The viscoelastic behavior of isotactic polypropylene with ultra-high molecular weight(UHPPH) and broad molecular weight distribution(MWD), produced in the presence of Ziegler-Natta catalyst, was investigated by means ...The viscoelastic behavior of isotactic polypropylene with ultra-high molecular weight(UHPPH) and broad molecular weight distribution(MWD), produced in the presence of Ziegler-Natta catalyst, was investigated by means of oscillatory rheometry at 180 and 200 ℃, whose loss modulus(G″) plots at 180 and 200 ℃ versus the natural logarithm of angular frequency(ω) present a pronounced maximum at 34.35 and 69.21 rad/s, respectively, and do not show a maximum peak at 0.01-100 rad/s for Ziegler-Natta catalyzing ethylene-propylene random copolymerization(PPR) with a conventional molecular weight and broad MWD. The fact indicates that the high molecular weight is responsible for a maximum peak of G″(ω) vs. lnω curves for UHPPH. This makes it possible to determine the plateau modulus(G 0_N) of UHPPH from a certain experimental temperature G″(ω) curve directly. For UHPPH, the G 0_N determined to be 4.28×10 5 and 3.62×10 5 Pa at 180 and 200 ℃, respectively, decreases with the increase of temperature and is independent of the molecular weight, which directly confirms reputation theoretical prediction that the G 0_N has no relation to the molecular weight.展开更多
This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequaliti...This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.展开更多
This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators o...This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.展开更多
For the step-weight function , we prove that the Holder spaces ∧a,p on the interval [-1,1], defined in terms of moduli of smoothness with the step-weight function ,are linearly isomorphic to some sequence spaces, an...For the step-weight function , we prove that the Holder spaces ∧a,p on the interval [-1,1], defined in terms of moduli of smoothness with the step-weight function ,are linearly isomorphic to some sequence spaces, and the isomorphism is given by the cofficients of function with respect to a system of orthonormal splines with knots uniformly distributed according to the measure with density . In case ∧a,p is contained in the space of continuous functions, we give a discrete characterization of this space, using only values of function at the appropriate knots. Application of these results to characterize the order of polynomial approximation is presented.展开更多
Let T1 be a singular integral with non-smooth kernel or ±I, let T2 and T4 be the linear operators and let T3 = ± I. Denote the Toeplitz type operator by Tb = T1M^b Ia T2 ＋ T3IaMbT4,where M^bf = bf, and Ib i...Let T1 be a singular integral with non-smooth kernel or ±I, let T2 and T4 be the linear operators and let T3 = ± I. Denote the Toeplitz type operator by Tb = T1M^b Ia T2 ＋ T3IaMbT4,where M^bf = bf, and Ib is the fractional integral operator. In this paper, we investigate the boundedness of the operator Tb on the weighted Morrey space when b belongs to the weighted BMO space.展开更多
In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent im...In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point equation, then introduces a smoothing function to obtain its approximation solutions. The convergence analysis of the algorithm was given, and the efficiency of the algorithms was verified by numerical experiments.展开更多
文摘The viscoelastic behavior of isotactic polypropylene with ultra-high molecular weight(UHPPH) and broad molecular weight distribution(MWD), produced in the presence of Ziegler-Natta catalyst, was investigated by means of oscillatory rheometry at 180 and 200 ℃, whose loss modulus(G″) plots at 180 and 200 ℃ versus the natural logarithm of angular frequency(ω) present a pronounced maximum at 34.35 and 69.21 rad/s, respectively, and do not show a maximum peak at 0.01-100 rad/s for Ziegler-Natta catalyzing ethylene-propylene random copolymerization(PPR) with a conventional molecular weight and broad MWD. The fact indicates that the high molecular weight is responsible for a maximum peak of G″(ω) vs. lnω curves for UHPPH. This makes it possible to determine the plateau modulus(G 0_N) of UHPPH from a certain experimental temperature G″(ω) curve directly. For UHPPH, the G 0_N determined to be 4.28×10 5 and 3.62×10 5 Pa at 180 and 200 ℃, respectively, decreases with the increase of temperature and is independent of the molecular weight, which directly confirms reputation theoretical prediction that the G 0_N has no relation to the molecular weight.
基金Supported by the National Natural Science Foundation of China (10771054, 10771221, 11071200)the Youth Foundation of Wuyi University (No. xq0930)
文摘This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.
基金Supported by the National Natural Science Foundation of China (10771054,11071200)the NFS of Fujian Province of China (No. 2010J01013)
文摘This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.
文摘For the step-weight function , we prove that the Holder spaces ∧a,p on the interval [-1,1], defined in terms of moduli of smoothness with the step-weight function ,are linearly isomorphic to some sequence spaces, and the isomorphism is given by the cofficients of function with respect to a system of orthonormal splines with knots uniformly distributed according to the measure with density . In case ∧a,p is contained in the space of continuous functions, we give a discrete characterization of this space, using only values of function at the appropriate knots. Application of these results to characterize the order of polynomial approximation is presented.
文摘Let T1 be a singular integral with non-smooth kernel or ±I, let T2 and T4 be the linear operators and let T3 = ± I. Denote the Toeplitz type operator by Tb = T1M^b Ia T2 ＋ T3IaMbT4,where M^bf = bf, and Ib is the fractional integral operator. In this paper, we investigate the boundedness of the operator Tb on the weighted Morrey space when b belongs to the weighted BMO space.
文摘In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point equation, then introduces a smoothing function to obtain its approximation solutions. The convergence analysis of the algorithm was given, and the efficiency of the algorithms was verified by numerical experiments.
