The integrable Boussinesq equation and it’s breather,lump and soliton solutions

The fourth-order nonlinear Boussinesq water wave equation, which explains the propagation of long waves in shallow water, is explored in this article. We used the Lie symmetry approach to analyze the Lie symmetries and vector fields. Then, by using similarity variables, we obtained the symmetry reductions and soliton wave solutions. In addition, the Kudryashov method and its modification are used to explore the bright and singular solitons while the Hirota bilinear method is effectively used to obtain a form of breather and lump wave solutions. The physical explanation of the extracted solutions was shown with the free choice of different parameters by depicting some 2-D, 3-D, and their corresponding contour plots.

     

Effect of three vitrification methods on development of two-cell mouse embryos

The purpose of this study was to investigate the effect of three vitrification procedures [conventional straw (CS), open pulled straw (OPS) and closed pulled straw (CPS)] on the development of two-cell mouse embryos. Two-cell mouse embryos were randomly divided into vitrified and non-vitrified control groups. Embryos in the vitrified group were cryopreserved within a combination of 5.5 M ethylene glycol and 1M sucrose as cryoprotectants, loaded within three different straws (CS, OPS and CPS) and warmed in stepwise sucrose solutions. The survived embryos from each procedure were cultured in human tubal fluid (HTF). The non-vitrified control embryos were also cultured in the same manner. The rates of the development in all the groups were daily determined and statistically compared. On day 4 of the cultivation period, several expanded blastocysts from each group were randomly selected and stained either with propidium iodide (PI) and bisbenzimide or with terminal transferase- mediate DNA end labeling (TUNEL) Technique. The mean number of the inner cell mass (ICM), trophoectoderm (TE), necrotic and apoptotic cells were counted and statistically compared. The survival rate of embryos in CPS was significantly higher than that in OPS and CS. The rate of hatched blastocysts did not differ in the three vitrification procedures, but in comparison with that of the control, CS and OPS showed a significant reduction. The mean number of ICM and TE decreased in CS and OPS, whereas in CPS it was almost identical to that of the control. The incidence of apoptosis and necrosis appeared to be almost similar in all the groups. In conclusion, CPS seems to be an effective, easy and rapid method for the cryopreservation of two-cell mouse embryos.     

Effect of dispersion on nonlinear phase noise in optical transmission systems

An analytic expression for the variance of nonlinear phase noise that uses a first-order perturbation technique is obtained. The results show that for highly dispersive transmission systems, amplified spontaneous emission-induced phase noise due to self-phase modulation becomes much smaller than that for the systems with no dispersion.     

Phospha-Michael addition of phosphorus nucleophiles to α,β-unsaturated malonates using 3-aminopropylated silica gel as an efficient and recyclable catalyst

3-Aminopropylated silica gel, which is prepared from commercially available and cheap starting materials, is introduced as an efficient and recyclable catalyst for the phospha-Michael addition of phosphorus nucleophiles to α,β-unsaturated malonates. Short reaction times, mild reaction conditions, ease of recovery and catalyst reusability make this method a new, economic and waste-free chemical process for the synthesis of β-phosphonomalonates.     

Multi-Class Cost-Constrained Random Coding for Correlated Sources over the Multiple-Access Channel

This paper studies a generalized version of multi-class cost-constrained random-coding ensemble with multiple auxiliary costs for the transmission of N correlated sources over an N-user multiple-access channel. For each user, the set of messages is partitioned into classes and codebooks are generated according to a distribution depending on the class index of the source message and under the constraint that the codewords satisfy a set of cost functions. Proper choices of the cost functions recover different coding schemes including message-dependent and message-independent versions of independent and identically distributed, independent conditionally distributed, constant-composition and conditional constant composition ensembles. The transmissibility region of the scheme is related to the Cover-El Gamal-Salehi region. A related family of correlated-source Gallager source exponent functions is also studied. The achievable exponents are compared for correlated and independent sources, both numerically and analytically.