Events in a Non-Commutative Space-Time

We treat the events determined by a quantum physical state in a noncommutative space-time, generalizing the analogous treatment in the usual Minkowski space-time based on positive-operator-valued measures (POVMs). We consider in detail the model proposed by Snyder in 1947 and calculate the POVMs defined on the real line that describe the measurement of a single coordinate. The approximate joint measurement of all the four space-time coordinates is described in terms of a generalized Wigner function (GWF). We derive lower bounds for the dispersion of the coordinate observables and discuss the covariance of the model under the Poincare' group. The unusual transformation law of the coordinates under space-time translations is interpreted as a failure of the absolute character of the concept of space-time coincidence. The model shows that a minimal length is compatible with Lorents covariance.Comment: 13 pages, revtex. Introductory part shortened and some arguments made more clea

Empagliflozin cardiovascular and renal effectiveness and safety compared to dipeptidyl peptidase-4 inhibitors across 11 countries in Europe and Asia : Results from the EMPagliflozin compaRative effectIveness and SafEty (EMPRISE) study

Background: Continued expansion of indications for sodium-glucose cotransporter-2 inhibitors increases importance of evaluating cardiovascular and kidney efficacy and safety of empagliflozin in patients with type 2 diabetes compared to similar therapies. Methods: The EMPRISE Europe and Asia study is a non-interventional cohort study using data from 2014 -2019 in seven European (Denmark, Finland, Germany, Norway, Spain, Sweden, United Kingdom) and four Asian (Israel, Japan, South Korea, Taiwan) countries. Patients with type 2 diabetes initiating empagliflozin were 1:1 propensity score matched to patients initiating dipeptidyl peptidase-4 inhibitors. Primary end-points included hospitalization for heart failure, all-cause mortality, myocardial infarction and stroke. Other cardiovascular, renal, and safety outcomes were examined.Findings: Among 83,946 matched patient pairs, (0.7 years overall mean follow-up time), initiation of empagli-flozin was associated with lower risk of hospitalization for heart failure compared to dipeptidyl peptidase-4 inhibitors (Hazard Ratio 0.70; 95% CI 0.60 to 0.83). Risks of all-cause mortality (0.55; 0.48 to 0.63), stroke (0. 82; 0.71 to 0.96), and end-stage renal disease (0.43; 0.30 to 0.63) were lower and risk for myocardial infarc-tion, bone fracture, severe hypoglycemia, and lower-limb amputation were similar between initiators of empagliflozin and dipeptidyl peptidase-4 inhibitors. Initiation of empagliflozin was associated with higher risk for diabetic ketoacidosis (1.97; 1.28 to 3.03) compared to dipeptidyl peptidase-4 inhibitors. Results were consistent across continents and regions.Interpretation: Results from this EMPRISE Europe and Asia study complements previous clinical trials and real-world studies by providing further evidence of the beneficial cardiorenal effects and overall safety of empagliflozin compared to dipeptidyl peptidase-4 inhibitors.(c) 2023 The Authors. Published by Elsevier Masson SAS. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)Peer reviewe

Deep Eutectic Solvents (DESs) and their applications [forthcoming]

Deep Eutectic Solvents (DESs) and Their Application

Maxima of increments of partial sums for certain subexponential distributions

We consider partial sums of i.i.d. random variables with moments E(X1)=0, E(X12)=[sigma]2 and and show thatwith some explicit function [phi](·). A related result for random variables with exponentially thin tails has recently been shown by Steinebach, extending a result given by Shao.Partial sums Independent random variables Maxima of increments Limit theorem Subexponential distributions a.s. convergence

Refined Baum-Katz laws for weighted sums of iid random variables

We consider weighted sums with iid random variables (Xn) and compare the tail probabilities of these sums with the moment conditions on X1. If X1 is in the domain of attraction of a stable law then refined Baum-Katz laws generalizing results of Heyde, Gut and other authors are presented. Some special examples of weights pnk originating from summability are discussed.Tail probabilities Baum-Katz laws Weighted means of iid random variables