The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit form...The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit formula with particular relations involving the trivial and non-trivial roots of the Riemann Zeta function and the Primes. The aim of the paper is to demonstrate this relation at the fixed points of iterations of explicit formula, defined by functions of the form limT∈Ν→∞fT(zw)=zw,where, zwis a real number.展开更多
We calculate the quark number susceptibility （QNS） around the chiral critical end point （CEP）. The CEP is found to be located at （μc,Tc）= （80 MeV, 148 MeV） where μc and Tc are the critical chemical potential...We calculate the quark number susceptibility （QNS） around the chiral critical end point （CEP）. The CEP is found to be located at （μc,Tc）= （80 MeV, 148 MeV） where μc and Tc are the critical chemical potential and temperature, respectively. The QNS is found to have the highest and sharpest peak at the CEP. It is also found that, when the chemical potential μ is in the range of 60MeV≤ μ ≤ 110MeV, the QNS near the transition temperature is larger than the free field result, which indicates that the space-like damping mode dominates the degree of freedom of motion near the CEP.展开更多
For the unsorted database quantum search with the unknown fraction λ of target items, there are mainly two kinds of methods, i.e., fixed-point and trail-and-error.(i) In terms of the fixed-point method, Yoder et al. ...For the unsorted database quantum search with the unknown fraction λ of target items, there are mainly two kinds of methods, i.e., fixed-point and trail-and-error.(i) In terms of the fixed-point method, Yoder et al. [Phys. Rev. Lett.113 210501(2014)] claimed that the quadratic speedup over classical algorithms has been achieved. However, in this paper, we point out that this is not the case, because the query complexity of Yoder’s algorithm is actually in O(1/λ01/2)rather than O(1/λ1/2), where λ0 is a known lower bound of λ.(ii) In terms of the trail-and-error method, currently the algorithm without randomness has to take more than 1 times queries or iterations than the algorithm with randomly selected parameters. For the above problems, we provide the first hybrid quantum search algorithm based on the fixed-point and trail-and-error methods, where the matched multiphase Grover operations are trialed multiple times and the number of iterations increases exponentially along with the number of trials. The upper bound of expected queries as well as the optimal parameters are derived. Compared with Yoder’s algorithm, the query complexity of our algorithm indeed achieves the optimal scaling in λ for quantum search, which reconfirms the practicality of the fixed-point method. In addition, our algorithm also does not contain randomness, and compared with the existing deterministic algorithm, the query complexity can be reduced by about 1/3. Our work provides a new idea for the research on fixed-point and trial-and-error quantum search.展开更多
For shaped charges,LS-DYNA software was adopted to explore the influence of number of initiation points on the penetrator formation numerically.Changed the number of initiation points from 4 to 36,the performance of p...For shaped charges,LS-DYNA software was adopted to explore the influence of number of initiation points on the penetrator formation numerically.Changed the number of initiation points from 4 to 36,the performance of penetrator under four different kinds of typical charge diameter was analyzed,and the effect of detonation wave pressure on the liner was discussed.The minimum number of initiation points to substitute for annular initiation was obtained for each of four warheads with different charge diameters,and the curve representing the relation between the number of initiation points and charge diameter was found out also by using polynomial fitting.The simulation result provides a reference for the design of multimode warhead.展开更多
文摘The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit formula with particular relations involving the trivial and non-trivial roots of the Riemann Zeta function and the Primes. The aim of the paper is to demonstrate this relation at the fixed points of iterations of explicit formula, defined by functions of the form limT∈Ν→∞fT(zw)=zw,where, zwis a real number.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11105122,11275097 and 11475085the Foundation of Graduate School of Nanjing University under Grant No 2014CL02
文摘We calculate the quark number susceptibility （QNS） around the chiral critical end point （CEP）. The CEP is found to be located at （μc,Tc）= （80 MeV, 148 MeV） where μc and Tc are the critical chemical potential and temperature, respectively. The QNS is found to have the highest and sharpest peak at the CEP. It is also found that, when the chemical potential μ is in the range of 60MeV≤ μ ≤ 110MeV, the QNS near the transition temperature is larger than the free field result, which indicates that the space-like damping mode dominates the degree of freedom of motion near the CEP.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11504430 and 61502526)the National Basic Research Program of China(Grant No.2013CB338002)
文摘For the unsorted database quantum search with the unknown fraction λ of target items, there are mainly two kinds of methods, i.e., fixed-point and trail-and-error.(i) In terms of the fixed-point method, Yoder et al. [Phys. Rev. Lett.113 210501(2014)] claimed that the quadratic speedup over classical algorithms has been achieved. However, in this paper, we point out that this is not the case, because the query complexity of Yoder’s algorithm is actually in O(1/λ01/2)rather than O(1/λ1/2), where λ0 is a known lower bound of λ.(ii) In terms of the trail-and-error method, currently the algorithm without randomness has to take more than 1 times queries or iterations than the algorithm with randomly selected parameters. For the above problems, we provide the first hybrid quantum search algorithm based on the fixed-point and trail-and-error methods, where the matched multiphase Grover operations are trialed multiple times and the number of iterations increases exponentially along with the number of trials. The upper bound of expected queries as well as the optimal parameters are derived. Compared with Yoder’s algorithm, the query complexity of our algorithm indeed achieves the optimal scaling in λ for quantum search, which reconfirms the practicality of the fixed-point method. In addition, our algorithm also does not contain randomness, and compared with the existing deterministic algorithm, the query complexity can be reduced by about 1/3. Our work provides a new idea for the research on fixed-point and trial-and-error quantum search.
文摘For shaped charges,LS-DYNA software was adopted to explore the influence of number of initiation points on the penetrator formation numerically.Changed the number of initiation points from 4 to 36,the performance of penetrator under four different kinds of typical charge diameter was analyzed,and the effect of detonation wave pressure on the liner was discussed.The minimum number of initiation points to substitute for annular initiation was obtained for each of four warheads with different charge diameters,and the curve representing the relation between the number of initiation points and charge diameter was found out also by using polynomial fitting.The simulation result provides a reference for the design of multimode warhead.
