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EN
The aim of the paper is to measure and forecast concentration of regional development potential on a regional basis. The study covered 14 GUS features, which measure the development potential. The forecast, nominal values and processes’ dynamics were calculated for data from 2010 to 2020, using author made method. The study reveals that key factors determining the diversification of the distribution of the potential include the relation of large agglomerations to their regional surroundings. Therefore, we are dealing with growth poles with different impact levels. Since 2010, the process of concentrating potential in Poland has taken different directions. In poorly developed regions, we observe constant distribution values. Most regions, especially those with medium and high levels of economic development, are characterized by a dynamic increase in the level of concentration 5% to 6% annually. This means that the growth poles «move away» from their surroundings and strengthen their position. Simultaneously, they slightly reduce the distance to the strongest developed region in Poland (Mazowsze). By 2020, these trends will remain unchanged, however regions with a moderately low level of development will observe the fastest growth.
EN
The paper presents a method for expanding the working range of separation elements, where the separation is conducted through the use of inertia particles. The presented dynamic separation elements work as the automatic control system (the regulating action is the elastic energy; the regulation object is the hydraulic resistance). It was taken the first step to the engineering method development for their calculation using analytical dependences of the finite element method. The critical velocity of the gas-liquid flow was determined, that causes a divergence phenomenon of dynamic separation device elements and expressions for generalized forces for the system “gas-liquid flow is a dynamic deflection element.” Two-knot finite elements with two degrees of freedom (transverse displacement and angle of the cross-section rotation) were used for dynamic deflection elements. The given number of degrees of freedom of the mechanical system “gas-liquid flow is a dynamic deflection element” due to the consideration of the transverse deformations of the plate allows simplifying the mathematical model. It was suggested to use aerohydroplastic phenomena of dynamic non-stability of dynamic deflection elements of separating devices, analogous to the method of applying acoustic oscillations to a heterogeneous stream, for the coagulation of dispersed particles in the flow.
EN
The results of numerical simulations presented in this paper are concerned with instability of a three member slender system subjected to Euler load. The investigated column is built up as a flat frame composed of three rods. In the internal one, the defect is present in form of a crack. The boundary problem has been formulated on the basis of a static criterion of instability. The boundary conditions associated with different types of supports are obtained by proper selection of parameters of the generalized load. On the basis of these results, the magnitude of bifurcation load can be determined.
4
Content available Some differential operators in the symmetric bundle
EN
Some natural differential operators in the bundles of symmetric tensors and symmetric tensors with values in the tangent bundle are investigated. Applications in geometry, physics and tomography are also reviewed.
EN
Based on the study of literature relating to the classification of forests using high resolution space images established that the main problem of classification is the separateness classes and close to the spectral brightness classes can not be identified with high accuracy. Classification using maximum likelihood algorithm, which generally gives better results compared with algorithms of spectral distance or Mahalanobis distance, does not lead to the definition of areas with a high probability. Therefore, the article examines approach of classification of forests using post-processing. Experimental studies were carried using an satellite image of the forested area of Precarpathian region obtained from QuickBird-2 (June 2010). Data collected during field research were used as Verification data to determine areas of different objects. The controlled classification has been performed using the method of the maximum likelihood, size of signatures for 8 classes were selected from 100 to 400 points. For these classes was calculated matrix of separation of classes, and was found a significant correlation between next classes: young conifer plantings and pine and mixed forest, and deciduous young plantings and deciduous forest. Post-processing significantly improves the reliability of determination of area, which consists in the assign to all pixel of the selected neighbourhood brightness of most points, although there is a dependency of reliability of determination of area from the size of the area. Accuracy of determination of areas are from 92 to 99%.
EN
The convergence and divergence are two common phenomena in swarm intelligence. To obtain good search results, the algorithm should have a balance on convergence and divergence. The premature convergence happens partially due to the solutions getting clustered together, and not diverging again. The brain storm optimization (BSO), which is a young and promising algorithm in swarm intelligence, is based on the collective behavior of human being, that is, the brainstorming process. The convergence strategy is utilized in BSO algorithm to exploit search areas may contain good solutions. The new solutions are generated by divergence strategy to explore new search areas. Premature convergence also happens in the BSO algorithm. The solutions get clustered after a few iterations, which indicate that the population diversity decreases quickly during the search. A definition of population diversity in BSO algorithm is introduced in this paper to measure the change of solutions’ distribution. The algorithm’s exploration and exploitation ability can be measured based on the change of population diversity. Different kinds of partial reinitialization strategies are utilized to improve the population diversity in BSO algorithm. The experimental results show that the performance of the BSO is improved by part of solutions re-initialization strategies.
EN
The classic Ziegler column under compressive follower force is considered now in a generalized form including a stabilizing spring acting at the end of the column. Damping in the joints is neglected. With increasing spring stiffness from zero to infinity one can observe evolution of the dynamic properties of the column from the original free-end form to the limit configuration with the end simply supported. Attention is focused not only on the stability of the straight-form equilibrium of the column but also on the eigen-frequencies, eigen-values and eigen-forms of motion of the column near the equilibrium. The follower force is responsible for loss of stability but the stabilizing spring considerably affects the stability boundary. The most interesting phenomena occur in the low zone of the spring stiffness where quite complicated interactions between flatter and divergence is observed under increasing follower force. Detailed analysis of the eigen-values is presented in the four regions of the parameter space to demonstrate new phenomena not reported in the literature.
EN
In this paper, the results of numerical studies on the divergence and flutter instability and vibration of a geometrically nonlinear column subjected to generalized load are presented. The system is loaded by axially applied external force P. The direction of action of the force is dependent on follower factor η. The Hamilton principle was used to formulate the boundary problem. Due to the geometric nonlinearity, the solution to the problem was performed by means of the perturbation method. The main purpose of this paper is to investigate the influence of the location of the crack on divergence and flutter loading as well as natural vibration frequency. The presented results of numerical calculations also concern the influence of rotational spring stiffness and follower factor η on the investigated parameters.
EN
Formalisms for description how much information on private actions can be obtained by observing public ones are presented. Two sets of private actions are considered. The set of actions which execution is guaranteed according to observations and the set of actions which execution is excluded according to observations. Since information flows could be realized also by means of different covert channels as time, termination and divergence this possibility is considered as well. Both qualitative and quantitative dimensions of the flow are considered.
EN
In the paper, the non-linear vibrations and stability of a compound tworod column with different bending rigidities of its members are investigated. The support of the column is pinned and has a rotational spring the stiffness of which can be either constant or dependent on the applied load. A perturbation technique is chosen to solve the problem. As the column is loaded by a partially follower load it loses its stability via divergence or flutter. For the case of the nonconservative load an adjoint system is formulated for finding the amplitude-frequency relation. The linear part of the natural frequency for adjoint systems is the same, but the non-linear terms differ for each system because they depend on the vibration modes. The support stiffening may lower the critical load of the column.
PL
Wpływ sztywności sprężyny podpierającej geometrycznie nieliniową kolumnę na jej drgania i stateczność. W pracy analizowane są drgania i stateczność kolumny złożonej z dwóch prętów i podpartej na sprężynie rotacyjnej, której sztywność jest stała lub zależna od przyłożonego obciążenia zewnętrznego. Ponieważ siła zewnętrzna jest częściowo śledząca, to kolumna może tracić stateczność przez dywergencję lub flatter. Celem znalezienia relacji amplituda-częstość dla obciążenia niezachowawczego znaleziono układ sprzężony. Wykazano, że liniowy składnik rozwinięcia częstości drgań obu układów jest taki sam, natomiast składowe nieliniowe są różne. Przeprowadzono badania numeryczne, na podstawie których stwierdzono m.in., że wzrost sztywności sprężyny podpierającej kolumnę może obniżać wartość jej siły krytycznej.
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