Development and application of a validated stability-indicating high-performance liquid chromatographic method using photodiode array detection for simultaneous determination of granisetron, methylparaben, propylparaben, sodium benzoate, and their main degradation products in oral pharmaceutical preparations

A simple, rapid, and sensitive RP-HPLC method using photodiode array detection was developed and validated for the simultaneous determination of granisetron hydrochloride, 1-methyl-1H-indazole-3-carboxylic acid (the main degradation product of granisetron), sodium benzoate, methylparaben, propylparaben, and 4-hydroxybenzoic acid (the main degradation product of parabens) in granisetron oral drops and solutions. The separation of the compounds was achieved within 8 min on a SymmetryShield RP18 column (100 x 4.6 mm id, 3.5 microm particle size) using the mobile phase acetonitrile--0.05 M KH2PO4 buffered to pH 3 using H3PO4 (3+7, v/v). The photodiode array detector was used to test the purity of the peaks, and the chromatograms were extracted at 240 nm. The method was validated, and validation acceptance criteria were met in all cases. The robust method was successfully applied to the determination of granisetron and preservatives, as well as their degradation products in different batches of granisetron oral drops and solutions. The method proved to be sensitive for determination down to 0.04% (w/w) of granisetron degradation product relative to granisetron and 0.03% (w/w) 4-hydroxybenzoic acid relative to total parabens.     

Bounds for increasing multi-state consecutive k-out-of-r-from-n: F system with equal components probabilities

The consecutive k-out-of-r-from-n: F system was generalized to multi-state case. This system consists of n linearly ordered components which are at state below j if and only if at least k_j components out of any r consecutive are in state below j. In this paper we suggest bounds of increasing multi-state consecutive-k-out-of-r-from-n: F system (k₁ ? k₂ ? ? ? k_M) by applying second order Boole–Bonferroni bounds and applying Hunter–Worsley upper bound. Also numerical results are given. The programs in V.B.6 of the algorithms are available upon request from the authors.     

A derivative concept with respect to an arbitrary kernel and applications to fractional calculus

In this paper, we propose a new concept of derivative with respect to an arbitrary kernel function. Several properties related to this new operator, like inversion rules and integration by parts, are studied. In particular, we introduce the notion of conjugate kernels, which will be useful to guaranty that the proposed derivative operator admits a right inverse. The proposed concept includes as special cases Riemann‐Liouville fractional derivatives, Hadamard fractional derivatives, and many other fractional operators. Moreover, using our concept, new fractional operators involving certain special functions are introduced, and some of their properties are studied. Finally, an existence result for a boundary value problem involving the introduced derivative operator is proved.     

On an inverse problem of reconstructing a subdiffusion process from nonlocal data

We consider a problem of modeling the thermal diffusion process in a closed metal wire wrapped around a thin sheet of insulation material. The layer of insulation is assumed to be slightly permeable. Therefore, the temperature value from one side affects the diffusion process on the other side. For this reason, the standard heat equation is modified, and a third term with an involution is added. Modeling of this process leads to the consideration of an inverse problem for a one‐dimensional fractional evolution equation with involution and with periodic boundary conditions with respect to a space variable. This equation interpolates heat equation. Such equations are also called nonlocal subdiffusion equations or nonlocal heat equations. The inverse problem consists in the restoration (simultaneously with the solution) of the unknown right‐hand side of the equation, which depends only on the spatial variable. The conditions for overdefinition are initial and final states. Existence and uniqueness results for the given problem are obtained via the method of separation of variables.     

Screening effect of Ti ions on the electrical conductivity and thermoelectric power of Mg ferrite

The samples Mg_1+xTi_xFe_2−2xO₄ were prepared in a single phase spinel structure as indicated from X-ray analysis. The preference of Mg²⁺ ions to the octahedral site decreases the ratio of the normal spinel in the investigated ferrite where the Mg²⁺ increases on the expense of the Fe³⁺ ions on the same site. The increase in the conductivity was found to be due to thermally activated mobility of charge carriers. The mobility data enhances the use of Verway model of conductivity which depends on the electron exchange between iron ions of different valences located on the same crystallographic sites. The existence of Ti⁴⁺ ions on the octahedral site screens the polarization and decreases the conductivity of the samples. Peculiar behavior was obtained for Ti content of 0.7 and 0.8 due to the presence of secondary phases.     

Multiaccess in all-optical networks with wavelength and code concurrency

A major obstacle in realizing fast packet switching in all-optical networks is the large tuning delays of tunable optical devices. This article proposes a multiaccess scheme for all-optical local area networks that employs both wavelength and code concurrency. In this scheme, several users share a wavelength channel through code multiplexing. The delay performance of hybrid wavelength/code division multiaccess is obtained under a simple, suboptimal access protocol based on cyclic search. Due to the reduction in the number of wavelength channels without an associated reduction in transmission concurrency, hybrid multiaccess is robust against tuning delays. At a given network throughput, the hybrid scheme achieves considerably lower delays than that of Wavelength Division Multiple Access even with a small amount of code concurrency. Conversely, the hybrid network can support a higher load when there is a maximum allowable value for the average packet delay.     

Untersuchung der Schwefelbilanz bei metallurgischen Prozessen unter Verwendung von 35S

Es werden Methoden und Ergebnisse der Untersuchung der Schwefelbilanz beim Krupp-Rennverfahren und beim Siemens- Martin-Prozeβ unter Verwendung von ³⁵S beschrieben. Die Markierungsverfahren für die Ausgangsstoffe werden angegeben.     

Blowing‐up solutions to two‐times fractional differential equations

Nonexistence results for a class of two‐times differential equations with fractional derivatives of orders between zero and one are presented. Furthermore, the result is extended to a two‐times system of two differential equations with fractional derivatives of orders between zero and one.     

On necessary and sufficient conditions for near-optimal singular stochastic controls

In this paper we discuss the necessary and sufficient conditions for near-optimal singular stochastic controls for the systems driven by a nonlinear stochastic differential equations (SDEs in short). The proof of our result is based on Ekeland’s variational principle and some delicate estimates of the state and adjoint processes. It is well known that optimal singular controls may fail to exist even in simple cases. This justifies the use of near-optimal singular controls, which exist under minimal conditions and are sufficient in most practical cases. Moreover, since there are many near-optimal singular controls, it is possible to choose suitable ones, that are convenient for implementation. This result is a generalization of Zhou’s stochastic maximum principle for near-optimality to singular control problem.