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Given a graph G and an integer [Formula: see text], a spanning subgraph H of G is called a [Formula: see text]-factor of G if every component of H is a path with at least k vertices. A graph G is [Formula: see text]-factor avoidable if for every edge [Formula: see text], G has a [Formula: see text]-factor excluding e. A graph G is said to be [Formula: see text]-factor critical avoidable if the graph [Formula: see text] is [Formula: see text]-factor avoidable for any [Formula: see text] with [Formula: see text]. Here we study the sharp bounds of toughness and isolated toughness conditions for the existence of [Formula: see text]-factor critical avoidable graphs. In view of graph theory approaches, this paper mainly contributes to verify that (i) An [Formula: see text]-connected graph is [Formula: see text]-factor critical avoidable if its toughness [Formula: see text]; (ii) An [Formula: see text]-connected graph is [Formula: see text]-factor critical avoidable if its isolated toughness [Formula: see text].

This study developed a low-salt Perilla shrimp paste by combining traditional preparation with the addition of yeast strain co-fermentation using oriental white shrimp and Perilla as raw materials. The effects of Perilla addition, salt addition, fermentation time and inoculation amount of koji seeds on the formula of low-salt Perilla shrimp paste were studied utilize the optimal process prediction obtained from Box-Behnken and make adjustments to the predicted process conditions based on actual production conditions. The results showed that the co-fermentation with yeast could effectively reduce the amount of salt added. The results indicated that the amount of shrimp added was fixed at 300 g. The sensory evaluation of the low-salt Perilla shrimp paste prepared under the conditions of 35% Perilla addition, 10% salt addition, and 3.5% yeast inoculation was 87.94 under the conditions of fermentation time of 5 d at 32 ℃. Its relative content of volatile flavor substances reached 97.82%, including 6 esters, 11 alcohols, 9 acids and 5 aldehydes. The contents of amino acid nitrogen, salt, protein, moisture and ash all met the requirements of SC/T 3602-2016 industry standard. Among them, the salt content was 106 mg/100 g, which was lower than the requirement of GB/T 23789-2009 national standard for salt content not higher than 120 mg/100 g. Compared to products in the market, it featured low salt and high protein content. The formulated products in this study are low-salt foods. It combines the freshness and flavor of shrimp paste with the slightly pungent and sweet aroma of Perilla.

Accurate diagnosis of plant diseases is crucial for crop health. This study introduces the EDA–ViT model, a Vision Transformer (ViT)-based approach that integrates adaptive entropy-based data augmentation for diagnosing custard apple (Annona squamosa) diseases. Traditional models like convolutional neural network and ViT face challenges with local feature extraction and large dataset requirements. EDA–ViT overcomes these by using a multi-scale weighted feature aggregation and a feature interaction module, enhancing both local and global feature extraction. The adaptive data augmentation method refines the training process, boosting accuracy and robustness. With a dataset of 8226 images, EDA–ViT achieved a classification accuracy of 96.58%, an F1 score of 96.10%, and a Matthews Correlation Coefficient (MCC) of 92.24%, outperforming other models. The inclusion of the Deformable Multi-head Self-Attention (DMSA) mechanism further enhanced feature capture. Ablation studies revealed that the adaptive augmentation contributed to a 0.56% accuracy improvement and a 0.34% increase in MCC. In summary, EDA–ViT presents an innovative solution for custard apple disease diagnosis, with potential applications in broader agricultural disease detection, ultimately aiding precision agriculture and crop health management.

Under the new demand model of Agriculture 4.0, automated spraying is a very complex task in precision agriculture, which needs to be combined with a computerized vision perception system to distinguish the plant leaf density and execute the spraying operation in real-time accordingly. Aiming at the accurate determination of grape leaf density, an image leaf density determination method based on the lightweight Vision Transformer (ViT) architecture is proposed, which designs a fusion data augmentation method containing a dual augmentation spatial extension and weather data augmentation method, where the former adopts the pixel augmentation and spatial augmentation for the original image processing, and the latter realizes the data augmentation from the empirical point of view adapted to the agricultural operation environment, and fuses the two in order to expand the sample capacity of the grape leaf density image, which then enhances the model's generalization ability and robustness. The lightweight ViT model has self-attention that can automatically and efficiently extract high-frequency local feature representations and use the two-branch structure to mix high-frequency and low-frequency information to form grapevine-leaf density features in the region of interest. The semantic analysis of the feature extraction layer is parsed using t-SNE and histogram methods, which improves the transparency of the model from the multidimensional with frequency domain distribution space. The experimental results show that the fusion data augmentation method can effectively improve the model recognition accuracy, and the accuracy of comparing the included data augmentation methods is improved by 0.55 % and 3.46 %, respectively. The accuracy of recognizing all four types of grape leaf densities exceeded 94 %, and the MCC reached 90.39 %. In addition, the proposed lightweight ViT improves the accuracy by at least 0.34 % with FLOPs of only 0.6 G compared to the popular MobileViT. The proposed method of this work has high recognition speed and accuracy, which can provide practical technical support for plant protection spraying robots and improve the profitability of growers based on the reduction of pesticide residues.

As global carbon reduction initiatives progress and the new energy sector rapidly develops, photovoltaic (PV) power generation is playing an increasingly significant role in renewable energy. Accurate PV output forecasting, influenced by meteorological factors, is essential for efficient energy management. This paper presents an optimal hybrid forecasting strategy, integrating bidirectional temporal convolutional networks (BiTCN), dynamic convolution (DC), bidirectional long short-term memory networks (BiLSTM), and a novel mixed-state space model (Mixed-SSM). The mixed-SSM combines the state space model (SSM), multilayer perceptron (MLP), and multi-head self-attention mechanism (MHSA) to capture complementary temporal, nonlinear, and long-term features. Pearson and Spearman correlation analyses are used to select features strongly correlated with PV output, improving the prediction correlation coefficient (R2) by at least 0.87%. The K-Means++ algorithm further enhances input data features, achieving a maximum R2 of 86.9% and a positive R2 gain of 6.62%. Compared with BiTCN variants such as BiTCN-BiGRU, BiTCN-transformer, and BiTCN-LSTM, the proposed method delivers a mean absolute error (MAE) of 1.1%, root mean squared error (RMSE) of 1.2%, and an R2 of 89.1%. These results demonstrate the model’s effectiveness in forecasting PV power and supporting low-carbon, safe grid operation.

AbstractA graph G is called a [Formula: see text]-factor deleted graph if G – e has a [Formula: see text]-factor for any [Formula: see text] A graph G is [Formula: see text]-factor critical deleted if for every subset [Formula: see text] with [Formula: see text] the graph [Formula: see text] is [Formula: see text]-factor deleted. Zhou, Bian and Pan [Discrete Appl. Math. (2021) in press] showed that an [Formula: see text]-connected graph G is [Formula: see text]-factor critical deleted if its binding number [Formula: see text] In this paper, we give a new binding number condition for [Formula: see text]-factor critical deleted graphs, which improves the above result.

The accurate detection and identification of plant diseases is an essential step in the development of intelligent and modernized agricultural production. This study proposes a deep learning model (PPLC-Net) incorporating dilated convolution, multi-level attention mechanism, and GAP layers. The model uses novel weather data augmentation to expand the sample size to enhance the generalization and robustness of feature extraction. The feature extraction network extends the perceptual field of the convolutional domain using sawtooth dilated convolution with a variable expansion rate, which can effectively address the problem of insufficient spatial information extraction. The lightweight CBAM attention mechanism is located in the middle layer of the feature extraction network. It is used to enhance the information representation of the model. the GAP layer prevents over-fitting of the model by reducing the number and complexity of parameters computed by the network. The validation of the retained test dataset shows that the recognition accuracy and F1 score of the PPLC-Net model are 99.702% and 98.442%, and the number of parameters and FLOPs are 15.486 M and 5.338G, respectively, which can meet the requirements of accurate and fast recognition. In addition, the proposed combined CAM visualization method can fully validate the effectiveness of the proposed model.

Detecting and eliminating sprouted potatoes is a basic measure before potato storage, which can effectively improve the quality of potatoes before storage and reduce economic losses due to potato spoilage and decay. In this paper, we propose an improved YOLOv5-based sprouted potato detection model for detecting and grading sprouted potatoes in complex scenarios. By replacing Conv with CrossConv in the C3 module, the feature similarity loss problem of the fusion process is improved, and the feature representation is enhanced. SPP is improved using fast spatial pyramid pooling to reduce feature fusion parameters and speed up feature fusion. The 9-Mosaic data augmentation algorithm improves the model generalization ability; the anchor points are reconstructed using the genetic algorithm $k$ -means to enhance small target features, and then multi-scale training and hyperparameter evolution mechanisms are used to improve the accuracy. The experimental results show that the improved model has 90.14% recognition accuracy and 88.1% mAP, and the mAP is 4.6%, 7.5%, and 12.4% higher compared with SSD, YOLOv5, and YOLOv4, respectively. In summary, the improved YOLOv5 model, with good detection accuracy and effectiveness, can meet the requirements of rapid grading in automatic potato sorting lines.

Crop leaf diseases can reflect the current health status of the crop, and the rapid and automatic detection of field diseases has become one of the difficulties in the process of industrialization of agriculture. In the widespread application of various machine learning techniques, recognition time consumption and accuracy remain the main challenges in moving agriculture toward industrialization. This article proposes a novel network architecture called YOLO V5-CAcT to identify crop diseases. The fast and efficient lightweight YOLO V5 is chosen as the base network. Repeated Augmentation, FocalLoss, and SmoothBCE strategies improve the model robustness and combat the positive and negative sample ratio imbalance problem. Early Stopping is used to improve the convergence of the model. We use two technical routes of model pruning, knowledge distillation and memory activation parameter compression ActNN for model training and identification under different hardware conditions. Finally, we use simplified operators with INT8 quantization for further optimization and deployment in the deep learning inference platform NCNN to form an industrial-grade solution. In addition, some samples from the Plant Village and AI Challenger datasets were applied to build our dataset. The average recognition accuracy of 94.24% was achieved in images of 59 crop disease categories for 10 crop species, with an average inference time of 1.563 ms per sample and model size of only 2 MB, reducing the model size by 88% and the inference time by 72% compared with the original model, with significant performance advantages. Therefore, this study can provide a solid theoretical basis for solving the common problems in current agricultural disease image detection. At the same time, the advantages in terms of accuracy and computational cost can meet the needs of agricultural industrialization.

In this paper, we shall study unilateral global bifurcation phenomenon for the following homogeneous Kirchhoff type problem \begin{equation*} \begin{cases} -\left(\int_0^1 \left\vert u'\right\vert^2\,dx\right)u''=\lambda u^3+h(x,u,\lambda)&\text{in}\,\, (0,1),\\ u(0)=u(1)=0. \end{cases} \end{equation*} As application of bifurcation result, we shall determine the interval of $\lambda$ in which there exist nodal solutions for the following homogeneous Kirchhoff type problem \begin{equation*} \begin{cases} -\left(\int_0^1 \left\vert u'\right\vert^2\,dx\right) u''=\lambda f(x,u)&\text{in}\,\, (0,1),\\ u(0)=u(1)=0, \end{cases} \end{equation*} where $f$ is asymptotically cubic at zero and infinity. To do this, we also establish a complete characterization of the spectrum of a homogeneous nonlocal eigenvalue problem.

In this article, we consider a Dancer-type unilateral global bifurcation for the Kirchhoff-type problem $$\displaylines{ -\Big(a+b\int_0^1 | u'|^2\,dx\Big)u'' =\lambda u+h(x,u,\lambda)\quad\text{in } (0,1),\cr u(0)=u(1)=0. }$$ Under natural hypotheses on h, we show that $(a\lambda_k,0)$ is a bifurcation point of the above problem. As applications we determine the interval of $\lambda$, in which there exist nodal solutions for the Kirchhoff-type problem $$\displaylines{ -\Big(a+b\int_0^1 | u'|^2\,dx\Big) u'' =\lambda f(x,u)\quad\text{in } (0,1),\cr u(0)=u(1)=0, }$$ where f is asymptotically linear at zero and is asymptotically 3-linear at infinity. To do this, we also establish a complete characterization of the spectrum of a nonlocal eigenvalue problem.

In recent decades, the existing IP network has little innovation, SDN may be the next round of the network technology revolution, and it will bring the huge market potential. From the SDN archiecture by analyzing the OpenDaylight project and the concept of bilateral market, a SDN resource management architecture based on bilateral market and a multi-platform selection algorithm based on the extension of FPM were proposed. In the simulation test, the advantages of the architecture were proved through task completion time and cost on single or double platform under different task allocation strategy, and the reasonable allocation of resources was implemented and the reliability in SDN was improved.

We study the unilateral global bifurcation for the nonlinear Sturm-Liouville problem $$\displaylines{ -(pu')'+qu=\lambda au+af(x,u,u',\lambda)+g(x,u,u',\lambda)\quad x\in(0,1),\cr b_0u(0)+c_0u'(0)=0,\quad b_1u(1)+c_1u'(1)=0, }$$ where $a\in C([0, 1], [0,+\infty))$ and $a(x)\not\equiv 0$ on any subinterval of $[0, 1]$, $f,g\in C([0,1]\times\mathbb{R}^3,\mathbb{R})$ and f is not necessarily differentiable at the origin or infinity with respect to u. Some applications are given to nonlinear second-order two-point boundary-value problems. This article is a continuation of [8].

In this paper, we study unilateral global bifurcation which bifurcates from the trivial solutions axis or from infinity for nonlinear Sturm--Liouville problems of the form \begin{equation} \left\{ \begin{array}{l} -\left(pu'\right)'+qu=\lambda au+af\left(x,u,u',\lambda\right)+g\left(x,u,u',\lambda\right)\,\,\text{for}\,\, x\in(0,1),\\ b_0u(0)+c_0u'(0)=0,\\ b_1u(1)+c_1u'(1)=0, \end{array} \right.\nonumber \end{equation} where $a\in C([0, 1], [0,+\infty))$ and $a(x)\not\equiv 0$ on any subinterval of $[0, 1]$, $f,g\in C([0,1]\times\mathbb{R}^3,\mathbb{R})$. Suppose that $f$ and $g$ satisfy \begin{equation} \vert f(x,\xi,\eta,\lambda)\vert\leq M_0\vert \xi\vert+M_1\vert \eta\vert,\,\, \forall x\in [0,1]\,\,\text{and}\,\,\lambda \in\mathbb{R}, \nonumber \end{equation} \begin{equation} g(x,\xi,\eta,\lambda)=o(\vert \xi\vert+\vert \eta\vert),\,\, \text{uniformly in}\,\, x\in [0,1]\,\,\text{and}\,\,\lambda \in \Lambda,\nonumber \end{equation} as either $\vert \xi\vert+\vert \eta\vert\rightarrow 0$ or $\vert \xi\vert+\vert \eta\vert\rightarrow +\infty$, for some constants $M_0$, $M_1$, and any bounded interval $\Lambda$.

In this article, we study elliptic problems with discontinuous nonlinearities involving the p-Laplacian both in bounded and unbounded domains. We prove that there exists a global branch of positive solutions under some suitable assumptions of the nonlinearities. Our results extend the corresponding ones of the Laplacian due to Ambrosetti, et al.

Existence of solutions and of extremal random solutions are proved for periodic boundary-value problems of fourth-order ordinary random differential equations. Our investigation is done in the space of continuous real-valued functions defined on closed and bounded intervals. Also we study the applications of the random version of a nonlinear alternative of Leray-Schauder type and an algebraic random fixed point theorem by Dhage.

In this paper, we study a class of nonlocal semilinear elliptic problems with inhomogeneous strong Allee effect. By means of variational approach, we prove that the problem has at least two positive solutions for large $\lambda$ under suitable hypotheses about nonlinearity. We also prove some nonexistence results. In particular, we give a positive answer to the conjecture of Liu-Wang-Shi.

This article concerns the existence and multiplicity of solutions for a p(x)-Kirchhoff-type systems with Dirichlet boundary condition. By a direct variational approach and the theory of the variable exponent Sobolev spaces, under growth conditions on the reaction terms, we establish the existence and multiplicity of solutions.

In this article we consider the differential inclusion $$displaylines{ -hbox{div}(| abla u|^{p(x)-2} abla u)in partial F(x,u) quadhbox{in }Omega,cr u=0 quad hbox{on }partial Omega }$$ which involves the $p(x)$-Laplacian. By applying the nonsmooth Mountain Pass Theorem, we obtain at least one nontrivial solution; and by applying the symmetric Mountain Pass Theorem, we obtain k-pairs of nontrivial solutions in $W_{0}^{1,p(x)}(Omega)$.

We prove existence and multiplicity of positive solutions for semipositone problems involving p-Laplacian in a bounded smooth domain of ℝN under the cases of sublinear and superlinear nonlinearities term.

We consider the systems of (-1)mu(2m)=λu+λv+uf(t,u,v), t∈(0,1), u(2i)(0)=u(2i)(1)=0, and 0≤i≤m-1, (-1)mv(2m)=μu+μv+vg(t, u,v), t∈(0,1), v(2i)(0)=v(2i)(1)=0, 0≤i≤m-1, where λ,μ∈R are real parameters. f,g:[0,1]×R2→R are Ck,k≥3 functions and f(t,0,0)=g(t,0,0)=0,t∈[0,1]. It will be shown that if the functions, f and g are “generic” then the solution set of the systems consists of a countable collection of 2-dimensional, Ck manifolds.