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Related Concept Videos

Rational Expressions01:28

Rational Expressions

Rational expressions are algebraic fractions in which both the numerator and the denominator are polynomials. These expressions follow the arithmetic rules of numerical fractions but require extra care due to the presence of variables. A fundamental part of working with rational expressions is identifying values that make the expression undefined, typically those that result in division by zero or undefined radicals.Determining the DomainThe domain of a rational expression includes all real...
Rationalizing Substitutions01:29

Rationalizing Substitutions

Integrals involving non-rational functions are often difficult to evaluate using standard techniques, especially when radicals appear in the integrand. Rationalizing substitution provides a systematic method for simplifying such integrals by converting them into rational forms that are easier to handle.Consider a rod whose linear mass density depends on a constant linear density, a characteristic length, and the distance from the left end of the rod. Determining the total mass requires...
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Parallel-axis Theorem

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Parallel-Axis Theorem for an Area

The moment of inertia is a fundamental concept in mechanical engineering that plays a significant role in designing rotationally symmetric objects such as flywheels, gears, and other mechanical systems. In this context, we will discuss the moment of inertia of a flywheel rotating about its centroidal axis and how it relates to the moment of inertia about an axis parallel to it.
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Phasor Arithmetics01:13

Phasor Arithmetics

Phasors and their corresponding sinusoids are interrelated, offering unique insights into the behavior of alternating current (AC) circuits. One way to understand this relationship is through the operations of differentiation and integration in both the time and phasor domains.
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Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station
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Error-free parallel rational arithmetic for optical and VLSI computing.

E V Krishnamurthy, V K Murthy

    Applied Optics
    |June 5, 2010
    PubMed
    Summary
    This summary is machine-generated.

    A novel parallel rational arithmetic system uses Para-Hensel codes for error-free computation. This system enables efficient arithmetic on bounded rational numbers for massively parallel processors.

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    Area of Science:

    • Computer Science
    • Number Theory
    • Parallel Computing

    Background:

    • Traditional rational arithmetic can be computationally intensive and prone to errors.
    • Efficient representation and manipulation of rational numbers are crucial for advanced computing.

    Purpose of the Study:

    • To introduce an error-free, carry-free parallel rational arithmetic system.
    • To enable efficient parallel computation with rational numbers using a novel coding scheme.

    Main Methods:

    • Encoding Farey rational numbers into Para-Hensel codes.
    • Performing parallel element-wise arithmetic operations on these codes.
    • Developing algorithms for encoding, decoding, and arithmetic operations.

    Main Results:

    • A functional parallel rational arithmetic system is established.
    • The system utilizes residue and p-adic representations for Para-Hensel codes.
    • Algorithms for code conversion and arithmetic are successfully described.

    Conclusions:

    • The developed Para-Hensel code system offers a robust method for parallel rational arithmetic.
    • This system holds significant potential for applications in massively parallel processing environments.