Division (mathematics)

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

T-Count optimized quantum circuit designs for single-precision floating-point division

Abstract: The implementation of quantum computing processors for scientific applications includes quantum floating points circuits for arithmetic operations. This work adopts the standard division algorithms for floating-point numbers with restoring, non-restoring, and Goldschmidt division algorithms for single-precision inputs. The design proposals are carried out while using the quantum Clifford+T gates set, and resource estimates in terms of numbers of qubits, T-count, and T-depth are provided for the proposed circuits. By improving the leading zero detector (LZD) unit structure, the proposed division circuits show a significant reduction in the T-count when compared to the existing works on floating-point division.

Image encoding and decoding device

Abstract: A picture encoding device may include a unit for selecting a division method of a target region, and a unit for dividing the target region into small regions using the division method, generating a prediction signal in the small region, generating a residual signal between the prediction signal and the original signal of the small region, generating quantized transform coefficients by performing frequency transform and quantization of the residual signal, selecting a map for mapping the quantized transform coefficients of the small region onto leaves of a tree structure that is common to a plurality of division methods in accordance with attribute information of the small region, mapping the quantized transform coefficients of the small region onto the leaves of the tree structure based on the map, and updating the states of the nodes and leaves of the tree structure according to the coefficient values of the respective leaves.

Subtraction and Division of Neutrosophic Numbers

Abstract: In this paper, we define the subtraction and the division of neutrosophic single-valued numbers. The restrictions for these operations are presented for neutrosophic singlevalued numbers and neutrosophic single-valued overnumbers / undernumbers / offnumbers. Afterwards, several numeral examples are presented.

Asymmetric Cell Division in the One-Cell C. elegans Embryo: Multiple Steps to Generate Cell Size Asymmetry.

Abstract: The first division of the one-cell C. elegans embryo has been a fundamental model in deciphering the mechanisms underlying asymmetric cell division. Polarization of the one-cell zygote is induced by a signal from the sperm centrosome and results in the asymmetric distribution of PAR proteins. Multiple mechanisms then maintain PAR polarity until the end of the first division. Once asymmetrically localized, PAR proteins control several essential aspects of asymmetric division, including the position of the mitotic spindle along the polarity axis. Coordination of the spindle and cytokinetic furrow positions is the next essential step to ensure proper asymmetric division. In this chapter, I review the different mechanisms underlying these successive steps of asymmetric division. Work from the last 30 years has revealed the existence of multiple and redundant regulatory pathways which ensure division robustness. Besides the essential role of PAR proteins, this work also emphasizes the importance of both microtubules and actomyosin throughout the different steps of asymmetric division.

Transmission methods for downlink ACK/NACK channels

Abstract: A method from transmitting data via multiple antennas. In this method, four information bits to be transmitted are multiplexed by using either one of a code division multiplexing scheme or a second code division multiplexing scheme combined with a real and imaginary multiplexing scheme, to generate a code division multiplexed symbol including four vectors. Then, the code division multiplexed symbol is repeatedly transmitted by alternatively applying two transmit diversity schemes via four transmission antennas.