Mathematical Operations Research Articles

Personalized assessment of the effectiveness of psychosocial rehabilitation: an innovative approach based on the process of analytical hierarchy

IntroductionIn psychosocial rehabilitation (PSR), rank scales are widely used to assess the severity of functional disorders in patients. The main problem of evaluating the effectiveness of PSR is related to the methods of processing data obtained using psychometric scales used to evaluate the effectiveness of interventions within PSR. J. Pfanzagl (1968) obtained the proof of the non-numerical nature of ranks. Incorrect processing of rank information obtained in the framework of psychosocial research leads to contradictions in the assessment of the patient’s condition. Consequently, rank processing does not allow classical mathematical operations (summation, average), which makes it impossible to correctly estimate the effectiveness of PSR numerically.ObjectivesDevelopment of algorithms for numerical evaluation of PSR efficiency based on rank information processing using the analytic hierarchy process (AHP) [1].MethodsClinical, psychometric, AHP algorithms.ResultsThe analysis of the problems of assessing the patient’s conditions on the basis of categorical and psychometric (rank) scales and subscales shows that these problems can be presented in the form of appropriate hierarchies [2], the structure of which must be taken into account when processing the initial information.According to the results of the analysis of the data of preliminary studies, the main areas of impaired functioning of patients affecting the evaluation of the effectiveness of PSR have been identified. Rank estimates of changes in the relevant areas of the patient’s dysfunction after the PSR program compared to the initial level are the basis for the conclusion about the effectiveness of the PSR components. Algorithms of the AHP normative approach were used to translate rank information into numerical information [2]. The weight of the areas of the patient’s functioning disorders was used in the formation of integral estimates of the effectiveness of PSR.The fundamental difference between AHP-based assessments and rank assessments is due to the fact that numerical estimates of the weight of the criteria and the corresponding changes in the patient’s condition are obtained, which depend on the qualifications of specialists, the characteristics of the scales used to measure violations in the relevant areas and the procedures of the PSR.ConclusionsObtaining the results of processing rank information in a numerical scale allows to obtain the correct integration of the patient’s personal characteristics when considering PSR procedures and to obtain correct models of the patient’s state. 1. Saaty T. European Journal of Operational Research.1990; 48(1):9-26. https://doi.org/10.1016/0377-2217(90)90057-I 2. Mitikhin V.G., Solokhina T.A. et al. Psychiatry, 2022; 20(2): 51-59. DOI: 10.30629/2618-6667-2022-20-2-51-59Disclosure of InterestNone Declared

Analysis attackers’ methods with hashing secure password using CSPRNG and PBKDF2

Using the Internet, nothing is secure and as we are in need of means of protecting our data, the use of passwords has become important in the electronic world. To ensure that there is no hacking and to protect the database that contains important information such as the ID card and banking information, the proposed system stores the username after hashing it using the 256 hash algorithm and strong passwords are saved to repel attackers using one of two methods: -The first method is to add a random salt to the password using the CSPRNG algorithm, then hash it using hash 256 and store it on the website. -The second method is to use the PBKDF2 algorithm, which salts the passwords and extends them (deriving the password) before being hashed and stored on the website. The results of the two methods are compared in terms of speed and resistance to attackers, then password attacks are analysed in addition to calculating the strength of the password, the time it takes for the user to log in, and the time required for the attacker to guess the passwords per second. The Wolfram Alpha is used to calculate the mathematic operations and system implementation was done by using IntelliJ IDEA with java FX.

The Deep Hybrid Neural Network and an Application on Polyp Detection

Mathematical morphology and convolution operators are two different methods to extract the characteristics and structures of images. Over the past decades, Deep Convolutional Neural Networks (DCNN) have been proven to be more powerful than traditional image-processing approaches. In this paper, we propose a novel structure called Deep Hybrid Neural Network (DHNN) by taking advantage of the convolution and morphological neural layers. Its practical application to polyp detection in medical images is illustrated. For experimental completeness, we adopt nine polyp image datasets, including publicly available data and our own collected data. For performance comparisons, we select three backbone models. Experimental results show that our DHNN achieves the best performance in comparisons in terms of computational complexity and accurate performance.

New solutions for the generalized q-deformed wave equation with q-translation symmetry

Abstract In this work, we explore the generalized discrete wave equation, which utilizes a specific irregular space interval. The introduction of this irregular space interval is motivated by its connection to the q-addition, a mathematical operation that arises in the nonextensive entropy theory. By taking the continuous limit, we obtain the wave equation with q-deformation, which captures the effects of the q-addition. To solve the generalized q-deformed wave equation, we investigate three different methods: the separation method, the reduced differential transform method, and the finite difference method. These methods offer distinct approaches for finding solutions to the equation. By comparing the results obtained from each method, we can evaluate their effectiveness and identify their respective strengths and limitations in solving the generalized q-deformed wave equation. The solutions obtained from this newly defined equation have potential applications in modeling physical systems with violated symmetries. The inclusion of the q-deformation allows for a more comprehensive description of such systems, which may exhibit nonextensive behavior or possess irregularities in their spatial intervals. By incorporating these features into the wave equation, we can improve our understanding and modeling capabilities of complex physical phenomena.

Maxwell Spectrum as a Parameter to Verify the Dose in Brain Cancer (Glioblastoma) by Boron Neutron Capture Therapy (BNCT) using Monte Carlo Method

To evaluate the efficiency of neutron capture therapy (BNCT) treatment in glioblastoma multiforme, it is necessary to evaluate the impact of the neutron beam on the tumor cell and find better results so that BNCT treatment is viable. Glioblastoma multiforme is one of the most lethal cancers and conventional radiotherapy is almost ineffective for this type of tumor. Among several approaches to describe the procedure and the neutron spectrum, the Maxwell spectrum in the epithermal neutron range was used. For this, T=0.0025 MeV was used to describe this spectrum. MCNP software was used to simulate a BNCT treatment using the Maxwell spectrum to describe the neutron source. The user provided the quantities of interest, such as fluence and dose. These are extremely important quantities to describe a BNCT planning protocol. A concentration of 30 ppm of Boron-10 was simulated in the tumor. Output data provides normalized values. It was necessary to carry out some mathematical operations to obtain values closer to reality. Thus, a dose of 32 Gy was obtained for the Maxwell spectrum described with T=0.0025 MeV and a neutron fluence of 1.5 x 1012 n/cm². The values calculated based on the simulation in MCNP5 described by an epithermal neutron source obeying a Maxwellian function, were in agreement with the reference values in the literature.

Automatic Extraction Method of Landslide Based on Digital Elevation Model and Digital Orthophoto Map Data Combined in Complex Terrain

This study aims to accurately determine the distribution of landslides in the complex terrain of Jiangdingya, Nanyu Township, Zhouqu County, Gansu Province. The digital orthophoto map (DOM) and digital elevation model (DEM) are used to accurately identify landslide areas and analyze associated data. Based on image-based supervised classification, the influence factor constraint analysis is used to further identify and delineate the landslide area. Three mathematical morphology operations—erosion, dilation, and opening—are then applied to automatically identify and extract landslides. Experimental results demonstrate that achieving an accuracy, precision, and recall of 98.02%, 85.24%, and 84.78% shows that it is possible to better avoid interference caused by complex terrain with rich features. High-resolution DEM and DOM data contain rich spectral and texture information. These data can accurately depict geomorphic features of complex terrain and aid in identifying landslide-prone areas when combined with mathematical morphology processing. This contribution is important for identifying landslides in complex terrain and emergency disaster management.

An Integrated All‐Optical Ising Machine with Unlimited Spin Array Size and Coupling

Artificial spin systems are used to solve combinatorial optimization problems by mapping them to the ground state search of the Ising model. Ising machines of various designs, in fields as diverse as photonics and electronics, have been proposed and demonstrated in recent years. One important mathematical operation required in photonic Ising machines for nearly all Hamiltonian minimization algorithms is repeated matrix–vector multiplication with the vector size limited by the physical size of the optical system. Herein, an integrated photonic Ising machine based on matrix partitioning and phase encoding, which effectively allows the use of physically small optical circuits to handle arbitrarily large spin vectors, is proposed. All the complicated calculations are carried out optically, rather than electronically, in this approach. How the required surface area of a hypothetical chip‐based photonic Ising machine can be resized according to convenience, with the trade‐off being the solution time, and that this trade‐off can be done in a way that does not impact the algorithm's efficacy, is shown. Through simulation, the system is predicted to have a high success rate, high noise tolerance, and high error tolerance.

SCTBEM: A scaled coordinate transformation boundary element method with 99-line MATLAB code for solving Poisson's equation

This study introduces the scaled coordinate transformation boundary element method (SCTBEM), a novel boundary-type method for solving three-dimensional potential problems. To apply the BEM to complex problems, it is common practice to use the fundamental solution corresponding to the partial governing equation operator to establish the integral equation. However, this approach introduces the domain integral, which may jeopardize the dimensionality reduction advantages of BEM. To preserve the benefits of dimensionality reduction, this study proposes a novel domain integral transformation method named SCT. The SCT is purely a mathematical operation that does not rely on a particular solution of the operators, which requires only discretization on the surface of the structure while remaining analytical in the radial direction. An even more significant advantage is that the lower-order singularity can be eliminated by the coordinate translation technique. To facilitate the wider adoption of BEM, the authors present an open-source 99-line MATLAB code. Numerical results demonstrate that the SCTBEM exhibits high numerical accuracy even when dealing with complex models.

Geogebra untuk Pengantar Pembelajaran Integral Tentu

Nowadays there are many technologies that can be utilized to support the educational process, including in the teaching of mathematics. In integral material, the usual approach involves explaining mathematical operations, giving an example, and doing the task. Students are not taught in-depth concepts about how integrals are obtained and the related issues with integrals. All of this could be due to the lack of use of media that supports stimulation and visualization of mathematics learning. One of the media that answers this problem is Geogebra. This article is a literature study that discusses the Geogebra application as an introduction to integral learning. Beside that, example of using Geogebra as a learning media to help students understand integral concepts are also presented.

DESIGN AND ANALYSIS OF NOVEL PARALLEL PREFIX ADDERS FOR VLSI CIRCUITS

Arithmetic Logic Unit is the brain of all processors, is composed of an Adder circuit. The main component of multiplier circuits is the adder, which performs subtraction (by 2’s complement arithmetic). Since the most fundamental operation in mathematics is addition, and the adder is the most essential part of the processor, the study of VLSI arithmetic has required many digital VLSI researchers. When designing digital systems employing the VLSI approach, the digital adder plays a major role. Low power VLSI based adder designs perform poorly because of the propagation delay issue. With the aid of the PPA design, an assessment of adders’ availability for low power VLSI designs with minimal propagation delay is conducted. Using these performance measures, this study compares and evaluates the performance of several parallel prefix adders, allowing readers to select the optimum adder architecture for their application Specific Integrated Circuits implementations. The three adder topologies taken into considered in this Article include the Han carlson adder, Brent kung, Kogge stone adders. Xilinx ZYNQ XC7Z020 (7000 series) SoC is used to implement the adders using the Vivado Design Suite 2014 and Verilog.

Playfulness in Mathematics Teaching in the 5th Grade of Elementary School at Tereza Lemos de Oliveira Santos State School in Atalaia do Norte-AM Municipality

The purpose of the present work is to verify if the teaching of mathematics can become interesting for the students of the 5th year of Elementary School, through the playfulness with the use of mathematical games. In this context, mathematical games: contig 60, multiplication domino, division marathon and integer race, emerged as an educational process, with the aim of promoting teaching and learning through play. As a methodology of qualitative documentary approach, a questionnaire was applied to find out the students’ level of learning, right after, there was a class on the contents of addition, subtraction, multiplication and division. As a complement, the games mentioned above were applied. When the questionnaire was applied again, there was a great improvement in the level of learning of the students in this 5th grade class, in relation to the four basic operations of mathematics. Thus, it can be noted that the use of games enabled the construction of students’ knowledge, thus awakening creativity, logical reasoning and their motor skills. Also, through these activities, a greater interest and curiosity in learning mathematics was noticed in the students.

Вычислительные диэлектрические метаповерхности в фотонных топологических устройствах обработки многомерных сигналов

A single-layer computational dielectric broadband metasurface (MS) with silicon nanodiscs is proposed to implement spatial differentiation and contour recognition operations. The variety of physical mechanisms of dielectric MSs for performing similar mathematical operations is considered. The necessity of such computational nanostructures for improving the numerous methods of topological texture-fractal processing of signals and fields in modern radio physics and radio electronics is revealed.

Rearranging equations to develop physics reasoning

Researchers generally agree that physics experts use mathematics in a way that blends mathematical knowledge with physics intuition. However, the use of mathematics in physics education has traditionally tended to focus more on the computational aspect (manipulating mathematical operations to get numerical solutions) to the detriment of building conceptual understanding and physics intuition. Several solutions to this problem have been suggested; some authors have suggested building conceptual understanding before mathematics is introduced, while others have argued for the inseparability of the two, claiming instead that mathematics and conceptual physics need to be taught simultaneously. Although there is a body of work looking into how students employ mathematical reasoning when working with equations, the specifics of how physics experts use mathematics blended with physics intuition remain relatively underexplored. In this paper, we describe some components of this blending, by analyzing how physicists perform the rearrangement of a specific equation in cosmology. Our data consist of five consecutive forms of rearrangement of the equation, as observed in three separate higher education cosmology courses. This rearrangement was analyzed from a conceptual reasoning perspective using Sherin’s framework of symbolic forms. Our analysis clearly demonstrates how the number of potential symbolic forms associated with each subsequent rearrangement of the equation decreases as we move from line to line. Drawing on this result, we suggest an underlying mechanism for how physicists reason with equations. This mechanism seems to consist of three components: narrowing down meaning potential, moving aspects between the background and the foreground and purposefully transforming the equation according to the discipline’s questions of interest. In the discussion section we highlight the potential that our work has for generalizability and how being aware of the components of this underlying mechanism can potentially affect physics teachers’ practice when using mathematics in the physics classroom.

Broadband angular spectrum differentiation using dielectric metasurfaces

Signal processing is of critical importance for various science and technology fields. Analog optical processing can provide an effective solution to perform large-scale and real-time data processing, superior to its digital counterparts, which have the disadvantages of low operation speed and large energy consumption. As an important branch of modern optics, Fourier optics exhibits great potential for analog optical image processing, for instance for edge detection. While these operations have been commonly explored to manipulate the spatial content of an image, mathematical operations that act directly over the angular spectrum of an image have not been pursued. Here, we demonstrate manipulation of the angular spectrum of an image, and in particular its differentiation, using dielectric metasurfaces operating across the whole visible spectrum. We experimentally show that this technique can be used to enhance desired portions of the angular spectrum of an image. Our approach can be extended to develop more general angular spectrum analog meta-processors, and may open opportunities for optical analog data processing and biological imaging.

A Study of Elliptic Curve Cryptography and Its Applications

This paper aims to provide a comprehensive review on Elliptic Curve Cryptography (ECC), a public key cryptographic system and its applications. The paper discusses important mathematical properties and operations of elliptic curves, like point addition and multiplication operations and its implementation in cryptographic methods such as encryption and decryption. This paper provides a detailed workout on important mathematical problems on elliptic curves and ECC which provides insight into working of essential cryptographic techniques in ECC. And the paper also provides a literature review of research works based on ECC in various fields such as Internet of Things (IoT), Cloud computing, Blockchain and Image Security. And the paper further provides insight into the recent applications of ECC in fields like IoT and Blockchain by comprehensively discussing the proposed mechanism for each of the recent applications and also briefly discussing the security of the proposed mechanism.

Probe with a metallic bowl termination to determine the electric material parameters from variable thicknesses

This paper discusses a new approach to determining the material electric parameters (dielectric constant and dissipation factor) through a technique based on identical material variation thicknesses. The copper bowl controls the material thicknesses and allows quick and safe measurements to get to the electromagnetic material information. This approach assumes that the discontinuities generated at the probe and bowl are identical and removed through mathematical operations. The material under test (MUT) gap thickness doesn’t exceed one millimeter. Some formulations have been developed to determine the discontinuity condensers and both capacitors of each thickness. Two proposed developments have been given to extract the complex effective and relative permittivities. A mathematical formula has been proposed to ensure the transition from effective to intrinsic parameters, where the MUT thicknesses and the probe’s outer diameter of the inner conductor are considered. A de-embedding operation is necessary, and the method is suitable but not limited to low-k. The coaxial probe is flat terminated, and the experimental validation has been made in the frequency ranges 1 MHz—2.2 GHz for FR-4 HTG-175 and 1 MHz—0.8 GHz for Alumina 99.5%. All MUTs are 5.0×5.0 cm2, except their thicknesses. The suggested approach is straightforward in sample insertion, simple in data acquisition and implementation, and precise in the final parameters’ results.

Fiboquadratic numbers and Rithmomachia

Abstract This paper shows our discovery of the fiboquadratic numbers, quadratic Fibonacci numbers in rithmomachia. This board game consists in performing mathematical operations to attack an opponent through geometric numbered pieces. We will show that the numbers on the board pieces are the first terms of six sequences that we will define through a recursive pattern of superpartients. We then prove that this extension is the solution of a recurrence relation with initial conditions, and therefore, is unique. The fiboquadratic numbers we introduce in this work are not limited to the context of this board. In general, we can generate any fiboquadratic sequence with arbitrary initial conditions.

Student’s Reversible Thinking Processes: An Analysis Based on Adversity Quotient Type Climbers

Reversibility thinking carried out mentally in mathematical operations has an important role in the process of understanding concepts as it involves developing a thinking process from beginning to end and from end to beginning. This qualitative research aims to describe students' reversible thinking processes in solving algebra problems, specifically in climber-type adversity quotient. A total of 2 students who have the climber type were selected as participants from 36 potential subjects involved in the research. Data collection was carried out by providing Adversity Response Profile questionnaires, Test of Thinking Reversible, and semi-structured interviews. Our participants solved problems according to polya stages and through forward and reverse processes. The results of data analysis show that in the forward process, there are 2 aspects of reversible thinking, namely negation and reciprocity, while in the reverse process, they involve 2 aspects of reversible thinking, namely the capability to return to initial data after obtaining the result and negation. The results suggest that student's ability to perform mental reversals indicates a strong reversible thought process, leading to more precise cognitive thinking.

Optimizing grid-connected PV systems with novel super-twisting sliding mode controllers for real-time power management

Over the past years, the use of renewable energy sources (RESs) has grown significantly as a means of providing clean energy to counteract the devastating effects of climate change. Reducing energy costs and pollution have been the primary causes of the rise in solar photovoltaic (PV) system integrations with the grid in recent years. A load that is locally connected to a GCPV requires both active and reactive power control. In order to control both active and reactive power, MAs and advanced controllers are essential. Researchers have used one of the recently developed MAs, known as the CAOA, which is based on mathematical arithmetic operators to tackle a few real-world optimization problems. Some disadvantages of CAOA include its natural tendency to converge to a local optimum and its limited capacity for exploration. By merging the PSO and CAOA methodologies, this article suggests the IAOA. To show how applicable IAOA is, its performance has been evaluated using four benchmark functions. The implementation of an IAOA-based ST-SMC for active and reactive power control is addressed in this article, which offers an innovative approach of research. In comparison to PSO-based ST-SMC and CAOA-based ST-SMC, the proposed IAOA-based ST-SMC appears to be superior, with settling time for active and reactive power control at a minimum of 0.01012 s and 0.5075 s. A real-time OPAL-RT 4510 simulator is used to validate the performance results of a 40 kW GCPV system after it has been investigated in the MATLAB environment.

Monitoring internal heat fluxes on Pulsating Heat Pipes using Kalman filter – Numerical and experimental results

The present study proposes an approach to monitor the wall-to-fluid internal heat flux on Pulsating Heat Pipes (PHP), which provides meaningful information about the efficiency and limiting operation conditions of such devices. In this sense, the current work adopts the Kalman Filter (KF) to estimate the heat flux between the working fluid and the internal tube wall along the adiabatic section of a PHP device by solving an inverse heat conduction problem. The KF is a well-known tracking technique, and therefore the current study is attractive due to the possibility of real-time evaluation of internal heat fluxes, a prospect that is extremely difficult to realize by standard whole domain inverse problem techniques. A high-speed and high-resolution infrared camera performs the temperature acquisition on the external wall of the PHP device. Two mathematical heat conduction models are considered: complete and thin-wall models. The complete model determines the temperature and heat flux evolution over time, and the thin-wall model is used to correct the random walk parameter on the KF formulation. Since the time step needed to the KF evolution model is smaller than the measurements acquisition interval, a matrix manipulation is used during the prediction step, reducing the number of mathematical operations. Hence, instead of predicting the states until reaching the measurement times, a proper mathematical manipulation reduces several mathematical operations to a single one. Then, the KF estimation capability is evaluated by considering synthetic data with different noise levels and different heat flux values. Subsequently, real experimental data are employed, and the results are compared with the ones obtained via a standard whole domain technique. The results obtained with the KF presented good visual agreement with the exact solution. Once the KF presents a delayed response, which is a characteristic of some filtering techniques, the errors with synthetic data were calculated offsetting the delay of the estimation in time in order to make a fair comparison, showing a maximum estimation error lower than 36 % considering the highest noise level. The synthetic data considered 20 s of time experiment, and the KF was able to estimate the PHP internal heat flux in less than 12 s, including the smoothing temperature step, showing fast and accurate results. For the real experimental data, the agreement between the KF and a whole domain technique is highly commendable, demonstrating a deviation of 25.5 % between both techniques. Moreover, the KF required significantly less computational time. The proposed methodology for heat flux estimation on PHPs is promising to evaluate their thermal behavior in real-time due to a low CPU time and computational memory required, as well as its simplicity to be implemented, possibly on embarked devices. Such information may therefore provide a thermal indicator of the correct functioning of PHPs in real time applications.