Abstract:
An acoustic method is presented for analyzing the time of falling motion. A ball is dropped from a measured height. The dropping device makes a distinct sound a well-determined time (roughly 14 milliseconds) after release. The ball subsequently makes a second distinct sound when it hits the surface below. These sounds are captured with a microphone resting on the surface and are readily apparent in the acoustic waveform. At each height (0.25m, 0.50m, 0.75m, and 1.00m), the measured drop time agrees with the drop time predicted by the law of falling bodies with a typical accuracy of 4.3 ms.

Abstract:
Perceived direction of gravity, as assessed by the subjective visual vertical (SVV), shows roll-angle dependent errors that drift over time and a bias upon return to upright. According to Bayesian observer theory, the estimated direction of gravity is derived from the posterior probability distribution by combining sensory input and prior knowledge about earth-vertical in a statistically optimal fashion. Here we aimed to further characterize the stability of SVV during and after prolonged roll-tilts. Specifically we asked whether the post-tilt bias is related to the drift pattern while roll-tilted. Twenty-nine healthy human subjects (23-56yo) repetitively adjusted a luminous arrow to the SVV over periods of 5min while upright, roll-tilted (±45°, ±90°), and immediately after returning to upright. Significant (p<0.05) drifts (median absolute drift-amplitude: 10°/5min) were found in 71% (±45°) and 78% (±90°) of runs. At ±90° roll-tilt significant increases in absolute adjustment errors were more likely (76%), whereas significant increases (56%) and decreases (44%) were about equally frequent at ±45°. When returning to upright, an initial bias towards the previous roll-position followed by significant exponential decay (median time-constant: 71sec) was noted in 47% of all runs (all subjects pooled). No significant correlations were found between the drift pattern during and immediately after prolonged roll-tilt. We conclude that the SVV is not stable during and after prolonged roll-tilt and that the direction and magnitude of drift are individually distinct and roll-angle-dependent. Likely sensory and central adaptation and random-walk processes contribute to drift while roll-tilted. Lack of correlation between the drift and the post-tilt bias suggests that it is not the inaccuracy of the SVV estimate while tilted that determines post-tilt bias, but rather the previous head-roll orientation relative to gravity. We therefore favor central adaptation, most likely a shift in prior knowledge towards the previous roll orientation, to explain the post-tilt bias.

Abstract:
We obtained the analytic solutions of relic gravitational waves (RGWs) for the slow-roll inflation with a power-law form potential of the scalar field, $V=\lambda\phi^n$. Based on a reasonable range of $n$ constrained by cosmic microwave background (CMB) observations, we give tight constraints of the tensor-to-scalar ratio $r$ and the inflation expansion index $\beta$ for the fixed scalar spectral index $n_s$. Even though, the spectrum of RGWs in low frequencies is hardly depends on any parameters, the high frequency parts will be affected by several parameters, such as $n_s$, the reheating temperature $T_{RH}$ and the index $\beta_s$ describing the expansion from the end of inflation to the reheating process. We analyzed in detail all the factors which would affect the spectrum of RGWs in high frequencies including the quantum normalization. We found that the future GW detectors SKA, eLISA, BBO and DECIGO are promising to catch the signals of RGWs. Furthermore, BBO and DECIGO have the potential not only to distinguish the spectra with different parameters but also to examine the validity of the quantum normalization.

Abstract:
A vertically hanging chain is released from rest and falls due to gravity on a scale pan. We discuss the various experimental and theoretical aspects of this classic problem. Careful time-resolved force measurements allow us to determine the differences between the idealized and its implementation in the laboratory problem. We observe that, in spite of the upward force exerted by the pan on the chain, the free end at the top falls faster than a freely falling body. Because a real chain exhibits a finite minimum radius of curvature, the contact at the bottom results in a tensional force which pulls the falling part downward.

Abstract:
The one-dimensional fall of a folded chain with one end suspended from a rigid support and a chain falling from a resting heap on a table is studied. Because their Lagrangians contain no explicit time dependence, the falling chains are conservative systems. Their equations of motion are shown to contain a term that enforces energy conservation when masses are transferred between subchains. We show that Cayley's 1857 energy nonconserving solution for a chain falling from a resting heap is incorrect because it neglects the energy gained when a transferred link leaves a subchain. The maximum chain tension measured by Calkin and March for the falling folded chain is given a simple if rough interpretation. Other aspects of this falling folded chain are briefly discussed.

Abstract:
We synthesized centimeter-scale single- to few-layer graphene (FLG) films via chemical vapor deposition (CVD) on Ni foils. We demonstrates that the precipitation mechanism may not be the only important mechanism in the formation of graphene by CVD in Ni system, and that controlling the cooling rate in the CVD process may not be the appropriate way to control the thickness of graphene films. In addition, we are the first to demonstrate the transfer of centimeter-scale FLG from Ni foil to transparent flexible polyethylene terephthalate substrates via an efficient roll-to-roll process. Comparing to rigid substrates, synthesis of graphene on flexible Ni foil has necessity for the use of a roll-to-roll transfer process.

Abstract:
Microtribological properties of vertically-aligned carbon-nanotube (VACNT) films have been studied. Adhesion forces were obtained by measuring force-displacement curves. Friction experiments were conducted in reciprocating sliding configurations. Effects of tip radius, applied force, scan speed, and relative humidity were investigated. A model of the friction of VACNT film is discussed on the basis of in-situ tribological experiments inside a scanning electron microscope (SEM).

Abstract:
On the basis of the theory of a falling shadow which was first formulated by Wang (1985), the notion of falling ？-ideals in -algebras is introduced, and related properties are investigated. Characterizations of a falling ？-ideal are established. Relations among falling ？-ideals, falling -ideals, falling #-ideals, falling -subalgebras, and falling BCK-ideals are discussed.

Abstract:
Based on the theory of a falling shadow which was first formulated by Wang (1985), a theoretical approach of the ideal structure in -algebras is established. The notions of a falling -subalgebra, a falling -ideal, a falling -ideal, and a falling -ideal of a -algebra are introduced. Some fundamental properties are investigated. Relations among a falling -subalgebra, a falling -ideal, a falling -ideal, and a falling -ideal are stated. Characterizations of falling -ideals and falling -ideals are discussed. A relation between a fuzzy -subalgebra and a falling -subalgebra is provided. 1. Introduction Iséki and Tanaka introduced two classes of abstract algebras -algebras and -algebras [1, 2]. It is known that the class of -algebras is a proper subclass of the class of -algebras. -algebras have several connections with other areas of investigation, such as: lattice ordered groups, -algebras, Wajsberg algebras, and implicative commutative semigroups. Font et al. [3] have discussed Wajsberg algebras which are term-equivalent to -algebras. Mundici [4] proved that -algebras are categorically equivalent to bounded commutative -algebras. Meng [5] proved that implicative commutative semigroups are equivalent to a class of -algebras. Neggers and Kim [6] introduced the notion of -algebras which is another useful generalization of -algebras. They investigated several relations between -algebras and -algebras as well as several other relations between -algebras and oriented digraphs. After that, some further aspects were studied in [7, 8]. Neggers et al. [9] introduced the concept of -fuzzy function which generalizes the concept of fuzzy subalgebra to a much larger class of functions in a natural way. In addition, they discussed a method of fuzzification of a wide class of algebraic systems onto along with some consequences. In the study of a unified treatment of uncertainty modelled by means of combining probability and fuzzy set theory, Goodman [10] pointed out the equivalence of a fuzzy set and a class of random sets. Wang and Sanchez [11] introduced the theory of falling shadows which directly relates probability concepts with the membership function of fuzzy sets. Falling shadow representation theory shows us the way of selection relaid on the joint degrees distributions. It is reasonable and convenient approach for the theoretical development and the practical applications of fuzzy sets and fuzzy logics. The mathematical structure of the theory of falling shadows is formulated in [12]. Tan et al. [13, 14] established a theoretical approach to define a fuzzy

Abstract:
This paper is concerned with the detailed behaviour of roll-waves undergoing a low-frequency perturbation. We rst derive the so-called Whitham's averaged modulation equations and relate the well-posedness of this set of equations to the spectral stability problem in the small Floquet-number limit. We then fully validate such a system and in particular, we are able to construct solutions to the shallow water equations in the neighbourhood of modulated roll-waves proles that exist for asymptotically large time.