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.
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.
•ZnONPs were biologically synthesized using palm fruit extract as reducing and stabilizing agent.•The size and shape of bio-synthesized ZnONPs depends on the concentrations of the extract.•In vitro ...studies on ZnONPs induce a significant reduction of Bcl-2 expression on MCF-7 cells.•In vivo evaluation verified the biocompatibility of DOX-ZnONPs, no significant toxicity on blood stream as well.
The green synthesis of zinc oxide nanoparticles (ZnONPs) using Borassus flabellifer fruit extract was characterized by UV–visible spectroscopy, FT-IR, XRD, TEM, Zeta potential and EDS analysis. The UV–visible spectrum showed an absorption peak at 368nm that reflects surface Plasmon resonance (SPR) ZnONPs. TEM photograph showed that the green synthesized ZnONPs were porous in nature and rod like structure with an average size of 55nm. The Zeta potential value of −21.5mV revealed the surface charge of green synthesized ZnONPs. In this study, we examined the synthesized DOX-ZnONPs exhibited a dose-dependent cytotoxicity against MCF-7 and HT-29. The inhibitory concentration (IC50) was found to be 0.125μgmL−1 for MCF-7 and HT-29 cells. An induction of apoptosis was evidenced by nuclear stain Hoechst 33258. In vivo toxicity assessment showed that DOX-ZnONPs have low systemic toxicity in murine model system. The results prove that the DOX-ZnONPs has low toxicity and high therapy efficacy, which provides convincing evidence for the green biosynthesized ZnO as a promising candidate for a drug delivery system.
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•Magnetic MnFe2O4 along with H2O2 was tested for catalytic oxidation of norfloxacin.•Norfloxacin could be removed efficiently at neutral pH.•Surface OH played a key role on ...norfloxacin removal.•Degradation intermediates were identified, and three degradation pathways were proposed.
Magnetic MnFe2O4 particles were prepared by sol-gel method and used to activate H2O2 for norfloxacin removal from water. The results of hydrodynamic particle size distribution and Zeta potential analyses show that the particle size ranged from 100 nm to 500 nm, and Zeta potential from −76 mV to −25 mV at pHintial = 7.0. The MnFe2O4/H2O2 system was able to remove 90.6% of norfloxacin at neutral pH, and the spent material can be reused in multiple cycles of operations. Fluorescence detection and DMPO capture analyses indicated that OH was the main free radicals, which played a primary role in degradation of norfloxacin. The valence variations of Mn and Fe were analyzed by XPS, and the results showed that coupled transformations of Mn2+/Mn3+ and Fe2+/Fe3+ were involved in generation of OH. Moreover, the removal rate in the MnFe2O4/H2O2 system showed a positive correlation with the adsorption efficiency of NOR by MnFe2O4. Eight degradation intermediates were detected by LC-QToF-MS/MS, and consequently, three degradation pathways were proposed, including defluorination, piperazinyl ring opening, and quinolone transformation. Further analyses of F−, NH4+, NO3− and NO2− before and after the reaction showed that defluorination process was the main degradation pathway. The MnFe2O4/H2O2 system may offer an efficient alterative for degradation of emerging persistent contaminants.
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