Division (mathematics)

About: Division (mathematics) is a research topic. Over the lifetime, 12717 publications have been published within this topic receiving 87814 citations.

Educational gaming apparatus

Abstract: An educational gaming apparatus consisting of a set of numbered blocks, at least six in number and dodecahedron in shape, and a single operator block, also of dodecahedron configuration, each of the number blocks bearing one of the digits zero to nine on each of its faces with an unbiased distribution of the digits zero to nine on the set of numbered blocks, the operator block bearing one or more of the basic mathematical symbols of addition, subtraction, multiplication or division or their equivalent on each of its faces such that at least one of the basic mathematical symbols or their equivalent is present on an uppermost face section of the operator block for any random toss by an individual who can then arrange the blocks in such an order that the uppermost faces of the blocks indicate a mathematical problem and its solution.

Reliability analysis and comparison of demodulation methods for dual-beam wavelength-modulation spectroscopy water vapor detection.

Abstract: Subtraction, division, and balanced ratiometric detection (BRD) are three extensively used demodulation methods for dual-beam wavelength-modulation trace gas detection. However, reliability comparisons among these methods under changing environmental conditions were rarely researched. In this paper, the influences of ambient temperature and bend loss of fibers are analyzed in detail, and the reliabilities of the subtraction, division, and BRD methods are quantitatively compared for the first time to our knowledge. When the ambient temperature is increased by 1°C, the deviation of the division method is only 0.29%, which obviously outperforms the subtraction method (2.90%) and the BRD method (0.55%). Furthermore, a concept, "power fluctuation rejection ratio," is introduced to compare the suppression effects of the subtraction, division, and BRD methods on the laser light source power fluctuation. The study results demonstrate that the division method provides better reliability when the ambient temperature or bending loss is varied. The validity and reliability are fully verified by the fact that the experimental results give good agreement with the theoretical simulation.

Compression of data transmission by use of prime exponents

Abstract: A method of compressing data utilizes the prime number series to generate unique compression parameters that may be used to recover an original data stream. The original data is converted from a binary form to a decimal form. Various compression parameters are selected to initialize the system. The compression parameters include the number of prime numbers which will be used in the compression process and an exponential value corresponding to each prime number. A header is constructed which includes the compression parameters. The data is compressed by a compression algorithm which performs successive division operations by the series of prime numbers selected. The compression algorithm generates a plurality of exponential values corresponding to each of the prime numbers. The header is then assembled with the exponential values and transmitted to a receiving station. In decompressing the data, the prime numbers are raised to the exponential value generated by the compression algorithm, and their product is taken. A fault parameter may be generated to compensate for numbers not readily divisible by the prime number selected in the initialization parameters.