This paper studies online scheduling of jobs with kind release times on a single machine. Here "kind release time" means that in online setting, no jobs can be released when the machine is busy. Each job J h...This paper studies online scheduling of jobs with kind release times on a single machine. Here "kind release time" means that in online setting, no jobs can be released when the machine is busy. Each job J has a kind release time r(J) ≥ 0, a processing time p(J) > 0 and a deadline d(J) > 0. The goal is to determine a schedule which maximizes total processing time( p(J)E(J)) or total number( E(J)) of the accepted jobs. For the first objective function p(J)E(J), we first present a lower bound 2(1/2), and then provide an online algorithm LEJ with a competitive ratio of 3. This is the first deterministic algorithm for the problem with a constant competitive ratio. When p(J) ∈ {1, k}, k > 1 is a real number, we first present a lower bound min{(1 + k)/k, 2 k/(1 + k)}, and then we show that LEJ has a competitive ratio of1 + k/k. In particular, when all the k length jobs have tight deadlines, we first present a lower bound max{4/(2 + k), 1}(for p(J)E(J)) and 4/3(for E(J)). Then we prove that LEJ is k/k-competitive for p(J)E(J) and we provide an online algorithm H with a competitive ratio of 2 k/( k + 1) for the second objective function E(J).展开更多
By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequ...By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.展开更多
This article is contributed to the Cauchy problem {δu/δt=△u＋K（｜x｜）u^p in R^n×（0,T）, u（x,0）=φ（x） in R^n;with initial function φ≡/0. The stability of positive radial steady state, which are positiv...This article is contributed to the Cauchy problem {δu/δt=△u＋K（｜x｜）u^p in R^n×（0,T）, u（x,0）=φ（x） in R^n;with initial function φ≡/0. The stability of positive radial steady state, which are positive solutions of △u ＋ K（｜x｜）u^p =0, is obtained when p is critical for general K（｜x｜）.展开更多
In this note, we study the existence of an initial trace of nonnegative solutions for the following problem ut-div（｜▽um｜p-2^▽um）＋uq = 0 in QT = Ω × （0, T ）. We prove that the initial trace is an outer r...In this note, we study the existence of an initial trace of nonnegative solutions for the following problem ut-div（｜▽um｜p-2^▽um）＋uq = 0 in QT = Ω × （0, T ）. We prove that the initial trace is an outer regular Borel measure, which may not be locally bounded for some values of parameters p, q, and m. We also study the corresponding Cauchy problems with a given generalized Borel measure as initial data.展开更多
The dissipative quantum Zakharov equations are mainly studied. The ex- istence and uniqueness of the solutions for the dissipative quantum Zakharov equations are proved by the standard Galerkin approximation method on...The dissipative quantum Zakharov equations are mainly studied. The ex- istence and uniqueness of the solutions for the dissipative quantum Zakharov equations are proved by the standard Galerkin approximation method on the basis of a priori esti- mate. Meanwhile, the asymptotic behavior of solutions and the global attractor which is constructed in the energy space equipped with the weak topology are also investigated.展开更多
Using the first-principles methods, we study the formation energetics properties of intrinsic defects, and the charge doping properties of extrinsic defects in transparent conducting oxides CuCrO2. Intrinsic defects, ...Using the first-principles methods, we study the formation energetics properties of intrinsic defects, and the charge doping properties of extrinsic defects in transparent conducting oxides CuCrO2. Intrinsic defects, some typical acceptortype, and donor-type extrinsic defects in their relevant charge state are considered. By systematically calculating the formation energies and transition energy, the results of calculation show that, Vcu, Oi, and Ocu are the relevant intrinsic defects in CuCrO2; among these intrinsic defects, Vcu is the most efficient acceptor in CuCrO2. It is found that all the donor-type extrinsic defects have difficulty in inducing n-conductivity in CuCrO2 because of their deep transition energy level. For all the acceptor-type extrinsic defects, substituting Mg for Cr is the most prominent doping aceeptor with relative shallow transition energy levels in CuCrO2. Our calculation results are expected to be a guide for preparing promising n-type and p-type materials in CuCrO2.展开更多
A warehouse layout problem where the warehouse has more than one level and both the distance from the cell to the receive/exit bay and demand of item types are fuzzy variables is proposed. The problem is to find a lay...A warehouse layout problem where the warehouse has more than one level and both the distance from the cell to the receive/exit bay and demand of item types are fuzzy variables is proposed. The problem is to find a layout with the minimum transportation cost subject to adjacency and other constraints. A fuzzy expected value model is given and an ant colony system is designed to solve the problem. Computational results indicate the efficiency and effectiveness of the method.展开更多
In order to design birefringent holey fiber with beat-length independent of wavelength, an asymmetric structure is introduced to reduce its wavelength-sensitivity. The influence of structural parameters on the modal b...In order to design birefringent holey fiber with beat-length independent of wavelength, an asymmetric structure is introduced to reduce its wavelength-sensitivity. The influence of structural parameters on the modal birefringence is calculated and analyzed. After optimizing the parameters, a flat dispersion curve of beat-length is obtained. The beat-length changes from 89.8 mm to 91.0 mm in wavelength range from 1.1 μm, to 1.7μm, and its relative variation is 1.38%. If this fiber is made into zero-order quarter wave plate, the phase delay can be easily controlled in （90±1）°.展开更多
In the paper, the optimal self-scaling strategy to the modified symmetric rank one (HSR1) update, which satisfies the modified quasi-Newton equation, is derived to improve the condition number of the updates. The scal...In the paper, the optimal self-scaling strategy to the modified symmetric rank one (HSR1) update, which satisfies the modified quasi-Newton equation, is derived to improve the condition number of the updates. The scaling factors are derived from minimizing the estimate of upper bounds on the condition number of the updating matrix. Theoretical analysis, and numerical experiments and comparisons show that introducing the optimal scaling factor into the modified symmetric rank one update preserves the positive definiteness of updates, and greatly improves the stability and numerical performance of the modified symmetric rank one algorithm.展开更多
Exact solutions to the shallow wave equation are studied based on the idea of the extended homoclinic test and bilinear method. Some explicit solutions, such as the one soliton solution, the doubly-periodic wave solut...Exact solutions to the shallow wave equation are studied based on the idea of the extended homoclinic test and bilinear method. Some explicit solutions, such as the one soliton solution, the doubly-periodic wave solution and the periodic solitary wave solutions, are obtained. In addition, the properties of the solutions are investigated.展开更多
基金Supported by the National Natural Science Foundation of China(11501279,11501171,11671188,and11401604)the Young Backbone Teachers of Luoyang Normal University(2018XJGGJS-10)Henan Colleges(2015GGJS-193)
文摘This paper studies online scheduling of jobs with kind release times on a single machine. Here "kind release time" means that in online setting, no jobs can be released when the machine is busy. Each job J has a kind release time r(J) ≥ 0, a processing time p(J) > 0 and a deadline d(J) > 0. The goal is to determine a schedule which maximizes total processing time( p(J)E(J)) or total number( E(J)) of the accepted jobs. For the first objective function p(J)E(J), we first present a lower bound 2(1/2), and then provide an online algorithm LEJ with a competitive ratio of 3. This is the first deterministic algorithm for the problem with a constant competitive ratio. When p(J) ∈ {1, k}, k > 1 is a real number, we first present a lower bound min{(1 + k)/k, 2 k/(1 + k)}, and then we show that LEJ has a competitive ratio of1 + k/k. In particular, when all the k length jobs have tight deadlines, we first present a lower bound max{4/(2 + k), 1}(for p(J)E(J)) and 4/3(for E(J)). Then we prove that LEJ is k/k-competitive for p(J)E(J) and we provide an online algorithm H with a competitive ratio of 2 k/( k + 1) for the second objective function E(J).
文摘By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.
基金the National Natural Science Foundation of China(10471052,10631030)the PHD specialized grant of Ministry of Education of China(20060511001)
文摘This article is contributed to the Cauchy problem {δu/δt=△u＋K（｜x｜）u^p in R^n×（0,T）, u（x,0）=φ（x） in R^n;with initial function φ≡/0. The stability of positive radial steady state, which are positive solutions of △u ＋ K（｜x｜）u^p =0, is obtained when p is critical for general K（｜x｜）.
文摘In this note, we study the existence of an initial trace of nonnegative solutions for the following problem ut-div（｜▽um｜p-2^▽um）＋uq = 0 in QT = Ω × （0, T ）. We prove that the initial trace is an outer regular Borel measure, which may not be locally bounded for some values of parameters p, q, and m. We also study the corresponding Cauchy problems with a given generalized Borel measure as initial data.
基金supported by the National Natural Science Foundation of China (No. 11061003)
文摘The dissipative quantum Zakharov equations are mainly studied. The ex- istence and uniqueness of the solutions for the dissipative quantum Zakharov equations are proved by the standard Galerkin approximation method on the basis of a priori esti- mate. Meanwhile, the asymptotic behavior of solutions and the global attractor which is constructed in the energy space equipped with the weak topology are also investigated.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11147195)the Science Fund from the Guangxi Experiment Centre of Science and Technology (Grant No. LGZXKF201204)the Science Plan Projects of the Education Department of Guangxi Zhuang Autonomous Region (Grant No. 200103YB102)
文摘Using the first-principles methods, we study the formation energetics properties of intrinsic defects, and the charge doping properties of extrinsic defects in transparent conducting oxides CuCrO2. Intrinsic defects, some typical acceptortype, and donor-type extrinsic defects in their relevant charge state are considered. By systematically calculating the formation energies and transition energy, the results of calculation show that, Vcu, Oi, and Ocu are the relevant intrinsic defects in CuCrO2; among these intrinsic defects, Vcu is the most efficient acceptor in CuCrO2. It is found that all the donor-type extrinsic defects have difficulty in inducing n-conductivity in CuCrO2 because of their deep transition energy level. For all the acceptor-type extrinsic defects, substituting Mg for Cr is the most prominent doping aceeptor with relative shallow transition energy levels in CuCrO2. Our calculation results are expected to be a guide for preparing promising n-type and p-type materials in CuCrO2.
基金This research is supported by the National Natural Science Foundation of China under Grant No. 60274007, and the Post Doctoral Foundation of China and the Excellent Young Program of the Education Department of Hunan Province under Grant No. 04B068, and the NSERC-Canada.
基金the National Natural Science Foundation of China (70471063 ,70171036)
文摘A warehouse layout problem where the warehouse has more than one level and both the distance from the cell to the receive/exit bay and demand of item types are fuzzy variables is proposed. The problem is to find a layout with the minimum transportation cost subject to adjacency and other constraints. A fuzzy expected value model is given and an ant colony system is designed to solve the problem. Computational results indicate the efficiency and effectiveness of the method.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.60777031, 11074164)the Shanghai Leading Academic Discipline Project (Grant No.S30108)
文摘In order to design birefringent holey fiber with beat-length independent of wavelength, an asymmetric structure is introduced to reduce its wavelength-sensitivity. The influence of structural parameters on the modal birefringence is calculated and analyzed. After optimizing the parameters, a flat dispersion curve of beat-length is obtained. The beat-length changes from 89.8 mm to 91.0 mm in wavelength range from 1.1 μm, to 1.7μm, and its relative variation is 1.38%. If this fiber is made into zero-order quarter wave plate, the phase delay can be easily controlled in （90±1）°.
文摘In the paper, the optimal self-scaling strategy to the modified symmetric rank one (HSR1) update, which satisfies the modified quasi-Newton equation, is derived to improve the condition number of the updates. The scaling factors are derived from minimizing the estimate of upper bounds on the condition number of the updating matrix. Theoretical analysis, and numerical experiments and comparisons show that introducing the optimal scaling factor into the modified symmetric rank one update preserves the positive definiteness of updates, and greatly improves the stability and numerical performance of the modified symmetric rank one algorithm.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10661002 and 10701076, the SRF for ROCS, the Guangxi Natural Science Foundation under Grant No 0832065, and the Cuangxi Excellent Talents Fund.
文摘Exact solutions to the shallow wave equation are studied based on the idea of the extended homoclinic test and bilinear method. Some explicit solutions, such as the one soliton solution, the doubly-periodic wave solution and the periodic solitary wave solutions, are obtained. In addition, the properties of the solutions are investigated.
