Determination of vanadium in titanate-based ferroelectrics by INAA with discriminating gamma-ray spectrometry

Instrumental neutron activation analysis was used for determination of vanadium mass fraction in crystals of incipient ferroelectric strontium titanate and ferroelectric barium titanate. In order to improve vanadium limit of detection, discriminating gamma-ray spectrometry was used by inserting an absorption filter between the samples and an HPGe detector. The use of the absorption lead filter 6-mm thick yielded improvement of the vanadium limit of detection by a factor of two. The vanadium mass fraction determined in a quality control sample, which was NIST standard reference material SRM 1648 Urban Particulate Matter, was in close agreement with the certified value.

     

On-capillary fluorescent labeling of saccharides for capillary electrophoresis

The feasibility of on-capillary derivatization of saccharides by aromatic amine-based fluorescent labeling agents was tested. To avoid the problematic evolution of gaseous hydrogen cyanide, the Schiff base reduction by sodium cyanoborohydride, as the second step of the standard reductive amination protocol, was omitted. Glucose was used as a model analyte and 7-amino-1,3-naphthalenedisulfonic acid as the labeling agent. Our experiments showed that the direct reaction of the saccharide with the labeling agent in 2.5-M acetic acid yields a labeled product that is sufficiently stable to be separated from the labeling agent in 20-mM phosphate buffer, pH 3.5, and detected using UV detection. The glucose and label zones were introduced separately into the capillary and mixed using a negative voltage. Mixing voltage, its duration, the concentration of acetic acid in the reaction zone, and the waiting time between mixing and separation were optimized. To show the applicability of the procedure to a broader range of analytes, a mixture of different types of saccharides, that is, xylose (pentose), fucose (hexose), glucose (hexose), N-acetylglucosamine (N-acetylaminosaccharide), and lactose (disaccharide), was subjected to derivatization and analysis under the optimal conditions. The linearity and repeatability of the process were evaluated as critical parameters for its analytical applications. Six-point calibration dependences in the 1–50 mM range showed excellent determination coefficients of 0.9992 or higher for all five saccharides tested. The repeatability of the labeled saccharide peak areas was between 2.2% and 4.3%.     

On the optimization of Gegenbauer operational matrix of integration

The theory of Gegenbauer (ultraspherical) polynomial approximation has received considerable attention in recent decades. In particular, the Gegenbauer polynomials have been applied extensively in the resolution of the Gibbs phenomenon, construction of numerical quadratures, solution of ordinary and partial differential equations, integral and integro-differential equations, optimal control problems, etc. To achieve better solution approximations, some methods presented in the literature apply the Gegenbauer operational matrix of integration for approximating the integral operations, and recast many of the aforementioned problems into unconstrained/constrained optimization problems. The Gegenbauer parameter α associated with the Gegenbauer polynomials is then added as an extra unknown variable to be optimized in the resulting optimization problem as an attempt to optimize its value rather than choosing a random value. This issue is addressed in this article as we prove theoretically that it is invalid. In particular, we provide a solid mathematical proof demonstrating that optimizing the Gegenbauer operational matrix of integration for the solution of various mathematical problems by recasting them into equivalent optimization problems with α added as an extra optimization variable violates the discrete Gegenbauer orthonormality relation, and may in turn produce false solution approximations.     

Probabilistic time-dependent vehicle routing problem

Central European Journal of Operations Research - The probabilistic time-dependent vehicle routing problem is presented in this paper. It is a novel variant of the vehicle routing problem. The...     

Solving boundary value problems,integral, and integro-differential equations using Gegenbauer integration matrices

We introduce a hybrid Gegenbauer (ultraspherical) integration method (HGIM) for solving boundary value problems (BVPs), integral and integro-differential equations. The proposed approach recasts the original problems into their integral formulations, which are then discretized into linear systems of algebraic equations using Gegenbauer integration matrices (GIMs). The resulting linear systems are well-conditioned and can be easily solved using standard linear system solvers. A study on the error bounds of the proposed method is presented, and the spectral convergence is proven for two-point BVPs (TPBVPs). Comparisons with other competitive methods in the recent literature are included. The proposed method results in an efficient algorithm, and spectral accuracy is verified using eight test examples addressing the aforementioned classes of problems. The proposed method can be applied on a broad range of mathematical problems while producing highly accurate results. The developed numerical scheme provides a viable alternative to other solution methods when high-order approximations are required using only a relatively small number of solution nodes.     

Ideals of a C *-algebra generated by an operator algebra

In this paper, we consider ideals of a C ^*-algebra C^*(B){C^*(\mathcal{B})} generated by an operator algebra B{\mathcal{B}} . A closed ideal J í C^*(B){J\subseteq C^*(\mathcal{B})} is called a K-boundary ideal if the restriction of the quotient map on B{\mathcal{B}} has a completely bounded inverse with cb-norm equal to K ⁻¹. For K = 1 one gets the notion of boundary ideals introduced by Arveson. We study properties of the K-boundary ideals and characterize them in the case when operator algebra λ-norms itself. Several reformulations of the Kadison similarity problem are given. In particular, the affirmative answer to this problem is equivalent to the statement that every bounded homomorphism from C^*(B){C^*(\mathcal{B})} onto B{\mathcal{B}} which is a projection on B{\mathcal{B}} is completely bounded. Moreover, we prove that Kadison’s similarity problem is decided on one particular C ^*-algebra which is a completion of the *-double of M₂(\mathbbC){M_2(\mathbb{C})} .     

Assessing Similarity of Random sets via Skeletons

Methodology and Computing in Applied Probability - The paper concerns a method for assessing similarity of realisations of random sets based on a construction of their morphological skeletons and a...