In this paper, we propose a novel approach to generate the topology-preserving mapping of structural shapes using self-organizing maps (SOMs). The structural information of the geometrical shapes is captured by relational attribute vectors. These vectors are quantised using an SOM. Using this SOM, a histogram is generated for every shape. These histograms are treated as inputs to train another ...

In this paper, we propose a novel approach to generating topology preserving mapping of structural shapes using the self-organising maps (SOM). The structural information of the geometrical shapes is captured by the relational vectors. These relational attribute vectors are quantised using an SOM. Using this quatisation SOM, a histogram is generated for every shape. These histograms are treated...

Two distinct projections of finite rank m are adjacent if their difference is an operator two or, equivalently, the intersection images (m−1)-dimensional. We extend this adjacency relation on other conjugacy classes finite-rank self-adjoint operators which leads to a natural generalization Grassmann graphs. Let C be class formed by with eigenspaces dimension greater than 1. Under assumption tha...

We establish pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two measure-preserving transformations on $$\sigma $$ -finite measure spaces. also corresponding maximal inequalities $$L^p$$ $$1<p\le \infty and $$\rho -variational $$L^2$$ $$2<\rho <\infty . This gives an affirmative answer to the Furstenberg–Bergelson–Leibman conje...

In this paper, we study the broadcasting performance of urban Vehicle-to-everything (V2X) communications at road intersections. such environments, dense buildings obstruct radio channel between vehicles in adjacent segments and Non-Line-Of-Sight (NLOS) signal propagation reduces received power level. Therefore, messages that originate from roads traveling a non-parallel direction usually have w...

In this paper  we give newresults on the best approximation  in the Hausdorff topological vectorspace and  consider relationship  with orthogonality. Also we determined under  what conditions the map $P_{K,f}$ is upper semicontinous.

Variance Inflation Factors (VIFs) are reexamined as conditioning diagnostics for models with intercept, with and without centering regressors to their means as oft debated. Conventional VIFs, both centered and uncentered, are flawed. To rectify matters, two types of orthogonality are noted: vector-space orthogonality and uncorrelated centered regressors.The key to our approach lies in feasible ...