We here present the main conclusions and theorems from a first rigorous inquiry into linear algebra. Although some basic definitions and lemmas have been omitted so to keep this exposition decently short, all the main theorems necesary to prove and understand the spectral, or diagonalization, theorem are here presented. A special attention has been placed on making the proofs not only proofs of...

Let r ≥ 2 and c > 0. If G is a graph of order n and the largest eigenvalue of its adjacency matrix satisfies μ (G) ≥ (1− 1/r + c)n, then G contains a complete r-partite subgraph with r − 1 parts of size ⌊

A nonconvex problem of constrained optimization is analyzed in terms of its ordinary Lagrangian function. New sufficient conditions are obtained for the duality gap to vanish. Among them, the main condition is that the objective and constraint functions be the sums of convex functionals and nonconvex quadratic forms with certain specific spectral properties. The proofs are related to extensions...

In this paper, we develop Leray-Serre-type spectral sequences to compute the intersection homology of the regular neighborhood and deleted regular neighborhood of the bottom stratum of a stratified PL-pseudomanifold. The E2 terms of the spectral sequences are given by the homology of the bottom stratum with a local coefficient system whose stalks consist of the intersection homology modules of ...

9:25 Opening Address from Chair 9:30 Spectral mapping theorem and asymptotic behavior of quantum walks on infinite graphs Etsuo SEGAWA (Tohoku Univ., JAPAN) 10:10 Tea Break 10:20 Seidel matrices with precisely three distinct eigenvalues Gary GREAVES (Tohoku Univ., JAPAN) 11:00 Tea Break 11:10 On the characteristic of a multiple eigenvalue of an Hermitian matrix whose graph is a tree Kenji TOYON...

Soil salinity undergoes significant spatial and temporal variations; therefore, salinity mapping is difficult, expensive, and time consuming. However, researchers have mainly focused on arid soils (bare) and less attention has been paid to halophyte plants and their role as salinity indicators. Accordingly, this paper aimed to investigate the relationship between soil properties, such as electr...