Exact travelling wave solutions for some nonlinear (N+1)-dimensional evolution equations

In this paper, we implement the tanh-coth function method to construct the travelling wave solutions for (N + 1)-dimensional nonlinear evolution equations. Four models, namely the (N + 1)-dimensional generalized Boussinesq equation, (N + 1)-dimensional sine-cosine-Gordon equation, (N + 1)-double sinh-Gordon equation and (N + 1)-sinh-cosinh-Gordon equation, are used as vehicles to conduct the analysis. These equations play a very important role in mathematical physics and engineering sciences. The implemented algorithm is quite efficient and is practically well suited for these problems. The computer symbolic systems such as Maple and Mathematica allow us to perform complicated and tedious calculations. Mathematical subject classification: 35K58, 35C06, 35A25

Decreased Immunoreactivities and Functions of the Chloride Transporters, KCC2 and NKCC1, in the Lateral Superior Olive Neurons of Circling Mice

Objectives. We tested the possibility of differential expression and function of the potassium-chloride (KCC2) and sodium-potassium-2 chloride (NKCC1) co-transporters in the lateral superior olive (LSO) of heterozygous (+/cir) or homozygous (cir/cir) mice.Methods. Mice pups aged from postnatal (P) day 9 to 16 were used. Tails from mice were cut for DNA typing. For Immunohistochemical analysis, rabbit polyclonal anti-KCC2 or rabbit polyclonal anti-NKCC1 was used and the density of immunolabelings was evaluated using the NTH image program. For functional analysis, whole cell voltage clamp technique was used in brain stem slices and the changes of reversal potentials were evaluated at various membrane potentials.Results. Immunohistochemical analysis revealed both KCC2 and NKCC1 immunoreactivities were more prominent in heterozygous (+/cir) than homozygous (cir/cir) mice on P day 16. In P9-P12 heterozygous (+/cir) mice, the reversal potential (E(gly)) of glycine-induced currents was shifted to a more negative potential by 50 mu M bumetanide, a known NKCC1 blocker, and the negatively shifted EA, was restored by additional application of 1 mM furosemide, a KCC2 blocker (-58.9 +/- 2.6 mV to -66.0 +/- 1.5 mV [bumetanide], -66.0 1.5 mV to -59.8 +/- 2.8 mV [furosemide+bumetanide], n=11). However, only bumetanide was weakly, but significantly effective (-60.1 +/- 2.9 mV to -62.7 +/- 2.6 mV [bumetanide], -62.7 +/- 2.6 mV to -62.1 +/- 2.5 mV [furosernide+bumetanide], n=7) in P9-P12 homozygous (cir/cir) mice.Conclusion. The less prominent immunoreactivities and weak or absent responses to bumetanide or furosemide suggest impaired function or delayed development of both transporters in homozygous (cir/cir) mice

Exact travelling wave solutions for some important nonlinear physical models

The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrodinger-KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical studies. In this paper, the Kudryashov method is used to seek exact travelling wave solutions of such physical models. Further, three-dimensional plots of some of the solutions are also given to visualize the dynamics of the equations. The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics

Direct approach for solving nonlinear evolution and two-point boundary value problems

Time-delayed nonlinear evolution equations and boundary value problems have a wide range of applications in science and engineering. In this paper, we implement the differential transform method to solve the nonlinear delay differential equation and boundary value problems. Also, we present some numerical examples including time-delayed nonlinear Burgers equation to illustrate the validity and the great potential of the differential transform method. Numerical experiments demonstrate the use and computational efficiency of the method. This method can easily be applied to many nonlinear problems and is capable of reducing the size of computational work

Bridging the gap with customers using machine learning on the NPS dataset

One of the key tools companies worldwide use to measure customer satisfaction is via the Net Promoter Score (NPS). This thesis tackles the problems in analyzing NPS data due to open text feedback, low response rates, and class imbalance in customer churn prediction. This research applies machine learning techniques such as natural language processing (NLP) and regression models to classify open-text feedback, fill in missing NPS scores and predict customer churn. To that end, SpaCy is used specifically to identify key drivers from open text feedback responses and categorize them to help draw meaningful insights. Customer satisfaction and loyalty were explored using sentiment analysis and predictive analysis models. The study also handles class imbalance indirectly through appropriate resampling techniques used as a condition to guarantee balanced and effective identification of churn rates. These results show that classifying feedback and predicting missing scores enhance the accuracy of NPS analysis and customer churn prediction yields actionable insights to inform retention strategies. In this work, we demonstrate how NLP and machine learning can solve some of the common challenges of customer satisfaction metrics and bolster machine learning based NPS analysis