ON PRESENTATION OF GELFOND—LEONTIEV OPERATORS OF GENERALIZED DIFFERENTIATION IN SIMPLY CONNECTED REGION by Alexander Vasilyevich Bratishchev

“…It is known to be presented as an operator of general complex convolution. The convolution kernel is generated by the many-valued function of one variable. …”
Get full text

On Symmetrical Sonin Kernels in Terms of Hypergeometric-Type Functions by Yuri Luchko

“…In this paper, a new class of kernels of integral transforms of the Laplace convolution type that we named symmetrical Sonin kernels is introduced and investigated. …”
Get full text

Weed Detection Algorithms in Rice Fields Based on Improved YOLOv10n by Yan Li, Zhonghui Guo, Yan Sun, Xiaoan Chen, Yingli Cao

“…Accurate weed detection is vital for implementing variable spraying with unmanned aerial vehicles (UAV) for weed control. …”
Get full text

MSVMD-Informer: A Multi-Variate Multi-Scale Method to Wind Power Prediction by Zhijian Liu, Jikai Chen, Hang Dong, Zizhuo Wang

“…Existing prediction methods demonstrate insufficient integration of multi-variate features, such as wind speed, temperature, and humidity, along with inadequate extraction of correlations between variables. This paper proposes a novel multi-variate multi-scale wind power prediction method named multi-scale variational mode decomposition informer (MSVMD-Informer). …”
Get full text

KERNEL DETERMINATION PROBLEM FOR ONE PARABOLIC EQUATION WITH MEMORY by Durdimurod K. Durdiev, Javlon Z. Nuriddinov

“…This paper studies the inverse problem of determining a multidimensional kernel function of an integral term which depends on the time variable \(t\) and \((n-1)\)-dimensional space variable \(x'= \left(x_1,\ldots, x_ {n-1}\right)\) in the \(n\)-dimensional diffusion equation with a time-variable coefficient at the Laplacian of a direct problem solution. …”
Get full text

A small underwater object detection model with enhanced feature extraction and fusion by Tao Li, Yijin Gang, Sumin Li, Yizi Shang

“…Next, a variable kernel convolution (VKConv) is proposed to dynamically adjust the convolution kernel size, enabling better multi-scale feature extraction. …”
Get full text

On variational formulations of inner boundary value problems for infinite systems of elliptic equations of special kind by Yu. A. Muzychuk, R. S. Chapko

“…We consider boundary value problems for infinite triangular systems of elliptic equations with variable coefficients in 3d Lipschitz domains. Variational formulations of Dirichlet, Neumann and Robin problems are received and their well posedness in corresponding Sobolev spaces is established. …”
Get full text

Water Quality Prediction Method Based on Reinforcement Learning Graph Neural Network by Mingming Yan, Zhe Wang

“…However, existing methods face two main challenges: the interaction between water quality variables and the environment is often overlooked, and even when considered, it is not effectively utilized. …”
Get full text

Real-time classroom student behavior detection based on improved YOLOv8s by Xiaojing Sheng, Suqiang Li, Sixian Chan

“…However, the field still faces specific challenges, primarily concerning the accuracy of identifying student behaviors within complex and variable classroom environments, as well as the real-time capabilities of detection algorithms. …”
Get full text

A Lightweight Person Detector for Surveillance Footage Based on YOLOv8n by Qicheng Wang, Guoqiang Feng, Zongzhe Li

“…Next, a heterogeneous PAFPN with improved MSBlock was formed using heterogeneous convolution kernels. Finally, AKConv, a variable kernel convolution, was applied to further reduce the number of parameters and the computational cost while improving accuracy. …”
Get full text

OPTIMAL CONTROL OF INVESTMENTS AROUND COURNOT POINT by Y. Aganin

“…The equations of dynamics of variables for equilibrium, developing and crisis markets in a linear approximation are obtained. …”
Get full text

Application of Modified Laplace Variational Iteration Hybrid Approach for Solving Time-Fractional Fourth-Order Parabolic PDEs by Mehari Fentahun Endalew, Xiaoming Zhang

“…The current study is aimed at obtaining analytical solutions of fourth-order parabolic partial differential equations of time-fractional derivative with variable coefficients. The modified Laplace variational iteration approach and the homotopy perturbation method were used to treat nonlinear, fourth-order, time-fractional partial differential equations with time-fractional derivatives. …”
Get full text

A Wind Power Forecasting Method Based on Lightweight Representation Learning and Multivariate Feature Mixing by Chudong Shan, Shuai Liu, Shuangjian Peng, Zhihong Huang, Yuanjun Zuo, Wenjing Zhang, Jian Xiao

“…However, the forecasting of wind power is subject to the complex influence of multiple variable features and their interrelationships, which poses challenges to traditional forecasting methods. …”
Get full text

Study on Color Detection of Korla Fragrant Pears by Near-Infrared Spectroscopy Combined with PLSR by Yifan Xia, Yang Liu, Hong Zhang, Jikai Che, Qing Liang

“…The full-spectrum data were pre-processed using six methods: Savitzky–Golay convolution smoothing (SGCS), Savitzky–Golay convolution derivative (SGCD), multiplicative scatter correction (MSC), vector normalization (VN), min–max normalization (MMN), and standard normal variate transformation (SNV). …”
Get full text

Intrusion Detection System to Advance Internet of Things Infrastructure-Based Deep Learning Algorithms by Hasan Alkahtani, Theyazn H. H. Aldhyani

“…The proposed framework attained the desired performance on a new variable dataset, and the system will be implemented in our university IoT environment. …”
Get full text

SIGNAL DETECTION WITH UNKNOWN PARAMETERS by Y. A. Sidorkina, V. V. Antipov

“…The effectiveness of this algorithm is determined by the sampling distribution of the maximum values of random variables distributed according to Rayleigh.…”
Get full text

A time-domain finite element formulation of the equivalent fluid model for the acoustic wave equation by Maurerlehner Paul, Mayrhofer Dominik, Kaltenbacher Manfred, Schoder Stefan

“…When transforming the acoustic wave equation for the EF model from the frequency domain to the time domain, convolution integrals arise. The auxiliary differential equation (ADE) method is used to circumvent the direct calculation of these convolution integrals. …”
Get full text

Analysis of Nonviscous Oscillators Based on the Damping Model Perturbation by Mario Lázaro, César F. Casanova, Ignacio Ferrer, Pedro Martín

“…After choosing one of them as independent variable, the key idea of the current paper is to obtain a differential equation whose solution can be considered, under certain conditions, a good approximation. …”
Get full text

A Massive Image Recognition Algorithm Based on Attribute Modelling and Knowledge Acquisition by Guohua Li, An Liu, Huajie Shen

“…To address the problem of incomplete model inputs due to the presence of missing values, we propose to treat and describe the missing values as system-level variables and realize the alternate update of network parameters and dynamic filling of missing values through iterative learning among subnets. …”
Get full text

Quantum Integral Inequalities with Respect to Raina’s Function via Coordinated Generalized Ψ-Convex Functions with Applications by Saima Rashid, Saad Ihsan Butt, Shazia Kanwal, Hijaz Ahmad, Miao-Kun Wang

“…In accordance with the quantum calculus, we introduced the two variable forms of Hermite-Hadamard- (HH-) type inequality over finite rectangles for generalized Ψ-convex functions. …”
Get full text