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This paper studies the forward–reflected–backward splitting algorithm with momentum terms for monotone inclusion problem of the sum of a maximal monotone and Lipschitz continuous monotone operators in Hilbert spaces. The forward–reflected–backward splitting algorithm is an interesting algorithm for inclusion problems with the sum of maximal monotone and Lipschitz continuous monotone operators due to the inherent feature of one forward evaluation and one backward evaluation per iteration it possesses. The results in this paper further explore the convergence behavior of the forward–reflected–backward splitting algorithm with momentum terms. We obtain weak, linear, and strong convergence results under the same inherent feature of one forward evaluation and one backward evaluation at each iteration. Numerical results show that forward–reflected–backward splitting algorithms with momentum terms are efficient and promising over some related splitting algorithms in the literature. [ABSTRACT FROM AUTHOR]

Concerns surrounding the environment along with inadequate energy supply and high cost of same are responsible for pollution, high energy demand, unpredictable and uneconomical power generation. These have contributed to the widespread agreement that sustainable renewable energy sources (RES) must be developed, particularly in isolated villages where expanding the grid may be challenging and financially unviable for power corporations. As a result, in order to effectively and cheaply utilize the plentiful renewable energy resources, an optimal sizing approach is required. This study is aimed at investigating the economic performance of the hybrid system of a stand-alone Small Hydropower/PV/Diesel generator with battery electricity production. The cost function was minimized using Dragonfly Algorithm (DA) in order to minimize the Cost of Energy (COE) generation. The decision variables are the number of small hydro turbines (NSHP), number of solar panels (NPV), number of batteries (NBATT) and the capacity of Diesel generator (PDG). The developed method is applied to a typical Kiri village in Shelleng Local Government area of Adamawa State. For uniformity, the hourly solar irradiance data were created by converting the monthly average solar irradiance data. A dragonfly optimization technique was utilized to reach an optimum solution for the hybrid system. The result obtained showed that the system components: small Hydropower, solar PV and Diesel generator were able to generate electrical power of 5,783,600 W, 56,259 W and 5.2941e-05 W respectively to meet the energy demand. Results obtained from the developed scheme were compared with those obtained when TORSCHE algorithm was used in optimizing the hybrid system. It was observed that a total energy cost of $5,224,500 was obtained for the developed technique while $5,839,600 was obtained as the total cost for the TORSCHE model. This showed that the developed scheme outperformed the system output from the TORSCHE algorithm in terms of cost of energy by 89.46%. [ABSTRACT FROM AUTHOR]

In this paper, a Halpern–Tseng-type algorithm for approximating zeros of the sum of two monotone operators whose zeros are J-fixed points of relatively J-nonexpansive mappings is introduced and studied. A strong convergence theorem is established in Banach spaces that are uniformly smooth and 2-uniformly convex. Furthermore, applications of the theorem to convex minimization and image-restoration problems are presented. In addition, the proposed algorithm is used in solving some classical image-recovery problems and a numerical example in a Banach space is presented to support the main theorem. Finally, the performance of the proposed algorithm is compared with that of some existing algorithms in the literature. [ABSTRACT FROM AUTHOR]

In this paper, relaxed and relaxed inertial modified Tseng algorithms for approximating zeros of sum of two monotone operators whose zeros are fixed points or J-fixed points of some nonexpansive-type mappings are introduced and studied. Strong convergence theorems are proved in the setting of real Banach spaces that are uniformly smooth and 2-uniformly convex. Furthermore, applications of the theorems to the concept of J-fixed point, convex minimization, image restoration and signal recovery problems are also presented. In addition, some interesting numerical implementations of our proposed methods in solving image recovery and compressed sensing problems are presented. Finally, the performance of our proposed methods are compared with that of some existing methods in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an inertial Halpern-type iterative algorithm for approximating a zero of the sum of two monotone operators in the setting of real Banach spaces that are 2-uniformly convex and uniformly smooth. Strong convergence of the sequence generated by our proposed algorithm is established by means of some new geometric inequalities proved in this paper that are of independent interest. Furthermore, numerical simulations in image restoration and compressed sensing problems are also presented. Finally, the performance of the proposed method is compared with that of some existing methods in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study an inertial algorithm for approximating solutions of split equality fixed point problem (SEFPP), involving quasi-phi-nonexpansive mappings in uniformly smooth and 2-uniformly convex real Banach spaces and establish a strong convergence theorem. We give applications of our result to split equality problem (SEP), split equality variational inclusion problem (SEVIP) and split equality equilibrium problem (SEEP). Our results extend, generalize and unify several recent inertial-type algorithms for approximating solutions of SEP and SEVIP. Moreover, to the best of our knowledge, our propose method which does not require any compactness type assumption on the operators is the first inertial algorithm for approximating solutions of SEFPP, SEP, SEVIP and SEEP in Banach spaces. [ABSTRACT FROM AUTHOR]

An exponentially weighted moving average (denoted as EWMA) chart is quite effective to detect small to moderate shifts. The adoption of the variable sampling interval (denoted as VSI) technique into the auxiliary information based EWMA chart (denoted as AIB-VSIEWMA) significantly improves the efficiency of the auxiliary information based EWMA (denoted as AIB-EWMA) chart in detecting small and moderate shifts, using the average time to signal (ATS) criterion when the precise shift size which must be detected quickly can be specified. However, in many industrial processes, the aforementioned size of the shift cannot be specified, particularly when practitioners have no prior knowledge about the process. This paper adopts the expected ATS (EATS) criterion based on the Markov chain approach to assess the efficiency of the AIB-VSIEWMA chart when the precise size of the shift cannot be specified. The AIB-VSIEWMA chart is compared with the AIB-EWMA chart using the ATS and EATS performance criteria. It is revealed that the AIB-VSIEWMA chart outperforms the AIB-EWMA chart as the former provides quicker detection of process shifts. [ABSTRACT FROM AUTHOR]

In this paper, we introduce three new inertial-like Bregman projection methods with a nonmonotone adaptive step-size for solving quasi-monotone variational inequalities in real Hilbert spaces. Under some suitable conditions, the weak convergence of these methods is proved without the prior knowledge of the Lipschitz constant of the operator and the strong convergence of some proposed methods under a strong quasi-monotonicity assumption of the mapping is also provided. Finally, several numerical experiments and applications in image restoration problems are provided to illustrate the performance of the proposed methods. [ABSTRACT FROM AUTHOR]

Deep-UV (DUV) supercontinuum (SC) sources based on gas-filled hollow-core fibers constitute perhaps the most viable solution towards ultrafast, compact, and tunable lasers in the UV spectral region, which can even also extend into the mid-infrared (IR). Noise and spectral stability of such broadband sources are key parameters that define their true potential and suitability towards real-world applications. In order to investigate the spectral stability and noise levels in these fiber-based DUV sources, we generate an SC spectrum that extends from 180 nm (through phase-matched dispersive waves - DWs) to 4 μm by pumping an argon-filled hollow-core anti-resonant fiber at a mid-IR wavelength of 2.45 μm. We characterize the long-term stability of the source over several days and the pulse-to-pulse relative intensity noise (RIN) of the DW at 275 nm. The results indicate no sign of spectral degradation over 110 hours, but the RIN of the DW pulses at 275 nm is found to be as high as 33.3%. Numerical simulations were carried out to investigate the spectral distribution of the RIN and the results confirm the experimental measurements and that the poor noise performance is due to the high RIN of the mid-IR pump laser, which was hitherto not considered in numerical modelling of these sources. The results presented herein provide an important step towards an understanding of the noise mechanism underlying such complex light-gas nonlinear interactions and demonstrate the need for pump laser stabilization. [ABSTRACT FROM AUTHOR]

Let B be a uniformly convex and uniformly smooth real Banach space with dual space B ∗ . Let F : B → B ∗ , K : B ∗ → B be maximal monotone mappings. An iterative algorithm is constructed and the sequence of the algorithm is proved to converge strongly to a solution of the Hammerstein equation u + K F u = 0 . This theorem is a significant improvement of some important recent results which were proved in real Hilbert spaces under the assumption that F and K are maximal monotone continuous and bounded. The continuity and boundedness restrictions on K and F have been dispensed with, using our new method, even in the more general setting considered in our theorems. Finally, numerical experiments are presented to illustrate the convergence of the sequence of our algorithm. [ABSTRACT FROM AUTHOR]

This paper summarizes the experience gained at Syngenta and at University of Aberdeen on visualization of gas-liquid mass transfer in agitated vessels. The aim is to show how simple experiments can be used to directly visualize the effect of vessel size, air flow rate, and agitation speed on the rate of mass transfer for gas-liquid reactions without the need for sophisticated probes or indirect calculations. The reaction used for visualization purposes is the "blue bottle" reaction, that is, the oxidation by oxygen of leucomethylene blue to methylene blue. This reaction produces a distinctive blue color, and its rate depends on the rate of oxygen mass transfer from the gas to the liquid phase. Therefore, this reaction can be used to visualize the rate of mass transfer and how this rate is affected by geometrical and operating parameters of agitated vessels. The described demonstration is furthermore highly convenient for educational purposes. This is the first demonstration visually illustrating scale-up effects in chemical processes. [ABSTRACT FROM AUTHOR]

new inertial iterative algorithm for approximating solution of split equality fixed point problem (SEFPP) for quasi-ϕ-nonexpansive mappings is introduced and studied in p-uniformly convex and uniformly smooth real Banach spaces, p > 1. A strong convergence theorem is proved without imposing any compactness-type condition on the mappings. Our theorems complement several important recent results that have been proved in 2-uniformly convex and uniformly smooth real Banach spaces. It is well known that these spaces do not include Lp, lp and the Sobolev spaces Wmp(Ω), for 2 < p < ∞. Our theorems, in particular, are applicable in these spaces. Furthermore, application of our theorem to split equality variational inclusion problem is presented. Finally, numerical examples are presented to illustrate the convergence of our algorithms. [ABSTRACT FROM AUTHOR]

An inertial algorithm for solving Hammerstein equations is presented. This algorithm is obtained as a consequence of a new inertial algorithm proposed and studied for solving nonlinear equations involving operators that are m-accretive. Some strong convergence theorems are proved in real Banach spaces that are uniformly smooth. Furthermore, comparisons of the numerical performance of our algorithms with the numerical performance of some recent important algorithms are presented. [ABSTRACT FROM AUTHOR]

Supercontinuum (SC) generation based on ultrashort pulse compression constitutes one of the most promising technologies towards ultra-wide bandwidth, high-brightness, and spatially coherent light sources for applications such as spectroscopy and microscopy. Here, multi-octave SC generation in a gas-filled hollow-core antiresonant fiber (HC-ARF) is reported spanning from 200 nm in the deep ultraviolet (DUV) to 4000 nm in the mid-infrared (mid-IR) having an output energy of 5 μJ. This was obtained by pumping at the center wavelength of the first anti-resonant transmission window (2460 nm) with ~100 fs pulses and an injected pulse energy of ~8 μJ. The mechanism behind the extreme spectral broadening relies upon intense soliton-plasma nonlinear dynamics which leads to efficient soliton self-compression and phase-matched dispersive wave (DW) emission in the DUV region. The strongest DW is observed at 275 nm which corresponds to the calculated phase-matching wavelength of the pump. Furthermore, the effect of changing the pump pulse energy and gas pressure on the nonlinear dynamics and their direct impact on SC generation was investigated. This work represents another step towards gas-filled fiber-based coherent sources, which is set to have a major impact on applications spanning from DUV to mid-IR. [ABSTRACT FROM AUTHOR]

Development of novel mid-infrared (MIR) lasers could ultimately boost emerging detection technologies towards innovative spectroscopic and imaging solutions. Photoacoustic (PA) modality has been heralded for years as one of the most powerful detection tools enabling high signal-to-noise ratio analysis. Here, we demonstrate a novel, compact and sensitive MIR-PA system for carbon dioxide (CO2) monitoring at its strongest absorption band by combining a gas-filled fiber laser and PA technology. Specifically, the PA signals were excited by a custom-made hydrogen (H2) based MIR Raman fiber laser source with a pulse energy of ⁓ 18 μJ, quantum efficiency of ⁓ 80% and peak power of ⁓ 3.9 kW. A CO2 detection limit of 605 ppbv was attained from the Allan deviation. This work constitutes an alternative method for advanced high-sensitivity gas detection. [ABSTRACT FROM AUTHOR]

An inertial iterative algorithm for approximating a point in the set of zeros of a maximal monotone operator which is also a common fixed point of a countable family of relatively nonexpansive operators is studied. Strong convergence theorem is proved in a uniformly convex and uniformly smooth real Banach space. This theorem extends, generalizes and complements several recent important results. Furthermore, the theorem is applied to convex optimization problems and to J-fixed point problems. Finally, some numerical examples are presented to show the effect of the inertial term in the convergence of the sequence of the algorithm. [ABSTRACT FROM AUTHOR]

As far as literature of quality control is concerned, this is the first article that advocates the run sum ratio scheme with measurement errors, called the RS‐RZ ME chart. The linear covariate error model is employed in designing the RS‐RZ ME chart in detecting increases and decreases in the ratio of two variables from the normal distribution. The average run length and expected average run length values of the RS‐RZ ME chart are obtained using the Markov chain model. A comparison of the RS‐RZ ME scheme with two measurement errors based charts in the literature, namely, the Shewhart ratio and standard run sum ratio charts is conducted. The results indicate the superiority of the RS‐RZ ME chart over the aforesaid existing charts for most of the shift sizes and shift intervals considered. The findings reveal that as the values of the parameters controlling the accuracy error of the measurement system, (θX,θY)$({{\theta _X},{\theta _Y}})$ increase, the RS‐RZ ME scheme's efficiency increases. In the same vein, as the values of the parameters controlling the precision of the measurement system, (ηX,ηY)$({{\eta _X},{\eta _Y}})$ decrease, the RS‐RZ ME scheme' efficiency increases. Furthermore, as the value of the correlation coefficient between variables X and Y increases, the RS‐RZ ME chart's efficiency increases. The application of the RS‐RZ ME scheme is illustrated using data from a food industry. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of the study was to determine how camel milk affects hyperglycemia, beta-cell function, oxidative stress, and inflammatory markers in type 2 diabetic pigs. Methods: Twenty-five (25) pigs were separated into five (5) groups of five pigs each, with five (5) non-diabetic and twenty (20) diabetic pigs in each group. Groups 1 and 2 received distilled water as the standard control and diabetic control groups, respectively, while Groups 3 and 4 received camel milk at 250 mL/day and 500 mL/day, respectively, and Group 5 received metformin at 500 mg/day. The experiment lasted ten weeks. At the end of the ten weeks, all the pigs were euthanized. Results: Treatments with camel milk substantially enhance glucose fasting levels by reducing hyperglycemia in diabetic pigs, significant level at (p < 0.05). When pigs given camel milk were compared with untreated diabetic pigs, there was a substantial rise (p < 0.05) in superoxide dismutase (SOD), catalase (CAT), and reduced glutathione (GSH) levels. Also, camel milk substantially lowered the levels of interleukin (IL-1β) and tumour necrosis factor-alpha (TNF-α) in diabetic pig serum. Similarly, immunohistochemical analysis of islet cells revealed an increase in insulin production, implying improved glycemic control and the eventual commitment of glucose to glycolysis. Conclusion: The bioactive-mediated anti-hyperglycemic and insulin release potential of camel milk treatments contributed to improving type 2 diabetes mellitus. Camel milk improved beta-cell function while reducing oxidative stress and inflammation in type 2 diabetic pigs. [ABSTRACT FROM AUTHOR]

In optimization theory, to speed up the convergence of iterative procedures, many mathematicians often use the inertial extrapolation method. In this article, based on the three‐term derivative‐free method for solving monotone nonlinear equations with convex constraints [Calcolo, 2016;53(2):133‐145], we design an inertial algorithm for finding the solutions of nonlinear equation with monotone and Lipschitz continuous operator. The convergence analysis is established under some mild conditions. Furthermore, numerical experiments are implemented to illustrate the behavior of the new algorithm. The numerical results have shown the effectiveness and fast convergence of the proposed inertial algorithm over the existing algorithm. Moreover, as an application, we extend this method to solve the LASSO problem to decode a sparse signal in compressive sensing. Performance comparisons illustrate the effectiveness and competitiveness of the method. [ABSTRACT FROM AUTHOR]

The realization of a table-top tunable deep-ultraviolet (UV) laser source with excellent noise properties would significantly benefit the scientific community, particularly within imaging and spectroscopic applications, where source noise has a crucial role. Here we provide a thorough characterization of the pulse-to-pulse relative intensity noise (RIN) of such a deep-UV source based on an argon (Ar)-filled anti-resonant hollow-core (AR HC) fiber. Suitable pump pulses are produced using a compact commercially available laser centered at 1030 nm with a pulse duration of 400 fs, followed by a nonlinear compression stage that generates pulses with 30 fs duration, 24.2 μJ energy at 100 kHz repetition rate and a RIN of < 1%. Pump pulses coupled into the AR HC fiber undergo extreme spectral broadening creating a supercontinuum, leading to efficient energy transfer to a phase-matched resonant dispersive wave (RDW) in the deep-UV spectral region. The center wavelength of the RDW could be tuned between 236 and 377 nm by adjusting the Ar pressure in a 140 mm length of fiber. Under optimal pump conditions the RIN properties were demonstrated to be exceptionally good, with a value as low as 1.9% at ~ 282 nm. The RIN is resolved spectrally for the pump pulses, the generated RDW and the broadband supercontinuum. These results constitute the first broadband RIN characterization of such a deep-UV source and provide a significant step forward towards a stable, compact and tunable laser source for applications in the deep-UV spectral region. [ABSTRACT FROM AUTHOR]