We prove that every reversible Markov semigroup which satisfies a Poincaré inequality matrix-valued for Hermitian d×d matrix valued functions, with the same constant. This generalizes recent results [ABY19, Kat20] establishing such inequalities specific semigroups and consequently yields new concentration inequalities. The short proof follows from spectral theory of generators.

The advent of rare earth elements (REEs) with optoelectronic properties has shifted the technology paradigm from digital to a smart and hybrid world. Their substantial uses also resulted in large piling up e-waste. Therefore, e-waste is now lucrative recycling target for recovery such critical raw materials. often challenged by dilute metal concentration, complex composition, difficult chemical...

A band is a semigroup consisting of idempotents. It is proved that for any field K and any band S with finitely many components, the semigroup algebra K[S] can be embedded in upper triangular matrices over a commutative K-algebra. The proof of a theorem of Malcev [4, Theorem 10] on embeddability of algebras into matrix algebras over a field is corrected and it is proved that if S = F ∪ E is a b...

−→ (Ak, φk) and the operator algebras A = lim −→ (Ak, φk) obtained as limits of direct sums of matrix algebras over E with respect to star-extendible homomorphisms. The invariants in the algebraic case consist of an additive semigroup, with scale, which is a right module for the semiring VE = Homu(E⊗K, E⊗K) of unitary equivalence classes of star-extendible homomorphisms. This semigroup is refer...

A new chelating resin, silica gel loaded with 1-phenyl-3-methyl-4-benzoylpyrazol-5-one (PMBP), was prepared and used for the preconcentration of trace amounts of rare earth elements (REEs) in water samples prior to their determination by inductively coupled plasma atomic emission spectrometry (ICP-AES). REEs (La, Eu, Yb and Y) were quantitatively retained on the column packed with modified sili...

We introduce 2-partitionable clutters as the simplest case of the class of kpartitionable clutters and study some of their combinatorial properties. In particular, we study properties of the rank of the incidence matrix of these clutters and properties of their minors. A well known conjecture of Conforti and Cornuéjols [1, 2] states: That all the clutters with the packing property have the max-...

Stochastic and bistochastic matrices providing positive maps for spin states (for qudits) are shown to form semigroups with dense intersection with the Lie groups IGL(n, R) and GL(n, R) respectively. The density matrix of a qudit state is shown to be described by a spin tomogram determined by an orbit of the bistochastic semigroup acting on a simplex. A class of positive maps acting transitivel...

Let I be a monomial ideal in a polynomial ring over a field k. If the Rees cone of I is quasi-ideal, we express the normalization of the Rees algebra of I in terms of an Ehrhart ring. We introduce the basis Rees cone of a matroid and study their facets. Then an application to Rees algebras is presented.

Proteins are considered the workhorses in the cellular machinery. They are often organized in a highly ordered conformation in the crowded cellular environment. These conformations display characteristic dynamics over a range of time scales. An emerging consensus is that protein function is critically dependent on its dynamics. The subtle interplay between structure and dynamics is a hallmark o...