Integral Properties Research Articles

On Lie symmetries, soliton interaction nature and conservation laws of Broer-Kaup-Kupershmidt system in shallow water of uniform depth

Abstract The exact solutions of nonlinear partial differential equations are significant to analyze the soliton nature of physical phenomena. Therefore, the Lie symmetry method is introduced to obtain exact solutions of the Broer-Kaup-Kupershmidt system. It represents two-dimensional propagation of nonlinear and dispersive long gravity waves in shallow water with uniform depth. The present work is devoted to derive symmetry reductions, soliton solutions, and conserved vectors under one-parameter Lie group transformations. Meanwhile, the invariance property of Lie groups validates the reducibility of the system. Therefore, a continual process of reductions transmutes the test system into a system of ordinary differential equations. Thus, this integrability property leads to generalized exact solutions with parametric constraints. These solutions entail all three arbitrary functions, f 1(y), f 2(t), f 3(t) existing in infinitesimals and various free parameters. On account of existing functions and free parameters, the obtained solutions are more admirable than those of preceding works (Kassem and Rasheed 2019 Chinese J. Phys. 57 90–104, Kumar et al 2022 Math. Comput. Simulat. 196 319–35, Tanwar and Kumar 2024 J. Ocean Eng. Sci. 9 199–206) and helpful to describe significant physical nature under wide parametric ranges. The deductions of previous results on imposing the particular values to arbitrary functions and constants ensure the generalness and novelty of derived results. Moreover, adjoint equations and conserved quantities associated with Lagrangian formulation have been evolved via Lie symmetries. We numerically simulate these solutions to analyze their physical nature. Consequently, soliton fusion and fission, line solitons, doubly solitons, multisolitons, and bright and dark soliton nature are discussed, which validate the physical relevance of the solutions.

Magnetic Properties, Heat Generation, and Apatite Formation Ability of Mg‐Ti Ferrite Particles Synthesized by Solid‐State Reaction and Polymerized Complex Methods

Titanium‐doped ferrite has garnered significant interest as thermoseeds for cancer hyperthermia because of its controllable Curie point near body temperature, which prevents overheating and ensures high biological safety. However, few studies examine the effect of the synthesis conditions on microstructure, magnetic properties, and heat generation in an alternating magnetic field. Herein, Mg1+xFe2−2xTixO4 (x = 0.35, 0.45) particles are synthesized by a solid‐state reaction and polymerized complex methods, followed by sintering at various temperatures. Their magnetic properties and heat generation behavior in an alternating magnetic field are investigated. Particles with x = 0.45 generate significantly less heat than those with x = 0.35, despite both being single‐phase ferrite. Particles synthesized by the polymerized complex method at a sintering temperature of 1200 °C exhibit lower saturation magnetization but higher temperature increases compared with the solid‐state reaction method. Additionally, in the sintering temperature range of 800–1000 °C, a temperature increase of more than 10 °C is observed in the polymerized complex method, likely a result of the inclusion of highly crystalline superparamagnetic particles. Furthermore, the ferrite particles form bone‐like apatite on their surface in simulated body fluid, suggesting their potential as a novel material combining hyperthermia and bone integration properties.

Development and Characterization of Lyophilized Chondroitin Sulfate-Loaded Solid Lipid Nanoparticles: Encapsulation Efficiency and Stability

This study explores the development and characterization of lyophilized chondroitin sulfate (CHON)-loaded solid lipid nanoparticles (SLN) as an innovative platform for advanced drug delivery. Background/Objectives: Solid lipid nanoparticles are increasingly recognized for their biocompatibility, their ability to encapsulate diverse compounds, their capacity to enhance drug stability, their bioavailability, and their therapeutic efficacy. Methods: CHON, a naturally occurring glycosaminoglycan with anti-inflammatory and regenerative properties, was integrated into SLN formulations using the hot microemulsion technique. Two formulations (SLN-1 and SLN-2) were produced and optimized by evaluating critical physicochemical properties such as particle size, zeta potential, encapsulation efficiency (EE%), and stability. The lyophilization process, with the addition of various cryoprotectants, revealed trehalose to be the most effective agent in maintaining nanoparticle integrity and functional properties. Results: Morphological analyses using transmission electron microscopy (TEM) and atomic force microscopy (AFM) confirmed the dimensions of the nanoscales and their structural uniformity. Differential scanning calorimetry (DSC) and X-ray diffraction (XRD) revealed minimal excipient interaction with CHON, ensuring formulation stability. Stability studies under different environmental conditions highlighted that SLN-2 is the most stable formulation, maintaining superior encapsulation efficiency (≥88%) and particle size consistency over time. Conclusions: These findings underscore the potential of CHON-loaded SLNs as promising candidates for targeted, sustained-release therapies in the treatment of inflammatory and degenerative diseases.

Exploring the bioactivity and antibacterial properties of silver and cerium co-doped borosilicate bioactive glass.

Bone defects resulting from trauma or diseases that lead to bone loss have created a growing need for innovative materials suitable for treating bone-related conditions. The purpose of this study is, therefore, to synthesize and analyse the synergistic effects of cerium (Ce) and cerium-silver (Ce-Ag) doping of borosilicate bioactive glass (BBG) on the bioactivity, antibacterial properties, and biocompatibility for potential applications in bone tissue engineering. This study utilized a sol-gel Stöber method to synthesize doped BBGs based on S49B4. Characterization techniques were utilized to evaluate the thermal stability, elemental composition, structural integrity, and morphological properties of the synthesized Ce and AgCe-BBGs. Cytotoxicity was evaluated using a GMSM-K gingival cell line, while antimicrobial tests were conducted using clinical isolates of Escherichia coli and Staphylococcus aureus. The characterization results confirmed the successful incorporation of Ce and Ag, resulting in elongated pineal to spherical nanosized BG particles (33-68 nm). Thermal analysis indicated that silver exhibited lower thermal stability compared to cerium. Bioactivity tests indicated that while silver has intrinsic bioactive qualities, elevated cerium levels above 0.5 wt% may inhibit or delay apatite formation by generating insoluble cerium phosphate ions. Lactate dehydrogenase assays demonstrated that among other BBGs, SBAgCe1 showed the highest LDH activity, suggesting mild cytotoxicity. The co-doped BBG exhibited strong antibacterial activity through a complex interaction between Ag and Ce ionic exchange. Nonetheless, a careful balance of Ce and Ag concentrations is critical, as high levels can compromise bioactivity and increase cytotoxicity. The results highlight the potential of SBAgCe0.5 as a candidate for bone tissue engineering applications due to its favourable bioactivity, and antibacterial and cytocompatible properties, emphasizing the importance of optimizing dopant concentrations for therapeutic applications in favour of good health and the well-being of humanity.

Graphene nanocoating on titanium maintains structural and antibiofilm properties post-sterilization

ObjectiveTo evaluate the impact of sterilization methods on the structural integrity and antimicrobial properties of graphene nanocoating on titanium (GN). MethodsGN was transferred to titanium using wet (WT) or dry transfer (DT) techniques and sterilized using an autoclave (AC), glutaraldehyde (GA), or ethylene oxide (EtO). The GN structure was characterized using Raman spectroscopy before and after sterilization. Additional specimens were characterized by Raman after AC and water jetting. Biofilm formation was assessed before and after AC using colony-forming units (CFU), biofilm biomass, and SEM (uncoated titanium was the control). Three independent samples were used for structural characterization and biofilm quantification. Statistical analyses were conducted using one-way analysis of variance (ANOVA) and Tukey's test (α = 0.05). ResultsWT and DT demonstrated high structural stability after sterilization and water jetting, with negligible coating quality or coverage loss. GN exhibited lower biofilm formation even after AC sterilization, as shown by the reduction in CFU counts, biofilm biomass, and SEM images compared to the control. SignificanceGN demonstrated high resistance to the stresses imposed by all sterilization methods tested, maintaining its structural integrity, resistance to water-jet cleaning, and antibiofilm potential. The findings suggest that standard industrial practices can effectively sterilize highly resilient GN on titanium implants and possibly other biomaterials.

Hopf link invariants and integrable hierarchies

The goal of this note is to study integrable properties of a generating function of the HOMFLY-PT invariants of the Hopf link colored with different representations. We demonstrate that such a generating function is a τ-function of the KP hierarchy. Furthermore, this Hopf generating function in the case of composite representations, which is a generating function of the 4-point functions in topological string (corresponding to the resolved conifold with branes on the four external legs), is a τ-function of the universal character(UC) hierarchy put on the topological locus. We also briefly discuss a simple matrix model associated with the UC hierarchy.

Physics-informed geometric operators to support surrogate, dimension reduction and generative models for engineering design

In this work, we propose a set of physics-informed geometric operators (GOs) to enrich the geometric data provided for training surrogate/discriminative models, dimension reduction, and generative models, typically employed for performance prediction, dimension reduction, and creating data-driven parameterisations, respectively. However, as both the input and output streams of these models consist of low-level shape representations, they often fail to capture shape characteristics essential for performance analyses. Therefore, the proposed GOs exploit the differential and integral properties of shapes — accessed through Fourier descriptors, curvature integrals, geometric moments, and their invariants — to infuse high-level intrinsic geometric information and physics into the feature vector used for training, even when employing simple model architectures or low-level parametric descriptions. We showed that for surrogate modelling, along with the inclusion of the notion of physics, GOs enact regularisation to reduce over-fitting and enhance generalisation to new, unseen designs. Furthermore, through extensive experimentation, we demonstrate that for dimension reduction and generative models, incorporating the proposed GOs enriches the training data with compact global and local geometric features. This significantly enhances the quality of the resulting latent space, thereby facilitating the generation of valid and diverse designs. Lastly, we also show that GOs can enable learning parametric sensitivities to a great extent. Consequently, these enhancements accelerate the convergence rate of shape optimisers towards optimal solutions.

Регуляторний вплив держави на діяльність банків як категорія системного управління (сутність і метрологія)

Introduction. System management is based on the recognition of management objects as integral groups. The essence of the regulatory influence of the state on the activities of a bank is considered as a way to change project standards and current indicators of its financial stability with the justification of organizational measures to ensure stable functioning and development. Problem Statement. System management of an integral group involves a systemic analysis of the management object as a single whole with the determination of the properties and relationships of the system components: input, process, output, goal, direct and feedback, and limitations. The purpose is to determine the market characteristics of the regulatory influence of the state on the activities of banks as a category of system management, its content, metrology, and signs of complexity. Methods. The conceptual provisions of system analysis, methods of clarifying the content, properties of integrity, self-organization and stability of the system, their structuring, as well as program-targeted design were used. Results. Market characteristics were systematized and the social status of the state's regulatory influence on the activities of banks as a category of systemic management was substantiated. The integrity of the state'scomplex regulatory influence on the activities of banks was substantiated by means of a “three-story” classification of its components and the results of their interaction. Conclusions. The use of the conceptual provisions of systems theory to clarify the nature of the state's regulatory influence on the activities of banks revealed the processes of its formation as a category of systemic management. The metrology of such influence consists in monitoring and comparative assessments of: indicators of financial stability and stability of banks with the economic standards of the NBU; leading indicators of measuring the financial condition and probability of bankruptcy of banks; dynamics of the market value of banks as a target criterion of complex regulatory influence.

Conversion of Flexible Spin Crossover Metal-Organic Frameworks Macrocrystals to Nanocrystals Using Ultrasound Energy: A Study on Structural Integrity by MicroED and Charge-Transport Properties.

Metal-Organic Frameworks (MOFs) attract attention for their intrinsic porosity, large surface area, and functional versatility. To fully utilize their potential in applications requiring precise control at smaller scales, it is essential to overcome challenges associated with their bulk form. This is particularly difficult for 3D MOFs with spin crossover (SCO) behavior, which undergo a reversible transition between high-spin and low-spin states in response to external stimuli. Maintaining their structural integrity and SCO properties at the nanoscale remains a significant challenge, yet these properties make them ideal candidates for sensors, data storage, and molecular switch applications. This study reports the synthesis of nanocrystals of the well-known SCO MOF [Fe2(H0.67bdt)3]·xH2O (1, x = 0-10, bdt2- = 1,4-benzeneditetrazolate), which exhibits both magnetic and charge transport properties. The nanocrystals are obtained through sonication of macrocrystals, and the preservation of their crystalline structure at the nanoscale is explored using Microcrystal Electron Diffraction (MicroED). A comparison between macro- and nanocrystals highlights the structural integrity and the preservation of charge-transport properties, underlining the potential for further miniaturization of MOFs for advanced technological applications.

Comprehensive Study of τ-Phase Mn–Al–C Magnets: Corrosion Resistance, Structural Integrity, and Magnetic Properties

Comprehensive Study of τ-Phase Mn–Al–C Magnets: Corrosion Resistance, Structural Integrity, and Magnetic Properties

Suppression of MT5-MMP Reveals Early Modulation of Alzheimer's Pathogenic Events in Primary Neuronal Cultures of 5xFAD Mice.

We previously reported that membrane-type 5-matrix metalloproteinase (MT5-MMP) deficiency not only reduces pathological hallmarks of Alzheimer's disease (AD) in 5xFAD (Tg) mice in vivo but also impairs interleukin-1 beta (IL-1β)-mediated neuroinflammation and Aβ production in primary Tg immature neural cell cultures after 11 days in vitro. We now investigate the effect of MT5-MMP on incipient pathogenic pathways that are activated in cortical primary cultures at 21-24 days in vitro (DIV), during which time neurons are organized into a functional mature network. Using wild-type (WT), MT5-MMP-/- (MT5-/-), 5xFAD (Tg), and 5xFADxMT5-MMP-/- (TgMT5-/-) mice, we generated primary neuronal cultures that were exposed to IL-1β and/or different proteolytic system inhibitors. We assessed neuroinflammation, APP metabolism, synaptic integrity, and electrophysiological properties using biochemical, imaging and whole-cell patch-clamp approaches. The absence of MT5-MMP impaired the IL-1β-mediated induction of inflammatory genes in TgMT5-/- cells compared to Tg cells. Furthermore, the reduced density of dendritic spines in Tg neurons was also prevented in TgMT5-/- neurons. IL-1β caused a strong decrease in the dendritic spine density of WT neurons, which was prevented in MT5-/- neurons. However, the latter exhibited fewer spines than the WT under untreated conditions. The spontaneous rhythmic firing frequency of the network was increased in MT5-/- neurons, but not in TgMT5-/- neurons, and IL-1β increased this parameter only in Tg neurons. In terms of induced somatic excitability, Tg and TgMT5-/- neurons exhibited lower excitability than WT and MT5-/-, while IL-1β impaired excitability only in non-AD backgrounds. The synaptic strength of miniature global synaptic currents was equivalent in all genotypes but increased dramatically in WT and MT5-/- neurons after IL-1β. MT5-MMP deficiency decreased endogenous and overexpressed C83 and C99 levels but did not affect Aβ levels. C99 appears to be cleared by several pathways, including γ-secretase, the autophagolysosomal system, and also α-secretase, via its conversion to C83. In summary, this study confirms that MT5-MMP is a pivotal factor affecting not only neuroinflammation and APP metabolism but also synaptogenesis and synaptic activity at early stages of the pathology, and reinforces the relevance of targeting MT5-MMP to fight AD.

Triboelectric multilayered electrospun co-polyamide-based wound dressings with inherent antibacterial properties

Abstract Wound healing is a challenging problem to healthcare and society, requiring the development of advanced materials that can enhance tissue rejuvenation and prevent infection. This article presents the design and synthesis of a multilayered copolyamide based electrospun membrane for wound healing applications. The dressing is engineered using a combination of copolymerisation and electrospinning techniques. The unique porous architecture, hydrophilicity, and adequate mechanical and thermal stability make the developed materials ideal candidates for skin regeneration. The inherent antibacterial effectiveness of the membrane was investigated on a range of pathogens that cause wound infections. The cytocompatibility of the membrane was studied on human monocyte cell lines, which play a vital role in immune response and skin regeneration. This multilayered membrane embodies a promising strategy for promoting wound care consequences through its combination of biocompatibility, structural integrity, and inherent antibacterial properties. The potential impact of this research on the field of wound healing is significant and inspiring. Graphical abstract

DensToolKit2: A comprehensive open-source package for analyzing the electron density and its derivative scalar and vector fields.

In this article, we provide details of the suite DensToolKit-v2, which consists of a set of cross-platform, optionally parallelized programs for analyzing the molecular electron density (ρ), as well as different fields and chemical indices derived from it. Notably, with this version, the user can compute the Non-Covalent Interaction index, the Density Overlap Regions Index, and fields related to single-spin-type molecular orbitals, such as the spin density. In addition, DensToolKit-v2 includes several programs for analyzing other less-known fields, such as the Density Matrix of order 1, the two-electron pair density function, and the Fourier transforms of these fields, that is, functionals in momentum space. A new sub-program to compute integrated properties of each of the fields released in the suite is included. A simple graphical user interface is released, which eases the visualization of ρ critical points topology. Most interestingly, this version includes a program that renders estimations of pKa's of carboxylic acids and pKb's of amines (primary, secondary, and tertiary) through refined relations between experimental data and the molecular electrostatic potential computed at isosurfaces of ρ. Details related to the speed of the programs and a few examples of how to use the program in workflows are discussed, and the source code is released through a git repository under the GPLv3 terms.

On a Model for Solving Mixed Fractional Integro Differential Equation

In this work, the mixed fractional integro differential equation (MfrIo-DE) of the second kind, under certain condition is considered, in the space L2(−1, 1)× C [0, T]; T < 1 T is the time. The position kernel k (|x−y|) of IE has a singularity. After integrating and using the properties of fractional integral, we have a MIE in position and time, where the kernel of position takes the singular form k (|x−y|), and the kernel of time takes the singular Abel form (t −τ)α−1 , 0 < α < 1. Then, using separation of variable method, under certain substitution, we obtain FIE in position, with variable fractional coefficients in time. Using the Toeplitz matrix method (TMM), we have a nonlinear algebraic system (NAS). Moreover, numerical results are obtained and discussed, especially when 0 < α < 1. Also, the solutions of the mixed equation are considered when α = 0, α = 1. Finally, the error estimate, in each case, is computed.

Integrability Properties of Generalized Liénard Differential Equations

Integrability Properties of Generalized Liénard Differential Equations

Effect of surface modification on interfacial microstructures and mechanical properties of continuous CF/Al composites

The interface structure and infiltration effect between reinforcement (CFs) and Al matrix have a significant impact upon comprehensive properties of the resulting carbon-fibre-reinforced Al matrix (CF/Al) composites. In present study, Ni coatings with different thicknesses were evenly coated onto carbon fibres (CFs) via electroplating for the purpose of promote the interface combining effect and reduce adverse interfacial reaction betwixt CFs and Al matrix. The influence of pH value (2, 3, 4, 5, 6), current density (0.1 A, 0.2 A, 0.3 A, 0.4 A, 0.5 A, 0.6 A), electroplating time (2 min, 4 min, 6 min) on surface appearance and tensile strength of Ni-coated CFs were discussed. The results show that the Ni-coated CFs with excellent integrity and mechanical properties was obtained at a current density of 0.4 A and a pH of 5. Subsequently, twin-roll casting and T6 heat treatment process were used to fabricate CF/Al composites with varying Ni coating thicknesses. Using SEM, TEM and tensile property testing, the impact of Ni coating thickness (0 μm, 0.35 μm, 0.58 μm, 0.76 μm) on interfacial microstructures and mechanical characteristics of CF/Al composites were examined. The results exhibit that the 0.76 μm Ni-coated CF/Al composites exhibit best UTS and elongation of 151.6 MPa and 11.7 %, respectively. This is due to a thicker Ni coating preventing the CFs against reaction with Al matrix during processing the composites, which reduces the generation of Al4C3 phase. However, when the coating thickness is 0.35 μm, adverse chemical interactions occur at interface of Al-CFs, leading to the formation of an Al4C3 phase. Finally, the strengthening mechanism of Ni-coated CF/Al composites was analyzed, and its strengthening model was established. This study can provide a pratical route to prepare and applicate the high-quality continuous CF/Al composites.

Temperature and Flexural Endurances of Aluminum-Doped Zinc Oxide Thin Films on Flexible Polyethylene Terephthalate Substrates: Pathways to Enhanced Flexibility and Conductivity

This work investigates the endurance and performance of aluminum-doped zinc oxide (AZO) thin films fabricated on flexible polyethylene terephthalate (PET) substrates, providing new insights into their degradation linked to mechanical flexing and accelerated thermal cycling (ATC). The current study uniquely combines cyclic bending fatigue at 23 °C and 70 °C with ATC between 0 °C and 100 °C, simulating operational stresses in real-world environments, in contrast to previous research that has focused primarily on either isolated mechanical or thermal effects. The 425 nm thick films showed high transparency and conductivity, making them suitable materials for flexible electronics and optoelectronic devices. In this work, electrical resistivity, one of the most important performance parameters, was investigated after each mechanical or thermal cycle. The results indicate that mechanical cycling at high temperatures can drastically enhance the crack formation and electrical degradation, with an over 250% change in the electrical resistance (PCER) after 12,000 cycles at 70 °C and more than 300% after 500 thermal cycles. The highly deleterious effects of combined stressors on the structural integrity and electrical properties of AZO films are underlined by these observations. This study further suggests that the design of more robust AZO-based materials/coatings would contribute toward achieving better durability in flexible electronic applications. These findings also go hand in glove with the ninth goal of the United Nations’ Sustainable Development Goals, specifically Target 9.5: Enhance Research and Upgrade Industrial Technologies.

Sustainable synthesis and environmental application of chitosan-Ocimum basilicum leaves-ZnO composite membrane for permanganate ion removal in wastewater treatment.

This study introduces a novel and environmentally friendly method for developing a cross-linked chitosan-Ocimum basilicum leaves-ZnO (ChOBLZnO) composite membrane, specifically designed for the adsorption of permanganate ions (MnO4-) from wastewater. Various characterization techniques, including Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and Brunauer-Emmett-Teller (BET) surface area analysis, were employed to confirm the membrane's synthesis quality, structural integrity, and surface properties crucial for adsorption. The BET analysis revealed a surface area of 228.64 m2/g, indicating a highly porous structure. The membrane exhibited a high adsorption capacity of 142.8mg/g and an outstanding removal efficiency of 98.5%. The adsorption kinetics were best described by the pseudo-second-order model, with a correlation coefficient (R2) of 0.998, while the Freundlich isotherm model provided the most accurate fit for the adsorption behavior, with an R2 of 0.995. Thermodynamic studies indicated that the adsorption process is spontaneous and endothermic, with negative Gibbs free energy and positive enthalpy and entropy values. Reusability tests showed that the ChOBLZnO composite membrane maintained a high removal efficiency across five cycles, with minimal performance loss. These results demonstrate the ChOBLZnO composite membrane's potential as an efficient and sustainable solution for wastewater treatment, offering both high efficiency and durability.

Effect of sterilization methods on quality and storage characteristics of tofu fermented by lactic acid bacteria

This study examined the effects of pasteurization (PAS), ultrasonic sterilization (ULS), and microwave sterilization (MWS) on the quality and storage characteristics of brine-fermented tofu (BFT) and fermented tofu (FT). Comparative analysis revealed that MWS had a negligible detrimental effect on the structural integrity and organoleptic properties of BFT and FT, while effectively maintaining its water-holding capacity (WHC) and exhibiting the least impact on its texture. In contrast, PAS and ULS increased hardness and chewiness significantly (P < 0.05), but ULS also enhanced the brightness of tofu. Throughout the storage period, the WHC, elasticity, and sensory properties of tofu generally decreased, whereas the hardness and chewiness increased. PAS-BFT and MWS-FT maintained sensory quality for the longest periods of 14 and 12 days respectively, and could be decomposed to more small molecule peptides within 0–8 days and 0–6 days, which are more easily to be absorbed by the body. The findings discovered that MWS is the most suitable method for sterilization of tofu, with superior capability in maintaining the quality, extending shelf life, and improving digestibility of tofu.

Efficient Synthesis and Characterization of Antibacterial Xanthan Gum–Based Self‐Healing Hydrogels: Conventional Versus Microwave Treated

ABSTRACTThe development of self‐healing hydrogels with mechanical integrity is vital for biomedical applications. This study synthesizes multi‐network (MN) self‐healing hydrogels using xanthan gum (XG) through conventional and microwave‐assisted methods via free‐radical polymerization. The synthesis materials included XG, acrylamide, acrylonitrile, sodium dodecyl sulfate, ferric chloride hexahydrate, and ammonium persulfate. Conventional synthesis took 60 min at 70°C, while microwave synthesis was completed in 4.5 min at 540 W, enhancing energy and material efficiency. Structural tests like FTIR and SEM confirmed the results. Microwave synthesis produced a layered structure with smaller pores, leading to slower swelling kinetics, and EDX mapping showed higher Fe3+ ion concentrations, indicating better crosslinking. Thermal gravimetric analysis demonstrated that degradation onset temperatures were 184°C for microwave‐assisted synthesis XG hydrogel (MHXG) and 163°C for the water bath XG hydrogel method (HXG), indicating a 20°C enhancement due to the coherent structure induced by microwave treatment. Evaluation of self‐healing capabilities through visual and rheological tests showed significant enhancements in MHXG, which exhibited a self‐healing time of 2 h compared to 1 day required by HXG, attributed to increased crosslink density and hydrogen bonding facilitated by microwave treatment. Rheological assessments confirmed that both hydrogel types maintained their structural integrity and viscoelastic properties after healing. MHXG exhibited a mechanical strength of 21.12 kPa and elasticity of 10 kPa, whereas HXG showed 11.59 kPa and 1 kPa, respectively. Microwave‐treated hydrogel showed enhanced antibacterial effectiveness against Staphylococcus aureus due to better distribution of agents in the matrix. This method for synthesizing XG‐based self‐healing hydrogels is promising for advanced biomedical applications.