Smith Method Research Articles

A Low-Rank Global Krylov Squared Smith Method for Solving Large-Scale Stein Matrix Equation

A Low-Rank Global Krylov Squared Smith Method for Solving Large-Scale Stein Matrix Equation

Seafloor topography of Huangyan seamount chain based on GA-BP algorithm from ship survey and gravity anomaly data

Seabed topography is important for marine geophysics and geodesy. However, conventional seabed topography inversion methods based on gravity data are constrained to a linear fitting, neglecting the impact of nonlinear terms. In this paper, we propose an innovative method for seabed topography inversion by establishing fresh mathematical relationships through machine learning techniques based on the Smith and Sandwell (SAS) method. Utilizing global sea depth data from the National Geophysical Data Center (NGDC) and gravity anomaly data from satellite altimetry, our study employs the SAS method for seabed topography inversion. The improved SAS method, enhanced by the Genetic Algorithm-Backpropagation (GA-BP) algorithm, is specifically applied to invert the Huangyan Seamount Chain topography in the South China Sea. The accuracy is evaluated by seabed topography models, including EOTPO1, GEBCO-2023, and S & S V19.1. The results show the GA-BP method significantly reduces residuals and improves the accuracy estimated by the SAS inversion method. The Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) are decreased by 14.98% and 5.07%, respectively. The proposed method has valuable reference significance for future marine exploration endeavours around the world.

Low-Rank Methods for Solving Discrete-Time Projected Lyapunov Equations

In this paper, we consider the numerical solution of large-scale discrete-time projected Lyapunov equations. We provide some reasonable extensions of the most frequently used low-rank iterative methods for linear matrix equations, such as the low-rank Smith method and the low-rank alternating-direction implicit (ADI) method. We also consider how to reduce complex arithmetic operations and storage when shift parameters are complex and propose a partially real version of the low-rank ADI method. Through two standard numerical examples from discrete-time descriptor systems, we will show that the proposed low-rank alternating-direction implicit method is efficient.

A nursing intervention based on the Zentangle® method: Experiences of patients diagnosed with borderline personality disorder

ObjectiveThe application of the Zentangle® Method in relation to relaxation and well-being has not been tested in patients with borderline personality disorder (BPD). This study was to analyze the practising Zentangle® experience in patients with BPD. MethodsWith a phenomenological interpretative approach, this qualitative study conducted semi-structured interviews with patients who participated in a 6-session Zentangle® program accomplished monthly over six months in a Personality Disorders Unit. A total of 15 patients were interviewed for this study. Smith, Flowers & Larkin method was applied for evaluation in the data analysis. ResultsBased on our findings, three categories were extracted: As you sow, so shall you reap (participants reported improvements in concentration, relaxation, interpersonal relationships, and interaction with their environment as well as positive experiences toward acceptance and change); Many hands make light work (patients admitted feeling better in a group and developed group membership. They described how a group environment influences individual behavior); Drawing your own path (this method provides a medium for self-expression and self-knowledge through drawing, improving well-being through emotional expression, enhancing creativity, and increasing self-confidence). ConclusionsBy practicing Zentangle®, patients achieve behavioral responses such as flexibility and adaptability, reaching greater emotional well-being through anxiety management, impulse control, learning to cope with problems, or improving self-esteem or concentration. Mental health nursing plays a critical active role in the comprehensive treatment of BPD, as well as the mobilization and coordination of complementary and diverse interventions.

Ultimate strength assessment of hull girders considering elastic shakedown based on Smith's method

The simplified progressive collapse method, Smith's method, for hull girders is one of the important methods for assessing the ultimate strengths of hull girders. The calculation accuracy primarily depends on the average stress–average strain relationship of the hull-stiffened plates. The vessel experiences cyclic bending moments during navigation due to waves, which lead to in-plane tensile–compressive loadings on the stiffened plates; thus, it is necessary to consider the elastic shakedown characteristics of the stiffened plates under cyclic loading. A novel average stress–average strain relationship for hull-stiffened plates considering the elastic shakedown limit state was developed by combining the nonlinear finite element method with beam–column theory. Furthermore, the obtained average stress–average strain relationship was introduced into Smith's method to evaluate the ultimate strengths of four hull girders and a scaled test model considering the elastic shakedown limit state. The results showed that the developed average stress–average strain relationship could accurately describe the elastic shakedown characteristics of hull-stiffened plates. Smith's method developed based on the above relationship could also effectively evaluate the ultimate strengths of hull girders under an elastic shakedown limit state.

A Phenomenological Study of Health Requirements regarding School Activity in Post-Corona Period

Background: In Iran, from the academic year 2021-2022, it was decided to reopen all schools. It is of great importance that the activities of schools be accompanied by principles, solutions, and requirements; so, concerns about students and school staff contracting this disease will be reduced. The present investigates the experiences of elementary school principals in Roodan city, in Hormozgan Province, Iran, about health requirements of school activity during post-corona era.
 Methods: This was a qualitative and phenomenological study. Data were analyzed by Smith's method after theoretical saturation of data obtained from an in-depth semi-structured interview. The interview contained 12 principals of elementary schools in Roodan city in the academic year of 2021-2022, who were selected through purposive sampling.
 Results: The experiences of elementary school principals about school activities were obtained in the form of 3 main themes including executive measures (provision of disinfectants, improvement of school infrastructure, absence of sick students and teachers in school, safe distance, creating a happy and safe environment for students to attend, and seeking support from benefactors and parents counseling sessions), educational and promotion-interventional measures (holding classes and remedial measures, teaching health issues to students, informing parents, environmental and virtual information, and counseling sessions), and supervisory measures (supervision of students, teachers, principals, and assistants of the school).
 Conclusions: The results of examining the experiences of elementary school principals about reopening of schools in the post-corona period showed that there is a need for many facilities and measures. Moreover, capable principals face various challenges and need to work with organizations, officials, students, and families.

Analisis Penjadwalan Produksi dengan Metode Campbell Dudek Smith untuk Meminimasi Makespan pada PT.XYZ

PT. XYZ is a wood-made furniture manufacturing company, one of which is a chair with a variety of types like arm chair, a bar drum, a drum counter and side chair. In the process, sometimes some orders are late. It's in the high-solution total time. Therefore, scheduling in the company requires a renewal of methods to identify which methods of scheduling efficiency in reducing production. Campbell dudek Smith's method is used because control processes are done according to the smallest working time used in production. Campbell dudek Smith's methods are appropriate and can be applied to help control the production with a flower-shop system that is more than two machines. Results from research obtained a large schedule at company scheduling FCFS method of 9613425 seconds with job sequence 1-2-3-4. While the Campbell dudek Smith method obtained a period of 9608298 seconds with the job sequence 2-3-1-4. The Campbell dudek Smith method was chosen as a proposal because it had the smallest byline of corporate methods.

Assessment of Ship Hull Ultimate Strength under Fire Conditions: The Fire Smith Method Approach

This article presents the fire Smith method, which integrates the plate model and the Smith method, to analyze the impact of fire temperature and extent on the buckling strength of frigates. This investigation focused on the frigate’s buckling strength and how it is affected by a fire, achieved by modifying both deck temperature and area. Leveraging the principle of oxygen consumption, a coefficient “D” was introduced to account for fire temperature and region variations. This enabled the characterization of buckling strength under varying temperature and regional conditions through 64 simulations conducted on a frigate model. The outcomes revealed that the disparity between simulation results and the fire Smith method remained below 10%, establishing a solid basis for engineering assessment. As the high-temperature area decreased and necessitated less oxygen, the ultimate strength initiated a decline. However, upon reaching a certain threshold temperature, the ultimate strength stabilized. Conversely, expansive high-temperature zones caused a decline in ultimate strength, coupled with an increased oxygen requirement. Under consistent oxygen consumption conditions, the rate of ultimate strength reduction intensified. Consequently, these divergent characteristics of ultimate strength in various high-temperature areas underscored that minimizing the expansive fire high-temperature zones can significantly enhance the ship’s fire resistance, safeguarding its structural integrity.

A methodology for ultimate strength assessment of ship hull girder accounting for enhanced corrosion degradation modelling

The presented work shows a methodology for the ultimate strength assessment of a ship hull, considering enhanced corrosion modelling. The approach is based on the classical Smith method. However, the recent findings regarding the impact of corrosion degradation on ultimate strength are incorporated. To this end, the stress–strain relationships for particular elements composing ship hull cross-section are modified using a specially developed correction factor. The proposed approach is validated with experimental results of the corroded box girders available in the literature, showing very good agreement. Further, a case study of a VLCC tanker ship is presented, and a comparison between contemporary and enhanced corrosion degradation modelling in terms of resulting ultimate strength is presented. The results indicate that the currently used method may significantly overestimate the hull’s structure capacity, especially considering the long exploitation period. Thus, current approaches lead to a non-conservative assessment of the ship hull girder’s ultimate strength, potentially increasing the risk of failure. It is therefore recommended to further investigate the proposed method, especially in the context of risk-based ship design approaches and holistic maritime transportation risk management.

Classical modeling of extrinsic degradation in polycrystalline perovskite solar cells; defect induced degradation

In the realm of photovoltaic devices, the future appears bright for polycrystalline perovskite solar cells. However, the promise of their efficiency is threatened by a myriad of degradation mechanisms. These mechanisms, like dark spots on a sunny day, create shadows of uncertainty on the performance of polycrystalline PSCs. Nonetheless, this article comprehensively explains these degradation mechanisms and their impact on grain boundaries in PSCs. The paper investigates grain boundaries’ effects on carrier lifetime by employing various models, such as the Matthiessen rule and the Drude–Smith method. The findings reveal that defect density is the primary factor affecting the material’s performance, and grain boundaries’ size influences its changes. Drude–Smith’s model provides a more precise estimation of the mobility, total scattering lifetime, and PL quantum yield in polycrystalline semiconductors with reduced scattering time. The presented method is verified by feeding extracted parameters into Drift-Diffusion equations and fitting them with reported experimental photovoltaic conversion efficiency data. Furthermore, based on the simulation results and the strong correlation between grain boundaries and the time factor, the study proposes a comprehensive model that can effectively predict PSCs’ degradation time.

A Bayesian analysis for the quantification of strength model uncertainty factor of ship structures in ultimate limit state

The assessment of ship structural reliability involves the quantification of hull girder ultimate bending capacity. Traditionally, Smith’s method is employed for the probabilistic modeling of capacity. The modeling uncertainty associated with Smith’s method is considered by an independent multiplicative random variable Xr. As real-scale data from hull collapses are not available, the quantification of Xr is usually based on the combination of engineering judgment with more objective information, such as non-linear finite element analysis (NLFEA). In this paper, we propose a Bayesian analysis for the determination of Xr. Specifically, we use Bayesian statistical inference to estimate the parameters that characterize the probabilistic model of Xr based on expert judgment and a limited number of high-fidelity NLFEA data. We demonstrate the applicability of the method on container ships, for which two typical load scenarios are considered: (i) pure hogging moment and (ii) combined hogging moment with local bottom loads. For each load scenario, the corresponding Xr is determined. For cases where specific information from a target ship is available, a classical Bayesian updating scheme is proposed to adjust the distribution of Xr based on the individual ship’s structural characteristics. We present a numerical demonstration for the case of the MOL Comfort at the time of the accident. Finally, the impact of the proposed Xr on the failure probability estimate of a 4,400 TEU and a 9,400 TEU container ship is investigated. We show that using the proposed Xr the estimate of the uncertainty in Smith’s model prediction in pure hogging condition is considerably reduced. In addition, we demonstrate that the action of bottom local loads, which considerably decreases the hull girder ultimate strength and the reliability level of container ships in hogging, can be captured by the proposed Xr without any intervention in the conventional Smith method.

The influence of teaching styles on students’ math score

There is a researching that three teachers with two different teaching methods in a junior high school, where students came from four different ethnic groups. Ruger and Smith used the standards-based method and Wesson used the traditional method, they were suggested to use the same teaching approach and the same textbook. The study aims to understand fully which teacher is best fitted for which ethnic group and which teaching approach is better. This research used statistical methods such as pie charts and bar plots to analyze data and used linear regression to investigate the relationships between the teaching methods and the students’ performance. The results showed that students who were taught by Ruger achieved the lowest math scores across all ethnics; Smith's teaching method suits Caucasian students; the traditional method resulted in higher math scores for students of African-American, Asian and Hispanic; and students who learnt using traditional method got higher scores compared to students learnt using standards-based method in average. Although each method has its own benefit, these results suggest that the traditional method is better than the standards-based method and these teachers should use the same teaching approach.

Factorized squared Smith method for large-scale Stein equations with high-rank terms

Solving large-scale Stein equations with high-ranked coefficient and constant terms is relatively difficult since the solution is no longer numerically low-ranked and its storage and outputting are nontrivial. This paper presents a factorized squared Smith method (FSS) that consists of banded and low-ranked parts to overcome this obstacle when the coefficient and the constant matrices are banded-plus-low-ranked. The deflation process as well as the partial truncation and compression are presented to control the growth of the columns of the low-ranked factors, effectively reducing the complexity of the FSS method. The convergence of the banded and the low-ranked parts is established and the banded part is shown being always numerically banded under some assumptions. The residual computation as well as the termination condition have been redesigned. Numerical examples indicate that for large-scale problems, the proposed FSS algorithm outperforms the Smith method with hierarchical HODLR structured toolkit on CPU time.

Doubling Smith Method for a Class of Large-Scale Generalized Fractional Diffusion Equations

The implicit difference approach is used to discretize a class of generalized fractional diffusion equations into a series of linear equations. By rearranging the equations as the matrix form, the separable forcing term and the coefficient matrices are shown to be low-ranked and of nonsingular M-matrix structure, respectively. A low-ranked doubling Smith method with determined optimally iterative parameters is presented for solving the corresponding matrix equation. In comparison to the existing Krylov solver with Fast Fourier Transform (FFT) for the sequence Toeplitz linear system, numerical examples demonstrate that the proposed method is more effective on CPU time for solving large-scale problems.

Optimization of production process scheduling at Mataram Convection using the Campbell-Dudek and Smith method and the Ho and Chang method

Konveksi Mataram (Djagoan Kaos dan Seragam) is one of the industries engaged in the manufacture of various types of clothing models with fabric as the basic material. So far, the scheduling method used by the company is the First Come First Serve method, in which the completion of production is based on order-to-order data. In this case, with high order intensity, companies often experience difficulties in completing orders according to a predetermined pick-up time. The problems experienced by the company were caused by the production process scheduling that was not optimal. Based on the problems encountered, the purpose of this research is to obtain the optimal scheduling sequence by determining the smallest makespan (minimum total completion time) of the application of the method to the production process. The methods used in this study are the Campbell-Dudek and Smith method and the Ho and Chang method and from these two methods, it is known that the smallest production process is optimal. Based on the results of calculations using the Campbell-Dudek and Smith method, the optimal scheduling sequence with the smallest makespan is 39163 minutes or the production process will be completed in 73 working days. While the results of calculations using the Ho and Chang method obtained the optimal scheduling sequence with the smallest makespan of 38660.50 minutes or the production process will be completed in 72 working days. From the makespans of the two methods, the Ho and Chang method is superior to the Campbell-Dudek and Smith method with a difference of 502.50 minutes or about 1 working day, whereas when compared to the company's initial method, namely First Serve First Come with a makespan of 43025.50 minutes, the HC method can make completion time efficient with a difference of 4365 minutes or about 8 working days.
 Keywords: Campbell-Dudek and Smith methods, first come first serve, Ho and Chang, makespan, production schedulingMSC2020: 90B30

Social vitality from the perspective of psychologists

Introduction: Joy and cheerfulness is the missing thing of contemporary man and the common desire of all people. Man is a purposeful being who seeks joy, happiness, and prosperity, and he does not feel joy, happiness, and prosperity until he achieves what he wants. The cheerfulness is one of the factors affecting economic, social, cultural, and political development and promotes sustainable development. Methods: The present study was conducted with a phenomenological social approach and with the aim of examining psychologists' experiences of social vitality. Data were collected through semi-structured interviews with 16 psychologists with PhD degrees and at least five years of teaching experience in the academic level. Findings: Smith's phenomenological method was used to analyze the data, during which eight main themes and 46 sub-themes were extracted from the data. Discussion: The results showed that in some sub-themes such as the definition of social vitality, consequences, obstacles, and causes, there is some alignment between the views of psychologists and the background; However, there are different results in the solutions. Psychologists, based on their psychological perspectives and experiences, have proposed various solutions for parents and organizations at the micro and macro levels. For example, their proposed solutions include not politicizing social vitality, careful selection of officials and meritocracy, reducing the distance between social classes, organizing the economic situation, having a scientific view on the issue of social vitality and several other strategies. The results of this study will pave the way for further research in the field of interventions related to social vitality.

Cross-Gramian-Based Model Reduction for Descriptor Systems

In this paper, we explore model order reduction for large-scale square descriptor systems. A balancing-free square-root method is proposed. The balancing-free square-root method is based on two cross Gramians, one of which is known as the proper cross Gramian and the other as the improper cross Gramian. The proper cross Gramian is the unique solution of a projected generalized continuous-time Sylvester equation, and the improper cross Gramian solves a projected generalized discrete-time Sylvester equation. In order to compute the low-rank factors of these two cross Gramians, we extend the low-rank iteration of the alternating direction implicit method and the Smith method to the projected generalized Sylvester equations. We illustrate the effectiveness of the balance truncation method with one numerical example.

New results of the IO iteration algorithm for solving Sylvester matrix equation

In this paper, the IO iteration algorithm proposed in Tian et al. [3] is further investigated, and some new results for solving the Sylvester matrix equation are obtained. At first, a new convergence property of the IO iteration algorithm is given for a wider convergence region associated with the parameter γ. Under the new convergence condition, a corresponding comparison result is established for the IO iteration algorithm compared with the Smith method. Moreover, if the matrices A,B in the Sylvester matrix equation are nonnegative, the IO iteration algorithm is proved to be convergent for any inner iteration number lk≥1 with 0<γ<1. Finally, three numerical examples are implemented to confirm the validity of the new results.

David Lindsay Abair and Jeanine Tesori’s Shrek the Musical

Postmodernism is an intellectual movement that characterizes by scepticism and fragmentation. Postmodernist writers return to traditional fairytales to question and challenge their norms and meanings. Shrek the Musical is a play based on classic fairytales of Rapunzel and Beauty and the Beast. Shrek the Musical will be studied according to postmodern techniques and strategies. They are many such as deconstruction and intertextuality. This play will be analyzed according to Kevin Paul Smith's method of intertextuality. This method traces the elements of fairytales in postmodernist literature and their unique alterations by using deconstruction theory that shows the false hierarchies and the false values upon which these classic tales are built.

Determination of the intensity of erosion processes by the Smith method of the Olenty river basin of the West Kazakhstan region

The article takes an actual topic for the present and carried out work to determine the intensity of erosion processes using the Smith method of the Olenty River basin of the West Kazakhstan region. The purpose of this work was to determine the process of soil erosion in the Olenty River basin for various types of land use. To determine soil flushing, the following were used: erosion potential of sediments, soil type, mechanical composition, slope steepness, vegetation, types of plowing, erosion forecast model, universal soil loss equation and the ArcGIS 10.4 program. The southern part of the river basin has a soil flushing rate from 0 to 0.06 t/ha per year. These lands are mainly used for pastures and small areas of territory for haymaking, located in most cases on chestnut soils and small salt marshes, the mechanical composition is mainly dominated by heavy loam. This territory occupies about 40% of the entire river basin. The central and northern parts have different indicators and range from the lowest to the highest. The highest rate of soil flushing is 1.57 – 5.96 t/ha per year are arable lands located mainly on chestnut soils, having a mechanical composition dominated by medium and heavy loam, and arable lands with the highest rate are characterized by a territory with high rainfall and a steeper slope. These indicators of soil flushing from 0.45 to 1.57 t/ha per year also belong to arable land, but unlike the previous class, these arable lands are located in most cases on soils that are mechanically related to medium loam. According to the results of the study, the highest rate of soil flushing falls on arable land, the average is about 1.50 t/ha per year, which corresponds to the “acceptable level of loss”. Key words: erosion processes, river basin, WKO, GIS, soil.