Three-dimensional hybrid networks based on aspartic acid

Three-dimensional achiral coordination polymers of the general formula M2(D, l-NHCH (COO)CH2COO)2·C4H4N2 where M = Ni and Co and pyrazine acts as the linker molecule have been prepared under hydrothermal conditions starting with [M(L-NHCH(COO)CH2COO)·3H2O] possessing a helical chain structure. A three-dimensional hybrid compound of the formula Pb2.5[N{CH(COO) CH2COO}22H2O] has also been prepared hydrothermally starting with aspartic acid and Pb(NO3)2. In this lead compound, where a secondary amine formed by the dimerisation of aspartic acid acts as the ligand, there is two-dimensional inorganic connectivity and one-dimensional organic connectivity.

Topological properties of the one dimensional exponential random geometric graph

In this article we study the one-dimensional random geometric (random interval) graph when the location of the nodes are independent and exponentially distributed. We derive exact results and limit theorems for the connectivity and other properties associated with this random graph. We show that the asymptotic properties of a graph with a truncated exponential distribution can be obtained using the exponential random geometric graph. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008.

Semigroups on Frechet spaces and equations with infinite delays

In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.

One-dimensional zig-zag type coordination polymers of Ni(II) and Cu(II) containing 1,3-benzenedicarboxylate and 1,3-diaminopropane: Structural, spectral and thermal studies

Two coordination polymers [Ni(ipt)(dap)(2)](n) (1) and [Cu(ipt)(dap)H2O](n) center dot nH(2)O (2) with an overall one-dimensional arrangement and having isophthalate (ipt) as bridging moieties and chelating 1,3-diaminopropane (dap) as structure modulating units have been prepared and characterized by crystallographic, spectroscopic and thermo-analytical studies. Both have an overall one-dimensional zig-zag nature but with a distorted octahedral NiN4O2 chromophore for 1 and a distorted square pyramidal CuN2O3 chromophore for 2. Even though the ipt units are acting as bridging units through mono-dentatively coordinating carboxylate functions in both polymers, compound 1 has the carboxylate oxygen linkages at the trans positions, while in 2 the oxygen linkages occur at the cis positions leading to a different type of zig-zag arrangement. Relevant spectral and bonding parameters also could be evaluated for the compounds using UV-Vis and EPR spectra. Thermal stability and possible structural modifications on thermal treatment of the compounds were also investigated and the relevant thermodynamic and kinetic parameters evaluated from the thermal data. (C) 2007 Elsevier B.V. All rights reserved.

Three-dimensional structure of heat shock protein 90 from Plasmodium falciparum: molecular modelling approach to rational drug design against malaria

We have recently implicated heat shock protein 90 from Plasmodium falciparum (PfHsp90) as a potential drug target against malaria. Using inhibitors specific to the nucleotide binding domain of Hsp90, we have shown potent growth inhibitory effects on development of malarial parasite in human erythrocytes. To gain better understanding of the vital role played by PfHsp90 in parasite growth, we have modeled its three dimensional structure using recently described full length structure of yeast Hsp90. Sequence similarity found between PfHsp90 and yeast Hsp90 allowed us to model the core structure with high confidence. The superimposition of the predicted structure with that of the template yeast Hsp90 structure reveals an RMSD of 3.31 angstrom. The N-terminal and middle domains showed the least RMSD (1.76 angstrom) while the more divergent C-terminus showed a greater RMSD (2.84 angstrom) with respect to the template. The structure shows overall conservation of domains involved in nucleotide binding, ATPase activity, co-chaperone binding as well as inter-subunit interactions. Important co-chaperones known to modulate Hsp90 function in other eukaryotes are conserved in malarial parasite as well. An acidic stretch of amino acids found in the linker region, which is uniquely extended in PfHsp90 could not be modeled in this structure suggesting a flexible conformation. Our results provide a basis to compare the overall structure and functional pathways dependent on PfHsp90 in malarial parasite. Further analysis of differences found between human and parasite Hsp90 may make it possible to design inhibitors targeted specifically against malaria.

Conformationally restricted formyl methionyl tripeptide chemoattractants: a three-dimensional structure-activity study of analogs incorporating a C alpha,alpha-dialkylated glycine at position 2

The conformationally restricted CHO-L-Met-Xxx-L-Phe-OY (where Xxx = Aib, Ac3c, Ac5c, Ac6c, and Ac7c; Y = H, Me) tripeptides, analogs of the chemoattractant CHO-L-Met-L-Leu-L-Phe-OH, have been synthesized in solution by classical methods and fully characterized. Compounds were compared to determine the combined effect of backbone conformational preferences and side-chain bulkiness on the relation of three-dimensional structure to biological activity. Each peptide was tested for its ability to induce granule enzyme secretion from rabbit peritoneal polymorphonuclear leukocytes. In parallel, a conformational analysis on the CHO-blocked peptide and their tertbutyloxycarbonylated synthetic precursors was performed in the crystal state and in solution using X-ray diffraction, infrared absorption, and 1H nuclear magnetic resonance. The biological and conformational data are discussed in relation to the proposed model of the chemotactic peptide receptor of rabbit neutrophils.

Non local scale effects on ultrasonic wave characteristics nanorods

In this paper, the nonlocal elasticity theory has been incorporated into classical Euler-Bernoulli rod model to capture unique features of the nanorods under the umbrella of continuum mechanics theory. The strong effect of the nonlocal scale has been obtained which leads to substantially different wave behaviors of nanorods from those of macroscopic rods. Nonlocal Euler-Bernoulli bar model is developed for nanorods. Explicit expressions are derived for wavenumbers and wave speeds of nanorods. The analysis shows that the wave characteristics are highly over estimated by the classical rod model, which ignores the effect of small-length scale. The studies also shows that the nonlocal scale parameter introduces certain band gap region in axial wave mode where no wave propagation occurs. This is manifested in the spectrum cures as the region where the wavenumber tends to infinite (or wave speed tends to zero). The results can provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave propagation properties of single-walled carbon nanotubes. (C) 2010 Elsevier B.V. All rights reserved.

Terahertz wave characteristics of a single-walled carbon nanotube containing a fluid flow using the nonlocal Timoshenko beam model

This paper presents the effect of nonlocal scaling parameter on the terahertz wave propagation in fluid filled single walled carbon nanotubes (SWCNTs). The SWCNT is modeled as a Timoshenko beam,including rotary inertia and transverse shear deformation by considering the nonlocal scale effects. A uniform fluid velocity of 1000 m/s is assumed. The analysis shows that, for a fluid filled SWCNT, the wavenumbers of flexural and shear waves will increase and the corresponding wave speeds will decrease as compared to an empty SWCNT. The nonlocal scale parameter introduces certain band gap region in both flexural and shear wave mode where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite (or wave speed tends to zero). The frequency at which this phenomenon occurs is called the ``escape frequency''. The effect of fluid density on the terahertz wave propagation in SWCNT is also studied and the analysis shows that as the fluid becomes denser, the wave speeds will decrease. The escape frequency decreases with increase in nonlocal scaling parameter, for both wave modes. We also show that the effect of fluid density and velocity are negligible on the escape frequencies of flexural and shear wave modes. (C) 2010 Elsevier B.V. All rights reserved.

Semigroups on Frechet spaces and equations with infinite delays

In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.

Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates

This paper presents a unified exact analysis for the statics and dynamics of a class of thick laminates. A three-dimensional, linear, small deformation theory of elasticity solution is developed for the bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. All the nine elastic constants of orthotropy are taken into account. The solution is formally exact and leads to simple infinite series for stresses and displacements in flexure, forced vibration and "beam-column" type problems and to closed form characteristic equations for free vibration and buckling problems. For free vibration of plates, the present analysis yields a triply infinite spectrum of frequencies instead of only one doubly infinite spectrum by thin plate theory or three doubly infinite spectra by Reissner-Mindlin type analyses. Some numerical results are presented for plates and laminates. Comparison of results from thin plate, Reissner and Mindlin analyses with these yield some important conclusions regarding the validity and effects of the assumptions made in the approximate theories.

An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates

A three-dimensional linear, small deformation theory of elasticity solution by the direct method is developed for the free vibration of simply-supported, homogeneous, isotropic, thick rectangular plates. The solution is exact and involves determining a triply infinite sequence of eigenvalues from a doubly infinite set of closed form transcendental equations. As no restrictions are placed on the thickness variation of stresses or displacements, this formulation yields a triply infinite spectrum of frequencies, instead of only one doubly infinite spectrum by thin plate theory and three doubly infinite spectra by Mindlin's thick plate theory. Further, the present analysis yields symmetric thickness modes which neither of the approximate theories can identify. Some numerical results from the two approximate theories are compared with those from the present solution and some important conclusions regarding the effect of the assumptions made in the approximate theories are drawn. The thickness variations of stresses and displacements are also discussed. The analysis is readily extended for laminated plates of isotropic materials. Numerical results are also given for three-ply laminates, and are used to assess the accuracy of thin plate theory predictions for laminates. Extension to general lateral surface conditions and forced vibrations is indicated.

A general treatment of two dimensional plane flows, for a micropolar fluid

In this paper we have studied the flow of a micropolar fluid, whose constitutive equations were given by Eringen, in two dimensional plane flow. In two notes, we have discussed the validity of the boundary condition v=a ω and its effect on the entire flow field. We have restricted our study to the case when Stokes' approximation is valid, i. e. slow motion for it is difficult to uncouple the equations in the most general case.

A class of one-dimensional steady-state flows in radiation-gas-dynamics

The study of steady-state flows in radiation-gas-dynamics, when radiation pressure is negligible in comparison with gas pressure, can be reduced to the study of a single first-order ordinary differential equation in particle velocity and radiation pressure. The class of steady flows, determined by the fact that the velocities in two uniform states are real, i.e. the Rankine-Hugoniot points are real, has been discussed in detail in a previous paper by one of us, when the Mach number M of the flow in one of the uniform states (at x=+∞) is greater than one and the flow direction is in the negative direction of the x-axis. In this paper we have discussed the case when M is less than or equal to one and the flow direction is still in the negative direction of the x-axis. We have drawn the various phase planes and the integral curves in each phase plane give various steady flows. We have also discussed the appearance of discontinuities in these flows.