Unitary W-algebras and three-dimensional higher spin gravities with spin one symmetry

We investigate whether there are unitary families of W-algebras with spin one fields in the natural example of the Feigin-Semikhatov W^(2)_n-algebra. This algebra is conjecturally a quantum Hamiltonian reduction corresponding to a non-principal nilpotent element. We conjecture that this algebra admits a unitary real form for even n. Our main result is that this conjecture is consistent with the known part of the operator product algebra, and especially it is true for n=2 and n=4. Moreover, we find certain ranges of allowed levels where a positive definite inner product is possible. We also find a unitary conformal field theory for every even n at the special level k+n=(n+1)/(n-1). At these points, the W^(2)_n-algebra is nothing but a compactified free boson. This family of W-algebras admits an 't Hooft limit that is similar to the original minimal model 't Hooft limit. Further, in the case of n=4, we reproduce the algebra from the higher spin gravity point of view. In general, gravity computations allow us to reproduce some leading coefficients of the operator product.Comment: 23 page

Dynamic Simulation, Parameter Optimization, and Control of a Reactive Distillation Column for Production of Isopropanol via Propylene Hydration

In this study, a reactive distillation column for production of isopropanol was investigated. Firstly, a dynamic model was developed for the process. The model of the process was then programmed, and the process simulated using a base case obtained from the literature. Results showed that distillate contained more than 58 mol% propylene-free isopropanol. In the next step, optimization of some operating variables was performed to maximize concentration of isopropanol in distillate with condenser temperature as constraint, which was considered to be above the freezing point of water. Several simulations were performed by changing operating parameters, and finally optimum isopropanol content in distillate was obtained above 58 mol%. Results of using classic controllers showed that PID controller had the best performance for both condenser temperature set-point tracking and disturbance rejection. This work is licensed under a Creative Commons Attribution 4.0 International License

Early Detection of Breast Cancer Using Machine Learning Techniques

Cancer is the second cause of death in the world. 8.8 million patients died due to cancer in 2015. Breast cancer is the leading cause of death among women. Several types of research have been done on early detection of breast cancer to start treatment and increase the chance of survival. Most of the studies concentrated on mammogram images. However, mammogram images sometimes have a risk of false detection that may endanger the patient’s health. It is vital to find alternative methods which are easier to implement and work with different data sets, cheaper and safer, that can produce a more reliable prediction. This paper proposes a hybrid model combined of several Machine Learning (ML) algorithms including Support Vector Machine (SVM), Artificial Neural Network (ANN), K-Nearest Neighbor (KNN), Decision Tree (DT) for effective breast cancer detection. This study also discusses the datasets used for breast cancer detection and diagnosis. The proposed model can be used with different data types such as image, blood, etc