A Sharp Inequality of Markov Type for Polynomials Associated with Laguerre Weight

AbstractThe best possible constant An in an inequality of Markov type [ddx(e−xpn(x))][0, ∞)⩽An‖e−xpn(x)‖[0, ∞), where ‖·‖[0, ∞) denotes the sup-norm on the half real line [0, ∞) and pn is an arbitrary polynomial of degree at most n, is determined in terms of the weighted Chebyshev polynomials associated with the Laguerre weight e−x on [0, ∞)

A study of the radiation-reaction on a point charge that moves along a constant applied electric field in an electromagnetic Bopp-Land\'e-Thomas-Podolsky vacuum

The relativistic problem of motion of a classical electrical point charge that has been placed between the plates of a charged capacitor and then released from rest is well-posed in Bopp-Land\'e-Thomas-Podolsky (BLTP) electrodynamics. That theory introduces a single new parameter, Bopp's $\varkappa$, a reciprocal length. The present article concerns the small-$\varkappa$ regime. Radiation-reaction effects on the motion are shown to appear at order $\varkappa^3$. It is found that in the initial phase the motion is accurately accounted for by test particle theory, with the inertia determined by the bare mass of the particle. Subsequently, radiation-reaction effects cause substantial deviations from the test particle motion.Comment: 13 pages, 1 improved figure; invited paper in remembrance of Detlef Duerr; referee's comments have been implemented in this mildly revised version; accepted for publication in a memorial collectio

Precalculus

From the preface, These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and in particular, many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use. An introduction to the TI-84 calculator together with the most common applications needed for this course is provided in appendix A. In the future we may expand on this by providing introductions to other calculators or computer algebra systems

Nonperturbative calculation of Born-Infeld effects on the Schroedinger spectrum of the hydrogen atom

We present the first nonperturbative numerical calculations of the nonrelativistic hydrogen spectrum as predicted by first-quantized electrodynamics with nonlinear Maxwell-Born-Infeld field equations. We also show rigorous upper and lower bounds on the ground state. When judged against empirical data our results significantly restrict the range of viable values of the new electromagnetic constant which is introduced by the Born-Infeld theory. We assess Born's own proposal for the value of his constant.Comment: 4p., 2 figs, 1 table; submitted for publicatio

Arithmetic | Algebra

Arithmetic | Algebra provides a customized open-source textbook for the math developmental students at New York City College of Technology. The book consists of short chapters, addressing essential concepts necessary to successfully proceed to credit-level math courses. Each chapter provides several solved examples and one unsolved “Exit Problem”. Each chapter is also supplemented by its own WeBWork online homework assignment. The book can be used in conjunction with WeBWork for homework (online) or with the Arithmetic | Algebra Homework handbook (traditional). The content in the book, WeBWork and the homework handbook are also aligned to prepare students for the CUNY Elementary Algebra Final Exam (CEAFE)

Effects of a high-dose 24-h infusion of tranexamic acid on death and thromboembolic events in patients with acute gastrointestinal bleeding (HALT-IT): an international randomised, double-blind, placebo-controlled trial

Background: Tranexamic acid reduces surgical bleeding and reduces death due to bleeding in patients with trauma. Meta-analyses of small trials show that tranexamic acid might decrease deaths from gastrointestinal bleeding. We aimed to assess the effects of tranexamic acid in patients with gastrointestinal bleeding. Methods: We did an international, multicentre, randomised, placebo-controlled trial in 164 hospitals in 15 countries. Patients were enrolled if the responsible clinician was uncertain whether to use tranexamic acid, were aged above the minimum age considered an adult in their country (either aged 16 years and older or aged 18 years and older), and had significant (defined as at risk of bleeding to death) upper or lower gastrointestinal bleeding. Patients were randomly assigned by selection of a numbered treatment pack from a box containing eight packs that were identical apart from the pack number. Patients received either a loading dose of 1 g tranexamic acid, which was added to 100 mL infusion bag of 0·9% sodium chloride and infused by slow intravenous injection over 10 min, followed by a maintenance dose of 3 g tranexamic acid added to 1 L of any isotonic intravenous solution and infused at 125 mg/h for 24 h, or placebo (sodium chloride 0·9%). Patients, caregivers, and those assessing outcomes were masked to allocation. The primary outcome was death due to bleeding within 5 days of randomisation; analysis excluded patients who received neither dose of the allocated treatment and those for whom outcome data on death were unavailable. This trial was registered with Current Controlled Trials, ISRCTN11225767, and ClinicalTrials.gov, NCT01658124. Findings: Between July 4, 2013, and June 21, 2019, we randomly allocated 12 009 patients to receive tranexamic acid (5994, 49·9%) or matching placebo (6015, 50·1%), of whom 11 952 (99·5%) received the first dose of the allocated treatment. Death due to bleeding within 5 days of randomisation occurred in 222 (4%) of 5956 patients in the tranexamic acid group and in 226 (4%) of 5981 patients in the placebo group (risk ratio [RR] 0·99, 95% CI 0·82–1·18). Arterial thromboembolic events (myocardial infarction or stroke) were similar in the tranexamic acid group and placebo group (42 [0·7%] of 5952 vs 46 [0·8%] of 5977; 0·92; 0·60 to 1·39). Venous thromboembolic events (deep vein thrombosis or pulmonary embolism) were higher in tranexamic acid group than in the placebo group (48 [0·8%] of 5952 vs 26 [0·4%] of 5977; RR 1·85; 95% CI 1·15 to 2·98). Interpretation: We found that tranexamic acid did not reduce death from gastrointestinal bleeding. On the basis of our results, tranexamic acid should not be used for the treatment of gastrointestinal bleeding outside the context of a randomised trial

A journey into convexity

Convexity is an important concept in optimization of functionals, and therefore in economics, in operation research, in physics, etc.. In this thesis we study this concept and some of the topics where convexity is applied. We study the geometry of convex sets, applications and properties of convex functions, and related inequalities. We also study integrability theorems of Askey, Leindler, Heywood, and Askey and Karlin and generalize some of the theorems of Askey and Karlin using Jensen\u27s inequality. Our result shows inclusion between Euler and Borel sequence spaces