Acute kidney injury (AKI) is a common complication after cardiac surgery. Recent studies have revealed emerging associations between the magnitude of acute glycemic fluctuations and intensive care unit (ICU) mortality rates. However, the effect of acute glycemic fluctuations on the development of postoperative AKI remains unclear. Thus, we aim to investigate the effect of the magnitude of acute...

Isaacs has defined a character to be super monomial if every primitive character inducing it is linear. Isaacs has conjectured that if G is an M -group with odd order, then every irreducible character is super monomial. We prove that the conjecture is true if G is an M -group of odd order where every irreducible character is a {p}-lift for some prime p. We say that a group where irreducible cha...

We establish character sum bounds of the form ∣∣∣∣ ∑ a≤x≤a+H b≤y≤b+H χ(x + ky) ∣∣∣∣ < p−τH2, where χ is a nontrivial character (mod p), p 1 4 +ε < H < p, and |a|, |b| < p H. As an application, we obtain that given k ∈ Z\{0}, x + k is a quadratic non-residue (mod p) for some 1 ≤ x < p 1 2e. Introduction. Let k be a nonzero integer. Let p be a large prime and let H ≤ p. We are interested in the c...

A Brauer character of a finite group may be lifted to an ordinary character if it lies in a block whose defect groups are contained in a normal p-solvable subgroup. By the Fong-Swan theorem [2, Theorem 72.1], an irreducible Brauer character of a finite p-solvable group G may be lifted to an ordinary (complex) character of G. In other words, every Brauer character is the restriction of some ...

While we were graduate students, Marty Isaacs and I worked together on the character theory of finite groups, studying in particular the character degrees of finite p-groups. Somewhat later, my interests turned to ring theory and infinite group theory. On the other hand, Marty continued with character theory and soon became a leader in the field. Indeed, he has had a superb career as a research...