Application of Acoustic Technique to Surveying a Buried Fault in Tianjin

We carried out surveying on the shallow structure and faulted-stratum of the Haihe fault in Tianjin using acoustic surveying methods such as the single-channel seismic technique. The result shows that the method can obtain satisfactory results in wide and deep river courses. It also shows that in the Tanggu area of Tianjin, the upper fault point of Haihe fault is about 30m beneath the river bed and the corresponding latest active period is Qp^3- Qh^1 , which is consistent with the former borehole survey result. In the offshore area of the Bohai Sea, Haihe fault shows as a NWW-NEE strike dense fault zone and its upper fault point is less than 30m beneath the seabed. It shows that the active characteristics of Haihe fault in the Bohai Sea correspond to the Tanggu area.

Kostka functions associated to complex reflection groups and a conjecture of Finkelberg-Ionov

Kostka functions K_(λ,μ)~±(t), indexed by r-partitions λ and μ of n, are a generalization of Kostka polynomials K_(λ,μ)(t) indexed by partitions λ,μ of n. It is known that Kostka polynomials have an interpretation in terms of Lusztig's partition function. Finkelberg and Ionov(2016) defined alternate functions K_(λ,μ)(t) by using an analogue of Lusztig's partition function, and showed that K_(λ,μ)(t) ∈Z≥0[t] for generic μ by making use of a coherent realization. They conjectured that K_(λ,μ)(t) coincide with K_(λ,μ)^-(t). In this paper, we show that their conjecture holds. We also discuss the multi-variable version, namely, r-variable Kostka functions K_(λ,μ)~±(t_1,…,t_r).

Reducibility of finite reflection groups

A finite (pseudo-)reflection group G naturally gives rise to a hyperplane arrangement,i.e.,its reflection arrangement.We show that G is reducible if and only if its reflection arrangement is reducible.

Proof of Murphy-Cohen Conjecture on One-Dimensional Hard Ball Systems

We prove the Murphy and Cohen＇s conjecture that the maximum number of collisions of n ＋ 1 elastic particles moving freely on a line is n（n＋1）/2 if no interior particle has mass less than the arithmetic mean of the masses of its immediate neighbors. In fact, we prove the stronger result that, for the same conclusion, the condition that no interior particle has mass less than the geometric mean, rather than the arithmetic mean, of the masses of its immediate neighbors suffices.

Dunkl's Theory and Best Approximation by Entire Functions of Exponential Type in L_2-metric with Power Weight

In this paper, we study the sharp Jackson inequality for the best approximation of f ∈L2,k（Rd） by a subspace Ek2（σ） （SEk2（σ））, which is a subspace of entire functions of exponential type （spherical exponential type） at most σ. Here L2,k（Rd） denotes the space of all d-variate functions f endowed with the L2-norm with the weight vk（x）=Пζ∈R＋}（ζ,x）}2k（ζ）,which is defined by a positive subsystem R＋ of a finite root system R Rd and a function k（ζ）：R→R＋ invariant under the reflection group G（R） generated by R. In the case G（R） = Z2d, we get some exact results. Moreover, the deviation of best approximation by the subspace Ek2（σ） （SE2（σ）） of some class of the smooth functions in the space L2,k（Rd） is obtained.