Computing the spectral decomposition of a normal matrix is among the most frequent tasks to numerical mathematics. A vast range of methods are employed to do so, but all of them suffer from instabilities when applied to degenerate matrices, i.e., those having multiple eigenvalues. We investigate the spectral representation’s effectivity properties on the sound formal basis of computable analysi...

using the riemann-liouville fractional differintegral operator, the lie theory is reformulated. the fractional poisson bracket over the fractional phase space as 3n state vector is defined to be the fractional lie derivative. its properties are outlined and proved. a theorem for the canonicity of the transformation using the exponential operator is proved. the conservation of its generator is p...

We prove a substantial extension of an inverse spectral theorem of Ambarzumyan, and show that it can be applied to arbitrary compact Riemannian manifolds, compact quantum graphs and finite combinatorial graphs, subject to the imposition of Neumann (or Kirchhoff) boundary conditions.

This paper is dedicated to present a proof of the Spectral Theorem, and to discuss how the Spectral Theorem is applied in combinatorics and graph theory. In this paper, we also give insights into the ways in which this theorem unveils some mysteries in graph theory, such as expander graphs and graph coloring.

Let μ (G) be the largest eigenvalue of a graph G and Tr (n) be the r-partite Turán graph of order n. We prove that if G is a graph of order n with μ (G) > μ (Tr (n)) , then G contains various large supergraphs of the complete graph of order r + 1, e.g., the complete r-partite graph with all parts of size log n with an edge added to the first part. We also give corresponding stability results.

This paper studies the spectrum of a multi-dimensional split-step quantum walk with defect that cannot be analyzed in previous papers by Fuda et al. (Quantum Inf Process 18:203–226, 2017; J Math Phys 59:082201, 2018). To this end, we have developed new technique which allow us to use spectral mapping theorem for one-defect model. We also derive time-averaged limit measure one-dimensional case a...

rice cultivated areas and yield information is indispensable for sustainable management and economic policy making for this strategic food crop. introduction of high spectral and special resolution satellite data has enabled production of such information in a timely and accurate manner. knowledge of the spectral reflectance of various land covers is a prerequisite for their identification and ...

a consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable hilbert space. it is proved, through a kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the hilbert space. as an application, this will naturally accomplish the work of kante...