Correct Solution Research Articles

Specifying angular reference for robust three-phase state estimation

While the phase angle of any of the bus voltages can be chosen as the angular reference in the state estimation formulation of positive sequence networks, the same approach does not readily extend to three-phase network state estimation problem. It is commonly assumed that there is at least one bus where the bus voltages are perfectly balanced with phase angles displaced ±120° and these balanced three phase voltages are used as the three-phase reference in solving the three-phase state estimation problem. This assumption may be quite realistic in transmission networks, and for distribution networks with a strong transmission system connection. However, it might not be realistic to assume existence of a perfectly balanced reference bus in today’s distribution systems with ever increasing penetration of renewable sources or for isolated operation of microgrids. In this paper, a novel state estimation formulation will be presented which facilitates correct solution irrespective of the existence of buses with perfectly balanced voltages. The new formulation is general, and lends itself to bad data processing. It yields accurate results in any three-phase power system irrespective of its operating conditions (balanced or highly unbalanced), configuration (isolated microgrid, connected to transmission system, etc.) and whether or not it contains any synchronous generators. The performance of the method is validated using the IEEE 123 bus three-phase system.

3D Numerical Cross-Section Analysis of a Tapered Beam Slice

Cross-section analysis is an important tool used to recover stresses and strains in a structure at specific cross-sections of arbitrary geometries, without the need for a full 3D model. This is particularly essential for large-scale structures such as aircrafts, wind turbine blades, etc. where making a full model can be computationally very expensive or impractical. The majority of currently available cross-section analysis frameworks are based on stepwise prismatic assumptions, which are hardly suited for the analysis of tapered beams. In fact, high-fidelity stress analysis obtained from analytical and full 3D models shows that predictions of stepwise prismatic approximations can significantly deviate from the correct solution of tapered beams. In this work, a prismatic 3D cross-section analysis method is extended to analyze a symmetrically tapered finite cross-section slice. In this study, the cross-section slice is discretized with 8-node and 20-node solid elements. The boundary conditions are applied as six constraint equations via the Lagrange multiplier method. The external nodal forces acting on the cross-section faces are obtained from the equivalent tractions induced by the cross-section forces. The developed numerical model is validated against the exact analytical solutions of a wedge as well as commercial finite element (FE) software COMSOL and it is shown that the numerically predicted displacement and stress fields agree well with those provided by the wedge’s analytical solution and the FE COMSOL results. This work contributes to the advancement of high-fidelity numerical tapered cross-section analysis methods with an application for many engineering structures.

Elastic, flat and rounded finite contacts: When should we use half-plane theory?

For a flat contact with radiused edges, it is shown that when the flat portion of the contact is small compared to the radius portion of the contact, half-plane theory may confidently be used, and the amount of coupling present is extremely small. When the flat region is large a good quality solution may be used by a different route, using the solution for a square-ended punch together with a corrective solution formed from a three-quarter plane problem but with a radius at the corner. The degree of coupling is captured well. Intermediate geometries are discussed in the text. A further, important, refinement is the fitting of a third solution, developed using half-plane theory for a slightly rounded, flat semi-infinite contact, as this provides an analytical description of the near-edge tractions, and is rigorously fitted into the edge of the three-quarter plane solution.

Interaction diagrams of thin-walled, open cross section PC beams

Thin-walled, open cross section PC (prestressed concrete) beams are widely used in precast structures. Nevertheless, the analytical computation of their load carrying capacity under bending and torsion is still an unsolved problem. This is because of the markedly non-linear behaviour of both steel and concrete and of the asymmetry of the behaviour of concrete in tension and compression. This involves a search for the correct solution from a physical point of view (among those mathematically admissible) based on trial-and-error methods of numerical analysis.This paper suggests a method to evaluate the interaction diagrams under bending and torsion. According to this method the solving system is made by two equilibrium plus two compatibility equations. Some examples show the outcomes of this approach.

The risk of hazards in laboratories of educational groups in the Faculty of Health, Shahid Sadougi University of Medical Sciences, Yazd-2023

Introduction: Improving the safety of working environments is one of the duties of any efficient system. Evaluating the risk of hazards is one of the most efficient ways for increasing safety important issues. Paying attention to the statistics of laboratory accidents and the positive effects of risk assessment in order to improve safety is of great importance. Materials and Methods: The present study was practical in terms of purpose, and cross-sectional in terms of descriptive-analytical method, which to evaluate the laboratories of Shahid Sadoqhi University of Medical Sciences, Yazd, using a quantitative three-dimensional cost equation. Based on the regular observation of existing processes and equipment, the evaluation team used a quantitative risk equation as an indication of safety performance at the level of laboratories. The ranking was based on the probability of risk, the frequency of effective exposure, and the maximum damage potential through a quantitative equation. Finally, the risk rate score of each laboratory was determined and the ranking of the risk level of the laboratories was announced. Suggested corrective solutions were presented and the evaluation was repeated. After collecting the data, it was entered into SPSS 20 software and interpreted using descriptive and analytical statistics. Results: In general, 52% of the risks identified in laboratories are at a low risk level. The highest and lowest average evaluation scores were 55.86 ± 30.89 for environmental chemistry and 28.38 ± 13.51 for food safety and health research laboratory, respectively. The highest evaluation score was given to the environment laboratory. There was a significant relationship between the risk components before and after providing the suggested solutions. Conclusion: According to the results of the research, the overall safety status of the educational laboratories in the Faculty of Health is at a relatively favorable level. However, chemical hazards and thermal safety are the highest priority to control and perform better regarding improvement.

The Effect of Visual Reasoning on Arithmetic Word Problem Solving

First-grade students often encounter challenges in understanding and solving arithmetic word problems due to their limited reading comprehension abilities. Despite these difficulties, students may employ arbitrary strategies, such as combining numbers based on specific keywords, even if they lack a full understanding of the problems. Research suggests that effective mathematical reasoning involves the use of visual mental representations during the problem-solving process. To address this, some studies have explored methods to enhance students’ comprehension of word problems. Building on this, the current study explores the impact of first-grade pupils creating visual representations of problem situations on their comprehension and the number of correct solutions. In a typical math class, 45 first graders received a paper-and-pencil task, and, in a visual context, they solved similar problems after reading and illustrating the situation. The findings reveal that while most participants correctly represented the problem situations through drawing, about half struggled to determine the numeric solutions. Nevertheless, the visual context led to an increase in the number of correct problem solutions compared to the normal context, suggesting the potential benefits of incorporating visual representations in enhancing comprehension and problem-solving skills.

Deep learning-based partial volume correction in standard and low-dose positron emission tomography-computed tomography imaging.

Positron emission tomography (PET) imaging encounters the obstacle of partial volume effects, arising from its limited intrinsic resolution, giving rise to (I) considerable bias, particularly for structures comparable in size to the point spread function (PSF) of the system; and (II) blurred image edges and blending of textures along the borders. We set out to build a deep learning-based framework for predicting partial volume corrected full-dose (FD + PVC) images from either standard or low-dose (LD) PET images without requiring any anatomical data in order to provide a joint solution for partial volume correction and de-noise LD PET images. We trained a modified encoder-decoder U-Net network with standard of care or LD PET images as the input and FD + PVC images by six different PVC methods as the target. These six PVC approaches include geometric transfer matrix (GTM), multi-target correction (MTC), region-based voxel-wise correction (RBV), iterative Yang (IY), reblurred Van-Cittert (RVC), and Richardson-Lucy (RL). The proposed models were evaluated using standard criteria, such as peak signal-to-noise ratio (PSNR), root mean squared error (RMSE), structural similarity index (SSIM), relative bias, and absolute relative bias. Different levels of error were observed for these partial volume correction methods, which were relatively smaller for GTM with a SSIM of 0.63 for LD and 0.29 for FD, IY with an SSIM of 0.63 for LD and 0.67 for FD, RBV with an SSIM of 0.57 for LD and 0.65 for FD, and RVC with an SSIM of 0.89 for LD and 0.94 for FD PVC approaches. However, large quantitative errors were observed for multi-target MTC with an RMSE of 2.71 for LD and 2.45 for FD and RL with an RMSE of 5 for LD and 3.27 for FD PVC approaches. We found that the proposed framework could effectively perform joint de-noising and partial volume correction for PET images with LD and FD input PET data (LD vs. FD). When no magnetic resonance imaging (MRI) images are available, the developed deep learning models could be used for partial volume correction on LD or standard PET-computed tomography (PET-CT) scans as an image quality enhancement technique.

Research on reconstruction of diffraction tomography based on prior information

Under coherent light illumination, several approaches need either angle scanning or diffuser rotating to reconstruct the image through opaque scattering media. We propose a linear model to restore the hidden object through the actual power spectrum with disturbance of the scattering layer. The experimental results confirm that, the algorithm quickly converge to the only correct reconstruction solution with the accuracy power spectrum pattern of Fourier transform, and the method can reconstruct the high accuracy image of the object hidden by the scattering media with one-shot power spectrum.

SAKKOKI'S POETIC WORKMANSHIP (EXAMPLE OF GHAZALS OF XAMD AND NAT)

As a result of the requirement to follow the principles of classism for almost a century before independence, many issues did not find their true and impartial, historically correct interpretation and solution. In fact, the study of these topics should be considered "a great positive event for our time, for the entire world literature." in this article, we will consider the ghazals of praise and praise given in "Devon of Mavlano Sakkoki" prepared for publication by literary scholars M. Hasanova, H. Sheraliyev.

Wrong Definition and Wrong Implications of Cosmic Red Shift (Correction and Possible Solutions)

Since 1912, cosmologists strongly believe in the currently accepted definition of cosmic red shift as - ratio of increase in wavelength to the laboratory wavelength of photon. We would like to emphasize the point that, this definition is absolutely wrong with reference to photon energy. Clearly speaking, true cosmic red shift must be defined as the ratio of loss in energy of photon to the energy of photon at laboratory. In terms of wavelength, photon red shift must be defined as the ratio of increase in wavelength to the observed wavelength of photon. We have published this definition in our recent publications and sincerely appeal the science community and cosmologists to review the basics of Lambda cosmology, cosmic acceleration and dark energy in an unbiased approach. Regarding Tolman Surface Brightness test, we sincerely appeal the cosmologists to review and reanalyze the observations and calculations as per the corrected cosmic redshift definition with reference to cosmic expansion and cosmic rotation. Here we would like to emphasize the point that, (1+z) should be replaced by (1+znew). Upper limit of (1+znew) is 2 and upper limit of (1+znew)4 is 16

A modified algebraic method of mathematical signal processing in radar problems

A new method for approximate solution of ill-posed inverse problems of reconstructing images of objects with angular resolution exceeding the Rayleigh criterion is proposed and justified, i.e. with super resolution. Angular super-resolution allows you to obtain images of objects with increased clarity and distinguish previously invisible details of images of complex objects. In addition, on this basis, the probability of correct solutions to problems of object recognition and identification increases. Mathematically, the problem is reduced to solving the linear Fredholm integral equation of the first kind of convolution type. Solutions are sought with additional conditions in the form of restrictions on the location and size of the desired radiation source, which makes it possible to regularize the problem. The method is a development of one of the parameterization methods the algebraic method. The solution is sought in the form of a representation of the desired function in the area where the source is located in the form of a series expansion over the input sequence of orthogonal functions with unknown coefficients. Thus, the inverse problem is parameterized and reduced to searching for expansion coefficients. The presented method is based on the use of a priori information about the localization area of the radiation source, or on an estimate of the location and size of this area obtained by scanning the viewing sector with a goniometer system. Using zero values of the function describing the source outside this region, for systems based on antenna arrays it is possible to find tens and even hundreds of expansion coefficients of the desired function in a Fourier series. The solution is constructed in the form of an iterative process with a consistent increase in the number of functions used in the expansion until the solution remains stable. The adequacy and stability of the solutions was verified during numerical experiments using a mathematical model. The results of numerical studies show that the presented methods of digital processing of received signals make it possible to achieve an effective angular resolution 3–10 times higher than the Rayleigh criterion. The proposed method makes it possible to miniaturize the antenna system without degrading its characteristics. Compared to known ones, it is relatively simple, which allows it to be used by systems in real time.

Heat transfer analysis of MHD oscillatory SWCNT/MWCNT‐H2O hybrid nanofluid flow in a channel

AbstractRegulating the thermal conductivity of the fluid in various heat exchange systems plays an important role. In this regard, the carbon nanotubes (CNTs), with their higher thermal conductivity, can enhance the heat transfer potential. The main objective of the present study is to explore the impact of suction and injection on the oscillatory flow of CNT‐based hybrid nanofluid through a channel under the influence of the magnetic field for analysing heat transfer perspectives. While developing a mathematical model of the problem, we also considered other relevant elements, such as thermal radiation for optically thin fluids and porous mediums. The behaviour of a water‐SWCNT + MWCNT hybrid nanofluid is studied concerning the volume fraction of CNTs. The governing flow equations have been solved to obtain the correct solutions for the distribution of velocities and temperatures. Graphs and tables are used to assess the impact of relevant parameters on the flow and derived quantities. Adding CNTs to a fluid reduces its temperature and velocity, making it ideal for cooling systems. However, plates exhibit a maximum heat transfer of 35.35% and 25.35%, respectively, for and . The magnetic and constant pressure parameters greatly diminish the fluid's velocity, while the thermal buoyancy forces strengthen the flow. The effectiveness of the current study is confirmed by comparing its results to those from previous investigations.

Evaluating GPT-4’s proficiency in addressing cryptography examinations

In the rapidly advancing domain of artificial intelligence, ChatGPT, powered by the GPT-4 model, has emerged as a state-of-the-art interactive agent, exhibiting substantial capabilities across various domains. This paper aims to assess the efficacy of GPT-4 in addressing and solving problems found within cryptographic examinations. We devised a multi-faceted methodology, presenting the model with a series of cryptographic questions of varying complexities derived from real academic examinations. Our evaluation encompasses both classical and modern cryptographic challenges, focusing on the model’s ability to understand, interpret, and generate correct solutions while discerning its limitations. The model was challenged with a spectrum of cryptographic tasks, earning 202 out of 208 points by solving fundamental queries inspired by an oral exam, 80.5 out of 90 points on a written Crypto 1 exam, and 287 out of 385 points on advanced exercises from the Crypto 2 course. The results demonstrate that while GPT-4 shows significant promise in grasping fundamental cryptographic concepts and techniques, certain intricate problems necessitate domain-specific knowledge that may sometimes lie beyond the model’s general training. Insights from this study can provide educators, researchers, and examiners with a deeper understanding of how cutting-edge AI models can be both an asset and a potential concern in academic settings related to cryptology. To enhance the clarity and coherence of our work, we utilized ChatGPT-4 to help us in formulating sentences in this paper.

Vibration characteristics of multilayer functionally graded microplates with variable thickness reinforced by graphene platelets resting on the viscoelastic medium under thermal effects

Due to their improved mechanical properties and adaptability, microplates with tailored variable thickness profiles are becoming essential parts of advanced micro- and nanoelectromechanical systems (MEMS and NEMS). This study conducts a thorough analytical analysis of the vibration properties of thermally loaded, multilayer functionally graded graphene platelet-reinforced composite (FG-GPLRC) microplates of linearly or parabolically varying thickness resting on viscoelastic medium under different boundary conditions. The Halpin–Tsai micromechanical model and the law of mixtures are employed to calculate the effective material characteristics for various reinforcement distributions in the microplate. These distributions encompass uniformly symmetric and asymmetric arrangements. The study utilized the first-order shear deformation theory (FSDT) in conjunction with the modified strain gradient theory (MSGT) and Hamilton's principle to generate the dynamic governing equations for the structure, accounting for size-dependent effects. The resulting equations are afterwards solved using the utilization of the Galerkin technique. This enables the evaluation of the proposed solution's correctness and precision. The impact of various factors on vibration behavior is investigated through numerical analysis. These factors encompass length scale parameters, temperature fluctuations, temperature distribution profiles, boundary conditions, the distribution pattern of the GPL, taper constants in both unidirectional and bidirectional scenarios, the weight fraction of the GPL.

A Fast Second-order Solver for Stiff Multifluid Dust and Gas Hydrodynamics

We present MDIRK: a multifluid second-order diagonally implicit Runge–Kutta method to study momentum transfer between gas and an arbitrary number (N) of dust species. The method integrates the equations of hydrodynamics with an implicit–explicit scheme and solves the stiff source term in the momentum equation with a diagonally implicit, asymptotically stable Runge–Kutta method (DIRK). In particular, DIRK admits a simple analytical solution that can be evaluated with O(N) operations, instead of standard matrix inversion, which is O(N)3 . Therefore, the analytical solution significantly reduces the computational cost of the multifluid method, making it suitable for studying the dynamics of systems with particle-size distributions. We demonstrate that the method conserves momentum to machine precision and converges to the correct equilibrium solution with constant external acceleration. To validate our numerical method we present a series of simple hydrodynamic tests, including damping of sound waves, dusty shocks, a multifluid dusty Jeans instability, and a steady-state gas–dust drift calculation. The simplicity of MDIRK lays the groundwork to build fast high-order, asymptotically stable multifluid methods.

Using worked examples to promote explanations of fractions concepts: A formative pilot study

This pilot study examined the feasibility of using worked examples as a mechanism to improve verbal explanations of fractions concepts among Grade 5 students with mathematics difficulties in a small-scale randomized controlled trial (RCT) before scaling up to a large-scale RCT. Students ( N = 49) were randomly assigned to a business-as-usual (BAU) comparison group and to two variants of intervention. One intervention condition received both correct and incorrect worked example solutions, the other received correct solutions only. On a measure of verbal explanations, intervention students significantly outperformed students in BAU. Furthermore, students who received both correct and incorrect solutions significantly outperformed students who received correct solutions only on verbal explanations. On fractions proficiency outcomes, results were not significant between intervention and BAU or between the two intervention groups; however, positive findings demonstrate promise for using worked examples to elicit and develop students’ verbal explanations of fractions concepts.

Do Performance-Contingent Incentives Help or Hinder Divergent Thinking?

ABSTRACT Toward the goal of reconciling conflicting arguments on whether performance-based incentives facilitate or impede divergent thinking, we identify a feature common to prior demonstrations of negative incentive effects: they generally involve tasks with only one correct solution. Our first experiment replicates a negative incentive effect when insight problems require “bottom-up” divergent thinking from an unexpected resource to the problem it is uniquely equipped to solve, whereas our second experiment finds a positive incentive effect in the more general case of problems that enable “top-down” divergent thinking from a problem to multiple potential solutions. We also observe a positive incentive effect in a third experiment that measures the time needed to generate a solution to problems that have multiple potential solutions and in a fourth experiment in which participants design insight problems. Overall, our findings suggest that any harmful effects of performance-based incentives are likely restricted to highly constrained settings. Data Availability: Data are available from the authors upon request. JEL Classifications: J33; M14; M41; M52.

Application of two-grid interpolation to enhance average gradient method for solving partial differential equations

Previously presented method of calculating local average gradients for solving partial differential equations (PDEs) is enhanced by using interpolating gridpoints and triangular grids. The interpolating mesh provides finer computational grid, which is then used for solving the PDE. The combined use of the finer interpolating grid together with the original sparser grid is a two-grid method. By comparing the previous application of rectilinear grid for diffusion from initial point concentration to the new triangular two grid method, it was found that the application of triangular two-grid method improves stability of the solution and it provides more rapid convergence to the correct analytical solution.

Robust Deformable Image Registration Using Cycle-Consistent Implicit Representations.

Recent works in medical image registration have proposed the use of Implicit Neural Representations, demonstrating performance that rivals state-of-the-art learning-based methods. However, these implicit representations need to be optimized for each new image pair, which is a stochastic process that may fail to converge to a global minimum. To improve robustness, we propose a deformable registration method using pairs of cycle-consistent Implicit Neural Representations: each implicit representation is linked to a second implicit representation that estimates the opposite transformation, causing each network to act as a regularizer for its paired opposite. During inference, we generate multiple deformation estimates by numerically inverting the paired backward transformation and evaluating the consensus of the optimized pair. This consensus improves registration accuracy over using a single representation and results in a robust uncertainty metric that can be used for automatic quality control. We evaluate our method with a 4D lung CT dataset. The proposed cycle-consistent optimization method reduces the optimization failure rate from 2.4% to 0.0% compared to the current state-of-the-art. The proposed inference method improves landmark accuracy by 4.5% and the proposed uncertainty metric detects all instances where the registration method fails to converge to a correct solution. We verify the generalizability of these results to other data using a centerline propagation task in abdominal 4D MRI, where our method achieves a 46% improvement in propagation consistency compared with single-INR registration and demonstrates a strong correlation between the proposed uncertainty metric and registration accuracy.

Investigating the role of spatial thinking in children’s design ideation through an open-ended design-by-analogy challenge

Spatial thinking is ubiquitous in design. Design education across all age groups encompasses a range of spatially challenging activities, such as forming and modifying mental representations of ideas, and visualizing the scenarios of design prototypes being used. While extensive research has examined the cognitive processes of spatial thinking and their relationships to science, technology, engineering, and mathematics learning, there remains a knowledge gap regarding the specific spatial thinking processes needed for open-ended problems, which may differ from those assessed in close-ended, analytical spatial tasks. To address this gap, we used educational design-based research to develop a nature-inspired, design-by-analogy project and investigate the spatial thinking processes of young, novice designers. 16 children from an international school in the Netherlands participated in this five-week design project. Multimodal evidence from classroom recordings and children’s design works were triangulated to offer insight into the key spatial thinking processes involved in their creation of nature-inspired, analogy-based design prototypes. Our results revealed spatial thinking processes that might not align with those assessed in conventional spatial tests and may be unique to design or open-ended problem-solving. These processes include abstracting spatial features to infer form-function relationships, retrieving a range of relevant visual information from memory, developing multiple possible analogical matches based on spatial features and relationships, elaborating and iterating on the design concepts and representations to make creative and suitable solutions for the design challenge, as well as visualizing design prototypes in practical usage scenarios. By highlighting the nuanced differences between spatial thinking in open-ended, divergent thinking tasks and conventional spatial tasks that demand single correct solutions, our research contributes to a deeper understanding of how children utilize spatial thinking in design and open-ended problem-solving contexts. Furthermore, this case study offers practical implications for scaffolding children's analogical reasoning and nurturing their spatial thinking in design education.