The Perron-Frobenius Theorem for irreducible higher order tensors does not guarantee simplicity of the unique positive eigenvalue nor does it guarantee the unique positive eigenvalue is strictly larger than the modulus of any other eigenvalue. Irreducibility of a tensor in relation to a graph is studied. A higher order tensor is essentially positive if it takes the positive cone to its interior...

The soil water retention curve (SWRC) relates moisture to energy (matrix potential). calculation of the volumetrichumidity considers sample volume. In retractable soils, this volume varies according drying or wetting soil, which can result in errors calculated moisture. objective study is quantify variation soils and elaborate SWRC via traditional method, does not consider retraction, a second ...

The following case of the Determinantal Conjecture of Marcus and de Oliveira is established. Let A and C be hermitian n × n matrices with prescribed eigenvalues a1, . . . , an and c1, . . . , cn, respectively. Let κ be a non-real unimodular complex number, B = κC, bj = κcj for j = 1, . . . , n. Then det(A− B) ∈ co 8< : n Y j=1 (aj − bσ(j)); σ ∈ Sn 9= ; , where Sn denotes the group of all permut...

The notion of an essentially slant Toeplitz operator on the space L is introduced and some of the properties of the set ESTO(L), the set of all essentially slant Toeplitz operators on L, are investigated. In particular the conditions under which the product of two operators in ESTO(L) is in ESTO(L) are discussed. The notion is generalized to kth-order essentially slant Toeplitz operators. The n...

In this paper we address some of the most fundamental questions regarding the differentiability structure of locally Lipschitz functions defined on separable Banach spaces. For example, we examine the relationship between integrability, D-representability, and strict differentiability. In addition to this, we show that on any separable Banach space there is a significant family of locally Lipsc...

Consider a Hilbert space obtained as the completion of the polynomials C[z ] in m-variables for which the monomials are orthogonal. If the commuting weighted shifts defined by the coordinate functions are essentially normal, then the same is true for their restrictions to invariant subspaces spanned by monomials. This generalizes the result of Arveson [4] in which the Hilbert space is the m-shi...

In this paper I offer a defence of a Russellian analysis of the referential uses of incomplete (mis) descriptions, in a contextual setting. With regard to descriptions (introduction), I will support the former against the latter. In 1. I explain what I mean by “essentially” incomplete descriptions: incomplete descriptions are context dependent descriptions. In 2. I examine one of the best versi...