Order Dispersion Research Articles

Formulation of Cefdinir Ternary Solid Dispersion and Stability Study under Harsh Conditions

Cefdinir (CEF) is classified as a third-generation cephalosporin within class IV of the Biopharmaceutical Classification System (BCS). Cefdinir has low solubility and permeability, which may reduce oral bioavailability. The aim of this research was the preparation of cefdinir ternary solid dispersion in order to enhance its solubility. Then, after evaluating this ternary SD, investigate its stability under harsh conditions. In addition, formulation and evaluation of CEF ternary SD as capsule dosage form. The ternary SD is prepared by the solvent evaporation method using CEF, curcumin, and polyvinylpyrrolidone k30 in a weight ratio of 1:1:1. The ternary SD is subject to evaluation using Differential Scanning Calorimetry (DSC), Powder X-ray Diffractometry (PXRD), and Fourier Transform Infrared Spectroscopy (FTIR), saturated solubility, release, antibacterial activity, and a two months stability study under conditions of 40 ºC and 75% relative humidity. Then, six different capsule formulas were prepared using different excipients; each formula contained 300 mg of CEF. The capsule formulas were subjected to pre-formulation and capsule evaluation tests, which included weight variation, drug content, disintegration time, and In-vitro dissolution tests. The selected optimum capsule formula was subjected to further antibacterial activity test. Evaluation of ternary SD showed that, the system is totally amorphous with enhanced dissolution, saturated solubility, and antibacterial activity compared to pure CEF. Stability studies showed that, ternary SD remains amorphous after two months. Compared to commercial capsules (Sefarin® 300 mg) and other formulas, the F6 formula released 90% of CEF in 30 min. Antibacterial activity test results showed that the F6 formula was active against Staphylococcus aureus and Proteus vulgaris bacterial isolate. This research concludes that CEF solubility, antibacterial activity enhancement, and stability insurance could be obtained by preparing CEF ternary SD. All the ternary SD prepared capsule formulas showed enhancements in release compared to commercial capsules.

Cloud computing: Innovative strategy towards effective pedagogy in Christian religious studies

Cloud computing is an emerging phenomenon within the realm of Information and Communication Technology (ICT) that holds significant potential for enhancing various aspects of skill acquisition, data analysis, critical thinking, knowledge updating, problem-solving, research data generation, and the facilitation of engaging and stimulating teaching and learning experiences, among other benefits. Cloud computing is widely recognized as a standard paradigm that offers efficient network access to a shared pool of computing resources. These resources can be provisioned and released with minimal effort and reciprocal agreements between service providers. Education, on the contrary, is a systematic procedure of imparting knowledge that necessitates consistent updating and application of internationally recognized best practices in its execution. Therefore, this paper articulates the significance of implementing and utilizing cloud computing as an innovative approach to future-oriented and efficient pedagogy in the field of Christian Religious Studies. The outcome of this interaction can best be illustrated from the experience of many seminaries and theological colleges that have adopted cloud-based Learning Management Systems (LMS) such as Moodle or Canvas. These platforms allow educators to share course materials, facilitate discussions, and assess student performance. The research design employed in this study is survey methodology. The study’s population included 540 participants, specifically 313 undergraduate students, 192 education lecturers, and 35 administrative staff members from a tertiary institution. The sample size of 230 respondents was determined using the YARO YAMENT formula and selected through a stratified random sampling technique. A questionnaire consisting of 30 items was utilized to collect data. The questionnaire was developed, validated, and its reliability was assessed using the CRONBACH alpha formula, yielding a coefficient of 0.84. The collected data underwent analysis utilizing measures of central tendency (mean) and dispersion (standard deviation) in order to address the research inquiries. Additionally, the null hypothesis was assessed through the application of ANOVA. The study revealed that achieving a global equilibrium in terms of information and materials accessible to cloud computing users is crucial. Specifically, online materials should be designed to incorporate both local and global content, ensuring their relevance and appeal to individuals regardless of their language or cultural background. Fifteen viable strategies for enhancing futuristic and effective pedagogy in the field of Christianity.

2.6 GW, mJ-class high-energy femtosecond laser system based on Yb:YAG single-crystal fiber amplifier

High-peak-intensity ultrafast fiber lasers show excellent prospect for ultrafast science and industrial applications. For simplicity as well as efficiency, chirped-pulse amplification (CPA) is an effective technique for the generation of high-energy sources and single crystal fiber (SCF) also shows great potential due to its convenient configuration. In this work, a high-peak-power hybrid CPA pulsed laser system based on a three-stage single-pass end-pumped Yb:YAG SCF amplifier is experimentally demonstrated. The amplification system emitted pulses with the maximum power of 103.2 W at 100 kHz repetition rate and we obtained the compressed output power of 84.2 W, corresponding to the pulse energy of 0.84 mJ. Considering the third order dispersion that induced by the stretcher and the accurate tuning effect for higher-order dispersion compensation of chirped fiber Bragg grating, we have demonstrated a nearly transform limited output pulse duration of 323 fs with the peak power exceeding 2.6 GW. It can be said that we present the results for the first implementation of the shortest pulse duration and highest peak power in such multi-stage Yb:YAG SCF amplifier. The well-preserved beam quality with the measured M2 value of 1.22 and 1.29 for the horizontal and vertical directions at the maximum achieved average power. With such outstanding combined features, the demonstrated high-energy ultrafast fiber lasers would enable broad applications.

Dynamic description of soliton solutions of nonlinear schrödinger equation with higher order dispersion and nonlinear terms

Abstract The article presents an analytical solution for the higher-order nonlinear Schrödinger equation (NLSE), which describes the propagation of short light pulses in monomode optical fibers. Various traveling wave solutions are obtained using the generalized exponential rational function method, a technique with substantial applications in physics and mathematics. Additionally, the parameters leading to the occurrence of optical bright and multipeak solitons in this medium are provided along with their formation conditions. The derived solutions are graphically displayed to enhance the understanding of the model’s physical phenomena. This approach is credible, potent, and successful in solving a wide variety of different models of this kind that arise in the applied sciences. Its robustness, strength, and efficiency make it suitable for addressing various higher-order nonlinear problems in current research fields, extending beyond the models encountered in the applied sciences.

A PROBLEM IN FRACTIONAL ORDER THERMO-VISCOELASTICITY THEORY FOR A POLYMER MICRO-ROD WITH AND WITHOUT ENERGY DISSIPATION

A new study has been developed that considers the size-dependent interaction between viscoelastic deformation and thermal fields, incorporating the fractional heat conduction law with and without energy dissipation. The model is used for a particular one-dimensional problem involving a polymer micro-rod of arbitrary length experiencing three different types of thermal loading without the presence of any heat source. The study uses Laplace transforms and numerical inversion to examine how fractional order, nonlocal elasticity, and nonlocal thermal conduction impact thermal dispersion and thermo-viscoelastic response. Comparative numbers demonstrate the effects of various parameters. Findings demonstrate that nonlocal thermal and viscoelastic characteristics have a significant impact on all recorded field values, offering possible suggestions for the creation and assessment of thermal-mechanical attributes in nanoscale devices.

Impact of higher order dispersion in the propagation of optical pulse in the photonic crystal fibers - A Projection Operator approach

Impact of higher order dispersion in the propagation of optical pulse in the photonic crystal fibers - A Projection Operator approach

Method for Controlling Dispersion in Order to Maintain a Quasi-Soliton Pulse Propagation Mode in High-Speed Fiber-Optic Communications System

Relevance: Every year, there is an increasing need to enhance the bandwidth and range of fiber-optic communication systems. The study of methods to control dispersion is relevant and helps maintain a quasi-soliton regime, which is essential for ensuring high-speed, reliable data transmission. Conducted modeling and calculations make this research practical and applicable. This will enable engineers to accurately predict the system's behavior and optimize its performance before implementing it in real-world networks.Problem statement: Investigation of the processes of maintaining a quasi-soliton regime in fibers with decreasing chromatic dispersion and alternating fibers with different signs of chromatic dispersion, both with and without initial chirping.Goal of the work: The development and analysis of techniques to control dispersion in order to maintain a quasi-soliton mode of light propagation in single-mode optical fibers.Methods: The study of the processes of maintaining a quasi-soliton regime was carried out by mathematical and numerical modeling. To substantiate the methods, theoretical analysis and calculations were carried out and schemes for a quasi-soliton fiber-optic communication system were developed and modeling was carried out.Result: The analysis of the results demonstrated the effectiveness of the proposed method and showed the efficiency and stability of the solutions in conditions that were close to real-world scenarios. Novelty: Models for maintaining a quasi-soliton regime and methods for studying them have been developed. The most effective ways to preserve quasi-soliton pulses over long distances have been analyzed.Practical significance: The developed models and research methods can be applied in the educational process and the development of real fiber-optic communication systems.

M-shaped, W-shaped and dark soliton propagation in optical fiber for nonlocal fourth order dispersive nonlinear Schrödinger equation under distinct conditions

The formation of soliton in optical fiber governed by nonlocal nonlinear Schrödinger (NLS) equation with fourth order dispersion is studied. The model of nonlocal NLS equation with fourth order dispersion is solved using the new extended auxiliary method and the solutions are obtained. The solutions are in the form of hyperbolic and trigonometric functions which are based on Jacobi elliptic function m. Shape changing soliton in optical fiber for nonlocal fourth order dispersive NLS equation is discussed by suitably choosing the values of kerr and quintic nonlinearities and by varying fourth order dispersion term. The effect of fourth order dispersion on soliton in fiber for different conditions of kerr and quintic nonlinearity is also discussed. In addition, the phase portraits of the system have been investigated and the stability of wave in optical fiber for nonlocal NLS equation is discussed using fourth order Runge-Kutta algorithm. This paper addresses a significant gap in the current literature by examining the impact of fourth order dispersion on the nonlocal NLS equation in optical fiber.

Circular code identified by the codon usage

Since 1996, circular codes in genes have been identified thanks to the development of 6 statistical approaches: trinucleotide frequencies per frame (Arquès and Michel, 1996), correlation functions per frame (Arquès and Michel, 1997), frame permuted trinucleotide frequencies (Frey and Michel, 2003, 2006), advanced statistical functions at the gene population level (Michel, 2015) and at the gene level (Michel, 2017). All these 3-frame statistical methods analyse the trinucleotide information in the 3 frames of genes: the reading frame and the 2 shifted frames. Notably, codon usage does not allow for the identification of circular codes (Michel, 2020). This has been a long-standing problem since 1996, hindering biologists’ access to circular code theory.By considering circular code conditions resulting from code theory, particularly the concept of permutation class, and building upon previous statistical work, a new statistical approach based solely on the codon usage, i.e. a 1-frame statistical method, surprisingly reveals the maximal C3 self-complementary trinucleotide circular code X in bacterial genes and in average (bacterial, archaeal, eukaryotic) genes, and almost in archaeal genes. Additionally, a new parameter definition indicates that bacterial and archaeal genes exhibit codon usage dispersion of the same order of magnitude, but significantly higher than that observed in eukaryotic genes. This statistical finding may explain the greater variability of codes in eukaryotic genes compared to bacterial and archaeal genes, an issue that has been open for many years. Finally, biologists can now search for new (variant) circular codes at both the genome level (across all genes in a given genome) and the gene level using only codon usage, without the need for analysing the shifted frames.

Exploring the dynamic interplay of intermodal and higher order dispersion in nonlinear negative index metamaterials

Our study delves into the intricate interplay of various factors within metamaterials, with a focus on modulation instability. Through our research, we elucidate the intricate dynamics involving intermodal dispersion, self-steepening effect, higher order dispersion, and plane wave amplitude, showcasing their competition and influence on modulation instability phenomena. We aim to explore the impact of intermodal dispersion and higher-order effects by numerically solving the generalized nonlinear Schrödinger equation (NLSE), which models the propagation of a few-cycle pulse in a nonlinear metamaterial. Our modulation instability (MI) analysis captures the complex dynamics these factors introduce. We demonstrate the spatiotemporal evolution of MI under different parameter values, revealing how these variations influence the instability’s development and characteristics. This approach provides a detailed understanding of the system’s behavior across various conditions, highlighting the roles of intermodal dispersion and higher-order effects. We demonstrate that the behavior of modulation instability bands and their reliance on parameters such as self-steepening and wave amplitude is contingent upon the specific characteristics of the optical setup and medium dispersion properties

Transmission of soliton for a coupled Radhakrishnan–Kundu–Lakshmanan equation in an optical fiber using the Jacobi elliptical sn function method

We examine a coupled Radhakrishnan–Kundu–Lakshmanan (cRKL) equation that includes self-phase modulation, third order dispersion, self-steepening, and cross-phase modulation effects. A propagating ultrafast pulse in nonlinear systems is described by the given equation. Utilizing the coupled Radhakrishnan–Kundu–Lakshmanan (cRKL) model, we explored the dynamics of various innovative optical solitons, such as wing-shaped, W-shaped, and brilliant solitons. We used mathematical methods like the Jacobi elliptical sn function method to get the exact analytical solution. Our results demonstrate that the self-phase modulation (SPM), self-steepening (SS), cross-phase modulation (XPM), and third order dispersion (TOD) can be effectively varied to influence the structure of the solitons. It is demonstrated that the precise balance between the self-steepening effect, the self-phase modulation, and the group velocity dispersion forms these novel W-shaped chirp-free dark solitons and dark and bright solitonic structures. By choosing appropriate settings for the physical variables, it is possible to create a graphic representation of the properties of optical solitons. The study and application of nonlinear materials with third order dispersion, cross-phase modulation, self-phase modulation effect, and self-steepening nonlinearity may take new paths as a result of our findings.

Accurate optical dispersion identification for linear deformable mirror with spatial-spectral interferometry

In ultrashort laser pulse systems, optical dispersion can cause severe distortion of the spectral phase and thus significantly affect the pulse shape. To address this problem, this study places a linear deformable mirror (LDM) at the Fourier plane of a blazed grating for dispersion control, and reconstructs the spectral phase modulated by the LDM using single-shot spatial-spectral interferometry. An iterative algorithm and closed-loop optimization process are used to drive the LDM to generate orthogonal modes of Legendre polynomials with a signal-to-background ratio (SBR) of more than 10 dB. The identified LDM modes are then used as the basis for spectral phase modulation. It is shown that the group delay dispersion (GDD), third order dispersion (TOD), fourth order dispersion (FOD), and fifth order dispersion (5OD) can be accurately obtained by the linear combination of identified Legendre modes. In addition, the maximum phase error between the generated and target dispersions is less than 0.15 rad, while the error between the pulse widths produced by the generated dispersion and the target dispersion, respectively, is less than 3.5 %. Overall, the results confirm that the linear superposition of the generated Legendre modes enables the accurate dispersion modulation of ultrashort laser pulses.

Decay of the radius of spatial analyticity for the modified KdV equation and the nonlinear Schrödinger equation with third order dispersion

Decay of the radius of spatial analyticity for the modified KdV equation and the nonlinear Schrödinger equation with third order dispersion

Dynamics of switching optical soliton in fiber with sixth order dispersion and inter modal dispersion

This work pertains to the study of switching soliton in fiber for nonlinear Schrödinger (NLS) equation with the presence of higher order dispersion and inter modal dispersion (IMD). The nonlinear wave in the optical fiber are described by the NLS equation which having the second order, fourth order, fifth order, sixth order dispersion, higher order nonlinearity and IMD. The main goal of the paper is to examine the sixth order dispersion on nonlinear wave in the fiber with the conditions of IMD. Hence, we employ the Bäcklund transformation of the Riccati equation (BTRE) approach to NLS equation and obtain the soliton solution. By the use of soliton solution along with graphical snapshots, we provide the conditions for forming switching solition in optical fiber and also analyze the effect of sixth order dispersion in fiber. The stability of the solution of NLS equation is also addressed.

Analysis of performance limits in optical communications due to fiber nonlinearity and third order dispersion

In this study, an analysis is conducted to treasure the expressions of the pulsation expansion factor, in addition to the standardized output, and solve the nonlinear Schrödinger equation (NLSE), reflecting the impact of XPM on third order dispersion. Using large effective area fiber (LEAF) and standard single-mode fiber (SSMF), the effects of transmission distances and varying input powers are assessed at various transmission speeds. The first and second order GVD XPM effects are the only factors influencing the pulse’s propagation. The second-order effects of GVD are not noticeable at short distances and low bit rates, but they become noticeable and impact system performance as the bit rate increases. The study discovered that input dominance has less of an impact on pulse width than data rate and fiber length. Methodical derivation and numerical simulation using the split-phase Fourier method at the same data rate and input power yield the SSMF and LEAF consequences. In comparison to LEAF fibers, XPM has a greater beneficial impact on second and third order dispersion in SSMF fibers.

Extraction of Solitons in Optical Fibers for the (2+1)-Dimensional Perturbed Nonlinear Schrödinger Equation Via the Improved Modified Extended Tanh Function Technique

The presented research investigates the (2+1)-dimensional perturbed nonlinear Schrödinger model. This model takes into account various effects such as fourth order dispersion, intermodal dispersion, nonlinear dispersion, group velocity dispersion, Kerr nonlinearity and self steepening effects. This model simulates the estimation of optical solitons and a variety of broadcasting networks’ transmission in nonlinear fiber optics. The proposed model is studied using the improved modified extended tanh function technique. For the proposed model, several solitons and other solutions are generated. These solutions including {bright, dark and singular} solitons, singular periodic and Jacobi elliptic solutions. By introducing the two- and three-dimensional graphs, the physical behavior of the retrieved solutions is displayed.

Enhanced antichemobrain activity of amino acid assisted ferulic acid solid dispersion in adult zebrafish (Danio rerio).

Chemotherapy-induced cognitive impairment (CICI), also known as "chemobrain," is a common side effect of breast cancer therapy which causes oxidative stress and generation of reactive oxygen species (ROS). Ferulic acid (FA), a natural polyphenol, belongs to BCS class II is confirmed to have nootropic, neuroprotective and antioxidant effects. Here, we have developed FA solid dispersion (SD) in order to enhance its therapeutic potential against chemobrain. An amorphous ferulic acid loaded leucin solid dispersion (FA-Leu SD) was prepared by utilizing amino acid through spray-drying technique. The solid-state characterization was carried out via Fourier-transform infrared spectroscopy (FT-IR), differential scanning calorimetry (DSC), X-ray diffraction (XRD), and field emission scanning electron microscopy (FE-SEM). Additionally, in-vitro release studies and antioxidant assay were also performed along with in-vivo locomotor, biochemical and histopathological analysis. The physical properties showed that FA-Leu SD so formed exhibited spherical, irregular surface hollow cavity of along with broad melting endotherm as observed from FE-SEM and DSC results. The XRD spectra demonstrated absence of sharp and intense peaks in FA-Leu SD which evidenced for complete encapsulation of drug into carrier. Moreover, in-vitro drug release studies over a period of 5h in PBS (pH 7.4) displayed a significant enhanced release in the first hr (68. 49 ± 5.39%) and in-vitro DPPH assay displayed greater antioxidant potential of FA in FA-Leu SD. Furthermore, the in-vivo behavioral findings of FA-Leu SD (equivalent to 150mg/kg of free FA) exhibited positive results accompanied by in-vivo biochemical and molecular TNF-α showed a significant difference (p < 0.001) vis-à-vis DOX treated group upon DOX + FA-Leu SD. Additionally, histopathological analysis revealed neuroprotective effects of FA-Leu SD together with declined oxidative stress due to antioxidant potential of FA which was induced by anticancer drug doxorubicin (DOX). Overall, the above findings concluded that spray-dried FA-Leu SD could be useful for the treatment of chemotherapy induced cognitive impairment.

Sharp Global Well-Posedness for the Cubic Nonlinear Schrödinger Equation with Third Order Dispersion

Sharp Global Well-Posedness for the Cubic Nonlinear Schrödinger Equation with Third Order Dispersion

Approximate controllability of third order dispersion systems

The current paper focuses on the approximate controllability of Volterra-Fredholm type integrodifferential third order dispersion system. The Banach fixed point theorem and semigroup operator are used to obtain the existence and uniqueness of mild solutions to the considered system. In order to examine the approximate controllability results, a different approach is used, namely, the sequential method.

Dispersive optical soliton solutions with the concatenation model incorporating quintic order dispersion using three distinct schemes

&lt;abstract&gt;&lt;p&gt;This paper addresses the new concatenation model incorporating quintic-order dispersion, incorporating four well-known nonlinear models. The concatenated models are the nonlinear Schrödinger equation, the Hirota equation, the Lakshmanan-Porsezian-Daniel equation, and the nonlinear Schrödinger equation with quintic-order dispersion. The model itself is innovative and serves as an encouragement for investigating and analyzing the extracted optical solitons. These models play a crucial role in nonlinear optics, especially in studying optical fibers. Three integration algorithms are implemented to investigate the optical solitons with the governing model. These techniques are the Weierstrass-type projective Riccati equation expansion method, the addendum to Kudryashov's method, and the new mapping method. The solutions obtained include various solitons, such as bright, dark, and straddled solitons. Additionally, the paper reports hyperbolic solutions and Weierstrass-type doubly periodic solutions. These solutions are novel and have never been reported before. Visual depictions of some selected solitons illustrate these solutions' dynamic behavior and wave structure.&lt;/p&gt;&lt;/abstract&gt;