Showing papers on "Division (mathematics) published in 2013"

Image processing device, image processing method and image processing program

Abstract: PROBLEM TO BE SOLVED: To output image data under a condition that a data amount is reduced while improving an output image quality of an output apparatusSOLUTION: In an image processing system 1, a data storage processing device DP acquires output apparatus information including at least a color reproduction area of image data of output apparatuses such as composite devices MF1-MFn and computers PC1-PCn as a predetermined number of output apparatuses outputting the image data stored in an image storage section at an apparatus information acquisition section; divides the image data into predetermined division image data according to the output apparatus information at an image division section and stores it in the image storage section; and synthesizes only the required division image data based on the output apparatus information of the output apparatus among the division image data, and create synthetic image data and outputs it to the output apparatus

Method and system for homomorphicly randomizing an input

Abstract: A fully homomorphic method and system for randomizing an input, wherein all computations are over a commutative ring is described. Equivalent methods for performing the randomization using matrices and polynomials are detailed, as well as ways to mix the matrix and polynomial functions. Addition, multiplication, and division of the matrix and polynomial functions is further described. By performing computations of the functions modulo N over a ring Z N , the functions are usable as encryption functions. The method and system can also be used for verifying that a returned result of a calculation performed by a third party is valid for any of the calculations described herein. Related methods, systems, and apparatus are also described.

Fun with semirings: a functional pearl on the abuse of linear algebra

Abstract: Describing a problem using classical linear algebra is a very well-known problem-solving technique. If your question can be formulated as a question about real or complex matrices, then the answer can often be found by standard techniques. It's less well-known that very similar techniques still apply where instead of real or complex numbers we have a closed semiring, which is a structure with some analogue of addition and multiplication that need not support subtraction or division. We define a typeclass in Haskell for describing closed semirings, and implement a few functions for manipulating matrices and polynomials over them. We then show how these functions can be used to calculate transitive closures, find shortest or longest or widest paths in a graph, analyse the data flow of imperative programs, optimally pack knapsacks, and perform discrete event simulations, all by just providing an appropriate underlying closed semiring.

Data decomposition of Monte Carlo particle transport simulations via tally servers

Abstract: United States. Dept. of Energy. Naval Reactors Division. Rickover Fellowship Program in Nuclear Engineering

N-Person cake-cutting: there may be no perfect division

Abstract: A cake is a metaphor for a heterogeneous, divisible good, such as land. A perfect division of cake is efficient (also called Pareto-optimal), envy-free, and equitable. We give an example of a cake in which it is impossible to divide it among three players such that these three properties are satisfied, however many cuts are made. It turns out that two of the three properties can be satisfied by a 3-cut and a 4-cut division, which raises the question of whether the 3-cut division, which is not efficient, or the 4-cut division, which is not envy-free, is more desirable (a 2-cut division can at best satisfy either envy-freeness or equitability but not both). We prove that no perfect division exists for an extension of the example for three or more players.

Quantum internet using code division multiple access.

Abstract: A crucial open problem inS large-scale quantum networks is how to efficiently transmit quantum data among many pairs of users via a common data-transmission medium. We propose a solution by developing a quantum code division multiple access (q-CDMA) approach in which quantum information is chaotically encoded to spread its spectral content, and then decoded via chaos synchronization to separate different sender-receiver pairs. In comparison to other existing approaches, such as frequency division multiple access (FDMA), the proposed q-CDMA can greatly increase the information rates per channel used, especially for very noisy quantum channels.

Self-correlation optical fiber communication system based on mode division multiplexing

Abstract: The invention discloses a self-correlation optical fiber communication system based on mode division multiplexing. The self-correlation optical fiber communication system based on mode division multiplexing comprises an optical carrier input unit, optical signal modulation units, a wavelength division multiplexing unit, a mode division multiplexing and demultiplexing unit, a wavelength division multiplexing unit and coherent reception units. The mode division multiplexing and reconciliation multiplexing unit comprises a mode multiplexer and mode demultiplexer, and the mode multiplexer and the mode demultiplexer are connected through few-mode optical fibers. The optical carrier input unit is connected with each optical signal modulation unit, the wavelength division multiplexing unit and the mode multiplexer through single-mode optical fibers. The mode multiplexer is connected with the mode demultiplexer through few-mode optical fibers. The mode demultiplexer is connected with the wavelength division multiplexing unit and each coherent reception unit through single-mode optical fibers. The optical carrier input unit is further connected with the wavelength division multiplexing unit. The self-correlation optical fiber communication system based on mode division multiplexing eliminates an expensive narrow line width adjustable local oscillator light source which is arranged at a reception end, enables a laser to be conveniently managed and maintained, is free from using frequency offset estimation in a digital signal processor (DSP) and phase retrieval algorithm, reduces complexity of the DSP and has the advantages of being high in spectrum effectiveness and big in nonlinearity tolerance.

Display apparatus and control method thereof

Abstract: A display apparatus according to the present invention comprises: an acquisition unit that acquires, for each of division regions, brightness information; a decision unit that decides light emission brightness for each of the division regions; a light emitting unit; and a display panel, wherein the decision unit sets light emission brightness of a division region, in which a displayed image does not include a predetermined region, at light emission brightness according to brightness information of the division region, and sets light emission brightness of a division region, in which a displayed image includes the predetermined region, at light emission brightness lower than the light emission brightness according to brightness information of the division region.

Combined sample preparation system

Abstract: The invention discloses a combined sample preparation system. The system comprises a supplied material conveying apparatus, a crushing division host and a controller; the crushing division host comprises a primary crusher, a secondary division device, a secondary crusher and a tertiary division device; a primary division device is used for dividing a material discharged from the primary crusher, the controller controls the primary division device to work when the amount of the supplied material of the supplied material conveying apparatus is large and not to work when the amount of the supplied material of the supplied material conveying apparatus is small, and the primary division apparatus comprises a first material discarding outlet and a first material outlet; the secondary division device is used for dividing a material from the first material outlet, the division ratio of the secondary division device is controlled by the controller, and the secondary division device comprises a second material discarding outlet, a second material outlet and a full-water sample material outlet connected with a full-water sample material boxy; the secondary crusher is used for crushing a material from the second material outlet; and the tertiary division device is used for dividing a material from the secondary crusher, the division ratio of the tertiary division device is controlled by the controller, and the tertiary division device comprises a third material discarding material outlet, an analysis sample material outlet and a preserved sample material outlet connected with a preserved sample material box. The combined sample preparation system can be convenient used by a user.

Cell clustering based configuration of flexible time division duplex communication

Abstract: There are provided measures for cell clustering based configuration of flexible time division duplex communication, such as e.g. in layered heterogeneous network deployments. Such measures may exemplarily comprise measures for specifying a desired uplink-downlink configuration for time division duplex communication in a subject cell of a cellular communication system, obtaining at least one desired uplink-downlink configuration for time division duplex communication in at least one neighboring cell of the cellular communication system, wherein the at least one neighboring cell and the subject cell belong to the same cell cluster, and defining an uplink-downlink configuration for time division duplex communication in at least the subject cell of the cell cluster out of a set of predefined uplink-downlink configurations with flexible subframe patterns for flexible time division duplex communication on the basis of the specified desired uplink-downlink configuration for the subject cell and the obtained at least one desired uplink-downlink configuration for the at least one neighboring cell.

Efficient approaches to design a reversible floating point divider

Abstract: In this paper, we propose a reversible n-bit divider, where n is the number of bits of the operands of dividend. Two approaches for constructing a compact reversible divider have been presented here. The first approach uses conventional division array and the second approach uses high speed division array. Both of the approaches can handle floating point numbers. Several theorems on the numbers of gates, garbage outputs and quantum cost of the reversible n-bit divider have been shown. The comparative study shows that the proposed designs can work with fractional numbers where as existing designs can not. Proposed designs are also much better than the existing approaches considering all the efficiency parameters of reversible logic design which includes numbers of gates used, quantum cost and garbage outputs.

Soft-Transition Sub-PCA Fault Monitoring of Batch Processes

Abstract: Inaccurate substage division problems often emerge when multiway principal component analysis is applied in fault monitoring of multistage batch processes. A new two-step stage division method based on support vector data description (SVDD) is proposed in order to avoid the hard-division and misclassification problems. The loading matrices of the MPCA model are modified using the idea of combining the mechanism knowledge with field data in the rough division step. The model differences are increased by introducing the sampling time to loading matrices, which can avoid division mistakes caused by the fault data. Detailed stage separation is realized here based on the SVDD hypersphere distance to divide the process strictly into steady or transition stages. Then a soft-transition sub-PCA model is given based on the hypersphere distance. The method is applied to monitoring a penicillin fermentation process online. Simulation results show that the proposed method can describe transition stage information in m...

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.

Image capturing apparatus and in-focus position detection method thereof

Abstract: It is provided a image capturing apparatus including a control unit that determines whether to set a division number to a first division number n or to a second division number m which is larger than n based on the status of a subject, calculating a divided area evaluation curve by calculating a correlation between first detection information and second detection information for each of divided areas formed by dividing a phase difference detection area into the n or the m, and acquires a defocus amount to drive and control a focus lens to the in-focus position from a total evaluation curve obtained by conducting a required calculation processing on the divided area evaluation curves of the plural divided areas.

3d zoom imager

Abstract: A 3D imager comprising two cameras having fixed wide-angle and narrow angle FOVs respectively that overlap to provide an active space for the imager and a controller that determines distances to features in the active space responsive to distances provided by the cameras and a division of the active space into near, intermediate, and far zones.

Balanced Splitting and Rebalanced Splitting

Abstract: United States. Dept. of Energy. Office of Basic Energy Sciences (Division of Chemical Sciences, Geosciences, and Biosciences Contract DE-FG02-98ER14914)

Subtraction-free complexity, cluster transformations, and spanning trees

Abstract: Subtraction-free computational complexity is the version of arithmetic circuit complexity that allows only three operations: addition, multiplication, and division. We use cluster transformations to design efficient subtraction-free algorithms for computing Schur functions and their skew, double, and supersymmetric analogues, thereby generalizing earlier results by P. Koev. We develop such algorithms for computing generating functions of spanning trees, both directed and undirected. A comparison to the lower bound due to M. Jerrum and M. Snir shows that in subtraction-free computations, "division can be exponentially powerful." Finally, we give a simple example where the gap between ordinary and subtraction-free complexity is exponential.

Optical unit and imaging apparatus

Abstract: PROBLEM TO BE SOLVED: To provide an optical unit and an imaging apparatus capable of presenting stereoscopic images without giving any discomfort feeling to a viewer without rotating an imaging element even when the positional direction of the viewer changes with respect to the object.SOLUTION: The optical unit includes: a collecting lens for collecting a beam of light coming from a subject; a pupil division polarization separation element that separates the collected light into two kinds of linear polarization, each of which has a different polarization direction in a left-eye polarization separation area and in a right-eye polarization separation area which are formed at both sides of a pupil division line as the interface crossing perpendicularly to the optical axis and outputs the same therefrom; a polarization direction conversion element that converts the polarized direction of the two kinds of linear polarization output from the pupil division polarization separation element; and a rotation drive section that rotates the pupil division polarization separation element and the polarization direction conversion element according to an instruction.

Fast fixed-point divider based on Newton-Raphson method and piecewise polynomial approximation

Abstract: Division is an operation extensively used in architectures for digital signal processing algorithms, which in portable devices require an implementation using fixed-point format. In this paper, a novel fixed-point divider is proposed. The divider architecture is based on a division algorithm that uses the reciprocal operation and a post-multiplication. In turn, reciprocal operation is based on the Newton-Raphson algorithm, where the seed is provided through piecewise polynomial approximation. Reciprocal operation is performed with only two clocks cycles and division operation requires only three clock cycles. A comparison between the proposed architecture and dividers based on coordinate rotation digital computer, shows that the proposed architecture achieves approximately 5-fold gain in execution time for applications in 50-100 MHz frequency range and higher signal-to-quantization-noise ratio.

Estimating the Division Rate of the Growth-Fragmentation Equation with a

Abstract: We consider the growth-fragmentation equation and we address the problem of estimating the division rate from the stable size distribution of the population, which is easily measured, but non-smooth. We propose a method based on the Mellin transform for growth-fragmentation equations with self-similar kernels. We build a sequence of functions which converges to the density of the population in division, simultaneously in several weighted L 2 spaces, as the measurement error goes to 0. This improves previous results for self-similar kernels and allows us to understand the partial results for general fragmentation kernels. Numerical simulations confirm the theoretical results. Moreover, our numerical method is tested on real biological data, arising from a bacteria growth and fission experiment.

Methods and architectures for extended range arbitrary ratio dividers

Abstract: One of the most important RF building blocks today is the frequency synthesizer, or more particularly the programmable frequency divider (divider). Such dividers preferably would support unlimited range with continuous division without incorrect divisions or loss of PLL lock. The inventors present multi-modulus dividers (MMDs) providing extended division range against the prior art and without incorrect divisions as the division ratio is switched back and forth across the boundary between two different ranges. Accordingly, the inventors present MMD frequency dividers without the drawbacks within the prior art.

A note on the existence of non-cyclic free subgroups in division rings

Abstract: A division ring D is said to be weakly locally finite if for every finite subset \({S \subset D}\), the division subring of D generated by S is centrally finite. It is known that the class of weakly locally finite division rings strictly contains the class of locally finite division rings. In this note we prove that every non-central subnormal subgroup of the multiplicative group of a weakly locally finite division ring contains a non-cyclic free subgroup. This generalizes the previous result by Goncalves for centrally finite division rings.

Multi-carrier code division multiplexing light transmission system and method based on ultra dense wavelength division multiplexing

Abstract: The invention discloses a multi-carrier code division multiplexing light transmission system and a multi-carrier code division multiplexing light transmission method based on ultra dense wavelength division multiplexing. The system comprises a multi-carrier light source generating part, a modulating part, a multiplexing part, a demultiplexing part, a demodulating part and a signal processing part which are sequentially connected. Firstly, a multi-carrier light source is generated by a single-frequency light source; then the modulating part modulates each branch electric signal onto a corresponding optical carrier; the multiplexing part is used for multiplexing each modulated optical carrier into an optical fiber channel; the demultiplexing part is used for separating each optical carrier in the signals to conduct signal recovery; the demodulating part is used for demodulating each branch signal; and the signal processing part is used for carrying out compensation on the demodulated signals. The method disclosed by the invention is fused with a code division multiplexing technology, a subcarrier modulating and demodulating technology, a wavelength division multiplexing and demultiplexing technology, a subcarrier demodulating technology based on coherent demodulation and the like. The multi-carrier code division multiplexing light transmission system and the multi-carrier code division multiplexing light transmission method based on ultra dense wavelength division multiplexing improve the message capacity of a network system and have the advantages of simpleness for capacity expansion, reliable performance and the like.

VHDL Implementation of Non Restoring DivisionAlgorithm Using High Speed Adder/Subtractor

Abstract: Binary division is basically a procedure to determine how many times the divisor D divides the dividend B thus resulting in the quotient Q. At each step in the process the divisor D either divides B into a group of bits or it does not. The divisor divides a group of bits when the divisor has a value less than or equal to the value of those bits. Therefore, the quotient is either 1 or 0. The division algorithm performs either an addition or subtraction based on the signs of the divisor and the partial remainder. There are number of binary division algorithm like Digit Recurrence Algorithm restoring, non-restoring and SRT Division (Sweeney, Robertson, and Tocher), Multiplicative Algorithm, Approximation Algorithms, CORDIC Algorithm and Continued Product Algorithm. This paper focus on the digit recurrence non restoring division algorithm, Non restoring division algorithm is designed using high speed subtractor and adder. High speed adder and subtractor are used to speed up the operation of division. Designing of this division algorithm is done by using VHDL and simulated using Xilinx ISE 8.1i software has been used and implemented on FPGA xc3s100e-5vq100.

A review of few-mode fibers for space-division multiplexed transmissions

Abstract: A review of the most recent advances on both weakly-coupled and strongly-coupled few-mode fibers is presented. The challenge of increasing the number of LP modes that can actually be used is also discussed.