Abstract:
Granular zero-valent iron (ZVI) has been widely used to construct permeable reactive barriers (PRB) for the in situ remediation of groundwater contaminated with halogenated hydrocarbons. In the anaerobic condition of most groundwater flow systems, iron undergoes corrosion by water and results in hydrogen gas generation. Several studies have shown that some of the hydrogen gas generated at the iron/water interface can diffuse into the iron lattice. Hydrogen gas also can be an electron donor for dechlorination of chlorinated compounds. In this study, the possibility of hydrogen gas bound in the lattice of ZVI playing a role in dehalogenation and improving the degradation efficiency of ZVI was evaluated. Two different granular irons were tested: one obtained from Quebec Metal Powders Ltd (QMP) and the other from Connelly-GPM. Ltd. For each type of iron, two samples were mixed with water and sealed in testing cells. Since the rate of hydrogen entry varies directly with the square root of the hydrogen pressure, one sample was maintained for several weeks under near-vacuum conditions to minimize the amount of hydrogen entering the iron lattice. The other sample was maintained for the same period at a hydrogen pressure of over 400 kPa to maximize the amount of hydrogen entering the iron lattice. The degradation abilities of the reacted ironsand the original iron materials were tested by running several sets of batch tests. The results of this study show little to no improvement of inorganic TCE degradation reactions due to the presence of lattice-stored hydrogen in iron material. This is probably due to the high energiesrequired to release hydrogen trapped in the iron lattice. However, there are certain chemical compounds that can promote hydrogen release from the iron lattice, and there may be bacteria that can utilize lattice-bound hydrogen to carry out dechlorination reactions.

Casting is an important rubber manufacturing
process for both production and material developments. A quick and flexible way
of testing the constitutive materials properties of rubber products is very
important for optimising the processing parameters and quality control. In many
cases, standard tests such as tensile or compression tests are time consuming
and require a large volume of materials. This work reports some recent work in
using a combined numerical and experimental approach to characterise the
properties of rubber materials during a casting process. Durometer shore
hardness is used to test silicone rubbers (as a model material) with different
compositions on different moulding planes and the linear elastic property is
estimated from the hardnesses. The predicted properties are systematically
compared with the experimental tests on hard and soft silicone rubber samples
with different compositions. The work shows that shore hardness can be used as
an effective way to monitor the materials properties during amoulding process
for process optimisation and quality control.

Abstract:
The cross-linking of food proteins is an interesting topic of food science in recent years and served successfully as an approach to modify protein functional properties. In the presented work, horseradish peroxidase (HRP, EC 1.11.1.7) was used to oxidative cross-link casein in presence of H2O2. The cross-linking of casein was demonstrated by capillary zone electrophoresis analysis. The central composite design using response surface methodology was used to optimize cross-linking conditions of casein. The optimal cross-linking conditions of casein were as follows: the addition level of HRP was 4.73 mkat·g-1 proteins, temperature was 37°C and reaction time was 2.9 h when casein concentration and pH of reaction medium were fixed at 5% (w/w) and 9.5, respectively. Cross-linked casein was prepared with these optimal conditions and used to analyze its emulsifying activity index, emulsifying stability index and microstructure of acidified gel. The emulsifying activity index and emulsifying stability index of the cross-linked casein were enhanced about 10 and 6% compared to that of casein. The microstructure of acid-induced gel of the cross-linked casein observed by scanning electron microscopy was more compact and uniform than that of casein without cross-linking. Cross-linking of food proteins induced by horseradish peroxidase might serve as an alternative approach to modify functional property of the proteins.

Abstract:
An implementation of uncertainty analysis (UA) and quantitative global sensitivity analysis (SA) is applied to the non-linear inversion of gravity changes and three-dimensional displacement data which were measured in and active volcanic area. A didactic example is included to illustrate the computational procedure. The main emphasis is placed on the problem of extended Fourier amplitude sensitivity test (E-FAST). This method produces the total sensitivity indices (TSIs), so that all interactions between the unknown input parameters are taken into account. The possible correlations between the output an the input parameters can be evaluated by uncertainty analysis. Uncertainty analysis results indicate the general fit between the physical model and the measurements. Results of the sensitivity analysis show quite different sensitivities for the measured changes as they relate to the unknown parameters of a physical model for an elastic-gravitational source. Assuming a fixed number of executions, thirty different seeds are observed to determine the stability of this method.

Abstract:
We present a unified parameterization of the fitting functions suitable for density profiles of dark matter haloes or elliptical galaxies. A notable feature is that the classical Einasto profile appears naturally as the continuous limiting case of the cored subfamily amongst the double power-law profiles of Zhao (1996). Based on this, we also argue that there is basically no qualitative difference between halo models well-fitted by the Einasto profile and the standard NFW model. This may even be the case quantitatively unless the resolutions of simulations and the precisions of fittings are sufficiently high to make meaningful distinction possible.

Abstract:
Koroljuk gave a summation formula for counting the number of lattice paths from $(0,0)$ to $(m,n)$ with $(1,0), (0,1)$-steps in the plane that stay strictly above the line $y=k(x-d)$, where $k$ and $d$ are positive integers. In this paper we obtain an explicit formula for the number of lattice paths from $(a,b)$ to $(m,n)$ above the diagonal $y=kx-r$, where $r$ is a rational number. Our result slightly generalizes Koroljuk's formula, while the former can be essentially derived from the latter. However, our proof uses a recurrence with respect to the starting points, and hereby presents a new approach to Koroljuk's formula.

Abstract:
In this note we introduce a determinant and then give its evaluating formula. The determinant turns out to be a generalization of the well-known ballot and Fuss-Catalan numbers, which is believed to be new. The evaluating formula is proved by showing that the determinant coincides with the number of lattice paths with (1,0), (0,1)-steps in the plane that stay below a boundary line of rational slope.

Abstract:
Let $\{P_n\}_{n\geq 0}$ denote the Catalan-Larcombe-French sequence, which naturally came up from the series expansion of the complete elliptic integral of the first kind. In this paper, we prove the strict log-concavity of the sequence $\{\sqrt[n]{P_n}\}_{n\geq 1}$, which was originally conjectured by Sun. We also obtain the strict log-concavity of the sequence $\{\sqrt[n]{V_n}\}_{n\geq 1}$, where $\{V_n\}_{n\geq 0}$ is the Fennessey-Larcombe-French sequence arising in the series expansion of the complete elliptic integral of the second kind.

Abstract:
The Alladi-Gordon identity plays an important role for the Alladi-Gordon generalization of Schur's partition theorem. By using Joichi-Stanton's insertion algorithm, we present an overpartition interpretation for the Alladi-Gordon key identity. Based on this interpretation, we further obtain a combinatorial proof of the Alladi-Gordon key identity by establishing an involution on the underlying set of overpartitions.

Abstract:
The new explicit linear three-order four-step methods with longest interval of absolute stability are proposed. Some numerical experiments are made for comparing different kinds of linear multistep methods. It is shown that the stability intervals of proposed methods can be longer than that of known explicit linear multistep methods. 1. Introduction For the initial value problem of the ordinary differential equation (ODE) where and with , there are a lot of numerical methods to be proposed for the numerical integration. Among them, linear multistep methods (LMMs) are a class of the most prominent and most widely used methods, see [1, 2] and the references therein. Adams methods are among the oldest of LMMs, dating back to the nineteenth century. Nevertheless, they continue to play a key role in efficient modern algorithms. The first to use such a method was Adams in solving a problem of Bashforth in connection with capillary action, see [3]. In contrast to one-step methods, where the numerical solution is obtained solely from the differential equation and the initial value , a linear multistep ( -step) method requires ( ) starting values and a multistep ( -step) formula to obtain an approximation to the exact solution, see [4]. So far as we know, explicit linear multistep methods (ELMMs) have some advantages such as simple calculation formulae, and small error constants. However, due to the famous Dahlquist barrier in [5], an explicit linear multistep method cannot be A-stable. Therefore, we try to find the new explicit linear multistep methods with the longest interval of stability region in this paper. And some numerical experiments are given to compare the proposed methods with existing methods such as Adams-Bashforth method, Adams-Moulton methods, and BDF methods. Practical calculations have shown that these proposed methods are adaptive. 2. Linear Multistep Methods Applying the linear multistep ( -step) methods to the initial value problem (1.1), we obtain the recurrence relation where denotes an approximation to the solution , , for , the constant steplength , and starting conditions are required. Here, and are constants subject to the condition . If , then the corresponding methods (2.1) are explicit, and implicit otherwise. Then, we define the first and second generating polynomials by where is a dummy variable. Consider the scalar test equation where and . Its characteristic polynomial can be written as where . Here, we quote some important definitions (see Sections , , and in the reference [2]). Definition 2.1. The set is called the region of