Most secant varieties of tangential varieties to Veronese varieties are nondefective

We prove a conjecture stated by Catalisano, Geramita, and Gimigliano in 2002, which claims that the secant varieties of tangential varieties to the $d$th Veronese embedding of the projective $n$-space $\mathbb{P}^n$ have the expected dimension, modulo a few well-known exceptions. As Bernardi, Catalisano, Gimigliano, and Id\'a demonstrated that the proof of this conjecture may be reduced to the case of cubics, i.e., $d=3$, the main contribution of this work is the resolution of this base case. The proposed proof proceeds by induction on the dimension $n$ of the projective space via a specialization argument. This reduces the proof to a large number of initial cases for the induction, which were settled using a computer-assisted proof. The individual base cases were computationally challenging problems. Indeed, the largest base case required us to deal with the tangential variety to the third Veronese embedding of $\mathbb{P}^{79}$ in $\mathbb{P}^{88559}$.Comment: 25 pages, 2 figures, extended the introduction, and added a C++ code as an ancillary fil

Modeling and simulation of standalone hybrid PV-wind renewable energy system base case study: Iraq

Energy is very important for countries growth and economy. The global warning of using fossil fuel to generate electricity increase which plays an important role to increase the demand for renewable energy to generate electricity. Renewable energy is the energy that collected from renewable sources like Solar, wind, waves and others. The problem of renewable sources that is unexpected and have intermittent nature. This thesis contain modeling of Photovoltaic renewable energy system to produces maximum 10 KW/h. Moreover, the study contains modeling of wind energy system to produces 14 KW/h. Reducing the effect of the intermittent nature of renewable sources on the electricity generation is a challenging task. The end of the project are proposed a hybrid modeling of both the PV and the wind systems by using DC link using Matlab 2017b Simulink software. The case study suffer huge shortage of electrical power production. The maximum power is 24 KW/h obtained using hybrid system. The demonstrated system as standalone or grid off system due to targeted the rural electrification. The resulted hybrid system noticed that it’s improve the power and the under worst case which the system tested on it the battery can charge and the system ready to extra load