In the letter we give new symmetries for the isospectral and non-isospectral Ablowitz-Ladik hierarchies by means of the zero curvature representations of evolution equations related to the Ablowitz-Ladik spectral problem. Lie algebras constructed by symmetries are further obtained. We also discuss the relations between the recursion operator and isospectral and non-isospectral flows. Our method can be generalized to other systems to construct symmetries for non-isospectral equations. IntroductionIt is well-known that infinitely many symmetries and their Lie algebra serve as one of mathematical structures of integrability for evolution equations [1]. In general, a Lax integrable isospectral evolution equation can have two sets of symmetries, isospectral and non-isospectral symmetries, or called K-and τ -symmetries, respectively. One efficient way to construct τ -symmetries was proposed by Fuchssteiner[2] by using the master symmetry. This method was later developed to many continuous (1+1)-dimensional Lax integrable systems [3,4], (1+2)-dimensional systems [5] and further to some differential-difference cases [6,7]. This letter will discuss K-and τ -symmetries for the isospectral Ablowitz-Ladik(AL) hierarchy, which is a well-known discrete hierarchy[8]- [11]. We will also construct new infinitely many symmetries for the non-isospectral AL hierarchy. The AL spectral problem can have two sets of isospectral hierarchies [12] which respectively correspond to positive and negative powers of the spectral parameter λ in the time-evolution part in Lax pair. The same results hold for the nonisospectral hierarchies as well, as shown in [7], where the algebraic relations between isospectral and non-isospectral flows related to positive powers of λ and the algebraic relations between isospectral and non-isospectral flows related to negative powers of λ were discussed, respectively.Our method to construct K-and τ -symmetries for the isospectral AL hierarchy is essentially the same as used in Ref. [7,6], and as well as a direct generalization of its continuous version [4]. Recently, we uniformed the two sets of isospectral flows (positive order and negative order) to one hierarchy with a uniform recursion operator [13]. This motivates us to do the same thing for the two sets of non-isospectral flows. Then we investigate the algebraic relations of the

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The direct air-cooling steam turbines have been operated more and more in the north of China. The backpressure of a turbine is affected easily with weather and varies very often in a short time. The variation of backpressure in a larger range from about 10 to 60 kPa causes many problems in design and operation of the turbine. To study the properties of the wet steam flow in the low pressure direct air-cooling steam turbine, an optical-pneumatic probe was developed based on the multi-wavelength light extinction and four-hole wedge probe. Measurements with this probe in a 300 MW direct air-cooling turbine were carried out. The measured local wetness, total wetness of exhaust steam, size distribution of fine droplets, and their profiles along the blade height are presented. The measured cylinder efficiency and total wetness agree well with the results obtained by the thermal performance tests.

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