Showing papers on "Division (mathematics) published in 2001"
TL;DR: It is shown that the IEEE standard's specification of operations involving the signed infinities, signed zeros, and the exact/inexact flag are such as to make a correct and optimal implementation more efficient.
Abstract: We start with a mathematical definition of a real interval as a closed, connected set of reals. Interval arithmetic operations (addition, subtraction, multiplication, and division) are likewise defined mathematically and we provide algorithms for computing these operations assuming exact real arithmetic. Next, we define interval arithmetic operations on intervals with IEEE 754 floating point endpoints to be sound and optimal approximations of the real interval operations and we show that the IEEE standard's specification of operations involving the signed infinities, signed zeros, and the exact/inexact flag are such as to make a correct and optimal implementation more efficient. From the resulting theorems, we derive data that are sufficiently detailed to convert directly to a program for efficiently implementing the interval operations. Finally, we extend these results to the case of general intervals, which are defined as connected sets of reals that are not necessarily closed.
363 citations
TL;DR: This paper describes log-depth, polynomial size, logspace-uniform, i.e. , NC 1 circuit family for integer division, and shows that division is in logspace.
Abstract: Beame, Cook and Hoover were the first to exhibit a log-depth, polynomial size circuit family for integer division. However, the family was not logspace-uniform. In this paper we describe log-depth, polynomial size, logspace-uniform, i.e. , NC 1 circuit family for integer division. In particular, by a well-known result this shows that division is in logspace. We also refine the method of the paper to show that division is in dlogtime-uniform NC 1 .
103 citations
Book•
01 Sep 2001
103 citations
Patent•
27 Dec 2001
TL;DR: In this article, an optical diffraction grating (110) is used to disperse the light being monitored onto a rotating polygon (115) having mirrors (120) on the facets of the polygon and a detector (225) is positioned in the interior of the cylinder to detect light passing through the filter (215).
Abstract: A wavelength monitoring system (100) for continuously monitoring the wavelengths of different optical channels transmitted through a wavelength division multiplexed (WDM) fiberoptic system. In one construction, an optical diffraction grating (110) is used to disperse the light being monitored onto a rotating polygon (115) having mirrors (120) on the facets (125) thereof, such that the rotating polygon (115) reflects the light onto a detector (130) located behind a slit (135). In a second construction, the light is projected onto a rotating, hollow transparent cylinder (210) having a thin film (215) deposited on a surface thereof, wherein the thin filter (215) comprises a Fabry-Perot structure which has a gap which varies as a function of its position on the rim of the cylinder, such that the varying gap allows for a varying transmission wavelength which varies as a function of angular position. A detector (225) is positioned in the interior of the cylinder to detect light passing through the filter (215).
93 citations
Posted Content•
TL;DR: In this article, the desingularization theorem of Hironaka holds for certain classes of infinitely differentiable functions (essentially, for subrings that exclude flat functions and are closed under differentiation and the solution of implicit equations).
Abstract: We show that a version of the desingularization theorem of Hironaka holds for certain classes of infinitely differentiable functions (essentially, for subrings that exclude flat functions and are closed under differentiation and the solution of implicit equations). Examples are quasianalytic classes, introduced by E. Borel a century ago and characterized by the Denjoy-Carleman theorem. These classes have been poorly understood in dimension > 1. Resolution of singularities can be used to obtain many new results; for example, topological Noetherianity, Lojasiewicz inequalities, division properties.
65 citations
08 Jul 2001
TL;DR: It is shown that indeed division is in uniform TC° and a key step of the proof is the discovery of a first-order formula expressing exponentiation modulo any number of polynomial size.
Abstract: Integer division has been known since 1986 [4, 13, 12] to be in slightly non-uniform TC°, ie, computable by polynomial-size, constant depth threshold circuits This has been perhaps the outstanding natural problem known to be in a standard circuit complexity class, but not known to be in its uniform version We show that indeed division is in uniform TC° A key step of our proof is the discovery of a first-order formula expressing exponentiation modulo any number of polynomial size
64 citations
04 Nov 2001
TL;DR: In this article, the authors proposed an analog readout system with functionally the same output as common charge division, but without a division chain connected to the detector outputs before signal amplification.
Abstract: Charge division readout provides a relatively simple electronic solution for data readout of position sensitive radiation detectors. Conventional charge division usually consists of some charge division media connected to the detector outputs to provide proportional charge division between two division chain outputs. Although offering some advantages such as simplicity and the reduction of the number of analog outputs, it reduces the detector spatial resolution and image quality, because of signal to noise reduction from the attenuation of the signal before reaching the amplifiers. An analog readout system with functionally the same output as common charge division, but without a division chain connected to the detector outputs before signal amplification was designed and evaluated. This readout system operates as a multi-channel analog signal converter which converts signals from multi-channel output position sensitive devices such as multianode PMTs or gamma cameras built of PSPMT arrays etc. to two per coordinate analog outputs with same amplitude correlation as common charge division position readout.
56 citations
01 Jan 2001
TL;DR: It is shown that P-systems with only division for elementary membranes suffice to solve these two problems in linear time and that (if P ≠ NP) deterministic P- systems without membrane division are not able to solve NP complete problems in polynomial time.
Abstract: A recently introduced variant of P-systems considers membranes which can multiply by division. These systems use two types of division: division for elementary membranes (Le. membranes not containing other membranes inside) and division for non-elementary membranes. In two recent papers it is shown how to solve the Satisfiability problem and the Hamiltonian Path problem (two well known NP complete problems) in linear time with respect to the input length, using both types of division. We show in this paper that P-systems with only division for elementary membranes suffice to solve these two problems in linear time. Is it possible to solve NP complete problems in polynomial time using P-systems without membrane division? We show, moreover, that (if P ≠ NP) deterministic P-systems without membrane division are not able to solve NP complete problems in polynomial time.
54 citations
Patent•
14 Jun 2001
TL;DR: In this paper, an improved DWD multiplexer for the separation of optical channels is proposed, which requires a lower insertion loss by requiring an optical signal to travel through fewer optical components in the separation process.
Abstract: An improved dense wavelength division multiplexer for the separation of optical channels is provided. The dense wavelength division multiplexer includes the inputting of an optical signal with the optical signal containing a plurality of optical channels; the separating of one or more of the plurality of optical channels from the optical signal using separators at least partly arranged in a multi-stage parallel cascade configuration; and the outputting of the separated plurality of channels along a plurality of optical paths. The dense wavelength division multiplexer of the present invention provides for a lower insertion loss by requiring an optical signal to travel through fewer optical components in the separation process.
34 citations
TL;DR: Using different frictional shear stress models, mesh division and number of elements in the deformation zone, this article analyzed the influence of friction variation on the convergence and results of simulation such as rolling pressure, forward slip and spread by 3D rigid-plastic FEM.
Patent•
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22 Feb 2001
TL;DR: In this article, a recording medium is divided into a plurality of regions, and an unused area in each region is written with dummy data that can be overwritten only by a specific application or a specific file.
Abstract: One recording medium accessed from a plurality of applications is generally divided into a plurality of regions. When partitions are used to control this region dividing, the sizes of the partitions are hard to change to thereby prevent an effective use of a recording medium. A recording medium is divided into a plurality of regions, and an unused area in each region is written with dummy data that can be overwritten only by a specific application or a specific file, thereby making easy the division into a plurality of regions and a change in size.
Patent•
31 Oct 2001TL;DR: In this article, a code division multiple access (CDMA) receiver is proposed to maintain the accuracy of the result of demodulation of a received signal at a good level without increasing the scale of circuits and the amount of computation.
Abstract: The present invention provides a code division multiple access receiver which can maintain the accuracy of the result of demodulation of a received signal at a good level without increasing the scale of circuits and the amount of computation. In the code division multiple access receiver, a control section 14 outputs amplitude-adjusting signals corresponding to the reception level of a received base band signal to an amplitude-adjusting section 20, and the amplitude-adjusting section 20 performs bit operation processes for removing invalid bit data from the complex correlation results of the received base band signal based on the amplitude-adjusting signals.
Patent•
21 Mar 2001
TL;DR: In this paper, a portable electronic viewer system for satisfying both the demand for portability and the demand of containing a large volume of contents is provided, consisting of a portable server division (500 ) provided with a hard disk ( 502 ) of 2.5 inches or smaller for storing book-type information containing at least either images or characters.
Abstract: A portable electronic viewer system is provided for satisfying both the demand for portability and the demand for containing a large volume of contents. The portable electronic viewer system comprises a portable server division ( 500 ) provided with a hard disk ( 502 ) of 2.5 inches or smaller for storing book-type information containing at least either images or characters and a viewer division ( 510 ) for displaying page-by-page the book-type information sent wirelessly from the portable server division at a transfer rate of less than 16 Mbps.
02 Sep 2001
TL;DR: A set of SIMULINK models and MATLAB files, which allow exhaustive behavioral simulations of fractional-N division frequency synthesizers based on PLL, are presented, which takes into account most of PLL's non-idealities.
Abstract: Presents a set of SIMULINK models and MATLAB files, which allow exhaustive behavioral simulations of fractional-N division frequency synthesizers based on PLL. The proposed set of models takes into account most of PLL's non-idealities. For each model we present a description of the considered effect as well as all of the implementable details. Simulation results on a fractional-N division frequency synthesizer based on PLL demonstrate the validity of the models proposed.
Patent•
01 Feb 2001
TL;DR: In this article, the authors proposed a dense wavelength division multiplexer (DWDM) for separating an optical signal into optical channels, which includes at least one birefringent plate (509), at least a half wave plate (510), a lens (513), and a nonlinear interferometer (514) for introducing a phase difference between the plurality of optical channels.
Abstract: The present invention provides a dense wavelength division multiplexer for separating an optical signal into optical channels. The dense wavelength division multiplexer (500) includes at least one birefringent plate (509) for separating an optical signal into a plurality of optical channels, at least one half wave plate (510), a lens (513) and a non-linear interferometer (514) for introducing a phase difference between the plurality of optical channels. The present invention provides for an ease in alignment and a higher tolerance to drifts.
Patent•
07 Mar 2001
TL;DR: An image/map association division displays map data stored in a map data storing division, and sets a plurality of segment points and a "path" (route) sandwiched by two segment points on a map as discussed by the authors.
Abstract: An image/map association division displays map data stored in a map data storing division, and sets a plurality of segment points and a “path” (route) sandwiched by two segment points on a map. The image/map association division reproduces video data stored in an image data storing division, and displays the map data stored in the map data storing division. If the route set on the map and desired frames of the video data being reproduced are designated via an operation division, association data for associating the segment points at both ends of the “route” with the designated frames is generated and it is stored in the association data storing division.
01 Jan 2001
Abstract: The Australian Institute of Family Studies is committed to the creation and dissemination of research-based information on family functioning and wellbeing. Views expressed in its publications are those of individual authors and may not reflect Institute policy or the opinions of the Editor of the Institute's Board of Management. Contents List of tables vi List of figures vi Acknowledgments vii Abstract viii Introduction 1 Legal framework 1 Current reform agenda 3 The changing context 4 The study 5 Research questions 5 Analytic approach 6 Methods 6 Sample 6 Demographic profile 7 Survey content 8 Methodological problems and conceptual issues 8 Question 1: What is the nature and value of assets on divorce? 8 Measures 9 Findings 10 Type of assets owned 10 Value of assets owned 11 Summary 13 Question 2: What share of property do women and men receive? 13 Measures 13 Findings 13 Percentage share of property received 14 Sources of variation 14 Relative value of share received 16 Summary 18 Question 3: What factors are associated with the division of property? 19 Measures 19 Contribution 19 Section 75(2) factors 20 Relationship context and other factors 20 Analytic procedure 20 Findings 21 Contribution 21 Section 75(2) factors 23 Relationship context and other factors 26 Final model 27 Summary 27 Question 4: What difference would equal shares of the matrimonial property make? 27 Measures 27 Findings 28 Percentage share of property received 28 Dollar share of property received 29 Summary 30 Summary of findings 30 Nature and value of the assets on divorce 30 Shares of property at distribution 31 Factors of influence 31 Impact of equal share 31 General discussion 31 Financial contributions count 32 Children first 33 Financial circumstances at separation 34 Conclusion 35 References 36 Cases 37 Appendix A: Demographic profiles of divorced respondents 38 Appendix B: Factors related to the share of property received by the wife: Significant results from the analyses of variance with multiple classification analysis 39 List of tables Table 1.1 Combined assets and liabilities of couple: percentage of respondents who reported owning assets and liabilities of different types at separation 10 Table 1.2 Percentage of respondents who reported owning assets and liabilities of different types by level of asset wealth 11 Table 1.3 Median net value of assets and liabilities 11 Table 1.4 Median net value of assets and liabilities by asset wealth 12 Table 3.1 Mean percentage share going to …
Patent•
12 Jan 2001TL;DR: In this paper, a degree-of-randomness calculation unit calculates the degrees of randomness of data values in the respective data sets as division results, on feature amount data at feature points of the signal waveforms obtained when an image pick-up unit picks up images of marks, while changing the data division form, in respective data division forms.
Abstract: A degree-of-randomness calculation unit calculates the degrees of randomness of data values in the respective data sets as division results, on feature amount data at feature points of the signal waveforms obtained when an image pick-up unit picks up images of marks, while changing the data division form, in the respective data division forms, and calculates the sum of the degrees of randomness. A classification calculation unit classifies the feature points in the data division form in which the sum of degrees of randomness is minimized, thereby classifying the feature amount data into signal data and noise data. A position calculation unit calculates mark position information on the basis of the position of the feature point determined as signal data by S/N discrimination with reference to such degrees of randomness. As a consequence, the position information of each mark formed on the object is accurately detected.
01 Aug 2001
TL;DR: A suite of optimizations for eliminating division, modulo, and remainder operations from programs are described, analogous to strength reduction techniques used for multiplications.
Abstract: Integer division, modulo, and remainder operations are expressive and useful operations. They are logical candidates to express complex data accesses such as the wrap-around behavior in queues using ring buffers. In addition, they appear frequently in address computations as a result of compiler optimizations that improve data locality, perform data distribution, or enable parallelization. Experienced application programmers, however, avoid them because they are slow. Furthermore, while advances in both hardware and software have improved the performance of many parts of a program, few are applicable to division and modulo operations. This trend makes these operations increasingly detrimental to program performance.
This paper describes a suite of optimizations for eliminating division, modulo, and remainder operations from programs. These techniques are analogous to strength reduction techniques used for multiplications. In addition to some algebraic simplifications, we present a set of optimization techniques that eliminates division and modulo operations that are functions of loop induction variables and loop constants. The optimizations rely on algebra, integer programming, and loop transformations.
Patent•
26 Mar 2001
TL;DR: In this paper, a minimum/maximum computation for an interval operation is performed by receiving at least four floating-point numbers, including a first floating point number, a second floating point, a third floating point and a fourth floating point.
Abstract: One embodiment of the present invention provides a system for performing a minimum/maximum computation for an interval operation. The system operates by receiving at least four floating-point numbers, including a first floating-point number, a second floating-point number, a third floating-point number and a fourth floating-point number. Next, the system computes a minimum/maximum of the at least four floating-point numbers, wherein if the at least four floating-point numbers include one or two default NaN (not-a-number) values and the remaining values are not default NaN values, the default NaN values are ignored in computing the minimum/maximum.
Patent•
16 Aug 2001
TL;DR: In this article, the deflection directions of laser beams are set different from each other, returned onto the same optical axis and separated according to the time division directions in the vicinity of machining heads 30A and 30B, and the laser beams were used for the machining.
Abstract: PROBLEM TO BE SOLVED: To save space by decreasing the number of elements for time division of a laser beam and sharing a part of optical parts after the time division. SOLUTION: The deflection directions of laser beams time-divided (42 and 44) are set different from each other, returned onto the same optical axis and separated according to the deflection directions in the vicinity of machining heads 30A and 30B, and the laser beams are used for the machining.
Patent•
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14 Feb 2001
TL;DR: In this article, the alignment of primary and secondary sides for improving ease of use in a non-contact coupler for transmitting power by magnetic coupling between the primary and SUs is discussed.
Abstract: PROBLEM TO BE SOLVED: To secure performance, at the same time, to reduce weight, and to give room to the alignment of primary and secondary sides for improving ease of use in a non-contact coupler for transmitting power by magnetic coupling between the primary and secondary sides. SOLUTION: A portion at least at mutually opposing sides of primary- and secondary-side magnetic cores 1 and 1 is divided for forming, and at the same time clearance for forming a spatial magnetic circuit (g) is included between division formation portions.
Patent•
11 May 2001TL;DR: In this article, a minimum computation for an interval multiplication operation with default NaN values is presented, where the default NaNs are ignored in computing the minimum and the minimum is set to negative infinity.
Abstract: One embodiment of the present invention provides a system for performing a minimum computation for an interval multiplication operation. This system receives four floating-point numbers, including a first floating-point number, a second floating-point number, a third floating-point number and a fourth floating-point number. The system then computes a minimum of the four floating-point numbers, wherein if the four floating-point numbers include one or more default NaN (not-a-number) values, the system sets the minimum to negative infinity. One embodiment of the present invention provides a system for performing a minimum computation for an interval division operation. This system receives four floating-point numbers, including a first floating-point number, a second floating-point number, a third floating-point number and a fourth floating-point number. The system then computes a minimum of the four floating-point numbers, wherein if the four floating-point numbers include one or more default NaN (not-a-number) values, the default NaN values are ignored in computing the minimum.
Patent•
13 Nov 2001
TL;DR: In this paper, the phase comparison result signal (PHASE) from the pulse width modulation circuit is sensed and the CPU sets a division number in a phase select block from a given minimum desired division number.
Abstract: When a CPU begins to monitor whether delay variation characteristics of a pulse width variation circuit have varied, it selects a basic delay setting value in a basic delay value setting block from a smallest one. The CPU sets a division number in a phase select block from a given minimum desired division number for pulse width modulation. The CPU senses the level of a phase comparison result signal (PHASE) from the pulse width modulation circuit. If the phase comparison result signal is stable at “1”, the CPU 1 fixes the division number. If the phase comparison result signal is “0” and the division number is not maximum, the CPU increases the division number and goes back to the setting of the division number. If the division number is maximum, the CPU increases the basic delay and goes back to the basic delay setting.
TL;DR: In this article, the working principle of grating-based wavelength division multiplexers (WD(D)M) for optical networks is reviewed, and several versions of highly reliable WD(DM) are developed, from coarse to dense, with low insertion loss and low cost.
Abstract: We first review the working principle of grating-based wavelength division (de)multiplexers [WD(D)M] for optical networks. We also address issues regarding optical design of grating-based WD(D)Ms for commercial uses. Next, several grating-based WD(D)M structures are analyzed. Based on these designs and analyses, we develop several versions of highly reliable WD(D)Ms, from coarse to dense, with low insertion loss and low cost. Last, we present the experimental data for these WD(D)Ms.
Patent•
07 Jun 2001TL;DR: In this article, a folding inverter is used to invert selected bits of the input and a table lookup value is obtained from the multipartite table system, which is then scaled by a function of the semi-complement term.
Abstract: The division and square root systems include a multiplier. The systems also include a multipartite table system, a folding inverter, and a complement inverter, each coupled to the multiplier. The division and square root functions can be performed using three scaling iterations. The system first determines both a first and a second scaling value. The first scaling value is a semi-complement term computed using the folding inverter to invert selected bits of the input. The second scaling value is a table lookup value obtained from the multipartite table system. In the first iteration, the system scales the input by the semi-complement term. In the second iteration, the resulting approximation is scaled by a function of the table lookup value. In the third iteration, the approximation is scaled by a value obtained from a function of the semi-complement term and the table lookup value. After the third iteration, the approximation is available for rounding.
Patent•
26 Dec 2001TL;DR: In this article, the division wall is made up of a plurality of division wall sections forming a passage wall of high temperature gas which are connected in the direction of arrangement of blades to form a wall surface having a roughly circular cross section as a whole.
Abstract: The division wall is made up of a plurality of division wall sections forming a passage wall of high temperature gas which are connected in the direction of arrangement of blades to form a wall surface having a roughly circular cross section as a whole, a gas flow restricting structure for preventing high temperature gas from passing through a gap formed at a connecting portion between the division wall sections in the flow direction of the high temperature gas from the opening on the upstream side of the high temperature gas in the gap, or a gas flow restricting structure for preventing the high temperature gas from being embraced in the gap, for example, a sealing member formed into a prism having a T-shape cross section as a whole composed of a plane portion as a sealing portion and a projected portion for filling the gap is provided.
Patent•
21 Jun 2001
TL;DR: In this article, a sub-band frame including an audio sample signal is divided into a plurality of divisions, and the absolute value of the peak of each division is acquired to suppress pre-echo noise and post-echo by more accurately generating a correction function to execute gain control.
Abstract: PROBLEM TO BE SOLVED: To surely suppress pre-echo noise and post-echo by more accurately generating a correction function to execute gain control. SOLUTION: A sub-band frame including an audio sample signal is divided into a plurality of divisions, and the absolute value of the peak of each division is acquired. A division (attack signal) including quick sound rise is discriminated, and divisions between the discriminated division of the attack signal and divisions corrected before are amplified to process the attack signal, and a division (release signal) including quick sound fall is discriminated, and divisions between the discriminated division of the release signal and divisions corrected before are attenuated to process the release signal, and thus the occurrence of pre-echo and post-echo is prevented.
Journal Article•
TL;DR: Complexity theory gives us an equally-valid way to ask about the complexity of division; what is the fastest division algorithm?
Abstract: All of us learn to do arithmetic in grade school. The algorithms for addition and subtraction take some time to master, and the multiplication algorithm is even more complicated. Eventually students learn the division algorithm; most students find it to be complicated, time-consuming, and tedious. Is there a better way to divide? For most practical purposes, the correct way to answer this question is to consider the time-complexity of division; what is the fastest division algorithm? That is not the subject of this article. I am not aware of any recent breakthrough on this question; any good textbook on design and analysis of algorithms will tell you about the current state of the art on that front. Complexity theory gives us an equally-valid way to ask about the complexity of division: