Preparation and characterization of an ordered 1-dodecanethiol monolayer on bare Si(111) surface

We have grown 1-dodecandthiol (DDT) monolayer on a bare Si(111) surface through ultraviolet-assisted photochemical reaction. The resulting monolayer was investigated by means of water contact angle measurement, synchrotron radiation-based high-resolution X-ray photoelectron spectroscopy, and polarization-dependent near-edge X-ray absorption fine structure spectroscopy. These combined probes for characterization reveal a hydrophobic ambient surface; the DDT was directly attached to Si through a Si-S bond, and the molecules formed an ordered monolayer with an average tilt angle of 57° of the alkyl chains relative to the substrate surface.     

On the Dirichlet's box principle

In this note, we will focus on several applications on the Dirichlet's box principle in Discrete Mathematics lesson and number theory lesson. In addition, the main result is an innovative game on a triangular board developed by the authors. The game has been used in teaching and learning mathematics in Discrete Mathematics and some high schools in Hong Kong.     

Impulsive torque control of biped gait with power packets

Nonlinear Dynamics - This paper concerns an investigation into the control of the transient vibration of an Euler–Bernoulli beam using a symmetric single-sided vibro-impact nonlinear energy...     

Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry

We give necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomial maps with arbitrary real exponents defined on the positive orthant. Our work relates and extends existing injectivity conditions expressed in terms of Jacobian matrices and determinants. In the context of chemical reaction networks with power-law kinetics, our results can be used to preclude as well as to guarantee multiple positive steady states. In the context of real algebraic geometry, our work recognizes a prior result of Craciun, Garcia-Puente, and Sottile, together with work of two of the authors, as the first partial multivariate generalization of the classical Descartes’ rule, which bounds the number of positive real roots of a univariate real polynomial in terms of the number of sign variations of its coefficients.     

Novel Microtensile Method for Monotonic and Cyclic Testing of Freestanding Copper Thin Films

This paper presents the results of new microtensile tests conducted to investigate the mechanical properties of submicron-thick freestanding copper films. The method, used in this study, allows the observation of materials response under uniaxial tensile loads with measurements of stress at strain rates up to 5.5 × 10⁻⁴/s. It also facilitates tension–tension fatigue experiments under a variety of mean stress conditions at cyclic loading frequencies to 20 Hz. The sample processes involve fabrication of a supporting frame with springs and alignment beams all made of electroplated nickel. Electroplating took place on top of a previously deposited sample rather than creating a structure by subtractive fabrication. Tensile sample loading is applied using a piezoelectric actuator. Load was measured using a capacitance gap sensor with a novel mechanical coupling to the sample. Tension–tension fatigue experiments were carried out with feedback to give load control. Fatigue tests were conducted on sputter-deposited 500 and 900 nm copper films with grain sizes ∼50 nm. Fatigue life reached 10⁵ cycles at low mean load, which decreased with an increase in the mean load. The results indicate decreasing plasticity with increasing mean load.     

The Laplacian spectral radius of graphs

The Laplacian spectral radius of a graph is the largest eigenvalue of the associated Laplacian matrix. In this paper, we improve Shi’s upper bound for the Laplacian spectral radius of irregular graphs and present some new bounds for the Laplacian spectral radius of some classes of graphs.     

Full friendly index sets of Cartesian products of two cycles

Let G =（V, E） be a connected simple graph. A labeling f ： V → Z2 induces an edge labeling f＊ ： E → Z2 defined by f＊（xy） = f（x） ＋f（y） for each xy ∈ E. For i ∈ Z2, let vf（i） = ｜f^-1（i）｜ and ef（i） = ｜f＊^-1（i）｜. A labeling f is called friendly if ｜vf（1） - vf（0）｜ ≤ 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by if（G） = e（1） - el（0）. The set [if（G） ｜ f is a friendly labeling of G} is called the full friendly index set of G, denoted by FFI（G）. In this paper, we will determine the full friendly index set of every Cartesian product of two cycles.     

Weak Gravity Conjecture and extremal black holes

Motivated by the desire to improve our understanding of the Weak Gravity Conjecture, we compute the one-loop correction of charged particles to the geometry and entropy of extremal black holes in 4D. We use the entropy function formalism to extend previous analysis that dealt with neutral particles, and obtain the corrections to the horizon entropy for different regimes of black hole masses. These corrections are small in general. They are furthermore reduced when supersymmetry is present, and disappear in N = 4 supergravity. We provide some speculative arguments that in a theory with only sub-extremal particles, classical Reissner-Nordstrom black holes actually possess an infinite microcanonical entropy, though only a finite amount is visible to an external observer, as shown by the horizon entropy computation.     

Dual-Output Mach–Zehnder Modulator for Optical Access Networks

This paper employs dual-output Mach–Zehnder Modulator (MZM) for optical access networks without optical filters. Light waves generated from multiple laser sources are multiplexed and fed into dual-output MZM. Biasing the dual-output MZM at null point generates central carriers in one output port and first-order sidebands in another output port. Reflective semiconductor optical amplifier modulates both the central carriers and sidebands with wired and wireless data, respectively. The modulated optical signals are combined by polarization beam splitter and transmitted through 25-km single-mode fiber. The performance of the proposed scheme is proved by clear eye-diagrams and great bit error rate (BER) curves. Moreover, the power penalty at the BER of 10^-9 is less than 1 dB for both wired and wireless signals. Therefore, the proposed system simultaneously transmits wired and wireless signals.     

Relaxation times and energy barriers of rubbing-induced birefringence in glass-forming polymers

The relaxations of rubbing-induced birefringence (RIB) in several glass-forming polymers, including polycarbonate and polystyrene (PS) derivatives with various modifications to the phenyl ring side group, are studied. Significant relaxations of RIB are observed at temperatures well below the glass transition temperature T _g . The relaxation times span a wide range from ∼ 10 s to probably geological time scale. Physical aging effects are absent in the RIB relaxations. The model proposed for the interpretation of RIB in PS describes well the RIB relaxations in all the polymers investigated here. The energy barriers are of the order of a few hundred kJ/mol and decrease with decreasing temperature, in opposition to the trend of Vogel-Fulcher form for polymer segmental relaxations above T _g . The relaxation behaviors of different polymers are qualitatively similar but somewhat different in quantitative details, such as in the values of the saturated birefringence, the shape of the initial barrier density distribution functions, the rates of barrier decrease with decreasing temperature, and the dependence of relaxation times on temperature and parameter , etc. The RIB relaxations are different from any of the other relaxations below T _g that have been reported in the literature, such as dielectric relaxations or optical probe relaxations. A microscopic model for the relaxations of RIB is much desired.