in this paper we study the impact of minkowski metric matrix on a projection in theminkowski space m along with their basic algebraic and geometric properties.the relationbetween the m-projections and the minkowski inverse of a matrix a in the minkowski spacemis derived. in the remaining portion commutativity of minkowski inverse in minkowski spacem is analyzed in terms of m-projections as an a...

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. Some basic operations on functions such as the inverse and composition are applicable to binary relations as well. Depending on the domain or range or both are fuzzy value fuzzy set, i...

In this paper we numerically investigate the effect of relative phase on thestability of temporal bright solitons in a Nano PT- Symmetric nonlinear directionalcoupler (NLDC) by considering gain in bar and loss in cross. We also study the effect ofrelative phase on the output perturbed bright solitons energies, in the range of   0 to 180 . By using perturbation theory three eigenfunctions an...

The symmetric-range accuracy A of a sampler is defined as the fractional range, symmetric about the true concentration, that includes a specified proportion of sampler measurements. In this article, we give an explicit expression for A assuming that the sampler measurements follow a normal distribution. We propose confidence limits for A based on the concept of a 'generalized confidence interva...

We prove that the range of a symmetric matrix over GF (2) always contains its diagonal. This is best possible in several ways, for example GF (2) cannot be replaced by any other field.

For each norm v on <en, we define a numerical range Z., which is symmetric in the sense that Z. =Z"D, where vD is the dual norm. We prove that, for aE <enn, Z.(a) contains the classical field of values V(a). In the special case that v is the lcnorm, Z.(a) is contained in a set G(a) of Gershgorin type defined by C. R. Johnson. When a is in the complex linear span of both the Hennitians and the v...

The concept of range symmetric matrix is introduced in Minkowski space m. Equivalent conditions for a matrix to be range symmetric are determined. The existence of the Minkowski inverse of a range symmetric matrix in m is discussed.

We study the range S(A) := {xT Ay : x, y are orthonormal in Rn}, where A is an n×n complex skew symmetric matrix. It is a compact convex set. Power inequality s(A) ≤ s(A), k ∈ N, for the radius s(A) := maxξ∈S(A) |ξ| is proved. When n = 3, 4, 5, 6, relations between S(A) and the classical numerical range and the k-numerical range are given. Axiomatic characterization of S(A) is given. Sharp poin...