Isotopic families of contact manifolds for elliptic PDE

A test for a function to be a solution of an elliptic PDE is given in terms of extensions, as solutions, from the boundaries inside the domains belonging to an isotopic family. It generalizes a result of Ehrenpreis for spheres moved along a straight line.

     

Polarized Lidar Reflectance Measurements of Vegetation at Near-Infrared and Green Wavelengths

There is growing interest in the use of lidar for remote sensing of vegetation owing to the emergence of reliable and rugged lasers and highly sensitive detectors. Lidar remote sensing has a distinct advantage over conventional techniques in vegetation remote sensing due to its capability for three-dimensional characterization of vegetative targets. The Multiwavelength Airborne Polarimetric Lidar (MAPL) system was developed primarily for vegetation remote sensing applications from an airborne platform of up to 1,000 -m altitude. The lidar system has full waveform capture and polarimetric measurement capability at two wavelengths in the near-infrared (1064 nm) and the green (532 nm) spectral regions. This study presents preliminary ground-based lidar reflectance measurements on a variety of deciduous and coniferous trees under fully foliated conditions with a view towards tree species discrimination. Variations in the reflectance characteristics of selected deciduous trees under unfoliated and fully foliated conditions were also investigated. Our study reveals distinct differences in the reflectance characteristics of various trees.     

Topology evolution and gelation mechanism of agarose gel

Kinetics as well as the evolution of the agarose gel topology is discussed, and the agarose gelation mechanism is identified. Aqueous high melting (HM) agarose solution (0.5% w/v) is used as the model system. It is found that the gelation process can be clearly divided into three stages: induction stage, gelation stage, and pseudoequilibrium stage. The induction stage of the gelation mechanism is identified using an advanced rheological expansion system (ARES, Rheometric Scientific). When a quench rate as large as 30 deg C/min is applied, gelation seems to occur through a nucleation and growth mechanism with a well-defined induction time (time required for the formation of the critical nuclei which enable further growth). The relationship between the induction time and the driving force which is determined by the final setting temperature follows the 3D nucleation model. A schematic representation of the three stages of the gelation mechanism is given based on turbidity and rheological measurements. Aggregation of agarose chains is promoted in the polymer-rich phase and this effect is evident from the increasing mass/length ratio of the fiber bundles upon gelation. Continuously increasing pore size during gelation may be attributed to the coagulation of the local polymer-rich phase in order to achieve the global minimum of the free energy of the gelling system. The gel pore size determined using turbidity measurements has been verified by electrophoretic mobility measurements.     

Preparation and thermal stability of trioxalatocobaltates of bivalent metals KM2+ [Co(C2O4)3]·xH2O

Trioxalatocobaltates of bivalent metals KM²⁺[Co(C₂O₄)₃]·x H₂O, with M²⁺ = Ba, Sr, Ca and Pb, have been prepared, characterized and their thermal behaviour studied. The compounds decompose to yield potassium carbonate, bivalent metal carbonate or oxide and cobalt oxide as final products. The formation of the final products of decomposition is influenced by the surrounding atmosphere. Bivalent metal cobaltites of the types KM²⁺CoO₃ and M²⁺CoO_3—x are not identified among the final products of decomposition. The study brings out the importance of the decomposition mode of the precursor in producing the desired end products.     

On the claisen rearrangement of 1,4-diaryloxy-2-butynes

A proton nmr follow-up provided conclusive evidence for the involvement of two sequential Claisen rearrangements in the thermal rearrangement of 1,4-diaryloxy-2-butynes $\text{1}$to 11a-methylpterocarpans $\text{3}$. A detailed study of the rearrangement of 1,4-diaryloxy-2-butynes $\text{1}$ in polyethyleneglycol-200 (PEG-200), indicated a definite possibility of selective synthesis of either benzofuron (3,2-b )benzofuran $\text{4}$ or benzofuro(2,3-b)benzofuran $\text{5}$ by varying the temperature of the reaction alone     

Anion mediated polytype selectivity among the basic salts of Co(II)

Basic salts of Co(II) crystallize in the rhombohedral structure. Two different polytypes, 3R₁ and 3R₂, with distinct stacking sequences of the metal hydroxide slabs, are possible within the rhombohedral structure. These polytypes are generated by simple translation of successive layers by (2/3, 1/3, z) or (1/3, 2/3, z). The symmetry of the anion and the mode of coordination influences polytype selection. Cobalt hydroxynitrate crystallizes in the structure of the 3R₂ polytype while the hydroxytartarate, hydroxychloride and α-cobalt hydroxide crystallize in the structure of the 3R₁ polytype. Cobalt hydroxysulfate is turbostratically disordered. The turbostratic disorder is a direct consequence of the mismatch between the crystallographically defined interlayer sites generated within the crystal and the tetrahedral symmetry of the SO₄²⁻ ions.     

Core modified meso-aryl corrole: first examples of CuII, NiII, CoII and RhI complexes

A variety of metal complexes of 5,10,15-triphenyl-21-monooxa-corrole 4 have been investigated. This monooxa corrole, where one of the pyrrole ring is replaced by a furan moiety, is synthesized by the alpha-alpha coupling reaction of 16-oxa tripyrrane and dipyrromethane. The single crystal X-ray structure of 4 indicates only small deviation of the inner-core heteroatoms from planarity and this macrocycle arrange themselves into a columnar structure. Insertion of metals further flattens the corrole framework. Specifically, oxacorrole 4 binds to Nil(II), Cu(II), and Co(II) with the participation of all heteroatoms in the coordination. However, Rh(I) ion binds to only one imino and one amino nitrogen of the macrocycle. The bond angles at the metal center in the Ni(II) and Rh(I) complexes reveal square planar geometry completed by two CO molecules for Rh(I). The EPR spectra of the paramagnetic that Cu(II) and Col(II) complexes display significant decreases in the metal hyperfine couplings compared with the corresponding porphyrin complexes. The presence of superhyperfine coupling in the Cu(II) complex suggests delocalization of unpaired electron density into the ligand orbitals. Electrochemical studies reveal easier oxidations and harder reductions relative to the corresponding porphyrin derivatives while, the metallated derivatives did not show their characteristic metal reductions due to the high energy of their LUMO.     

Kinetics of lamellar-to-cubic and intercubic phase transitions of pure and cytochrome c containing monoolein dispersions monitored by time-resolved small-angle X-ray diffraction

We investigated the effect of incorporation of a small aqueous peripheral membrane protein (cyt c) into the three-dimensional periodic nanochannel structures formed by the lipid monoolein (MO) on its rich phase behavior as a function of temperature, pressure, and protein concentration using synchrotron X-ray small-angle diffraction. By simultaneous use of the pressure-jump relaxation technique and time-resolved synchrotron X-ray diffraction, we also studied the kinetics of various lipid mesophase transformations of the system for understanding the mechanistic pathways of their formation influenced by the protein-lipid interactions. Cyt c incorporated into the bicontinuous cubic phase Ia3d of MO has a significant effect on the lipid structure and the pressure stability of the system already at low protein concentrations. Concentrations higher than 0.2 wt % of cyt c led to an increase in interfacial curvature due to interaction of the protein with the lipid headgroups. This promotes the formation of a new, probably partially micellar cubic phase of crystallographic space group P4(3)32. Upon pressurization, the P4(3)32 phase undergoes a phase transition to a cubic Pn3m phase with smaller partial specific volume. Increase in protein concentration increases the pressure stability of the P4(3)32 phase. The formation of this phase from the cubic phase Pn3m is a slow process taking many seconds and having a time lag in the beginning. It seems to occur as a two-state process without ordered intermediate states. At temperatures above 60 degrees C, the P4(3)32 phase is unable to accommodate the unfolded protein and transforms to a bicontinuous cubic Ia3d phase. Time-resolved small-angle X-ray scattering studies show that the L(alpha) --> Ia3d transition in pure MO dispersions under limited hydration conditions occurs within a time interval of 1 s at 35 degrees C preceded by a lag phase of 1.5 s. The Ia3d cubic phase initially forms with a much larger lattice constant due to hydration and experiences an initially lower curvature that relaxes within about 1 s. Interestingly, no other cubic phases are involved as intermediates in the transition, i.e., the gyroid cubic phase is able to form directly from the L(alpha) phase. The mechanism behind the L(alpha) --> Ia3d transition in pure MO dispersions has been discussed within the framework of recent stalk models for membrane fusion. In the presence of cyt c, the L(alpha) --> Ia3d transition is much slower. The rather long relaxation times of the order of seconds are probably due to a kinetic trapping of the system and limitation by the transport and redistribution of water and lipid in the evolving new lipid phases. We also studied the transition from the pure lamellar L(alpha) phase to the Ia3d-P4(3)32 two phase region and observed a rather complex transition behavior with transient lamellar and cubic intermediate states.