In this paper, a class of slightly perturbed equations of the form F(x)= ξ -x+αΦ(x) will be treated graphically and symbolically, where Φ(x) is an analytic function of x. For graphical developments, we set up a si...In this paper, a class of slightly perturbed equations of the form F(x)= ξ -x+αΦ(x) will be treated graphically and symbolically, where Φ(x) is an analytic function of x. For graphical developments, we set up a simple graphical method for the real roots of the equation F(x)=0 illustrated by four transcendental equations. In fact, the graphical solution usually provides excellent initial conditions for the iterative solution of the equation. A property avoiding the critical situations between divergent to very slow convergent solutions may exist in the iterative methods in which no good initial condition close to the root is available. For the analytical developments, literal analytical solutions are obtained for the most celebrated slightly perturbed equation which is Kepler’s equation of elliptic orbit. Moreover, the effect of the orbital eccentricity on the rate of convergence of the series is illustrated graphically.展开更多
This series of hanging charts is easy to read and contains the common symbols used in daily life.The complete series of hanging charts includes traffic,safety and environmental protection symbols。
A national flag is the representative symbol of a country.It is displayed on many occasions in society.A code comprised of three letters is delegated to each countryand is often used in
GPU (Graphics Processing Unit) is used in various areas. Therefore, the demand for the verification of GPU programs is increasing. In this paper, we suggest the method to detect bank conflict by using symbolic executi...GPU (Graphics Processing Unit) is used in various areas. Therefore, the demand for the verification of GPU programs is increasing. In this paper, we suggest the method to detect bank conflict by using symbolic execution. Bank conflict is one of the bugs happening in GPU and it leads the performance of programs lower. Bank conflict happens when some processing units in GPU access the same shared memory. Symbolic execution is the method to analysis programs with symbolic values. By using it, we can detect bank conflict on GPU programs which use many threads. We implement a prototype of the detector for bank conflict and evaluate it with some GPU programs. The result states that we can detect bank conflict on the programs with no loop regardless of the number of threads.展开更多
文摘In this paper, a class of slightly perturbed equations of the form F(x)= ξ -x+αΦ(x) will be treated graphically and symbolically, where Φ(x) is an analytic function of x. For graphical developments, we set up a simple graphical method for the real roots of the equation F(x)=0 illustrated by four transcendental equations. In fact, the graphical solution usually provides excellent initial conditions for the iterative solution of the equation. A property avoiding the critical situations between divergent to very slow convergent solutions may exist in the iterative methods in which no good initial condition close to the root is available. For the analytical developments, literal analytical solutions are obtained for the most celebrated slightly perturbed equation which is Kepler’s equation of elliptic orbit. Moreover, the effect of the orbital eccentricity on the rate of convergence of the series is illustrated graphically.
文摘This series of hanging charts is easy to read and contains the common symbols used in daily life.The complete series of hanging charts includes traffic,safety and environmental protection symbols。
文摘A national flag is the representative symbol of a country.It is displayed on many occasions in society.A code comprised of three letters is delegated to each countryand is often used in
文摘GPU (Graphics Processing Unit) is used in various areas. Therefore, the demand for the verification of GPU programs is increasing. In this paper, we suggest the method to detect bank conflict by using symbolic execution. Bank conflict is one of the bugs happening in GPU and it leads the performance of programs lower. Bank conflict happens when some processing units in GPU access the same shared memory. Symbolic execution is the method to analysis programs with symbolic values. By using it, we can detect bank conflict on GPU programs which use many threads. We implement a prototype of the detector for bank conflict and evaluate it with some GPU programs. The result states that we can detect bank conflict on the programs with no loop regardless of the number of threads.
