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Search Results: 1 - 10 of 599 matches for " curvature "
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Probability and Curvature in Physics  [PDF]
Xinzhong Wu
Journal of Modern Physics (JMP) , 2015, DOI: 10.4236/jmp.2015.615222
Abstract: Probability concept in physics entered into statistical physics and quantum physics by molecules kinematics; and curvature concept in physics as applying differential geometry to physics, entered into analytical mechanics long ago. Along with introducing space-time curvature concept into general relativity, curvature concept became more important; gauge field theory regards field intensity as curvature of fibre bundles. Curvature concept in quantum mechanics germinated from original derivation of Schrodinger equation; catastrophe scientist Rene Thom advanced curvature interpretations of ψ function and entropy according to differential geometry. Guoqiu Zhao advanced curvature interpretation of quantum mechanics; this new interpretation made relativity theory and quantum mechanics more harmonious, and regarded ψ function as a curvature function. So far Zhao’s quantum curvature interpretation is nearest to Schrodinger’s scientific thought and Einstein’s physics ideal.
Design and Development of an Electronic Sensor to Detect and Measure Curvature of Spaces Using Curvature Energy  [PDF]
Francisco Bulnes, Isaías Martínez, Antonio Mendoza, Manuel Landa
Journal of Sensor Technology (JST) , 2012, DOI: 10.4236/jst.2012.23017
Abstract: Using fine electromagnetic signals to measure observables of other fields like curvature and torsion of a space, and the corresponding value of their integrals of the action of perception of curvature through electronic signals that detect curvature on a curved surface, it is designed and constructed a sensor of curvature of accelerometer type that detects and curvature measures in 2 and 3-dimensional spaces using the programming of shape operators on spheres and the value of their integrals along the curves and geodesics in their principal directions.
The Riemannian Structure of the Three-Parameter Gamma Distribution  [PDF]
William W. S. Chen, Samuel Kotz
Applied Mathematics (AM) , 2013, DOI: 10.4236/am.2013.43077
Abstract: In this paper, we will utilize the results already known in differential geometry and provide an intuitive understanding of the Gamma Distribution. This approach leads to the definition of new concepts to provide new results of statistical importance. These new results could explain Chen [1-3] experienced difficulty when he attempts to simulate the sampling distribution and power function of Cox’s [4,5] test statistics of separate families of hypotheses. It may also help simplify and clarify some known statistical proofs or results. These results may be of particular interest to mathematical physicists. In general, it has been shown that the parameter space is not of constant curvature. In addition, we calculated some invariant quantities, such as Sectional curvature, Ricci curvature, mean curvature and scalar curvature.
On the Curvature of Rotating Objects  [PDF]
Martin Tamm
Journal of Modern Physics (JMP) , 2015, DOI: 10.4236/jmp.2015.66087
Abstract: In this paper, we investigate a certain property of curvature which differs in a remarkable way between Lorentz geometry and Euclidean geometry. In a certain sense, it turns out that rotating topological objects may have less curvature (as measured by integrating the square of the scalar curvature) than non-rotating ones. This is a consequence of the indefinite metric used in relativity theory. The results in this paper are mainly based of computer computations, and so far there is no satisfactory underlying mathematical theory. Some open problems are presented.
Determination of Statistical Properties of Microtubule Populations  [PDF]
Tyson DiLorenzo, Lee Ligon, Donald Drew
Applied Mathematics (AM) , 2016, DOI: 10.4236/am.2016.713125
Abstract: Microtubules are structures within the cell that form a transportation network along which motor proteins tow cargo to destinations. To establish and maintain a structure capable of serving the cell’s tasks, microtubules undergo deconstruction and reconstruction regularly. This change in structure is critical to tasks like wound repair and cell motility. Images of fluorescing microtubule networks are captured in grayscale at different wavelengths, displaying different tagged proteins. The analysis of these polymeric structures involves identifying the presence of the protein and the direction of the structure in which it resides. This study considers the problem of finding statistical properties of sections of microtubules. We consider the research done on directional filters and utilize a basic solution to find the center of a ridge. The method processes the captured image by centering a circle around pre-determined pixel locations so that the highest possible average pixel intensity is found within the circle, thus marking the center of the microtubule. The location of these centers allows us to estimate angular direction and curvature of the microtubules, statistically estimate the direction of microtubules in a region of the cell, and compare properties of different types of microtubule networks in the same region. To verify accuracy, we study the results of the method on a test image.
Describe Quantum Mechanics in Dual 4 d Complex Space-Time and the Ontological Basis of Wave Function  [PDF]
Guoqiu Zhao
Journal of Modern Physics (JMP) , 2014, DOI: 10.4236/jmp.2014.516168
Abstract: Micro-object is both particle and wave, so the traditional Particle Model (mass point model) is actually not applicable for it. Here to describe its motion, we expand the definition of time and space and pick up the spatial degrees of freedom hidden by particle model. We say that micro-object is like a rolling field-matter-ball, which has four degrees of freedom including one surface curvature degree and three mapping degrees in the three-dimensional phenomenal space. All the degrees are described by four curvature coordinate components, namely “k1, k2, k3, k4”, which form the imaginary part of a complex phase space, respectively. While as to the real part, we use “x1, x2, x3, x4” to describe the micro object’s position in our real space. Consequently, we build a Dual 4-dimensional complex phase space whose imaginary part is 4-dimension k space and real part is 4-dimension x space to describe the micro-object’s motion. Furthermore, we say that wave function can describe the information of a field-matter-ball’s rotation & motion and also matter-wave can spread the information of micro-object’s spatial structure & density distribution. Matter-wave and probability-wave can transform to each other though matter-wave is a physical wave. The non-point property is the foundational source of the probability in Quantum Mechanics.
Curvature Estimation Methods and Its Application in Surface Detection

邵晓芳, 彭志刚
Computer Science and Application (CSA) , 2015, DOI: 10.12677/CSA.2015.56031
Curvature extraction is required for many applications in image processing and computer vision. Therefore, curvature estimation is a basic task of these applications. This paper gives a classification and summary for existing curvature estimation methods to facilitate further investigations based on describing the original mathematical curvature, Gauss curvature, circle-based discrete curvature, parabola-based curvature, Gauss-Bonnet based curvature, Euler-based curvature etc. Experimental results show that curvature information can improve the robustness to noise in surface detection.
Evolution of curvature tensors under mean curvature flow
Revista Colombiana de Matemáticas , 2009,
Abstract: we obtain the evolution equations for the riemann tensor, the ricci tensor and the scalar curvature induced by the mean curvature flow. the evolution of the scalar curvature is similar to the ricci flow, however, negative, rather than positive, curvature is preserved. our results are valid in any dimension.
The Harmonic Functions on a Complete Asymptotic Flat Riemannian Manifold  [PDF]
Huashui Zhan
Advances in Pure Mathematics (APM) , 2011, DOI: 10.4236/apm.2011.12003
Abstract: Let be a simply connected complete Riemannian manifold with dimension n≥3 . Suppose that the sectional curvature satisfies , where p is distance function from a base point of M, a, b are constants and . Then there exist harmonic functions on M .
The Computation of Scalar Curvature in the Four-State Mixed Spin Model and the Investigation of Its Behavior: A Computational Study  [PDF]
Alireza Heidari, Mohammadali Ghorbani
Journal of Modern Physics (JMP) , 2012, DOI: 10.4236/jmp.2012.31005
Abstract: The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the authors’ name: Alireza Heidari, Foad Khademi,Jahromi and Roozbeh Amiri. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No.4 334-339, 2012, has been removed from this site.
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