The gradient model of two-dimensional defectless medium is formulated. A graphene sheet is examined as an example of such two-dimensional medium. The problem statement of a graphene sheet deforming in its plane and th...The gradient model of two-dimensional defectless medium is formulated. A graphene sheet is examined as an example of such two-dimensional medium. The problem statement of a graphene sheet deforming in its plane and the bending problem are examined. It is ascertained that the statement of the first problem is equivalent to the flat problem statement of Toupin gradient theory. The statement of the bending problem is equivalent to the plate bending theory of Timoshenko with certain reserves. The characteristic feature of both statements is the fact that the mechanical properties of the sheet of graphene are not defined by “volumetric” moduli but by adhesive ones which have different physical dimension that coincides with the dimension of the corresponding stiffness of classical and nonclassical plates.展开更多
The purpose of this paper is to introduce an unknown method for finding a real possible x value of any degree polynomial equation and to show how this can be applied to make computers which are at least x1000 （one th...The purpose of this paper is to introduce an unknown method for finding a real possible x value of any degree polynomial equation and to show how this can be applied to make computers which are at least x1000 （one thousand times） faster than today＇s existing highest speed computers. Since one of the Milennium Prize Problems offered by Claymath asks about whether P （Deterministic Polynomial） is equal to NP （Non-Deterministic Polynomial） （what that means informally is that whether we can design a computer which can quickly solve a certain complicated problem can also verify the solution quickly （and vice versa）. Fortunately, the answer to P vs. NP problem based on my findings in certain algebraic algorythms is yes although there have been many people who claimed the answer is no. What that means is that humans can make machines that work very fast and close to human intelligence in the identification of, say, certain proteins and amino acids, in case my theory is proven to be a fact. This paper is therefore an initial stage of planting the first seeds of the process, in terms of describing how exactly this can happen, theoretically of course, since everything in Science begins with a theory based on the outcome of a hypothesis.展开更多
An optimization method for sound absorption of gradient(multi-layered) sintered metal fiber felts is presented. The theoretical model based on dynamic flow resistivity is selected to calculate the sound absorption coe...An optimization method for sound absorption of gradient(multi-layered) sintered metal fiber felts is presented. The theoretical model based on dynamic flow resistivity is selected to calculate the sound absorption coefficient of the sintered metal fiber felts since it only requires three key morphological parameters: fiber diameter, porosity and layer thickness. The model predictions agree well with experimental measurements. Objective functions and constraint conditions are then set up to optimize separately the distribution of porosity, fiber diameter, and simultaneous porosity and fiber diameter in the metal fiber. The optimization problem for either a sole frequency or a pre-specified frequency range is solved using a genetic algorithm method. Acoustic performance comparison between optimized and non-optimized metal fibers is presented to confirm the effectiveness of the optimization method. Gradient sintered metal fiber felts hold great potential for noise control applications particularly when stringent restriction is placed on the total volume and/or weight of sound absorbing material allowed to use.展开更多
In this paper, the authors consider an on-line scheduling problem of rn （m≥ 3） identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance tim...In this paper, the authors consider an on-line scheduling problem of rn （m≥ 3） identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance time interval is larger than the largest processing time of jobs, the authors prove that any on-line algorithm has not a constant competitive ratio. For the case that the length of maintenance time interval is less than or equal to the largest processing time of jobs, the authors prove a lower bound of 3 on the competitive ratio. The authors give an on-line algorithm with competitive 1 ratio 4 - 1/m. In particular, for the case of m = 3, the authors prove the competitive ratio of the on-line algorithm is 10/3.展开更多
文摘The gradient model of two-dimensional defectless medium is formulated. A graphene sheet is examined as an example of such two-dimensional medium. The problem statement of a graphene sheet deforming in its plane and the bending problem are examined. It is ascertained that the statement of the first problem is equivalent to the flat problem statement of Toupin gradient theory. The statement of the bending problem is equivalent to the plate bending theory of Timoshenko with certain reserves. The characteristic feature of both statements is the fact that the mechanical properties of the sheet of graphene are not defined by “volumetric” moduli but by adhesive ones which have different physical dimension that coincides with the dimension of the corresponding stiffness of classical and nonclassical plates.
文摘The purpose of this paper is to introduce an unknown method for finding a real possible x value of any degree polynomial equation and to show how this can be applied to make computers which are at least x1000 （one thousand times） faster than today＇s existing highest speed computers. Since one of the Milennium Prize Problems offered by Claymath asks about whether P （Deterministic Polynomial） is equal to NP （Non-Deterministic Polynomial） （what that means informally is that whether we can design a computer which can quickly solve a certain complicated problem can also verify the solution quickly （and vice versa）. Fortunately, the answer to P vs. NP problem based on my findings in certain algebraic algorythms is yes although there have been many people who claimed the answer is no. What that means is that humans can make machines that work very fast and close to human intelligence in the identification of, say, certain proteins and amino acids, in case my theory is proven to be a fact. This paper is therefore an initial stage of planting the first seeds of the process, in terms of describing how exactly this can happen, theoretically of course, since everything in Science begins with a theory based on the outcome of a hypothesis.
基金supported by the National Natural Science Foundation of China(Grant No.51528501)the Fundamental Research Funds for Central Universities(Grant No.2014qngz12)Xin is supported by China Scholarship Council as a visiting scholar to Harvard University
文摘An optimization method for sound absorption of gradient(multi-layered) sintered metal fiber felts is presented. The theoretical model based on dynamic flow resistivity is selected to calculate the sound absorption coefficient of the sintered metal fiber felts since it only requires three key morphological parameters: fiber diameter, porosity and layer thickness. The model predictions agree well with experimental measurements. Objective functions and constraint conditions are then set up to optimize separately the distribution of porosity, fiber diameter, and simultaneous porosity and fiber diameter in the metal fiber. The optimization problem for either a sole frequency or a pre-specified frequency range is solved using a genetic algorithm method. Acoustic performance comparison between optimized and non-optimized metal fibers is presented to confirm the effectiveness of the optimization method. Gradient sintered metal fiber felts hold great potential for noise control applications particularly when stringent restriction is placed on the total volume and/or weight of sound absorbing material allowed to use.
基金supported by the National Natural Science Foundation of China under Grant Nos.11271338,11171313,61070229,10901144,11001117supported by the Ph.D.Programs Foundation of Ministry ofEducation of China under Grant No.20111401110005the Henan Province Natural Science Foundation under Grant No.112300410047
文摘In this paper, the authors consider an on-line scheduling problem of rn （m≥ 3） identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance time interval is larger than the largest processing time of jobs, the authors prove that any on-line algorithm has not a constant competitive ratio. For the case that the length of maintenance time interval is less than or equal to the largest processing time of jobs, the authors prove a lower bound of 3 on the competitive ratio. The authors give an on-line algorithm with competitive 1 ratio 4 - 1/m. In particular, for the case of m = 3, the authors prove the competitive ratio of the on-line algorithm is 10/3.
