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Related Concept Videos

Sums of Power01:22

Sums of Power

172
In definite integration, Riemann sums approximate the area under a curve by dividing it into subintervals and summing the areas of rectangles. When these approximations follow predictable numerical patterns, such as arithmetic or polynomial sequences, sum formulas offer a more efficient and accurate way to compute the result. In particular, the sum of consecutive integers, squares, and cubes plays an essential role in simplifying these calculations, especially when dealing with uniform...
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Midpoint Rule01:20

Midpoint Rule

185
Approximating areas under curved boundaries is a common problem in applied mathematics, particularly when an exact calculation is difficult or impractical. One effective numerical method for this purpose is the Midpoint Rule, which provides an estimate of the area under a curve by using rectangular approximations over a specified interval.Description of the Midpoint RuleThe Midpoint Rule begins by dividing the given interval into a number of equal subintervals. For each subinterval, the...
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Area Problem01:26

Area Problem

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Determining the area of a region with straight edges is straightforward, as geometric formulas for rectangles, triangles, and polygons can be applied directly. However, traditional geometric methods are insufficient when a region has a curved boundary, such as the area under a function.fromThe area problem involves finding a systematic way to measure such regions. One approach to solving this problem is through approximation. Instead of attempting to compute the area exactly at the outset, the...
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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

397
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
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Sum and Difference OpAmps01:22

Sum and Difference OpAmps

1.5K
Operational amplifiers (op-amps) are versatile devices that extend beyond amplification. In this context, two specific op-amp configurations are explored: the summing and difference amplifiers.
A summing amplifier, or an adder, utilizes an op-amp to merge multiple input signals into a single output signal. When audio signals are introduced into its input channels, the input resistors initiate currents that traverse feedback resistors, resulting in an output voltage. Applying Kirchhoff's current...
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Method of Superposition01:20

Method of Superposition

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The method of superposition is a crucial technique in structural engineering, used to analyze the effect of multiple loads on beams. This approach involves calculating the deflection and slope for each load on a beam separately, and then summing these effects to determine the overall impact. It is applicable only when the beam material remains within its elastic limit, ensuring that deformations are linearly elastic.
When applying the method of superposition, each type of load—whether...
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Related Experiment Video

Updated: Mar 28, 2026

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Development of the modified sum-peak method and its application.

Y Ogata1, H Miyahara2, M Ishihara3

  • 1Radioisotope Research Center, Nagoya University, Nagoya, Japan.

Applied Radiation and Isotopes : Including Data, Instrumentation and Methods for Use in Agriculture, Industry and Medicine
|December 22, 2015
PubMed
Summary
This summary is machine-generated.

A new modified sum-peak method simplifies radionuclide measurement by using only peak and sum peak count rates. This practical approach accurately quantifies multiple radionuclides, overcoming limitations of traditional methods.

Keywords:
Absolute measurement of radioactivityCo-60Coincidence summingCs-134Na-22Sum-peak method

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Area of Science:

  • Nuclear spectroscopy
  • Radiochemistry
  • Analytical chemistry

Background:

  • The traditional sum-peak method for radionuclide quantification requires total, peak, and sum peak count rates.
  • This method faces challenges in complex samples containing multiple radionuclides.
  • Accurate quantification is crucial for environmental monitoring, nuclear safety, and research.

Purpose of the Study:

  • To develop a simplified and practical method for radionuclide quantification.
  • To overcome the limitations of the traditional sum-peak method in multi-nuclide samples.
  • To provide a robust technique for accurate measurement of multiple radionuclides.

Main Methods:

  • Development of a modified sum-peak method utilizing only peak and sum peak count rates.
  • Theoretical validation of the new method.
  • Experimental verification using known radionuclides: Cobalt-60 ((60)Co), Sodium-22 ((22)Na), and Cesium-134 ((134)Cs).

Main Results:

  • The modified sum-peak method was successfully developed and validated.
  • Experimental results confirmed the theoretical predictions.
  • The method demonstrated effectiveness in quantifying radionuclides even in the presence of others.

Conclusions:

  • The modified sum-peak method offers a simpler and more practical alternative to the traditional approach.
  • This technique is highly effective for the accurate measurement of multiple radionuclides simultaneously.
  • The method is suitable for various applications requiring precise radionuclide analysis.