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Time of Concentration (TC) is a widely utilized time variable in hydrological studies. Various approaches exist to estimate TC, including direct measurements, empirical relations, and graphical method (GM). The GM is commonly regarded as a standard by researchers. Nevertheless, this approach faces obstacles due to the scarcity of records in many watersheds.. This research explores a novel technique for TC estimation, focusing on the examination and recommendation of two-dimensional (2D) hydraulic modeling. The proposed method leverages available satellite data to obtain the necessary input for the 2D simulation. Additionally, several empirical relations were evaluated for TC determination. The GM served as reference point for evaluating the results obtained from empirical relations and hydraulic modeling. To accomplish this, analysis was conducted on four distinct watersheds in Iran, comprising a total of 28 recorded rainfall-runoff data.. In numerical modeling, TC was defined as the duration required for a water parcel to traverse from the headwater to the outlet of a basin. In all studied watersheds, the maximum relative error between the benchmark (GM) and the 2-D modeling was limited to less than 10%. This observation establishes the reliability of hydraulic modeling as a viable method for TC calculation, particularly in ungauged watersheds where the GM cannot be employed. [ABSTRACT FROM AUTHOR]

This paper develops a general and complete solution for the undrained cylindrical cavity expansion problem in nonassociated Mohr‐Coulomb soil under nonhydrostatic initial stress field (i.e., arbitrary K0${{K}_0}$ values of the earth pressure coefficient), by expanding a unique and efficient graphical solution procedure recently proposed by Chen and Wang in 2022 for the special in situ stress case with K0=1${K}_{0}=1$. It is interesting to find that the cavity expansion deviatoric stress path is always composed of a series of piecewise straight lines, for all different case scenarios of K0 being involved. When the cavity is sufficiently expanded, the stress path will eventually end, exclusively, in a major sextant with Lode angle θ in between 5π3$\frac{{5\pi }}{3}$ and 11π6$\frac{{11\pi }}{6}$ or on the specific line of θ=11π6$\theta = \frac{{11\pi }}{6}$. The salient advantage/feature of the present general graphical approach lies in that it can deduce the cavity expansion responses in full closed form, nevertheless being free of the limitation of the intermediacy assumption for the vertical stress and of the difficulty existing in the traditional zoning method that involves cumbersome, sequential determination of distinct Mohr–Coulomb plastic regions. Some typical results for the desired cavity expansion curves and the limit cavity pressure are presented, to investigate the impacts of soil plasticity parameters and the earth pressure coefficient on the cavity responses. The proposed graphical method/solution will be of great value for the interpretation of pressuremeter tests in cohesive‐frictional soils. [ABSTRACT FROM AUTHOR]

This study investigated the role of mobile applications as aids in solving systems of linear equations with two variables through the graphical method. The use of mobile applications was examined in a group of primary and lower school students to evaluate their effectiveness in learning mathematics and improving their skills in solving systems of linear equations. The main goal of this scientific paper is to investigate and evaluate the role of mobile applications as aids in solving systems of linear equations, involving students in the research process. The research method included a mixed-methods design including quantitative analysis of mobile application results and qualitative analysis of students' experiences and opinions. Data collection was conducted through individual interviews and classroom observations. The results show that the use of these technological tools has a positive impact on the involvement of students, increasing the interest and efficiency of learning. The findings also highlight challenges and suggestions for improving the use of mobile applications in the mathematics teaching context. This study contributes to the understanding of the use of mobile technology for the development of mathematical skills at the lower secondary school level. [ABSTRACT FROM AUTHOR]

Unit distributions, exhibiting inherent symmetrical properties, have been extensively studied across various fields. A significant challenge in these studies, particularly evident in parameter estimations, is the existence and uniqueness of estimators. Often, it is challenging to demonstrate the existence of a unique estimator. The major issue with maximum likelihood and other estimator-finding methods that use iterative methods is that they need an initial value to reach the solution. This dependency on initial values can lead to local extremes that fail to represent the global extremities, highlighting a lack of symmetry in solution robustness. This study applies a very simple, and unique, estimation method for unit Weibull and unit Burr XII distributions that both attain the global maximum value. Therefore, we can conclude that the findings from the obtained propositions demonstrate that both the maximum likelihood and graphical methods are symmetrically similar. In addition, three real-world data applications are made to show that the method works efficiently. [ABSTRACT FROM AUTHOR]

Stress and deformation analysis of a cavity in an infinite/finite medium is a fundamental applied mechanics problem of interest in multiple physics and engineering disciplines. This paper develops a complete semianalytical solution for the cylindrical cavity expansion in nonassociated Mohr–Coulomb materials, by using the graphical approach and Lagrangian formulation of the cavity boundary value problem (through tracing the responses of a single material point at the cavity wall). The novelty of the new solution framework lies not only in the relaxation of the stringent intermediacy assumption for the vertical stress as usually adopted in the previous analyses, but also in the comprehensive consideration of nonhydrostatic initial stress conditions via arbitrary values of K0 (the coefficient of earth pressure at rest defined as the ratio between the horizontal and vertical initial stresses). The essence of the so-called graphical method, i.e., the unique geometrical analysis and tracking of the deviatoric stress trajectory, is fulfilled by leveraging the deformation requirement that during cavity expansion the progressive development of the radial and tangential strains must maintain to be compressive and tensile, respectively. With the incorporation of the radial equilibrium condition, the problem is formulated to solve a single first-order differential equation for the internal cavity pressure with respect to a pivotal auxiliary variable, for all the distinct scenarios of K0 being covered. Some selected results are presented for the calculated cavity pressure-expansion curve and limit cavity pressure through an example analysis. The definitive semianalytical solution proposed will be not only substantially advancing the current state of knowledge on the fundamental cavity expansion theory, but also able to serve as a unique benchmark for truly verifying the correctness and capability of the classical cornered Mohr–Coulomb constitutive model built in commercial finite element programs. [ABSTRACT FROM AUTHOR]

The powerful image analysis and statistical capabilities of computers can effectively solve problems such as insufficient precision in clastic rock particle size measurements and the heavy workload during the process. The MATLAB programming language was employed to process the samples of the Zhoutian Formation in the Upper Cretaceous of the Huichang Basin through techniques such as grayscale transformation, binarization, adaptive median filtering, and color annotation, accurately measuring their grain size parameters. The results indicate the following. The average grain size obtained using MATLAB,s direct calculation method and the graphical method are 4. 008φ and 3. 103φ, respectively. The standard deviations are 0. 8φ and 0. 803φ, the skewness values are - 0. 195φ and - 0. 041φ, and the kurtosis values are 0. 911φ and 0. 916φ. The standard deviation and kurtosis errors are small, allowing for mutual substitution between the two calculation methods, while the standard deviation and skewness errors are relatively large, making them unsuitable for mutual substitution. Both MATLAB,s direct calculation method and microscopic rock mineral identification indicate a relatively poor roundness of the Zhoutian Formation as a whole, with angular to sub-angular clastic particles. The sedimentary environment discrimination formula reflects the formation of the Zhoutian Formation in a fluvial depositional environment, consistent with the geological background and microscopic observation results. Through the MATLAB programming language, it is possible to accurately identify particle outlines and calculate various parameters in clastic rocks, providing great convenience for sediment grain size research, eliminating subjective interference, and improving work efficiency [ABSTRACT FROM AUTHOR]

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This paper introduces a more streamlined and convenient graphical approach to investigate the stability of fractional-order dynamical systems comprehensively. In particular, we focus on the utilization of Kharitonov theorem, renowned for robust stability analysis of incommensurate fractional-order systems in the presence of uncertainty. A novel graphical framework is illustrated, promising to streamline the stability analysis of such systems, which leads to reducing the computational burden. Using the proposed method, we can achieve the least possible Kharitonov polynomials among the existing methods to analyze the robust stability of the incommensurate fractional-order systems. To validate our approach, we perform numerical simulations on four illustrative examples, demonstrating its effectiveness. Simulation results underscore the real-world utility of our methodology, emphasizing its potential significance in fractional-order system analysis. [ABSTRACT FROM AUTHOR]

A four-bar mechanism is a basic kinematic chain in most of planar mechanisms. Four-bar chains are synthesized for a specific task. The output deviates from the desired one due to many reasons broadly from the group of systematic and random input sources. The work presented herewith deals with the error estimation in the four-bar path generation mechanism under link tolerance. The primary estimation of error is carried out using a Taylor series approximation with a modified error equation. The inaccuracy is estimated using sample independent variables. A geometrical method for the estimation of specific errors is developed. The results are verified using the CAD model. The appropriateness of the Taylor series approximation with modified error equation estimations is compared with exact solutions from the geometrical method. The methodology is demonstrated through a sample case of the four-bar mechanism presented to compare the capability of the two methods. The deviations due to single systematic inaccuracy are exposed, and one of the methods- i.e. the geometrical method is found to be the robust method of error evaluation. [ABSTRACT FROM AUTHOR]

Through data mining, this paper completes collecting and mining information in the database using artificial intelligence. Secondly, the graphical method is analyzed, image normalization calculation is carried out to complete the technical support for green concept packaging design, and a green concept product packaging design system based on artificial intelligence technology is constructed. Finally, the ease of use experiment and user satisfaction test confirmed it. The user satisfaction test showed a satisfaction rate of 95% for response time and 97% for material recycling. The fact that other test options are above 90% indicates that the green concept product packaging design based on artificial intelligence technology is feasible.

Unit distributions, exhibiting inherent symmetrical properties, have been extensively studied across various fields. A significant challenge in these studies, particularly evident in parameter estimations, is the existence and uniqueness of estimators. Often, it is challenging to demonstrate the existence of a unique estimator. The major issue with maximum likelihood and other estimator-finding methods that use iterative methods is that they need an initial value to reach the solution. This dependency on initial values can lead to local extremes that fail to represent the global extremities, highlighting a lack of symmetry in solution robustness. This study applies a very simple, and unique, estimation method for unit Weibull and unit Burr XII distributions that both attain the global maximum value. Therefore, we can conclude that the findings from the obtained propositions demonstrate that both the maximum likelihood and graphical methods are symmetrically similar. In addition, three real-world data applications are made to show that the method works efficiently.

The pinch analysis technique circumvents the drawbacks of local optima in the design of production processes and determines energy targets from a systemic design perspective. It has now evolved into a comprehensive methodology for process industry integration. As research deepens in traditional industrial domains, the exploration of applications in emerging fields is gradually expanding. However, solely relying on the analysis and summarization within a singular domain is insufficient for driving broader applications across diverse fields. Therefore, this paper discusses the pinch analysis techniques across various fields, from energy exchange networks to mass transfer networks. By examining their technical principles and categorizing method types, different technologies are horizontally compared, and their key characteristics are revealed. Subsequently, this paper explores future development directions and imminent challenges of the pinch analysis technique in power systems, aiming to offer new perspectives for expansion and to address existing issues such as load balance analysis, planning rationality, and reliability assessment in power systems. • Pinch analysis methods in various fields are analyzed comprehensively. • Analogous graphic methods and numerical methods of pinch analysis are compared across different fields respectively. • The underlying mathematical structure of pinch analysis techniques and principle of graphical methodology are revealed. • The prospects and a novel approach to applying pinch analysis in power systems are proposed. [ABSTRACT FROM AUTHOR]

This paper presents a design for five conventional superconducting magnet structures to meet the high magnetic load demand of superconducting motors while reducing the superconducting tapes consumption. A 45° highest efficiency line is proposed based on the graphical method, and the magnet structure is optimized by combining finite element and PSO algorithms. Additionally, a correlation function is established using the vertical magnetic field to estimate the critical current, describing the nonlinear relationship between the two. The optimization method can maintain the airgap flux density waveform before and after optimization, reduce tapes consumption and perpendicular field on the tapes, refine the field distribution, and improve the safety margin of superconducting coils. The magnet design scheme can be selected with low tape consumption or high safety margin according to actual demand. This research can be used to optimize the electromagnetic design of superconducting electric motors, as well as other superconducting magnet applications, such as superconducting magnetic bearings, nuclear magnetic resonance, and large-scale scientific installations for high-energy physics. The aim is to achieve the exhaustive use of superconducting tapes. [ABSTRACT FROM AUTHOR]