Max-plus analogues of linear spaces, convex sets, and polyhedra have appeared in several works. We survey their main geometrical properties, including max-plus versions of the separation theorem, existence of linear and non-linear projectors, max-plus analogues of the Minkowski-Weyl theorem, and the characterization of the analogues of “simplicial” cones in terms of distributive lattices.

Some Lie algebra analogues of Schur's theorem and its converses are presented. As a result, it is shown that for a capable Lie algebra L we always have dim L=Z(L) 2(dim(L2))2. We also give give some examples sup- porting our results.

The generalization of p-frame in Banach spaces is considered in this paper. The concepts of an $tilde{X}$-frame and a system conjugate to $tilde{X}$-frame were introduced. Analogues of the results on the existence of conjugate system were obtained. The stability of $tilde{X}$-frame having a conjugate system is studied.

In this paper, we prove a general fixed point theorem in $textrm{S}$-metric spaces for maps satisfying an implicit relation on complete metric spaces. As applications, we get many analogues of fixed point theorems in metric spaces for $textrm{S}$-metric spaces.

Objective: Cancer has risen as the main cause of diseases with the highest rate of mortality in the world. Drugs used in cancer, usually demonstrate side effects on normal tissues. On the other hand, anticancer small peptides, effective on target tissues, should be safe on healthy organs, as being naturally originated compounds. In addition, they may have good pharmacokinetic properties. carnos...

Received (received date) Revised (revised date) Quantum relative entropy D(ρσ) def = Tr ρ(log ρ − log σ) plays an important role in quantum information and related fields. However, there are many quantum analogues of relative entropy. In this paper, we characterize these analogues from information geometrical viewpoint. We also consider the naturalness of quantum relative entropy among these an...

A facile synthesis of a series of benzene ring acylated analogues of harmaline has been achieved by Friedel-Crafts acylation under solvent-free conditions at room temperature using acyl halides/acid anhydrides and AlCl3. The reaction afforded 10- and 12-acyl analogues of harmaline in good yield, along with minor quantities of N-acyl-tryptamines and 8-acyl analogues of N-acyltryptamines.

Bile salts are essential for phospholipid secretion into the bile. To study the relevance of the structure of phospholipids for their interaction with bile salts, we used spin-labeled or fluorescent phospholipid analogues of different head groups and acyl chain length. Those analogues form micelles in aqueous suspension. Their solubilization by bile salts resulting in the formation of mixed mic...

Analogues of Texas red incorporating the heavy chalcogens S, Se, and Te atoms in the xanthylium core were prepared from the addition of aryl Grignard reagents to appropriate chalcogenoxanthone precursors. The xanthones were prepared via directed metalation of amide precursors, addition of dichalcogenide electrophiles, and electrophilic cyclization of the resulting chalcogenides with phosphorus ...