The goal of this paper is to unify and extend the generating functions of the generalized Bernoulli polynomials, the generalized Euler polynomials and the generalized Genocchi polynomials associated ...with the positive real parameters
a
and
b
and the complex parameter
β
. By using this generating function, we derive recurrence relations and other properties for these polynomials. By applying the Mellin transformation to the generating function of the unification of Bernoulli, Euler and Genocchi polynomials, we construct a unification of the zeta functions. Furthermore, we give many properties and applications involving the functions and polynomials investigated in this paper.
In recent years, studying degenerate versions of some special polynomials, which was initiated by Carlitz in an investigation of the degenerate Bernoulli and Euler polynomials, regained lively ...interest of many mathematicians. In this paper, as a degenerate version of polyexponential functions introduced by Hardy, we study degenerate polyexponential functions and derive various properties of them. Also, we introduce new type degenerate Bell polynomials, which are different from the previously studied partially degenerate Bell polynomials and arise naturally in the recent study of degenerate zero-truncated Poisson random variables, and deduce some of their properties. Furthermore, we derive some identities connecting the polyexponential functions and the new type degenerate Bell polynomials.
The purpose of this paper is two-fold. First, we consider the classical Mordell–Tornheim zeta values and their alternating version. It is well-known that these values can be expressed as rational ...linear combinations of multiple zeta values (MZVs) and the alternating MZVs, respectively. We show that, however, the spaces generated by the Mordell–Tornheim zeta values over the rational numbers are in general much smaller than the MZV space and the alternating MZV space, respectively, which disproves a conjecture of Bachmann, Takeyama and Tasaka. Second, we study supercongruences of some finite sums of multiple integer variables. This kind of congruences is a variation of the so called finite multiple zeta values when the moduli are primes instead of prime powers. In general, these objects can be transformed to finite analogs of the Mordell–Tornheim sums which can be reduced to multiple harmonic sums. This approach not only simplifies the proof of a few previous results but also generalizes some of them. At the end of the paper, we provide a general conjecture involving this type of sums, which is supported by strong numerical evidence.
We provide explicit upper bounds of the order logt/loglogt for |ζ′(s)/ζ(s)| and |1/ζ(s)| when σ is close to 1. These improve existing bounds for ζ(s) on the 1-line.
Adequate characterization of NPs (nanoparticles) is of paramount importance to develop well defined nanoformulations of therapeutic relevance. Determination of particle size and surface charge of NPs ...are indispensable for proper characterization of NPs. DLS (dynamic light scattering) and ZP (zeta potential) measurements have gained popularity as simple, easy and reproducible tools to ascertain particle size and surface charge. Unfortunately, on practical grounds plenty of challenges exist regarding these two techniques including inadequate understanding of the operating principles and dealing with critical issues like sample preparation and interpretation of the data. As both DLS and ZP have emerged from the realms of physical colloid chemistry – it is difficult for researchers engaged in nanomedicine research to master these two techniques. Additionally, there is little literature available in drug delivery research which offers a simple, concise account on these techniques. This review tries to address this issue while providing the fundamental principles of these techniques, summarizing the core mathematical principles and offering practical guidelines on tackling commonly encountered problems while running DLS and ZP measurements. Finally, the review tries to analyze the relevance of these two techniques from translatory perspective.
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Nanofluids are complex fluids, mainly proposed to improve the efficiency of thermal systems. However, their poor stability, caused by the agglomeration and sedimentation of ...nanoparticles over time, has limited their practical application. A common technique to increase the stability of nanofluids is to add surfactants, which produce electrostatic or steric repulsion between nanoparticles, thus avoiding their agglomeration. This work evaluated the effects of surfactants and their concentration on the zeta potential and hydrodynamic diameter at different pH values as an indicator of nanofluids stability. Commercial alumina nanoparticles (0.1 wt.%) were dispersed in deionized water using two surfactants (cetyltrimethylammonium bromide, CTAB and sodium dodecylbenzenesulfonate, SDBS) at different concentrations, and the pH values were varied (2–12) by adding hydrochloric acid and sodium hydroxide. The results show the importance of the critical micelle concentration value in the nanofluids stabilization by electrostatic repulsion between nanoparticles and indicate that SDBS at a concentration of 0.064 wt.% (critical micelle concentration) offers the best dispersion conditions according with their zeta potential values, allowing high stability regardless of the pH value of the suspension.
We examine an unstudied manuscript of N.S. Koshliakov over 150 pages long and containing the theory of two interesting generalizations ζp(s) and ηp(s) of the Riemann zeta function ζ(s), which we call ...Koshliakov zeta functions. His theory has its genesis in a problem in the analytical theory of heat distribution which was analyzed by him. In this paper, we further build upon his theory and obtain two new modular relations in the setting of Koshliakov zeta functions, each of which gives an infinite family of identities, one for each p∈R+. The first one is a generalization of Ramanujan's famous formula for ζ(2m+1) and the second is an elegant extension of a modular relation on page 220 of Ramanujan's Lost Notebook. Several interesting corollaries and applications of these modular relations are obtained including a new representation for ζ(4m+3).
It is difficult to yield a high combustible matter recovery in the flotation of low rank coal with common oily collectors. This study focuses on the enhancement in flotation performance of low rank ...coal by combining diesel oil with didodecyldimethylammonium bromide (DDAB), as well as its corresponding intensifying mechanism. The adsorption of DDAB and/or diesel oil on the pure coal and quartz surfaces was investigated based on the zeta potential and FTIR analyses, while the floatability of the coal and quartz samples before and after pretreatment was evaluated by the attachment time and flotation results. The results indicated that DDAB had great effects on the zeta potentials of coal and quartz, and the isoelectric points of these two samples were observed at the DDAB concentrations of about 0.007 and 0.006 g/L, respectively. Additionally, according to the FTIR analyses, the physical and chemical adsorptions were proposed to interpret the adsorption of DDAB, and diesel oil and mixed diesel oil/DDAB on the coal surface, respectively. Meanwhile, the diesel oil’s adsorption of on the coal surface was enhanced by the conditioning process with the mixed DDAB/diesel oil. In contrast, diesel oil adsorption on the quartz was very little in quantity. As a result, a great difference in surface hydrophobicity between the coal and the quartz was attained, and an excellent flotation performance was obtained by using the mixed DDAB/diesel oil. However, a too low surface tension of flotation pulp caused by the excessive DDAB seems to be unfavorable to the flotation of coal samples. In this case, water with less surface tension was readier to spread on the coal surface than diesel oil, thereby making the coal hydrophilic and meanwhile hindering the diesel oil’s spreading on its surface.
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Crude oil, water and rock (CWR) surface chemistry is a key parameter in oil and gas recovery from hydrocarbon reservoirs. This paper presents the chemistry of CWR interaction in ...presence of two water soluble nanoparticles for carbonate rocks. Two most common nanoparticles of aluminium oxide (Al2O3) and silica (SiO2) were selected and utilised for this study. Calcite was first modified to an oil-wet system to resemble the reservoir wetting condition then treated with nano-fluids containing under study nanoparticles at different concentrations. Alteration of wettability was then quantified using contact angle measurements, and zeta potential analysis. The change in fluid chemistry of the water due to presence of nanoparticles was also monitored before and after treatment of carbonate rock. The results show that after treatment of the oil-wet samples with nano-fluids, the solution’s pH decreased for SiO2 while it increased slightly for Al2O3. The contact angle results show a decrease trend for both nanoparticles but more pronounced for Al2O3. These results are in line with zeta potential results in which very negative surface charge for an oil-wet rock was converted to less negative or even positive for certain concentrations of nano-particles. Floating phenomenon also applied to calculate the level of water percentage between floated and sank powder for the modified calcite where amount of water level increased significantly when nanoparticles added to water solutions. Comparison of all tests show that silica nano-fluid with concentration between 0.1 and 2 wt % can be efficient EOR agent. High salinity is definitely not a good option to formulate nano-fluids such as alumina and silica at high concentrations showing inverse effects.
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