In this paper, we investigate the space-time fractional symmetric regularized long wave equation. By using the Backlund transformations and nonlinear superposition formulas of solutions to Riccati equation, we present...In this paper, we investigate the space-time fractional symmetric regularized long wave equation. By using the Backlund transformations and nonlinear superposition formulas of solutions to Riccati equation, we present infinite sequence solutions for space-time fractional symmetric regularized long wave equation. This method can be extended to solve other nonlinear fractional partial differential equations.展开更多
A general method of finding the complex fundamental solutions for semi-infinite plane and infinite plane with hole under various boundary conditions has be established by using Riemann-Schwarz symmetric principle and ...A general method of finding the complex fundamental solutions for semi-infinite plane and infinite plane with hole under various boundary conditions has be established by using Riemann-Schwarz symmetric principle and superposition principle of the solutions of elasticity. More than ten solutions have been derived respectively.展开更多
We evaluate the monogamy inequality for symmetric, non-symmetric pure states of importance in terms of squared concurrence, squared entanglement of formation, squared negativity of partial transpose and compare the co...We evaluate the monogamy inequality for symmetric, non-symmetric pure states of importance in terms of squared concurrence, squared entanglement of formation, squared negativity of partial transpose and compare the corresponding tangles. We show that though concurrence and concurrence tangle are zero for two special classes of mixed entangled states, both negativity tangle and entanglement of formation（EOF） tangle turn out to be non-zero. A comparison of different tangles is carried out in each case and it is shown that while the concurrence tangle captures the genuine multiqubit entanglement in N-qubit pure states with N distinct spinors（containing GHZ and superposition of W-, obverse W states）either negativity tangle or EOF tangle is to be used as a better measure of entanglement in the W-class of states with two distinct spinors and in the special classes of mixed multiqubit states.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
基金Acknowledgments This work is supported by the National Natural Science Foundation of China （Grant No. 11462019） and the Scientific Research Foundation of Inner Mongolia University for Nationalities （Grant No. NMD1306）. The author would like to thank the referees for their time and comments.
文摘In this paper, we investigate the space-time fractional symmetric regularized long wave equation. By using the Backlund transformations and nonlinear superposition formulas of solutions to Riccati equation, we present infinite sequence solutions for space-time fractional symmetric regularized long wave equation. This method can be extended to solve other nonlinear fractional partial differential equations.
文摘A general method of finding the complex fundamental solutions for semi-infinite plane and infinite plane with hole under various boundary conditions has be established by using Riemann-Schwarz symmetric principle and superposition principle of the solutions of elasticity. More than ten solutions have been derived respectively.
基金support of the Department of Science and Technology (DST),Govt.of India through the award of the INSPIRE fellowship
文摘We evaluate the monogamy inequality for symmetric, non-symmetric pure states of importance in terms of squared concurrence, squared entanglement of formation, squared negativity of partial transpose and compare the corresponding tangles. We show that though concurrence and concurrence tangle are zero for two special classes of mixed entangled states, both negativity tangle and entanglement of formation（EOF） tangle turn out to be non-zero. A comparison of different tangles is carried out in each case and it is shown that while the concurrence tangle captures the genuine multiqubit entanglement in N-qubit pure states with N distinct spinors（containing GHZ and superposition of W-, obverse W states）either negativity tangle or EOF tangle is to be used as a better measure of entanglement in the W-class of states with two distinct spinors and in the special classes of mixed multiqubit states.
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.
