Classically, null designs were defined on the poset of subsets of a given finite set (boolean algebra). A null design is defined as a collection of weighted k-subsets such that the sum of the weights of ksubsets containing a t-subset is 0 for every t-subset, where 0 ≤ t < k ≤ n. Null designs are useful to understand designs or to construct new designs from a known one. They also deserve research as pure combinatorial objects. In particular, people have been interested in the minimum number of k-subsets of non-zero weight to make a non-zero null design, and the characterization of the null designs with the minimal number of k-subsets of non-zero weight, which we call minimal null designs. Minimal null designs were used to construct explicit bases of the space of null designs.The definition of null designs can be extended to any poset which has graded structure (ranked poset) as the boolean algebra does. In this paper, we prove general theorems on the structure of the null designs of finite ranked posets, which also yield a density theorem of finite ranked posets. We apply the theorems to two special posets-the boolean algebra and the generalized (q-analogue of) boolean algebra-to characterize the minimal null t-designs.

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The formulation of approximate solutions to equations that embody the dominant characteristics of the orbital motion of a two-satellite tethered system are studied. The orbital motion of the system is viewed as perturbed two-body motion, and a restricted tether problem is obtained by neglecting librational motion. An exact analytical solution to this restricted problem in terms of elliptic functions is presented. An approximate solution to the restricted tether problem obtained by applying the method of averaging is also provided. An approximation for small-amplitude librational motion is formulated, whose solution is based on methods for solving equations with variable coef cients. The analytical solutions are good approximations to the orbital motion of the tetherperturbed satellite and the librational motion of the system when the libration is small. The restricted tether motion approximation is then utilized to solve the identi cation problem of a tethered satellite system. Nomenclature a ¤ = apparent semimajor axis e ¤ = apparent eccentricity F = incomplete elliptic integral of the rst kind h = nondimensionalangular momentum K = complete elliptic integral of the rst kind K 0 = associate complete elliptic integral of the rst kind k = modulus of Jacobian elliptic functions and integral k 0 = complementary modulus of Jacobian elliptic functions and integral m; m p = masses of satellites q = Jacobi's nome r = nondimensionalradial distance, radial distance/r E r E = radius of the Earth, 6,378,000 m sn = Jacobian elliptic function t = time t ¤ = nondimensionaltime, t p .¹=r 3 E / D t £ 0:0012394 u = 1=r X = state vector ®;¯;°; » = variable coef cients "= tether parameter, m p ½=.m C m p /r E µ = orbital angle (true anomaly) µ 2 = out-of-plane libration angle µ 3 = in-plane libration angle ¹ = gravitational constant of the Earth ½ = tether length '; ' ¤ = amplitudes ! = orbital frequency

In this work, plasma enhanced atomic layer deposition process (PEALD) was used for the depositing SiO 2 as the insulating layer with various plasma power. We investigated the effect of plasma power on the TFT performance in top-gate structure.

In this paper, we present the architecture of oxide TFT selected from diverse TFT structures for the application to the high resolution mobile display. Due to the selection of proper materials and process, we can achieve highly stable BCE TFT and show the promise of vertical oxide TFT with the smallest TFT footprint.