A scrutiny of the contributions of key mathematicians and scientists shows that there has been much controversy (throughout the development of mathematics and science) concerning the use of mathematics and the nature ...A scrutiny of the contributions of key mathematicians and scientists shows that there has been much controversy (throughout the development of mathematics and science) concerning the use of mathematics and the nature of mathematics too. In this work, we try to show that arithmetical operations of approximation lead to the existence of a numerical uncertainty, which is quantic, path dependent and also dependent on the number system used, with mathematical and physical implications. When we explore the algebraic equations for the fine structure constant, the conditions exposed in this work generate paradoxical physical conditions, where the solution to the paradox may be in the fact that the fine-structure constant is calculated through different ways in order to obtain the same value, but there is no relationship between the fundamental physical processes which underlie the calculations, since we are merely dealing with algebraic relations, despite the expressions having the same physical dimensions.展开更多
Modifications of the Weyl-Heisenberg algebra are proposed where the classical limit corresponds to a metric in (curved) momentum spaces. In the simplest scenario, the 2D de Sitter metric of constant curvature in momen...Modifications of the Weyl-Heisenberg algebra are proposed where the classical limit corresponds to a metric in (curved) momentum spaces. In the simplest scenario, the 2D de Sitter metric of constant curvature in momentum space furnishes a hierarchy of modified uncertainty relations leading to a minimum value for the position uncertainty . The first uncertainty relation of this hierarchy has the same functional form as the stringy modified uncertainty relation with a Planck scale minimum value for at . We proceed with a discussion of the most general curved phase space scenario (cotangent bundle of spacetime) and provide the noncommuting phase space coordinates algebra in terms of the symmetric and nonsymmetric metric components of a Hermitian complex metric , such . Yang’s noncommuting phase-space coordinates algebra, combined with the Schrodinger-Robertson inequalities involving angular momentum eigenstates, reveals how a quantized area operator in units of emerges like it occurs in Loop Quantum Gravity (LQG). Some final comments are made about Fedosov deformation quantization, Noncommutative and Nonassociative gravity.展开更多
The problems of unattainable infinity and infinitesimal are discussed. Limitations connected with the absolute zero of temperature and the maximal velocity are considered, as well as the consequences of these limitati...The problems of unattainable infinity and infinitesimal are discussed. Limitations connected with the absolute zero of temperature and the maximal velocity are considered, as well as the consequences of these limitations. A geometric approach is proposed as an alternative to the wave-particle duality to explain the anomalous motion of micro objects. The basis of the geometric approach is a comparison between two geometries differing from each other in the metric of infinitesimal. The interconnection of these geometries is possible through the direct and inverse Weierstrass transformation. The application of this transformation allows one to explain diffraction effects.展开更多
This work presents the uncertainty evaluation associated with the measurement of linear parameters that define the weld geometry, specifically the width, using a profile projector, in order to meet the current technic...This work presents the uncertainty evaluation associated with the measurement of linear parameters that define the weld geometry, specifically the width, using a profile projector, in order to meet the current technical standards. The following steps were proposed and implemented: identification of linear parameters that define the weld geometry;identification and study of variables that affect the measurement of these parameters;the adoption of the mathematical model to estimate the uncertainty;planning and execution of experiments for data collection, calculation of uncertainty and, finally, analysis and discussion of the results. Through the results analysis it was concluded that the weld in overhead position produces the lowest front bead width values and the vertical weld produces the largest width values. The expanded uncertainty values were between 0.016 mm and 0.075 mm for all measurements, and the overhead position showed, on average, the highest values.展开更多
Deposition of fluvial sandbodies is controlled mainly by characteristics of the system, such as the rate of avulsion and aggradation of the fluvial channels and their geometry. The impact and the interaction of these ...Deposition of fluvial sandbodies is controlled mainly by characteristics of the system, such as the rate of avulsion and aggradation of the fluvial channels and their geometry. The impact and the interaction of these parameters have not received adequate attention. In this paper, the impact of geological uncertainty resulting from the interpretation of the fluvial geometry, maximum depth of channels, and their avulsion rates on primary production is studied for fluvial reservoirs. Several meandering reservoirs were generated using a process-mimicking package by varying several con- trolling factors. Simulation results indicate that geometrical parameters of the fluvial channels impact cumulative pro- duction during primary production more significantly than their avulsion rate. The most significant factor appears to be the maximum depth of fluvial channels. The overall net-to-gross ratio is closely correlated with the cumulative oil production of the field, but cumulative production values for individual wells do not appear to be correlated with the local net-to-gross ratio calculated in the vicinity of each well. Connectedness of the sandbodies to each well, defined based on the minimum time-of-flight from each block to the well, appears to be a more reliable indicator of well-scale production.展开更多
文摘A scrutiny of the contributions of key mathematicians and scientists shows that there has been much controversy (throughout the development of mathematics and science) concerning the use of mathematics and the nature of mathematics too. In this work, we try to show that arithmetical operations of approximation lead to the existence of a numerical uncertainty, which is quantic, path dependent and also dependent on the number system used, with mathematical and physical implications. When we explore the algebraic equations for the fine structure constant, the conditions exposed in this work generate paradoxical physical conditions, where the solution to the paradox may be in the fact that the fine-structure constant is calculated through different ways in order to obtain the same value, but there is no relationship between the fundamental physical processes which underlie the calculations, since we are merely dealing with algebraic relations, despite the expressions having the same physical dimensions.
文摘Modifications of the Weyl-Heisenberg algebra are proposed where the classical limit corresponds to a metric in (curved) momentum spaces. In the simplest scenario, the 2D de Sitter metric of constant curvature in momentum space furnishes a hierarchy of modified uncertainty relations leading to a minimum value for the position uncertainty . The first uncertainty relation of this hierarchy has the same functional form as the stringy modified uncertainty relation with a Planck scale minimum value for at . We proceed with a discussion of the most general curved phase space scenario (cotangent bundle of spacetime) and provide the noncommuting phase space coordinates algebra in terms of the symmetric and nonsymmetric metric components of a Hermitian complex metric , such . Yang’s noncommuting phase-space coordinates algebra, combined with the Schrodinger-Robertson inequalities involving angular momentum eigenstates, reveals how a quantized area operator in units of emerges like it occurs in Loop Quantum Gravity (LQG). Some final comments are made about Fedosov deformation quantization, Noncommutative and Nonassociative gravity.
文摘The problems of unattainable infinity and infinitesimal are discussed. Limitations connected with the absolute zero of temperature and the maximal velocity are considered, as well as the consequences of these limitations. A geometric approach is proposed as an alternative to the wave-particle duality to explain the anomalous motion of micro objects. The basis of the geometric approach is a comparison between two geometries differing from each other in the metric of infinitesimal. The interconnection of these geometries is possible through the direct and inverse Weierstrass transformation. The application of this transformation allows one to explain diffraction effects.
基金The authors are grateful to FAPEMIG/BrazilCAPES/PROEX for financial support.
文摘This work presents the uncertainty evaluation associated with the measurement of linear parameters that define the weld geometry, specifically the width, using a profile projector, in order to meet the current technical standards. The following steps were proposed and implemented: identification of linear parameters that define the weld geometry;identification and study of variables that affect the measurement of these parameters;the adoption of the mathematical model to estimate the uncertainty;planning and execution of experiments for data collection, calculation of uncertainty and, finally, analysis and discussion of the results. Through the results analysis it was concluded that the weld in overhead position produces the lowest front bead width values and the vertical weld produces the largest width values. The expanded uncertainty values were between 0.016 mm and 0.075 mm for all measurements, and the overhead position showed, on average, the highest values.
文摘Deposition of fluvial sandbodies is controlled mainly by characteristics of the system, such as the rate of avulsion and aggradation of the fluvial channels and their geometry. The impact and the interaction of these parameters have not received adequate attention. In this paper, the impact of geological uncertainty resulting from the interpretation of the fluvial geometry, maximum depth of channels, and their avulsion rates on primary production is studied for fluvial reservoirs. Several meandering reservoirs were generated using a process-mimicking package by varying several con- trolling factors. Simulation results indicate that geometrical parameters of the fluvial channels impact cumulative pro- duction during primary production more significantly than their avulsion rate. The most significant factor appears to be the maximum depth of fluvial channels. The overall net-to-gross ratio is closely correlated with the cumulative oil production of the field, but cumulative production values for individual wells do not appear to be correlated with the local net-to-gross ratio calculated in the vicinity of each well. Connectedness of the sandbodies to each well, defined based on the minimum time-of-flight from each block to the well, appears to be a more reliable indicator of well-scale production.
