Abstract We derive a sharp lower bound for the scalar curvature of non-flat and non-compact expanding gradient Ricci soliton provided that is non-negative potential function proper. Upper expander with nonpositive will also be given. Furthermore, we provide sufficient condition being non-negative. Curvature estimates solitons in dimensions three four established. As an application, prove gap th...

Understanding the effects of processing pulses is required for their effective incorporation into livestock feed. To determine impact processing, Canadian peas, lentils, chickpeas, and faba beans, plus soybean meal (SBM; as a comparison), were ground fine coarse products pelleted at three different temperatures (60–65, 70–75, 80–85 °C). Grinding increased crude protein content in all ( P < 0...

In this paper, we consider a structural and geometric property of graphs, namely the presence large expanders. The problem finding such structures was first considered by Krivelevich [SIAM J. Disc. Math. 32 1 (2018)]. Here, show that induced subgraph is an expander can be reduced to simpler topological minor expander. Our proof constructive, which helpful in algorithmic setting.
 We also e...

This protocol describes how to prepare rat liver rough microsomes that contain undegraded membrane-bound polysomes and can function very well in an in vitro translation system. It uses endogenous ribonuclease inhibitor in all steps, avoiding pelleting rough microsomes in all steps and sacrificing good recovery.

We show how to compute O( √ logn)-approximations to Sparsest Cut and Balanced Separator problems in Õ(n) time, thus improving upon the recent algorithm of Arora, Rao and Vazirani (2004). Their algorithm uses semidefinite programming and required Õ(n) time. Our algorithm relies on efficiently finding expander flows in the graph and does not solve semidefinite programs. The existence of expander ...