Rectification for airborne linear images is an indispensable preprocessing step. This paper presents in detail a two-step rectification algorithm. The first step is to establish the model of direct georeference positi...Rectification for airborne linear images is an indispensable preprocessing step. This paper presents in detail a two-step rectification algorithm. The first step is to establish the model of direct georeference position using the data provided by the Po- sitioning and Orientation System (POS) and obtain the mathematical relationships between the image points and ground reference points. The second step is to apply polynomial distortion model and Bilinear Interpolation to get the final precise rectified images. In this step, a reference image is required and some ground control points (GCPs) are selected. Experiments showed that the final rectified images are satisfactory, and that our two-step rectification algorithm is very effective.展开更多
It is widely known that the equation 2xx= has and only has two roots 0 and 1. Jiglevich A.B. and Petrov N. N. discovered that equation has two other roots, i.e. infinite place’s numbers (called super numbers): 821289...It is widely known that the equation 2xx= has and only has two roots 0 and 1. Jiglevich A.B. and Petrov N. N. discovered that equation has two other roots, i.e. infinite place’s numbers (called super numbers): 8212890625X=L and 1787109376Y=L, and obtained 4 (super number) roots of the equation2xx=. For progressing to wider conditions, with the way of exactly divisible and mutually orthogonal Latin squares, three attractive results are obtained: 1) A kind of polynomial 1()()niiPxxa==P-, ,1,2,,iain?KZ has and only has different n2 super number roots; 2) When n>2 and n 6, those n2 roots of the polynomial ()Px can be arranged in an n-order square matrix, of which n roots of every row and every column satisfy Vieta Formula of roots and coefficients; 3) In *Z ring of super number, the polynomial1()()niiPxxa==P-, ,1,2,,iain?KZ has n! different factorizations.展开更多
Terrain texture analysis is an important method of digital terrain analysis in quantitative geomorphological research and in the exploration of the spatial heterogeneity and autocorrelation of terrain features. Howeve...Terrain texture analysis is an important method of digital terrain analysis in quantitative geomorphological research and in the exploration of the spatial heterogeneity and autocorrelation of terrain features. However, a major issue often neglected in previous studies is the calculation unit of the terrain texture, that is, the stability analysis unit. As the test size increases, the derived terrain textures become increasingly similar so that their differences can be ignored. The test size of terrain texture is defined as the stability analysis unit. This study randomly selected 48 areas within the Loess Plateau in northern Shaanxi in China as the study sites and used the gray level co-occurrence matrix to calculate the terrain texture. The stability analysis unit of the terrain texture was then extracted, and its spatial distribution pattern in the Loess Plateau was studiedusing spatial interpolation method. Four terrain texture metrics, i.e., homogeneity, energy, correlation, and contrast, were extracted on the basis of the stability analysis unit, and the spatial variation patterns of these parameters were studied. Results showed that the spatial distribution pattern and the terrain texture metrics reflected a trend of high–low–high from north to south, which correlated with the spatial distribution of the landforms at the Loess Plateau. In addition, the terrain texture measures was significantly correlated with the terrain factors of gully density and slope, and this relationship showed that terrain texture measures based on the stability analysis unit could reflect the basic characteristics of terrain morphology. The stability analysis unit provided a reasonable analytical scale for terrain texture analysis and could be used as a measure of the regional topography to accurately describe basic terrain characteristics.展开更多
With the increasing number of web services, it becomes a difficult task for an ordinary user to select an appropriate service. Hence, it is conventional that users in a digital community network take part in a collabo...With the increasing number of web services, it becomes a difficult task for an ordinary user to select an appropriate service. Hence, it is conventional that users in a digital community network take part in a collaborative mechanism for the purpose of service selection. The participation usually brings unnecessary burdens for users, such as giving opinions, storing service information. Extra communication overhead hinders the performance of the network. Thus, the community administrators are facing a problem of how to obtain an overall service selection result for the whole community readily and effectively. To address this problem, we present a k-median facility location agent model. The model analyzes the procedure of service selection through five entities and six types of messages. Two algorithms are elaborated in pursuit of a global optimization concerning connection costs between users and facilities where services are deployed. To evaluate our model, we conduct extensive simulations and present a detailed analysis of the simulation results.展开更多
This paper presents the closed-form expression to the expected density of progress for wireless ad hoc networks with Nakagami-m fading. The expected density of progress is defined as the expectation of a product betwe...This paper presents the closed-form expression to the expected density of progress for wireless ad hoc networks with Nakagami-m fading. The expected density of progress is defined as the expectation of a product between the number of simultaneous successful transmission per unit area and the distance towards the destination. Numerical results show that the expected density of progress is determined by two factors, terminal density and the probability that a terminal attempts to transmit.展开更多
Arch is a typical complex structure comparing with beam and plate in bridge system. This paper investigates the damage characteristic combining the crack location with the crack intensity in arch. Initially, the first...Arch is a typical complex structure comparing with beam and plate in bridge system. This paper investigates the damage characteristic combining the crack location with the crack intensity in arch. Initially, the first four displacement modes of intact and different damaged arch are simulated and the displacement mode changes are obtained. Next, the wavelet transformation is applied to the displacement mode changes in arch and wavelet coefficients at damage loci are picked. Finally, the damage index including damage location and damage intensity in arch is provided and plotted. The results show that wavelet coefficient module maximum of mode changes can be the damage indicator and is influenced by damage location and damage intensity. The damage indicator is proportional to the damage intensity and present monotonic trend according to damage location which depend on the mode order. At the same time, the large modulus maximum corresponds to small damage combination of location and intensity in the first four modes.展开更多
This paper deals with the analytical derivation of phasor-domain statistical properties of crosstalk in random wire cables due to the superposition of several sources of electromagnetic interference.In this study,stat...This paper deals with the analytical derivation of phasor-domain statistical properties of crosstalk in random wire cables due to the superposition of several sources of electromagnetic interference.In this study,statistical characterization of crosstalk in cable bundles,which is available in literature for the case of one source of interference,is extended to the case of several sources operating simultaneously.The superposition of crosstalk effects is analysed in statistical terms,also taking into account the correlation between crosstalk contributions.A further random contribution,which is included in the proposed statistical model,is given by the phase relationship between the sources of interference.Analytical approximate expressions for the crosstalk mean value,variance,and probability density function are derived as functions of the cable bundle features and sources.展开更多
Smweillance system using active tracking camera has no distance limitation of surveillance range compared to supersonic or sound sensors. However, complex motion tracking algorithm requires huge amount of computation,...Smweillance system using active tracking camera has no distance limitation of surveillance range compared to supersonic or sound sensors. However, complex motion tracking algorithm requires huge amount of computation, and it often requires exfmasive DSPs or embedded processors. This paper proposes a novel motion tracking trait based on different image for fast and simple motion tracking. It uses configuration factor to avoid noise and inaccuracy. It reduces the required computation significantly, so as to be implemented on Field Programmable Gate Array(FFGAs ) instead of expensive Digital Signal Processing(DSPs). It also performs calculation for motion estimation in video compression, so it can be easily combined with surveil system with video recording functionality based on video compression. The proposed motion tracking system implemented on Xilinx Vertex-4 FPGA can process 48 frames per second, and operating frequency of motion tracking trait is 100 MHz.展开更多
This paper presents an innovative switched-mode auto gain control (AGC) circuit with internally created reset module for DC-10Mb/s burst-mode unbalanced (BMU) optical data transmission. Conventional AGC circuit is...This paper presents an innovative switched-mode auto gain control (AGC) circuit with internally created reset module for DC-10Mb/s burst-mode unbalanced (BMU) optical data transmission. Conventional AGC circuit is inappropriate for BMU data transmission because it is based on average level detection and requires considerable time to settle on a predefined gain. Therefore, we adopt a fast switched-mode AGC based on peak level detection. After the gain is adjusted, the peak level detectors need to re-detect the peak level of the input signal. Thus, we develop an internally created reset module. This AGC with reset module exhibits a fast operation and achieves an adjusted stable gain within one-bit, avoiding any bit loss up to 10Mb/s data rate. During power-up, the peak level detectors possibly hold an uncertain level resulting in the bit-errors. We propose a power-up reset circuit to solve this problem. Designed in a 0.5μm CMOS technology, the circuit achieves an optical sensitivity of better than -30dBm and a wide dynamic range of over 30dB with a power dissipation of only 30 mW from a 5V supply.展开更多
This paper presents a low order stabilized hybrid quadrilateral finite element method for ReissnerMindlin plates based on Hellinger-Reissner variational principle,which includes variables of displacements,shear stress...This paper presents a low order stabilized hybrid quadrilateral finite element method for ReissnerMindlin plates based on Hellinger-Reissner variational principle,which includes variables of displacements,shear stresses and bending moments.The approach uses continuous piecewise isoparametric bilinear interpolations for the approximations of the transverse displacement and rotation.The stabilization achieved by adding a stabilization term of least-squares to the original hybrid scheme,allows independent approximations of the stresses and moments.The stress approximation adopts a piecewise independent 4-parameter mode satisfying an accuracy-enhanced condition.The approximation of moments employs a piecewise-independent 5-parameter mode.This method can be viewed as a stabilized version of the hybrid finite element scheme proposed in [Carstensen C,Xie X,Yu G,et al.A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner-Mindlin plates.Comput Methods Appl Mech Engrg,2011,200:1161-1175],where the approximations of stresses and moments are required to satisfy an equilibrium criterion.A priori error analysis shows that the method is uniform with respect to the plate thickness t.Numerical experiments confirm the theoretical results.展开更多
Asymptotic energy expansion method is extended for polynomial potentials having rational powers. New types of recurrence relations are derived for the potentials of the form rig, mN are positive integers while coeffic...Asymptotic energy expansion method is extended for polynomial potentials having rational powers. New types of recurrence relations are derived for the potentials of the form rig, mN are positive integers while coefficients bk ∈ C. As in the case of even degree polynomial potentials with integer powers, all the integrals in the expansion can be evaluated analytically in terms of F functions. With the help of two examples, we demonstrate the usefulness of these expansions in getting analytic insight into the quantum systems having rational power polynomial potentials.展开更多
Suppose that q is not a root of unity, it is proved in this paper that the center of the quantum group Uq(sl4) is isomorphic to a quotient algebra of polynomial algebra with four variables and one relation.
The authors mainly concern the set Uf of c E C such that the power deformation z(f-(z)/z)c is univalent in the unit disk |z|〈 1 for a given analytic univalent function f(z) = z + a2z2 + ... in the unit disk...The authors mainly concern the set Uf of c E C such that the power deformation z(f-(z)/z)c is univalent in the unit disk |z|〈 1 for a given analytic univalent function f(z) = z + a2z2 + ... in the unit disk. It is shown that Uf is a compact, polynomially convex subset of the complex plane C unless f is the identity function. In particular, the interior of Uf is simply connected. This fact enables us to apply various versions of the X-lemma for the holomorphic family z(f(z)/z)c of injections parametrized over the interior of Uf. The necessary or sufficient conditions for Uf to contain 0 or 1 as an interior point are also given.展开更多
In this paper,the effects of foundation damage and water-level change on vibration characteristics of gravity-type caisson structure are examined by analyzing modal parameters extracted from output-only information.To...In this paper,the effects of foundation damage and water-level change on vibration characteristics of gravity-type caisson structure are examined by analyzing modal parameters extracted from output-only information.To achieve the objective,the following approaches are implemented.Firstly,vibration response analysis methods are selected to estimate power spectral density and modal parameters such as natural frequency,damping ratio and mode shape of a lab-scale caisson structural system.Secondly,vibration tests on the lab-scale caisson system are performed under a series of test scenarios which include three water-level changes and three damage levels.Thirdly,experimental modal parameters corresponding to the damaging cases as well as the water level cases are extracted by frequency domain decomposition method and stochastic subspace identification method.Finally,the effects of the water-level variation and foundation damage on the extracted modal parameters are examined to assess the feasibility of the vibration-based damage detection in gravity-type caisson structures under water-level uncertainty.展开更多
The discrete logarithm problem is analyzed from the perspective of Tate local duality. Local duality in the multiplicative case and the case of Jacobians of curves over p-adic local fields are considered. When the loc...The discrete logarithm problem is analyzed from the perspective of Tate local duality. Local duality in the multiplicative case and the case of Jacobians of curves over p-adic local fields are considered. When the local field contains the necessary roots of unity, the case of curves over local fields is polynomial time reducible to the multiplicative case, and the multiplicative case is polynomial time equivalent to computing discrete logarithm in finite fields. When the local field does not contains the necessary roots of unity, similar results can be obtained at the cost of going to an extension that contains these roots of unity. There was evidence in the analysis that suggests that the minimal extension where the local duality can be rationally and algorithmically defined must contain the roots of unity. Therefore, the discrete logarithm problem appears to be well protected against an attack using local duality. These results are also of independent interest for algorithmic study of arithmetic duality as they explicitly relate local duality in the case of curves over local fields to the multiplicative case and Tate-Lichtenbaum pairing (over finite fields).展开更多
基金Project (No. 02DZ15001) supported by Shanghai Science and Technology Development Funds, China
文摘Rectification for airborne linear images is an indispensable preprocessing step. This paper presents in detail a two-step rectification algorithm. The first step is to establish the model of direct georeference position using the data provided by the Po- sitioning and Orientation System (POS) and obtain the mathematical relationships between the image points and ground reference points. The second step is to apply polynomial distortion model and Bilinear Interpolation to get the final precise rectified images. In this step, a reference image is required and some ground control points (GCPs) are selected. Experiments showed that the final rectified images are satisfactory, and that our two-step rectification algorithm is very effective.
文摘It is widely known that the equation 2xx= has and only has two roots 0 and 1. Jiglevich A.B. and Petrov N. N. discovered that equation has two other roots, i.e. infinite place’s numbers (called super numbers): 8212890625X=L and 1787109376Y=L, and obtained 4 (super number) roots of the equation2xx=. For progressing to wider conditions, with the way of exactly divisible and mutually orthogonal Latin squares, three attractive results are obtained: 1) A kind of polynomial 1()()niiPxxa==P-, ,1,2,,iain?KZ has and only has different n2 super number roots; 2) When n>2 and n 6, those n2 roots of the polynomial ()Px can be arranged in an n-order square matrix, of which n roots of every row and every column satisfy Vieta Formula of roots and coefficients; 3) In *Z ring of super number, the polynomial1()()niiPxxa==P-, ,1,2,,iain?KZ has n! different factorizations.
基金supported by the National Natural Science Foundation of China (Grant Nos. 41471316, 41571383, 41671389)the Priority Academic Program Development of Jiangsu Higher Education Institutions-PAPD (Grant No. 164320H101)the Key Project of Natural Science Research of Anhui Provincial Department of Education (Grant No. KJ2015A171)
文摘Terrain texture analysis is an important method of digital terrain analysis in quantitative geomorphological research and in the exploration of the spatial heterogeneity and autocorrelation of terrain features. However, a major issue often neglected in previous studies is the calculation unit of the terrain texture, that is, the stability analysis unit. As the test size increases, the derived terrain textures become increasingly similar so that their differences can be ignored. The test size of terrain texture is defined as the stability analysis unit. This study randomly selected 48 areas within the Loess Plateau in northern Shaanxi in China as the study sites and used the gray level co-occurrence matrix to calculate the terrain texture. The stability analysis unit of the terrain texture was then extracted, and its spatial distribution pattern in the Loess Plateau was studiedusing spatial interpolation method. Four terrain texture metrics, i.e., homogeneity, energy, correlation, and contrast, were extracted on the basis of the stability analysis unit, and the spatial variation patterns of these parameters were studied. Results showed that the spatial distribution pattern and the terrain texture metrics reflected a trend of high–low–high from north to south, which correlated with the spatial distribution of the landforms at the Loess Plateau. In addition, the terrain texture measures was significantly correlated with the terrain factors of gully density and slope, and this relationship showed that terrain texture measures based on the stability analysis unit could reflect the basic characteristics of terrain morphology. The stability analysis unit provided a reasonable analytical scale for terrain texture analysis and could be used as a measure of the regional topography to accurately describe basic terrain characteristics.
基金This work is supported by Program for the Key Program of NSFC-Guangdong Union Foundation (U1135002), Major national S&T program (2011ZX03005-002), National Natural Science Foundation of China (60872041, 61072066), the Fundamental Research Funds for the Central Universities (JY10000903001, JY10000901034, K5051203010) and the GAD Pre-Research Foundation (9140A 15040210HK61 ).
文摘With the increasing number of web services, it becomes a difficult task for an ordinary user to select an appropriate service. Hence, it is conventional that users in a digital community network take part in a collaborative mechanism for the purpose of service selection. The participation usually brings unnecessary burdens for users, such as giving opinions, storing service information. Extra communication overhead hinders the performance of the network. Thus, the community administrators are facing a problem of how to obtain an overall service selection result for the whole community readily and effectively. To address this problem, we present a k-median facility location agent model. The model analyzes the procedure of service selection through five entities and six types of messages. Two algorithms are elaborated in pursuit of a global optimization concerning connection costs between users and facilities where services are deployed. To evaluate our model, we conduct extensive simulations and present a detailed analysis of the simulation results.
基金Supported by the National High Technology and Development Program of China (No.2007AA10Z235) , the National Basic Research Program of China(No.2009CB320407), the National Natural Science Foundation of China(No.60872049,60871042,60971082,60972073), and the National Science Specific Project(2009ZX03003-011).
文摘This paper presents the closed-form expression to the expected density of progress for wireless ad hoc networks with Nakagami-m fading. The expected density of progress is defined as the expectation of a product between the number of simultaneous successful transmission per unit area and the distance towards the destination. Numerical results show that the expected density of progress is determined by two factors, terminal density and the probability that a terminal attempts to transmit.
文摘Arch is a typical complex structure comparing with beam and plate in bridge system. This paper investigates the damage characteristic combining the crack location with the crack intensity in arch. Initially, the first four displacement modes of intact and different damaged arch are simulated and the displacement mode changes are obtained. Next, the wavelet transformation is applied to the displacement mode changes in arch and wavelet coefficients at damage loci are picked. Finally, the damage index including damage location and damage intensity in arch is provided and plotted. The results show that wavelet coefficient module maximum of mode changes can be the damage indicator and is influenced by damage location and damage intensity. The damage indicator is proportional to the damage intensity and present monotonic trend according to damage location which depend on the mode order. At the same time, the large modulus maximum corresponds to small damage combination of location and intensity in the first four modes.
文摘This paper deals with the analytical derivation of phasor-domain statistical properties of crosstalk in random wire cables due to the superposition of several sources of electromagnetic interference.In this study,statistical characterization of crosstalk in cable bundles,which is available in literature for the case of one source of interference,is extended to the case of several sources operating simultaneously.The superposition of crosstalk effects is analysed in statistical terms,also taking into account the correlation between crosstalk contributions.A further random contribution,which is included in the proposed statistical model,is given by the phase relationship between the sources of interference.Analytical approximate expressions for the crosstalk mean value,variance,and probability density function are derived as functions of the cable bundle features and sources.
基金sponsored by the MKE(The Ministry of Knowledge Economy,Korea),the ITRC(Information Technology Research Center)support program(NIPA-2009-(C1090-0902-0007))the System Semiconductor Industry Development Center,Human Resource Development Project for IT SOC Architecture
文摘Smweillance system using active tracking camera has no distance limitation of surveillance range compared to supersonic or sound sensors. However, complex motion tracking algorithm requires huge amount of computation, and it often requires exfmasive DSPs or embedded processors. This paper proposes a novel motion tracking trait based on different image for fast and simple motion tracking. It uses configuration factor to avoid noise and inaccuracy. It reduces the required computation significantly, so as to be implemented on Field Programmable Gate Array(FFGAs ) instead of expensive Digital Signal Processing(DSPs). It also performs calculation for motion estimation in video compression, so it can be easily combined with surveil system with video recording functionality based on video compression. The proposed motion tracking system implemented on Xilinx Vertex-4 FPGA can process 48 frames per second, and operating frequency of motion tracking trait is 100 MHz.
基金Supported by the Natural Science Foundation of Jiangsu Province ( BK2010411 ) and the National International Cooperation Project of China-Korea (2011DFA11310).
文摘This paper presents an innovative switched-mode auto gain control (AGC) circuit with internally created reset module for DC-10Mb/s burst-mode unbalanced (BMU) optical data transmission. Conventional AGC circuit is inappropriate for BMU data transmission because it is based on average level detection and requires considerable time to settle on a predefined gain. Therefore, we adopt a fast switched-mode AGC based on peak level detection. After the gain is adjusted, the peak level detectors need to re-detect the peak level of the input signal. Thus, we develop an internally created reset module. This AGC with reset module exhibits a fast operation and achieves an adjusted stable gain within one-bit, avoiding any bit loss up to 10Mb/s data rate. During power-up, the peak level detectors possibly hold an uncertain level resulting in the bit-errors. We propose a power-up reset circuit to solve this problem. Designed in a 0.5μm CMOS technology, the circuit achieves an optical sensitivity of better than -30dBm and a wide dynamic range of over 30dB with a power dissipation of only 30 mW from a 5V supply.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171239 and 11226333)Scientific Research Foundation for the Returned Overseas Chinese Scholars and Foundation for Excellent Young Scholars of Sichuan University (Grant No. 2011SCU04B28)
文摘This paper presents a low order stabilized hybrid quadrilateral finite element method for ReissnerMindlin plates based on Hellinger-Reissner variational principle,which includes variables of displacements,shear stresses and bending moments.The approach uses continuous piecewise isoparametric bilinear interpolations for the approximations of the transverse displacement and rotation.The stabilization achieved by adding a stabilization term of least-squares to the original hybrid scheme,allows independent approximations of the stresses and moments.The stress approximation adopts a piecewise independent 4-parameter mode satisfying an accuracy-enhanced condition.The approximation of moments employs a piecewise-independent 5-parameter mode.This method can be viewed as a stabilized version of the hybrid finite element scheme proposed in [Carstensen C,Xie X,Yu G,et al.A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner-Mindlin plates.Comput Methods Appl Mech Engrg,2011,200:1161-1175],where the approximations of stresses and moments are required to satisfy an equilibrium criterion.A priori error analysis shows that the method is uniform with respect to the plate thickness t.Numerical experiments confirm the theoretical results.
文摘Asymptotic energy expansion method is extended for polynomial potentials having rational powers. New types of recurrence relations are derived for the potentials of the form rig, mN are positive integers while coefficients bk ∈ C. As in the case of even degree polynomial potentials with integer powers, all the integrals in the expansion can be evaluated analytically in terms of F functions. With the help of two examples, we demonstrate the usefulness of these expansions in getting analytic insight into the quantum systems having rational power polynomial potentials.
基金supported by National Natural Science Foundation of China (Grant No.10771182)Doctorate Foundation Ministry of Education of China (Grant No. 200811170001)
文摘Suppose that q is not a root of unity, it is proved in this paper that the center of the quantum group Uq(sl4) is isomorphic to a quotient algebra of polynomial algebra with four variables and one relation.
基金Project supported by Yeungnam University(2011)(No.211A380226)the JSPS Grant-in-Aid forScientific Research(B)(No.22340025)
文摘The authors mainly concern the set Uf of c E C such that the power deformation z(f-(z)/z)c is univalent in the unit disk |z|〈 1 for a given analytic univalent function f(z) = z + a2z2 + ... in the unit disk. It is shown that Uf is a compact, polynomially convex subset of the complex plane C unless f is the identity function. In particular, the interior of Uf is simply connected. This fact enables us to apply various versions of the X-lemma for the holomorphic family z(f(z)/z)c of injections parametrized over the interior of Uf. The necessary or sufficient conditions for Uf to contain 0 or 1 as an interior point are also given.
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry ofEducation,Science and Technology(Grant no.NRF-2013R1A1A2A10012040)the financial support of the project Development of Inspection Equipment Technology for Harbor Facilities funded by Korea Ministry of Land,Transportation,and Maritime Affairs
文摘In this paper,the effects of foundation damage and water-level change on vibration characteristics of gravity-type caisson structure are examined by analyzing modal parameters extracted from output-only information.To achieve the objective,the following approaches are implemented.Firstly,vibration response analysis methods are selected to estimate power spectral density and modal parameters such as natural frequency,damping ratio and mode shape of a lab-scale caisson structural system.Secondly,vibration tests on the lab-scale caisson system are performed under a series of test scenarios which include three water-level changes and three damage levels.Thirdly,experimental modal parameters corresponding to the damaging cases as well as the water level cases are extracted by frequency domain decomposition method and stochastic subspace identification method.Finally,the effects of the water-level variation and foundation damage on the extracted modal parameters are examined to assess the feasibility of the vibration-based damage detection in gravity-type caisson structures under water-level uncertainty.
文摘The discrete logarithm problem is analyzed from the perspective of Tate local duality. Local duality in the multiplicative case and the case of Jacobians of curves over p-adic local fields are considered. When the local field contains the necessary roots of unity, the case of curves over local fields is polynomial time reducible to the multiplicative case, and the multiplicative case is polynomial time equivalent to computing discrete logarithm in finite fields. When the local field does not contains the necessary roots of unity, similar results can be obtained at the cost of going to an extension that contains these roots of unity. There was evidence in the analysis that suggests that the minimal extension where the local duality can be rationally and algorithmically defined must contain the roots of unity. Therefore, the discrete logarithm problem appears to be well protected against an attack using local duality. These results are also of independent interest for algorithmic study of arithmetic duality as they explicitly relate local duality in the case of curves over local fields to the multiplicative case and Tate-Lichtenbaum pairing (over finite fields).