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Keywords = diamond-α integral

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12 pages, 1931 KiB  
Article
Voltammetric Determination of the Total Content of the Most Commonly Occurring Estrogens in Water Media
by Jaromíra Chýlková, Jan Bartáček, Natálie Měchová, Miloš Sedlák and Jiří Váňa
Molecules 2025, 30(3), 751; https://doi.org/10.3390/molecules30030751 - 6 Feb 2025
Viewed by 797
Abstract
Estrogens in aquatic environments pose significant ecological and health risks due to their cumulative effects rather than individual impacts. This study investigates the voltammetric behavior of estrone (E1), 17β-estradiol (E2), estriol (E3), and 17α-ethinylestradiol (EE2), presenting a cost-effective and straightforward method for their [...] Read more.
Estrogens in aquatic environments pose significant ecological and health risks due to their cumulative effects rather than individual impacts. This study investigates the voltammetric behavior of estrone (E1), 17β-estradiol (E2), estriol (E3), and 17α-ethinylestradiol (EE2), presenting a cost-effective and straightforward method for their simultaneous determination. Using differential pulse voltammetry (DPV) with a boron-doped diamond electrode, the method demonstrates high precision (deviations under 4%) and a linear dynamic range of 15.35–134.55 µmol·L−1. Integration of a vacuum evaporation step reduced detection limits to 10−8 mol·L−1, enabling effective analysis of real water samples. This optimized approach ensures practical applicability for monitoring total estrogen content in aquatic systems, providing an accessible and reliable alternative to conventional methods. Full article
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25 pages, 8892 KiB  
Article
Effects of Heat Treatment and Diamond Burnishing on Fatigue Behaviour and Corrosion Resistance of AISI 304 Austenitic Stainless Steel
by Jordan Maximov, Galya Duncheva, Angel Anchev, Vladimir Dunchev, Yaroslav Argirov and Maria Nikolova
Appl. Sci. 2023, 13(4), 2570; https://doi.org/10.3390/app13042570 - 16 Feb 2023
Cited by 17 | Viewed by 2568
Abstract
The surface cold working (SCW) of austenitic stainless steel (SS) causes martensitic transformation in the surface layers, and the percentage fraction of the strain-induced martensite depends on the degree of SCW. Higher content of α′−martensite increases the surface micro-hardness and fatigue strength, but [...] Read more.
The surface cold working (SCW) of austenitic stainless steel (SS) causes martensitic transformation in the surface layers, and the percentage fraction of the strain-induced martensite depends on the degree of SCW. Higher content of α′−martensite increases the surface micro-hardness and fatigue strength, but deterioration of the corrosion resistance is possible. Therefore, the desired operational behaviour of austenitic SS can be ensured by the corresponding degree of SCW and heat treatment. This article evaluates the effects of SCW performed by diamond burnishing (DB) and heat treatment on the surface integrity (SI), rotating fatigue strength, and corrosion resistance of AISI 304 austenitic SS for two initial states: as-received hot-rolled bar and initially heat-treated at 1100 °C for one hour followed by quenching in water. Then, DB was implemented as a smoothing and hardening process, both alone and in combination with heat treatment at 350 °C for three hours after DB. The electrochemical performance was examined by open circuit potential measurements, followed by potentiodynamic tests. For both initial states, smoothing DB provided the lowest roughness, whereas an improvement in the maximum surface micro-hardness was obtained after hardening DB and subsequent heat treatment. The maximum fatigue strength was obtained by hardening multi-pass DB without subsequent heat treatment for the as-received initial state. Smoothing DB and subsequent heat treatment maximised the surface corrosion resistance for the two initial states, whereas a minimum corrosion rate was obtained for the initially heat-treated state. For the as-received state, smoothing DB and subsequent heat treatment simultaneously lead to a high fatigue limit (equal to that obtained by hardening single-pass DB) and a low corrosion rate. Full article
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12 pages, 7844 KiB  
Article
Effect of Cu-Sn Addition on Corrosion Property of Pressureless Sintered Fe-Cu-Co Substrate Alloys
by Hongliang Tao, Yunzhu Ma, Yuhui Chen, Shuai Du, Haojun Zhou, Yuhang Yin, Yimin Li and Fenghua Luo
Materials 2023, 16(2), 728; https://doi.org/10.3390/ma16020728 - 11 Jan 2023
Cited by 1 | Viewed by 1580
Abstract
Fe-Cu-Co prealloyed powder is used for bonding metal of diamond tools. In order to obtain diamond tools with good mechanical properties by pressureless sintering, it is necessary to add Cu-Sn sintering aids. The substrate also has high corrosion resistance requirements, which is conducive [...] Read more.
Fe-Cu-Co prealloyed powder is used for bonding metal of diamond tools. In order to obtain diamond tools with good mechanical properties by pressureless sintering, it is necessary to add Cu-Sn sintering aids. The substrate also has high corrosion resistance requirements, which is conducive to the chemical erosion of diamond tools. This paper mainly studies the effects of Cu-Sn on the corrosion behavior of pressureless sintered Fe-Cu-Co substrate. The results show that the linear contraction rate and relative density of pressureless sintered Fe-Cu-Co alloy at 875 °C reach their peak when the Cu-Sn content is 8 wt.%, 15.13% and 97.5%, respectively. The substrate is mainly composed of α-Fe and Cu-rich phases, and selective corrosion occurs during electrochemical corrosion; namely, α-Fe grains are more prone to corrosion than Cu-rich grains to form porous corrosion surfaces. With the increase in Cu-Sn addition, the volume fraction of the Cu-rich phase increases, the corrosion current density and the passive current density gradually decrease, and the corrosion resistance of the alloy is improved. The amount and integrity of anodic passive film on the Fe-Cu-Co surface increases with the increase in Cu-Sn addition. The oxygen content of the anodic passivation film is lower than that of the active corrosion products of the α-Fe phase, thus reducing the oxygen concentration gradient and slowing down the corrosion. The addition of Cu-Sn is conducive to improving the corrosion resistance of Fe-Cu-Co alloy as the substrate of diamond tools. Full article
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10 pages, 270 KiB  
Article
Diamond-α Hardy-Type Inequalities on Time Scales
by Ahmed A. El-Deeb and Jan Awrejcewicz
Symmetry 2022, 14(10), 2047; https://doi.org/10.3390/sym14102047 - 30 Sep 2022
Cited by 5 | Viewed by 1728
Abstract
In the present article, we prove some new generalizations of dynamic inequalities of Hardy-type by utilizing diamond-α dynamic integrals on time scales. Furthermore, new generalizations of dynamic inequalities of Hardy-type in two variables on time scales are proved. Moreover, we present Hardy [...] Read more.
In the present article, we prove some new generalizations of dynamic inequalities of Hardy-type by utilizing diamond-α dynamic integrals on time scales. Furthermore, new generalizations of dynamic inequalities of Hardy-type in two variables on time scales are proved. Moreover, we present Hardy inequalities for several functions by using the diamond-α dynamic integrals on time scales. The results are proved by using the dynamic Jensen inequality and the Fubini theorem on time scales. Our main results extend existing results of the integral and discrete Hardy-type inequalities. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. Full article
(This article belongs to the Section Mathematics)
16 pages, 334 KiB  
Article
New Diamond-α Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces
by Ksenija Smoljak Kalamir
Axioms 2022, 11(7), 323; https://doi.org/10.3390/axioms11070323 - 1 Jul 2022
Cited by 7 | Viewed by 1809
Abstract
In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-α-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive σ-finite measures in time scale calculus. Moreover, as a special case, we [...] Read more.
In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-α-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive σ-finite measures in time scale calculus. Moreover, as a special case, we obtain these inequalities for the delta and the nabla integral. By using the relation between calculus on time scales T and differential calculus on R, we obtain already-known Steffensen-type inequalities. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
17 pages, 310 KiB  
Article
On Some New Weighted Steffensen-Type Inequalities on Time Scales
by Ahmed A. El-Deeb, Omar Bazighifan and Jan Awrejcewicz
Mathematics 2021, 9(21), 2670; https://doi.org/10.3390/math9212670 - 21 Oct 2021
Cited by 8 | Viewed by 1416
Abstract
The motivation of this paper is to explore some new inequalities of Steffensen-type which were demonstrated by Pečarić and Kalamir in 2014. The main idea is to investigate a class of certain inequalities by employing diamond-α dynamic integral on time scales. In [...] Read more.
The motivation of this paper is to explore some new inequalities of Steffensen-type which were demonstrated by Pečarić and Kalamir in 2014. The main idea is to investigate a class of certain inequalities by employing diamond-α dynamic integral on time scales. In addition, to obtain some new inequalities as special cases, we also extend our results to continuous and discrete calculations. Full article
13 pages, 773 KiB  
Article
A Variety of Dynamic Steffensen-Type Inequalities on a General Time Scale
by Ahmed Abdel-Moneim El-Deeb, Omar Bazighifan and Jan Awrejcewicz
Symmetry 2021, 13(9), 1738; https://doi.org/10.3390/sym13091738 - 18 Sep 2021
Cited by 8 | Viewed by 1767
Abstract
This work is motivated by the work of Josip Pečarić in 2013 and 1982 and the work of Srivastava in 2017. By the utilization of the diamond-α dynamic inequalities, which are defined as a linear mixture of the delta and nabla integrals, [...] Read more.
This work is motivated by the work of Josip Pečarić in 2013 and 1982 and the work of Srivastava in 2017. By the utilization of the diamond-α dynamic inequalities, which are defined as a linear mixture of the delta and nabla integrals, we present and prove very important generalized results of diamond-α Steffensen-type inequalities on a general time scale. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. Full article
24 pages, 336 KiB  
Article
Qi Type Diamond-Alpha Integral Inequalities
by Zhong-Xuan Mao, Ya-Ru Zhu, Bao-Hua Guo, Fu-Hai Wang, Yu-Hua Yang and Hai-Qing Zhao
Mathematics 2021, 9(4), 449; https://doi.org/10.3390/math9040449 - 23 Feb 2021
Cited by 3 | Viewed by 2183
Abstract
In this paper, we establish sufficient conditions for Qi type diamond-alpha integral inequalities and its generalized form on time scales. Full article
13 pages, 327 KiB  
Article
A New Approach for the Fractional Integral Operator in Time Scales with Variable Exponent Lebesgue Spaces
by Lütfi Akın
Fractal Fract. 2021, 5(1), 7; https://doi.org/10.3390/fractalfract5010007 - 8 Jan 2021
Cited by 7 | Viewed by 2837
Abstract
Integral equations and inequalities have an important place in time scales and harmonic analysis. The norm of integral operators is one of the important study topics in harmonic analysis. Using the norms in different variable exponent spaces, the boundedness or compactness of the [...] Read more.
Integral equations and inequalities have an important place in time scales and harmonic analysis. The norm of integral operators is one of the important study topics in harmonic analysis. Using the norms in different variable exponent spaces, the boundedness or compactness of the integral operators are examined. However, the norm of integral operators on time scales has been a matter of curiosity to us. In this study, we prove the equivalence of the norm of the restricted centered fractional maximal diamond-α integral operator Ma,δc to the norm of the centered fractional maximal diamond-α integral operator Mac on time scales with variable exponent Lebesgue spaces. This study will lead to the study of problems such as the boundedness and compactness of integral operators on time scales. Full article
19 pages, 293 KiB  
Article
More on Hölder’s Inequality and It’s Reverse via the Diamond-Alpha Integral
by M. Zakarya, H. A. Abd El-Hamid, Ghada AlNemer and H. M. Rezk
Symmetry 2020, 12(10), 1716; https://doi.org/10.3390/sym12101716 - 18 Oct 2020
Cited by 10 | Viewed by 2221
Abstract
In this paper, we investigate some new generalizations and refinements for Hölder’s inequality and it’s reverse on time scales through the diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals, which are used in various [...] Read more.
In this paper, we investigate some new generalizations and refinements for Hölder’s inequality and it’s reverse on time scales through the diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals, which are used in various problems involving symmetry. We develop a number of those symmetric inequalities to a general time scale. Our results as special cases extend some integral dynamic inequalities and Qi’s inequalities achieved on time scales and also include some integral disparities as particular cases when T=R. Full article
(This article belongs to the Special Issue Theory and Applications of Special Functions in Mathematical Physics)
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