A complete solution of the Kepler problem is given; the SO(4) action on (TS,Ω4) is discussed; and the incomplete Kepler hamiltonian vector field is regularized by the LS map, embedding it into (TS, ω̃4). [2] did excellent work on these topics. I read through them and write this report. O Introduction Kepler problem is a famous and classical problem in both mathematics and physics. Since Kepler, ...

objective(s): in this study we evaluate the impact of the different aspects of gold nano-particles (gnps) on the target absorptive dose enhancement factor (def) during external targeted radiotherapy with photon beams ranging from kilovolt to megavolt energies using monte carlo simulation. methods: we have simulated the interaction of photon beams with various energies of radiation using water s...

A polynomial-time algorithm for computing the permanent in any field of characteristic 3 is presented in this article. The principal objects utilized for that purpose are the Cauchy and Vandermonde matrices, the discriminant function and their generalizations of various types. Classic theorems on the permanent such as the Binet-Minc identity and Borchadt's formula are widely applied, while a sp...

Abstract The high cost of maintenance, repair and retrofitting concrete infrastructure to keep these structures durable serviceable is not sustainable, so the design process needs consider all aspects deterioration mechanism/s that can potentially occur in a structure. ideal solution should contribute sustainability by enhancing durability elements supporting circular economy. We studied delaye...

We propose Deep Estimators of Features (DEFs), a learning-based framework for predicting sharp geometric features in sampled 3D shapes. Differently from existing data-driven methods, which reduce this problem to feature classification, we regress scalar field representing the distance point samples closest line on local patches. Our approach is first that scales massive clouds by fusing distanc...

A theorem which establishes the solutions of a given optimization problem as stable points in the state space of single-layer relaxation-type recurrent neural networks is proposed. This theorem establishes the necessary conditions for the neural network to converge to a solution by proposing certain values for the constraint weight parameters of the network. Convergence performance of the discr...