An algebra $\mathcal{A}$ of $n\times n$ complex matrices is said to be \textit{idempotent compressible} if $E\mathcal{A}E$ an for all idempotents $E\in\mathbb{M}_n(\mathbb{C})$. Analogously, \textit{projection $P\mathcal{A}P$ orthogonal projections $P$ in $\mathbb{M}_n(\mathbb{C})$. In this paper we construct several examples unital algebras that admit these properties. addition, a complete cla...

This paper proposes a neural network approach for solving two classical problems in the two-dimensional inverse wave scattering: far field pattern problem and seismic imaging. The mathematical of scattering is to recover scatterer medium based on boundary measurement scattered from medium, which high-dimensional nonlinear. For under circular experimental setup, perturbative analysis shows that ...

Fractals have gained great attention from researchers due to their wide applications in engineering and applied sciences. Especially, several topics of sciences, the iterated function systems theory has important roles. As is well known, examples fractals are derived fixed point for suitable operators spaces with complete or compact structures. In this article, a new generalization Hausdorff di...

We present a theory for analyzing residence times of single molecules in fixed detection area scanning tunneling microscope (STM). The approach is developed one-dimensional molecule diffusion and can be extended to two dimensions by using the same methodology. Explicit results are derived an harmonic attractive repulsive tip-molecule interaction. Applications allows one estimate type strength i...

Abstract In this short note, we reformulate the task of calculating pair correlation statistics a Kronecker sequence as lattice point counting problem. This can be done analogously to based approach which was used (re-)prove famous three gap property for sequences. We show that recently developed techniques then applied derive certain class sequences have $$\beta $$ <mml:math xmlns:mml="http://...

We define the weak intermediate boundary conditions for triharmonic operator −Δ3. analyse sensitivity of this type upon domain perturbations. construct a perturbation (Ωϵ)ϵ > 0 smooth Ω ℝ N which on ∂Ωϵ are not preserved in limit ∂Ω, analogously to Babuška paradox hinged plate. Four different can be produced limit, depending convergence ∂Ω. In one particular case, we obtain ‘strange’ condition ...

Analogously to the construction of Suzuki and Vazirani, we construct representations GLm-type Double Affine Hecke Algebra at roots unity. These are graded weight spaces for X-variables parametrized by combinatorial objects call doubly periodic tableaux. We show that our exhaust all X-semisimple representations, direct sum is faithful. Jordan Vazirani rectangular DAHA can be interpreted in terms...

Today, mechanisms and mechanistic explanation are very popular in philosophy of science and are deemed a welcome alternative to laws of nature and deductive-nomological explanation. Starting from Mitchell’s pragmatic notion of laws, I cast doubt on their status as a genuine alternative. I argue that (1) all complex-systems mechanisms ontologically must rely on stable regularities, while (2) the...

We describe a general technique for expressing domain knowledge in constraint satisfaction problems, and using it to develop optimized parallel arc consistency algorithms for the solution of problems in the domain. The technique is applied to reduce the space complexity of the the massively parallel AC Chip algorithm. Results of the optimizations are shown for an object recognition domain in wh...

For a set D ⊂ Zn, the distance graph Pn(D) has Zn as its vertex set and the edges are between vertices i and j with |i − j| ∈ D. The circulant graph Cn(D) is defined analogously by considering operations modulo n. The minimum feedback vertex set problem consists in finding the smallest number of vertices to be removed in order to cut all cycles in the graph. This paper studies the minimum feedb...