A New Clark-Type Layered Double Hydroxides-Enzyme Biosensor for H2O2 Determination in Highly Diluted Real Matrices: Milk and Cosmetics

A new catalase amperometric biosensor for hydroperoxides detection has been built as part of research aimed at the development of biosensors based on layered double hydroxides (LDH) used as support for enzyme immobilization. The fabricated device differs from those developed so far, usually based on an LDH enzyme nanocomposite adsorbed on a glassy carbon (GC) electrode and cross-linked by glutaraldehyde, since it is based on an amperometric gas diffusion electrode (Clark type) instead of a GC electrode. The new biosensor, which still uses LDH synthesized by us and catalase enzyme, is robust and compact, shows a lower LOD (limit of detection) value and a linearity range shifted at lower concentrations than direct amperometric GC biosensor, but above all, it is not affected by turbidity or emulsions, or by the presence of possible soluble species, which are reduced to the cathode at the same redox potential. This made it possible to carry out accurate and efficient determination of H2O2 even in complex or cloudy real matrices, also containing very low concentrations of hydrogen peroxide, such as milk and cosmetic products, i.e., matrices that would have been impossible to analyze otherwise, using conventional biosensors based on a GC–LDH enzyme. An inaccuracy ≤7.7% for cosmetic samples and ≤8.0% for milk samples and a precision between 0.7 and 1.5 (as RSD%), according to cosmetic or milk samples analyzed, were achieved.

When Does a Dual Matrix Have a Dual Generalized Inverse?

This paper deals with the existence of various types of dual generalized inverses of dual matrices. New and foundational results on the necessary and sufficient conditions for various types of dual generalized inverses to exist are obtained. It is shown that unlike real matrices, dual matrices may not have {1}-dual generalized inverses. A necessary and sufficient condition for a dual matrix to have a {1}-dual generalized inverse is obtained. It is shown that a dual matrix always has a {1}-, {1,3}-, {1,4}-, {1,2,3}-, {1,2,4}-dual generalized inverse if and only if it has a {1}-dual generalized inverse and that every dual matrix has a {2}- and a {2,4}-dual generalized inverse. Explicit expressions, which have not been reported to date in the literature, for all these dual inverses are provided. It is shown that the Moore–Penrose dual generalized inverse of a dual matrix exists if and only if the dual matrix has a {1}-dual generalized inverse; an explicit expression for this dual inverse, when it exists, is obtained irrespective of the rank of its real part. Explicit expressions for the Moore–Penrose dual inverse of a dual matrix, in terms of {1}-dual generalized inverses of products, are also obtained. Several new results related to the determination of dual Moore-Penrose inverses using less restrictive dual inverses are also provided.

An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices

A proof of the statement per(A ∘ B) ≤ per(A)per(B) is given for 4 × 4 positive semidefinite real matrices. The proof uses only elementary linear algebra and a rather lengthy series of simple inequalities.

Preservers of partial orders on the set of all variance-covariance matrices

Let H+n(R) be the cone of all positive semidefinite n x n real matrices. Two of the best known partial orders that were mostly studied on subsets of square complex matrices are the L?wner and the minus partial orders. Motivated by applications in statistics we study these partial orders on H+ n (R). We describe the form of all surjective maps on H+ n (R), n > 1, that preserve the L?wner partial order in both directions. We present an equivalent definition of the minus partial order on H+ n (R) and also characterize all surjective, additive maps on H+ n (R), n ? 3, that preserve the minus partial order in both directions.

The minimality of determinantal varieties

The determinantal variety {\Sigma_{pq}} is defined to be the set of all {p\times q} real matrices with {p\geq q} whose ranks are strictly smaller than q. It is proved that {\Sigma_{pq}} is a minimal cone in {\mathbb{R}^{pq}} and all its strata are regular minimal submanifolds.

Ninety-Six Distinct Real Matrices for Representing a Quaternion Number

In this paper, we investigate on the number of all possible real matrices representing a quaternion number as three 4 × 4 skew-symmetric matrices plus the identity matrix of order 4, and how to determine these matrices. We establish that there are 96 distinct real matrices having this property, and by matrix row operations, we obtain these matrices.

Rational Criteria for Diagonalizability of Real Matrices

The purpose of this note is to obtain rational criteria for diagonalizability of real matrices through the analysis of the moment and Gram matrices associated to a given real matrix. These concepts were introduced by Horn and Lopatin in [R.A. Horn and A.K. Lopatin. The moment and Gram matrices, distinct eigenvalues and zeroes, and rational criteria for diagonalizability. Linear Algebra and its Applications, 299:153-163, 1999] for complex matrices. However, when the matrix is real, it is possible to combine their results with the Borchardt-Jacobi Theorem, in order to get new and noteworthy rational criteria.