Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Existence and approximations of solutions to some fractional order functional integral equations

In this paper we shall study a fractional order functional integral equation. In the first part of the paper, we proved the existence and uniqueness of mile and global solutions in a Banach space. In the second part of the paper, we used the analytic semigroups theory oflinear operators and the fixed point method to establish the existence, uniqueness and convergence of approximate solutions of the given problem in a separable Hilbert space. We also proved the existence and convergence of Faedo-Galerkin approximate solution to the given problem. Finally, we give an example.

Asymmetric cross-coupled differential pair configuration to realize neuron activation function and its derivative

In this brief, we present a new circuit technique to generate the sigmoid neuron activation function (NAF) and its derivative (DNAF). The circuit makes use of transistor asymmetry in cross-coupled differential pair to obtain the derivative. The asymmetry is introduced through external control signal, as and when required. This results in the efficient utilization of the hard-ware by realizing NAF and DNAF using the same building blocks. The operation of the circuit is presented in the subthreshold region for ultra low-power applications. The proposed circuit has been experimentally prototyped and characterized as a proof of concept on the 1.5-mum AMI technology.

Synthesis, Structure, Spirocyclization Mechanism, and Glutathione Peroxidase-like Antioxidant Activity of Stable Spirodiazaselenurane and Spirodiazatellurane

The first examples of stable spirodiazaselenurane and spirodiazatellurane were synthesized by oxidative spirocyclization of the corresponding diaryl selenide and telluride and were structurally characterized. X-ray crystal structures of the spirodiazaselenurane and spirodiazatellurane suggest that the structures are distorted trigonal bipyramidal (TBP) with the electronegative nitrogen atoms occupying the apical positions and two carbon atoms and the lone pair of Se/Te occupying the equatorial positions. Interestingly, the spirodiazatellurane underwent spontaneous chiral resolution during crystallization, and the absolute configurations of its enantiomers were confirmed by single-crystal X-ray analyses. A detailed mechanistic study indicates that the cyclization to spirodiazaselenurane and spirodiazatellurane occurs via selenoxide and telluroxide intermediates. The chalcogenoxides cyclize to the corresponding spiro compounds in a stepwise manner via the involvement of hydroxyl chalcogenurane intermediates, and the activation energy for them spirocyclization reaction decreases in the order S > Se > Te. In addition to the synthesis, characterization, and mechanism of cyclization, the glutathione peroxidase (GPx) mimetic activity of the newly synthesized compounds was evaluated. These studies suggest that the tellurium compounds are more effective as GPx mimics than their selenium counterparts due to the fast oxidation of the tellurium center in the presence of peroxide and the involvement of an efficient redox cycle between the telluride and telluroxide intermediate.

Solution structures of conformationally equilibrium forms of holo-acyl carrier protein (PfACP) from Plasmodium falciparum provides insight into the mechanism of activation of ACPs

Acyl Carrier Protein (ACP) from the malaria parasite, Plasmodium falciparum (PfACP) in its holo form is found to exist in two conformational states in solution. Unique 3D solution structures of holo-PfACP have been determined for both equilibrium conformations, using high-resolution NMR methods. Twenty high-resolution solution structures for each of the two forms of holo-PfACP have been determined on the basis of 1226 and 1218 unambiguously assigned NOEs (including NOEs between 4 '-phosphopantetheine prosthetic group (4 '-PP) and protein), 55 backbone dihedral angles and 26 hydrogen bonds. The atomic rmsd values of the determined structures of two equilibrium forms, about the mean coordinates of the backbone and heavy atoms, are 0.48 +/- 0.09 and 0.92 +/- 0.10 and 0.49 +/- 0.08 and 0.97 +/- 0.11 angstrom, respectively. The interaction of 4 '-PP with the polypeptide backbone is reported here for the first time for any of the ACPs. The structures of holo-PfACP consist of three well-defined helices that are tightly packed. The structured regions of the molecule are stabilized by extensive hydrophobic interactions. The difference between the two forms arises from a reorientation of the 4 '-PP group. The enthalpy difference between the two forms, although small, implies that a conformational switch is essential for the activation of holo-ACP. Sequence and structures of holo-PfACP have been compared with those of the ACPs from type I and type II fatty acid biosynthesis pathways (FAS), in particular with the ACP from rat and the butyryl-ACP from E. coli. The PfACP structure, thus determined has several novel features hitherto not seen in other ACPs.

Thermodynamic and kinetic studies on the mechanism of binding of methylumbelliferyl glycosides to jacalin

The binding of Artocarpus integrifolia lectin (jacalin) to 4-methylumbelliferyl (Meumb)-glycosides, Gal alpha Meumb, Gal beta Meumb, GalNAc alpha Meumb, GalNAc beta-Meumb, and Gal beta 3GalNAc beta Meumb was examined by extrinsic fluorescence quenching titration and stopped flow spectrofluorimetry. The binding was characterized by 100% quenching of fluorescence of Meumb-glycosides. Their association constants range from 2.0 x 10(4) to 1.58 x 10(6) M-1 at 15 degrees C. Entropic contribution is the major stabilizing force for avid binding of Meumb-glycosides indicating the existence of a hydrophobic site that is complementary to their methylumbelliferyl group. The second order association rate constants for interaction of these sugars with lectin at 15 degrees C vary from 8.8 x 10(5) to 3.24 x 10(6) M-1 S-1, at pH 7.2. The first order dissociation rate constants range from 2.30 to 43.0 S-1 at 15 degrees C. Despite the differences in their association rate constants, the overall values of association constants for these saccharides are determined by their dissociation rate constants. The second order rate constant for the association of Meumb-glycosides follows a pattern consistent with the magnitude of the activation energies involved therin. Activation parameters for association of all ligands illustrate that the origin of the barrier between binding of jacalin to Meumb-glycosides is entropic, and the enthalpic contribution is small. A correlation between these parameters and the structure of the ligands on the association rates underscores the importance of steric factors in determining protein saccharide recognitions.

Hall thruster sequencer using Intel-8051 microcontroller for ion thrust measurement

Hall thrusters, such as Stationary Plasma Thruster (SPT), have been widely used on board modern satellites placed in geo-synchronows orbits for reasons such as orbit maintenance, repositioning and attitude control. In order to study the performance of the stationary plasma thruster, the thrust produced by it has been measured, using a thrust balance with strain gauge sensors under vacuum conditions, by activating the thruster. This activation of thruster has been carried out by switching ON and switching OFF of the necessary power supplies and control of other feed system such as the propellant flow in a particular sequence. Hitherto, these operations were done manually in the required sequence. This paper reports the attempt made to automate the sequential operation of the power supplies and the necessary control valves of the feed system using Intel 8051 microcontroller. This automation has made thrust measurements easier and more sophisticated.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Theory of laminar flame propagation with non-normal diffusion.

A study has been made of the problem of steady, one-dimensional, laminar flame propagation in premixed gases, with the Lewis number differing from (and equal to) unity. Analytical solutions, using the method of matched asymptotic expansions, have been obtained for large activation energies. Numerical solutions have been obtained for a wide range of the reduced activation temperature parameter (n {geometrically equal to} E/RTb), and the Lewis number δ. The studies reveal that the flame speed eigenvalue is linear in Lewis number for first order and quadratic in Lewis number for second order reactions. For a quick determination of flame speeds, with reasonable accuracy, a simple rule, expressing the flame speed eigenvalue as a function of the Lewis number and the centroid of the reaction rate function, is proposed. Comparisons have been made with some of the earlier works, for both first and second order reactions.

On the study of a third-order mechanical oscillator

In this paper, the study of a third-order mechanical oscillator is presented by demonstrating its equivalence to the well-known R.C. multivibrator with two additional reactive elements. The conditions for the oscillator's possession of periodic solutions are presented. It is also shown that under certain conditions, the study of the given third-order autonomous system can be reduced to the study of an equivalent second-order, non-autonomous system.

Levitation effect in zeolites: Quasielastic neutron scattering and molecular dynamics study of pentane isomers in zeolite NaY

We report the quasielastic neutron scattering (QENS) and molecular dynamics (MD) investigations into diffusion of pentane isomers in zeolite NaY. The molecular cross section perpendicular to the long molecular axis varies for the three isomers while the mass and the isomer-zeolite interaction remains essentially unchanged. Both QENS and MD results show that the branched isomers neopentane and isopentane have higher self-diffusivities as compared with n-pentane at 300 K in NaY zeolite. This result provides direct experimental evidence for the existence of nonmonotonic, anomalous dependence of self-diffusivity on molecular diameter known as the levitation effect. The energetic barrier at the bottleneck derived from MD simulations exists for n-pentane which lies in the linear regime while no such barrier is seen for neopentane which is located clearly in the anomalous regime.Activation energy is in the order E-a(n-pentane)>E-a(isopentane)>E-a(neopentane) consistent with the predictions of the levitation effect. In the liquid phase, it is seen thatD(n pentane)>D(isopentane)>D(neopentane) and E-a(n-pentane)< E-a(isopentane)< E-a(neopentane). Intermediate scattering function for small wavenumbers obtained from MD follows a single exponential decay for neopentane and isopentane. For n-pentane, a single exponential fit provides a poor fit especially at short times. Cage residence time is largest for n-pentane and lowest for neopentane. For neopentane, the width of the self-part of the dynamic structure factor shows a near monotonic decrease with wavenumber. For n-pentane a minimum is seen near k=0.5 A degrees(-1) suggesting a slowing down of motion around the 12-ring window, the bottleneck for diffusion. Finally, the result that the branched isomer has a higher diffusivity as compared with the linear analog is at variation from what is normally seen.

Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the type y″ = f (x;y, y′) with given initial conditions. The method is based on geometrical interpretation of the equation, which suggests a simple geometrical construction of the integral curve. We then translate this geometrical method to the numerical procedure adaptable to desk calculators and digital computers. We have studied the efficacy of this method with the help of an illustrative example with known exact solution. We have also compared it with Runge-Kutta method. We have then applied this method to a physical problem, namely, the study of the temperature distribution in a semi-infinite solid homogeneous medium for temperature-dependent conductivity coefficient.