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We investigated the wave solitons for stochastic (3+1)-dimensional nonlinear Schrödinger equation with multiplicative white noise in the Itô sense which can be used to identify various nonlinear phenomena and mechanisms in the fields of optical fibers, physics, electric communication, engineering sciences and many others. The modified extended direct algebraic method is used to conduct the study. Many wave solutions are achieved like bright solitons, dark solitons, singular solitons, periodic wave solutions and singular periodic wave solutions. The impact of the noise is illustrated graphically using examples of some of the retrieved solutions with various noise strengths. [ABSTRACT FROM AUTHOR]

One of the core concepts of contemporary control theory is the idea that a dynamical system can be controlled. Several abstract settings have been developed to describe the distributed control systems in a domain in which the control is acted through the boundary. In this manuscript, we investigate the boundary approximate controllability (ABC) of stochastic differential inclusion (SDI) with Hilfer fractional derivative (HFD) and nonlocal condition by implementing the principle of stochastic analysis, the fixed-point theorem, fractional calculus and multi-valued map. Moreover, an example is offered to define the primary results. [ABSTRACT FROM AUTHOR]

The motivation behind this work is the preparation of polyurethane-magnesium aluminum layered double hydroxide (PU-LDH) nanocomposite and its application as a coating for steel protection. The coating was prepared with different doses of LDH, ranging from 0 to 2% of the coating weight. The effect of different concentrations on the mechanical, adhesion, and surface properties of PU coating is studied. Firstly, LDH was prepared via the coprecipitation process and then distributed in PU matrix. The nanocomposites were then crosslinked in the form of coating layers on steel. The preparation of the thermally stable crystalline LDH nanoparticles with 89 nm particle size was confirmed by FTIR, XRD, DLS, and TGA. SEM photos showed the dispersed and intercalated structure. The coating characteristics demonstrate that addition of LDH decreased the drying time and increased the dry film thickness of PU up to 1.5% due to the crosslinking between the large surface area nanofiller and polyurethane matrix. Furthermore, the prepared LDH nanofiller increased the adhesion strength, impact resistance, abrasion resistance, modulus, and flexibility of PU due to the strong polymeric network structure. The 2% nanocomposite coating shows poor properties due to the excess concentration and heterogeneous dispersion of nanoparticles within the PU polymer. The resistance to fire and some chemicals was supported by the thermally and physically stable LDH nanoclay. The former characterizations state that the proposed PU-LDH nanocomposite is an enhanced and applicable coating. [ABSTRACT FROM AUTHOR]

We investigated the extended sixth-order Korteweg–de Vries (KdV6) equation which describes many nonlinear phenomena. The improved modified (IM) extended tanh-function method is used to conduct the study. Many exact solutions, like dark, combo singular-dark and singular soliton are achieved. Moreover, hyperbolic solutions, singular periodic solutions, rational solutions, exponential solutions and Jacobi elliptic function (JEF) solutions are derived. Graphical illustrations are presented to visually depict the dynamics of selected solutions. [ABSTRACT FROM AUTHOR]

Two probiotics were evaluated for their impact on neutral detergent fiber (NDF) and acid detergent fiber (ADF) as well as in vitro dry matter disappearance (DMD) of palm kernel cake (PKC), as a source of dietary protein and/or energy for ruminants. The treatments were four different rations: CS (control), PS (PKC as source of energy), P (PKC as source of energy and protein), and PC; two commercial probiotics formulas (ZAD and ICEC-Trol) were applied with four applications (control: without probiotic, Z: ZAD, ZI: combination of ZAD + ICEC-Trol, and I: ICEC-Trol). Using Cornell Net Carbohydrate and Protein System (CNCPS) v6.5, the experimental diets' chemical analysis and fermentability were assessed. Adding the ZAD + ICEC and ICEC was improved (P < 0.05) DM disappearance (15%), NDF digestibility (14%), and ADF digestibility (26%). Using the CNCPS indicated that PS, P, and PC rations were higher in NDF than CS ration by about 28%, and CS and PC rations were higher in NSC, NFC, and total carbohydrate (CHO) by 34, 33, and 9% respectively more than PS and P rations. CS and PC rations occurred improvement in fermentability in organic matter, total carbohydrate, and starch by 19.5, 18.5, and 16.5%, respectively. In conclusion, using probiotics with PKC resulted in a greater elimination of dry matter disappearance and improved NDF and ADF degradation, and feeding ruminants palm kernel cake as a source of protein or energy and supplementing their diets with probiotics. [ABSTRACT FROM AUTHOR]

In this paper, a new model of a nanobeam of silicon nitride based on thermomass motion and the generalized thermoviscoelasticity theory is used. Ramp-type heat conduction has thermally loaded a simply supported thermoviscoelastic nanobeam. The governing equations have been constructed and solved in the Laplace transform domain. The numerical results have been represented in figures to show the effects of the thermoviscoelastic, drift velocity, and ramp-time heat parameters. Mechanical relaxation time has a significant impact on the mechanical wave. Moreover, the drift velocity and ramp-time heat parameters significantly affect all the studied functions. [ABSTRACT FROM AUTHOR]

In the current work, we investigate the optical solitons and exact solutions for the conformable time fractional generalized Radhakrishnan–Kundu–Lakshmanan (GRKL)equation with the polynomial law of nonlinearity which represent the mathematical model of pulse propagation in a nonlinear medium in optical fibers. The modified extended direct algebraic method is presented to get the exact solutions for this model. Many varieties of traveling wave solutions are established like, solitons (bright, dark, singular, combo singular-dark), combo periodic solutions, periodic solutions, Jacobi elliptic solutions, exponential solutions and Weierstrass elliptic solutions. The impact of the fractional derivative is illustrated graphically using examples of some of the retrieved solutions with various values of fractional order. [ABSTRACT FROM AUTHOR]

The optimal reactive power dispatch (ORPD) problem is a critical factor in maintaining the safe and efficient operation of electric networks. Due to its mixed-variable nonlinear nature, addressing this problem requires an appropriate optimization algorithm. In this study, a novel approach based on the combination of artificial rabbits optimization (ARO) and gradient-based optimization (GBO) algorithms was proposed to solve the ORPD problem in electric networks. The performance of the proposed AROGBO algorithm were verified on 7 numerical optimization test functions. To evaluate the effectiveness of this hybrid AROGBO technique, standard IEEE-30, IEEE-57 bus, and IEEE-118 bus test systems were employed, with two objective functions tested for each system: minimum total power loss and minimum total voltage deviations. The AROGBO, ARO, and GBO algorithms were utilized in each case to determine the optimal values of the generator voltage, transformer tap changer positions, and reactive power compensation values. A comprehensive comparison was made between the results obtained from the hybrid AROGBO algorithm, standard ARO and GBO algorithms, and other metaheuristic optimization techniques. The simulation attainments verify the accuracy and stability of the proposed AROGBO methodology in solving the ORPD problem. [ABSTRACT FROM AUTHOR]

This article explores a wide range of envelope soliton pulses and their behavior during propagation through a birefringent optical fiber. The propagation of light in such fibers is governed by two coupled non-linear Schrödinger equations (CNLSEs), which account for both coherent and incoherent non-linear couplings. To investigate these solitons, an improved modified extended tanh function scheme (IMETFS) is employed. The study focuses on elliptical core optical fibers and examines the significance of various optical solitons in the presence of group-velocity dispersion and third-order nonlinearity. The findings illustrate that birefringent optical fibers can generate a diverse array of nonlinear periodic waves and localized pulses. The different types of soliton solutions identified include singular, bright, rational, exponential, Jacobi elliptic functions (JEFs), Weierstrass elliptic doubly periodic solutions, and singular periodic solutions. Comparisons with existing literature highlight the novelty and substantive contributions of the discovered wave solutions to current research in nonlinear optics. The success of this approach suggests its potential applicability in addressing nonlinear challenges across different fields, particularly in soliton theory, where similar models are frequently encountered. Additionally, the article presents visual representations of these solutions through 3D and 2D plots, aiding in the understanding of their behaviors. [ABSTRACT FROM AUTHOR]

In this paper, a novel application of the improved modified extended tanh function has been implemented to derive analytical solutions for the longitudinal wave equation in a magneto-electro-elastic annular bar model. Singular, bright, dark, rational wave, Weierstrass elliptic doubly periodic, and exponential forms, are generated. These solutions are depicted through surface plots that are derived from numerical simulations, providing valuable insights into their dynamic characteristics. It is anticipated that a substantial contribution will be made to advancing the nonlinear scientific community by these results. This work uncovers novel traveling wave solutions, demonstrating a unique contribution to the field. It is noteworthy that Wolfram Mathematica® software is employed in the exploration and visualization of dynamic solitary perturb solutions. The diverse solutions are presented through 2D, 3D, and contour charts, concluding the work. [ABSTRACT FROM AUTHOR]

As delays are common, persistent, and ingrained in daily life, it is imperative to take them into account. In this work, we explore the averaging principle for impulsive Atangana–Baleanu fractional stochastic delay differential equations driven by Lévy noise. The link between the averaged equation solutions and the equivalent solutions of the original equations is shown in the sense of mean square. To achieve the intended outcomes, fractional calculus, semigroup properties, and stochastic analysis theory are used. We also provide an example to demonstrate the practicality and relevance of our research. [ABSTRACT FROM AUTHOR]

The development of polymer composites, considering the environmental issues, is aimed for minimizing the industrial content. New environmental-friendly nanocomposites, based on silicone rubber matrix and different concentrations of natural fiber/chromium oxide fillers, are prepared for the first time. The microstructural analysis confirms the successful obtaining of microfibers after treatment and chromium oxide nanoparticles and the formation of the final composite. The nanocomposites achieved improved physical and mechanical properties due to the dual effect of both fillers and attachment to the matrix. The 1% optimized nanocomposite achieved the highest modulus, dielectric properties, hydrophobicity, and surface stability. The effect of exposure to weathering conditions was studied. The characterization sentence asserts the preparation of a novel silicone rubber nanocomposite with improved properties, along with the environmental impact, regarding the dual effect of natural fiber waste and chromium oxide nanoparticles. [ABSTRACT FROM AUTHOR]

In this article, the modified extended direct algebraic method is applied for the perturbed highly dispersive nonlinear Schrödinger equation with conformable fractional derivative and sextic-power law refractive index. Various types of solutions are extracted such as bright solitons, dark solitons, combo bright-dark solitons, singular solitons, singular periodic wave solutions, exponential wave solutions and rational solutions. The impact of the fractional derivative is illustrated graphically using examples of some of the retrieved solutions with various values of fractional order. [ABSTRACT FROM AUTHOR]

In the ongoing study, the modified extended direct algebraic method (MEDAM) is used to study an extended (2+1)-dimensional perturbed nonlinear Schrödinger equation (PNLSE) with Kerr law nonlinearity in a nano optical fiber. This equation mimic the wave actuation through optical fibers. Different optical solitary waves are established such bright, dark and singular solitons. Moreover, we extract several kind of solutions like hyperbolic and Weierstrass elliptic solutions. To show the physical characteristics of the established solutions, many selected solutions are visually depicted. [ABSTRACT FROM AUTHOR]

Our goal in this paper is to obtain the stochastic wave solutions of the stochastic perturbed Schrödinger–Hirota equation. Our study mainly depends on applying the modified extended direct algebraic approach as well as the new Jacobi elliptic function method to get the soliton solutions and other exact solutions of our model of interest, such as bright solitons, singular solitons, periodic solutions and hyperbolic solutions. The impact of the noise is illustrated graphically using examples of some of the retrieved solutions with various noise strengths. [ABSTRACT FROM AUTHOR]

This study investigates optical solitons and other traveling wave solutions in fiber Bragg gratings for coupled nonlinear Schrödinger equations with cubic quadratic nonlinearity using the improved modified extended tanh-function method (IMETFM). We discover a highly dispersive solitons in fiber Bragg such as bright solitons, dark solitons, combo bright–dark solitons and singular solitons. Moreover, we obtain hyperbolic solutions, combo hyperbolic solutions, combo periodic solutions, singular periodic solutions, rational solutions, exponential solutions, and Jacobi elliptic solutions. By comparing our obtained travelling wave solutions with existing literature, we demonstrate their novelty and substantive contribution to current research. The success of our approach suggests its potential applicability to address various nonlinear challenges in different fields, particularly within soliton theory, since the analyzed model appears in a multitude of applications. These findings are of great significance for the further development of optical communication systems. Additionally, the physical meaning of the geometrical structures for some solutions is discussed for different choices of the free parameters. It is important to mention that our proposed method is highly effective, consistent, and impactful and can be utilized to solve different physical models. [ABSTRACT FROM AUTHOR]

This study examines the analytic wave solutions of a highly dispersive perturbed complex Ginzburg–Landau equation (CGLE) with conformable fractional derivative and polynomial law of nonlinearity using the improved modified extended tanh-function method. The results show a wide range of solutions including (bright, dark, singular) solitons, Jacobi elliptic solutions, exponential solutions, and Weierstrass elliptic solutions. The obtained soliton solutions showcase diverse dynamics, encompassing different solitary waves and localized structures. The polynomial nonlinearity adds complexity to the dynamics, resulting in the emergence of new solitons with distinct characteristics. The impact of the fractional derivative is illustrated graphically using examples of some of the retrieved solutions with various values of fractional order. [ABSTRACT FROM AUTHOR]

The optical soliton and exact solutions of the stochastic concatenation model are obtained by using the modified extended direct algebraic method. This method provides a wide variety of stochastic solutions, including stochastic bright solitons, stochastic dark solitons, stochastic dark combo solitons, stochastic singular combo solitons, stochastic periodic solutions, stochastic rational solutions, stochastic Jacobi elliptic functions solutions and stochastic Weierstrass elliptic functions solutions. For a variety of nonlinear partial differential equations, this method offers a practical and effective method for determining exact solutions. The impact of the noise is illustrated graphically using examples of some of the retrieved solutions with various noise strengths. [ABSTRACT FROM AUTHOR]

This paper provides six metaheuristic algorithms, namely Fast Cuckoo Search (FCS), Salp Swarm Algorithm (SSA), Dynamic control Cuckoo search (DCCS), Gradient-Based Optimizer (GBO), Northern Goshawk Optimization (NGO), Opposition Flow Direction Algorithm (OFDA) to efficiently solve the optimal power flow (OPF) issue. Under standard and conservative operating settings, the OPF problem is modeled utilizing a range of objectives, constraints, and formulations. Five case studies have been conducted using IEEE 30-bus and IEEE 118-bus standard test systems to evaluate the effectiveness and robustness of the proposed algorithms. A performance evaluation procedure is suggested to compare the optimization techniques' strength and resilience. A fresh comparison methodology is created to compare the proposed methodologies with other well-known methodologies. Compared to previously reported optimization algorithms in the literature, the obtained results show the potential of GBO to solve various OPF problems efficiently. [ABSTRACT FROM AUTHOR]

This article studies high dispersion solitons in optical couplers that are composed of metamaterials using the modified extended direct algebraic method (MEDAM). Different dynamic behaviors of unique soliton waves that include singular and combo-soliton solutions are raised using the MEDAM. The solutions that are produced include singular periodic solutions, bright and dark soliton solutions, Jacobi elliptic functions, and singular soliton solutions. Furthermore, the physical depiction of the found solutions is given through contour graphs, 2D, and 3D graphics. The main objective of this paper is to incorporate meta-materials into a governing model for highly dispersive solitons in optical couplers. The modified extended direct algebraic technique, reveals several solitons, where the uniqueness is found. Moreover, by the end of this work, we present 2D, 3D, and contour charts of the various obtained solutions to further highlight our findings. [ABSTRACT FROM AUTHOR]

Studying the highly dispersive model with arbitrary refractive index initiated by Kudryashov is the subject of this work. This model depicts the behavior of soliton propagation via polarization-preserving fibers. To secure a dark soliton and like-solitons with singularities solution for the proposed model, the generalized Kudryashov's integration approach has been utilized. This method do not have any constraints on how to find solutions. Some significant solutions have been graphically elaborated in the form of 2D and 3D plots by selecting the appropriate parameters to provide a better physical illustration and understanding of the dynamical physical properties of this model. [ABSTRACT FROM AUTHOR]

This study centers on examining the characteristics of the recently extended (3 + 1) -dimensional nonlinear equation proposed by Kudryashov. The extended F-expansion technique is employed to derive solitons and other exact wave solutions for this model. Applying this technique results in a diverse set of solutions, encompassing bright solitons, dark solitons, singular solitons, hyperbolic solutions, periodic solutions, singular periodic solutions, exponential solutions, rational solutions, and solutions involving Jacobi elliptic functions (JEF). This method proves to be a dependable and efficient approach for obtaining exact solutions for various nonlinear partial differential equations (NPDE). Visual representations through graphical illustrations are provided to depict the dynamics of selected solutions, and the influence of the parameter n on the obtained solutions is scrutinized and presented in pertinent figures. These discoveries not only advance our comprehension of nonlinear wave phenomena but also hold practical significance for fields related to wave propagation, nonlinear optics, and optical systems. [ABSTRACT FROM AUTHOR]

In this research article, the stochastic complex Ginzburg–Landau equation with Kerr law nonlinearity and chromatic dispersion is studied, which has been the focus of many studies and continues to be important in this field of study of nonlinear optics. The improved modified extended tanh technique is utilized in this work. This method depends on the extended Riccati equation. So, numerous stochastic exact solutions including singular solitons, dark solitons, bright solitons, exponential solutions and singular periodic solutions are offered by this method. This technique presents a realistic and successful strategy for deriving exact solutions to various nonlinear partial differential equations. Graphical representations of some of the extracted solutions using different noise intensities are shown to demonstrate the influence of the noise. The optical solitons produced in respect to this form have never been explored by the proposed technique before, and the results have never been published. [ABSTRACT FROM AUTHOR]

This work explores the effect of fractional derivative on the fourth-order nonlinear Schrödinger equation with Kerr law nonlinearity, a highly significant equation in the study of wave propagation in dispersive media. By employing the improved modified extended tanh-function method, a variety of optical soliton solutions are derived. These solutions including dark solitons, bright solitons, and singular solitons. Moreover, singular periodic solutions and exponential solutions are raised. These solutions offer valuable insights into the dynamic behavior of nonlinear wave phenomena. The impact of the fractional derivative is illustrated graphically using examples of some of the retrieved solutions with various values of fractional order. Bright and dark solitons, pivotal components of our findings, play a critical role in fiber optics by facilitating the transmission of high-power optical signals with exceptional attributes such as shape preservation. These properties eliminate the need for external pulse compression, simplifying the design and operation of optical systems. The outcomes of this study contribute in advancing our knowledge of wave propagation in dispersive media and have practical implications for the development of efficient and robust optical communication technologies. [ABSTRACT FROM AUTHOR]

The use of optical fiber for communication has grown at a rapid pace due to the demands of the modern information era. In this paper, the modified extended direct algebraic method is implemented to explore optical solitons and other exact wave solutions for the coupled system of perturbed highly dispersive complex Ginzburg–Landau equation with polynomial nonlinearity law which describe the transmission of solitons in birefringent fibers. The obtained solutions include bright solitons, dark solitons, singular solitons and combo dark-singular solitons. Additionally, Jacobi elliptic function solutions, exponential solutions, and singular periodic solutions are also offered. To ensure the existence of the obtained soliton solutions, we set some constraints on the parameters. In addition, some selected solutions are visually shown to demonstrate the physical properties of the exact solutions. [ABSTRACT FROM AUTHOR]

One of the natural consequences of soliton propagation is a birefringence phenomenon occurring due to bending, twisting or rough handling of fibres, which produce a bit of detrimental effect. In this research, we find optical soliton solutions and other exact solutions for the high-order coupled nonlinear Schrödinger system which describe the transmission of solitons in birefringent fibers. The study is conducted with the aid of the improved modified extended tanh function method. A variety of distinct traveling wave solutions are furnished. The obtained solutions include dark solitons, bright solitons, and singular solitons. Additionally, hyperbolic solutions, periodic solutions, singular periodic solutions, rational solutions, exponential solutions, Jacobi elliptic function solutions and Weierstrass elliptic doubly periodic type solutions are also offered. To help readers physically grasp the acquired solutions, graphical representations of some of the extracted solutions are provided. [ABSTRACT FROM AUTHOR]

Our goal in this paper is to obtain the travelling wave solutions of the (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili equation (DSKPE), which considered as a fundamental tool in studying a variety of phenomena appear in many applications of fluid mechanics and ocean engineering. This equation is used to describe the non-elastic and elastic interactions between internal waves. The novelty of this equation is due to the involvement of complex time which further holds importance within the theory of advanced modern nonlinearity. Our Study mainly depend on applying the modified extended mapping method to get the solitary wave solutions and other exact solutions of our model of interest. Many classification of solutions are established like (bright, dark, singular, combo dark-singular) soliton, also hyperbolic wave solution, as well as periodic, singular periodic, exponential and rational solutions. The three-dimensional and contour plots are depicted for some selected solutions to show the dynamics of the extracted solutions. [ABSTRACT FROM AUTHOR]

In this study, the (2 + 1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation (KP-BBME) is examined. KP-BBM is used as a water wave model to mimic the wave propagation for fluid flows and to describe bidirectional propagating water wave surface. Studying is conducted by applying the modified extended mapping method to construct various and novel solutions for the proposed model. These solutions including {dark, bright, and singular} solitons, Weierstrass elliptic, exponential and singular periodic solutions. The extracted solutions confirmed the efficacy and strength of the current technique. To illustrate the physical characteristics of the established solutions, 3D, 2D and contour plots are depicted for many selected solutions. [ABSTRACT FROM AUTHOR]

Our goal in this paper is to obtain the analytic solutions for stochastic fourth-order (2+1)-dimensional nonlinear Schrödinger equation (NLSE) with higher order odd and even terms. Our Study mainly depends on applying the improved modified extended tanh function method (IMETFM) to get the soliton wave solutions and other exact wave solutions of our model of interest. These solutions such as (bright, dark, singular) solitons, hyperbolic solutions, periodic solutions, singular periodic solutions, rational solutions, Jacobi elliptic functions solutions and Weierstrass elliptic functions solutions. Graphical representations of some of the extracted solutions using different noise intensities are shown to demonstrate the influence of the noise. [ABSTRACT FROM AUTHOR]

Background: Critical illness myopathy (CIM) has negative impact on patient outcomes. We aimed to explore the diagnostic value of bedside ultrasonography for early identification of CIM in septic patients and its correlation with other diagnostic methods. This prospective observational study included 40 ICU patients diagnosed with sepsis on admission or within 48 h later according to the third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3). They were evaluated using muscle ultrasound, electrodiagnostic and clinical muscle assessment (Medical Research Council, MRC) at two time points, the first was between days 2 and 5 and the second was between days 10 and 15. Results: There was significant deterioration of neuromuscular function between the two evaluation points demonstrated by decline in MRC, abnormal nerve conduction and electromyography (EMG) and increased muscle echogenicity on ultrasonography (P ≤ 0.001). Sepsis-Related Organ Failure Assessment (SOFA) score significantly correlated with different neuromuscular assessment tools. MRC had significant correlation with myopathic EMG (P ≤ 0.001, r = − 0.869) and increased muscle echogenicity (P ≤ 0.001, r = − 0.715). Abnormal ultrasonographic muscle architecture had sensitivity of 100%, specificity of 75% and positive likelihood ratio of 4 in detecting muscle dysfunction compared to myopathic EMG. Conclusions: Bedside peripheral muscle ultrasound echogenicity grade could be used as an additional screening test in ICU septic patients for early detection of CIM. [ABSTRACT FROM AUTHOR]

In this study, the generalized nonlinear Schrödinger equation (GNLSE) is examined. This model takes into account the group velocity dispersion, dual-power law nonlinearity and self-frequency shift. This model is used to mimic the wave propagation over nano optical fibers. Studying is conducted by applying the modified extended direct algebraic method (MEDAM). Based on this method, various types of solutions, such as bright solitons, dark solitons, singular solitons, singular periodic solutions, exponential solutions and Weierstrass elliptic solutions are extracted. The extracted solutions confirmed the efficacy and strength of the current technique. Moreover, the graphs for some solutions are presented to demonstrate their physical nature. [ABSTRACT FROM AUTHOR]

Many mathematical models describe the optical solitons propagation through optical fibers such as nonlinear Schrödinger's equation. In this work, we study the generalized derivative resonant nonlinear Schrödinger equation that encompasses cubic–quintic nonlinearity. Studying is conducted by implementing the improved modified extended tanh-function method which denotes various types of solutions. These solutions including bright solitons, dark solitons, triangular solutions, hyperbolic solutions, Jacobi elliptic functions solutions, exponential solutions and Weierstrass elliptic doubly periodic solutions. The extracted solutions confirmed the efficacy and strength of the current technique. To illustrate the physical characteristics of the established solutions, some selected solutions are visually depicted. [ABSTRACT FROM AUTHOR]

The present article deals with a new mathematical model of a thermoelastic semiconducting solid sphere based on the Green-Naghdi theories (type-I, type-II, and type-III) to study the photothermal interaction. The fractional-order strain consideration has been applied. The bounding surface of the sphere has been thermally loaded by ramp-type heating. Laplace's transform has been carried out, and its inversions have been computed numerically using the Tzou method. The numerical results have been presented in figures with various values of the fractional order and ramp-time heat parameters. The fractional-order and ramp-time heat parameters significantly affect all the studied functions. The ramp-time heat parameter could be used to tune the thermomechanical energy among the interaction of the thermoelastic body due to thermal loading. [ABSTRACT FROM AUTHOR]

The present study focuses on enhancing the mechanical, thermal, and degradation behavior of polylactic acid (PLA) by adding carbon nanotubes (CNTs) with different concentrations of 0.5, 1, 3, and 5%. The CNTs were prepared using catalytic chemical vapor deposition, and the prepared PLA/CNTs nanocomposite films were characterized using techniques such as FT-IR, Raman spectroscopy, TGA, SEM, and XRD. The distinct diffraction patterns of multi-walled carbon nanotubes (MWCNTs) at 2θ angles of 25.7° and 42.7° were no longer observed in the prepared nanocomposites, indicating uniform dispersion of MWCNTs within the PLA matrix. The presence of MWCNTs enhanced the crystallinity of PLA as the CNT loading increased. Mechanical tests demonstrated that incorporating CNTs positively influenced the elongation at the break while decreasing the ultimate tensile strength of PLA. The PLA-3%CNTs composition exhibited the highest elongation at break (51.8%) but the lowest tensile strength (64 MPa). Moreover, thermal gravimetric analysis confirmed that the prepared nanocomposites exhibited greater thermal stability than pure PLA. Among the nanocomposites, PLA-5% CNTs exhibited the highest thermal stability. Furthermore, the nanocomposites demonstrated reduced surface degradation in accelerated weathering tests, with a more pronounced resilience to UV radiation and moisture-induced deterioration observed in PLA-3% CNTs. [ABSTRACT FROM AUTHOR]

The study focuses on the combination of three mathematical models, namely nonlinear Schrödinger's equation, Lakshmanan–Porsezian–Daniel model, and Sasa–Satsuma model, which is called the concatenation model. The study investigates optical solitons and other exact solutions using a modified extended mapping approach. The solutions derived include bright solitons, dark solitons, combo bright-dark soliton solutions, singular solitons, periodic and singular periodic solutions, exponential and rational solutions, and Jacobi elliptic solutions. The study considers constraints on the parameters to ensure the existence of the obtained soliton solutions. Selected solutions are depicted graphically to demonstrate their physical nature. [ABSTRACT FROM AUTHOR]

In this work, we study the coupled nonlinear Maccari systems (NMS) which have been extensively developed in various fields of nonlinear optics, deep water theory, plasma physics, nonlinear optics, and so on. Studying is conducted by implementing the modified extended mapping method (MEMM) which denotes various types of solutions. These solutions including (bright, dark, singular) solitons. In addition, singular periodic, rational type, Weierstrass elliptic and exponential solutions are derived. To show the nature of the extracted solutions, 3D and 2D graphical representations are introduced. [ABSTRACT FROM AUTHOR]

The current research investigates the behavior of femtosecond solitary waves in an inhomogeneous optical fiber using the generalized derivative nonlinear Schrödinger equation with quintic nonlinearity. The extended F-expansion technique is utilized to obtain various exact solutions such as bright soliton solutions, dark soliton solutions, combo bright–dark soliton solutions, singular soliton solutions, periodic solutions, Jacobi elliptic functions solutions, rational solutions, Weierstrass elliptic solutions, exponential solutions. The obtained solutions are presented in three-dimensional and contour graphics by selecting appropriate parameters. Ibragimov's conservation technique is also applied to obtain conservation laws for the given model. These findings are crucial for comprehending various of scientific and physical applications. [ABSTRACT FROM AUTHOR]

To get new optical soliton solutions for the nonlinear longitudinal wave equation in magneto-electro-elastic circular rod, the modified simple equation approach and the extended auxiliary equation method are implemented. New bright soliton, singular soliton and singular periodic solutions are extracted. Moreover, for more physical illustration of the extracted solutions, three- and two-dimensional plots for the solutions are presented. [ABSTRACT FROM AUTHOR]

Postmenopausal osteoporosis is a critical issue for female health worldwide. This current study was designed to evaluate the role of nanopowder eggshell (NPES) in healthy and ovariectomy-induced osteoporosis rats. Fifty-six female rats were divided into healthy rats (35) and ovariectomized rats (21). The healthy rats were subdivided into five groups (G1–G5) and received one of the following treatments: saline, 20 or 40 mg/kg of calcium carbonate, and 20 or 40 mg/kg of NPES. The 21 ovariectomized rats were divided into three groups (G6–G8) and received either saline, 40 mg/kg of calcium carbonate, or 40 mg/kg of NPES. Biochemical and histopathological assessments of bone formation and resorption were performed. Biomarkers of bone formation (calcium and osteocalcin (OCN)) and calcium content in left femur ashes were significantly higher in healthy rats given 40-mg/kg NPES than in healthy control rats and healthy rats given 40-mg/kg calcium carbonate. The ovariectomized groups had significantly lower levels of vitamin D3, OCN, and osteoprotegerin (OPG) than the healthy control. Alanine transaminase (ALT), alkaline phosphatase (ALP), and receptor activator of nuclear factor-κB ligand (RANKL) were significantly increased in the ovariectomized group than in the healthy control group. Treatment with NPES and calcium carbonate reduced liver enzymes in ovariectomized rats. NPES treatment significantly increased Vit D3, OCN, OPG, and bone ash mineral content (calcium, magnesium, zinc, and phosphorus) in ovariectomized rats. NPES also increased femur cortical thickness, osteoblast number, and collagen fiber. The current study suggests that NPES can modulate bone turnover biomarkers and increase bone trace elements. Moreover, NPES alleviates bone resorption in ovariectomy-induced osteoporosis. [ABSTRACT FROM AUTHOR]

The generalised Schrödinger equation is a nonlinear equation that is frequently encountered in modern physics study. Additionally, it is an important equation for researching problems with light pulse transmission in nonlinear dispersive optical medium. Schrödinger–Hirota model is very important in communication systems because its refer to motion of solitary wave in optical fiber. In the ongoing study, the modified extended direct algebraic integration technique is applied to study the generalized Schrödinger–Hirota equation. Based on this method, various types of solutions, such as bright solitons, dark solitons, singular solitons, singular periodic solutions, exponential solutions, Weierstrass elliptic solutions and complexiton solutions are extracted. The extracted solutions confirmed the efficacy and strength of the current technique. To illustrate the physical characteristics of the established solutions, many selected solutions are visually depicted. [ABSTRACT FROM AUTHOR]

This manuscript investigates the cubic–quartic optical solitons in magneto-optical waveguides and other traveling wave solutions to coupled Biswas–Milovic equations with Kudryashov's nonlinear form. The solutions are extracted using the extended F-expansion method. Jacobi elliptical solutions, (bright–dark–singular) soliton solutions, hyperbolic solutions, periodic solutions, rational solutions, and exponential solutions are presented. moreover, a graphical illustration of a few selected results are present to clarify the potency and nature of the raised solutions. [ABSTRACT FROM AUTHOR]

The major goal of this research is to establish a new theory of generalized thermoelasticity for thermomass gas flow with low velocity and linear resistance based on the general non-Fourier law of heat conduction. The resistance effect has been included in the general heat conduction equation, which is based on the total derivative of the thermomass gas velocity. Using the governing equations of that unique model, two numerical applications of homogeneous, isotropic, and thermoelastic one-dimensional rods have been constructed. The two applications were solved using the Laplace transform and numerical inversion methods. In terms of thermal and mechanical wave distributions, the latest findings illustrate the contrasts between the Lord–Shulman model and the present revolutionary thermoelasticity model. The parameters of the current general non-Fourier equation of heat conduction have a major impact on thermomechanical waves. [ABSTRACT FROM AUTHOR]

This paper discusses the existence of a diverse range of novel periodic nonlinear waves in the generalized (3+1)-dimensional Sasa–Satsuma equation. This equation models the transmission of femtosecond light pulses through optical fibers, taking into account third-order dispersion, self-frequency shift, and self-steepening effects in all three spatial dimensions of the system. The article presents newly derived periodic wave solutions expressed in terms of Jacobi elliptic functions and also obtains bright and dark soliton solutions in the long-wave limit of the periodic wave solutions. Moreover, a reduction technique employed to obtain another soliton solution and first integral of the considered model. Additionally, the article highlights the necessary fiber parameters required for the existence of these structures and provides graphical illustrations of selected solutions to demonstrate their physical nature. [ABSTRACT FROM AUTHOR]

This paper introduces a novel methodology for determining wind turbines' optimal site matching. Our framework's key component is establishing four new probabilistic models to model wind turbines' capacity factors. First, we used the sum square of errors (SSE) and the determination coefficient (R2) to assess the accuracy of the proposed models. The developed models were then generalized to estimate wind farm capacity factors. After that, the proposed methodology's validity is tested by applying it to a known wind data site. We modeled the available wind data using Weibull distribution. Five different methods were used to determine Weibull parameters. The equivalent energy method combined with the invasive weed optimization algorithm yields the optimal values for these parameters. Finally, under the support of the presented models, the novel methodology is applied to a pool of 24 commercial turbines to choose the optimal ones. A comparison is made between the obtained capacity factor curves using the suggested models and other previous models for the selected wind turbines. When the presented models are utilized, the capacity factor of commercial wind turbines with non-ideal electrical power curves is more precisely predicted. [ABSTRACT FROM AUTHOR]

Higher-order nonlinear Schrödinger equation is necessarily needed to suit with the light propagation in optical fibers, wherein the effect of higher-order nonlinear and dispersive effects should be taken into account. Due to the increase of these physical effects, the theoretical analysis and experimental observation of optical solitons are more difficult, but the generated optical solitons will bring more novel nonlinear phenomena and reveal more fundamental nonlinear mechanisms. In this paper, we study the eighth order non-linear Schrödinger equation (NLSE) with ninth power law of nonlinearity. Studying is conducted by applying the improved modified extended tanh method to secure various optical soliton solutions. These solutions are important in applied physics and engineering. The obtained results can be used to understand and elucidate the physical nature of waves spread in a dispersive medium. The extracted solutions including dark, bright and singular solitons. In addition, we extract periodic solutions, singular periodic solutions and Weierstrass elliptic solutions for the proposed model. Furthermore, graphical simulations for some solutions are depicted to demonstrate the powerful of these solutions. This influential, consistent, and effective method can be used to solve a variety of other models in physics and other applied sciences. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the generalized Kundu-Eckhaus equation (KEE) with extra-dispersion, which describes the propagation of the ultra-short femtosecond pulses in an optical fiber. Many exact solutions are constructed with the aid of improved modified extended tanh-function method and a new transformation. As a result, we have found a variety of new families of exact traveling wave solutions including bright solitons, dark solitons, singular solitons, Weierstrass elliptic doubly periodic solutions, Jacobi elliptic solutions, periodic solutions and rational solutions. Physical interpretation for some of the obtained solutions are illustrated in Figures. [ABSTRACT FROM AUTHOR]

The Correction Notice in the journal "Applied Biochemistry & Biotechnology" addresses missing data in an article on the dietary effects of nanopowder eggshells on bone health in rats. The corrections include specifying the rat breed used in the study and clarifying the blood sampling procedure. The authors assure that these changes do not impact the overall results and conclusions of the study. The correction was authored by Ragaa H. M. Salama, Safaa S. Ali, Tarek Hamdy M. Salama, Mohamed Abu Almged, Tasneem A. Alsanory, Aya A. Alsanory, Hesham Aboutaleb, and Ghada M. Ezzat. [Extracted from the article]

In this paper, we discussed analytically the nonlinear Schrödinger's equation having Kudryashov's quintuple power law of refractive index together with dual form of generalized nonlocal nonlinearity with the aid of extended F-expansion method. As a result, we have found a variety of new families of exact traveling wave solutions including bright soliton solutions, dark soliton solutions, singular soliton solutions, periodic solutions, Jacobi elliptic function solutions, rational solutions and exponential solutions. In this work, periodic solutions, rational solutions and exponential solutions are obtained to the governing model for the first time. For physical description of our newly obtained solutions, we have expressed them graphically to explain more efficiently the behavior of different shapes of solutions. [ABSTRACT FROM AUTHOR]

In this paper, the improved extended modified tanh function method is applied to hierarchy of nonlinear partial evolution equation that model the propagation of a pulse in optical fibers with first-order dispersion ( M = 1 ). Bright, dark and singular soliton solutions are obtained. Also, periodic singular solutions and elliptic Weierstrass doubly periodic type solution are acquired. Graphs of some of the obtained results are presented. [ABSTRACT FROM AUTHOR]