This paper studies numerically the dark incoherent spatial solitons propagating in logarithmically saturable nonlinear media by using a coherent density approach and a split-step Fourier approach for the first time. U...This paper studies numerically the dark incoherent spatial solitons propagating in logarithmically saturable nonlinear media by using a coherent density approach and a split-step Fourier approach for the first time. Under odd and even initial conditions, a soliton triplet and a doublet are obtained respectively for given parameters. Simultaneously, coherence properties associated with the soliton triplet and doublet are discussed. In addition, if the values of the parameters are properly chosen, five and four splittings from the input dark incoherent spatial solitons can also form. Lastly, the grayness of the soliton triplet and that of the doublet are studied, in detail.展开更多
The metric, that enables measurement of structural data from diffraction in quasicrystals, is analyzed. A modified compromise spacing effect is the consequence of scattering of periodic electromagnetic or electron wav...The metric, that enables measurement of structural data from diffraction in quasicrystals, is analyzed. A modified compromise spacing effect is the consequence of scattering of periodic electromagnetic or electron waves by atoms arranged on a geometric grid in an ideal hierarchic structure. This structure is infinitely extensive, uniquely aligned and uniquely icosahedral. The approximate analytic factor that converts the geometric terms base τ, into periodic terms modulo 2π, is . It matches the simulated metric cs=0.947, consistently used in second (Bragg) order, over a wide scale from atomic dimensions to sixth order superclusters.展开更多
In this paper, we consider the logarithmically improved regularity criterion for the supercritical quasi-geostrophic equation in Besov space B ∞,∞ -r （R2）. The result shows that if 0 is a weak solutions satisfies ...In this paper, we consider the logarithmically improved regularity criterion for the supercritical quasi-geostrophic equation in Besov space B ∞,∞ -r （R2）. The result shows that if 0 is a weak solutions satisfies ∫ 0 T ｜｜ θ （·,s）｜｜a/a-r B ∞,∞ -r /（1＋ln（e＋｜｜ ⊥（·,s）｜｜ L r2） ds〈∞ for some 0〈r〈a and 0〈a〈1,then θ is regular at t = T. In view of the embedding L 2/r M p 2/r B ∞,∞ -r with 2≤p〈2/r and 0≤r〈1, we see that our result extends the results due to [20] and [31].展开更多
In this note, we investigate the existence of the minimal solution and the uniqueness of the weak extremal （probably singular） solution to the biharmonic equation △2ω=λg（ω）with Dirichlet boundary condition in ...In this note, we investigate the existence of the minimal solution and the uniqueness of the weak extremal （probably singular） solution to the biharmonic equation △2ω=λg（ω）with Dirichlet boundary condition in the unit ball in Rn, where the source term is logarithmically convex. An example is also given to illustrate that the logarithmical convexity is not a necessary condition to ensure the uniqueness of the extremal solution.展开更多
In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):104...In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].展开更多
In this paper,we consider the following logarithmic Schrödinger equation:−Δu+ωu=u log|u|^(2),u∈H^(1)(R^(N)),where N≥3,and ω>0 is a constant.With an auxiliary equation,we obtain the existence of normalized...In this paper,we consider the following logarithmic Schrödinger equation:−Δu+ωu=u log|u|^(2),u∈H^(1)(R^(N)),where N≥3,and ω>0 is a constant.With an auxiliary equation,we obtain the existence of normalized solutions by using the constrained variational method.展开更多
In this paper,we investigate the blow-up phenomenon for a class of logarithmic viscoelastic equations with delay and nonlocal terms under acoustic boundary conditions.Using the energy method,we prove that nontrivial s...In this paper,we investigate the blow-up phenomenon for a class of logarithmic viscoelastic equations with delay and nonlocal terms under acoustic boundary conditions.Using the energy method,we prove that nontrivial solutions with negative initial energy will blow up in finite time,and provide an upper bound estimate for the blow-up time.Additionally,we also derive a lower bound estimate for the blow-up time.展开更多
A non-orthogonal multiple access(NOMA) power allocation scheme on the basis of the sparrow search algorithm(SSA) is proposed in this work. Specifically, the logarithmic utility function is utilized to address the pote...A non-orthogonal multiple access(NOMA) power allocation scheme on the basis of the sparrow search algorithm(SSA) is proposed in this work. Specifically, the logarithmic utility function is utilized to address the potential fairness issue that may arise from the maximum sum-rate based objective function and the optical power constraints are set considering the non-negativity of the transmit signal, the requirement of the human eyes safety and all users' quality of service(Qo S). Then, the SSA is utilized to solve this optimization problem. Moreover, to demonstrate the superiority of the proposed strategy, it is compared with the fixed power allocation(FPA) and the gain ratio power allocation(GRPA) schemes. Results show that regardless of the number of users considered, the sum-rate achieved by SSA consistently outperforms that of FPA and GRPA schemes. Specifically, compared to FPA and GRPA schemes, the sum-rate obtained by SSA is increased by 40.45% and 53.44% when the number of users is 7, respectively. The proposed SSA also has better performance in terms of user fairness. This work will benefit the design and development of the NOMA-visible light communication(VLC) systems.展开更多
We consider large-time behaviors of weak solutions to the evolutionary p-Laplacian with logarithmic source of time-dependent coefficient.We find that the weak solutions may neither decay nor blow up,provided that the ...We consider large-time behaviors of weak solutions to the evolutionary p-Laplacian with logarithmic source of time-dependent coefficient.We find that the weak solutions may neither decay nor blow up,provided that the initial data u(·,t_(0))is on the Nehari manifold N:={v∈W_(0)^(1,p)(Ω):I(v,to)=0,||▽v||P^(P)≠0}.This is quite different from the known results that the weak solutions may blow up as,u(·,to)∈N^(+):={v∈W_(0)^(1,p)(Ω):I(v,t_(0))<0}and weak solutions may decay as u(·,t_(0))∈N^(+):={v∈W_(0)^(1,p)(Ω):I(v,t_(0))>0}.展开更多
In order to improve the security of the signature scheme, a digital signature based on two hard-solved problems is proposed. The discrete logarithm problem and the factoring problem are two well known hard- solved mat...In order to improve the security of the signature scheme, a digital signature based on two hard-solved problems is proposed. The discrete logarithm problem and the factoring problem are two well known hard- solved mathematical problems. Combining the E1Gamal scheme based on the discrete logarithm problem and the OSS scheme based on the factoring problem, a digital signature scheme based on these two cryptographic assumptions is proposed. The security of the proposed scheme is based on the difficulties of simultaneously solving the factoring problem and the discrete logarithm problem. So the signature scheme will be still secure under the situation that any one of the two hard-problems is solved. Compared with previous schemes, the proposed scheme is more efficient in terms of space storage, signature length and computation complexities.展开更多
Circuit design of 32 bit logarithmic skip adder (LSA) is introduced to implement high performance,low power addition.ELM carry lookahead adder is included into groups of carry skip adder and the hybrid structure cost...Circuit design of 32 bit logarithmic skip adder (LSA) is introduced to implement high performance,low power addition.ELM carry lookahead adder is included into groups of carry skip adder and the hybrid structure costs 30% less hardware than ELM.At circuit level,a carry incorporating structure to include the primary carry input in carry chain and an 'and xor' structure to implement final sum logic in 32 bit LSA are designed for better optimization.For 5V,1μm process,32 bit LSA has a critical delay of 5 9ns and costs an area of 0 62mm 2,power consumption of 23mW at 100MHz.For 2 5V,0 25μm process,critical delay of 0 8ns,power dissipation of 5 2mW at 100MHz is simulated.展开更多
In the paper, we consider Moran-type sets E;given by sequences {a;};and{n;};. we prove that E;may be decompose into the disjoint union of level sets. Moreover,we define three type of equivalence between two dimension ...In the paper, we consider Moran-type sets E;given by sequences {a;};and{n;};. we prove that E;may be decompose into the disjoint union of level sets. Moreover,we define three type of equivalence between two dimension functions associated to two Morantype sets, respectively, and we classify Moran-type sets by these equivalent relations.展开更多
The paper brings an important integral inequality, which includes the famous Polya-Szego inequality and the logarithmical-arithmetic mean inequality as special cases.
基金Project supported by the Major Program of the National Natural Science Foundation of China (Grant No 10674176)
文摘This paper studies numerically the dark incoherent spatial solitons propagating in logarithmically saturable nonlinear media by using a coherent density approach and a split-step Fourier approach for the first time. Under odd and even initial conditions, a soliton triplet and a doublet are obtained respectively for given parameters. Simultaneously, coherence properties associated with the soliton triplet and doublet are discussed. In addition, if the values of the parameters are properly chosen, five and four splittings from the input dark incoherent spatial solitons can also form. Lastly, the grayness of the soliton triplet and that of the doublet are studied, in detail.
文摘The metric, that enables measurement of structural data from diffraction in quasicrystals, is analyzed. A modified compromise spacing effect is the consequence of scattering of periodic electromagnetic or electron waves by atoms arranged on a geometric grid in an ideal hierarchic structure. This structure is infinitely extensive, uniquely aligned and uniquely icosahedral. The approximate analytic factor that converts the geometric terms base τ, into periodic terms modulo 2π, is . It matches the simulated metric cs=0.947, consistently used in second (Bragg) order, over a wide scale from atomic dimensions to sixth order superclusters.
文摘In this paper, we consider the logarithmically improved regularity criterion for the supercritical quasi-geostrophic equation in Besov space B ∞,∞ -r （R2）. The result shows that if 0 is a weak solutions satisfies ∫ 0 T ｜｜ θ （·,s）｜｜a/a-r B ∞,∞ -r /（1＋ln（e＋｜｜ ⊥（·,s）｜｜ L r2） ds〈∞ for some 0〈r〈a and 0〈a〈1,then θ is regular at t = T. In view of the embedding L 2/r M p 2/r B ∞,∞ -r with 2≤p〈2/r and 0≤r〈1, we see that our result extends the results due to [20] and [31].
文摘In this note, we investigate the existence of the minimal solution and the uniqueness of the weak extremal （probably singular） solution to the biharmonic equation △2ω=λg（ω）with Dirichlet boundary condition in the unit ball in Rn, where the source term is logarithmically convex. An example is also given to illustrate that the logarithmical convexity is not a necessary condition to ensure the uniqueness of the extremal solution.
基金Supported by NSFC(Nos.11661025,12161024)Natural Science Foundation of Guangxi(Nos.2020GXNSFAA159118,2021GXNSFAA196045)+2 种基金Guangxi Science and Technology Project(No.Guike AD20297006)Training Program for 1000 Young and Middle-aged Cadre Teachers in Universities of GuangxiNational College Student's Innovation and Entrepreneurship Training Program(No.202110595049)。
文摘In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].
基金supported by the Natural Science Research Project of Department of Education of Guizhou Province(No.QJJ2023062)the National Natural Science Foundation of China(No.52174184)。
文摘In this paper,we consider the following logarithmic Schrödinger equation:−Δu+ωu=u log|u|^(2),u∈H^(1)(R^(N)),where N≥3,and ω>0 is a constant.With an auxiliary equation,we obtain the existence of normalized solutions by using the constrained variational method.
基金supported by the National Natural Sciences Foundation of China(No.62363005)。
文摘In this paper,we investigate the blow-up phenomenon for a class of logarithmic viscoelastic equations with delay and nonlocal terms under acoustic boundary conditions.Using the energy method,we prove that nontrivial solutions with negative initial energy will blow up in finite time,and provide an upper bound estimate for the blow-up time.Additionally,we also derive a lower bound estimate for the blow-up time.
基金supported by the Cooperative Research Project between China Coal Energy Research Institute Co.,Ltd. and Xidian University (No.N-KY-HX-1101-202302-00725)the Key Research and Development Program of Shaanxi Province (No.2017ZDCXL-GY-06-02)。
文摘A non-orthogonal multiple access(NOMA) power allocation scheme on the basis of the sparrow search algorithm(SSA) is proposed in this work. Specifically, the logarithmic utility function is utilized to address the potential fairness issue that may arise from the maximum sum-rate based objective function and the optical power constraints are set considering the non-negativity of the transmit signal, the requirement of the human eyes safety and all users' quality of service(Qo S). Then, the SSA is utilized to solve this optimization problem. Moreover, to demonstrate the superiority of the proposed strategy, it is compared with the fixed power allocation(FPA) and the gain ratio power allocation(GRPA) schemes. Results show that regardless of the number of users considered, the sum-rate achieved by SSA consistently outperforms that of FPA and GRPA schemes. Specifically, compared to FPA and GRPA schemes, the sum-rate obtained by SSA is increased by 40.45% and 53.44% when the number of users is 7, respectively. The proposed SSA also has better performance in terms of user fairness. This work will benefit the design and development of the NOMA-visible light communication(VLC) systems.
文摘We consider large-time behaviors of weak solutions to the evolutionary p-Laplacian with logarithmic source of time-dependent coefficient.We find that the weak solutions may neither decay nor blow up,provided that the initial data u(·,t_(0))is on the Nehari manifold N:={v∈W_(0)^(1,p)(Ω):I(v,to)=0,||▽v||P^(P)≠0}.This is quite different from the known results that the weak solutions may blow up as,u(·,to)∈N^(+):={v∈W_(0)^(1,p)(Ω):I(v,t_(0))<0}and weak solutions may decay as u(·,t_(0))∈N^(+):={v∈W_(0)^(1,p)(Ω):I(v,t_(0))>0}.
基金The National Natural Science Foundation of China(No60402019)the Science Research Program of Education Bureau of Hubei Province (NoQ200629001)
文摘In order to improve the security of the signature scheme, a digital signature based on two hard-solved problems is proposed. The discrete logarithm problem and the factoring problem are two well known hard- solved mathematical problems. Combining the E1Gamal scheme based on the discrete logarithm problem and the OSS scheme based on the factoring problem, a digital signature scheme based on these two cryptographic assumptions is proposed. The security of the proposed scheme is based on the difficulties of simultaneously solving the factoring problem and the discrete logarithm problem. So the signature scheme will be still secure under the situation that any one of the two hard-problems is solved. Compared with previous schemes, the proposed scheme is more efficient in terms of space storage, signature length and computation complexities.
文摘Circuit design of 32 bit logarithmic skip adder (LSA) is introduced to implement high performance,low power addition.ELM carry lookahead adder is included into groups of carry skip adder and the hybrid structure costs 30% less hardware than ELM.At circuit level,a carry incorporating structure to include the primary carry input in carry chain and an 'and xor' structure to implement final sum logic in 32 bit LSA are designed for better optimization.For 5V,1μm process,32 bit LSA has a critical delay of 5 9ns and costs an area of 0 62mm 2,power consumption of 23mW at 100MHz.For 2 5V,0 25μm process,critical delay of 0 8ns,power dissipation of 5 2mW at 100MHz is simulated.
基金supported by NSFC (11201152)supported by NSFC(11371148)+4 种基金STCSM(13dz2260400)FDPHEC(20120076120001)Fundamental Research Funds for the central Universities,scut(2012zz0073)Fundamental Research Funds for the Central Universities SCUT(D2154240)Guangdong Natural Science Foundation(2014A030313230)
文摘In the paper, we consider Moran-type sets E;given by sequences {a;};and{n;};. we prove that E;may be decompose into the disjoint union of level sets. Moreover,we define three type of equivalence between two dimension functions associated to two Morantype sets, respectively, and we classify Moran-type sets by these equivalent relations.
基金the Scientific Research fund of Pingyuan University(2005006)
文摘The paper brings an important integral inequality, which includes the famous Polya-Szego inequality and the logarithmical-arithmetic mean inequality as special cases.
