Retrospective Analysis of Training Intensity Distribution Based on Race Pace Versus Physiological Benchmarks in Highly Trained Sprint Kayakers

Background Research results on the training intensity distribution (TID) in endurance athletes are equivocal. This non-uniformity appears to be partially founded in the different quantification methods that are implemented. So far, TID research has solely focused on sports involving the lower-body muscles as prime movers (e.g. running). Sprint kayaking imposes high demands on the upper-body endurance capacity of the athlete. As there are structural and physiological differences between upper- and lower-body musculature, TID in kayaking should be different to lower-body dominant sports. Therefore, we aimed to compare the training intensity distribution during an 8-wk macrocycle in a group of highly trained sprint kayakers employing three different methods of training intensity quantification. Methods Heart rate (HR) and velocity during on-water training of nine highly trained German sprint kayakers were recorded during the final 8 weeks of a competition period leading to the national championships. The fractional analysis of TID was based on three zones (Z) derived from either HR (TIDBla-HR) or velocity (TIDBla-V) based on blood lactate (Bla) concentrations (Z1 ≤ 2.5 mmol L−1 Bla, Z2 = 2.5–4.0 mmol L−1 Bla, Z3 ≥ 4.0 mmol L−1 Bla) of an incremental test or the 1000-m race pace (TIDRace): Z1 ≤ 85% of race pace, Z2 = 86–95% and Z3 ≥ 95%. Results TIDBla-V (Z1: 68%, Z2: 14%, Z3: 18%) differed from TIDBla-HR (Z1: 91%, Z2: 6%, Z3: 3%) in each zone (all p < 0.01). TIDRace (Z1: 73%, Z2: 20%, Z3: 7%) differed to Z3 in TIDBla-V (p < 0.01) and all three TIDBla-HR zones (all p < 0.01). Individual analysis revealed ranges of Z1, Z2, Z3 fractions for TIDBla-HR of 85–98%, 2–11% and 0.1–6%. For TIDBla-V, the individual ranges were 41–82% (Z1), 6–30% (Z2) and 8–30% (Z3) and for TIDRace 64–81% (Z1), 14–29% (Z2) and 4–10% (Z3). Conclusion The results show that the method of training intensity quantification substantially affects the fraction of TID in well-trained sprint kayakers. TIDRace determination shows low interindividual variation compared to the physiologically based TIDBla-HR and TIDBla-V. Depending on the aim of the analysis TIDRace, TIDBla-HR and TIDBla-V have advantages as well as drawbacks and may be implemented in conjunction to maximize adaptation.

Fractional Analysis of MHD Boundary Layer Flow over a Stretching Sheet in Porous Medium: A New Stochastic Method

In this article, an effective computing approach is presented by exploiting the power of Levenberg-Marquardt scheme (LMS) in a backpropagation learning task of artificial neural network (ANN). It is proposed for solving the magnetohydrodynamics (MHD) fractional flow of boundary layer over a porous stretching sheet (MHDFF BLPSS) problem. A dataset obtained by the fractional optimal homotopy asymptotic (FOHA) method is created as a simulated data simple for training (TR), validation (VD), and testing (TS) the proposed approach. The experiments are conducted by computing the results of mean-square-error (MSE), regression analysis (RA), absolute error (AE), and histogram error (HE) measures on the created dataset of FOHA solution. During the learning task, the parameters of trained model are adjusted by the efficacy of ANN backpropagation with the LMS (ANN-BLMS) approach. The ANN-BLMS performance of the modeled problem is verified by attaining the best convergence and attractive numerical results of evaluation measures. The experimental results show that the approach is effective for finding a solution of MHDFF BLPSS problem.

Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings

The theory of fractional analysis has been a focal point of fascination for scientists in mathematical science, given its essential definitions, properties, and applications in handling real-life problems. In the last few decades, many mathematicians have shown their considerable interest in the theory of fractional calculus and convexity due to their wide range of applications in almost all branches of applied sciences, especially in numerical analysis, physics, and engineering. The objective of this article is to establish Hermite-Hadamard type integral inequalities by employing the k-Riemann-Liouville fractional operator and its refinements, whose absolute values are twice-differentiable h-convex functions. Moreover, we also present some special cases of our presented results for different types of convexities. Moreover, we also study how q-digamma functions can be applied to address the newly investigated results. Mathematical integral inequalities of this class and the arrangements associated have applications in diverse domains in which symmetry presents a salient role.

Development of computer program for automatic X-ray analysis of quality of vegetable seeds

Traditional morphometric methods of seed quality analysis, although they are accurate, are less informative, labor-intensive and long-term in execution. In modern conditions, in seed science and seed control, the use of more informative and high-speed instrumental methods is required. The method of microfocus X-ray of seeds is one of them, it allows you to visualize the internal structure of seeds. In the joint work of employees of the Federal Scientific Vegetable Center, Agrophysical Research Institute and St. Petersburg State Electrotechnical University, Research Institute for Storage Problems of "Rosrezerv", a method of X-ray analysis of the quality of vegetable seeds was developed and tested. Currently, programming, automation of this method is underway. The method of digital analysis of X-ray images in automatic mode comes as a replacement for the previously applied visual analysis of seed radiographs. A modernized software and hardware complex was developed and tested, a program algorithm was compiled, consisting of several stages. As a result, the quality analysis of seeds is significantly accelerated by visualizing their internal structure. The newly developed computer program "Sortsemkontrol-2" recognizes seeds according to the following qualitative indicators: full-value, underdevelopment, undevelopment, monstrous. The analysis results are automatically reported as a log. The fractional analysis of the seed batch is also carried out, the dimensional characteristic of each fraction is given, according to the two largest adjacent fractions, the equalization of the seed batch is determined. Fractional analysis of a batch of seeds is of great practical importance for pre-production of seeds. In the future, the application of the computer program "Sortsemkontrol-2" will provide an accelerated, at the same time informative analysis of the quality of seeds, which is very important in the conditions of commercialization of seed turnover.

A Comparative Study of the Fractional-Order System of Burgers Equations

This paper is related to the fractional view analysis of coupled Burgers equations, using innovative analytical techniques. The fractional analysis of the proposed problems has been done in terms of the Caputo-operator sense. In the current methodologies, first, we applied the Elzaki transform to the targeted problem. The Adomian decomposition method and homotopy perturbation method are then implemented to obtain the series form solution. After applying the inverse transform, the desire analytical solution is achieved. The suggested procedures are verified through specific examples of the fractional Burgers couple systems. The current methods are found to be effective methods having a close resemblance with the actual solutions. The proposed techniques have less computational cost and a higher rate of convergence. The proposed techniques are, therefore, beneficial to solve other systems of fractional-order problems.

On New Generalizations of Hermite-Hadamard Type Inequalities via Atangana-Baleanu Fractional Integral Operators

Fractional operators are one of the frequently used tools to obtain new generalizations of clasical inequalities in recent years and many new fractional operators are defined in the literature. This development in the field of fractional analysis has led to a new orientation in various branches of mathematics and in many of the applied sciences. Thanks to this orientation, it has brought a whole new dimension to the field of inequality theory as well as many other disciplines. In this study, a new lemma has been proved for the fractional integral operator defined by Atangana and Baleanu. Later with the help of this lemma and known inequalities such as Young, Jensen, Hölder, new generalizations of Hermite-Hadamard inequality are obtained. Many reduced corollaries about the main findings are presented for classical integrals.

A Graphical Stability Analysis Method for Cascade Conjugate Order Systems

The theory and applications of complex fractional analysis have recently become a hot topic in the fields of mathematics and engineering. Therefore, studies on the complex order systems and their subset called the complex conjugate order systems began to appear in the control community. On the other hand, the concept of stability has always been an important issue, especially in the analysis and control of dynamical systems. In this paper, a graphical method for stability analysis of the complex conjugate order systems is presented. Since the proposed method is based on the Mikhailov stability criterion known from the stability theory of integer order systems, it is named the generalized modified Mikhailov stability criterion. This method gives stability information about the higher order complex conjugate order systems, i.e. cascade conjugate order systems, according to whether it encloses the origin in the complex plane or not. Three simulation examples for the cascade conjugate order systems are given to show the effectiveness and reliability of the method presented. The results are verified by the poles on the first sheet of Riemann surface and also time responses of the systems, which are calculated analytically in a very complex way.

Chaotic Dynamics and Chaos Control in a Fractional-Order Satellite Model and Its Time-Delay Counterpart

Fractional analysis provides useful tools to describe natural phenomena, and therefore, it is more convenient to describe models of satellites. This work illustrates rich chaotic behaviors that exist in a fractional-order model for satellite with and without time-delay. The proof for existence and uniqueness of the satellite model’s solution with and without time-delay is shown. Chaos control is achieved in this system via a simple linear feedback control criterion. Chaotic attractors and chaos control are also found in a time-delay version of the proposed fractional-order satellite system. Various tools based on numerical simulations such as 2D and 3D attractors and bifurcation diagrams are used to illustrate the variety of rich chaotic dynamics in the satellite models.