The appearance of Marshall and Olkin’s 1979 book on inequalities with special emphasis on majorization generated a surge of interest in potential applications of majorization and Schur convexity in a broad spectrum of fields. After 25 years this continues to be the case. The present article presents a sampling of the diverse areas in which majorization has been found to be useful in the past 25...

Given an approximate invariant subspace we discuss the effectiveness of majorization bounds for assessing the accuracy of the resulting Rayleigh-Ritz approximations to eigenvalues of Hermitian matrices. We derive a slightly stronger result than previously for the approximation of k extreme eigenvalues, and examine some advantages of these majorization bounds compared with classical bounds. From...

In this paper, we obtain extensions of majorization type results and extensions of weighted Favard’s and Berwald’s inequality. We prove positive semi-definiteness of matrices generated by differences deduced from majorization type results and differences deduced from weighted Favard’s and Berwald’s inequality. This implies a surprising property of exponentially convexity and log-convexity of th...

A new notion of coneigenvalue was introduced by Ikramov in [Kh.D. Ikramov. On pseudo-eigenvalues and singular numbers of a complex square matrix (in Russian). Zap. Nauchn. Semin. POMI, 334:111–120, 2006.]. This paper presents some majorization inequalities for coneigenvalues, which extend some classical majorization relations for eigenvalues and singular values, and may serve as a basis for fur...

AIM We examined the effect of proinflammatory and anti-inflammatory interleukins on jejunal nutrient transport and expression of the sodium-glucose linked cotransporter (SGLT-1). METHODS 3-O-methyl glucose and L-proline transport rates were examined in New Zealand White rabbit stripped, short circuited jejunal tissue. The effects of the proinflammatory cytokines interleukin (IL)-1alpha, IL-6,...

Recent studies demonstrated that endoplasmic reticulum (ER) stress regulates glucose homeostasis and that ER stress preconditioning which induces an adaptive, protective unfolded protein response (UPR) offers cytoprotection against nephrotoxins. Thus the aim of the present study was to use renal proximal tubule cells (PTCs) to further elucidate the link between the BSA-induced ER stress and alp...

Na(+)-glucose cotransporter 1 (SGLT1)-mediated glucose uptake leads to activation of Na(+)-H(+) exchanger 3 (NHE3) in the intestine by a process that is not dependent on glucose metabolism. This coactivation may be important for postprandial nutrient uptake. However, it remains to be determined whether SGLT-mediated glucose uptake regulates NHE3-mediated NaHCO3 reabsorption in the renal proxima...

INTRODUCTION Sodium-glucose co-transporter 2 inhibitors (SGLT-2i) increase urinary glucose excretion through a reduced renal glucose reabsorption. We plan to perform a systematic review of SGLT-2i for treatment of type 2 diabetes. METHODS AND ANALYSIS A systematic review with meta-analyses of randomised clinical trials on SGLT-2i versus placebo, other oral glucose lowering drugs or insulin fo...

Accustomed to managing diabetes with agents that mostly act by modulating the secretion and actions of insulin, with the advent of sodium-glucose linked transporter-2 (SGLT-2) inhibitors, physicians are now aware that the kidney also needs to be considered in the spectrum of action of anti-hyperglycaemic agents. Though familiar with the need for dose adjustment when prescribing many of our curr...

We are reporting a timely case of atypical euglycemic diabetic ketoacidosis in a type 1 diabetic patient treated with sodium-glucose cotransporter-2 (SGLT-2) inhibitor canagliflozin. The clinical history, physical examination findings and laboratory values are described. Other causes of acidosis such as salicylate toxicity or alcohol intoxication were excluded. Ketoacidosis resolved after incre...