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.

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.

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.

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.

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.

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 “k_{1}, k_{2}, k_{3}, k_{4}”, which form the imaginary
part of a complex phase space, respectively. While as to the real part, we use “x_{1}, x_{2}, x_{3}, x_{4}” 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.

曲线或曲面的曲率信息是图像处理和计算机视觉的许多应用领域均需提取的重要信息，因而曲率估计成为底层处理的基本任务之一。在对原始曲率、高斯和平均曲率，基于圆的离散曲率，基于抛物线的离散曲率、基于Gauss-Bonnet理论的算法和基于Euler理论的算法等曲率计算方法进行基本描述的基础上，将现有的曲率估计方法进行了分类和总结，并通过实验验证了加入曲率估计可有效提高曲面检测方法的抗噪性。 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.

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.

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 .

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.