The classical limit definition of a derivative is expressed in a more general form. The general form includes two arbitrary functions of the parameter for which the limit is calculated. A special case of the general form, which includes scaling and translational symmetry transformations of the limiting parameter, is also discussed. The errors in using the classical definition and the generalized form are calculated for small values of the limiting parameter. The derivatives of some known functions are proven using the new definition. For some well-known functions, a suitable selection of the generalized form may introduce simplicity in calculating the derivatives.

The resonance spectrum of surface resistance derivative in quasi-two dimensional layered organic conductors has been calculated numerically for the out-of-plane and in-plane magnetic field. Not all but some of the resonances in a given series of transitions are present in the spectra. They are observed at the positions corresponding to the maxima in the surface resistance derivative curve and are in a good agreement with previously calculated magnetic field resonance positions. For tilted magnetic fields, there are more resonances present in the spectrum than in the case of a non-tilted field. Apart from the resonances corresponding to the transitions between the adjacent surface states there also appear resonances involving the transitions between the more distant surface states. This is correlated with the specific topology of Fermi surface of the organic conductors. The presented calculations will allow correct interpretation of the experimental curves for the resonance spectrum, and also to obtain information on the surface properties of these materials for their possible implementation in fabrication of devices based on organic molecular conductors.

In option pricing, we often deal with options whose payoffs depend on multiple factors such as foreign exchange rates, stocks, etc. Usually, it leads to a knowledge of the joint distributions and complicated integration procedures. The paper develops an alternative approach that converts the option pricing problem to a dual one and presents a solution to the problem in the optional semimartingale setting. The paper contains several examples which illustrate results in terms of the parameters of models and options.

Metal-organic frameworks (MOFs) have been subject of extensive scientific investigation in the last three decades and, currently, are one of the type of compounds most studied to be potentially applied in a wide range of distinct catalytic processes. Pristine MOF compounds provide several intriguing benefits for catalytic applications, including high interior surface areas and densities of active sites, allowing high catalytic reaction rates per volume, post-synthesis modified with com-plementary catalytic groups, enabling multiple functional groups to catalyze the reaction. Most of large-scale catalytic applications, including those in fuel processing, gas emission reduction and chemical synthesis, nevertheless the pristine MOFs often reveal limited stabilities and opportuni-ties for regeneration at high temperatures. As a result, the real applications of MOFs in these tech-nologies are likely to be constrained, and their controlled thermal modification aiming the prepa-ration of MOF-derivative compounds has been applied to induce crystalline structural changes and increase their structural stability, enhancing its potential applicability in more severe catalytic processes. Recent advances concerning the use of this strategy to boost the catalytic potential of the MOF-derivative compounds are outlined in this short-review article.

Modification of electrode surface with a selective layer gives the possibility to detect target ana-lytes of forensic interest. 3-(4-trifluoromethyl)-phenyl)-thiophene (ThPhCF3) was deposited on a graphite (G) electrode by electrochemical oxidation and characterized as a receptor for the recognition of synthetic stimulants (2-aminoindane, buphedrone, naphyrone). First, the structural characterization of the polymeric layer were obtained from Raman spectroscopy. Second, the electrochemical profiles of selected synthetic stimulants and their affinity to ThPhCF3/G-modified electrodes were studied using square wave voltammetry and electrochemical impedance spec-troscopy. The values of the adsorption constant show the importance of – PhCF3 groups in the interaction with synthetic stimulants, namely recognition by the formation of hydrogen bonds (Kads (buphedrone) < Kads (2-AI)) and interaction with aromatic H atoms (Kads (buphedrone) < Kads (naphyrone)). It was demonstrated that the polymeric layer derived from thiophene with – PhCF3 group is capable to increase the intensity of the electrochemical signal.

Recent technological advancements in produced water for the oil and gas industry have a long history that spreads over centuries and has roots with many mathematicians, physicists, engineers, and inventors. Working to understand the many ideas and questions has helped to bring the produced water technologies to where we are today. Fluid mechanics is an essential factor in the world of engineering because it comes with significant benefits when designing the necessary equipment to overcome the challenging endeavors of daily operations. Many of us believe certain ideas or products were developed within a specific year not fully understanding the idea or concept might be hundreds of years old. For example, when we think of fluid mechanics, we do not think of Archimedes' immersing King Hiero II crown in water. Archimedes did this to determine the displacement of the water as he knew gold was denser than silver. Archimedes was one of the pioneers who was part of the beginning of fluid mechanics. Another interesting fact is the first valve invented was in 1 AD by Heron of Alexandria. This valve can be described as the very first hydraulic valve. The evolution of technology over hundreds of years has made considerable innovations benefiting engineers all over the world. These innovations come in the form of PLCs, RTUs, PIDs, mathematical formulas, processing methods, and SCADA systems.