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 ...

This work was presented in part at The Annual Meeting of the American Federation for Clinical Research, Atlantic City, N. J., May 1976. (1) The present address for Dr. Kolhouse and Dr. Allen is: Division of Hematology, University of Colorado Medical Center, Denver, Colo. 80220. Received for publication 11 May 1977 and in revisedform 3 August 1977. with native Cbl when it is present in plasma in...

PURPOSE To investigate the effects of topical prostaglandin analogue drugs on the differentiation of adipocytes. METHODS Differentiation of 3T3-L1 preadipocytes was induced with isobutylmethylxanthine, dexamethasone, and insulin. 3T3-L1 cells were exposed to 0.008, 0.08, 0.2 µM of latanoprost and travoprost. Reverse transcription polymerase chain reaction for mRNA expression of lipoprotein li...