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Keywords = multiplier techniques

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12 pages, 1363 KB  
Article
Physical Properties of New Silica-Based Denture Surface Coating
by Kazuhiro Akutsu-Suyama, Reiko Tokuyama-Toda, Chiaki Tsutsumi-Arai, Chika Terada-Ito, Yoko Iwamiya, Zenji Hiroi, Mitsuhiro Shibayama and Kazuhito Satomura
Nanomaterials 2025, 15(21), 1652; https://doi.org/10.3390/nano15211652 - 29 Oct 2025
Viewed by 110
Abstract
Denture stomatitis is a common issue among denture users, primarily caused by pathogenic microorganisms such as Candida albicans that adhere to and multiply on the denture surface. While previous approaches have focused on incorporating antimicrobial agents into denture base resins, this study introduces [...] Read more.
Denture stomatitis is a common issue among denture users, primarily caused by pathogenic microorganisms such as Candida albicans that adhere to and multiply on the denture surface. While previous approaches have focused on incorporating antimicrobial agents into denture base resins, this study introduces a novel surface coating strategy for polymethyl-methacrylate (PMMA) using hinokitiol—a natural antibacterial and antifungal compound derived from Hiba. This method enables the formation of a uniform silica–resin layer containing hinokitiol, achieved through a simple immersion process. Using X-ray and neutron reflectivity techniques, we discovered that a uniform silica–resin layer could form on PMMA with significant amounts of hinokitiol present. Time-dependent neutron reflectivity analysis revealed the presence of the following two types of hinokitiol molecules within the silica–resin layer: one type desorbs rapidly with weak capture near the surface, and the other desorbs slowly with strong capture near the PMMA interface, facilitated by hydrogen bonding in the silica–resin nanopores. These findings demonstrate a new mechanism for controlled release of antimicrobial agents from denture surfaces and highlight the potential of this coating technique as a practical and effective strategy for preventing denture-related infections. Full article
(This article belongs to the Special Issue Nanobiocomposite Materials: Synthesis, Properties and Applications)
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22 pages, 9138 KB  
Article
Low-Power Radix-22 FFT Processor with Hardware-Optimized Fixed-Width Multipliers and Low-Voltage Memory Buffers
by Gennaro Di Meo, Camillo Perna, Davide De Caro and Antonio G. M. Strollo
Electronics 2025, 14(21), 4217; https://doi.org/10.3390/electronics14214217 - 28 Oct 2025
Viewed by 110
Abstract
In this paper, we propose a novel low-power implementation of the radix-22 Fast Fourier Transform (FFT) processor that exploits optimized multiplications and low-voltage memory buffers. The FFT computation requires complex products between input samples and precomputed coefficients, known as twiddle factors, as [...] Read more.
In this paper, we propose a novel low-power implementation of the radix-22 Fast Fourier Transform (FFT) processor that exploits optimized multiplications and low-voltage memory buffers. The FFT computation requires complex products between input samples and precomputed coefficients, known as twiddle factors, as well as a large number of memory elements to store intermediate signals. To reduce power consumption, we bypass multiplications when twiddle factors are equal to zero or one. Furthermore, we introduce a fixed-width technique that lowers multiplier complexity for non-trivial coefficients by pruning the least significant columns of the partial product matrix and discarding the most significant partial products with low activation probability. To further minimize power consumption, we lower the supply voltage of memory buffers, creating two power domains in the design. Post-synthesis analysis in 28 nm technology shows that the proposed FFT achieves superior SNR and MSE compared to existing implementations, with reductions of 33% in power consumption and 30% in the power-delay product. In an OFDM receiver, the design also achieves optimal bit error rate performance under various levels of channel noise. Full article
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37 pages, 3038 KB  
Article
Research on the Relationship Between Lean Management and Digital Transformation Strategy and Sustainable Development: A Case Study of the Automotive Industry in Taiwan
by Po-Yen Lai and An-Yuan Chang
Sustainability 2025, 17(21), 9572; https://doi.org/10.3390/su17219572 - 28 Oct 2025
Viewed by 150
Abstract
Sustainable Development (SD) has increasingly become a core strategic direction. This study centers on the automotive industry, serving as the primary focus for both research and empirical analysis. If Taiwan’s automotive industry can successfully achieve transformation, it will generate a more advanced multiplier [...] Read more.
Sustainable Development (SD) has increasingly become a core strategic direction. This study centers on the automotive industry, serving as the primary focus for both research and empirical analysis. If Taiwan’s automotive industry can successfully achieve transformation, it will generate a more advanced multiplier effect on the overall development of Taiwan’s industries. The study confirms that Lean Management (LM) and SD can effectively produce synergistic effects. Digital Transformation (DT) is increasingly recognized as a key driver of future business development. Exploring the interrelationships among SD, LM, and DT presents a strategic and practical research direction. Findings from this study suggest that integrating LM and DT can generate synergies that enhance resource efficiency, minimize waste, and improve both environmental and social performance. The primary objective of this study is to develop a structured framework connecting SD, LM, and DT by utilizing the House of Quality (HoQ) from the Quality Function Deployment methodology. The research employs multiple attribute decision-making techniques, including the Fuzzy Delphi Method, the Fuzzy Analytic Hierarchy Process, and the Compromise Ranking Method. By constructing and analyzing two HoQs, the study identifies key LM practices and DT technologies that serve as critical strategies for advancing SD performance. Finally, with regard to LM practices, no previous research has attempted to conduct a hierarchical classification. This study is the first to construct a hierarchical structure for Just-in-Time and Jidoka. Full article
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16 pages, 955 KB  
Article
A Multiplierless Architecture for Image Convolution in Memory
by John Reuben, Felix Zeller, Benjamin Seiler and Dietmar Fey
J. Low Power Electron. Appl. 2025, 15(4), 63; https://doi.org/10.3390/jlpea15040063 - 23 Oct 2025
Viewed by 180
Abstract
Image convolution is a commonly required task in machine vision and Convolution Neural Networks (CNNs). Due to the large data movement required, image convolution can benefit greatly from in-memory computing. However, image convolution is very computationally intensive, requiring [...] Read more.
Image convolution is a commonly required task in machine vision and Convolution Neural Networks (CNNs). Due to the large data movement required, image convolution can benefit greatly from in-memory computing. However, image convolution is very computationally intensive, requiring (n(k1))2 Inner Product (IP) computations for convolution of a n×n image with a k×k kernel. For example, for a convolution of a 224 × 224 image with a 3 × 3 kernel, 49,284 IPs need to be computed, where each IP requires nine multiplications and eight additions. This is a major hurdle for in-memory implementation because in-memory adders and multipliers are extremely slow compared to CMOS multipliers. In this work, we revive an old technique called ‘Distributed Arithmetic’ and judiciously apply it to perform image convolution in memory without area-intensive hard-wired multipliers. Distributed arithmetic performs multiplication using shift-and-add operations, and they are implemented using CMOS circuits in the periphery of ReRAM memory. Compared to Google’s TPU, our in-memory architecture requires 56× less energy while incurring 24× more latency for convolution of a 224 × 224 image with a 3 × 3 filter. Full article
(This article belongs to the Special Issue Energy Consumption Management in Electronic Systems)
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12 pages, 2809 KB  
Article
High-Efficiency Multistage Charge Pump Rectifiers Design
by Ying Wang, Ce Wang and Shiwei Dong
Energies 2025, 18(20), 5350; https://doi.org/10.3390/en18205350 - 11 Oct 2025
Viewed by 295
Abstract
This paper presents an advanced radio frequency (RF)–direct current (DC) power conversion architecture based on a multistage Cockcroft–Walton topology. The proposed design achieves an enhanced voltage conversion ratio while maintaining superior RF-DC conversion efficiency under low input power conditions. To address the inherent [...] Read more.
This paper presents an advanced radio frequency (RF)–direct current (DC) power conversion architecture based on a multistage Cockcroft–Walton topology. The proposed design achieves an enhanced voltage conversion ratio while maintaining superior RF-DC conversion efficiency under low input power conditions. To address the inherent limitations of cascading Cockcroft–Walton topologies with class-F load networks, a novel ground plane isolation technique was developed, which utilizes the reverse-side metallization of the circuit board. A 5.8 GHz two-stage Cockcroft–Walton voltage multiplier rectifier was fabricated and characterized. Measurement results demonstrate that the circuit achieves a maximum output voltage of 7.4 V and a peak conversion efficiency of 70.5% with an input power of only 30 mW, while maintaining stable performance across varying load conditions. A comparison with a two-stage Dickson rectifier reveals that the Cockcroft–Walton rectifier exhibits superior output voltage and conversion efficiency. The proposed architecture delivers significant improvements in power conversion efficiency and voltage multiplication capability compared to conventional designs, establishing a new benchmark for low-power wireless energy harvesting applications. Full article
(This article belongs to the Special Issue Design, Modelling and Analysis for Wireless Power Transfer Systems)
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28 pages, 1955 KB  
Article
Comparative Analysis of High-Voltage High-Frequency Pulse Generation Techniques for Pockels Cells
by Edgard Aleinikov and Vaidotas Barzdenas
Appl. Sci. 2025, 15(19), 10830; https://doi.org/10.3390/app151910830 - 9 Oct 2025
Viewed by 502
Abstract
This paper presents a comprehensive comparative analysis of high-voltage, high-frequency pulse generation techniques for Pockels cell drivers. These drivers are critical in electro-optic systems for laser modulation, where nanosecond-scale voltage pulses with amplitudes of several kilovolts are required. The study reviews key design [...] Read more.
This paper presents a comprehensive comparative analysis of high-voltage, high-frequency pulse generation techniques for Pockels cell drivers. These drivers are critical in electro-optic systems for laser modulation, where nanosecond-scale voltage pulses with amplitudes of several kilovolts are required. The study reviews key design challenges, with particular emphasis on thermal management strategies, including air, liquid, solid-state, and phase-change cooling methods. Different high-voltage, high-frequency pulse generation architectures including vacuum tubes, voltage multipliers, Marx generators, Blumlein structures, pulse-forming networks, Tesla transformers, switching-mode power supplies, solid-state switches, and high-voltage operational amplifiers are systematically evaluated with respect to cost, complexity, stability, and their suitability for driving capacitive loads. The analysis highlights hybrid approaches that integrate solid-state switching with modular multipliers or pulse-forming circuits as offering the best balance of efficiency, compactness, and reliability. The findings provide practical guidelines for developing next-generation high-performance Pockels cell drivers optimized for advanced optical and laser applications. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
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40 pages, 457 KB  
Article
Large-Number Optimization: Exact-Arithmetic Mathematical Programming with Integers and Fractions Beyond Any Bit Limits
by Josef Kallrath
Mathematics 2025, 13(19), 3190; https://doi.org/10.3390/math13193190 - 5 Oct 2025
Viewed by 378
Abstract
Mathematical optimization, in both continuous and discrete forms, is well established and widely applied. This work addresses a gap in the literature by focusing on large-number optimization, where integers or fractions with hundreds of digits occur in decision variables, objective functions, or constraints. [...] Read more.
Mathematical optimization, in both continuous and discrete forms, is well established and widely applied. This work addresses a gap in the literature by focusing on large-number optimization, where integers or fractions with hundreds of digits occur in decision variables, objective functions, or constraints. Such problems challenge standard optimization tools, particularly when exact solutions are required. The suitability of computer algebra systems and high-precision arithmetic software for large-number optimization problems is discussed. Our first contribution is the development of Python implementations of an exact Simplex algorithm and a Branch-and-Bound algorithm for integer linear programming, capable of handling arbitrarily large integers. To test these implementations for correctness, analytic optimal solutions for nine specifically constructed linear, integer linear, and quadratic mixed-integer programming problems are derived. These examples are used to test and verify the developed software and can also serve as benchmarks for future research in large-number optimization. The second contribution concerns constructing partially increasing subsequences of the Collatz sequence. Motivated by this example, we quickly encountered the limits of commercial mixed-integer solvers and instead solved Diophantine equations or applied modular arithmetic techniques to obtain partial Collatz sequences. For any given number J, we obtain a sequence that begins at 2J1 and repeats J times the pattern ud: multiply by 3xj+1 and then divide by 2. Further partially decreasing sequences are designed, which follow the pattern of multiplying by 3xj+1 and then dividing by 2m. The most general J-times increasing patterns (ududd, udududd, …, ududududddd) are constructed using analytic and semi-analytic methods that exploit modular arithmetic in combination with optimization techniques. Full article
(This article belongs to the Special Issue Innovations in Optimization and Operations Research)
11 pages, 823 KB  
Article
Closed-Form Solution Lagrange Multipliers in Worst-Case Performance Optimization Beamforming
by Tengda Pei and Bingnan Pei
Signals 2025, 6(4), 55; https://doi.org/10.3390/signals6040055 - 4 Oct 2025
Viewed by 364
Abstract
This study presents a method for deriving closed-form solutions for Lagrange multipliers in worst-case performance optimization (WCPO) beamforming. By approximating the array-received signal autocorrelation matrix as a rank-1 Hermitian matrix using the low-rank approximation theory, analytical expressions for the Lagrange multipliers are derived. [...] Read more.
This study presents a method for deriving closed-form solutions for Lagrange multipliers in worst-case performance optimization (WCPO) beamforming. By approximating the array-received signal autocorrelation matrix as a rank-1 Hermitian matrix using the low-rank approximation theory, analytical expressions for the Lagrange multipliers are derived. The method was first developed for a single plane wave scenario and then generalized to multiplane wave cases with an autocorrelation matrix rank of N. Simulations demonstrate that the proposed Lagrange multiplier formula exhibits a performance comparable to that of the second-order cone programming (SOCP) method in terms of signal-to-interference-plus-noise ratio (SINR) and direction-of-arrival (DOA) estimation accuracy, while offering a significant reduction in computational complexity. The proposed method requires three orders of magnitude less computation time than the SOCP and has a computational efficiency similar to that of the diagonal loading (DL) technique, outperforming DL in SINR and DOA estimations. Fourier amplitude spectrum analysis revealed that the beamforming filters obtained using the proposed method and the SOCP shared frequency distribution structures similar to the ideal optimal beamformer (MVDR), whereas the DL method exhibited distinct characteristics. The proposed analytical expressions for the Lagrange multipliers provide a valuable tool for implementing robust and real-time adaptive beamforming for practical applications. Full article
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19 pages, 4477 KB  
Article
Non-Contact Heart Rate Variability Monitoring with FMCW Radar via a Novel Signal Processing Algorithm
by Guangyu Cui, Yujie Wang, Xinyi Zhang, Jiale Li, Xinfeng Liu, Bijie Li, Jiayi Wang and Quan Zhang
Sensors 2025, 25(17), 5607; https://doi.org/10.3390/s25175607 - 8 Sep 2025
Viewed by 1284
Abstract
Heart rate variability (HRV), which quantitatively characterizes fluctuations in beat-to-beat intervals, serves as a critical indicator of cardiovascular and autonomic nervous system health. The inherent ability of non-contact methods to eliminate the need for subject contact effectively mitigates user burden and facilitates scalable [...] Read more.
Heart rate variability (HRV), which quantitatively characterizes fluctuations in beat-to-beat intervals, serves as a critical indicator of cardiovascular and autonomic nervous system health. The inherent ability of non-contact methods to eliminate the need for subject contact effectively mitigates user burden and facilitates scalable long-term monitoring, thus attracting considerable research interest in non-contact HRV sensing. In this study, we propose a novel algorithm for HRV extraction utilizing FMCW millimeter-wave radar. First, we developed a calibration-free 3D target positioning module that captures subjects’ micro-motion signals through the integration of digital beamforming, moving target indication filtering, and DBSCAN (Density-Based Spatial Clustering of Applications with Noise) clustering techniques. Second, we established separate phase-based mathematical models for respiratory and cardiac vibrations to enable systematic signal separation. Third, we implemented the Second Order Spectral Sparse Separation Algorithm Using Lagrangian Multipliers, thereby achieving robust heartbeat extraction in the presence of respiratory movements and noise. Heartbeat events are identified via peak detection on the recovered cardiac signal, from which inter-beat intervals and HRV metrics are subsequently derived. Compared to state-of-the-art algorithms and traditional filter bank approaches, the proposed method demonstrated an over 50% reduction in average IBI (Inter-Beat Interval) estimation error, while maintaining consistent accuracy across all test scenarios. However, it should be noted that the method is currently applicable only to scenarios with limited subject movement and has been validated in offline mode, but a discussion addressing these two issues is provided at the end. Full article
(This article belongs to the Section Biomedical Sensors)
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13 pages, 1865 KB  
Article
Social Trusty Algorithm: A New Algorithm for Computing the Trust Score Between All Entities in Social Networks Based on Linear Algebra
by Esra Karadeniz Köse and Ali Karcı
Appl. Sci. 2025, 15(17), 9744; https://doi.org/10.3390/app15179744 - 4 Sep 2025
Viewed by 682
Abstract
The growing importance of social networks has led to increased research into trust estimation and interpretation among network entities. It is important to predict the trust score between users in order to minimize the risks in user interactions. This article enables the identification [...] Read more.
The growing importance of social networks has led to increased research into trust estimation and interpretation among network entities. It is important to predict the trust score between users in order to minimize the risks in user interactions. This article enables the identification of the most reliable and least reliable entities in a network by expressing trust scores numerically. In this paper, the social network is modeled as a graph, and trust scores are calculated by taking the powers of the ratio matrix between entities and summing them. Taking the power of the proportion matrix based on the number of entities in the network requires a lot of arithmetic load. After taking the powers of the eigenvalues of the ratio matrix, these are multiplied by the eigenvector matrix to obtain the power of the ratio matrix. In this way, the arithmetic cost required for calculating trust between entities is reduced. This paper calculates the trust score between entities using linear algebra techniques to reduce the arithmetic load. Trust detection algorithms use shortest paths and similar methods to eliminate paths that are deemed unimportant, which makes the result questionable because of the loss of data. The novelty of this method is that it calculates the trust score without the need for explicit path numbering and without any data loss. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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36 pages, 2219 KB  
Article
Automated Malware Source Code Generation via Uncensored LLMs and Adversarial Evasion of Censored Model
by Raúl Acosta-Bermejo, José Alexis Terrazas-Chavez and Eleazar Aguirre-Anaya
Appl. Sci. 2025, 15(17), 9252; https://doi.org/10.3390/app15179252 - 22 Aug 2025
Viewed by 2974
Abstract
Malicious programs, commonly called malware, have had a pervasive presence in the world for nearly forty years and have continued to evolve and multiply exponentially. On the other hand, there are multiple research works focused on malware detection with different strategies that seem [...] Read more.
Malicious programs, commonly called malware, have had a pervasive presence in the world for nearly forty years and have continued to evolve and multiply exponentially. On the other hand, there are multiple research works focused on malware detection with different strategies that seem to work only temporarily, as new attack tactics and techniques quickly emerge. There are increasing proposals to analyze the problem from the attacker’s perspective, as suggested by MITRE ATT&CK. This article presents a proposal that utilizes Large Language Models (LLMs) to generate malware and understand its generation from the perspective of a red team. It demonstrates how to create malware using current models that incorporate censorship, and a specialized model is trained (fine-tuned) to generate code, enabling it to learn how to create malware. Both scenarios are evaluated using the pass@k metric and a controlled execution environment (malware lab) to prevent its spread. Full article
(This article belongs to the Special Issue Information Security: Threats and Attacks)
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12 pages, 7715 KB  
Article
Hardware Accelerator Design by Using RT-Level Power Optimization Techniques on FPGA for Future AI Mobile Applications
by Achyuth Gundrapally, Yatrik Ashish Shah, Sai Manohar Vemuri and Kyuwon (Ken) Choi
Electronics 2025, 14(16), 3317; https://doi.org/10.3390/electronics14163317 - 20 Aug 2025
Viewed by 981
Abstract
In resource-constrained edge environments—such as mobile devices, IoT systems, and electric vehicles—energy-efficient Convolution Neural Network (CNN) accelerators on mobile Field Programmable Gate Arrays (FPGAs) are gaining significant attention for real-time object detection tasks. This paper presents a low-power implementation of the Tiny YOLOv4 [...] Read more.
In resource-constrained edge environments—such as mobile devices, IoT systems, and electric vehicles—energy-efficient Convolution Neural Network (CNN) accelerators on mobile Field Programmable Gate Arrays (FPGAs) are gaining significant attention for real-time object detection tasks. This paper presents a low-power implementation of the Tiny YOLOv4 object detection model on the Xilinx ZCU104 FPGA platform by using Register Transfer Level (RTL) optimization techniques. We proposed three RTL techniques in the paper: (i) Local Explicit Clock Enable (LECE), (ii) operand isolation, and (iii) Enhanced Clock Gating (ECG). A novel low-power design of Multiply-Accumulate (MAC) operations, which is one of the main components in the AI algorithm, was proposed to eliminate redundant signal switching activities. The Tiny YOLOv4 model, trained on the COCO dataset, was quantized and compiled using the Tensil tool-chain for fixed-point inference deployment. Post-implementation evaluation using Vivado 2022.2 demonstrates around 29.4% reduction in total on-chip power. Our design supports real-time detection throughput while maintaining high accuracy, making it ideal for deployment in battery-constrained environments such as drones, surveillance systems, and autonomous vehicles. These results highlight the effectiveness of RTL-level power optimization for scalable and sustainable edge AI deployment. Full article
(This article belongs to the Special Issue Hardware Acceleration for Machine Learning)
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20 pages, 4156 KB  
Article
A Model-Driven Multi-UAV Spectrum Map Fast Fusion Method for Strongly Correlated Data Environments
by Shengwen Wu, Hui Ding, He Li, Zhipeng Lin, Jie Zeng, Qianhao Gao, Weizhi Zhong and Jun Zhou
Drones 2025, 9(8), 582; https://doi.org/10.3390/drones9080582 - 17 Aug 2025
Viewed by 537
Abstract
Spectrum map fusion has emerged as an effective technique to enhance the accuracy of spectrum map construction. However, many existing fusion methods fail to address the strong correlation between spectrum data, resulting in sub-optimal performance. In this paper, we propose a new multi-unmanned [...] Read more.
Spectrum map fusion has emerged as an effective technique to enhance the accuracy of spectrum map construction. However, many existing fusion methods fail to address the strong correlation between spectrum data, resulting in sub-optimal performance. In this paper, we propose a new multi-unmanned aerial vehicle (UAV) spectrum map fusion method based on differential ridge regression. We first construct spectrum maps of UAVs by using differential features of spectrum data. Next, we present a spectrum map fusion model by leveraging the spatial distribution characteristic of spectrum data. To reduce the sensitivity of the fusion model to the strongly correlated data, a new map fusion regularization term is designed, which introduces l2-norm to constrain the fusion regularization parameters and compress the ridge regression coefficient sizes. As a result, accurate spectrum maps can be constructed for the environments with highly correlated spectrum data. We then formulate a model-driven solution to the spectrum map fusion problem and derive its lower bound. By combining the propagation characteristics of the spectrum signal with the developed Lagrange duality, we can guarantee the convergence of map fusion processing while enhancing the convergence rate. Finally, we propose an accelerated maximally split alternating directions method of multipliers (AMS-ADMM) to reduce the computational complexity of spectrum map construction. Simulation results demonstrate that our proposed method can effectively eliminate external noise interference and outliers, and achieve an accuracy improvement of more than 27% compared to state-of-the-art fusion methods in spectrum map construction with low complexity. Full article
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33 pages, 1196 KB  
Article
Theoretical Formulations of Integral-Type Frequency–Amplitude Relationships for Second-Order Nonlinear Oscillators
by Chein-Shan Liu, Chia-Cheng Tsai and Chih-Wen Chang
Vibration 2025, 8(3), 45; https://doi.org/10.3390/vibration8030045 - 11 Aug 2025
Cited by 1 | Viewed by 1036
Abstract
The development of simple and yet accurate formulations of frequency–amplitude relationships for non-conservative nonlinear oscillators is an important issue. The present paper is concerned with integral-type frequency–amplitude formulas in the dimensionless time domain and time domain to accurately determine vibrational frequencies of nonlinear [...] Read more.
The development of simple and yet accurate formulations of frequency–amplitude relationships for non-conservative nonlinear oscillators is an important issue. The present paper is concerned with integral-type frequency–amplitude formulas in the dimensionless time domain and time domain to accurately determine vibrational frequencies of nonlinear oscillators. The novel formulation is a balance of kinetic energy and the work during motion of the nonlinear oscillator within one period; its generalized formulation permits a weight function to appear in the integral formula. The exact values of frequencies can be obtained when exact solutions are inserted into the formulas. In general, the exact solution is not available; hence, low-order periodic functions as trial solutions are inserted into the formulas to obtain approximate values of true frequencies. For conservative nonlinear oscillators, a powerful technique is developed in terms of a weighted integral formula in the spatial domain, which is directly derived from the governing ordinary differential equation (ODE) multiplied by a weight function, and integrating the resulting equation after inserting a general trial ODE to acquire accurate frequency. The free parameter is involved in the frequency–amplitude formula, whose optimal value is achieved by minimizing the absolute error to fulfill the periodicity conditions. Several examples involving two typical non-conservative nonlinear oscillators are explored to display the effectiveness and accuracy of the proposed integral-type formulations. Full article
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17 pages, 438 KB  
Article
Analytic Solutions and Conservation Laws of a 2D Generalized Fifth-Order KdV Equation with Power Law Nonlinearity Describing Motions in Shallow Water Under a Gravity Field of Long Waves
by Chaudry Masood Khalique and Boikanyo Pretty Sebogodi
AppliedMath 2025, 5(3), 96; https://doi.org/10.3390/appliedmath5030096 - 31 Jul 2025
Viewed by 369
Abstract
The Korteweg–de Vries (KdV) equation is a nonlinear evolution equation that reflects a wide variety of dispersive wave occurrences with limited amplitude. It has also been used to describe a range of major physical phenomena, such as shallow water waves that interact weakly [...] Read more.
The Korteweg–de Vries (KdV) equation is a nonlinear evolution equation that reflects a wide variety of dispersive wave occurrences with limited amplitude. It has also been used to describe a range of major physical phenomena, such as shallow water waves that interact weakly and nonlinearly, acoustic waves on a crystal lattice, lengthy internal waves in density-graded oceans, and ion acoustic waves in plasma. The KdV equation is one of the most well-known soliton models, and it provides a good platform for further research into other equations. The KdV equation has several forms. The aim of this study is to introduce and investigate a (2+1)-dimensional generalized fifth-order KdV equation with power law nonlinearity (gFKdVp). The research methodology employed is the Lie group analysis. Using the point symmetries of the gFKdVp equation, we transform this equation into several nonlinear ordinary differential equations (ODEs), which we solve by employing different strategies that include Kudryashov’s method, the (G/G) expansion method, and the power series expansion method. To demonstrate the physical behavior of the equation, 3D, density, and 2D graphs of the obtained solutions are presented. Finally, utilizing the multiplier technique and Ibragimov’s method, we derive conserved vectors of the gFKdVp equation. These include the conservation of energy and momentum. Thus, the major conclusion of the study is that analytic solutions and conservation laws of the gFKdVp equation are determined. Full article
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