Mas et al. adapted the notion of smoothness, introduced by Godo and Sierra, and discussed two kinds of smooth implications (a discrete counterpart of continuous fuzzy implications) on a finite chain. This work is devoted to exploring the formal relations between smoothness and other six properties of implications on a finite chain. As a byproduct, several classes of smooth implications on a finite chain are characterized.
In this article, a new solution to the steering control problem of nonholonomic systems, which are transformable into chained form is investigated. A smooth super twisting sliding mode control technique is used to steer nonholonomic systems. Firstly, the nonholonomic system is transformed into a chained form system, which is further decomposed into two subsystems. Secondly, the second subsystem is steered to the origin by using smooth super twisting sliding mode control. Finally, the first subsystem is steered to zero using signum function. The proposed method is tested on three nonholonomic systems, which are transformable into chained form; a two-wheel car model, a model of front-wheel car, and a fire truck model. Numerical computer simulations show the effectiveness of the proposed method when applied to chained form nonholonomic systems.
This work addresses the problem of overfitting the training data. We suggest smoothing the decision boundaries by eliminating border instances from the training set before training Artificial Neural Networks (ANNs). This is achieved by using a variety of instance reduction techniques. A large number of experiments were performed using 21 benchmark data sets from UCI machine learning repository, the experiments were performed with and without the introduction of noise in the data set. Our empirical results show that using a noise filtering algorithm to filter out border instances before training an ANN does not only improve the classification accuracy but also speeds up the training process by reducing the number of training epochs. The effectiveness of the approach is more obvious when the training data contains noisy instances.
Let $B^{H_{i},K_i}=\{B^{H_{i},K_i}_t, t\geq 0 \}$, $i=1,2$ be two independent, $d$-dimensional bifractional Brownian motions with respective indices $H_i\in (0,1)$ and $K_i\in (0,1]$. Assume $d\geq 2$. One of the main motivations of this paper is to investigate smoothness of the collision local time $$ \ell _T=\int _{0}^{T}\delta (B_{s}^{H_{1},K_1}-B_{s}^{H_{2},K_2}) {\rm d} s, \qquad T>0, $$ where $\delta $ denotes the Dirac delta function. By an elementary method we show that $\ell _T$ is smooth in the sense of Meyer-Watanabe if and only if $\min \{H_{1}K_1,H_{2}K_2\}<{1}/{(d+2)}$.
Robots for automatic motion inside pipelines of various diameters from 100 up to 1000 mm, having essentially different geometrical parameters (radiuses and a configuration of bending, length, etc.) and transporting the various environment (gas, oil, water, etc.) is the modern direction of an application robotics, very demanded by the industry. This paper presents some examples of such robots intended for execution of various technological operations, diagnostics, repairing, clearing, welding, etc. One of the most complex operations is the painting demanding heightened smoothness of the robot motion. Paper introduces new approaches in design and calculations of this robotic system. and Obsahuje seznam literatury
Our aim in this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator on grand Morrey spaces of variable exponents over non-doubling measure spaces. As an application of the boundedness of the maximal operator, we establish Sobolev's inequality for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces. We are also concerned with Trudinger's inequality and the continuity for Riesz potentials.
Armenak Antinyan, Vardan Baghdasaryan, Aleksandr Grigoryan., Částečně tištěno napříč, Obsahuje bibliografii a bibliografické odkazy, and České a anglické resumé