In this paper, we study a new class of quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having a complex e...In this paper, we study a new class of quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having a complex ellipse x^2 ＋ y^2 ＋ 1 = 0 as invariant algebraic curve. We provide all the different topological phase portraits that this class exhibits in the Poincare disc.展开更多
The present work deals with the possibility of propagation of torsional surface wave in an inhomogeneous crustal layer over an inhomogeneous half space. The layer has inhomogeneity which varies linearly with depth whe...The present work deals with the possibility of propagation of torsional surface wave in an inhomogeneous crustal layer over an inhomogeneous half space. The layer has inhomogeneity which varies linearly with depth whereas the inhomogeneous half space exhibits inhomogeneity of three types, namely, exponential, quadratic, and hyperbolic discussed separately. The dispersion equation is deduced for each case in a closed form. For a layer over a homogeneous half space, the dispersion equation agrees with the equa- tion of the classical case. It is observed that the inhomogeneity factor due to linear variation in density in the inhomogeneous crustal layer decreases as the phase velocity increases, while the inhomogeneity factor in rigidity has the reverse effect on the phase velocity.展开更多
In this paper,a new method is presented for designing M-band biorthogonal symmetric wavelets.The design problem of biorthogonal linear-phase scaling filters and wavelet filters as a quadratic programming problem with ...In this paper,a new method is presented for designing M-band biorthogonal symmetric wavelets.The design problem of biorthogonal linear-phase scaling filters and wavelet filters as a quadratic programming problem with the linear constraints is formulated.The closed-form solution is given and a design example is presented.展开更多
On the basis of the uniform design method, six kinds of martensitic hot work die steels were designed. The phase transformation temperatures including Ac1 , Ac3 , and Ms were measured by DIL805A quenching dilatometer....On the basis of the uniform design method, six kinds of martensitic hot work die steels were designed. The phase transformation temperatures including Ac1 , Ac3 , and Ms were measured by DIL805A quenching dilatometer. The influences of the main elements on phase transformation temperatures were analyzed by quadratic stepwise regression analysis, and three corresponding equations were obtained. These equations, in which the interactions of the elements were considered, showed more effectiveness than the traditional ones. In addition, the thermal expansion coefficients of these steels in annealed state and quenched state were also obtained during the tests. The influences of chemical composition and temperature on the thermal expansion coefficient were analyzed; the equations obtained were verified by using several kinds of steels. The predicted values were in accordance with the results of the experiments.展开更多
基金partially supported by a MINECO/FEDER grant MTM2013-40998-Pan AGAUR grant number 2014 SGR568+2 种基金the grants FP7-PEOPLE-2012-IRSES 318999 and 316338the MINECO/FEDER grant UNAB13-4E-1604partially supported by FCT/Portugal through UID/MAT/04459/2013
文摘In this paper, we study a new class of quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having a complex ellipse x^2 ＋ y^2 ＋ 1 = 0 as invariant algebraic curve. We provide all the different topological phase portraits that this class exhibits in the Poincare disc.
文摘The present work deals with the possibility of propagation of torsional surface wave in an inhomogeneous crustal layer over an inhomogeneous half space. The layer has inhomogeneity which varies linearly with depth whereas the inhomogeneous half space exhibits inhomogeneity of three types, namely, exponential, quadratic, and hyperbolic discussed separately. The dispersion equation is deduced for each case in a closed form. For a layer over a homogeneous half space, the dispersion equation agrees with the equa- tion of the classical case. It is observed that the inhomogeneity factor due to linear variation in density in the inhomogeneous crustal layer decreases as the phase velocity increases, while the inhomogeneity factor in rigidity has the reverse effect on the phase velocity.
文摘In this paper,a new method is presented for designing M-band biorthogonal symmetric wavelets.The design problem of biorthogonal linear-phase scaling filters and wavelet filters as a quadratic programming problem with the linear constraints is formulated.The closed-form solution is given and a design example is presented.
基金Item Sponsored by Shanghai Leading Academic Discipline Project(T0101)Science and Technology Commission of Shanghai Municipality(065211028)
文摘On the basis of the uniform design method, six kinds of martensitic hot work die steels were designed. The phase transformation temperatures including Ac1 , Ac3 , and Ms were measured by DIL805A quenching dilatometer. The influences of the main elements on phase transformation temperatures were analyzed by quadratic stepwise regression analysis, and three corresponding equations were obtained. These equations, in which the interactions of the elements were considered, showed more effectiveness than the traditional ones. In addition, the thermal expansion coefficients of these steels in annealed state and quenched state were also obtained during the tests. The influences of chemical composition and temperature on the thermal expansion coefficient were analyzed; the equations obtained were verified by using several kinds of steels. The predicted values were in accordance with the results of the experiments.
