Euler’s partition theorem for all moduli and new companions to Rogers–Ramanujan–Andrews–Gordon identities

The Ramanujan Journal - We generalise Euler’s partition theorem involving odd parts and distinct parts for all moduli and provide new companions to...     

The Green polynomials via vertex operators

An iterative formula for the Green polynomial is given using the vertex operator realization of the Hall-Littlewood function. Based on this, (1) a general combinatorial formula of the Green polynomial is given; (2) several compact formulas are given for Green's polynomials associated with upper partitions of length ≤3 and the diagonal lengths ≤3; (3) a Murnaghan-Nakayama type formula for the Green polynomial is obtained; and (4) an iterative formula is derived for the bitrace of the finite general linear group G and the Iwahori-Hecke algebra of type A on the permutation module of G by its Borel subgroup.     

Numerical simulation of two droplets impacting upon a dynamic liquid film

The impact of droplets on the liquid film is widely involved in industrial and agricultural fields. In recent years, plenty of works are limited to dry walls or stationary liquid films, and the research of multi-droplet impact dynamic films is not sufficient. Based on this, this paper employs a coupled level set and volume of fluid (CLSVOF) method to numerically simulate two-droplet impingement on a dynamic liquid film. In our work, the dynamic film thickness, horizontal central distance between the droplets, droplets' initial impact speed, and simultaneously the flow velocity of the moving film are analyzed. The evolution phenomenon and mechanism caused by the collision are analyzed in detail. We find that within a certain period of time, the droplet spacing does not affect the peripheral crown height; when the droplet spacing decreases or the initial impact velocity increases, the height of the peripheral crown increases at the beginning, and then, because the crown splashed under Rayleigh-Plateau instability, this results in the reduction of the crown height. At the same time, it is found that when the initial impact velocity increases, the angle between the upstream peripheral jet and the dynamic film becomes larger. The more obvious the horizontal movement characteristics, the more restrained the crown height; the spread length increases with the increase of the dynamic film speed, droplet spacing and the initial impact velocity. When the liquid film is thicker, more fluid enters the crown, due to the crown being unstable, the surface tension is not enough to overcome the weight of the rim at the end of the crown, resulting in droplets falling off.     

Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction–diffusion terms

Both exponential stability and periodic solutions are considered for a class of bi-directional associative memory (BAM) neural networks with delays and reaction–diffusion terms by constructing suitable Lyapunov functional and some analysis techniques. The general sufficient conditions are given ensuring the global exponential stability and existence of periodic solutions of BAM neural networks with delays and reaction–diffusion terms. These presented conditions are in terms of system parameters and have important leading significance in the design and applications of globally exponentially stable and periodic oscillatory neural circuits for BAM with delays and reaction–diffusion terms.     

On a Damped Vibration Problem Involving p-Laplacian Operator: Fast Homoclinic Orbits

In this paper, we deal with the nonlinear second-order differential equation with damped vibration term involving p-Laplacian operator. Of particular interest is the resolution of an open problem. An interesting outcome from our result is that we can obtain the fast homoclinic solution with general superlinear growth assumption in suitable Sobolev space. To our knowledge, our theorems appear to be the first such result about damped vibration problem with p-Laplacian operator.     

Periodic traveling wave solution for non-homogeneous BBM and KdVB equations

In this paper the Green’s function method and results about fixed point are used to get existence results on periodic traveling wave solution for non-homogeneous problems of generalized versions of the BBM and KdVB equations. It is shown through the constructions of explicit Green’s functions that the periodic boundary value problems for the traveling wave solutions of the BBM and KdVB equations are equivalent to integral equations which generate compact operators in the space of periodic functions. These integral representations allowed us to prove that if the speed of the wave propagation is suitably chosen, then the BBM and KdVB equations will admit periodic traveling wave solution.     

点传递线性空间

本文是关于点传递线性空间的一个分类工作. 设${\mathcal{S}}$是一个点数为51的正则线性空间,其线长为6, $G$ 是${\cal S}$的一个自同构群.本文证明了群$G$不可能点传递.     

Response of the REWARD detection system to the presence of a Radiological Dispersal Device

The objective of the REWARD project consisted in building a mobile system for real time, wide area radiation surveillance, using a CdZnTe detector for gamma radiation and a neutron detector based on novel silicon technologies. The sensing unit includes a GPS system and a wireless communication interface to send the data remotely to a monitoring base station, where it will be analyzed in real time and correlated with historical data from the tag location, in order to generate an alarm when an abnormal situation is detected. The main objective of this work consisted in making predictions regarding the behavior of the REWARD system in the presence of a Radiological Dispersion Device (RDD), one of the reference scenarios foreseen for REWARD, using experimental data and the Monte Carlo simulation program MCNP6. Experimental tests were performed at the Fire Brigades Facilities in Rome and at the Naples Fire Brigades. The response of the REWARD detection system to the presence of an RDD is predicted and discussed.