This paper presents a C2 Pythagorean-Hodograph (PH) spline curve interpolator for high speed contouring applications. With the knot vector and control points given, the C2 PH quintic spline curve is a "good" interpolant to the nodal points of the cubic B-spline curve, with the same knot vector and control points. To generate the C2 PH quintic spline CURVES, a uniform knot sequence is employed.The S-curve motion planning architecture, with variable feedrate for a planar C2 PH quintic spline curve, is also developed. In particular, C1 cubic feed acceleration/deceleration is imposed on the first and last PH quintic spline segments. Several closed C2 PH quintic spline curve contouring tasks, along with a simple position loop controller, were conducted to verify the effectiveness of the proposed interpolation algorithm. The experimental results were analyzed and discussed. It is found that the proposed CNC interpolator is not only feasible for machining the complicated parametric CURVES represented in the C2 PH quintic spline form, but also yields a satisfactory contouring performance for variable feedrate control.

In this paper, Pythagorean-hodograph (PH) quantic spline CURVES constructed by several connected PH CURVES with C2 continuity are used to designing the tool path in machining operation. To generate the tool path commands, the acceleration/deceleration phase of motion and the middle regions of the tool path are devised by time-dependent and constant velocity interpolation algorithms, respectively. In the aforementioned interpolation algorithm, the exponential functions are employed to modify the feedrate profile and subsequently using the Pattern Search algorithm (PSA), the proposed feedrate profile is optimized to maintain the maximum jerk within allowable physical limits. Finally, high speed CNC machining for two cases of open and closed C2 PH quantic spline CURVES along with the commonly used feed forward/feedback controller is simulated in Simulink Matlab software and the contouring error is studied and analyzed.

Advanced model-based control of pH processes is noticeably a chemical modeling issue, because it can have a profound effect on the attainable control quality. This is especially the case when the pH regulation of streams, consisting of hundreds of constituents with varying concentrations, is encountered. The severe non-linear behavior of pH processes is reflected in the titration curve of the process stream. The performances of all model-based controllers are highly dependent on the accuracy of the model. Considering a great number of parameters such as dissociation constants, solubility products and characteristic concentrations places the designer in a dilemma of choosing between approximate physicochemical models and empirical ones, both having their own merits and shortcomings. Using radial basis function artificial neural networks, a new modeling approach for approximating the titration curve is proposed in this article and some physical interpretations for selecting the neural network parameters are given. Both off-line and on-line training for adaptive control strategy can be used. The effectiveness of the proposed scheme is demonstrated by simulation and experimental studies.

Lactation length is different in individual cows, which is generally converted to a 305-day standard using curve fitting models for genetic and management practices. Individual CURVES do not have a standard shape in all cases, and can deviate from the standard pattern according to factors such as individual differences, and type of fitted models. These non-standard CURVES, called atypical, resulted from incorrect estimated parameters of the CURVES; which consist of: continuously increasing or decreasing and reversed standards. This study was conducted to investigate the importance of atypical CURVES in estimation of 305-day milk production, by fitting two nonlinear models? Wood (empirical) and Pollott (biological), on 7659 and 6692 test-day milk yield of 977 and 776 first calving Iranian Simmental and Jersey cows, during 2007-2020, using R software. Different patterns obtained based on the combination of increasing (b) and decreasing (c) phase parameters of CURVES. The number of standard CURVES from the Pollott and Wood models were 85.5% and 62.2% for Simmental, and 83.1% and 70.6% for Jersey cows, respectively. Only continuously increasing CURVES were observed in both breeds in Pollott model (14.8% and 16.9%, Simmental and Jersey cows, respectively); Whereas in Wood model, all 3 groups of atypical CURVES were observed, which the reversed standard was the most (22.3% and 16.5%, Simmental and Jersey cows, respectively). Based on the findings, at the time of standardizing the production of dairy cows (national evaluations), not only differences between breeds, but also special attention to the production of atypical CURVES, should be paid (to correct or discard them).

In this paper simple quartic trigonometric polynomial blending functions, with a tension parameter, are presented. These type of functions are useful for constructing trigonometric Bezier CURVES and surfaces, they can be applied to construct continuous shape preserving interpolation spline CURVES with shape parameters. To better visualize objects and graphics a tension parameter is included. In this work we constructed the Trigonometric Bezier CURVES followed by a construction of the shape preserving interpolation spline CURVES with local shape parameters and finally several numerical examples are presented such as open shape preserving interpolation curve, closed shape preserving interpolation curve and surfaces. As a direct application we computed the area surrounded by a closed curve.

 The purpose of this study was relationship between spinal CURVES and specialized movements of Bastanykaran. Study sample included 73 athletes from Bastanykaran 18-36 years Kerman that had at least 2 years experience. Flexible ruler was used for measuring spinal CURVES. For data analysis of statistical methods at two levels of descriptive and inferential (Chi square ( c2) coefficient of agreement C) through the statistical software SPSS, were used. Results showed that %47.9 of Bastanykaran have hyperkyphosis and %32.9 of this community have hyperlordosis. The findings was significant relationship between movement of Turning the Meel (p<0.05, c2=8.70) and movement of Whirling (p<0.05, c2=9.20) with the amount kyphosis arch, and movement of Kabbadeh Workouts and amount lordosis curve of Bastanykaran (p<0.05, c2=8.64).