Fully homomorphic encryption is faced with two problems now. One is candidate fully homomorphic encryption schemes are few. Another is that the efficiency of fully homomorphic encryption is a big question. In this pap...Fully homomorphic encryption is faced with two problems now. One is candidate fully homomorphic encryption schemes are few. Another is that the efficiency of fully homomorphic encryption is a big question. In this paper, we propose a fully homomorphic encryption scheme based on LWE, which has better key size. Our main contributions are： （1） According to the binary-LWE recently, we choose secret key from binary set and modify the basic encryption scheme proposed in Linder and Peikert in 2010. We propose a fully homomorphic encryption scheme based on the new basic encryption scheme. We analyze the correctness and give the proof of the security of our scheme. The public key, evaluation keys and tensored ciphertext have better size in our scheme. （2） Estimating parameters for fully homomorphic encryption scheme is an important work. We estimate the concert parameters for our scheme. We compare these parameters between our scheme and Bral2 scheme. Our scheme have public key and private key that smaller by a factor of about logq than in Bral2 scheme. Tensored ciphertext in our scheme is smaller by a factor of about log2q than in Bral2 scheme. Key switching matrix in our scheme is smaller by a factor of about log3q than in Bra12 scheme.展开更多
The hydrodynamic behavior of multiple bubbles rising upward is a field of ongoing research since various aspects of their interaction require further analysis. Shape deformation, rise velocity, and drag coefficient ar...The hydrodynamic behavior of multiple bubbles rising upward is a field of ongoing research since various aspects of their interaction require further analysis. Shape deformation, rise velocity, and drag coefficient are some of the uncertainties to be determined in a bubble upward flow. For this study the predictions of the three-dimensional numerical simulations of the volume of fluid（VOF） CFD model were first compared with experimental results available in the literature, serving as benchmark cases. Next, 28 cases of pairs of equal and unequal-sized in-line pairs of bubbles moving upwards were simulated. The bubble size varied between 2.0–10 mm. Breakthrough of the present study is the small initial distance of 2.5 R between the center of the bubbles. To provide a more practical nature in this study material properties were selected to match methane gas and seawater properties at deepsea conditions of 15 MPa and 4 ℃, thus yielding a fluid-to-bubble density ratio λ = 7.45 and viscosity ratio n = 100.46. This is one of the few studies to report results of the coalescence procedure in this context. The hydrodynamic behavior of the leading and trailing bubbles was thoroughly studied. Simulation results of the evolution of the rise velocity and the shape deformation with time indicate that the assumption that the leading bubble is rising as a free rising single one is not valid for bubbles between 2.0–7.0 mm. Finally, results of the volume of the daughter bubble exhibited an oscillating nature.展开更多
Lamb waves have a relatively slow geometrical decay of amplitude with propagation distance, which makes them well suited for wide-area inspection and SHM （structural health monitoring）. This paper presents an extens...Lamb waves have a relatively slow geometrical decay of amplitude with propagation distance, which makes them well suited for wide-area inspection and SHM （structural health monitoring）. This paper presents an extensive computational study of the interaction of the fundamental symmetrical Lamb wave mode （SO） with a through-thickness edge crack in an isotropic plate. The incident wave is generated by a point source that is symmetrical with respect to the plate＇s midplane, and whose time dependence is a 10-cycle Harmed windowed toneburst of centre frequency below the cut-off for the first order shear-horizontal mode （SH 1）, so that the only propagating modes are SO and SH0. Results are presented showing the angular dependence of the SO and SH0 scattered fields for various angles of incidence. The dependence of scattering amplitude on crack size is also studied, with a view to facilitating the inverse problem of determining crack size from measurements of the scattered field. It is shown that the scattered field due to a small crack can be considered to be equivalent to a point source consisting of a combination of force doublets that depend on the angle of incidence. The implications of these results for SHM are briefly discussed.展开更多
Let(X, Y) be a balanced pair in an abelian category. We first introduce the notion of cotorsion pairs relative to(X, Y), and then give some equivalent characterizations when a relative cotorsion pair is hereditary or ...Let(X, Y) be a balanced pair in an abelian category. We first introduce the notion of cotorsion pairs relative to(X, Y), and then give some equivalent characterizations when a relative cotorsion pair is hereditary or perfect. We prove that if the X-resolution dimension of Y(resp. Y-coresolution dimension of X)is finite, then the bounded homotopy category of Y(resp. X) is contained in that of X(resp. Y). As a consequence, we get that the right X-singularity category coincides with the left Y-singularity category if the X-resolution dimension of Y and the Y-coresolution dimension of X are finite.展开更多
基金The first author would like to thank for the Fund of Jiangsu Innovation Program for Graduate Education，the Fundamental Research Funds for the Central Universities,and Ningbo Natural Science Foundation，the Chinese National Scholarship fund,and also appreciate the benefit to this work from projects in science and technique of Ningbo municipal.The third author would like to thank for Ningbo Natural Science Foundation
文摘Fully homomorphic encryption is faced with two problems now. One is candidate fully homomorphic encryption schemes are few. Another is that the efficiency of fully homomorphic encryption is a big question. In this paper, we propose a fully homomorphic encryption scheme based on LWE, which has better key size. Our main contributions are： （1） According to the binary-LWE recently, we choose secret key from binary set and modify the basic encryption scheme proposed in Linder and Peikert in 2010. We propose a fully homomorphic encryption scheme based on the new basic encryption scheme. We analyze the correctness and give the proof of the security of our scheme. The public key, evaluation keys and tensored ciphertext have better size in our scheme. （2） Estimating parameters for fully homomorphic encryption scheme is an important work. We estimate the concert parameters for our scheme. We compare these parameters between our scheme and Bral2 scheme. Our scheme have public key and private key that smaller by a factor of about logq than in Bral2 scheme. Tensored ciphertext in our scheme is smaller by a factor of about log2q than in Bral2 scheme. Key switching matrix in our scheme is smaller by a factor of about log3q than in Bra12 scheme.
文摘The hydrodynamic behavior of multiple bubbles rising upward is a field of ongoing research since various aspects of their interaction require further analysis. Shape deformation, rise velocity, and drag coefficient are some of the uncertainties to be determined in a bubble upward flow. For this study the predictions of the three-dimensional numerical simulations of the volume of fluid（VOF） CFD model were first compared with experimental results available in the literature, serving as benchmark cases. Next, 28 cases of pairs of equal and unequal-sized in-line pairs of bubbles moving upwards were simulated. The bubble size varied between 2.0–10 mm. Breakthrough of the present study is the small initial distance of 2.5 R between the center of the bubbles. To provide a more practical nature in this study material properties were selected to match methane gas and seawater properties at deepsea conditions of 15 MPa and 4 ℃, thus yielding a fluid-to-bubble density ratio λ = 7.45 and viscosity ratio n = 100.46. This is one of the few studies to report results of the coalescence procedure in this context. The hydrodynamic behavior of the leading and trailing bubbles was thoroughly studied. Simulation results of the evolution of the rise velocity and the shape deformation with time indicate that the assumption that the leading bubble is rising as a free rising single one is not valid for bubbles between 2.0–7.0 mm. Finally, results of the volume of the daughter bubble exhibited an oscillating nature.
文摘Lamb waves have a relatively slow geometrical decay of amplitude with propagation distance, which makes them well suited for wide-area inspection and SHM （structural health monitoring）. This paper presents an extensive computational study of the interaction of the fundamental symmetrical Lamb wave mode （SO） with a through-thickness edge crack in an isotropic plate. The incident wave is generated by a point source that is symmetrical with respect to the plate＇s midplane, and whose time dependence is a 10-cycle Harmed windowed toneburst of centre frequency below the cut-off for the first order shear-horizontal mode （SH 1）, so that the only propagating modes are SO and SH0. Results are presented showing the angular dependence of the SO and SH0 scattered fields for various angles of incidence. The dependence of scattering amplitude on crack size is also studied, with a view to facilitating the inverse problem of determining crack size from measurements of the scattered field. It is shown that the scattered field due to a small crack can be considered to be equivalent to a point source consisting of a combination of force doublets that depend on the angle of incidence. The implications of these results for SHM are briefly discussed.
基金supported by National Natural Science Foundation of China(Grant No.11171142)
文摘Let(X, Y) be a balanced pair in an abelian category. We first introduce the notion of cotorsion pairs relative to(X, Y), and then give some equivalent characterizations when a relative cotorsion pair is hereditary or perfect. We prove that if the X-resolution dimension of Y(resp. Y-coresolution dimension of X)is finite, then the bounded homotopy category of Y(resp. X) is contained in that of X(resp. Y). As a consequence, we get that the right X-singularity category coincides with the left Y-singularity category if the X-resolution dimension of Y and the Y-coresolution dimension of X are finite.
