Porous-DeepONet:Learning the Solution Operators of Parametric Reactive Transport Equations in Porous Media

Reactive transport equations in porous media are critical in various scientific and engineering disciplines,but solving these equations can be computationally expensive when exploring different scenarios,such as varying porous structures and initial or boundary conditions.The deep operator network(DeepONet)has emerged as a popular deep learning framework for solving parametric partial differential equations.However,applying the DeepONet to porous media presents significant challenges due to its limited capability to extract representative features from intricate structures.To address this issue,we propose the Porous-DeepONet,a simple yet highly effective extension of the DeepONet framework that leverages convolutional neural networks(CNNs)to learn the solution operators of parametric reactive transport equations in porous media.By incorporating CNNs,we can effectively capture the intricate features of porous media,enabling accurate and efficient learning of the solution operators.We demonstrate the effectiveness of the Porous-DeepONet in accurately and rapidly learning the solution operators of parametric reactive transport equations with various boundary conditions,multiple phases,and multiphysical fields through five examples.This approach offers significant computational savings,potentially reducing the computation time by 50–1000 times compared with the finite-element method.Our work may provide a robust alternative for solving parametric reactive transport equations in porous media,paving the way for exploring complex phenomena in porous media.

PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.

RANK ONE OPERATORS AND TRIANGULAR ALGEBRAS

In this paper, a necessary condition for a maximal triangular algebra to be closed is given. A necessary and sufficient condition for a maximal triangular algebra to be strongly reducible is obtained.

Medical Diagnosis Based on Multi-Attribute Group Decision-Making Using Extension Fuzzy Sets,Aggregation Operators and Basic Uncertainty Information Granule

Accurate medical diagnosis,which involves identifying diseases based on patient symptoms,is often hindered by uncertainties in data interpretation and retrieval.Advanced fuzzy set theories have emerged as effective tools to address these challenges.In this paper,new mathematical approaches for handling uncertainty in medical diagnosis are introduced using q-rung orthopair fuzzy sets(q-ROFS)and interval-valued q-rung orthopair fuzzy sets(IVq-ROFS).Three aggregation operators are proposed in our methodologies:the q-ROF weighted averaging(q-ROFWA),the q-ROF weighted geometric(q-ROFWG),and the q-ROF weighted neutrality averaging(qROFWNA),which enhance decision-making under uncertainty.These operators are paired with ranking methods such as the similarity measure,score function,and inverse score function to improve the accuracy of disease identification.Additionally,the impact of varying q-rung values is explored through a sensitivity analysis,extending the analysis beyond the typical maximum value of 3.The Basic Uncertain Information(BUI)method is employed to simulate expert opinions,and aggregation operators are used to combine these opinions in a group decisionmaking context.Our results provide a comprehensive comparison of methodologies,highlighting their strengths and limitations in diagnosing diseases based on uncertain patient data.

Robust Principal Component Analysis Integrating Sparse and Low-Rank Priors

Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.

Leveraging ROTI map derived from Indonesian GNSS receiver network for advancing study of Equatorial Plasma Bubble in Southeast/East Asia

This paper highlights the crucial role of Indonesia’s GNSS receiver network in advancing Equatorial Plasma Bubble(EPB)studies in Southeast and East Asia,as ionospheric irregularities within EPB can disrupt GNSS signals and degrade positioning accuracy.Managed by the Indonesian Geospatial Information Agency(BIG),the Indonesia Continuously Operating Reference Station(Ina-CORS)network comprises over 300 GNSS receivers spanning equatorial to southern low-latitude regions.Ina-CORS is uniquely situated to monitor EPB generation,zonal drift,and dissipation across Southeast Asia.We provide a practical tool for EPB research,by sharing two-dimensional rate of Total Electron Content(TEC)change index(ROTI)derived from this network.We generate ROTI maps with a 10-minute resolution,and samples from May 2024 are publicly available for further scientific research.Two preliminary findings from the ROTI maps of Ina-CORS are noteworthy.First,the Ina-CORS ROTI maps reveal that the irregularities within a broader EPB structure persist longer,increasing the potential for these irregularities to migrate farther eastward.Second,we demonstrate that combined ROTI maps from Ina-CORS and GNSS receivers in East Asia and Australia can be used to monitor the development of ionospheric irregularities in Southeast and East Asia.We have demonstrated the combined ROTI maps to capture the development of ionospheric irregularities in the Southeast/East Asian sector during the G5 Geomagnetic Storm on May 11,2024.We observed simultaneous ionospheric irregularities in Japan and Australia,respectively propagating northwestward and southwestward,before midnight,whereas Southeast Asia’s equatorial and low-latitude regions exhibited irregularities post-midnight.By sharing ROTI maps from Indonesia and integrating them with regional GNSS networks,researchers can conduct comprehensive EPB studies,enhancing the understanding of EPB behavior across Southeast and East Asia and contributing significantly to ionospheric research.

NEW LIMITED MEMORY SYMMETRIC RANK ONE ALGORITHM FOR LARGE-SCALE UNCONSTRAINED OPTIMIZATION

A new limited memory symmetric rank one algorithm is proposed. It combines a modified self-scaled symmetric rank one （SSR1） update with the limited memory and nonmonotone line search technique. In this algorithm, the descent search direction is generated by inverse limited memory SSR1 update, thus simplifying the computation. Numerical comparison of the algorithm and the famous limited memory BFGS algorithm is given. Comparison results indicate that the new algorithm can process a kind of large-scale unconstrained optimization problems.

OPG/RANKL/RANK信号通路在脓毒症相关急性肾损伤小鼠中的研究

目的:探讨骨保护素(OPG)/核因子⁃κB受体活化因子配体(RANKL)/核因子⁃κB受体激活因子(RANK)信号通路因子在脓毒症相关急性肾损伤(SA⁃AKI)小鼠中的改变及可能的作用,为SA⁃AKI的机制研究探索新的思路。方法:通过盲肠结扎穿孔手术(CLP)建立SA⁃AKI模型组(CLP组),对照组为假手术组(Sham组),只行开腹不做盲肠结扎穿孔操作。术后24 h采血并处死留取小鼠肾脏组织,用试剂盒检测血清Scr、BUN水平,酶联免疫测定法(ELISA)检验血清中IL⁃6、TNF⁃α、IL⁃1β水平,苏木精⁃伊红染色(HE)观测肾组织病理学变化,聚合酶链反应(RT⁃qPCR)和蛋白质印迹实验(Western blotting)检验小鼠肾组织中OPG、RANKL、RANK的mRNA和蛋白水平。结果:与Sham组对比,CLP组Scr、BUN、IL⁃6、TNF⁃α、IL⁃1β水平显著升高,差异均具有统计学意义(P<0.05);与Sham组对比,CLP组肾小球充血水肿,部分缺血皱缩,球囊间隙扩大,部分肾小管中可见坏死的上皮细胞,管腔扩大,肾间质水肿,少量炎性细胞浸润;与Sham组相比较,CLP组肾组织中OPG和RANK的mRNA表达显著上调,而RANKL的mRNA表达明显下降,差异均具有统计学意义(P<0.05);与Sham组相比较,CLP组肾脏组织中OPG及RANK的蛋白表达均升高,而RANKL的蛋白表达明显下降,差异均具有统计学意义(P<0.05)。结论:在脓毒症的小鼠模型中OPG及RANK表达升高,RANKL表达下降,表明OPG/RANKL/RANK信号通路可能参与了SA⁃AKI的病理生理过程。

膝关节置换术后患者血清RANKL、sVCAM-1、ESR表达水平及其与预后的相关性

目的 探讨膝关节置换术后患者血清核因子-κB受体活化因子配基(RANKL)、可溶性血管细胞黏附分子-1(sVCAM-1)、红细胞沉降率(ESR)的表达意义及其与预后的关系。方法 回顾性分析2020年1月至2022年9月安阳市人民医院收治的118例膝关节置换手术患者的临床资料,根据术后6个月Lysholm评分将患者分为预后不良组(总分<70分,27例)和预后良好组(总分≥70分,91例)。比较两组术后1、3个月血清RANKL、sVCAM-1、ESR表达水平,分析其与Lysholm评分的相关性,评估上述血清学指标联合检测对患者术后预后不良的预测价值。结果 术后1、3个月预后不良组血清RANKL、sVCAM-1、ESR水平高于预后良好组(P <0.05),术后1、3个月血清RANKL、sVCAM-1、ESR水平与Lysholm评分呈负相关(P <0.05),联合预测患者术后预后不良的曲线下面积(AUC)优于各血清指标单独预测(P <0.05)。结论 血清RANKL、sVCAM-1、ESR水平升高可提示膝关节置换术患者预后不良风险的增加,联合检测可作为预测预后不良、判断病情转归的参考依据。

The Spectrum of High Rank Differential Operators of the C_0 Semigroups

In this paper,the author study the spectrum of high rank differential operators T (n) (t) of C 0 Semigroup T(t) ,given an approach to construct the spectral set opetator T (n) (t) ,and discussed the relation between the spectral points of both T (n) (t) and infinitesimal generator A of T(t) .

Ozone Emitted During Copying Process-A Potential Cause of Pathological Oxidative Stress and Potential Oxidative Damage in the Bodies of Operators

To estimate the impact of copying on the indoor air quality, and to investigate whether ozone emitted during such a process induces pathological oxidative stress and potential oxidative damage in the bodies of operators. Methods 67 copying operators (CO) and 67 healthy volunteers (HV) were enrolled in a random control study, in which levels of lipoperoxide (LPO) in plasma and erythrocytes, and levels of vitamin C (VC), vitamin E (VE) and b-carotene (b-CAR) in plasma as well as activities of superoxide dismutase (SOD), catalase (CAT) and glutathione peroxidase (GPX) in erythrocytes were determined by spectrophotometric methods. Results Compared with the HV group, the average values of LPO in plasma and erythrocytes in the CO group were significantly increased (P<0.0001), while those of VC, VE and b-CAR in plasma as well as those of SOD, CAT and GPX in erythrocytes in the CO group were significantly decreased (P<0.0001). Pearson product-moment correlation analysis showed that with increase of ozone level in copying sites and duration of exposure to ozone, the values of LPO in plasma and erythrocytes in the bodies of operators were gradually increased,while those of VC, VE, b-CAR, SOD, CAT and GPX were decreased in the same manner. Odds ratio (OR) of risk of biochemical parameters reflecting potential oxidative damage of the copying operators ranged from 4.440 to 13.516, and 95 % CI of OR was from 2.113 to 34.061. Reliability coefficient () of the biochemical parameters used to reflect the potential oxidative damage of the operators was 0.8156, standardized item =0.9929, P<0.0001. Conclusion Findings in the present study suggest that there exist a series of free radical chain reactions and pathological oxidative stress induced by high dose ozone in the operators, thereby causing potential oxidative and lipoperoxidative damages in their bodies.

脱氢胆酸调控OPG/RANK和TRAF3抑制破骨细胞分化

目的探讨脱氢胆酸(dehydrocholic acid,DHCA)对破骨细胞(osteoclasts,OCs)分化及功能的影响。方法采用粒细胞-巨噬细胞集落刺激因子和核因子κB受体活化因子配体(receptor activator of nuclear factor kappa B(NF-κB)-ligand,RANKL)诱导成熟骨髓来源的巨噬细胞分化为OCs。通过抗酒石酸酸性磷酸酶(tartrate-resistant acid phosphatase,TRAP/ACP5)染色,确定DHCA抑制OCs形成的最佳浓度。qRT-PCR检测OCs分化和功能相关基因TRAP/ACP5、组织蛋白酶K(cathepsin K,CTSK)和基质金属蛋白酶9(matrix metalloproteinase 9,MMP9)的基因表达。Western blot检测OCs中TNF受体相关因子3(TNF receptor-associated factor 3,TRAF3)、NF-κB受体活化因子(receptor activator of NF-κB,RANK)和骨保护素(osteoprotegerin,OPG)的蛋白水平。结果DHCA浓度为200μmol/L是抑制OCs形成的最佳剂量(P<0.01)。DHCA抑制OCs分化和功能相关基因ACP5、CTSK和MMP9的表达(P<0.01)。DHCA通过下调RANK蛋白和增加TRAF3和OPG蛋白的表达来抑制OCs的分化(P<0.01)。结论DHCA通过调控OPG/RANK和TRAF3抑制OCs分化,这可能是一种有效的骨质疏松前体药物。

ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION CM WITH THEIR SHIFTS AND DIFFERENCE OPERATORS

In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf（z） be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f（z）, f（z＋c）, and △n cf（z） share 0 CM, then f（z＋c）≡Af（z）, where A（≠0） is a complex constant. Moreover, let a（z）, b（z）（ O） ∈ S（f） be periodic entire functions with period c and if f（z） - a（z）, f（z ＋ c） - a（z）, △cn f（z） - b（z） share 0 CM, then f（z ＋ c） ≡ f（z）.

General Approach to Antinormally Ordering Boson Exponential Quadratic Operators and Its Applications

A general approach to antinormally ordering the boson exponential quadratic operators(EQOs)is presented.By the approach,some important EQOs,including squeezed operator of one mode and two mode,linear quantum transformation operator,Bogolubov transformation operator are antinormally ordered.

Parameterized Littlewood-Paley Operators and Their Commutators on Lebesgue Spaces with Variable Exponent

In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley gλ^＊- functions, is established on the Lebesgue spaces with variable exponent. Furthermore, the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.

Two Theorems for General n-Mode Boson Exponential Quadratic Operators

By the aid of the generalized linear quantum transform theory,we present for the multimode boson exponential quadratic operators two theorems to change the operator expressions among usual,normal and anti-normal orderings.

Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings

In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.

Multilinear Calder′on Zygmund operators on variableexponent Morrey spaces over domains

The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this type multilinear operators on product ofvariable exponent Morrey spaces over domains is shown in the paper.

The Fractional Maximal Operator and Marcinkiewicz Integrals Associated with Schr?dinger Operators on Morrey Spaces with Variable Exponent

In this paper, we prove the boundedness of the fractional maximal operator, Hardy-Littlewood maximal operator and marcinkiewicz integrals associated with Schrodinger operator on Morrey spaces with variable exponent.

Estimation of the Stress-Strength Reliability for Exponentiated Pareto Distribution Using Median and Ranked Set Sampling Methods

In reliability analysis,the stress-strength model is often used to describe the life of a component which has a random strength(X)and is subjected to a random stress(Y).In this paper,we considered the problem of estimating the reliability𝑅𝑅=P[Y<X]when the distributions of both stress and strength are independent and follow exponentiated Pareto distribution.The maximum likelihood estimator of the stress strength reliability is calculated under simple random sample,ranked set sampling and median ranked set sampling methods.Four different reliability estimators under median ranked set sampling are derived.Two estimators are obtained when both strength and stress have an odd or an even set size.The two other estimators are obtained when the strength has an odd size and the stress has an even set size and vice versa.The performances of the suggested estimators are compared with their competitors under simple random sample via a simulation study.The simulation study revealed that the stress strength reliability estimates based on ranked set sampling and median ranked set sampling are more efficient than their competitors via simple random sample.In general,the stress strength reliability estimates based on median ranked set sampling are smaller than the corresponding estimates under ranked set sampling and simple random sample methods.Keywords:Stress-Strength model,ranked set sampling,median ranked set sampling,maximum likelihood estimation,mean square error.corresponding estimates under ranked set sampling and simple random sample methods.