分数阶Riccati方程的Bäcklund变换及其应用

基于整数阶辅助方程法的相关结论,给出了分数阶Riccati方程的包含广义双曲函数解和广义三角函数解的Mittag-Leffler函数新解、Bäcklund变换和解的非线性叠加公式.在此基础上,借助符号计算系统Mathematica,构造了分数阶KdV-mKdV方程、分数阶(3+1)维Zakharov-Kuznetsov方程和分数阶Boussinesq方程的无穷序列新解.

一类特殊Riccati微分方程通解理论的分析及其统一

Riccati微分方程在实际工程中有着广泛的应用,但由于不可积的特性,使其解法具有挑战性。针对相关文献中有关Riccati微分方程通解的问题,利用Riccati微分方程的不变量关系式进行分析讨论,揭示该微分方程解的内在本质,并且将相关文献中的Riccati微分方程解法统一起来,达到求解的简单美。

一类耦合代数Riccati方程的解

耦合代数Riccati方程在控制论中具有广泛的应用,文章研究了一类耦合代数Riccati方程的解。基于M-矩阵和非负矩阵的理论,在一定假设条件下,证明了这类耦合代数Riccati方程存在最小非负解。最后通过数值算例,验证了所得结果的有效性。

Hemorrhagic transformation in patients with large-artery atherosclerotic stroke is associated with the gut microbiota and lipopolysaccharide

Hemorrhagic transformation is a major complication of large-artery atheroscle rotic stroke(a major ischemic stro ke subtype)that wo rsens outcomes and increases mortality.Disruption of the gut microbiota is an important feature of stroke,and some specific bacteria and bacterial metabolites may contribute to hemorrhagic transformation pathogenesis.We aimed to investigate the relationship between the gut microbiota and hemorrhagic transformation in largearte ry atheroscle rotic stro ke.An observational retrospective study was conducted.From May 2020 to September 2021,blood and fecal samples were obtained upon admission from 32 patients with first-ever acute ischemic stroke and not undergoing intravenous thrombolysis or endovascular thrombectomy,as well as 16 healthy controls.Patients with stro ke who developed hemorrhagic transfo rmation(n=15)were compared to those who did not develop hemorrhagic transformation(n=17)and with healthy controls.The gut microbiota was assessed through 16S ribosomal ribonucleic acid sequencing.We also examined key components of the lipopolysaccharide pathway:lipopolysaccharide,lipopolysaccharide-binding protein,and soluble CD14.We observed that bacterial diversity was decreased in both the hemorrhagic transformation and non-hemorrhagic transfo rmation group compared with the healthy controls.The patients with ischemic stro ke who developed hemorrhagic transfo rmation exhibited altered gut micro biota composition,in particular an increase in the relative abundance and dive rsity of members belonging to the Enterobacteriaceae family.Plasma lipopolysaccharide and lipopolysaccharide-binding protein levels were higher in the hemorrhagic transformation group compared with the non-hemorrhagic transfo rmation group.lipopolysaccharide,lipopolysaccharide-binding protein,and soluble CD14 concentrations were associated with increased abundance of Enterobacte riaceae.Next,the role of the gut microbiota in hemorrhagic transformation was evaluated using an experimental stroke rat model.In this model,transplantation of the gut microbiota from hemorrhagic transformation rats into the recipient rats triggered higher plasma levels of lipopolysaccharide,lipopolysaccharide-binding protein,and soluble CD14.Ta ken togethe r,our findings demonstrate a noticeable change in the gut microbiota and lipopolysaccharide-related inflammatory response in stroke patients with hemorrhagic transformation.This suggests that maintaining a balanced gut microbiota may be an important factor in preventing hemorrhagic transfo rmation after stro ke.

Formation and transformation of metastable LPSO building blocks clusters in Mg-Gd-Y-Zn-Zr alloys by spinodal decomposition and heterogeneous nucleation

To study the formation and transformation mechanism of long-period stacked ordered(LPSO)structures,a systematic atomic scale analysis was conducted for the structural evolution of long-period stacked ordered(LPSO)structures in the Mg-Gd-Y-Zn-Zr alloy annealed at 300℃~500℃.Various types of metastable LPSO building block clusters were found to exist in alloy structures at different temperatures,which precipitate during the solidification and homogenization process.The stability of Zn/Y clusters is explained by the first principles of density functional theory.The LPSO structure is distinguished by the arrangement of its different Zn/Y enriched LPSO structural units,which comprises local fcc stacking sequences upon a tightly packed plane.The presence of solute atoms causes local lattice distortion,thereby enabling the rearrangement of Mg atoms in the different configurations in the local lattice,and local HCP-FCC transitions occur between Mg and Zn atoms occupying the nearest neighbor positions.This finding indicates that LPSO structures can generate necessary Schockley partial dislocations on specific slip surfaces,providing direct evidence of the transition from 18R to 14H.Growth of the LPSO,devoid of any defects and non-coherent interfaces,was observed separately from other precipitated phases.As a result,the precipitation sequence of LPSO in the solidification stage was as follows:Zn/Ycluster+Mg layers→various metastable LPSO building block clusters→18R/24R LPSO;whereas the precipitation sequence of LPSO during homogenization treatment was observed to be as follows:18R LPSO→various metastable LPSO building block clusters→14H LPSO.Of these,14H LPSO was found to be the most thermodynamically stable structure.

Defect Detection Model Using Time Series Data Augmentation and Transformation

Time-series data provide important information in many fields,and their processing and analysis have been the focus of much research.However,detecting anomalies is very difficult due to data imbalance,temporal dependence,and noise.Therefore,methodologies for data augmentation and conversion of time series data into images for analysis have been studied.This paper proposes a fault detection model that uses time series data augmentation and transformation to address the problems of data imbalance,temporal dependence,and robustness to noise.The method of data augmentation is set as the addition of noise.It involves adding Gaussian noise,with the noise level set to 0.002,to maximize the generalization performance of the model.In addition,we use the Markov Transition Field(MTF)method to effectively visualize the dynamic transitions of the data while converting the time series data into images.It enables the identification of patterns in time series data and assists in capturing the sequential dependencies of the data.For anomaly detection,the PatchCore model is applied to show excellent performance,and the detected anomaly areas are represented as heat maps.It allows for the detection of anomalies,and by applying an anomaly map to the original image,it is possible to capture the areas where anomalies occur.The performance evaluation shows that both F1-score and Accuracy are high when time series data is converted to images.Additionally,when processed as images rather than as time series data,there was a significant reduction in both the size of the data and the training time.The proposed method can provide an important springboard for research in the field of anomaly detection using time series data.Besides,it helps solve problems such as analyzing complex patterns in data lightweight.

A new insight into LPSO phase transformation and mechanical properties uniformity of large-scale Mg-Gd-Y-Zn-Zr alloy prepared by multi-pass friction stir processing

A large-scale fine-grained Mg-Gd-Y-Zn-Zr alloy plate with high strength and ductility was successfully prepared by multi-pass friction stir processing(MFSP)technology in this work.The structure of grains and long period stacking ordered(LPSO)phase were characterized,and the mechanical properties uniformity was investigated.Moreover,a quantitative relationship between the microstructure and tensile yield strength was established.The results showed that the grains in the processed zone(PZ)and interfacial zone(IZ)were refined from 50μm to 3μm and 4μm,respectively,and numerous original LPSO phases were broken.In IZ,some block-shaped 18R LPSO phases were transformed into needle-like 14H LPSO phases due to stacking faults and the short-range diffusion of solute atoms.The severe shear deformation in the form of kinetic energy caused profuse stacking fault to be generated and move rapidly,greatly increasing the transformation rate of LPSO phase.After MFSP,the ultimate tensile strength,yield strength and elongation to failure of the large-scale plate were 367 MPa,305 MPa and 18.0% respectively.Grain refinement and LPSO phase strengthening were the major strengthening mechanisms for the MFSP sample.In particularly,the strength of IZ was comparable to that of PZ because the strength contribution of the 14H LPSO phase offsets the lack of grain refinement strengthening in IZ.This result opposes the widely accepted notion that IZ is a weak region in MFSP-prepared large-scale fine-grained plate.

Intrahepatic portal venous systems in adult patients with cavernous transformation of portal vein: Imaging features and a new classification

Background: Cavernous transformation of the portal vein(CTPV) due to portal vein obstruction is a rare vascular anomaly defined as the formation of multiple collateral vessels in the hepatic hilum. This study aimed to investigate the imaging features of intrahepatic portal vein in adult patients with CTPV and establish the relationship between the manifestations of intrahepatic portal vein and the progression of CTPV. Methods: We retrospectively analyzed 14 CTPV patients in Beijing Tsinghua Changgung Hospital. All patients underwent both direct portal venography(DPV) and computed tomography angiography(CTA) to reveal the manifestations of the portal venous system. The vessels measured included the left portal vein(LPV), right portal vein(RPV), main portal vein(MPV) and the portal vein bifurcation(PVB). Results: Nine males and 5 females, with a median age of 40.5 years, were included in the study. No significant difference was found in the diameters of the LPV or RPV measured by DPV and CTA. The visualization in terms of LPV, RPV and PVB measured by DPV was higher than that by CTA. There was a significant association between LPV/RPV and PVB/MPV in term of visibility revealed with DPV( P = 0.01), while this association was not observed with CTA. According to the imaging features of the portal vein measured by DPV, CTPV was classified into three categories to facilitate the diagnosis and treatment. Conclusions: DPV was more accurate than CTA for revealing the course of the intrahepatic portal vein in patients with CTPV. The classification of CTPV, that originated from the imaging features of the portal vein revealed by DPV, may provide a new perspective for the diagnosis and treatment of CTPV.

Matrix Riccati Equations in Optimal Control

In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated. This article proposes a change of variable that allows to find explicit solution of the Matrix Riccati equation. We then apply this solution to Optimal Control.

Unraveling the nexus between cellular senescence and malignant transformation:a paradigm shift in cancer research

Cellular senescence, a natural process wherein cells cease division and undergo irreversible growth arrest, has long captivated the curiosity of scientists because of its many implications in aging and disease. Recent research has shed light on the nexus between cellular senescence and malignant transformation, thus leading to a paradigm shift in understanding cancer development and progression.

Effects of Biochar Inoculation with Bacillus megaterium on Rice Soil Phosphorus Fraction Transformation and Bacterial Community Dynamics

Rice husk biochar inoculated with Bacillus megaterium(BM)(referred to as BM-inoculated biochar, BMB) and uninoculated rice husk biochar(RHB) were added to soil at two rates(0.5%, as BMB1 and RHB1, respectively, and 1.0%, as BMB2 and RHB2, respectively) in an incubation experiment to comprehensively evaluate their effects on basic soil properties, phosphorus(P) fractions, bacterial community composition, and P-cycling genes.

Hydrogen-based mineral phase transformation mechanism investigation of pyrolusite ore

Pyrolusite comprises the foremost manganese oxides and is a major source of manganese production.An innovative hydrogenbased mineral phase transformation technology to pyrolusite was proposed,where a 96.44%distribution rate of divalent manganese(Mn^(2+))was observed at an optimal roasting temperature of 650℃,a roasting time of 25 min,and an H2 concentration of 20vol%;under these conditions.The manganese predominantly existed in the form of manganosite.This study investigated the generation mechanism of manganosite based on the reduction kinetics,phase transformation,and structural evolution of pyrolusite and revealed that high temperature improved the distribution rate,and the optimal kinetic model for the reaction was the random nucleation and growth model(reaction order,n=3/2)with an activation energy(E_(a))of 24.119 kJ·mol^(−1).Throughout the mineral phase transformation,manganese oxide from the outer layer of particles moves inward to the core.In addition,pyrolusite follows the reduction sequence of MnO_(2)→Mn_(2)O_(3)→Mn_(3)O_(4)→MnO,and the reduction of manganese oxides in each valence state simultaneously proceeds.These findings provide significant insight into the efficient and clean utilization of pyrolusite.

The nitrogen transformation behavior based on the pyrolysis products of wheat straw

In order to provide basic design parameters for the industrial pyrolysis process,the transformation behavior of nitrogen was investigated using wheat straw as raw material.The distributions of nitrogen in pyrolysis char,oil,and gas were obtained and the nitrogenous components in the products were analyzed systematically by X-ray photoelectron spectroscopy(XPS),pyrolysis-gas chromatography/mass spectrometry(Py-GC/MS)and thermogravimetric-Fourier transform infrared spectrometry(TG-FTIR).The nitrogen distribution ranges of the pyrolysis char,oil,and gas were 37.34%–54.82%,32.87%–40.94%and 10.20%–28.83%,respectively.More nitrogen was retained in char at lower pyrolysis temperature and the nitrogen distribution of oil was from rise to decline with increasing temperature.The most abundant N-containing compounds in three-phase products were pyrrole-N,amines,and HCN,respectively.In addition,the transformation mechanism of nitrogen from wheat straw to pyrolysis products was concluded.

Critical approaches in the catalytic transformation of sugar isomerization and epimerization after Fischer-History,challenges,and prospects

The transformation of aldose to ketose or common sugars into rare saccharides,including rare ketoses and aldoses,is of great value and interest to the food industry and for saccharidic biomass utilization,medicine,and the synthesis of drugs.Nowadays,high-fructose corn syrup(HFCS)is industrially produced in more than 10 million tons annually using immobilized glucose isomerase.Some low-calorie saccharides such as tagatose and psicose,which are becoming popular sweeteners,have also been produced on a pilot scale in order to replace sucrose and HFCS.However,current catalysts and catalytic processes are still difficult to utilize in biomass conversion and also have strong substrate dependence in producing high-value,rare sugars.Considering the specific reaction properties of saccharides and catalysts,since the pioneering discovery by Fischer,various catalysts and catalytic systems have been discovered or developed in attempts to extend the reaction pathways,improve the reaction efficiency,and to potentially produce commercial products.In this review,we trace the history of sugar isomerization/epimerization reactions and summarize the important breakthroughs for each reaction as well as the difficulties that remain unresolved to date.

Influence mechanism of government subsidy on the green transformation of coal company in China

The optimization of government subsidies to enhance the efficiency of coal companies’green transformation constitutes a critical component in the pursuit of global sustainability.We investigate the influence mechanism of government subsidies on the green transformation using data from the listed coal companies in China from 2007 to 2022.According to our findings and hypothesis testing,previous government subsidies did not have a significant direct impact on coal companies’green transformation.Nevertheless,government subsidies can help coal companies transition to greener practices by promoting innovative green initiatives.Furthermore,we confirmed an indirect route:that government subsidies enable the adoption of low-carbon initiatives,which in turn could facilitate the transition of coal companies towards green practices.In addition,we discovered that the coal company’s digitization will improve this indirect route.Thus,we propose increasing the effectiveness of government subsidies in facilitating coal companies’transition to green practices by focusing on technological advancements and enhancing company digitalization.

Phase transformation in titanium alloys:A review

Due to a series of exceptional properties,titanium and titanium alloys have received extensive attention in recent years.Different from other alloy systems,there are two allotropes and a sequence of metastable phases in titanium alloys.By summarizing the recent investigations,the phase transformation processes corresponding to the common phases and also some less reported phases are reviewed.For the phase transformation only involvingαandβphases,it can be divided intoβ→αtransformation and a reverse transformation.The former one has been demonstrated from the orientation relationship betweenαandβphases and the regulation ofαmorphology.For the latter transformation,the role of the stress has been discussed.In terms of the metastable phases,the mechanisms of phase formation and their effects on microstructure and mechanical properties have been discussed.Finally,some suggestions about the development of titanium alloys have been proposed.

Pre-existing orthorhombic embryos-induced hexagonal-orthorhombic martensitic transformation in MnNiSi_(1-x)(CoNiGe)_x alloy

The thermal-elastic martensitic transformation from high-temperature Ni_(2)In-type hexagonal structure to low-temperature TiNiSi-type orthorhombic structure has been widely studied in MnMX(M=Ni or Co,and X=Ge or Si)alloys.However,the answer to how the orthorhombic martensite nucleates and grows within the hexagonal parent is still unclear.In this work,the hexagonal-orthorhombic martensitic transformation in a Co and Ge co-substituted MnNiSi is investigated.One can find some orthorhombic laths embedded in the hexagonal parent at a temperature above the martensitic transformation start temperature(M_(s)).With the the sample cooing to M_(s),the laths turn broader,indicating that the martensitic transformation starts from these pre-existing orthorhombic laths.Microstructure observation suggests that these pre-existing orthorhombic laths do not originate from the hexagonal-orthorhombic martensitic transformation because of the difference between atomic occupations of doping elements in the hexagonal parent and those in the preexisting orthorhombic laths.The phenomenological crystallographic theory and experimental investigations prove that the pre-existing orthorhombic lath and generated orthorhombic martensite have the same crystallography relationship to the hexagonal parent.Therefore,the orthorhombic martensite can take these pre-existing laths as embryos and grow up.This work implies that the martensitic transformation in MnNiSi_(1-x)(CoNiGe)_(x) alloy is initiated by orthorhombic embryos.

Are gender inclusiveness and rural transformation interlinked?The case of Bangladesh

Gender inclusiveness is important in the rural transformation process of Bangladesh as rural women play key roles in both agricultural and non-agricultural sectors.Gender inclusiveness also leads to gender equity.We empirically evaluate relationships between rural transformation and gender inclusiveness in Bangladesh.We consider three rural transformation indicators:high-value commodities’share in agricultural output values,non-farm employment’s share in rural labor employment,and non-agricultural GDP’s share in total GDP.Indicators capturing gender inclusiveness include the per capita rural income of males and females,ratio of investments into gender programs,female access to education,access to healthcare,employment participation,land ownership,and asset ownership.We test the effect of the difference in per capita rural income of males and females and the ratio of their incomes and check for the robustness of the gender variables across different model specifications.Analyzing 128 district-level observations from 32 districts of Bangladesh across four time periods(2000,2005,2010 and 2016),we use both ordinary least squares and fixed effects panel regression models.We find that female land and asset ownership and access to education and healthcare are robust determinants of various stages of rural transformation.Thus,our results suggest that improving women’s ownership of land and assets and investing in women’s education and healthcare will likely contribute to a more inclusive rural transformation.

Precise regulation of the phase transformation for pyrolusite during the reduction roasting process

The mechanism involved in the phase transformation process of pyrolusite (MnO_(2)) during roasting in a reducing atmosphere was systematically elucidated in this study,with the aim of effectively using low-grade complex manganese ore resources.According to single-factor experiment results,the roasted product with a divalent manganese (Mn^(2+)) distribution rate of 95.30% was obtained at a roasting time of 25 min,a roasting temperature of 700℃,a CO concentration of 20at%,and a total gas volume of 500 mL·min^(-1),in which the manganese was mainly in the form of manganosite (MnO).Scanning electron microscopy and Brunauer–Emmett–Teller theory demonstrated the microstructural evolution of the roasted product and the gradual reduction in the pyrolusite ore from the surface to the core Thermodynamic calculations,X-ray photoelectron spectroscopy,and X-ray diffractometry analyses determined that the phase transformation of pyrolusite followed the order of MnO_(2)→Mn_(2)O_(3)→Mn_(3)O_(4)→MnO phase by phase,and the reduction of manganese oxides in each valence state proceeded simultaneously.

Green transformation paths of resource-based cities in China from the configuration perspective

Green transformation is an unavoidable choice for resource-based cities(RBCs)that face resource depletion and environmental pollution.Existing research has focused primarily on specific RBCs,making it challenging to apply green transformation strategies universally across cities.The fuzzy set qualitative comparative analysis(fsQCA)is a combination of qualitative and quantitative analyses that can handle multiple concurrent causality problems and determine how different conditions combine into configurations and generate an outcome.Thus,to address this gap,in this study,we established a research framework for green transformation and utilized the fsQCA to examine the configurations of 113 RBCs in China.By incorporating the element of time,this study explored the dynamic evolution of solutions in 2013,2016,and 2019.The main findings indicate that individual elements do not constitute the necessary conditions for improving the green transformation efficiency(GTE),and the systematic combination of multiple conditions is an effective path for realizing the improvement of the GTE in RBCs.Green transformation paths of RBCs exhibit the same destination through different paths.Additionally,the combination of system environment elements and system structure elements is both complementary and alternative.Differences in RBCs have led to various factor combinations and development paths,but there are some similarities in the key elements of the factor combinations at different stages.Economic environment,government support,and technological innovation are key factors that universally enhance the GTE in RBCs.These insights can assist city managers in formulating policies to drive green transformation and contribute to a better theoretical understanding of green transformation paths in RBCs.