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.

Legendre-Jacobi’s Elliptic Integrals Shed Light on the Luminosity Distance in Cosmology

This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward mathematical formulation for the luminosity distance as function of the transverse comoving distance for all cosmology cases with a non-zero cosmological constant by adopting a different mindset. The applied method deals with incomplete elliptical integrals of the first kind associated with the polynomial roots admitted in the comoving distance integral according to the scientific literature. The outcome shows that the luminosity distance can be obtained by the combination of an analytical solution followed by a numerical integration in order to account for the redshift. This solution is solely compared to the current Gaussian quadrature method used as basic recognized algorithm in standard cosmology.

A Cauchy integral formula for(p,q)-monogenic functions withα-weight

Firstly,some properties for(p,q)-monogenic functions withα-weight in Clifford analysis are given.Then,the Cauchy-Pompeiu formula is proved.Finally,the Cauchy integral formula and the Cauchy integral theorem for(p,q)-monogenic functions withα-weight are given.

Some convergence theorems of fuzzy concave integral on fuzzyσ-algebra

In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.

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. .

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.

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.

Joint User Association and Satellite Selection for Satellite-Terrestrial Integrated networks

In this paper, we investigate a cooperation mechanism for satellite-terrestrial integrated networks. The terrestrial relays act as the supplement of traditional small cells and cooperatively provide seamless coverage for users in the densely populated areas.To deal with the dynamic satellite backhaul links and backhaul capacity caused by the satellite mobility, severe co-channel interference in both satellite backhaul links and user links introduced by spectrum sharing,and the difference demands of users as well as heterogeneous characteristics of terrestrial backhaul and satellite backhaul, we propose a joint user association and satellite selection scheme to maximize the total sum rate. The optimization problem is formulated via jointly considering the influence of dynamic backhaul links, individual requirements and targeted interference management strategies, which is decomposed into two subproblems: user association and satellite selection. The user association is formulated as a nonconvex optimization problem, and solved through a low-complexity heuristic scheme to find the most suitable access point serving each user. Then, the satellite selection is resolved based on the cooperation among terrestrial relays to maximize the total backhaul capacity with the minimum date rate constraints. Finally,simulation results show the effectiveness of the proposed scheme in terms of total sum rate and power efficiency of TRs' backhaul.

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.

Wave propagation of a functionally graded plate via integral variables with a hyperbolic arcsine function

Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.

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.

Joint Active and Passive Beamforming Design for Hybrid RIS-Aided Integrated Sensing and Communication

Integrated sensing and communication(ISAC) is considered an effective technique to solve spectrum congestion in the future. In this paper, we consider a hybrid reconfigurable intelligent surface(RIS)-assisted downlink ISAC system that simultaneously serves multiple single-antenna communication users and senses multiple targets. Hybrid RIS differs from fully passive RIS in that it is composed of both active and passive elements, with the active elements having the effect of amplifying the signal in addition to phase-shifting. We maximize the achievable sum rate of communication users by collaboratively improving the beamforming matrix at the dual function base station(DFBS) and the phase-shifting matrix of the hybrid RIS, subject to the transmit power constraint at the DFBS, the signal-to-interference-plus-noise-ratio(SINR) constraint of the radar echo signal and the RIS constraint are satisfied at the same time. The builtin RIS-assisted ISAC design problem model is significantly non-convex due to the fractional objective function of this optimization problem and the coupling of the optimization variables in the objective function and constraints. As a result, we provide an effective alternating optimization approach based on fractional programming(FP) with block coordinate descent(BCD)to solve the optimization variables. Results from simulations show that the hybrid RIS-assisted ISAC system outperforms the other benchmark solutions.

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 multidisciplinary team-based integrated traditional Chinese medicine and Western medicine in rotator cuff injury patients undergoing arthroscopic surgery

BACKGROUND Arthroscopic rotator cuff repair is a common surgical treatment for rotator cuff injuries(RCIs).Although this procedure has certain clinical advantages,it requires rehabilitation management interventions to ensure therapeutic efficacy.AIM To investigate the effect of integrated traditional Chinese medicine and Western medicine(TCM-WM)under the multidisciplinary team(MDT)model on the postoperative recovery of patients undergoing arthroscopic surgery for RCIs.METHODS This study enrolled 100 patients who underwent arthroscopic rotator cuff repair for RCIs at the Seventh People’s Hospital of Shanghai University of Traditional Chinese Medicine between June 2021 and May 2024.They were divided into a control group(n=48)that received routine rehabilitation treatment and an experimental group(n=52)that received TCM-WM under the MDT model(e.g.,acupuncture,TCM traumatology and orthopedics,and rehabilitation).The results of the Constant–Murley Shoulder Score(CMS),Visual Analogue Scale(VAS),Shoulder Pain and Disability Index(SPADI),muscular strength evaluation,and shoulder range of motion(ROM)assessments were analyzed.RESULTS After treatment,the experimental group showed significantly higher CMS scores in terms of pain,functional activity,shoulder joint mobility,and muscular strength than the baseline and those of the control group.The experimental group also exhibited significantly lower VAS and SPADI scores than the baseline and those of the control group.In addition,the experimental group showed significantly enhanced muscular strength(forward flexor and external and internal rotator muscles)and shoulder ROM(forward flexion,abduction,and lateral abduction)after treatment compared with the control group.CONCLUSION TCM-WM under the MDT model improved shoulder joint function,relieved postoperative pain,promoted postoperative functional recovery,and facilitated the recovery of muscular strength and shoulder ROM in patients with RCIs who underwent arthroscopic rotator cuff repair.