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Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
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A relation is a function if each input x is associated with exactly one output y. For example, the equation      y = 2x + 5 defines a function because every value of x yields a unique y. However, x = y² + 1 is not a function of x, since a single x-value, such as x = 2, corresponds to two possible y-values: y = 1 and y = -1.The vertical line test helps determine whether a graph represents a function. If a vertical line intersects a curve more than once, the curve fails the test and does not...
Kirchhoff's Rules01:21

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Gustav Kirchhoff (1824–1887) devised two rules known as Kirchhoff's rules to analyze complex circuits, which cannot be analyzed with series-parallel techniques. These rules can be used to analyze any circuit, simple or complex.
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Rules for Significant Figures01:44

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In any measurement, the precision of the measuring tool is an essential factor. An ordinary ruler, for example, can measure length to the closest millimeter; a caliper, on the other hand, can measure length to the nearest 0.01 mm. As a result, the caliper is a more precise measurement tool because it can measure extremely minute changes in length. The measurements will be more accurate if the measuring tool is more precise.
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Hückel's Rule Diagram of π MOs: Frost Circle01:08

Hückel's Rule Diagram of π MOs: Frost Circle

The Frost circle or the inscribed polygon method is a graphical method for determining the relative energies of π molecular orbitals (MOs) for planar, fully conjugated, and monocyclic compounds. This method was first described by A. A. Frost and Boris Musulin in 1953.
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Kirchoff's Rules: Application01:22

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Updated: Jul 4, 2026

Systematic Bronchoscopy: the Four Landmarks Approach
04:47

Systematic Bronchoscopy: the Four Landmarks Approach

Published on: June 23, 2023

The Four Rules.

Biren B Kamdar1,2,3

  • 1Division of Pulmonary, Critical Care, and Sleep Medicine, University of California, San Diego (UCSD), La Jolla, CA, USA.

The American Journal of Hospice & Palliative Care
|June 5, 2025
PubMed
Summary
This summary is machine-generated.

This essay shares a physician's memorable case on end-of-life care, offering a template for delivering bad news with clarity, honesty, and empathy. It emphasizes the importance of presence during critical patient moments.

Keywords:
bad newsbreaking bad newscardiopulmonary resuscitationdeathend-of-life carefamily meeting

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Area of Science:

  • Medical Education
  • Clinical Practice
  • End-of-Life Care

Background:

  • A physician reflects on a challenging case from internal medicine residency.
  • The essay was initially written for a hospital magazine on end-of-life care.

Purpose of the Study:

  • To share a timeless message on delivering bad news with empathy.
  • To provide a template for physicians on effective communication during end-of-life discussions.
  • To highlight the significance of physician presence and empathy in patient care.

Main Methods:

  • Personal reflection and narrative essay.
  • Sharing a case study from clinical experience.
  • Revisiting and republishing a previously written piece.

Main Results:

  • The essay serves as a template for clear, honest, and empathetic delivery of bad news.
  • It underscores the profound impact of a physician's presence and attentiveness.
  • The narrative highlights enduring lessons in end-of-life care communication.

Conclusions:

  • Physician presence and empathetic communication are crucial in end-of-life care.
  • Clear and honest delivery of bad news is a vital clinical skill.
  • Reflective practice can yield timeless lessons for medical professionals.