Simple Problem Research Articles

Critical Analysis Of The Evolving Role Of Dentistry In Preventive And Restorative Medicine

Dentistry has kept up with this trend towards preventive and restorative health care in the patient practice pattern. In the past, dentistry primarily concentrated on simple problems like filling in cavities and pulling out of teeth, it is today a health science of immense value. In recent years, preventive oral health care intervention, which aims to identify latent oral pathoses and elevate community health oral hygiene standards, is increasingly appreciated for suppressing systemic diseases, including cardiovascular illnesses, diabetes, and respiratory ailments. In addition, restorative dentistry has developed a new material, techniques, and technology that enhance the quality of life for patients with dentistry disability. This review looks at dentistry's current and future trends in health promotion and restoration capacity, with special reference to health systems. This article discusses the evolution of dental practices, how dentistry interfaces with other branches of medicine, and some of the issues that have affected this field. Further, it throws light on the new advancements in dental technology, patient care diplomacy, and novel concepts of healthcare delivery systems.

Application of machine learning for ‘what if?’ stress analysis

Analysis of stresses in components of even modestly complex geometries often require the use of finite element analysis (FEA). For testing a large number of design options quickly, FEA can be time consuming and provides more accuracy than required. In this project, a machine learning-based system is developed to provide quick and approximate solutions to stress analysis problems in parametrised compressor disc geometries. Simple mechanics problems were completed preliminarily to test the practicality of machine learning approaches for this application. This included applying instance selection by the [Formula: see text]-medoids algorithm to a 2D FEA problem. A parametrised compressor disc geometry was designed and defined by eight dimensions. Stress fields were produced from two superimposed loading schemes: the rotational body force and the force exerted on the disc by the blades 495,338 samples of training data were collected from 4374 FEA simulations. Four networks were trained to predict stresses caused by each loading scheme in order to produce stress fields. The best network was of the structure 9/20/20/2 and used normalised training data. For the geometry tested, it predicted stresses with a root-mean-square error of 1.51%. The code took 0.7 s to run in total, from start-up to completion of a stress plot. The importance of the inputs in the training data set were scored with a feature selection algorithm to aid further optimisation of the system. The low computation time makes this system suitable for the early stages in a design process.

Higher-order fractional equations and related time-changed pseudo-processes

We study Cauchy problems of fractional differential equations in both space and time variables by expressing the solution in terms of “stochastic composition” of the solutions to two simpler problems. These Cauchy sub-problems respectively concern the space and the time differential operator involved in the main equation. We provide some probabilistic and pseudo-probabilistic applications, where the solution can be interpreted as the pseudo-transition density of a time-changed pseudo-process. To extend our results to higher order time-fractional problems, we introduce stable pseudo-subordinators as well as their pseudo-inverses. Finally, we present our results in the case of more general differential operators and we interpret the results by means of a linear combination of pseudo-subordinators and their inverse processes.

System Tautochronic Path for Pendulum Vibration Absorber Based on Simple Harmonic Oscillator Transformation

Abstract Centrifugal pendulum vibration absorbers (CPVAs) are essentially collections of pendulums attached to a rotating component or components within a mechanical system for the purpose of mitigating the typical torsional surging that is inherent to internal combustion engines and electric motors. The dynamic stability and performance of CPVAs are highly dependent on the motion path defined for their pendulous masses. Assemblies of absorbers are tuned by adjusting these paths such that the pendulums respond to problematic orders (multiples of average rotation speed) in a way that smooths the rotational accelerations arising from combustion or other nonuniform rotational acceleration events. For most motion paths, pendulum tuning indeed shifts as a function of the pendulum response amplitude. For a given motion path, the tuning shift that occurs as pendulum amplitude varies produces potentially undesirable dynamic instabilities. Large amplitude pendulum motion that mitigates a high percentage of torsional oscillation while avoiding instabilities brought on by tuning shift introduces complexity and hazards into CPVA design processes. Therefore, identifying pendulum paths whose tuning order does not shift as the pendulum amplitude varies, so-called tautochronic paths, may greatly simplify engineering design processes for generating high-performing CPVAs. To illustrate this new approach and results, a tautochronic cutout shape producing constant period system motion is obtained for a simplified problem involving a mass sliding in the cutout of a larger mass that is free to translate horizontally without friction in a constant gravitational field, where the translating base mass replaces the rotating rotor in the centrifugal field.

Run-and-tumble particles in slit geometry as a splitting probability problem

Run-and-tumble particles confined between two walls seem like a simple enough problem to possess analytical tractability. Yet, to date no satisfactory analysis is available for dimensions higher than one. This work contributes to the theoretical understanding of this system by reinterpreting it as a splitting probability problem. Such reinterpretation permits us to formulate the problem as the integral equation, rather than a more standard formulation based on the Fokker–Planck equation. In addition to providing an analogy with another phenomenon, the reinterpretation permits a new type of analysis, yields useful results, and offers some analytical tractability.

Distillation column optimization: A formal method using stage-to stage computations and distributed streams

This work addresses the complexities of optimizing the number of stages in a distillation column, which typically lead to challenging non-linear mixed-integer optimization problems. To simplify this, we employ distributed streams, thereby eliminating discrete degrees of freedom. To avoid sophisticated initialization procedures, the optimization problem is reformulated by employing a sequence of stage-to-stage calculations, each reduced to maintaining only the MESH (mass, equilibrium, summation, heat) equations for a single stage.Our numerical experiments show the efficiency and stability of solving the simplified optimization problem in various scenarios, including single and multiple distillation columns. For a single column scenario, we compare the accuracy of our optimization method with a full enumeration approach. Additionally, for a pressure swing flowsheet designed to separate an azeotropic mixture, we illustrate potential energy savings by optimizing a stage distribution versus using a predetermined stage distribution.

USING ARTIFICIAL INTELLIGENCE IN MATHEMATICS TEACHING

In modern education, there is a growing need for innovative teaching approaches, particularly in the context of using artificial intelligence. The relevance of the issue under consideration lies in exploring the potential of ChatGPT for automating the creation of mathematical problems, which can significantly reduce the workload of teachers. The aim of the research is to assess the potential of ChatGPT in generating high-quality math problems across various topics in the school curriculum. To achieve this goal, methods of theoretical analysis of scientific literature and an empirical experiment were applied, during which ChatGPT was used to create tasks on proportionality, combinatorics, algebra, and geometry. The research results demonstrate that ChatGPT can effectively generate both simple and complex mathematical problems, opening new opportunities for automating teachers' preparatory work. This allows teachers to automate part of the preparation process and focus on more creative aspects of teaching. However, certain limitations are identified, such as the dependence of task quality on the clarity of queries and the presence of errors in complex calculations. Overall, the research emphasizes that artificial intelligence can become a valuable tool for math teachers, but its use requires an understanding of its capabilities and limitations. Further research may include researching the impact of using ChatGPT on the student motivation and academic achievements, developing of methods for assessing the quality of ChatGPT-generated tasks, integrating ChatGPT with other learning tools (e.g. learning management systems), exploring the possibility of using ChatGPT to create more complex mathematical tasks that require a creative approach.

Linear Programming-Based Sparse Kernel Regression with L1-Norm Minimization for Nonlinear System Modeling

This paper integrates L1-norm structural risk minimization with L1-norm approximation error to develop a new optimization framework for solving the parameters of sparse kernel regression models, addressing the challenges posed by complex model structures, over-fitting, and limited modeling accuracy in traditional nonlinear system modeling. The first L1-norm regulates the complexity of the model structure to maintain its sparsity, while another L1-norm is essential for ensuring modeling accuracy. In the optimization of support vector regression (SVR), the L2-norm structural risk is converted to an L1-norm framework through the condition of non-negative Lagrange multipliers. Furthermore, L1-norm optimization for modeling accuracy is attained by minimizing the maximum approximation error. The integrated L1-norm of structural risk and approximation errors creates a new, simplified optimization problem that is solved using linear programming (LP) instead of the more complex quadratic programming (QP). The proposed sparse kernel regression model has the following notable features: (1) it is solved through relatively simple LP; (2) it effectively balances the trade-off between model complexity and modeling accuracy; and (3) the solution is globally optimal rather than just locally optimal. In our three experiments, the sparsity metrics of SVs% were 2.67%, 1.40%, and 0.8%, with test RMSE values of 0.0667, 0.0701, 0.0614 (sinusoidal signal), and 0.0431 (step signal), respectively. This demonstrates the balance between sparsity and modeling accuracy.

Hüquq texnologiyaları və onların vəkillik sahəsinə inteqrasiyası

Since the end of the last century, the wide spread of digital technologies has had an important impact on the development of many fields. Technological innovations, like in other professional fields, are increasing their impact on the field of advocacy day by day. Some legal technologies reduce lawyers' bureaucratic burdens and perform repetitive tasks, while others help citizens or companies solve simple legal problems without the need for a lawyer. This article examines the concept of Legal Tech, the areas of use of legal technologies, their categories and their application in the field of advocacy, and highlights how lawyers can provide more efficient and better quality legal assistance by using legal technologies in the performance of their profession. The article also touched upon the issues of using artificial intelligence in the legal profession, the practice of applying legal technologies in foreign countries and the level of development of these technologies in our country. Thus, the extensive use of legal technologies by a number of advanced countries of the world, especially the application of technologies based on artificial intelligence in international and national legal systems, has made an important contribution to the development of this field. Keywords: legal technologies, lawyer, electronic advocacy, artificial intelligence, e-government, e-court, e-discovery, technological applications, data security.

Study of the Group Mentality of University Students under Educational Involution

With the rapid development of the society, the phenomenon of educational internalization is becoming more and more common. Its performance in colleges and universities for students need to constantly strive to improve their academic performance and comprehensive quality to make themselves stand out in the fierce competition for college admission or employment. In the second case, the mentality of the bound college students is gradually changing, and the tendency of "inner roll" is mixed with the tone of "lying flat".As a component part of the youth group and an important force in the youth team, students play an essential role in social development, cultural inheritance and national construction.The group mentality of college students "lying in the middle volume" under the education involves the physical and mental development of college students learning and success, and the guidance of popular culture. It is not only a simple educational problem, but also a social problem.Through the appearance of "lying flat" and "inner volume", the mentality of "lying in the middle volume" of college students, grasp the law of college students, is conve to promoting the power of talents, which is the proper meaning of the work of young talents.duci.

A scattering matrix approach to the effective mass dependence of tunneling current through heterojunctions

A scattering matrix technique is used to calculate the longitudinal and transverse energy dependence of the transmission probability through various heterostructures using both the BenDaniel–Duke (BD) and the lesser known Zhu–Kroemer (ZK) boundary conditions to take into account the spatial dependence of the effective mass. We first illustrate the large difference in the transmission probabilities calculated using both boundary conditions for the simple problems of tunneling through a potential step, a single rectangular barrier, and a resonant tunneling device. Then, we present numerical calculations of the external electric field dependence of the field emission (FE) current from a n-doped GaAs semiconductor/vacuum interface using both boundary conditions, showing that the BD boundary conditions underestimate the FE current for large values of the applied external electrostatic field. A comparison of calculated FE characteristics with FE data may be a way to determine the appropriate boundary conditions to solve tunneling problems through heterostructures with spatially varying effective mass.

Weakening the effect of boundaries: “diffusion-free” boundary conditions as a “do least harm” alternative to Neumann

In this note, we discuss a poorly known alternative boundary condition to the usual Neumann or “stress-free” boundary condition typically used to weaken boundary layers when diffusion is present but very small. These “diffusion-free” boundary conditions were first developed (as far as the authors know) in 1995 (Sureshkumar and Beris J. Non-Newtonian Fluid Mech. 60, 53–80, 1995) in viscoelastic flow modelling but are worthy of general consideration in other research areas. To illustrate their use, we solve two simple ODE problems and then treat a PDE problem – the inertial wave eigenvalue problem in a rotating cylinder, sphere and spherical shell for small but non-zero Ekman number E. Where inviscid inertial waves exist (cylinder and sphere), the viscous flows in the Ekman boundary layer are O ( E 1 / 2 ) weaker than for the corresponding stress-free layer and fully O ( E ) weaker than in a non-slip layer. These diffusion-free boundary conditions can also be used with hyperdiffusion and provide a systematic way to generate as many further boundary conditions as required. The weakening effect of this boundary condition could allow precious numerical resources to focus on other areas of the flow and thereby make smaller, more realistic values of diffusion accessible to simulations.

A Single-Variable Method for Solving the Min–Max Programming Problem with Addition–Overlap Function Composition

Min–max programming problems with addition–min constraints have been studied in the literature to model data transfer in BitTorrent-like peer-to-peer file-sharing systems. It is well known that the class of overlap functions contains various operators, including the “min” operator. The aim of this paper is to generalize the above min–max programming problem with addition–overlap function constraints. We demonstrate that this new optimization problem can be transformed into a simplified single-variable optimization problem, which makes it easier to find an optimal solution. The bisection method will be used to find this optimal solution. In addition, when the overlap function is explicitly specified, an iterative method is given to compute the optimal objective value with a polynomial time complexity. A numerical example is provided to illustrate the procedures.

The effectiveness of perspective video modelling training on one‐stage word problem‐solving skills in children with autism spectrum disorder

AbstractSingle‐subject research can provide adequate justification when developing successful evidence‐based educational practices for children with autism spectrum disorder (ASD), which can help such students thrive academically. This research investigates whether point‐of‐view video modelling effectively improved the word problem‐solving addition performances of primary‐school‐aged students with ASD. The effectiveness of the intervention on each participant's ability to solve single‐digit addition by a single digit, effectively view the video on a tablet and generalise a learned skill was investigated by utilising a design that included several participant baselines. All participants saw an improvement in their ability to solve simple addition problems due to using point‐of‐view video modelling. Between the baseline and intervention phases, each participant's rate of digits correctly entered per minute and total number of steps completed significantly increased. A generalisation phase was performed at home. After receiving the intervention, people with ASD could independently complete word problems involving addition with a single digit. The findings suggest that this technology could practically support the education of the growing number of children and young people with ASD by mollifying the particular learning obstacles their impairment brings.

Chaos: From celestial mechanics to climate

Abstract Chaos is unpredictable behaviour arising in systems governed by deterministic laws. Since its ‘discovery’ in the 1960s by Edward Lorenz in his studies of meteorological systems, chaos has become an important way of understanding seemingly random behaviour in many other areas. These include the double pendulum, the climate, El Niño and electrical oscillators. Understanding chaos allows the limits of the predictability of a system to be determined. However, despite this recent activity this paper will show that the theory of chaos has a rich history and chaotic behaviour was originally identified in the 1890s by Henri Poincaré in his investigations of the three-body problem in celestial mechanics. But remarkably this paper will also show that chaotic behaviour can be found in such a simple problem as multiplication by 10 and it is closely linked to the question (studied by the ancient Greeks) of whether a number is rational or irrational.

Adaptive Neurodynamic Approach to Multiple Constrained Distributed Resource Allocation.

In this article, an adaptive neurodynamic approach over multiagent systems is designed to solve nonsmooth distributed resource allocation problems (DRAPs) with affine-coupled equality constraints, coupled inequality constraints, and private set constraints. It is to say, agents focus on tracking the optimal allocation to minimize the team cost under more general constraints. Among the considered constraints, multiple coupled constraints are dealt with by introducing auxiliary variables to make Lagrange multipliers reach consensus. Furthermore, aiming to address private set constraints, an adaptive controller is proposed with the aid of the penalty method, thus avoiding the disclosure of global information. Through using the Lyapunov stability theory, the convergence of this neurodynamic approach is analyzed. In addition, to reduce the communication burden of systems, the proposed neurodynamic approach is improved by introducing an event-triggered mechanism. In this case, the convergence property is also explored, and the Zeno phenomenon is excluded. Finally, a numerical example and a simplified problem on a virtual 5G system are implemented to demonstrate the effectiveness of the proposed neurodynamic approaches.

Support vector machine based on the quadratic unconstrained binary optimization model

Abstract Support vector machine (SVM) is a powerful supervised machine learning model that is often used in binary classification algorithms. As Moore’s Law approaches its theoretical limits and the demand for machine learning to handle large-scale, high-dimensional data analysis intensifies, the necessity of adopting non-traditional computational approaches becomes evident. Quantum computing, in particular, emerges as a vital solution for the effective training of SVM models, providing capabilities beyond those of classical computing systems. To solve the above problems, a QUBO (quadratic unconstrained binary optimization) model is proposed to transform the SVM machine learning model into a quadratic unconstrained binary optimization problem so that they can be effectively trained on the D-Wave platform using adiabatic quantum computer. The results show that the QUBO model can transform the SVM model into a simple quadratic programming problem, which makes it suitable for adiabatic quantum computer processing. When processing large-scale and high-dimensional data, this transformation shows a natural advantage and significantly improves computational efficiency. The application potential of this transformation technology is huge in the medical field.

Modified Cattaneo-Vernotte equation for heat transfer in solids

We propose a modified relation between heat flux and temperature gradient, which leads to a second-order equation describing the evolution of temperature in solids with finite rate of propagation. A comparison of the temperature field spreading in the framework of Fourier, Cattaneo-Vernotte (CV) and modified Cattaneo-Vernotte (MCV) equations is discussed. The comparative analysis of MCV and Fourier solutions is carried out on the example of simple one-dimensional problem of a plate cooling.

Derivation of analytic formulae for several resonance frequencies of the SparkJet actuator

Building on previous research that emphasized the importance of focusing on resonance frequencies for a fundamental understanding of the thrust and complex internal flow phenomena of the SparkJet actuators, this study theoretically derives analytic formulae for several important resonance frequencies. The research addresses the typical configuration of the SparkJet actuators, which consists of a cylindrical cavity and orifice connected by a conical converging nozzle. While the resonance frequencies of the SparkJet actuators can be obtained by solving the eigenvalue problem presented in previous studies, this eigenvalue problem, despite being a typical boundary value problem in the form of an elliptic partial differential equation, is challenging to solve using conventional numerical methods such as iterative methods, because the eigenvalue is included as an unknown in the operator. Consequently, Boundary Element Method (BEM) or methods using the Green functions have been proposed to obtain numerical solutions, but these still require handling large matrix data, resulting in significant computational costs and memory consumption. To overcome this, the current study first simplifies the eigenvalue problem using the conformal mapping presented in previous research. Then, referencing prior studies that claim that three types of resonance frequencies (Helmholtz resonance frequency and resonance frequencies representing streamwise or radial directional oscillation) significantly affect the thrust of the SparkJet actuators, characteristics of these frequencies are mathematically defined. Using these mathematical characteristics, the study derives the asymptotic and approximate solutions of the simplified eigenvalue problem, from which the resonance frequencies are obtained. The analytic formulae proposed in this study theoretically explain the already known geometric tendencies of the resonance frequencies and reveal new geometric factors influencing resonance frequencies, which were previously unknown. This approach is expected to facilitate obtaining several important resonance frequencies of the SparkJet actuator more promptly and accurately and to provide a deeper understanding of the nature of the complex oscillation phenomena inside the actuator.

Gemini-Assisted Deep Learning Classification Model for Automated Diagnosis of High-Resolution Esophageal Manometry Images.

Background/Objectives: To develop a deep learning model for esophageal motility disorder diagnosis using high-resolution manometry images with the aid of Gemini. Methods: Gemini assisted in developing this model by aiding in code writing, preprocessing, model optimization, and troubleshooting. Results: The model demonstrated an overall precision of 0.89 on the testing set, with an accuracy of 0.88, a recall of 0.88, and an F1-score of 0.885. It presented better results for multiple categories, particularly in the panesophageal pressurization category, with precision = 0.99 and recall = 0.99, yielding a balanced F1-score of 0.99. Conclusions: This study demonstrates the potential of artificial intelligence, particularly Gemini, in aiding the creation of robust deep learning models for medical image analysis, solving not just simple binary classification problems but more complex, multi-class image classification tasks.