Parameter tuning and repeated application of the IMT-type transformation in numerical quadrature

Summary The IMT rule, which is especially suited for the integration of functions with end-point singularities, is generalized by introducing parameters and also by repeatedly applying the parametrized IMT transformation. The quadrature formulas thus obtained are improved considerably both in efficiency and in robustness against end-point singularities. Asymptotic error estimates and numerical results are also given.     

Eventually constant solutions of a rational difference equation

We describe all the solutions of a rational difference equation from Putnam’s mathematical competition, which are eventually equal to its positive equilibrium . As a consequence we give a new, elegant and short proof of the fact that the equation has a positive solution which is not eventually equal to one. Moreover, we show that almost all solutions of the equation are not eventually equal to one.     

Network theory and transversal matroids

Various matroidal models for the solvability of active linear networks are described in a unified way and compared with one another. One of the conclusions is that different authors used the concept of “generality” in different ways and their methods are not equivalent. Another conclusion is that some of the seemingly equivalent data structures can be better for storing the models of the network devices in a computer. Finally, a hierarchy of network devices is introduced from this point of view. The classes of this hierarchy are proved to be characterized by transversal and fundamental transversal matroids.     

Easily Prepared Co3O4 Doped Porous Carbon Material Decorated with Single-wall Carbon Nanotubes Applied in Voltammetric Sensing of Antioxidant α-lipoic Acid

The homemade, porous carbon material, thermolysis prepared from Novolac phenol-formaldehyde resin, in situ modified with Co₃O₄ nanoparticles and mixed with single-wall carbon nanotubes, was used in selective sensing of prominent antioxidant α-lipoic acid (LA). XRD, SEM and EIS measurements were used for characterization of material composition, structure, morphology and improved conductivity. The quantification of LA at TPCo₃O₄&SWCNTCPE was done by a square-wave voltammetric technique in BR buffer solution at pH 6. The linear working range was recorded from 2 to 100 μM of LA and the proposed electrode material was successfully applied in the determination of LA in dietary supplements.     

The Stochastic Approach in Analysis—the Structures with Vacancies and Impurities

The stochastic approach to the problem of deformed bulk structures is a unique possibility for obtaining a so–so real picture of physical processes in these structures. The chain of identical atoms with random distances between neighbours as well as the chain with random masses at equal distances is analysed. These analyses were generalized to complex chains, which are spatially and mass deformed. The approximations used were incommensurability; one and more rough, continual approximation. The probabilities are of exponential type. It means that the error in estimation on the basis of stochastical method can go to 100% maximally.     

Integrability of vector and multivector fields associated with interior point methods for linear programming

In the feasible region of a linear programming problem, a number of desirably good directions have been defined in connexion with various interior point methods. Each of them determines a contravariant vector field in the region whose only stable critical point is the optimum point. Some interior point methods incorporate a two- or higher-dimensional search, which naturally leads us to the introduction of the corresponding contravariant multivector field. We investigate the integrability of those multivector fields, i.e., whether a contravariantp-vector field isX _p -forming, is enveloped by a family ofX _q 's (q > p) or envelops a family ofX _q 's (q < p) (in J.A. Schouten's terminology), whereX _q is aq-dimensional manifold.Immediate consequences of known facts are: (1) The directions hitherto proposed areX ₁-forming with the optimum point of the linear programming problem as the stable accumulation point, and (2) there is anX ₂-forming contravariant bivector field for which the center path is the critical submanifold. Most of the meaningfulp-vector fields withp 3 are notX _p -forming in general, though they envelop that bivector field. This observation will add another circumstantial evidence that the bivector field has a kind of invariant significance in the geometry of interior point methods for linear programming.For a kind of appendix, it is noted that, if we have several objectives, i.e., in the case of multiobjective linear programs, extension to higher dimensions is easily obtained.     

Infrared spectra of carbon monoxide on evaporated nickel films: A low temperature thermal detection technique

A novel thermal detection scheme has been developed and combined with the techniques of rapid scan Fourier transform infrared spectroscopy to make sensitive, high resolution measurements of the vibrational spectrum of carbon monoxide molecules on evaporated nickel films. Adsorbed molecules are detected by attaching a germanium resistance thermometer to the sample, cooling the assembly to liquid helium temperatures, and measuring the temperature changes which occur when infrared radiation is absorbed. Spectra are presented for a range of CO coverages on an evaporated nickel film and a film damaged by ion bombardment. The positions, shapes, and intensities of the spectral lines from linear and bridge bonded CO molecules give information about the surface structure of the metal films and about the different ordered phases of the adsorbed molecules.