simulations were carried out to better characterize the distinct behavior of both sterols in a DPPC-membrane. The calculated parameters agreed quite well with the experimental results and a molecular model is proposed to explain differences in the sterols molecules and their effect on the DPPC-bilayer.     

Direct synthesis of NNN-donor enantiopure scorpionate ligands by an efficient diastereoselective nucleophilic addition to imines

New enantiopure imines (1-9) with a chiral substrate to control the stereochemistry of a newly created stereogenic center have been synthesized by reaction of the commercially available (1R)-(-)-myrtenal and different primary amines. The diastereomerically enriched lithium-scorpionate compounds [Li(κ(3)-mobpza)(THF)] (10) (mobpza = N-p-methylphenyl-(1R and 1S)-1-[(1R)-6,6-dimethylbicyclo[3.1.1]-2-hepten-2-yl]-2,2-bis(3,5-dimethylpyrazol-1-yl)ethylamide), [Li(κ(3)-mobpza)(THF)] (11) (mobpza = N-p-methoxyphenyl-(1R and 1S)-1-[(1R)-6,6-dimethylbicyclo[3.1.1]-2-hepten-2-yl]-2,2-bis(3,5-dimethylpyrazol-1-yl)ethylamide), [Li(κ(3)-fbpza)(THF)] (12) (fbpza = N-p-fluorophenyl-(1R and 1S)-1-[(1R)-6,6-dimethylbicyclo[3.1.1]-2-hepten-2-yl]-2,2-bis(3,5-dimethylpyrazol-1-yl)ethylamide), and [Li(κ(3)-clbpza)(THF)] (13) (clbpza = N-p-chlorophenyl-(1R and 1S)-1-[(1R)-6,6-dimethylbicyclo[3.1.1]-2-hepten-2-yl]-2,2-bis(3,5-dimethylpyrazol-1-yl)ethylamide) were obtained by a diastereoselective 1,2-addition of an organolithium reagent to imines in good yield and with good diastereomeric excess (ca. 80%). The complexes [LiCl(κ(2)-R,R-fbpzaH)(THF)] (14) and [LiCl(κ(2)-R,R-clbpzaH)(THF)] (15) were obtained in enantiomerically pure form by the treatment of THF solutions of 12 or 13 with NH(4)Cl. The enantiomerically pure amines (R,R-mbpzaH) (16), (R,R-mobpzaH) (17), (R,R-fbpzaH) (18), and (R,R-clbpzaH) (19) were obtained by hydrolysis of the lithium-scorpionate compounds 10-13 with H(2)O. The lithium compound 12 was reacted with [TiCl(4)(THF)(2)] or [ZrCl(4)] to give the enantiopure complexes [MCl(3)(κ(3)-R,R-fbpza)] [M = Ti (20), Zr (21)]. The amine compound 18 reacted with [MX(4)] (M = Ti, X = O(i)Pr, OEt; M = Zr; X = NMe(2)) to give the complexes [MX(3)(κ(3)-R,R-fbpza)] (22-24). The reaction of Me(3)SiCl with [Zr(NMe(2))(3)(κ(3)-R,R-fbpza)] (24) in different molar ratios led to the halide-amide-containing complexes [ZrCl(NMe(2))(2)(κ(3)-R,R-fbpza)] (25) and [ZrCl(2)(NMe(2))(κ(3)-R,R-fbpza)] (26) and the halide complex 21. The isolation of only one of the three possible diastereoisomers of complexes 25 and 26 revealed that chiral induction from the ligand to the zirconium center took place. The structures of these compounds were elucidated by (1)H and (13)C{(1)H} NMR spectroscopy, and the X-ray crystal structures of 5, 12, 14, 15, and 24 were also established.