error estimations
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The acceptance of tele-robotics and teleoperations through networked control system (NCS) is increasing day-by-day. NCS involves the feedback control loop system wherein the control components such as actuators and sensors are controlled and allowed to share their feedback over real time network with distributed users spread geographically. The performance and surgical complications majorly depend upon time delay, packet dropout and jitter induced in the system. The delay of data packet to the receiving side not only causes instability but also affect the performance of the system. In this article, author designed and simulate the functionality of a model-based Smith predictive controller. The model and randomized error estimations are employed through Markov approach and Kalman techniques. The simulation results show a delay of 49.926ms from master controller to slave controller and 79.497ms of delay from sensor to controller results to a total delay of 129.423ms. This reduced delay improve the surgical accuracy and eliminate the risk factors to criticality of patients’ health.

AbstractIn this paper, the authors derive some new generalizations of fractional trapezium-like inequalities using the class of harmonic convex functions. Moreover, three new fractional integral identities are given, and on using them as auxiliary results some interesting integral inequalities are found. Finally, in order to show the efficiency of our main results, some applications to special means for different positive real numbers and error estimations for quadrature formulas are obtained.

Abstract This paper presents the kinematic calibration of a 4-DOF high-speed parallel robot. In order to improve the calibration effect by decreasing the influence of the unobservable disturbance variables introduced by error measurement, a measurement configuration optimization method is proposed. Configurations are iteratively selected inside the workspace by a searching algorithm, then the selection results are evaluated through an index associated with the condition number of the identification Jacobian matrix, finally the number of optimized configurations are determined. Since the searching algorithm has been shown to be sensitive to local minima, a meta-heuristic method has been applied to decrease this sensibility. To verify the effectiveness of the algorithm and kinematic calibration, computation validations, pose error estimations and experiments are performed. The results show that the identification accuracy and calibration effect can be significantly improved by using the optimized configurations.

In this chapter, firstly we apply the iterative method to establish the existence of the positive solution for a type of nonlinear singular higher-order fractional differential equation with fractional multi-point boundary conditions. Explicit iterative sequences are given to approximate the solutions and the error estimations are also given. Secondly, we cover the multi-valued case of our problem. We investigate it for nonconvex compact valued multifunctions via a fixed point theorem for multivalued maps due to Covitz and Nadler. Two illustrative examples are presented at the end to illustrate the validity of our results.

Numerical approximations of definite integrals and related error estimations can be made using Simpson’s rules (inequalities). There are two well-known rules: Simpson’s 13 rule or Simpson’s quadrature formula and Simpson’s 38 rule or Simpson’s second formula. The aim of the present paper is to extend several inequalities that hold for Simpson’s 13 rule to Simpson’s 38 rule. More precisely, we prove a weighted version of Simpson’s second type inequality and some Simpson’s second type inequalities for Lipschitzian, bounded variations, convex functions and the functions that belong to Lq. Some applications of the second type Simpson’s inequalities relate to approximations of special means and Simpson’s 38 formula, and moments of random variables are made.

In this research, we have introduced Galerkin method for finding approximate solutions of Fredholm Volterra Integral Equation (FVIE) of 2nd kind, and this method shows the result in respect of the linear combinations of basis polynomials. Here, BF (product of Bernstein and Fibonacci polynomials), CH (product of Chebyshev and Hermite polynomials), CL (product of Chebyshev and Laguerre polynomials), FL (product of Fibonacci and Laguerre polynomials) and LLE (product of Legendre and Laguerre polynomials) polynomials are established and considered as basis function in Galerkin method. Also, we have tried to observe the behavior of all these approximate solutions finding from Galerkin method for different problems and then a comparison is shown using some standard error estimations. In addition, we observe the error graphs of numerical solutions in Galerkin method for different problems of FVIE of second kind. GANITJ. Bangladesh Math. Soc.41.1 (2021) 1–14

AbstractSome new integral inequalities for strongly $(\alpha ,h-m)$ ( α , h − m ) -convex functions via generalized Riemann–Liouville fractional integrals are established. The outcomes of this paper provide refinements of some fractional integral inequalities for strongly convex, strongly m-convex, strongly $(\alpha ,m)$ ( α , m ) -convex, and strongly $(h-m)$ ( h − m ) -convex functions. Also, the refinements of error estimations of these inequalities are obtained by using two fractional integral identities. Moreover, using a parameter substitution and a constant multiplier, k-fractional versions of established inequalities are also given.

In this article, we prove some fractional versions of Hadamard-type inequalities for strongly exponentially α , h − m -convex functions via generalized Riemann–Liouville fractional integrals. The outcomes of this paper provide inequalities of strongly convex, strongly m -convex, strongly s -convex, strongly α , m -convex, strongly s , m -convex, strongly h − m -convex, strongly α , h − m -convex, strongly exponentially convex, strongly exponentially m -convex, strongly exponentially s -convex, strongly exponentially s , m -convex, strongly exponentially h − m -convex, and exponentially α , h − m -convex functions. The error estimations are also studied by applying two fractional integral identities.

In the evaluation of Lagrangian particle tracking (LPT) measurement data the use of spatially binned flow statistics in the form of one, two or multi-point statistics is often an essential step towards better understanding of the measured flow fields. Increasingly there is a focus towards uncertainty quantification of the measurement system however these evaluations are seldom used to directly improve the statistics by directly involving them into the calculation. We present our Functional Binning approach which makes use of such uncertainty information as a core component for the calculation of improved statistics. The improvements towards prior approaches are shown utilizing synthetic data as well as data from a real-world subsonic jet experiment. Beyond the initial formulation for one-point statistics, we show that this approach is readily extended towards two-point statistics and explore more advanced utilizations of uncertainty information for the optimal selection of particle pairs. Furthermore, the benefits of more individualized particle error estimations are investigated and some strategies for archiving such information are investigated.