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Search results for: LEGENDRE POLYNOMIALS EXPANSION
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SUICIDES FOR ECONOMIC REASONS AS A MEASURE OF THE STATE OF THE ECONOMY: THE CASE OF POLAND
PublicationSuicides are a phenomenon observed in many countries. The causes of a decision so drastic as far as consequences are concerned include i.a. economic reasons. The question arises whether the changing number of suicides reflects the state of the economy. The direct link between the state of the economy and suicides has not been sufficiently studied so far. The authors of this article attempted to identify the links between selected...
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Medium-sized cyclic bis(anisylphosphonothioyl)- disulfanes and their corresponding cyclic sulfane-structures and most characteristic reactions
PublicationCyclic 8-, 9-, 10-, and 12-membered bis(anisylphosphonothioyl)disulfanes were synthesized. Next, structurally related 7 to 9-membered cis and trans sulfanes were isolated as a result of sulfur atom extrusion from the parent cyclic disulfanes. The results of the desulfurization of the disulfanes were compared to the results obtained for desulfurization of the respective bis(anisylphosphodithioates). Cyclic disulfanes predominantly...
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Non-Newtonian Mathematics Instead of Non-Newtonian Physics: Dark Matter and Dark Energy from a Mismatch of Arithmetics
PublicationNewtonian physics is based on Newtonian calculus applied to Newtonian dynamics. New paradigms such as ‘modified Newtonian dynamics’ (MOND) change the dynamics, but do not alter the calculus. However, calculus is dependent on arithmetic, that is the ways we add and multiply numbers. For example, in special relativity we add and subtract velocities by means of addition β1⊕β2=tanh(tanh−1(β1)+tanh−1(β2)), although multiplication β1⊙β2=tanh(tanh−1(β1)⋅tanh−1(β2)),...
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A new model of fuel spray shape at early stage of injection in a marine Diesel engine
PublicationIn the cylinders of a marine diesel engine, self-ignition occurs in very shortly time after the fuel injection into the combustion chamber. Therefore, the paper present was to develop a model of diesel fuel spray for the early stage of fuel spray for in marine diesel engine. There were taken into consideration the main aspects technical such as nozzle diameter of marine engine injector and backpressure in combustion chamber. In...