Showing papers on "Division (mathematics) published in 1978"

Behaviour of recursive division surfaces near extraordinary points

Abstract: The behaviour of the limits surface defined by a recursive division construction can be analysed in terms of the eigenvalues of a set of matrices. This analysis predicts effects actually observed, and leads to suggestions for the further improvement of the method.

A Simultaneous Equation Model for the Division of Household Labor

Abstract: In this paper a three-equation, nonrecursive model for the household division of labor is proposed based on recent work in the New Home Economics. The model is estimated with data from a sample of ...

Loop carrier system for telecommunication and data services

Abstract: A versatile loop communication system is disclosed wherein recurring frames of the ring carrier signal are divided by a movable partition into a dynamically allocated time division channel portion and a data packet communication portion. A common signal channel, in the ring carrier frame, is used to logically connect and disconnect stations for either circuit or packet communication on a common bus extending from terminals located in the loop. The loop controller automatically forms a contiguous group of time division channels or signal bytes at one end of the ring carrier frame. The format of the time division multiplexing channels is such that dynamic time slot interchanges of signal bytes are produced by the controller without the necessity of counting circuitry in the terminals to identify specific channel locations. The dynamic time slot interchange or byte displacement function is provided by additional memory arrangements both for the signals being transported by the ring and control functions in the time division switch located in the controller. The remaining portion of the frame serves as a shared channel for packet header switched data. In order to provide a flexible basis for packet switching, the controller assigns address tags and retains a map of the system.

Higher radix on-line division

Abstract: We present a formal proof of correctness of the on-line division algorithm specified in an earlier paper [1]. We also derive two radix 4 on-line division algorithms, with non-redundant and redundant operands respectively.

A high speed division method in residue arithmetic

Abstract: This thesis is concerned with the operation of division in residue (modular) number systems. Theoretically, residue arithmetic offers the possibility of "carry-free' arithmetic as far as the operations of addition, subtraction and multiplication are concerned. Since a residue number system is not a weighted number system, the operations of division and sign detection are not simple. Therefore, in special purpose applications, where addition, subtraction and multiplication operations constitute a major part of the computations, residue arithmetic can potentially offer a fairly high speed gain over weighted arithmetic. Residue codes are introduced and the basic residue arithmetic operations are defined. Previous results on residue division are outlined. A well-known integer division algorithm is used and adapted for residue division . A new method is proposed for choosing an approximate divisor, approximate dividends and the partial quotients. The proposed method yields correct quotients faster than the existing methods and is general in its application i.e., it is not restricted by the choice of moduli as long as they are relatively prime.

The theory and implementations of high-radix division

Abstract: This report derives the theory of high-radix division in terms of the properties of the overlapped regions of the P-D plot. The minimum precision requirements in quotient selection are discussed. The methods of implementations in hardware and in read-only memory are explored.

Controller of copying machines

Abstract: PURPOSE:To make possible recognition of data of each use division by providing a collective memory means which segments copying sheet number data by each use division of the copying machine and collectively accumulates and totalizes the same and assigning the segments of the foregoing memory means with portable information recording media distributed to each use division. CONSTITUTION:Portable information recording media such as magnetic cards or the like having been distributed to each use division are read as electric signals with a read means 100, and these signals are detected witha detecting means 200 which in turn emits normal read signals. A command means 300 commands operation to a copying machine 600 with the normal read signal. A collective memory means 400 assigns the memory address conforming to the division information by the signal indicating the division information from the detecting means and has the memory addresses 4a thru 4c having been assigned according to the division information by controlling the copying sheet number data from the copying machine 600 in a counter control part 4. A display menas 500 reads out the copying sheet number data having been stored in each address and displays the same.

P-division points on certain elliptic curves

Abstract: © Foundation Compositio Mathematica, 1978, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Design of arithmetic elements for Burroughs Scientific Processor

Abstract: The design criteria and implementation of the Arithmetic Element (AE) of the Burroughs Scientific Processor, a vector machine intended for scientific computation requiring speed of up to 50 million floating-point operations per second, is discussed. An array of 16 AEs operate in lockstep mode, executing the same instruction on 16 sets of data. The 16 AEs are one stage in a pipeline which consists of 17 memory modules, an input alignment network, and an output alignment network. The AE itself is not pipelined. It can perform over one hundred different operations including a floating-point addition, subtraction and multiplication, division, square root, among the others. Eight registers are provided for the storage of intermediate values and results. Modulo 3 residue arithmetic is used for checking hardware failures.

Microprocessor having multiply/divide circuitry

Abstract: A microprocessor having the capability of performing either a multiply or divide operation from a single instruction for each operation is provided. Much of the standard circuitry of a microprocessor is used along with a multiply/divide cycle counter, logic circuitry, and a shift network separate from the arithmetic logic unit. The microprocessor has the capability of performing unsigned integer multiplication and division. A shift and add algorithm is used for multiplication while for division a non-restoring divide algorithm is used.

Sonic leak detector and method

Abstract: Sonic type leak detector system for liquid storage tanks or the like. It uses a hydrophone to convert sonic waves in the liquid to electrical signals. The electrical signals are divided by two band pass filters. The division is into one band which contains any leak signals, and another band which contains only noise signals. Then both bands are blanked whenever the noise signal amplitude exceeds a predetermined amount. There is a differential amplifier that acts on the outputs of both band pass filters to amplify the difference after averaging of each, whenever signals are not blanked. And, there is an indicator to show when a leak is present. The indicator is actuated whenever the output of the differential amplifier exceeds a predetermined amplitude.

Apparatus for digital division computation

Abstract: A division A/B where A and B are represented in a radix D (assuming the absolute value of D is greater than one) can be accomplished by evaluating a power series. It is very important not only for the power series to converge but also to converge quickly in practical application. When the convergence rate of the power series is close to one, the convergence is slow. Usually it results in lengthy and time-consuming computation to obtain a reasonably good approximation of the reciprocal of the divisor B. The invention that accelerates the convergence could be used in a digital computation system for performing a faster division A/B. In digital system, the dividend A and the divisor B are stored in digital registers. This invented apparatus determines acceleration constants from the stored digits of the divisor B and the determinate constants are multiplied to the stored numbers A and B. Then, the convergence rate of the power series of A'/B' where A' and B' are the constant multiplied A and B, respectively, becomes a smaller number so that an evaluation of the power series can be performed very quickly. Thus, the power series implementation to division process is useful in practical application.

Unipotent matrix groups over division rings

Abstract: Abstract If G is a unipotent group of n×n matrices over a division ring of characteristic 0 or prime p greater than (n- 1) (n-[n/2]) where [n/2] is the greatest integer less than or equal to n/2, then it is proved that G can be simultaneously triangularized.

Variable divider circuit

Abstract: PURPOSE:To constitute an integrated variable divider circuit which is suited for the division of the high-frequency signal, by using the I L logic gate effectively to realize an integration and also avoiding the deterioration of the operation speed caused by the I L logic gate.

Super Stable Division Rings

Abstract: Publisher Summary This chapter discusses super stable division rings. A structure is called stable, super-stable, or ѡ-stable if its first order theory has the corresponding property. An ѡ-stable field is finite or algebraically closed; however, it is not known whether other super-stable fields exist. The chapter proves that when D is a super-stable division ring, then D is finite dimensional over its center. This result implies that an ѡ-stable division ring is commutative. The theorem also implies that if D is assumed as a division ring of infinite dimension over its center, T as the first order theory of D, and κ > א o a cardinal, then T has 2 κ nonisomrphic models of cardinality κ .

Electronic apparatus with time-division drive

Abstract: An electronic apparatus comprises a phase signal generator for generating mutually different phase signals, one of which is selectively supplied to plurality means driven by a time-division drive.

Electronic switching system

Abstract: In a telephone exchange system comprising a time division exchange system and space division concentrators connected to said exchange system with a PCM lines, said concentrators are controlled by said exchange system, thus those volume of hardware in the concentrators can be considerably reduced. Said concentrator comprises a space division switching network having self-latched electronic contacts, which are controlled by a periodical drive pulse from a cyclic readout type memory.

Signal recording/reproducing method

Abstract: PURPOSE: To secure an equal speed between recording and reproducing by recording the PCM signals and others with the speed different with every circular region of the different disks and then controlling in steps the revolution speed of the disk based on the reproduction signals. CONSTITUTION: The information of PCM signals and the like recorded at circular regions 3 1 , 3 2 and so on of disk 1 in the different revolution speeds is reproduced through head 5. As this reproduced information features different bit frequencies every circular region, resonance circuits 6 1 , 6 2 and so on produce the resonance output corresponding to the circular regions to read out the matrix-type memory contents of ROM7 in the form of the decision signals of the circular regions. And the division output of program counter 9 is controlled according to the circular regions for motor control circuit 8. Thus the motor of circuit 8 is controlled in steps in accordance with the circular regions to secure the equal speed for both recording and reproducing with every region. As a result, the recording density can be increased if the recording speed is decided higher in accordance with the regions. COPYRIGHT: (C)1980,JPO&Japio

Time division multiplication system and its apparatus

Abstract: PURPOSE:To increase the transmission efficiency and to cope with the application for the digital network by packet exchange, by realizing both the character multiplication simultaneously in a high-speed data flow in accordance with the request of the terminal.

Electric energized sintering apparatus

Abstract: PURPOSE:The said apparatus in which large uniform compacted good can be obtained by the use of small capacity electric source by the division of the compressing punch and anvil into plural parts insulated electrically so as to energize separately the powder material.