In this paper, we analyze the enthalpy, enthalpy energy density, thermodynamic volume, and the equation of state of a modified white hole. We obtain new possible mathematical connections with some sectors of Number Th...In this paper, we analyze the enthalpy, enthalpy energy density, thermodynamic volume, and the equation of state of a modified white hole. We obtain new possible mathematical connections with some sectors of Number Theory, Ramanujan Recurring Numbers, DN Constant and String Theory, that enable us to extract the quantum geometrical properties of these thermodynamic equations and the implication to the quantum vacuum spacetime geometry of our early universe as they act as the constraints to the nature of quantum gravity of the universe.展开更多
We investigated the longitudinal positional dependence of CT number in 320-row Cone Beam Computed Tomography (CBCT) volume scan (320-row volume scan) using a simple geometric phantom (SGP) and a chest simulation phant...We investigated the longitudinal positional dependence of CT number in 320-row Cone Beam Computed Tomography (CBCT) volume scan (320-row volume scan) using a simple geometric phantom (SGP) and a chest simulation phantom (CSP) in order to evaluate its effect on proton range calculation. The SGP consisted of lung substitute material (LSM) and a cylindrical phantom (CP) made of high-density polyethylene. The CSP was an anthropomorphic phantom similar to the human chest. The two phantoms were scanned using 320-row volume scan in various longitudinal positions from the central beam axis. In experiments using the SGP, an image blur at the boundary of the two materials became gradually evident when the LSM was placed far away from the beam central axis. The image blur of the phantom was consistent with the gradation in CT number. The maximum difference in CT numbers between the 64-row helical scan and 320-row volume scan at the boundary of the two materials was consistent with approximately 50% of the relative proton stopping power. In contrast, the CT number profile in each longitudinal position was fairly consistent and longitudinal positional dependence rarely occurred in the CSP experiments. Pass lengths of CT beams through areas with widely different electron densities were shorter, and thus did not significantly impact CT numbers. Based on findings from the CSP experiments, we considered 320-row volume scan to be feasible for proton range calculation in clinical settings, although the relatively large longitudinal positional dependence of CT number should be accounted for when doing so.展开更多
The well-known Yau＇s uniformization conjecture states that any complete noncompact Kahler manifold with positive bisectional curvature is bi-holomorphic to the Euclidean space. The conjecture for the case of maximal ...The well-known Yau＇s uniformization conjecture states that any complete noncompact Kahler manifold with positive bisectional curvature is bi-holomorphic to the Euclidean space. The conjecture for the case of maximal volume growth has been recently confirmed, by G. Liu in [23]. In the first part, we will give a survey on thc progress. In the second part, we will consider Yau＇s conjecture for manifolds with non-maximal volume growth. We will show that the finiteness of the first Chern number Cn1 is an essential condition to solve Yau＇s conjecture by using algebraic embedding method. Moreover, we prove that, under bounded curvature conditions, Cn1 is automatically finite provided that there exists a positive line bundle with finite Chern number. In particular, we obtain a partial answer to Yau＇s uniformization conjecture on Kahler manifolds with minimal volume growth.展开更多
The multi-orifice plate gas sparger, mainly composed of a multi-orifice plate and a gas chamber, is one of the most common sparger facilities.The aeration performance of multi-orifice plate has a close relation with t...The multi-orifice plate gas sparger, mainly composed of a multi-orifice plate and a gas chamber, is one of the most common sparger facilities.The aeration performance of multi-orifice plate has a close relation with the multiorifice plate configuration.In addition, the weeping phenomenon has a considerable influence on the gas chamber condition which affects the bubble detachment volume directly.This paper conducts a set of visual experiments to study the influence of multi-orifice configuration and gas chamber condition on the aeration performance of gas sparger.For multi-orifice plate, an improved theoretical model is proposed which considers the wave effect of the previous bubbles generated from adjacent orifices and the variance of the number of active bubbling orifice.A parameter is proposed to evaluate the aeration performance in order to overcome the difficulty caused by the randomness of bubble formation process.The experimental results suggest that the gas chamber filled with water is in favor of large bubble formation.The influence of the pitch of orifice on aeration performance can only be observed in high-restricted case.According to the theoretical model and experimental results, the influences of gas flow rate and the number of open orifices on the aeration performance are analyzed and a design criterion for the number of open orifice is proposed.展开更多
Recently attention has been drawn to the frequently observed fifth power of the golden mean in many disciplines of science and technology. Whereas in a forthcoming contribution the focus will be directed towards <i...Recently attention has been drawn to the frequently observed fifth power of the golden mean in many disciplines of science and technology. Whereas in a forthcoming contribution the focus will be directed towards <i>Fibonacci</i> number-based helical structures of living as well as inorganic matter, in this short letter the geometry of the Great Pyramid of the ancient Egyptians was investigated once more. The surprising main result is that the ratio of the in-sphere volume of the pyramid and the pyramid volume itself is given by π⋅<i>φ</i><sup>5</sup>, where <i>φ</i> = 0.618033987<span style="white-space:nowrap;">⋅<span style="white-space:nowrap;">⋅</span><span style="white-space:nowrap;">⋅</span></span> is nature’s most important number, the golden mean. In this way not only phase transitions from microscopic to cosmic scale are connected with <i>φ</i><sup>5</sup>, also ingenious ancient builders have intuitively guessed its magic before.展开更多
A diagnostics method was presented that uses emission and scattering techniques to simultaneously determine the distributions of soot particle diameter and number density in hydrocarbon flames. Two manta G-504 C camer...A diagnostics method was presented that uses emission and scattering techniques to simultaneously determine the distributions of soot particle diameter and number density in hydrocarbon flames. Two manta G-504 C cameras were utilized for the scattering measurement, with consideration of the attenuation effect in the flames according to corresponding absorption coefficients. Distributions of soot particle diameter and number density were simultaneously determined using the measured scattering coefficients and absorption coefficients under multiple wavelengths already measured with a SOC701 V hyper-spectral imaging device, according to the Mie scattering theory. A flame was produced using an axisymmetric laminar diffusion flame burner with 194 mL/min ethylene and 284 L/min air, and distributions of particle diameter and number density for the flame were presented. Consequently, the distributions of soot volume fraction were calculated using these two parameters as well, which were in good agreement with the results calculated according to the Rayleigh approximation,demonstrating that the proposed diagnostic method is capable of simultaneous determination of the distributions of soot particle diameter and number density.展开更多
文摘In this paper, we analyze the enthalpy, enthalpy energy density, thermodynamic volume, and the equation of state of a modified white hole. We obtain new possible mathematical connections with some sectors of Number Theory, Ramanujan Recurring Numbers, DN Constant and String Theory, that enable us to extract the quantum geometrical properties of these thermodynamic equations and the implication to the quantum vacuum spacetime geometry of our early universe as they act as the constraints to the nature of quantum gravity of the universe.
文摘We investigated the longitudinal positional dependence of CT number in 320-row Cone Beam Computed Tomography (CBCT) volume scan (320-row volume scan) using a simple geometric phantom (SGP) and a chest simulation phantom (CSP) in order to evaluate its effect on proton range calculation. The SGP consisted of lung substitute material (LSM) and a cylindrical phantom (CP) made of high-density polyethylene. The CSP was an anthropomorphic phantom similar to the human chest. The two phantoms were scanned using 320-row volume scan in various longitudinal positions from the central beam axis. In experiments using the SGP, an image blur at the boundary of the two materials became gradually evident when the LSM was placed far away from the beam central axis. The image blur of the phantom was consistent with the gradation in CT number. The maximum difference in CT numbers between the 64-row helical scan and 320-row volume scan at the boundary of the two materials was consistent with approximately 50% of the relative proton stopping power. In contrast, the CT number profile in each longitudinal position was fairly consistent and longitudinal positional dependence rarely occurred in the CSP experiments. Pass lengths of CT beams through areas with widely different electron densities were shorter, and thus did not significantly impact CT numbers. Based on findings from the CSP experiments, we considered 320-row volume scan to be feasible for proton range calculation in clinical settings, although the relatively large longitudinal positional dependence of CT number should be accounted for when doing so.
文摘The well-known Yau＇s uniformization conjecture states that any complete noncompact Kahler manifold with positive bisectional curvature is bi-holomorphic to the Euclidean space. The conjecture for the case of maximal volume growth has been recently confirmed, by G. Liu in [23]. In the first part, we will give a survey on thc progress. In the second part, we will consider Yau＇s conjecture for manifolds with non-maximal volume growth. We will show that the finiteness of the first Chern number Cn1 is an essential condition to solve Yau＇s conjecture by using algebraic embedding method. Moreover, we prove that, under bounded curvature conditions, Cn1 is automatically finite provided that there exists a positive line bundle with finite Chern number. In particular, we obtain a partial answer to Yau＇s uniformization conjecture on Kahler manifolds with minimal volume growth.
基金Supported by the Fundamental Research Funds for the Central Universities(HEUCFM181203)
文摘The multi-orifice plate gas sparger, mainly composed of a multi-orifice plate and a gas chamber, is one of the most common sparger facilities.The aeration performance of multi-orifice plate has a close relation with the multiorifice plate configuration.In addition, the weeping phenomenon has a considerable influence on the gas chamber condition which affects the bubble detachment volume directly.This paper conducts a set of visual experiments to study the influence of multi-orifice configuration and gas chamber condition on the aeration performance of gas sparger.For multi-orifice plate, an improved theoretical model is proposed which considers the wave effect of the previous bubbles generated from adjacent orifices and the variance of the number of active bubbling orifice.A parameter is proposed to evaluate the aeration performance in order to overcome the difficulty caused by the randomness of bubble formation process.The experimental results suggest that the gas chamber filled with water is in favor of large bubble formation.The influence of the pitch of orifice on aeration performance can only be observed in high-restricted case.According to the theoretical model and experimental results, the influences of gas flow rate and the number of open orifices on the aeration performance are analyzed and a design criterion for the number of open orifice is proposed.
文摘Recently attention has been drawn to the frequently observed fifth power of the golden mean in many disciplines of science and technology. Whereas in a forthcoming contribution the focus will be directed towards <i>Fibonacci</i> number-based helical structures of living as well as inorganic matter, in this short letter the geometry of the Great Pyramid of the ancient Egyptians was investigated once more. The surprising main result is that the ratio of the in-sphere volume of the pyramid and the pyramid volume itself is given by π⋅<i>φ</i><sup>5</sup>, where <i>φ</i> = 0.618033987<span style="white-space:nowrap;">⋅<span style="white-space:nowrap;">⋅</span><span style="white-space:nowrap;">⋅</span></span> is nature’s most important number, the golden mean. In this way not only phase transitions from microscopic to cosmic scale are connected with <i>φ</i><sup>5</sup>, also ingenious ancient builders have intuitively guessed its magic before.
基金Project supported by the National Key Research and Development Program of China(Grant No.2017YFB0601900)the National Natural Science Foundation of China(Grant Nos.51827808,51821004,and 51406095)+1 种基金the Fundamental Research Funds for the Central Universities,China(Grant Nos.2018ZD03 and2017ZZD005)Science and Technology Partnership Program,Ministry of Science and Technology of China(Grant No.KY201401003)
文摘A diagnostics method was presented that uses emission and scattering techniques to simultaneously determine the distributions of soot particle diameter and number density in hydrocarbon flames. Two manta G-504 C cameras were utilized for the scattering measurement, with consideration of the attenuation effect in the flames according to corresponding absorption coefficients. Distributions of soot particle diameter and number density were simultaneously determined using the measured scattering coefficients and absorption coefficients under multiple wavelengths already measured with a SOC701 V hyper-spectral imaging device, according to the Mie scattering theory. A flame was produced using an axisymmetric laminar diffusion flame burner with 194 mL/min ethylene and 284 L/min air, and distributions of particle diameter and number density for the flame were presented. Consequently, the distributions of soot volume fraction were calculated using these two parameters as well, which were in good agreement with the results calculated according to the Rayleigh approximation,demonstrating that the proposed diagnostic method is capable of simultaneous determination of the distributions of soot particle diameter and number density.
