Bücher zum Thema „One-Way equations“

This chapter introduces the Main Lemma that implies the existence of continuous solutions. According to this lemma, there exist constants K and C such that the following holds: Let ϵ‎ > 0, and suppose that (v, p, R) are uniformly continuous solutions to the Euler-Reynolds equations on ℝ x ³, with v uniformly bounded⁷ and suppR ⊆ I x ³ for some time interval. The Main Lemma implies the following theorem: There exist continuous solutions (v, p) to the Euler equations that are nontrivial and have compact support in time. To establish this theorem, one repeatedly applies the Main Lemma to produce a sequence of solutions to the Euler-Reynolds equations. To make sure the solutions constructed in this way are nontrivial and compactly supported, the lemma is applied with e(t) chosen to be any sequence of non-negative functions whose supports are all contained in some finite time interval.

The dissertation states: 1. The main provisions of the theory of the finite element method in the form of a classical mixed method. 2. Methods for obtaining physical and mathematical models of finite elements with mixed unknowns in the main system. 3. Construction of resolving equations based on the obtained mathematical models of finite elements and development of algorithms for their solution. 4. Algorithms for solving problematic problems: accounting for FE displacements as a rigid whole, accounting for rigid inclusions and holes. 5. Features of physical and mathematical models of problems of dynamics and stability of structures and the calculation algorithms that implement them. 6. Physical and mathematical models of reduction methods for lowering the order of large systems of frequency resolving equations. 7. Physical and mathematical models and algorithms for solving geometrically nonlinear problems and problems of calculating structurally nonlinear systems with one-way connections.

This chapter embarks on the study of Newton’s law of gravitation. It first discusses gravitational mass and inertial mass, a measure of the ‘resistance’ of the point particle to an applied force. The numerical value of the inertial mass of a body can in principle be obtained from collision experiments by assigning to a reference body a unit inertial mass of one kilogram or, more rigorously, one ‘inertial kilogram’. Next, the chapter considers the ratio of gravitational and inertial masses. It considers that, in the absence of friction, all objects, no matter what their inertial mass, or the nature of their constituents, or the internal energy or cohesive forces of their constituents, fall in the same way in an external gravitational field. Finally, this chapter studies Newton’s gravitational force and field, as well as the Poisson equation and the gravitational Lagrangian.

Within the Jaina tradition, the ideal and most celebrated death is a voluntary, fully conscious fast which aims to “scratch out the body” for the sake of the soul. Called sallekhanā, the fast is understood to be the pinnacle of nonviolence, because it entails the complete eradication of the passions that are the root cause of violence. But above all, sallekhanā is understood by Jains to be heroic; it is the ultimate culmination of a courageous life dedicated to the soul’s emancipation from the cycle of birth and death. The equation of sallekhanā with heroism is an ancient one in the Jain imagination, and continues to govern the way in which the religious death is understood and practiced by Jains in the early twenty-first century. This chapter explores the central role that heroism plays within the ritual fast to death and, more fundamentally, within the Jain tradition.

The transfer of nonequilibrium spin polarization between the electron and nuclear subsystems is studied in detail. Usually, a thermal orientation of nuclei in magnetic field is negligible due to their small magnetic moments, but if electron spins are optically oriented, efficient nuclear spin polarization can occur. The microscopic approach to the dynamical nuclear polarization effect based on the kinetic equation method, along with a phenomenological but very powerful description of dynamical nuclear polarization in terms of the nuclear spin temperature concept is given. In this way, one can account for the interaction between neighbouring nuclei without solving a complex many-body problem. The hyperfine interaction also induces the feedback of polarized nuclei on the electron spin system giving rise to a number of nonlinear effects: bistability of nuclear spin polarization and anomalous Hanle effect, dragging and locking of optical resonances in quantum dots. Theory is illustrated by experimental data on dynamical nuclear polarization.

Is technological control taking the place of what appeared uncannily uncontrollable? Or is it itself becoming uncanny? Two seemingly contradictory narratives have shaped the history and theory of technology. The narrative of disenchantment describes how nature, experienced as something foreign and dangerous, was tamed by becoming scientific and mechanised. Secondly, the narrative of (re-)enchantment recounts how artefacts and technological possibilities become uncanny, especially by way of their seeming independence and by confronting us with an ‘autonomous’ logic of their own. In today's debates about self-learning, ubiquitous, invisible and opaque technologies, the uncanny moment resonates of a technology with ‘a life of its own’. Following up on the mechanisation and automation discourses of the 20th century, this contributes to the ‘demonisation’ of technology. On the one hand, technology makes the world familiar and comprehensible, e.g. by equating understanding with technical reconstruction. On the other hand, the technical reproduction of the world – or its radical transformation into an alienated one – is experienced as something disturbing. When artefacts appear to do ‘what they want’ or when large technical systems shape the world according to their ‘own logic’, a limit is reached that was already mentioned by Freud – we become uncertain whether we are still living in the modern world at all.

The book takes a political-culture perspective on the struggle between democracy and autocracy by examining how these regimes fare in the eyes of their citizens. Taking a globally comparative approach, it studies both the levels as well as the individual- and system-level sources of political support in democracies and autocracies worldwide. The book develops an explanatory model of regime support which includes both individual- and system-level determinants and specifies not only the general causal mechanisms and pathways through which these determinants affect regime support but also spells out how these effects might vary between the two types of regimes. It empirically tests its propositions using multi-level structural equation modeling and a comprehensive dataset that combines recent public-opinion data from six cross-national survey projects with aggregate data from various sources for more than one hundred democracies and autocracies. It finds that both the levels and individual-level sources of regime support are the same in democracies and autocracies, but that the way in which system-level context factors affect regime support differs between the two types of regimes. The results enhance our understanding of what determines citizen support for fundamentally different regimes, help assessing the present and future stability of democracies and autocracies, and provide clear policy implications to those interested in strengthening support for democracy and/or fostering democratic change in autocracies.

Hard coal mining is characterised by features that pose numerous challenges to its current operations and cause strategic and operational problems in planning its development. The most important of these include the high capital intensity of mining investment projects and the dynamically changing environment in which the sector operates, while the long-term role of the sector is dependent on factors originating at both national and international level. At the same time, the conditions for coal mining are deteriorating, the resources more readily available in active mines are being exhausted, mining depths are increasing, temperature levels in pits are rising, transport routes for staff and materials are getting longer, effective working time is decreasing, natural hazards are increasing, and seams with an increasing content of waste rock are being mined. The mining industry is currently in a very difficult situation, both in technical (mining) and economic terms. It cannot be ignored, however, that the difficult financial situation of Polish mining companies is largely exacerbated by their high operating costs. The cost of obtaining coal and its price are two key elements that determine the level of efficiency of Polish mines. This situation could be improved by streamlining the planning processes. This would involve striving for production planning that is as predictable as possible and, on the other hand, economically efficient. In this respect, it is helpful to plan the production from operating longwalls with full awareness of the complexity of geological and mining conditions and the resulting economic consequences. The constraints on increasing the efficiency of the mining process are due to the technical potential of the mining process, organisational factors and, above all, geological and mining conditions. The main objective of the monograph is to identify relations between geological and mining parameters and the level of longwall mining costs, and their daily output. In view of the above, it was assumed that it was possible to present the relationship between the costs of longwall mining and the daily coal output from a longwall as a function of onerous geological and mining factors. The monograph presents two models of onerous geological and mining conditions, including natural hazards, deposit (seam) parameters, mining (technical) parameters and environmental factors. The models were used to calculate two onerousness indicators, Wue and WUt, which synthetically define the level of impact of onerous geological and mining conditions on the mining process in relation to: —— operating costs at longwall faces – indicator WUe, —— daily longwall mining output – indicator WUt. In the next research step, the analysis of direct relationships of selected geological and mining factors with longwall costs and the mining output level was conducted. For this purpose, two statistical models were built for the following dependent variables: unit operating cost (Model 1) and daily longwall mining output (Model 2). The models served two additional sub-objectives: interpretation of the influence of independent variables on dependent variables and point forecasting. The models were also used for forecasting purposes. Statistical models were built on the basis of historical production results of selected seven Polish mines. On the basis of variability of geological and mining conditions at 120 longwalls, the influence of individual parameters on longwall mining between 2010 and 2019 was determined. The identified relationships made it possible to formulate numerical forecast of unit production cost and daily longwall mining output in relation to the level of expected onerousness. The projection period was assumed to be 2020–2030. On this basis, an opinion was formulated on the forecast of the expected unit production costs and the output of the 259 longwalls planned to be mined at these mines. A procedure scheme was developed using the following methods: 1) Analytic Hierarchy Process (AHP) – mathematical multi-criteria decision-making method, 2) comparative multivariate analysis, 3) regression analysis, 4) Monte Carlo simulation. The utilitarian purpose of the monograph is to provide the research community with the concept of building models that can be used to solve real decision-making problems during longwall planning in hard coal mines. The layout of the monograph, consisting of an introduction, eight main sections and a conclusion, follows the objectives set out above. Section One presents the methodology used to assess the impact of onerous geological and mining conditions on the mining process. Multi-Criteria Decision Analysis (MCDA) is reviewed and basic definitions used in the following part of the paper are introduced. The section includes a description of AHP which was used in the presented analysis. Individual factors resulting from natural hazards, from the geological structure of the deposit (seam), from limitations caused by technical requirements, from the impact of mining on the environment, which affect the mining process, are described exhaustively in Section Two. Sections Three and Four present the construction of two hierarchical models of geological and mining conditions onerousness: the first in the context of extraction costs and the second in relation to daily longwall mining. The procedure for valuing the importance of their components by a group of experts (pairwise comparison of criteria and sub-criteria on the basis of Saaty’s 9-point comparison scale) is presented. The AHP method is very sensitive to even small changes in the value of the comparison matrix. In order to determine the stability of the valuation of both onerousness models, a sensitivity analysis was carried out, which is described in detail in Section Five. Section Six is devoted to the issue of constructing aggregate indices, WUe and WUt, which synthetically measure the impact of onerous geological and mining conditions on the mining process in individual longwalls and allow for a linear ordering of longwalls according to increasing levels of onerousness. Section Seven opens the research part of the work, which analyses the results of the developed models and indicators in individual mines. A detailed analysis is presented of the assessment of the impact of onerous mining conditions on mining costs in selected seams of the analysed mines, and in the case of the impact of onerous mining on daily longwall mining output, the variability of this process in individual fields (lots) of the mines is characterised. Section Eight presents the regression equations for the dependence of the costs and level of extraction on the aggregated onerousness indicators, WUe and WUt. The regression models f(KJC_N) and f(W) developed in this way are used to forecast the unit mining costs and daily output of the designed longwalls in the context of diversified geological and mining conditions. The use of regression models is of great practical importance. It makes it possible to approximate unit costs and daily output for newly designed longwall workings. The use of this knowledge may significantly improve the quality of planning processes and the effectiveness of the mining process.