This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide th...This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide the original set of support points into some subsets (blocks). Then construct each block by using symmetric branched continued fraction. Finally assemble these blocks by Newton’s method to shape the whole interpolation scheme. Our new method offers many flexible bivariate blending rational interpolation schemes which include the classical bivariate Newton’s polynomial interpolation and symmetric branched continued fraction interpolation as its special cases. The block based bivariate blending rational interpolation is in fact a kind of tradeoff between the purely linear interpolation and the purely nonlinear interpolation. Finally, numerical examples are given to show the effectiveness of the proposed method.展开更多
An equilibrium-based YinYang bipolar dynamic Generalization of CPT (G-CPT) symmetry is introduced based on energy/information conservational quantum emergence-submergence. As a bottleneck of quantum computing, quantum...An equilibrium-based YinYang bipolar dynamic Generalization of CPT (G-CPT) symmetry is introduced based on energy/information conservational quantum emergence-submergence. As a bottleneck of quantum computing, quantum decoherence or collapse has been plaguing quantum mechanics for decades. It is suggested that the crux of the problem can trace its origin back to the incompleteness of CPT symmetry due to the lack of holistic representation for equilibrium-based bipolar coexistence. In this work, the notion of quantum emergence-submergence is coined as two opposite processes with bipolar energy/information conservation. The new notion leads to G-CPT symmetry supported by a Bipolar Quantum Cellular Automata (BQCA) interpretation of quantum mechanics. It is shown that the new interpretation further leads to the unification of electromagnetic particle-antiparticle bipolarity and gravitational action-reaction bipolarity as well as CPT symmetry and CP violation into a philosophically, geometrically and logically different quantum gravity theory. On one hand, G-CPT symmetry enables a Bipolar Quantum Agent (BQA) to emerge as a bipolar quantum superposition or entanglement coupled to a globally coherent BQCA;on the other hand, G-CP violation supports a causal theory of BQA submergence or decoupling from the global coherence. In turn, BQAs can submerge from one world but emerge in another within YinYang bipolar quantum geometry. It is suggested that all logical, physical, social, biological and mental worlds are bipolar quantum entangled under G-CPT symmetry. It is contended that G-CPT symmetry constitutes an analytical paradigm of quantum mechanics and quantum gravity—a fundamental departure from “what goes around comes around”. The new paradigm leads to a number of predictions and challenges.展开更多
A novel carbon foam with microporous structure(CFMS),with the advantages of a simple fabrication process,low energy consumption,large specific surface area and high conductivity,has been prepared by a facile one-step ...A novel carbon foam with microporous structure(CFMS),with the advantages of a simple fabrication process,low energy consumption,large specific surface area and high conductivity,has been prepared by a facile one-step carbonization.In addition,the carbon foam possesses suitable interlayer spacing in short range which is flexible to accommodate the deformation of carbon layer caused by the ion insertion and deinsertion at the charge and discharge state.Furthermore,a low cost carbon-based symmetric potassium dual-ion capacitor(PDIC),which integrates the virtues of potassium ion capacitors and dual-ion batteries,is successfully established with CFMS as both the battery-type cathode and the capacitor-type anode.PDIC displays a superior rate performance,an ultra-long cycle life(90%retention after 10000 cycles),and a high power density of 7800 W kg^-1 at an energy density of 39Whkg^-1.The PDIC also exhibits excellent ultrafast charge and slow discharge properties,with a full charge in just 60 s and a discharge time of more than 3000 s.展开更多
When an image, which is decomposed by bi-orthogonal wavelet bases, is reconstructed, some information will be lost at the four edges of the image. At the same time, artificial discontinuities will be introduced. We us...When an image, which is decomposed by bi-orthogonal wavelet bases, is reconstructed, some information will be lost at the four edges of the image. At the same time, artificial discontinuities will be introduced. We use a method called symmetric extension to solve the problem. We only consider the case of the two-band filter banks, and the results can be applied to M-band filter banks. There are only two types of symmetric extension in analysis phrase, namely the whole-sample symmetry (WS), the half-sample symmetry (HS), while there are four types of symmetric extension in synthesis phrase, namely the WS, HS, the whole-sample anti-symmetry (WA), and the half-sample anti-symmetry (HA) respectively. We can select the exact type according to the image length and the filter length, and we will show how to do these. The image can be perfectly reconstructed without any edge effects in this way. Finally, simulation results are reported. Key words edge effect - image compression - wavelet - biorthogonal bases - symmetric extension CLC number TP 37 Foundation item: Supported by the National 863 Project (20021111901010)Biography: Yu Sheng-sheng (1944-), male, Professor, research direction: multimedia information processing, SAN.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10171026, No. 60473114) the AnhuiProvincial Natural Science Foundation, China (No. 03046102)the Research Funds for Young InnovationGroup, Education Department of Anhui Province (No. 2005TD03).
文摘This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide the original set of support points into some subsets (blocks). Then construct each block by using symmetric branched continued fraction. Finally assemble these blocks by Newton’s method to shape the whole interpolation scheme. Our new method offers many flexible bivariate blending rational interpolation schemes which include the classical bivariate Newton’s polynomial interpolation and symmetric branched continued fraction interpolation as its special cases. The block based bivariate blending rational interpolation is in fact a kind of tradeoff between the purely linear interpolation and the purely nonlinear interpolation. Finally, numerical examples are given to show the effectiveness of the proposed method.
文摘An equilibrium-based YinYang bipolar dynamic Generalization of CPT (G-CPT) symmetry is introduced based on energy/information conservational quantum emergence-submergence. As a bottleneck of quantum computing, quantum decoherence or collapse has been plaguing quantum mechanics for decades. It is suggested that the crux of the problem can trace its origin back to the incompleteness of CPT symmetry due to the lack of holistic representation for equilibrium-based bipolar coexistence. In this work, the notion of quantum emergence-submergence is coined as two opposite processes with bipolar energy/information conservation. The new notion leads to G-CPT symmetry supported by a Bipolar Quantum Cellular Automata (BQCA) interpretation of quantum mechanics. It is shown that the new interpretation further leads to the unification of electromagnetic particle-antiparticle bipolarity and gravitational action-reaction bipolarity as well as CPT symmetry and CP violation into a philosophically, geometrically and logically different quantum gravity theory. On one hand, G-CPT symmetry enables a Bipolar Quantum Agent (BQA) to emerge as a bipolar quantum superposition or entanglement coupled to a globally coherent BQCA;on the other hand, G-CP violation supports a causal theory of BQA submergence or decoupling from the global coherence. In turn, BQAs can submerge from one world but emerge in another within YinYang bipolar quantum geometry. It is suggested that all logical, physical, social, biological and mental worlds are bipolar quantum entangled under G-CPT symmetry. It is contended that G-CPT symmetry constitutes an analytical paradigm of quantum mechanics and quantum gravity—a fundamental departure from “what goes around comes around”. The new paradigm leads to a number of predictions and challenges.
基金financially supported by the National Natural Science Foundation of China(Nos.51672078 and 21473052)Hunan University State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body Independent Research Project(No.71675004)+2 种基金the Fundamental Research Funds for the Central UniversitiesHunan Natural Science Foundation(2019JJ40031)Foundation of State Key Laboratory of Coal Conversion(Grant J1718-903)。
文摘A novel carbon foam with microporous structure(CFMS),with the advantages of a simple fabrication process,low energy consumption,large specific surface area and high conductivity,has been prepared by a facile one-step carbonization.In addition,the carbon foam possesses suitable interlayer spacing in short range which is flexible to accommodate the deformation of carbon layer caused by the ion insertion and deinsertion at the charge and discharge state.Furthermore,a low cost carbon-based symmetric potassium dual-ion capacitor(PDIC),which integrates the virtues of potassium ion capacitors and dual-ion batteries,is successfully established with CFMS as both the battery-type cathode and the capacitor-type anode.PDIC displays a superior rate performance,an ultra-long cycle life(90%retention after 10000 cycles),and a high power density of 7800 W kg^-1 at an energy density of 39Whkg^-1.The PDIC also exhibits excellent ultrafast charge and slow discharge properties,with a full charge in just 60 s and a discharge time of more than 3000 s.
文摘When an image, which is decomposed by bi-orthogonal wavelet bases, is reconstructed, some information will be lost at the four edges of the image. At the same time, artificial discontinuities will be introduced. We use a method called symmetric extension to solve the problem. We only consider the case of the two-band filter banks, and the results can be applied to M-band filter banks. There are only two types of symmetric extension in analysis phrase, namely the whole-sample symmetry (WS), the half-sample symmetry (HS), while there are four types of symmetric extension in synthesis phrase, namely the WS, HS, the whole-sample anti-symmetry (WA), and the half-sample anti-symmetry (HA) respectively. We can select the exact type according to the image length and the filter length, and we will show how to do these. The image can be perfectly reconstructed without any edge effects in this way. Finally, simulation results are reported. Key words edge effect - image compression - wavelet - biorthogonal bases - symmetric extension CLC number TP 37 Foundation item: Supported by the National 863 Project (20021111901010)Biography: Yu Sheng-sheng (1944-), male, Professor, research direction: multimedia information processing, SAN.
