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Related Concept Videos

Weak Base Solutions03:21

Weak Base Solutions

25.3K
Some compounds produce hydroxide ions when dissolved by chemically reacting with water molecules. In all cases, these compounds react only partially and so are classified as weak bases. These types of compounds are also abundant in nature and important commodities in various technologies. For example, global production of the weak base ammonia is typically well over 100 metric tons annually, being widely used as an agricultural fertilizer, a raw material for chemical synthesis of other...
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Weak Acid Solutions04:02

Weak Acid Solutions

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Few compounds act as strong acids. A far greater number of compounds behave as weak acids and only partially react with water, leaving a large majority of dissolved molecules in their original form and generating a relatively small amount of hydronium ions. Weak acids are commonly encountered in nature, being the substances partly responsible for the tangy taste of citrus fruits, the stinging sensation of insect bites, and the unpleasant smells associated with body odor. A familiar example of a...
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Titration of a Weak Acid with a Weak Base01:08

Titration of a Weak Acid with a Weak Base

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Weak acids and bases do not undergo dissociation completely, and titrations between these two are rarely studied. When such studies are performed, say, for the titration of a weak acid with a weak base, the titration curve plots the change in pH as a function of the volume of base added. Take the titration of acetic acid with ammonia, for instance. During the titration, these two species form ammonium acetate and water, but the pH change is slow and gradual.
As a result, there is no simple...
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Titration Calculations: Weak Acid - Strong Base03:55

Titration Calculations: Weak Acid - Strong Base

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Calculating pH for Titration Solutions: Weak Acid/Strong Base
For the titration of 25.00 mL of 0.100 M CH3CO2H with 0.100 M NaOH, the reaction can be represented as:
49.3K
Survival Curves01:18

Survival Curves

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Survival curves are graphical representations that depict the survival experience of a population over time, offering an intuitive way to track the proportion of individuals who remain event-free at each time point. These curves are widely used in fields such as medicine, public health, and reliability engineering to visualize and compare survival probabilities across different groups or conditions.
The Kaplan-Meier estimator is the most common method for constructing survival curves. This...
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Survival Tree01:19

Survival Tree

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Survival trees are a non-parametric method used in survival analysis to model the relationship between a set of covariates and the time until an event of interest occurs, often referred to as the "time-to-event" or "survival time." This method is particularly useful when dealing with censored data, where the event has not occurred for some individuals by the end of the study period, or when the exact time of the event is unknown.
 Building a Survival Tree
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Survivable Stereotaxic Surgery in Rodents
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Survival and weak chaos.

Sean Nee1

  • 1The Braithwaite Group in: Department of Ecosystem Science and Management, The Pennsylvania State University, 410 Forest Resources Building, University Park, PA 16802, USA.

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|June 13, 2018
PubMed
Summary
This summary is machine-generated.

This study integrates chaotic dynamics into survival analysis, revealing how weak chaos explains infant mortality and sudden failures in biological and mechanical systems without external factors.

Keywords:
Pomeau–Manneville mapchaosinfant mortalitylife-history theoryreliability theorysurvival analysis

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Area of Science:

  • Interdisciplinary science
  • Dynamical systems theory
  • Reliability engineering

Background:

  • Classical survival analysis and reliability theory model unit functioning.
  • Chaotic dynamics offers new insights into system behavior and failure patterns.

Purpose of the Study:

  • To incorporate chaotic dynamics into classical survival analysis.
  • To explain phenomena like infant mortality and sudden failures using weak chaos theory.

Main Methods:

  • Applying dynamical systems theory to survival analysis.
  • Distinguishing between strong and weak chaos and their effects on survivorship curves.

Main Results:

  • Strong chaos generates Type II survivorship curves internally.
  • Weak chaos explains "infant mortality" (decreasing hazard) and sudden failures in normally functioning systems.
  • These phenomena are observed without external random forces or defects.

Conclusions:

  • Chaotic dynamics provides a unified framework for understanding diverse failure patterns.
  • Weak chaos explains "no-fault-found" failures, early miscarriages, and sudden cardiac events.
  • This approach enhances the predictive power of survival analysis in biology and engineering.