Showing papers on "Division (mathematics) published in 1970"

On Division by Functional Iteration

Abstract: In order to avoid the time delays associated with linearly convergent division based on subtraction, other iterative schemes can be used. These are based on 1) series expansion of the reciprocal, 2) multiplicative sequence, or 3) additive sequence convergent to the quotient. These latter techniques are based on finding the root of an arbitrary function at either the quotient or reciprocal value. A Newton-Raphson iteration or root finding iteration can be used.

Generation of Products and Quotients Using Approximate Binary Logarithms for Digital Filtering Applications

Abstract: An approximate method for rapid multiplication or division with relatively simple digital circuitry is described. The algorithm consists of computing approximate binary logarithms, adding or subtracting the logarithms, and computing the approximate anti- logarithm of the resultant. Using a criteria of minimum mean square error, coefficients for the approximations are developed. An error analysis is given for three cases in which the algorithm is useful. Finally, applications to digital filtering computations are considered which illustrate that log-antilog multiplication is not simpler than an array multiplier for computing single products, but is useful for parallel digital filter banks and multiplicative digital filters.

Design of the Arithmetic Units of ILLIAC III: Use of Redundancy and Higher Radix Methods

Abstract: In keeping with the experimental nature of the Illinois Pattern Recognition Computer (ILLIAC III), the arithmetic units are intended to be a practical testing ground for recent theoretical work in computer arithmetic. This paper describes the use of redundant number systems and the design of a structure with which multiplication and division are executed radix 256. The heart of the unit is the stored-sign subtracter, a recently discovered member of the family of borrow-save subtracters and carry-save adders. A cascade of these subtracters, controlled by a multiplier recoder, provides multiplication. The same structure, controlled by a "model division" (a quotient recoder), performs division.

On Range-Transformation Techniques for Division

Abstract: This note points out the close relationship between some of the recently described division techniques, in which the divisor is transformed to a range close to unity. A brief theoretical analysis is presented which examines the choice of quotient digit when this type of division technique is used for conventional and signed-digit number systems.

Fluid-mixing device

Abstract: Fluid-mixing apparatus which includes a plurality of stationary mixing units, formed of planar members, disposed in series longitudinally of a passage for sequentially and repeatedly dividing and recombining fluid flows during the travel thereof through the passage, with the fluid flows being directed along different serpentine paths after each division thereof.

Nonrestoring binary division using a cellular array

Abstract: An iterative array for nonrestoring division is described. It uses a logic cell which has been proposed for an array for binary square-root extraction. The array for binary division is fully iterative in terms of cell logic and in the interconnection pattern between the cells.

On Optimal Ierative Schemes for High-Speed Division

Abstract: This paper describes division schemes which are derived from the classical functional iterative schemes. These schemes are compared with t he schemes currently used in the high- speed digital computers.

A requirement of polyamines for bacterial division

Abstract: Synchronous cell division in an arginine auxotroph and a histidine auxotroph of Escherichia coli was obtained after starving for the required amino acid for 1 hr. However, cell division was not synchronized after starvation for 1 hr in another arginine auxotroph. This difference is proposed to depend on differences in the concentrations of polyamines in the cells. During amino acid starvation the ratio of putrescine concentration to spermidine concentration decreased in all strains, but it recovered afterward more rapidly in the third strain than in the other two. The cells divided when the ratio returned to normal in the Arg(-) mutants. Added putrescine permitted some of the cells of the first two mutants to divide sooner after amino acid starvation and thus eliminated synchrony. Spermidine added alone had no effect, but, when it was added together with putrescine, it restored synchronous division. Synchrony was established in the third mutant by adding spermidine after arginine starvation. Thus, both the variations in polyamine content and the effects of added polyamines suggest that the polyamines are essential in permitting cell division. We suggest that the molar ratio of putrescine to spermidine can be a critical factor for cell division. This effect of polyamines seems to be specific for cell division. Amino acid starvation does not induce delays in subsequent mass increase or deoxyribonucleic acid synthesis. Possible mechanisms of polyamine action are discussed.

Time division switching system

Abstract: Control memories actuate space division switching matrices to connect plural time division multiplex lines to different input and output connections of time slot unit storage locations for performing plural time slot interchange functions simultaneously and independently in different portions of the locations. In two embodiments the locations are in a dynamic form as the respective stages of a reentrant shift register and the respective locations in a circulating delay line. In another embodiment the locations are in a static form as the respective memory devices in a random access memory. In any embodiment status and compare circuits evaluate storage location control signals for finding an available path of suitable length in the time-storage domain of the locations for establishing new connections between calling and called lines.

A survey of cell length and frequency of multiplicative divisions in the cambium of conifers

Abstract: Study of many species of conifers has revealed certain trends with respect to cell length and rate of anticlinal division in the multiplication of fusiform initials in the cambium. In the stem, rate of anticlinal division tends to be high when annual rings are narrow, and to stabilize at a relatively low level when rings exceed 2 mm in width. Cell length at division is usually greatest when rings are about 1 mm wide, and decreases with both widening and narrowing of the rings from the optimal width. Significant differences occur between species in both rate of anticlinal division and cell length. In general, rate of anticlinal division and cell length are inversely related, but in some species there is wide deviation from the common trend.

A multiple-precision division algorithm

Abstract: A generalized division algorithm for use with positive integral operands is presented. Depending upon the algebraic relationship of the first two ciphers of the divisor, one or at most two adjustments to the original divisor and dividend must be performed before the division operation can be initiated. The uniqueness of this method will cause each trial cipher in the quotient to be either equal to or one greater than its final replacement.

Improvements relating to Printing Rollers

Abstract: 1,198,863. Printing surfaces. MACLELLAN RUBBER Ltd. 22 July, 1968 [20 July, 1967], No. 33291/67. Heading B6C. [Also in Division F2] In a printing roller of the kind having a cylindrical core with a covering of rubber engraveable by cutting to a predetermined depth to provide the required printing pattern, an intermediate layer of a rubber-treated material is provided in the rubber covering and is spaced from the outer surface of the covering at a distance equal to the required engraving depth. As described, a metal or copolymer core 1 is first either rough-turned, varnished and coated with a thin layer of vulcanite, or is smoothed turned and an adhesive coating applied thereto. A thicker layer 2 of unvulcanized rubber, either natural or synthetic, or a mix of these which may include some plastics, is applied over the vulcanite layer or adhesive, the thickness and hardness of the layer 2 being selected in accordance with the required resilience of the finished roller. The layer 2 is now semi-cured and its surface ground to provide a smooth surface to which is applied a solution of unvulcanized rubber. An intermediate layer 3 of cotton canvas proofed with rubber is now spirally or circumferentially wound on the layer 2 and over this is applied the engraving rubber layer 4 of a thickness, usually 1/8-1/4 inch, corresponding to the depth of engraving. The whole roller is now bound with a strip of fabric and completely cured, after which the fabric is removed. The engraved parts can be formed by making incisions in the layer 4 to the depth of the layer and peeling off the parts forming the pattern. Where a surface is required having two depths of engraving, two additional layers 3, 4 may be added.

Space division multiplexed holographic apparatus

Abstract: HOLOGRAPHIC APPARATUS INCLUDING A PLURALITY OF SPATIALLY COMPLEMENTARY SAMPLING MASKS FOR SPACE DIVISION MULTIPLEXING RESPECTIVE OBJECT SIGNALS IN SUCH A WAY THAT EACH RECORDING IS DISTRIBUTED THROUGHOUT SUBSTANTIALLY THE FULL AREA OF THE HOLOGRAPHIC STORAGE MEDIUM. INDIVIDUAL MASKS ARE USED FOR SUCCESSIVELY RECORDING THE VARIOUS OBJECTS AND THE MASK CORRESPONDING TO A PARTICULAR RECORDING IS USED IN PLAYBACK APPARATUS FOR PRODUCING RESPECTIVE IMAGES OF SAID OBJECTS.

A device for use in detaching a cylindrical member from a supporting structure

Abstract: 1,201,663. Gripping tools. E. M. ARTHUR. 14 Jan., 1969 [26 Jan., 1968], No. 4103/68. Heading B4W. [Also in Division B3] A device for use in detaching a generally cylindrical member from a supporting structure with which it is in threaded engagement consists of the combination of a flexible band 10 including a pair of closed loops 11, 12, with a tool consisting of a shaft 15 and a pair of spacedapart projections 17, 18. The flexible band may be of metal strip (as shown) or may take the form of a chain, belt, or other flexible element. The band may be adjustable for use with different diameter cylindrical members to be unscrewed. In use, the shaft 15 is engaged and turned by a wrench, for example.

Time shared positioning system for numerical control

Abstract: A numerical control system of the point-to-point type for a three-axis machine wherein a single arithmetic unit accommodates the arithmetic operations for all three axes in a time division multiplexed fashion.

Digital function generator

Abstract: A digital function generator which may be programmed to provide an output signal which is an arbitrary function of the applied input is disclosed. An input signal is applied simultaneously to a counter and binary divider. The input counter and divider are interconnected by logic circuitry which controls the division rate in accordance with the number in the counter whereby the output of the divider will be commensurate with the number of input pulses delivered to the function generator divided by the factors decoded from the incremental position of those input pulses during each sampling period.

Malfunction monitoring equipment for a time division multiplexed transmission system

Abstract: A malfunction monitoring system for the analog circuit of a time division multiplexed pulse code modulation system uses a noise signal as the pilot signal.

Improvements in or relating to Aircraft

Abstract: 1,176,371. Closed circuit television indicators on aircraft. T. K. H. PRIESTNALL. 22 May, 1968 [22 Feb., 1967], No. 8495/67. Heading B7W. [Also in Division H4] In an aircraft a plurality of television cameras and television display screens are provided so that the passengers and/or the pilot may observe views outside and inside the aircraft. The screen displays may be controlled by video tapes, and may be arranged to show cine film. The pilot may train at least one of the camers in different directions.

A self-aligning bearing

Abstract: 1,214,111 Ball and socket joint H ELGES 19 Feb, 1969 [12 June, 1968], No 8911/69 Heading E2F [Also in Division F2] A ball and socket joint comprises a onepiece outer ring b having a spherical bore and provided with annular grooves c on the inner surface at the edges, the grooves being provided with ring seals d of elastic material

Improvements relating to the continuous casting of metals

Abstract: 1,178,981 Toothed gearing CAMPBELL GIFFORD & MORTON Ltd 7 March, 1967 [15 Feb, 1966], No 6690/66 Heading F2Q [Also in Division B3] At least one pin 35 on a driving wheel 36 co-operates with radial or curved slots 34 in a wheel 33 to drive intermittently a shaft 30 by which extraction rolls for a continuous casting (see Division B3) are driven To lock the driven wheel 33 during dwell periods, a moon-shaped disc 45, mounted for rotation with the driving wheel 36, slides into peripheral recesses 46

Pcm time division multiplex process

Abstract: A process for jointly completing a connection for both transmission directions in a pulse code modulated telecommunication network having a plurality of exchange stations connected over four wire time division multiplex lines. The system operates according to the invention to complete a connection in segments simultaneously for both transmission directions without the need for frame equalization.

Arithmetic game in which slots in playing pieces give solutions to arithmetic problems

Abstract: A mathematical game having a game board divided into four sections, each of which is coded. Each of the sections is divided into numbered areas with the numbers increasing progressively from the center of the board outwardly to the side of the board. Each of the areas is divided into one system of basic mathematics, division, subtraction, addition and multiplication, and each of such areas is progressively increasingly numbered from left to right, top to bottom, with numerals impressed thereon. A set of playing blocks is provided for each of the sections and is also coded to match the correspondingly coded section; a slot is cut in each of said blocks for positioning according to the number of such block with the position of such slot being determined by the number of the block with the numerical order being from left to right, top to bottom, such that, for example, a block for the numeral two would have a slot positioned inwardly from the left-hand side of such block and along the upper edge of such block.