The neutral differential equation (1.1) $$ \frac{{\mathrm{d}}^n}{{\mathrm{d}} t^n} [x(t)+x(t-\tau)] + \sigma F(t,x(g(t))) = 0, $$ is considered under the following conditions: $n\ge 2$, $\tau >0$, $\sigma = \pm 1$, $F(t,u)$ is nonnegative on $[t_0, \infty) \times (0,\infty)$ and is nondecreasing in $u\in (0,\infty)$, and $\lim g(t) = \infty$ as $t\rightarrow \infty$. It is shown that equation (1.1) has a solution $x(t)$ such that (1.2) $$ \lim_{t\rightarrow \infty} \frac{x(t)}{t^k}\ \text{exists and is a positive finite value if and only if} \int^{\infty}_{t_0} t^{n-k-1} F(t,c[g(t)]^k){\mathrm{d}} t < \infty\text{ for some }c > 0. $$ Here, $k$ is an integer with $0\le k \le n-1$. To prove the existence of a solution $x(t)$ satisfying (1.2), the Schauder-Tychonoff fixed point theorem is used.
Does there exist an atomic lattice effect algebra with non-atomic subalgebra of sharp elements? An affirmative answer to this question (and slightly more) is given: An example of an atomic MV-effect algebra with a non-atomic Boolean subalgebra of sharp or central elements is presented.
On the example of Ostrów Tumski in Wrocław (Silesia, Polish lands) an attempt of identification of places associated with trade and exchange in early medieval strongholds was made. The alleged marketplace existed in the stronghold from the end of the 11th century to the end of the 12th century. Its existence would be confirmed by the empty square between buildings, the accumulation of finds related to trade and exchange as well as spending free time. The connection of some buildings form Ostrów Tumski with commercial activities is also not excluded. On the basis of analogies from the main centers of the Piast state and selected sites from the Bohemian and Moravian territories, the potential location of the marketplaces was analyzed. Attention was drawn to the relationship between finds related to trade and exchange with other manifestations of economic activity (e.g. non-ferrous metallurgy). An attempt was also made to answer the question when and in what political and economic conditions such places could be created.
We developed an automated miniature constant-head tension infiltrometer that measures very small infiltration rates at millimetre resolution with minimal demands on the operator. The infiltrometer is made of 2.9 mm internal radius glass tube, with an integrated bubbling tower to maintain constant negative head and a porous mesh tip to avoid air-entry. In the bubbling tower, bubble formation and release changes the electrical resistance between two electrodes at the air-inlet. Tests were conducted on repacked sieved sands, sandy loam soil and clay loam soil, packed to a soil bulk density ρd of 1200 kg m-3 or 1400 kg m-3 and tested either air-dried or at a water potential ψ of -50 kPa. The change in water volume in the infiltrometer had a linear relationship with the number of bubbles, allowing bubble rate to be converted to infiltration rate. Sorptivity measured with the infiltrometer was similar between replicates and showed expected differences from soil texture and ρd, varying from 0.15 ± 0.01 (s.e.) mm s-1/2 for 1400 kg m-3 clay loam at ψ = -50 kPa to 0.65 ± 0.06 mm s-1/2 for 1200 kg m-3 air dry sandy loam soil. An array of infiltrometers is currently being developed so many measurements can be taken simultaneously.
An effective and novel roller bearing fault diagnosis technique based on empirical mode decomposition (EMD) energy entropy and support vector machine (SVM) is put forward in this article. The vibration signal of roller bearing is decomposed by EMD and the first 5 intrinsic mode function (IMF) components are obtained. SVM served as a fault diagnosis classifier and the extracted energy features of the first 5 IMFs are taken as network input vectors, and then the fault bearing and the normal bearing can be distinguished. An technique for fault of roller bearing by SVM is evaluated against a series of fault diagnosis methods that are widely used in machinery, with particular regard to the effect of training set size on fault diagnosis accuracy. We trained the SVM using RBF kernel function. We compare our experimental results with the existing results given by SMO and SVM-light algorithms. It can be seen that the fault diagnosis method based on SVM-light is superior to that based on SMO in diagnosis accuracy of roller bearing. In addition to the SVM, the same datasets were classified using RBF NN and Hopfield NN. The experimental results show that the technique of support vector machine based on EMD energy entropy has higher fault diagnosis ability.
Designing a wavelet neural network (WNN) needs to be done judiciously in attaining the optimal generalization performance. Its prediction competence relies highly on the initial value of translation vectors. However, there is no established solution in determining the appropriate initial value for the translation vectors at this moment. In this paper, we propose a novel enhanced fuzzy c-means clustering algorithm - specifically, the modified point symmetry-based fuzzy c-means (MPSDFCM) algorithm - in initializing the translation vectors of the WNNs. The effectiveness of embedding different activation functions in WNNs will be investigated as well. The categorization effectiveness of the proposed WNNs model was then evaluated in classifying the type 2 diabetics, and was compared with the multilayer perceptrons (MLPs) and radial basis function neural networks (RBFNNs) models. Performance assessment shows that our proposed model outperforms the rest, since a 100% superior classification rate was achieved.
Color quantization is an important process for image processing and various applications. Up to now, many color quantization methods have been proposed. The self-organizing maps (SOM) method is one of the most effective color quantization methods, which gives excellent color quantization results. However, it is slow, so it is not suitable for real-time applications. In this paper, we present a color importance{based SOM color quantization method. The proposed method dynamically adjusts the learning rate and the radius of the neighborhood using color importance. This makes the proposed method faster than the conventional SOM-based color quantization method. We compare the proposed method to 10 well-known color quantization methods to evaluate performance. The methods are compared by measuring mean absolute error (MAE), mean square error (MSE), and processing time. The experimental results show that the proposed method is effective and excellent for color quantization. Not only does the proposed method provide the best results compared to the other methods, but it uses only 67.18% of the processing time of the conventional SOM method.
An algorithm for correction of two-axes laser mount direction and gates in case of atmospheric drag induces diviations from the predicted satellite motion is described. Results of numerical simulations are shown.
The additive mixture rules have been extended for calculation of the effective longitudinal elasticity modulus of the composite (Functionally Graded Materials - FGM's) beams with both the polynomial longitudinal variation of the constituent's elasticity modulus. Stiffness matrix of the composite Bernoulli-Euler beam has been established which contains the transfer constants. These transfer constants describe very accurately the polynomial uni-axially variation of the effective longitudinal elasticity modulus, which is calculated using the extended mixture rules.
The mixture rules have been extended for calculation of the effective elasticity modulus for stretching and flexural bending of the layer-wise symmetric composite (FGM's) sandwich beam finite element as well. The polynomial longitudinal and transversally symmetric layer-wise variation of the sandwich beam stiffness has been taken into the account. Elastic behaviour of the sandwich beam will be modelled by the laminate theory. Stiffness matrix of such new sandwich beam element has been established. The nature and quality of the matrix reinforcement interface have not been considered. Four examples have been solved using the extended mixture rules and the new composite (FGM's) beam elements with varying stiffness. The obtained results are evaluated, discussed and compared. and Obsahuje seznam literatury