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Search Results (523)

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Keywords = cutting equation

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10 pages, 1663 KB  
Article
Periods of Energy Exchange Under the Mutual Effects of Four-Wave Mixing, Self-Phase Modulation and Cross-Phase Modulation
by Zara Kasapeteva, Anelia Dakova-Mollova, Diana Dakova, Kamen Kovachev, Lubomir Kovachev and Anjan Biswas
Optics 2026, 7(2), 27; https://doi.org/10.3390/opt7020027 - 8 Apr 2026
Viewed by 170
Abstract
In the present work a new regime of periodical energy exchange between pump, signal and idler waves, under the influence of the process of four-wave mixing (FWM), with additional consideration of the effects of self-phase modulation (SPM) and cross-phase modulation (XPM), is presented. [...] Read more.
In the present work a new regime of periodical energy exchange between pump, signal and idler waves, under the influence of the process of four-wave mixing (FWM), with additional consideration of the effects of self-phase modulation (SPM) and cross-phase modulation (XPM), is presented. In our previous papers a theoretical model which successfully describes the amplification and periodic energy exchange between the three optical waves in CW regime of laser source propagation (short-cut equations) was developed. Exact analytical solutions, describing the periodic changes in the intensities of pump, signal and idler waves, were found and expressed by the Jacobi elliptic functions. The period of the energy exchange between the waves can be presented by elliptic integral of the first kind. In the current research, the periods of energy exchange between the pump, signal and idler waves in the process of FWM, additionally taking into account the effects of SPM and XPM, are investigated. A comparison between the obtained results has been made. It is shown that the effects of self-phase modulation and cross-phase modulation increase the period of energy exchange. Full article
(This article belongs to the Section Nonlinear Optics)
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16 pages, 4729 KB  
Article
Analysis of Cutting Equation for Micro-Groove Tool and Its Impact on Shear Angle and Cutting Force in Tuning AISI201
by Wenfeng Yang, Lingyun Yang, Jian Liu and Jinxing Wu
Coatings 2026, 16(4), 427; https://doi.org/10.3390/coatings16040427 - 3 Apr 2026
Viewed by 234
Abstract
The face of cutting tools serves as the critical interface for chip–tool interaction and wear initiation, significantly influencing tool performance and service life. By implementing micro-groove structures on the face to reduce the chip–tool contact area, the cutting mechanics of the tool are [...] Read more.
The face of cutting tools serves as the critical interface for chip–tool interaction and wear initiation, significantly influencing tool performance and service life. By implementing micro-groove structures on the face to reduce the chip–tool contact area, the cutting mechanics of the tool are altered. Theoretical analysis indicates that the cutting equations of the grooved tool have changed, with the modified tool exhibiting a larger shear angle compared to the original design. Finite element simulations and experiments demonstrate that grooved tool exhibit optimized cutting mechanics, characterized by a larger shear angle and improved edge sharpness. The shear angle of grooved tool is increased by about 3 degrees and the chip thickness is reduced by about 0.05 mm. Cutting tests confirm that the grooved tool reduces the main cutting force by more than 18%, with a smaller wear area on the face and improved wear conditions near the cutting edge. Due to materials such as stainless steel and titanium alloy, which have similar difficult-to-machine properties. The present results are based on AISI 201 and the specific groove geometry used in this study, and further work is required before generalizing to other difficult-to-cut materials and groove designs. In summary, based on the experimental data, the micro-groove cutting tool outperforms the original tool in terms of shear angle, cutting force, and durability. Specifically, the shear angle of the micro-groove cutting tool is larger, the cutting force is reduced, and the wear on the face is decreased. Full article
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17 pages, 566 KB  
Article
Life Cycle Assessment of Microplastic Fouling Mitigation Strategies in Membrane Filtration
by Rendra Hakim Hafyan, Vithushan Indrakumar, Judy Lee and Siddharth Gadkari
Membranes 2026, 16(4), 136; https://doi.org/10.3390/membranes16040136 - 1 Apr 2026
Viewed by 297
Abstract
While membrane technologies are critical for preventing microplastics (MPs) release into aquatic ecosystems, MPs-induced fouling remains a persistent bottleneck, necessitating energy-intensive cleaning strategies that introduce their own environmental burdens. This study presents a systematic life cycle assessment (LCA) of fouling mitigation strategies, rigorously [...] Read more.
While membrane technologies are critical for preventing microplastics (MPs) release into aquatic ecosystems, MPs-induced fouling remains a persistent bottleneck, necessitating energy-intensive cleaning strategies that introduce their own environmental burdens. This study presents a systematic life cycle assessment (LCA) of fouling mitigation strategies, rigorously comparing hydraulic forward flushing and nitrogen (N2) gas scouring across both unmodified and plasma-modified (acrylic acid, cyclopropylamine, and hexamethyldisiloxane) polysulfone membranes. Results reveal a stark divergence between operational performance and environmental sustainability. Baseline operations and the hydraulic flushing of unmodified membranes have environmentally costly global warming potential (GWP) ~150 kg CO2-eq/m3), driven primarily by high electricity consumption and frequent membrane replacement. Conversely, cyclopropylamine (CPAm) plasma-modified membranes emerging as the optimal strategy, reducing global warming potential to 68 kg CO2-eq/m3 and cutting electricity demand by 44% through superior fouling resistance. Crucially, the study uncovers a significant trade-off regarding gas scouring: While it achieves the highest technical performance (minimal flux decline of 0.33% h−1), the upstream burdens of N2 supply increased environmental impacts by over 100% across all categories. These findings challenge the assumption that maximum fouling control equates to sustainability, suggesting that surface engineering via plasma modification, rather than aggressive physical cleaning, offers the most viable pathway for sustainable MPs remediation. Full article
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23 pages, 1003 KB  
Article
Impact of BPO Outsourcing on Competitiveness in Logistics: A Structural Equation Modeling Approach in the Croatian Context
by Marko Šarić and Marjan Sternad
Systems 2026, 14(4), 371; https://doi.org/10.3390/systems14040371 - 31 Mar 2026
Viewed by 241
Abstract
Purpose & Research Gap: While Business Process Outsourcing (BPO) is widely studied, there is a lack of empirical research analyzing its specific impact on competitiveness within the logistics sector of emerging markets. This study addresses the gap regarding how BPO transitions from a [...] Read more.
Purpose & Research Gap: While Business Process Outsourcing (BPO) is widely studied, there is a lack of empirical research analyzing its specific impact on competitiveness within the logistics sector of emerging markets. This study addresses the gap regarding how BPO transitions from a cost-saving tool to a strategic expertise-driven model. Methodology: Data were collected from 132 logistics companies in Croatia. Structural Equation Modeling (SEM) was applied to test the hypotheses and mediation effects, as it allows for a robust analysis of complex causal relationships between latent constructs. Key Findings: SEM results reveal that BPO engagement alone does not guarantee competitiveness. The primary finding indicates that the expertise of BPO providers and strategic partnerships exert a significantly stronger positive effect on operational efficiency and market differentiation than simple cost reduction. Contribution: The paper contributes to the literature by redefining BPO as a strategic driver of innovation rather than a mere cost-cutting measure, providing logistics managers with evidence-based insights for knowledge-oriented outsourcing. Full article
(This article belongs to the Section Supply Chain Management)
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28 pages, 7672 KB  
Article
Optimization of CNC Milling Parameters of SKD11 Material for Core Component with Different Tool Path Strategies Based on Integration Approach of Taguchi Method, Response Surface Method and Lichtenberg Optimization Algorithm
by Minh Phung Dang, Thi Van Anh Duong and Chi Thien Tran
Appl. Sci. 2026, 16(7), 3261; https://doi.org/10.3390/app16073261 - 27 Mar 2026
Viewed by 265
Abstract
This study proposes a useful multi-criteria optimization approach for defining the proper fabrication factors for the CNC milling process on the inclined surfaces of SKD 11 material. The method is to be used in mold fabrication technology within the field of mechanical engineering. [...] Read more.
This study proposes a useful multi-criteria optimization approach for defining the proper fabrication factors for the CNC milling process on the inclined surfaces of SKD 11 material. The method is to be used in mold fabrication technology within the field of mechanical engineering. A combination technique of the Taguchi technique (TM), response surface method (RSM), and Lichtenberg optimization algorithm (LA) was proposed to optimize the fabrication factors for enriching the superiority attributes. In the first stage, several initial experiments of the fabricating parameters were generated by the TM. Secondly, the mathematical equations among the main fabricating parameters, the surface roughness, the flatness, and the CNC milling time were then established by the RSM. Significant influences of fabrication elements on surface roughness, flatness, and CNC milling time were evaluated by variance analysis and sensitivity analysis based on three distinct CNC milling toolpath strategies. Finally, the Lichtenberg optimization algorithm was carried out based on regression equations to define the optimized factors for three cutting strategies. The optimized results showed that the reverse CNC milling toolpath strategy was the best for achieving the three quality responses. Furthermore, the results demonstrated that the inaccuracies among optimized as well as experiment confirmations for the surface roughness, flatness and CNC milling time were 6.54%, 18.182% and 11.972%, respectively. The verifications of experiment results were relatively suitable with the anticipated consequences. The outcomes reveal that an integration optimization methodology is a successful approach to tackling the multi-objective optimal problem of determining the best CNC milling parameters for the cartwheel specimen made of SKD11 material in injection mold technology. It can also be expanded to apply to complicated multi-criteria optimization problems. Full article
(This article belongs to the Special Issue Advances in Manufacturing and Machining Processes)
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22 pages, 8894 KB  
Article
Study on the Rock Breaking and Vibration Reduction Mechanisms of Wedge Cut Delayed Blasting in Tunnel
by Yu Hu, Renshu Yang, Jinjing Zuo, Wangjing Hu, Genzhong Wang, Depeng Hua and Yongli Guan
Eng 2026, 7(4), 148; https://doi.org/10.3390/eng7040148 - 25 Mar 2026
Viewed by 308
Abstract
To overcome the drawbacks of conventional wedge cut blasting—high peak particle velocity (PPV), low blasthole utilization, and a high proportion of large fragments—this paper proposes a delayed blasting method for wedge cut blasting. By integrating the rock-fracturing process of wedge cut blasting, the [...] Read more.
To overcome the drawbacks of conventional wedge cut blasting—high peak particle velocity (PPV), low blasthole utilization, and a high proportion of large fragments—this paper proposes a delayed blasting method for wedge cut blasting. By integrating the rock-fracturing process of wedge cut blasting, the mechanisms of rock breaking and vibration reduction are investigated and confirm the method through field tests. The results indicate that the rock breaking process can be divided into two stages, the stage of fracture propagation and the stage of cavity ejection, and a rock breaking criterion for wedge cut delayed blasting is established. Considering differences in the vibration waveforms generated by different types of cut holes, a vibration waveform fitting method for wedge cut delayed blasting is proposed. Furthermore, the generation time of the blast-induced free surface during the rock breaking process is calculated, and a calculation Equation for the optimal delayed time is derived. Field tests in the Qi Jiazhuang tunnel show that, compared with conventional blasting, the proposed delayed blasting method increases blasthole utilization by 23.8%, reduces the large fragment rate by 67.4%, lowers PPV by 53.7%, and increases the dominant vibration frequency by 42.0%. These results significantly improve the wedge cut blasting performance and construction safety. Full article
(This article belongs to the Section Chemical, Civil and Environmental Engineering)
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23 pages, 1222 KB  
Article
From Forest Land Easements to Broader Conservation Agreements: An Analysis of Pathways to Community Support in China’s National Park Pilot
by Fangbing Hu, Zhen Sun, Guangyu Wang, Wanting Peng and Chengzhao Wu
Forests 2026, 17(4), 403; https://doi.org/10.3390/f17040403 - 24 Mar 2026
Viewed by 155
Abstract
Conservation easements (CEs) represent a complex policy instrument designed to mediate the feedback loops within coupled human and natural systems in protected areas. However, their efficacy is often constrained by a lack of systemic understanding of the localized drivers of community support. Building [...] Read more.
Conservation easements (CEs) represent a complex policy instrument designed to mediate the feedback loops within coupled human and natural systems in protected areas. However, their efficacy is often constrained by a lack of systemic understanding of the localized drivers of community support. Building upon the successful implementation of Forest Land Easements (FLEs) within China’s Qianjiangyuan National Park Pilot, this study investigates the potential to expand this policy model to other land types. This study investigates the multilevel factors influencing residents’ willingness to adopt three types of CEs, including forest land (FLE), agricultural land (ALE) and homestead land (HLE) easements in China’s Qianjiangyuan National Park Pilot, the country’s primary CE reform site. We conceptualize a hierarchical support model wherein community participation (CP) and human well-being (HW) interact with support for park management (SM), forming a subsystem that drives decisions within the broader land-use. Utilizing structural equation modelling (SEM) and stepwise regression analysis on survey data from 336 households, we tested this model. The results reveal that SM acts as a critical direct mediator and positive driver of CE acceptance, while CP and HW exert significant indirect effects through SM, demonstrating a key feedback pathway. Regression analyses further elucidate that support for different CE types is driven by distinct configurations of factors, highlighting the heterogeneous nature of subsystems. Notably, livelihood benefits and prior participation experiences emerged as consistent, cross-cutting systemic leverages. It demonstrates that leveraging the implementation experience and community support gained from existing forest land easements is crucial. This study concludes that effective CE design must move beyond one-size-fits-all approaches. It necessitates differentiated, adaptive policies that are coherently aligned with local livelihood subsystems and strategically strengthen participatory feedback mechanisms initiated by successful FLEs. Our findings provide an evidence-based framework for designing resilient, socially sustainable conservation policies in complex protected area systems, grounded in proven practice. Full article
(This article belongs to the Special Issue Forestry Economy Sustainability and Ecosystem Governance)
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21 pages, 842 KB  
Article
A Fourth-Order Difference Scheme for Solving the Generalized Nonlinear Time-Fractional Burgers-Type Equation
by Weiyan Zhang and Xuehua Yang
Fractal Fract. 2026, 10(4), 210; https://doi.org/10.3390/fractalfract10040210 - 24 Mar 2026
Viewed by 187
Abstract
In the present study, we propose a new nonlinear finite difference method for solving the generalized nonlinear time-fractional Burgers-type equation, which can achieve fourth-order accuracy in the spatial direction. The L1 formula is employed to discretize the time-fractional derivative on a graded mesh. [...] Read more.
In the present study, we propose a new nonlinear finite difference method for solving the generalized nonlinear time-fractional Burgers-type equation, which can achieve fourth-order accuracy in the spatial direction. The L1 formula is employed to discretize the time-fractional derivative on a graded mesh. Spatial discretization is accomplished by introducing a nonlinear fourth-order difference operator and a linear compact difference operator, and ultimately a nonlinear difference scheme with a temporal accuracy of order 2α and a spatial accuracy of the fourth order is deduced. For the proposed difference scheme, the existence and boundedness of its solution have been theoretically verified; meanwhile, combined with the cut-off function method, the uniqueness and convergence of the solution to this scheme are further proved. The optimal convergence result is attained under the L2 norm. Eventually, two numerical examples are provided, both of which match the theoretical analysis well. Full article
(This article belongs to the Section Numerical and Computational Methods)
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28 pages, 5247 KB  
Article
Comparative Analysis of High-Fidelity and Reduced-Order Models for Nonlinear Wave–Bathymetry and Wave–Structure Interactions
by Wen-Huai Tsao and Christopher E. Kees
J. Mar. Sci. Eng. 2026, 14(7), 594; https://doi.org/10.3390/jmse14070594 - 24 Mar 2026
Viewed by 271
Abstract
This paper presents a computational study of wave–bathymetry and wave–structure interaction problems using advanced numerical techniques based on high-fidelity, two-phase Navier–Stokes (TpNS) flow and reduced-order, fully nonlinear potential flow models. For high-fidelity simulations, the TpNS equations are discretized using the finite-element method, with [...] Read more.
This paper presents a computational study of wave–bathymetry and wave–structure interaction problems using advanced numerical techniques based on high-fidelity, two-phase Navier–Stokes (TpNS) flow and reduced-order, fully nonlinear potential flow models. For high-fidelity simulations, the TpNS equations are discretized using the finite-element method, with free-surface evolution captured through a hybrid level-set (LS) and volume-of-fluid (VOF) formulation. A monolithic, phase-conservative LS equation is introduced to mitigate mass loss and interface smearing, combined with a semi-implicit projection scheme. Hydrodynamic forces are resolved using a high-order, phase-resolving cut finite-element method (CutFEM), which enables the representation of complex solid geometries within a fixed background mesh. An equivalent polynomial of Heaviside and Dirac distributions ensures accurate evaluation of surface and volume integrals. Hence, no explicit generation of cut cell meshes, adaptive quadrature, or local refinement is required. For reduced-order modeling, a fast regularized boundary integral method (RBIM) is employed to solve the fully nonlinear potential flow. Singular and near-singular integrals are treated using a subtract-and-addition technique based on auxiliary functions derived from Stokes’ theorem, allowing direct application of high-order quadrature without conventional boundary element discretization. An arbitrary Lagrangian–Eulerian (ALE) formulation is adopted to enforce free-surface boundary conditions while avoiding excessive mesh distortion. The proposed approaches are applied to investigate highly nonlinear wave transformation over complex bathymetry and wave-induced dynamics of floating structures, including eddy-making damping effects. Numerical results are validated against experimental measurements. These two modeling approaches represent complementary levels of physical fidelity and computational efficiency, and their systematic comparison clarifies the trade-offs between computational accuracy, efficiency, and cost for practical marine problems. Full article
(This article belongs to the Special Issue Wave–Structure–Seabed Interaction)
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10 pages, 381 KB  
Article
Spectral Signatures of Prime Factorization
by Giuseppe Mussardo and Andrea Trombettoni
Entropy 2026, 28(3), 363; https://doi.org/10.3390/e28030363 - 23 Mar 2026
Viewed by 287
Abstract
We present a protocol for integer factorization for all integers N below a certain cut-off Λ=2d, grounded in the theory of quantum measurement. In this framework, the factorization of an integer NΛ is achieved in a number [...] Read more.
We present a protocol for integer factorization for all integers N below a certain cut-off Λ=2d, grounded in the theory of quantum measurement. In this framework, the factorization of an integer NΛ is achieved in a number of steps equal to the total number I of primes present in its factorization; explicitly, the procedure consists of a sequence of I quantum measurements. The method requires a single-purpose quantum device designed to perform measurements of an observable with a prescribed spectrum. Crucially, the construction of this device involves solving, once and for all, a set of approximately 2d differential equations, independently of the specific integer to be factorized. We argue that the initialization task of this device can be efficiently implemented on a quantum computer in d steps, thereby decoupling the computational cost of device preparation from the factorization process itself. Full article
(This article belongs to the Section Quantum Information)
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10 pages, 1125 KB  
Article
Predicting Flexural Properties of Thermo–Vacuum-Treated Wood Using Non-Destructive Tests
by Hızır Volkan Görgün
Appl. Sci. 2026, 16(6), 3030; https://doi.org/10.3390/app16063030 - 20 Mar 2026
Viewed by 229
Abstract
Non-destructive and destructive test methods are applied to wood to characterize this heterogeneous natural material. There have been multiple studies to characterize and investigate the change after the treatment (impregnation, thermal modification, etc.). In terms of thermal modification, there have been few studies [...] Read more.
Non-destructive and destructive test methods are applied to wood to characterize this heterogeneous natural material. There have been multiple studies to characterize and investigate the change after the treatment (impregnation, thermal modification, etc.). In terms of thermal modification, there have been few studies on thermo–vacuum treatment, which is performed in a continuous vacuum atmosphere. With this method, the objective was to attempt to reduce the strength decrease after the thermal treatment. The aim of this study was to estimate the flexural properties of thermo–vacuum-treated Scots pine wood with destructive and acoustic-based non-destructive test methods. Wood was treated at 180 °C and 360 mm Hg. Both treated and untreated samples were cut into small specimens to ensure they were free of defects and were tested with acoustic-based non-destructive (longitudinal vibration and stress wave) and static bending test methods. The results show a decrease in equilibrium moisture content, demonstrating the efficiency of the treatment. When the results were compared with destructive test results, higher correlations (R2 > 0.858) were found when estimating the modulus of elasticity (MOE) for both the untreated and treated wood, while lower correlations (R2 < 0.440) were found for the modulus of rupture (MOR). When an additional equation was developed, stronger correlations (R2 > 0.8986) were obtained between the non-destructive and destructive test results. Full article
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20 pages, 375 KB  
Article
Higher-Order Fuzzy Difference Equations: Existence, Stability, and Illustrative Numerical Examples
by Hashem Althagafi and Ahmed Ghezal
Mathematics 2026, 14(6), 1051; https://doi.org/10.3390/math14061051 - 20 Mar 2026
Viewed by 211
Abstract
This paper examines the dynamics of positive solutions to a system of fuzzy difference equations, which provide effective tools for modeling dynamical systems with uncertain or imprecise parameters. The main objective is to establish the existence, uniqueness, and qualitative properties of positive solutions [...] Read more.
This paper examines the dynamics of positive solutions to a system of fuzzy difference equations, which provide effective tools for modeling dynamical systems with uncertain or imprecise parameters. The main objective is to establish the existence, uniqueness, and qualitative properties of positive solutions within a fuzzy framework. After recalling some fundamental notions from fuzzy set theory, we analyze the dynamics of the proposed system. The main results prove the existence of a unique positive fuzzy solution under suitable conditions and establish the boundedness, continuity, and convergence of the solutions. In particular, all solutions converge to a unique positive equilibrium point. Numerical experiments for (l1,l2)=(2,3) and (l1,l2)=(4,1) with uncertainty levels γ=0.2 and γ=0.8 illustrate the theoretical results and confirm the convergence toward the unique positive equilibrium. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, Chaos, and Mathematical Physics)
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19 pages, 3344 KB  
Article
2D and 3D Stability Analysis of Rectangular Tunnel Roof Based on Tensile Cut-Off Criterion
by Wenqian Cai, De Zhou, Chaoqun Hou, Yongxin Li, Long Xia and Guihua Long
Buildings 2026, 16(6), 1132; https://doi.org/10.3390/buildings16061132 - 12 Mar 2026
Viewed by 195
Abstract
Tunnel roof is subjected to a complex tension-shear stress state after excavation. A tensile cut-off strength criterion is introduced in this study and combined with the upper bound limit analysis method to investigate the stability of a rectangular tunnel roof. First, the expression [...] Read more.
Tunnel roof is subjected to a complex tension-shear stress state after excavation. A tensile cut-off strength criterion is introduced in this study and combined with the upper bound limit analysis method to investigate the stability of a rectangular tunnel roof. First, the expression for the internal energy dissipation rate is derived for the circular cut-off segment of the failure criterion. Power functionals Φ are established for both two-dimensional and three-dimensional rotational collapse mechanisms. The analytical equations for the failure surface are obtained using the variational method. The strength reduction method that incorporates the cut-off criterion is proposed to quantify roof stability. The investigation into the morphology of the collapsing block indicates that the supporting pressure and the reduction coefficient ξ have a significant influence on the collapse shape of the tunnel, suggesting that attention should be paid to the suspension effect of the tunnel roof on stability. The range of the collapsing block under three-dimensional conditions is found to be larger than that under two-dimensional conditions. Parametric influences on the safety factor are examined. Finally, dimensionless design charts for the critical reinforcement pressure are provided for practical tunnel support design. Full article
(This article belongs to the Special Issue Solid Mechanics as Applied to Civil Engineering)
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17 pages, 4097 KB  
Article
Research on Coordinated Technology for Coal Mining Progress and Roof Water Drainage at the Working Face
by Ziwei Qian, Cunjin Lu, Xiaoyuan Cao, Xianshuai Wu and Haobo Zheng
Water 2026, 18(6), 664; https://doi.org/10.3390/w18060664 - 11 Mar 2026
Viewed by 242
Abstract
To address the challenges of water hazard control in the thick water-rich sandstone aquifer of the roof under monoclinal structure conditions at Panel 110504 of Wangwa Coal Mine, as well as the problems of excessive ineffective drainage and high cost associated with the [...] Read more.
To address the challenges of water hazard control in the thick water-rich sandstone aquifer of the roof under monoclinal structure conditions at Panel 110504 of Wangwa Coal Mine, as well as the problems of excessive ineffective drainage and high cost associated with the traditional full-face pre-drainage method, a study on the coordinated technology of mining progress and roof water drainage was carried out. By analyzing the geological and hydrogeological conditions of the panel, it was determined that the height of the water-conducting fracture zone reaches 228 m, which has penetrated the Yan’an Formation and entered the sandstone aquifer of the Zhiluo Formation, forming a unified composite water-filling source from the two aquifers. Based on calculations using the Theis equation and field drainage tests, the stable drainage time was determined to be 95 d and the advance drainage distance 300 m. Accordingly, a coordinated technical scheme of “sectional drainage while mining” was proposed, optimizing the layout parameters of drainage boreholes and the division of drainage sections. Field application results show that this technology reduced the average water inflow of the panel by 255.94 m3/h compared with the traditional mode, cumulatively saved 5.1413 million m3 of drainage water, cut drainage costs by 20.5652 million CNY, and no water hazard occurred. The research results can provide a technical reference for mining coal seams with water-rich roof under similar monoclinal structure conditions. Full article
(This article belongs to the Section Hydrogeology)
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22 pages, 967 KB  
Article
Solutions of a Fuzzy Difference Equation with Maximum
by Lirong Ma, Changyou Wang and Yue Sun
Axioms 2026, 15(3), 202; https://doi.org/10.3390/axioms15030202 - 9 Mar 2026
Viewed by 250
Abstract
This paper systematically investigates the dynamical properties of a class of max-type fuzzy difference equation. The study first establishes the existence and uniqueness of the solution sequence under given initial conditions with positive fuzzy numbers. Subsequently, by applying the cut-set theory, the fuzzy [...] Read more.
This paper systematically investigates the dynamical properties of a class of max-type fuzzy difference equation. The study first establishes the existence and uniqueness of the solution sequence under given initial conditions with positive fuzzy numbers. Subsequently, by applying the cut-set theory, the fuzzy equation is transformed into a system coupled by two ordinary difference equations. Through a combination of case analysis and mathematical induction, the study rigorously demonstrates that the solutions of this system exhibit global periodicity with a period of 4, while also deriving the exact closed-form expressions of the periodic solutions. Based on the periodic solutions obtained from the ordinary difference system, the research successfully reveals the periodic characteristics of the solutions to the original fuzzy difference equation and rigorously analyzes their boundedness and persistence. Finally, numerical simulations conducted with Matlab 2016 provide robust data support for the theoretical conclusions and the effectiveness of the methodology. Full article
(This article belongs to the Special Issue Delay Differential Equations: Theory, Control and Applications)
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