Synchronized and controlled release of metformin hydrochloride/glipizide from elementary osmotic delivery

The combination of metformin hydrochloride (MTF) and glipizide (GLZ) is second-line medication for diabetes mellitus type 2 (DMT2). In the present study, elementary osmotic pump(EOP)tablet is designed to deliver the combination of MTF and GLZ in a sustained and synchronized manner. By analyzing different variables of the formulation, sodium hydrogen carbonate is introduced as pH modifier to improve the release of GLZ, while ethyl cellulose acts as release retardant to reduce the burst release phase of MTF. A two factor, three level face-centered central composite design (FCCD) is applied to investigate the impact of different factors on drug release profile. Compared with conventional tablets, the elementary osmotic pump (EOP) tablet demonstrates a controlled release behavior with relative bioavailability of 99.2% for MTF and 99.3% for GLZ. Data also shows EOP tablet is able to release MTF and GLZ in a synchronized and sustained manner both in vitro and in vivo

Spectrally isometric elementary operators

We present criteria for unital elementary operators (of small length) on unital semisimple Banach algebras to be spectral isometries. The surjective ones among them turn out to be algebra automorphisms.

More elementary operators that are spectrally bounded

We discuss some necessary and some sufficient conditions for an elementary operator x↦∑ⁿ_i=1a_ixb_i on a Banach algebra A to be spectrally bounded. In the case of length three, we obtain a complete characterisation when A acts irreducibly on a Banach space of dimension greater than three.

Locally quasi-nilpotent elementary operators

Let A be a unital dense algebra of linear mappings on a complex vector space X. Let φ = Σⁿ _i=1 M_ai,_bi be a locally quasi-nilpotent elementary operator of length n on A. We show that, if {a1, . . . , an} is locally linearly independent, then the local dimension of V (φ) = span{b_ia_j : 1 ≤ i, j ≤ n} is at most n(n−1) 2 . If ldim V (φ) = n(n−1) 2 , then there exists a representation of φ as φ = Σⁿ _i=1 M_ui,_vi with v_iu_j = 0 for i ≥ j. Moreover, we give a complete characterization of locally quasinilpotent elementary operators of length 3.

Elementary operators-still not elementary?

Properties of elementary operators, that is, finite sums of two-sided multiplications on a Banach algebra, have been studied under a vast variety of aspects by numerous authors. In this paper we review recent advances in a new direction that seems not to have been explored before: the question when an elementary operator is spectrally bounded or spectrally isometric. As with other investigations, a number of subtleties occur which show that elementary operators are still not elementary to handle.