Trajectory tracking guidance of interceptor via prescribed performance integral sliding mode with neural network disturbance observer

This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost phase.Indeed,the velocity control in such trajectory tracking guidance systems of missiles is challenging.As our contribution,the velocity control channel is designed to deal with the intractable velocity problem and improve tracking accuracy.The global prescribed performance function,which guarantees the tracking error within the set range and the global convergence of the tracking guidance system,is first proposed based on the traditional PPF.Then,a tracking guidance strategy is derived using the integral sliding mode control techniques to make the sliding manifold and tracking errors converge to zero and avoid singularities.Meanwhile,an improved switching control law is introduced into the designed tracking guidance algorithm to deal with the chattering problem.A back propagation neural network(BPNN)extended state observer(BPNNESO)is employed in the inner loop to identify disturbances.The obtained results indicate that the proposed tracking guidance approach achieves the trajectory tracking guidance objective without and with disturbances and outperforms the existing tracking guidance schemes with the lowest tracking errors,convergence times,and overshoots.

Approximate solution of Volterra-Fredholm integral equations using generalized barycentric rational interpolant

It is well-known that interpolation by rational functions results in a more accurate approximation than the polynomials interpolation.However,classical rational interpolation has some deficiencies such as uncontrollable poles and low convergence order.In contrast with the classical rational interpolants,the generalized barycentric rational interpolants which depend linearly on the interpolated values,yield infinite smooth approximation with no poles in real numbers.In this paper,a numerical collocation approach,based on the generalized barycentric rational interpolation and Gaussian quadrature formula,was introduced to approximate the solution of Volterra-Fredholm integral equations.Three types of points in the solution domain are used as interpolation nodes.The obtained numerical results confirm that the barycentric rational interpolants are efficient tools for solving Volterra-Fredholm integral equations.Moreover,integral equations with Runge’s function as an exact solution,no oscillation occurrs in the obtained approximate solutions so that the Runge’s phenomenon is avoided.

Obstacles to the Integrated Care of Children Aged 6 to 59 Months Suffering from Acute and Severe Malnutrition at the Chu-Me and HATC of N’Djamena/Chad

Introduction: the problem of Severe Acute Malnutrition (SAM) and its consequences concern and challenge all social actors worldwide. The objective of the study was to identify the real obstacles that actors face in the integrated management of children aged 6 - 59 months suffering from SAM at the University Hospital of Mother and Child (CHUME) and the Chad-China Friendship Hospital (HATC) of N’Djamena. Methodology: this is a cross-sectional descriptive and interpretative study conducted from January to October 2023 at the CHUME and HATC of N’Djamena. It is based on questionnaires and direct observation of two hundred and thirty-six (236) parents or guardians of malnourished children admitted to these health facilities. All 236 agreed to participate freely in this study. Results: it appears from this study that the obstacles to the integrated management of malnourished children were: poor care-care relationship (26.7%) permanent product breaks (22.9%), the direct costs of services ranged from 30,000 to 60,000 FCFA (41.53%), drugs used for the treatment of patients came from the street (66.10%), malaria and anemia occupy an important place (27.5%), 57.2% respondents had monthly income below 60,000 CFAF. Conclusion: the present study carried out has identified the real bottlenecks to the integrated management of children suffering from SAM in the therapeutic nutritional units of the city of N’Djamena. .

Feynman Path Integral Using Operator Integration in Banach Space

Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector-valued measure. We will demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with LBS integration approach.

CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS

Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.

The Construction of Integrated Nursing Model Prevention of Oxaliplatin Chemotherapy-Induced Peripheral Nerve Injury

Objective: To investigate the effect of the integrated nursing model in the prevention of chemotherapy-induced peripheral injury. Methods: A total of 60 tumor patients receiving oxaliplatin for 1 - 6 cycles of chemotherapy from January to September 2023 were selected. 30 patients were selected from January to March and divided into the control group, and 30 patients were selected from July to 9 as the experimental group. The control group received conventional chemotherapy nursing, while the experimental group received integrated nursing. Anxiety, peripheral nerve toxicity stage and quality of life score were compared between the two groups before and after intervention. Results: After intervention, the scores of the self-rating Anxiety Scale (SAS) and the total scores of the oxaliplatin Levi specific sensory neurotoxicity scale in the experimental group were significantly lower than those in the control group, and the differences were statistically significant (P< 0.05);The Quality of Life Scale (FACT-G) score of cancer patients was higher than that of control group, and the difference was statistically significant (P< 0.05). Conclusion: The integrated nursing model can effectively reduce the anxiety of patients, reduce the incidence of peripheral nerve injury and improve the quality of life of patients.

Design of integral sliding mode guidance law based on disturbance observer

With the increasing precision of guidance,the impact of autopilot dynamic characteristics and target maneuvering abilities on precision guidance is becoming more and more significant.In order to reduce or even eliminate the autopilot dynamic operation and the target maneuvering influence,this paper suggests a guidance system model involving a novel integral sliding mode guidance law(ISMGL).The method utilizes the dynamic characteristics and the impact angle,combined with a sliding mode surface scheme that includes the desired line-ofsight angle,line-of-sight angular rate,and second-order differential of the angular line-of-sight.At the same time,the evaluation scenario considere the target maneuvering in the system as the external disturbance,and the non-homogeneous disturbance observer estimate the target maneuvering as a compensation of the guidance command.The proposed system’s stability is proven based on the Lyapunov stability criterion.The simulations reveale that ISMGL effectively intercepted large maneuvering targets and present a smaller miss-distance compared with traditional linear sliding mode guidance laws and trajectory shaping guidance laws.Furthermore,ISMGL has a more accurate impact angle and fast convergence speed.

Results Involving Partial Differential Equations and Their Solution by Certain Integral Transform

In this study,we aimto investigate certain triple integral transformand its application to a class of partial differentialequations.We discuss various properties of the new transformincluding inversion, linearity, existence, scaling andshifting, etc. Then,we derive several results enfolding partial derivatives and establish amulti-convolution theorem.Further, we apply the aforementioned transform to some classical functions and many types of partial differentialequations involving heat equations,wave equations, Laplace equations, and Poisson equations aswell.Moreover,wedraw some figures to illustrate 3-D contour plots for exact solutions of some selected examples involving differentvalues in their variables.

Jintan in Jiangsu: Deep Integration of ‘Intangible Cultural Heritage+Tourism’

Through the deep integration of Intangible Cultural Heritage and tourism,Jintan has transformed the resources of Intangible Cultural Heritage into a "golden business card"of tourism,injected inexhaustible new momentum of culture and tourism into rural revitalization,and contributed to the city's popularity.

The tangential k-Cauchy-Fueter type operator and Penrose type integral formula on the generalized complex Heisenberg group

The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.

Existence of Solutions of a Convolution Integral Equation

In this study, we prove the of existence of solutions of a convolution Volterra integral equation in the space of the Lebesgue integrable function on the set of positive real numbers and with the standard norm defined on it. An operator P was assigned to the convolution integral operator which was later expressed in terms of the superposition operator and the nonlinear operator. Given a ball Br belonging to the space L it was established that the operator P maps the ball into itself. The Hausdorff measure of noncompactness was then applied by first proving that given a set M∈ B r the set is bounded, closed, convex and nondecreasing. Finally, the Darbo fixed point theorem was applied on the measure obtained from the set E belonging to M. From this application, it was observed that the conditions for the Darbo fixed point theorem was satisfied. This indicated the presence of at least a fixed point for the integral equation which thereby implying the existence of solutions for the integral equation.

Solvability and Construction of a Solution to the Fredholm Integral Equation of the First Kind

The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.

Fuzzy Henstock-Kurzweil Triple Integral on a Type 1 Quasi-Fuzzy Parallelepipedal Domain

In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.

Application of Choquet Integral-Importance-Performance Analysis and TOPSIS Methods in Approaching the Preference Factors of Calligraphy and Seal Engraving Imagery

Classical Chinese characters,presented through calligraphy,seal engraving,or painting,can exhibit different aesthetics and essences of Chinese characters,making them the most important asset of the Chinese people.Calligraphy and seal engraving,as two closely related systems in traditional Chinese art,have developed through the ages.Due to changes in lifestyle and advancements in modern technology,their original functions of daily writing and verification have gradually diminished.Instead,they have increasingly played a significant role in commercial art.This study utilizes the Evaluation Grid Method(EGM)and the Analytic Hierarchy Process(AHP)to research the key preference factors in the application of calligraphy and seal engraving imagery.Different from the traditional 5-point equal interval semantic questionnaire,this study employs a non-equal interval semantic questionnaire with a golden ratio scale,distinguishing the importance ratio of adjacent semantic meanings and highlighting the weighted emphasis on visual aesthetics.Additionally,the study uses Importance-Performance Analysis(IPA)and Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)to obtain the key preference sequence of calligraphy and seal engraving culture.Plus,the Choquet integral comprehensive evaluation is used as a reference for IPA comparison.It is hoped that this study can provide cultural imagery references and research methods,injecting further creativity into industrial design.

ANTICIPATED BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS WITH JUMPS AND APPLICATIONS TO DYNAMIC RISK MEASURES

In this paper, we focus on anticipated backward stochastic Volterra integral equations(ABSVIEs) with jumps. We solve the problem of the well-posedness of so-called M-solutions to this class of equation, and analytically derive a comparison theorem for them and for the continuous equilibrium consumption process. These continuous equilibrium consumption processes can be described by the solutions to this class of ABSVIE with jumps.Motivated by this, a class of dynamic risk measures induced by ABSVIEs with jumps are discussed.

The Model of“Post,Course,Competition,Certificate”Integrated Education for Electronic Information Engineering Technology Major in Higher Vocational Colleges

The core education function of higher vocational colleges is to train technical talents with high quality,so as to meet the needs of talents in the development stage of our society.Under the guidance of talent training,higher vocational colleges need to pay attention to establishing an all-round and three-dimensional education model,and promote innovation of higher vocational education on the basis of this.It is also a way to promote the innovation of higher vocational education to vigorously promote the construction of“post,course,competition,certificate”mode in the construction of education mode.Through the construction of“post,course,competition,certificate”mode,the education mode of higher vocational colleges is gradually improved,so as to strengthen the effectiveness of talent training in higher vocational colleges.Therefore,in this paper,the author puts forward some suggestions to promote the construction of the integrated education mode of the electronic information engineering technology major in higher vocational colleges,so as to help improve the talent training level of higher vocational colleges.

Numerical and experimental study on the particle erosion and gas–particle hydrodynamics in an integral multi-jet swirling spout-fluidized bed

In this paper,using the computational fluid dynamics based on Euler Lagrange and the commercial software Barracuda VR,the gas-particle hydrodynamics and the erosion of particles on the inner wall and internal components of the spouted bed in the integrated multi-jet swirling spout-fluidized bed(IMSSFB)are studied.Erosion experiments have obtained the characterization of particle erosion on internal components and verified the relevant numerical models.The results show that:the particle distribution within the IMSSFB is uneven due to the cyclonic effect of the axial swirl vane(ASV),resulting in particle erosion for the ASV being concentrated on one side;when the gas reaches the top,too high an erosion gas velocity leads to gas backflow.As the filling height increases,there is a tendency for the erosion position of the particles on the ASV to expand upwards.However,the effect of increasing gas velocity on the erosion position is insignificant.

CONSERVATION LAW AND APPLICATION OF J-INTEGRAL IN MULTI-MATERIALS

The conservation law of J-integral in two-media with a crack paralleling to the interface of the two media was firstly proved by analytical and numerical finite element method. Then a schedule model was established that an interface crack is inserted in four media. According to the J-integral conservation law on multi-media, the energy release ratio of Ⅰ-type crack was considered to be conservation when the middle medium layers are very thin. And the conservation law was also convinced by numerical method. By means of the dimension analysis on the model, the asymptotic results and formula calculating the energy release ratio and complex stress intensity factor are presented.

吴氏理筋手法结合J型针刀治疗术后肘关节僵硬的临床研究

目的 探讨吴氏理筋手法结合J型针刀治疗术后肘关节僵硬的临床应用价值。方法 选取江西省南昌市洪都中医院康复科2020年6月—2021年6月收治的60例术后肘关节僵硬患者,以单盲随机法分为对照组(关节松动术)与治疗组(吴氏理筋手法结合J型针刀),各30例。治疗4周后,比较两组Mayo肘关节功能评分(MEPS)与视觉模拟量表(VAS)评分,同时对疗效开展评估。结果 治疗后,与对照组相比,治疗组MEPS评分较高,而VAS评分较低(P<0.05);且治疗组总有效率为100.00%(30/30),明显高于对照组的83.33%(25/30)(P<0.05)。结论 吴氏理筋手法结合J型针刀治疗术后肘关节僵硬患者,能实现肘关节功能的恢复,并减轻患者疼痛,效果确切,具有较高的推广价值。

基于正交切削逆识别井下管柱的Johnson-Cook本构模型

在有限元仿真金属切削过程中,本构模型是仿真的基础,目前井下生产管柱J55油管材料的本构模型参数尚不明确,为此,提出一种基于正交切削理论逆识别油管材料Johnson-Cook(J-C)本构模型参数的方法。首先,通过准静态拉伸试验得到油管材料的应力-应变曲线,根据曲线拟合确定J55油管的初始屈服强度A、应变硬化系数B和应变硬化因子n;其次,通过正交切削试验获得切削力以及进给力,根据正交切削试验和平行剪切区模型,计算正交切削过程主剪切区中的流动应力、应变、应变率以及切削温度,并将这些参数与计算出的A、B、n代入J-C模型中,得到多组应变率敏感性参数C以及热软化效应参数m,从而确定其约束范围;第三,采用自适应权重粒子群算法在约束范围中搜索出参数C和m的最优值,进而确定J55油管材料本构模型参数;最后,使用逆识别法得出的J-C本构模型进行有限元仿真,将仿真结果与试验结果进行了对比。研究结果表明:与试验相比,有限元仿真的切削力和进给力最大相对误差分别为14.4%和13.64%,有限元仿真模拟温度与实际测量温度的最大相对误差为10.57%,仿真模型和实际切削过程在切屑形态上表现出了一致规律,验证了逆识别方法可行性和本构模型的可靠性。