The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

Solving the subset sum problem by the quantum Ising model with variational quantum optimization based on conditional values at risk

The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or scheduling,and integer partitions.An accurate search algorithm with polynomial time complexity has not been found,which makes it challenging to be solved on classical computers.To effectively solve this problem,we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk.The proposed model needs only n qubits to encode 2ndimensional search space,which can effectively save the encoding quantum resources.The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise,and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era.We investigate the effects of the scalability,the variational ansatz type,the variational depth,and noise on the model.Moreover,we also discuss the performance of the model under different conditional values at risk.Through computer simulation,the scale can reach more than nine qubits.By selecting the noise type,we construct simulators with different QVs and study the performance of the model with them.In addition,we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem.This model provides a new perspective for solving the subset sum problem.

Necessary Optimality Conditions for Multi-Objective Semi-Infinite Variational Problem

In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.

THE ELLIPTIC VARIATIONAL INEQUALITIES WITH DOUBLE DEGENERATE AND GENERAL GROWTH CONDITIONS

A class of quasilinear elliptic variational inequalities with double degenerate is discussed in this paper. We extend the Keldys-Fichera boundary value problem and the first boundary problem of degenerate elliptic equation to the variationalinequalities. We establish the existence and uniqueness of the weak solution of ocrresspending problem under nonstandard growth conditions.

Exploring Variational Auto-encoder Architectures, Configurations, and Datasets for Generative Music Explainable AI

Generative AI models for music and the arts in general are increasingly complex and hard to understand.The field of ex-plainable AI(XAI)seeks to make complex and opaque AI models such as neural networks more understandable to people.One ap-proach to making generative AI models more understandable is to impose a small number of semantically meaningful attributes on gen-erative AI models.This paper contributes a systematic examination of the impact that different combinations of variational auto-en-coder models(measureVAE and adversarialVAE),configurations of latent space in the AI model(from 4 to 256 latent dimensions),and training datasets(Irish folk,Turkish folk,classical,and pop)have on music generation performance when 2 or 4 meaningful musical at-tributes are imposed on the generative model.To date,there have been no systematic comparisons of such models at this level of com-binatorial detail.Our findings show that measureVAE has better reconstruction performance than adversarialVAE which has better musical attribute independence.Results demonstrate that measureVAE was able to generate music across music genres with inter-pretable musical dimensions of control,and performs best with low complexity music such as pop and rock.We recommend that a 32 or 64 latent dimensional space is optimal for 4 regularised dimensions when using measureVAE to generate music across genres.Our res-ults are the first detailed comparisons of configurations of state-of-the-art generative AI models for music and can be used to help select and configure AI models,musical features,and datasets for more understandable generation of music.

A novel deep learning framework with variational auto-encoder for indoor air quality prediction

Exposure to poor indoor air conditions poses significant risks to human health, increasing morbidity and mortality rates. Soft measurement modeling is suitable for stable and accurate monitoring of air pollutants and improving air quality. Based on partial least squares (PLS), we propose an indoor air quality prediction model that utilizes variational auto-encoder regression (VAER) algorithm. To reduce the negative effects of noise, latent variables in the original data are extracted by PLS in the first step. Then, the extracted variables are used as inputs to VAER, which improve the accuracy and robustness of the model. Through comparative analysis with traditional methods, we demonstrate the superior performance of our PLS-VAER model, which exhibits improved prediction performance and stability. The root mean square error (RMSE) of PLS-VAER is reduced by 14.71%, 26.47%, and 12.50% compared to single VAER, PLS-SVR, and PLS-ANN, respectively. Additionally, the coefficient of determination (R2) of PLS-VAER improves by 13.70%, 30.09%, and 11.25% compared to single VAER, PLS-SVR, and PLS-ANN, respectively. This research offers an innovative and environmentally-friendly approach to monitor and improve indoor air quality.

Variational Calculus With Conformable Fractional Derivatives

Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of invariance are obtained. As particular cases, we prove fractional versions of Noether's symmetry theorem. Invariant conditions for fractional optimal control problems, using the Hamiltonian formalism, are also investigated. As an example of potential application in Physics, we show that with conformable derivatives it is possible to formulate an Action Principle for particles under frictional forces that is far simpler than the one obtained with classical fractional derivatives.

Stable Perturbed Algorithms for a New Class of Generalized Nonlinear Implicit Quasi Variational Inclusions in Banach Spaces

In this work, a new class of variational inclusion involving T-accretive operators in Banach spaces is introduced and studied. New iterative algorithms for stability for their class of variational inclusions and its convergence results are established.

A New Variational Formulation for a Kind of Reaction-diffusion Problem in Broken Sobolev Space

In this paper, a new variational formulation for a reaction-diffusion problem in broken Sobolev space is proposed. And the new formulation in the broken Sobolev space will be proved that it is well-posed and equivalent to the standard Galerkin variational formulation. The method will be helpful to easily solve the original partial differential equation numerically. And the method is novel and interesting, which can be used to deal with some complicated problem, such as the low regularity problem, the differential-integral problem and so on.

Variational Approach for the Adapted Solution of Backw ard Stochastic Differential Equations with Locally Lipschitz Diffusion Coefficients

One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, a new approach method is proposed and the existence of the solution was proved for the BSDEs if the diffusion coefficients satisfy the locally Lipschitz condition. In the special case the solution was a Brownian bridge. The uniqueness is also considered in the meaning of "F0-integrable equivalent class" . The new approach method would give us an efficient way to control the main object instead of the "noise".

Variation Trends of Dust Storms in Relation to Meteorological Conditions and Anthropogenic Impacts in the Northeast Edge of the Taklimakan Desert, China

To reveal the multivariate relationships between man-made and meteorological factors on dust storm frequency, the LUCC data, NDVI remote sensing data and meteorological data for the period of 1983-2013 were combined with dust storm frequency data, and the possible impacts of meteorological and anthropogenic factors on dust storm frequency were analyzed by using regression analysis and PCA (Principal Component Analysis). Results show that the inter-annual dust storm frequency increased gradually. In particular, an increasing trend in recent years, after 2009, is conspicuous. The monthly frequency of dust storms shows higher values between the months of February and May, with the highest mean number of events occurring in April, which accounts for 29% of the annual dust storm frequency. The annual dust storm frequency is positively correlated with wind speed and negatively correlated with precipitation;the monthly dust storm frequency is positively correlated with wind speed, but no significant correlation can be found with precipitation. The relationship between temperature and dust storms is not simply linear, however, a certain correlation with an unremarkable statistical significance can be found between them. Human activities also affect the dynamics of dust storms indirectly via changing vegetation coverage and direct dust emissions. The multivariate analysis further confirmed the association between dust storm frequency and meteorological factors and NDVI. The high loadings of dust storm frequency, wind speed, precipitation and NDVI on a PC indicate that the increased precipitation and NDVI will decrease dust storm frequency, and increased wind speed will increase dust storm frequency.

New smooth gap function for box constrained variational inequalities

A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.

MERIT FUNCTION AND GLOBAL ALGORITHMFOR BOX CONSTRAINED VARIATIONALINEQUALITIES

The authors consider optimization methods for box constrained variational inequalities. First, the authors study the KKT-conditions problem based on the original problem. A merit function for the KKT-conditions problem is proposed, and some desirable properties of the merit function are obtained. Through the merit function, the original problem is reformulated as minimization with simple constraints. Then, the authors show that any stationary point of the optimization problem is a solution of the original problem. Finally, a descent algorithm is presented for the optimization problem, and global convergence is shown.

QUASI-VARIATIONAL PRINCIPLE FOR THE VORTEX-POTENTIAL FUNCTION OF ROTATIONAL FLOW IN THREE-DIMENSION PIPE

The variational analysis of the Pseudo-potential function-vortex-potential function model, a new mathematical model, was developed and by which the flow field with transonic speed and curl was decided, and different sorts of the variational principle for vortex potential function were established by transforming the original equation for vortex-function, the boundary conditions for vortex-potential function was raised.

基于条件变分自编码器的熔铸炸药成型缺陷快速模拟和预测

为了实现凝固缺陷的快速模拟和预测,提出了一种基于条件变分自编码器(CVAE)的熔铸炸药成型缺陷预测模型;以注液温度、冒口预热温度等工艺参数为条件,通过条件变分自编码器建立工艺参数与熔铸炸药缺陷的条件概率模型;采用多层神经网络和变分推断方法结合进行模型训练,实现了RHT和DNP基熔铸炸药凝固成型缺陷预测。结果表明,成功构建了熔铸炸药凝固过程数值模拟的条件概率分布,实现了基于仿真数据的RHT和DNP基熔铸炸药凝固缺陷预测;与有限元直接数值计算结果比较,CVAE算法计算缺陷位置的准确率可达到99%,计算时间小于2 s;CVAE在熔铸炸药缺陷概率分布建模上具有性能高、泛化性强的特点,能有效实现熔铸炸药成型缺陷的智能预测。

2000-2020年内蒙古NDVI时空动态及其对水热条件的响应

[目的]了解植被生态现状,剖析植被变化影响因素,为区域生态环境治理和规划提供科学依据。[方法]基于MOD13A3 NDVI数据和气象数据,采用Sen趋势分析、M-K检验、Hurst指数、相关系数等方法研究了内蒙古地区NDVI时空变化及其对水热条件的响应。[结果]内蒙古NDVI显著增长(p<0.01),空间分布呈东高西低的特征,大部分地区NDVI以增加趋势为主,耕地增长率最大且呈增加趋势面积占比最大。研究期内NDVI变化相对稳定,林地的稳定性最好。未来内蒙古NDVI变化以反持续性为主,反持续性和持续性面积占比分别为76.51%,23.49%。NDVI与气温呈负相关的区域占78.25%,其中极显著和显著负相关的区域占19.92%;与降水、土壤湿度呈正相关的区域占93.16%,93.53%,其中极显著和显著正相关的区域分别占51.37%,55.85%。[结论]内蒙古地区植被生态整体趋于改善,未来植被生态可能退化,土壤湿度是影响内蒙古植被生长的主导因子。

具有手性边界条件的耦合Dirac系统

本文研究具有手性边界条件的Dirac系统解的存在性.通过在恰当的分数阶索伯列夫乘积空间上建立解析框架,给出了具有超二次增长的非线性项的Dirac系统解的存在性,把GONG和LU(2017)研究的结果推广到手性边界条件下的情形.

宜昌市颗粒物污染浓度特征及气象条件影响分析

通过气象观测手段,监测分析宜昌市颗粒物污染浓度特征及气象影响因素,为研究三峡水利枢纽对局地气候的影响以及水库气候效应分析提供数据支撑和资料基础,具有重要意义。目前针对宜昌市的颗粒物尤其是黑碳(black carbon,BC)气溶胶颗粒物的相关研究很少。本文利用宜昌国家基本气象站2014年4月—2022年12月的大气颗粒物PM_(2.5)、PM_(10)和黑碳气溶胶连续观测资料,结合同期气象要素资料进行数理分析,研究PM_(2.5)、PM_(10)和黑碳质量浓度的变化特征及其气象影响条件。结果显示:(1)宜昌市PM_(2.5)和PM_(10)质量浓度总体呈逐年下降趋势,黑碳气溶胶质量浓度在2018年前总体下降,后呈较缓波动趋势,春季和冬季浓度较高,夏季、秋季较低,日变化呈双峰态势;(2)颗粒物质量浓度高低值分布与主导风向高度吻合,与风速、降水量呈显著负相关;(3)黑碳气溶胶质量浓度与PM_(2.5)、PM_(10)颗粒物质量浓度变化趋势高度相似,呈显著性正相关,相关系数分别为0.845和0.747,表明宜昌城市大气中颗粒物具有很强的同源性。总体来看,经济社会发展对生态环境变化产生一定的主导作用,新型有效的经济环保政策实施对于长江经济带的生态环境建设意义重大。

DCVAE与DPC融合的网络入侵检测模型研究

入侵检测是主动防御网络中攻击行为的技术,以往入侵检测模型因正常网络流量与未知攻击内在特征区分度不足,导致对未知攻击识别率不够高,本文设计基于判别条件变分自编码器与密度峰值聚类算法的入侵检测模型(DCVAE-DPC).利用判别条件变分自编码器能够生成指定类别样本的能力,学习正常网络流量特征的隐空间表示并计算其重建误差,增加其与未知攻击间的特征区分度,并使用密度峰值聚类算法求出正常网络流量重建误差的分布,提高未知攻击识别率.实验结果表明,在NSL-KDD数据集中与当前流行的入侵检测模型相比,模型的分类准确率可以达到97.08%,具有更高的未知攻击检测能力,面对当前复杂网络环境,有更强的入侵检测性能.

临界点理论在分数阶微分方程边值问题中的应用

用临界点理论和变分法研究Banach空间中带Sturm-Liouville边值条件的Caputo型分数阶微分方程解的存在性.通过定义适当的分数阶导数空间,将分数阶微分方程边值问题解的存在性转化为寻找定义在某个空间上对应泛函的临界点,得到了该边值问题存在一系列无界的广义解.