Fractional differential equations of motion in terms of combined Riemann-Liouville derivatives

In this paper, we focus on studying the fractional variational principle and the differential equations of motion for a fractional mechanical system. A combined Riemann-Liouville fractional derivative operator is defined, and a fractional Hamilton principle under this definition is established. The fractional Lagrange equations and the fractional Hamilton canonical equations are derived from the fractional Hamilton principle. A number of special cases are given, showing the universality of our conclusions. At the end of the paper, an example is given to illustrate the application of the results.

Noether's theorems of a fractional Birkhoffian system within Riemann-Liouville derivatives

The Noether symmetry and the conserved quantity of a fractional Birkhoffian system are studied within the Riemann–Liouville fractional derivatives. Firstly, the fractional Birkhoff＇s equations and the corresponding transversality conditions are given. Secondly, from special to general forms, Noether＇s theorems of a standard Birhoffian system are given, which provide an approach and theoretical basis for the further research on the Noether symmetry of the fractional Birkhoffian system. Thirdly, the invariances of the fractional Pfaffian action under a special one-parameter group of infinitesimal transformations without transforming the time and a general one-parameter group of infinitesimal transformations with transforming the time are studied, respectively, and the corresponding Noether＇s theorems are established. Finally, an example is given to illustrate the application of the results.

Fractional Noether's Theorems for El-Nabulsi's Fractional Birkhoffian Systems in Terms of Riemann-Liouville Derivatives

The fractional Pfaffian variational problem and Noether’s theorems were investigated in terms of Riemann-Liouville derivatives on the basis of El-Nabulsi fractional model.The problem of the calculus of variations with fractional derivatives is a hot topic recently.Firstly,within Riemann-Liouville derivatives,the ElNabulsi Pfaffian variational problem was presented,the fractional Pfaff-Birkhoff-d’Alembert principle was established,and the fractional Birkhoff equations and the corresponding transversality conditions were obtained.Then,the Noether’s theorems in terms of Riemann-Liouville derivatives for the Birkhoffian system on the basis of El-Nabulsi fractional model are investigated under the special and the general transformations respectively.Finally,an example is given to illustrate the methods and results appeared in this paper.

协同拟凸函数的Riemann-Liouville分数阶积分不等式

基于Riemann-Liouville分数阶积分,对协同拟凸函数的Hermite-Hadamard分数阶积分不等式进行了研究。剖析Riemann-Liouville分数阶积分的运算特点,深入探究SAR?KAYA给出的Riemann-Liouville分数阶积分恒等式。在该Riemann-Liouville分数阶积分恒等式的基础上,利用二元函数的单调性和协同拟凸性,巧妙应用三角不等式和H?lder不等式等经典不等式,建立了若干个协同拟凸函数的Hermite-Hadamard分数阶积分不等式。

Organic solar cells with D18 or derivatives offer efficiency over 19%

In recent years,organic solar cells(OSCs)have garnered significant attention due to their distinctive attributes,such as flexibility,lightweight,and solution processing,which position them as alternatives for next-generation solar technologies[1−5].Thanks to breakthroughs in materials development,the power conversion efficiency(PCE)for single-junction OSCs has already surpassed 19%[6−13].The development of photoactive materials is pivotal in enhancing the PCEs,and several reviews have provided insights into materials design[14−18].Herein,we highlight single-junction OSCs based on D18 and its derivatives[19,20].

Fullerenes and derivatives as electrocatalysts: Promises and challenges

Carbon-based metal-free nanomaterials are promising alternatives to precious metals as electrocatalysts of key energy storage and conversion technologies.Of paramount significance are the establishment of design principles by understanding the catalytic mechanisms and identifying the active sites.Distinct from sp2-conjugated graphene and carbon nanotube,fullerene possesses unique characteristics that are growingly being discovered and exploited by the electrocatalysis community.For instance,the well-defined atomic and molecular structures,the good electron affinity to tune the electronic structures of other substances,the intermolecular self-assembly into superlattices,and the on-demand chemical modification have endowed fullerene with incomparable advantages as electrocatalysts that are otherwise not applicable to other carbon ma-terials.As increasing studies are being reported on this intriguing topic,it is necessary to provide a state-of-the-art overview of the recent progress.This review takes such an initiative by summarizing the promises and challenges in the electrocatalytic applications of fullerene and its derivatives.The content is structured according to the composition and structure of fullerene,including intact fullerene(e.g.,fullerene composite and superlattices)and fullerene derivatives(e.g.,doped,endohedral,and disintegrated fullerene).The synthesis,characterization,catalytic mechanisms,and deficiencies of these fullerene-based materials are explicitly elaborated.We conclude it by sharing our perspectives on the key aspects that future efforts shall consider.

Discovery and structure-activity relationship studies of novel tetrahydro-β-carboline derivatives as apoptosis initiators for treating bacterial infections

Developing and excavating new agrochemicals with highly active and safe is an important tactic for protecting crop health and food safety.In this paper,to discover the new bactericide candidates,we designed,prepared a new type of1,2,3,4-tetrahydro-β-carboline(THC)derivatives and evaluated the in vitro and in vivo bioactivities against the Xanthomonas oryzae pv.oryzae(Xoo),Xanthomonas axonopodis pv.citri(Xac),and Pseudomonas syringae pv.actinidiae(Psa).The in vitro bioassay results exhibited that most title molecules possessed good activity toward the three plant pathogenic bacteria,the compound A17 showed the most active against Xoo and Xac with EC50 values of 7.27 and 4.89 mg mL^(-1)respectively,and compound A8 exhibited the best inhibitory activity against Psa with EC50value of 4.87 mg mL^(-1).Pot experiments showed that compound A17 exhibited excellent in vivo antibacterial activities to manage rice bacterial leaf blight and citrus bacterial canker,with protective efficiencies of 52.67 and 79.79%at 200 mgmL^(-1),respectively.Meanwhile,compound A8 showed good control efficiency(84.31%)against kiwifruit bacterial canker at 200 mg mL^(-1).Antibacterial mechanism suggested that these compounds could interfere with the balance of the redox system,damage the cell membrane,and induce the apoptosis of Xoo cells.Taken together,our study revealed that tetrahydro-β-carboline derivatives could be a promising candidate model for novel broadspectrum bactericides.

High-Value-Added Utilization of Turpentine:Screening of Anti-Influenza Virus Agents fromβ-Pinene Derivatives

Turpentine is a renewable and resourceful forest product.The deep processing and utilization of turpentine,particularly its primary componentβ-pinene,has garnered widespread attention.This study aimed to synthesize 40 derivatives ofβ-pinene,including nopinone,3-cyanopyridines of nopinone,myrtanyl acid,myrtanyl acylthioureas,and myrtanyl amides.We assessed the antiviral activities of theseβ-pinene derivatives against influenza virus A/Puerto Rico/8/34(H1N1)using the 3-(4,5-dimetylthiazol-2-yl)-2,5-diphenyltetrazolium bromide method.Theβ-pinene derivatives were used before and after cellular infection with the influenza virus to evaluate their preventive and therapeutic effects against the H1N1 virus.The results showed that only compound 10o exhibited a preventive effect against the H1N1 virus with a half-maximal inhibitory concentration(IC50)value of 47.6μmol/L.Among the compounds,4e,4i,and 4l demonstrated therapeutic effects against cellular infection,with compound 4e displaying the most potent therapeutic effect(IC50=17.5μmol/L),comparable to the positive control ribavirin.These findings indicated that certainβ-pinene derivatives exhibited in vitro antiviral activity against the H1N1 influenza A virus,warranting further investigation as potential anti-influenza agents.

Identification of key genes regulating the synthesis of quercetin derivatives in Rosa roxburghii through integrated transcriptomics and metabolomics

Rosa roxburghii fruit is rich in flavonoids, but little is known about their biosynthetic pathways. In this study, we employed transcriptomics and metabolomics to study changes related to the flavonoids at five different stages of R. roxburghii fruit development. Flavonoids and the genes related to their biosynthesis were found to undergo significant changes in abundance across different developmental stages, and numerous quercetin derivatives were identified. We found three gene expression modules that were significantly associated with the abundances of the different flavonoids in R. roxburghii and identified three structural UDP-glycosyltransferase genes directly involved in the synthesis of quercetin derivatives within these modules. In addition, we found that RrBEH4, RrLBD1 and RrPIF8could significantly increase the expression of downstream quercetin derivative biosynthesis genes. Taken together,these results provide new insights into the metabolism of flavonoids and the accumulation of quercetin derivatives in R. roxburghii.

Tailored multifunctional hydrazine derivatives for efficient printable hole-conductive-free mesoscopic perovskite solar cells via enhancing defect passivation

The low-cost and easy large-scale fabrication advantages of printable mesoscopic perovskite solar cells(p-MPSCs)are overshadowed by their limited photovoltaic conversion efficiency(PCE).Here,we introduce the hydrazide derivative of 4-Hydroxybenzoylhydrazine(4-HBH)to improve the PCE of p-MPSCs by inducing enhanced defect passivation.Both carbonyl and hydrazine groups in hydrazide groups present strong interaction with perovskite.The hydroxyl group,as an electron donor group,increases the electron cloud density of the hydrazide group in 4-HBH under the conjugation of the benzene ring,and thus enhances its interaction with perovskite.Additionally,the hydroxy group itself interacts with perovskite and passivates defects synergistically.The hydrazine agents can also reduce I2and suppress the loss of iodine in perovskite films,which inhibits the formation of iodine-related defects.Consequently,p-MPSCs with 4-HBH achieve a high PCE of 19.21%,and present well improved stability.

Preparation of kakkatin derivatives and their anti-tumor activity

BACKGROUND Modern pharmacological studies have confirmed that plant-derived compounds from Puerariae flos(PF)has significant biological activities against liver damage,tumors and inflammation.Kakkatin is an isoflavone polyphenolic compound isolated from PF flower.However,the effect of kakkatin and its derivatives on anti-tumor has not been well explored.AIM To design and synthesize a kakkatin derivative[6-(hept-6-yn-1-yloxy)-3-(4-hydroxyphenyl)-7-methoxy-4H-chromen-4-one(HK)]to explore its anti-tumor biological activity.METHODS Hept-6-yn-1-yl ethanesulfonate was introduced to replace hydrogen at the hydroxyl position of kakkatin phenol,and the derivative of kakkatin was prepared;the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide was used to detect cell viability,a clone formation assay was adopted to detect cell proliferation,apoptosis,necrosis,and cell cycles were analyzed by Annexin V/propidium iodide staining and flow cytometry.Cell migration and invasion ability were evaluated by cell scratch assay and transwell assay.The potential mechanism of HK on hepatocellular carcinoma(HCC)SMMC-7721 cells was explored through network pharmacology and molecular docking,and finally real-time PCR assays was used to verify the potential targets and evaluate the biological activity of HK.RESULTS Compared with kakkatin,the modified HK did not significantly increase the inhibitory activity of gastric cancer MGC803 cells,but the inhibitory activity of HCC SMMC-7721 cells was increased by about 30 times,with an IC50 value of 2.5μM,and the tumor inhibition effect was better than cisplatin,which could significantly inhibit the cloning,invasion and metastasis of HCC SMMC-7721 cells,and induce apoptosis and G2/M cycle arrest.Its mechanism of action is mainly related to the upregulation of PDE3B and NFKB1 target proteins in the cAMP pathway.CONCLUSION HK have a significant inhibitory effect on HCC SMMC-7721 cells,and the targets of their action may be PDE3B and NFKB1 proteins in the cAMP pathway,making it a good lead drug for the treatment of HCC.

Study on Antitumor Activity of Piperidine Derivatives

[Objectives]This study was conducted to investigate the effects of piperidine derivatives on the proliferation and apoptosis of tumor cells(Hele).[Methods]The target end product(piperidine derivative)was synthesized through a series of organic reactions.The MTT assay was adopted to detect the effect of piperidine derivative on the proliferation activity of Hele cells.The ROS fluorescence probe method was used to detect the changes of reactive oxygen species.The JC-1 method was applied to detect the changes of MMP in Hele cells.Flow cytometry was adopted to detect the apoptosis of Hele cells.[Results]The cell survival rates were 70.84%,65.46%and 54.48%when the drug concentration was 100,110 and 120μmol/L,respectively.When the drug concentration increased to 120μmol/L,the cell survival rate decreased by nearly half.The fluorescence intensity of active oxygen in the control group was 1,and when the drug concentrations were 100,110 and 120μmol/L,the fluorescence intensity of active oxygen was,respectively,1.315,1.478 and 1.677,which were higher than that in the control group.The red/green fluorescence intensity of the MMP control group was 1.819,and that of drug groups was,respectively,1.643,1.164 and 0.665,which were lower than that of the control group.The apoptosis rates were 10.79%,22.91%and 38.54%at the drug concentrations of 100,110 and 120μmol/L,respectively,showing a concentration dependent effect.The results showed that the piperidine derivative could inhibit the proliferation of Hele cells and induce apoptosis,which was positively correlated with the concentration.[Conclusions]This study provides theoretical basis and reference for the anti-tumor research of piperidine.

Sepsis Prediction Using CNNBDLSTM and Temporal Derivatives Feature Extraction in the IoT Medical Environment

Background:Sepsis,a potentially fatal inflammatory disease triggered by infection,carries significant healthimplications worldwide.Timely detection is crucial as sepsis can rapidly escalate if left undetected.Recentadvancements in deep learning(DL)offer powerful tools to address this challenge.Aim:Thus,this study proposeda hybrid CNNBDLSTM,a combination of a convolutional neural network(CNN)with a bi-directional long shorttermmemory(BDLSTM)model to predict sepsis onset.Implementing the proposed model provides a robustframework that capitalizes on the complementary strengths of both architectures,resulting in more accurate andtimelier predictions.Method:The sepsis prediction method proposed here utilizes temporal feature extraction todelineate six distinct time frames before the onset of sepsis.These time frames adhere to the sepsis-3 standardrequirement,which incorporates 12-h observation windows preceding sepsis onset.All models were trained usingthe Medical Information Mart for Intensive Care III(MIMIC-III)dataset,which sourced 61,522 patients with 40clinical variables obtained from the IoT medical environment.The confusion matrix,the area under the receiveroperating characteristic curve(AUCROC)curve,the accuracy,the precision,the F1-score,and the recall weredeployed to evaluate themodels.Result:The CNNBDLSTMmodel demonstrated superior performance comparedto the benchmark and other models,achieving an AUCROC of 99.74%and an accuracy of 99.15%one hour beforesepsis onset.These results indicate that the CNNBDLSTM model is highly effective in predicting sepsis onset,particularly within a close proximity of one hour.Implication:The results could assist practitioners in increasingthe potential survival of the patient one hour before sepsis onset.

Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives

In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.

基于Riemann-Liouville分数阶积分Bernstein-Kantorovich算子的逼近性质

文章构造一种基于Riemann-Liouville分数阶积分的Bernstein-Kantorovich算子。利用一阶、二阶光滑模、Peetre’-K泛函和Lipschitz型极大函数等工具研究该算子的近似性质。然后利用一阶、二阶和四阶中心矩对该算子建立Vorononskaja型渐进公式。该算子的构建使得在曲线曲面造型方面对于给定的函数将会有更小的近似误差。

Avoiding the Use of Lagrange Multipliers. II. Constrained Extrema of Functionals and the Evaluation of Constrained Derivatives

A method for determining the extrema of a real-valued and differentiable function for which its dependent variables are subject to constraints and that avoided the use of Lagrange multipliers was previously presented (Corti and Fariello, Op. Res. Forum 2 (2021) 59). The method made use of projection matrices, and a corresponding Gram-Schmidt orthogonalization process, to identify the constrained extrema. Furthermore, information about the second-derivatives of the given function with constraints was generated, from which the nature of the constrained extrema could be determined, again without knowledge of the Lagrange multipliers. Here, the method is extended to the case of functional derivatives with constraints. In addition, constrained first-order and second-order derivatives of the function are generated, in which the derivatives with respect to a given variable are obtained and, concomitantly, the effect of the variations of the remaining chosen set of dependent variables are strictly accounted for. These constrained derivatives are valid not only at the extrema points, and also provide another equivalent route for the determination of the constrained extrema and their nature.

Fourth Order Difference Approximations for Space Riemann-Liouville Derivatives Based on Weighted and Shifted Lubich Difference Operators

High order discretization schemes playmore important role in fractional operators than classical ones.This is because usually for classical derivatives the stencil for high order discretization schemes is wider than low order ones;but for fractional operators the stencils for high order schemes and low order ones are the same.Then using high order schemes to solve fractional equations leads to almost the same computational cost with first order schemes but the accuracy is greatly improved.Using the fractional linear multistep methods,Lubich obtains the n-th order(n≤6)approximations of the a-th derivative(a>0)or integral(a<0)[Lubich,SIAM J.Math.Anal.,17,704-719,1986],because of the stability issue the obtained scheme can not be directly applied to the space fractional operator with a∈(1,2)for time dependent problem.By weighting and shifting Lubich’s 2nd order discretization scheme,in[Chen&Deng,SINUM,arXiv:1304.7425]we derive a series of effective high order discretizations for space fractional derivative,called WSLD operators there.As the sequel of the previous work,we further provide new high order schemes for space fractional derivatives by weighting and shifting Lubich’s 3rd and 4th order discretizations.In particular,we prove that the obtained 4th order approximations are effective for space fractional derivatives.And the corresponding schemes are used to solve the space fractional diffusion equation with variable coefficients.

Riemann-Liouville型分数阶导数的非线性估计

本文主要研究任意有界连续信号的Riemann-Liouville分数阶导数估计问题.当分数阶α属于0到1时,首先利用滑模技术提出一种有界连续信号分数阶导数的非线性估计方法;然后将其结果推广至分数阶α∈R+的情况,并给出相应的非线性估计方案.借助Riemann-Liouville分数阶微积分频率分布模型,本文详细分析讨论了所给分数阶导数非线性估计的收敛性问题,并得到相应闭环系统是渐近稳定的结论.文中所提方法的主要优点是在事先未知给定信号分数阶导数上界的情况下,不仅能自适应地估计其Riemann-Liouville分数阶导数,而且当信号中含有随机噪声和不确定扰动时依然能正常工作.数值仿真实例验证了本文所给估计方法的可行性和有效性.

一类Riemann-Liouville分数阶时滞随机发展方程的Ulam-Hyers稳定性

用不动点定理研究Hilbert空间中一类含α∈(0,1)阶Riemann-Liouville分数阶导数的时滞随机发展方程温和解的存在唯一性,并证明该解的Ulam-Hyers稳定性.最后举例说明所得结论的适用性.

Applications of Metal–Organic Frameworks and Their Derivatives in Electrochemical CO_(2)Reduction

Electrochemically reducing CO_(2)to more reduced chemical species is a promising way that not only enables the conversion of intermittent energy resources to stable fuels,but also helps to build a closed-loop anthropogenic carbon cycle.Among various electrocatalysts for electrochemical CO_(2)reduction,multifunctional metal–organic frameworks(MOFs)have been employed as highly efficient and selective heterogeneous electrocatalysts due to their ultrahigh porosity and topologically diverse structures.Up to now,great progress has been achieved in the design and synthesis of highly active and selective MOF-related catalysts for electrochemical CO_(2)reduction reaction(CO_(2)RR),and their corresponding reaction mechanisms have been thoroughly studied.In this review,we summarize the recent progress of applying MOFs and their derivatives in CO_(2)RR,with a focus on the design strategies for electrocatalysts and electrolyzers.We first discussed the reaction mechanisms for different CO_(2)RR products and introduced the commonly applied electrolyzer configurations in the current CO_(2)RR system.Then,an overview of several categories of products(CO,HCOOH,CH_(4),CH_(3)OH,and multi-carbon chemicals)generated from MOFs or their derivatives via CO_(2)RR was discussed.Finally,we offer some insights and perspectives for the future development of MOFs and their derivatives in electrochemical CO_(2)reduction.We aim to provide new insights into this field and further guide future research for large-scale applications.