Showing papers on "Division (mathematics) published in 1971"

Function generation by approximation employing interative interpolation

Abstract: A method of solving a function for values of a variable when values of an independent variable are given, the method being especially valuable for use in or with a computer, an advantage being minimization of storage requirements. The method is an extension of the branch of mathematics known as numerical analysis, and specifically of the division of that branch known as approximation. An expression is developed for a locus of points which approach points on the given function, i.e., a polynomial expression having a high degree of convergence. The method includes finding solutions to the terms of the polynomial expression by reiterated interpolation. Only a relatively small number of factors need be stored. The method can be employed to calculate values to predetermined accuracy, and is suitable for many functions although it is especially well suited for many transcendental functions. Embodiments of apparatus suitable for performing the method are also disclosed. The apparatus includes elements of electronic data processing such as shift registers, adders, and the like to perform the interpolation involving addition, subtraction and division by 2. The algorithm developed as a manifestation of this method is describable as an add-shift algorithm.

Photocontrol of the orientation of cell division in Adiantum : II. Effects of the direction of white light on the apical cell of gametophytes.

Abstract: Two-dimensional prothallia of Adiantum capillus-veneris always expanded in a plane which was at a right angle to any given direction of irradiation with continuous white light. The expansion began with a longitudinal division of the apical cell, in the filamentous protonema, and the orientation of the mitotic cell plate of this first longitudinal division as well as the subsequent divisions was always parallel to the direction of the incident light. When three irradiations with white light, interrupted by periods of darkness, were given, two transverse and one subsequent longitudinal division were induced. When the last two irradiations were given from the same direction, the cell plate of the first longitudinal division in most protonemata was oriented parallel to the direction of light. However, when the direction of light during the third irradiation was at right angle to that during the second, the frequency of the longitudinal division greatly decreased but that of the third transverse division increased. Thus, the orientation of the first longitudinal division appeared to be controlled in some way not only by the irradiation which actually induced the third division but also by that inducing the preceding transverse division, while the direction of light for the first transverse division had little effect on the orientation of the third division.

Improvements in or relating to means for supporting a gas turbine engine in an aircraft

Abstract: 1,236,917. Gas turbine engines; mounting in aircraft. ROLLS-ROYCE Ltd. 28 May, 1968 [14 June, 1967], No. 27415/67. Heading B7G. [Also in Divisions E2 and F1] Support means for a gas turbine engine in an aircraft includes a set of supporting links that takes the full load, together with additional links that only take a load upon failure of one or more of the supporting links. The links are distributed tangentially to the engine in transverse planes at the front and back of the engine casing and also longitudinally there of either parallel to the axis or at an acute angle thereto (Figs. 2, 3, 4, not shown) the additional links are provided with resilient bushes so that they do not normally carry load (see Division E2).

Economical Iterative and Range-Transformation Schemes for Division

Abstract: It is shown that the Wilkes-Harvard and Newton-Raphson iterative division schemes with an order of convergence more than two or three are uneconomical for realization in computers.

Concise cellular array for multiplication and division

Abstract: This letter describes how the combination of one of the simplest arithmetic cells and a new control?arithmetic cell can be used to form a versatile array for multiplication and division which uses fewer cells, and fewer gates per cell, than existing comparable arrays.

Comparison of restoring and nonrestoring cellular-array dividers

Abstract: Recent letters have described restoring and nonrestoring cellular-array dividers. It has been implied that nonrestoring division is the less complex and faster technique. Here, a comparison is made which shows that restoring division can use a simpler cell, is marginally faster than nonrestoring division and has the added advantage that the true remainder is available.

A catalog of models for multiplication and division of whole numbers

Abstract: The above catalog contains fifteen headings, each of which indicates a collection of families of models for multiplication and division of whole numbers. The catalog refers to somewhat more than sixteen families of models which are easily distinguished one from the other.

Structural members for use in the construction of a spherical or part-spherical structure

Abstract: 1,255,636. Jig saw puzzles. G. A. WEMYSS. 25 Nov., 1969 [25 Nov., 1968], No. 55741/68. Heading A6H. [Also in Division El] A toy in the form of a spherical or part spherical jig saw puzzle is formed by a framework of identical members 1, twenty four of which will form a complete sphere. Each of the members are joined at their vertices to adjacent members and spherical triangular plates are clipped to the framework each over one triangular aperture therein to provide a dissected spherical surface carrying a picture or design.

Storage system and stackable container

Abstract: 1,219,456 Pins ILTUR-A-G 10 April, 1968, No 17399/68 Heading F2H [Also in Division B8] A pin 3 is in one form, Fig 9, integral with an arm 5 on a frame 2 and pivoted downwards from the full-line position shown to secure the frame to the wall 1a of a box (see Division B8) In another form, each pin 3, Fig 13, is separate from the frame and has a rectangular head 3a

Asynchronous binary restoring divider array

Abstract: The timing of an asynchronous restoring division array is investigated, and it is shown that this array is substantially faster than the synchronous array and marginally faster than the asynchronous nonrestoring division array.

Apparatus for delivering bulk material

Abstract: 1,237,284. Weighing apparatus. CARL SCHENCK MASCHINENFABRIK G. m. b. H. Aug. 13, 1968 [Aug. 29, 1967; Oct. 4, 1967], No. 38730/68. Heading G1W. [Also in Division G3] Apparatus for delivering material at a substantially constant rate comprises a feed belt 4, a storage belt 9 for receiving material discharged from the feed belt 4, a measuring device 8 for determining the loading on the storage belt 9 and for controlling the position of the discharge end of the feed belt relative to the storage belt 9 so as to achieve a substantially constant load of the bulk material on the storage belt. As shown, the measuring device 8 is a load sensing device connected to a weighbridge 6 having rollers 11 over which a part of the storage belt 9 travels, the measuring device being connected to a device 12 which is arranged to shift the feed belt 4 bodily by an amount depending upon the weight sensed by the device 8, such movement being detected by a member 21 which actuates a controller 22. The controller 22 is arranged to vary the supply of material to the feed belt 4 and may also be arranged to adjust the speed of belt 4 in accordance with the load sensed on the storage belt 9. The controller may also be controlled by a weighing belt 14 arranged at the delivery end of the storage belt 9. The material may be supplied from a store 2 to the feed belt 4 by a bucket wheel 1 and conveyer belts 3. The load on the storage belt 9 may alternatively be measured by volumetric or other means.

Improvements in apparatus for distance measurement or control

Abstract: 1,234,791. Non-linear amplifiers. SABA SCHAEZWALDER APPARATE - BAU - ANSTALT AUGUST SCHWER SOHNE G.m.b.H. 31 May, 1968, No. 26296/68. Heading G4G. [Also in Division H4] In a distance-determining system (see Division H4) a non-linear amplifier (see curve 10 on Fig. 3, not shown) comprises transistors T 10 ... T 15 and associated circuitry.

Right Shift for Low-Cost Multiply and Divide

Abstract: Although integrated-circuit technology promises to reduce the cost of logic, there are still situations where low-cost multiplication and/or division algorithms must be implemented in today's technology. This can be accomplished by the algorithms presented here: repetitive addition (subtraction) algorithms for multiplication (division), employing a right shift. The result of the operation is truncated, which limits the accurqcy but reduces significantly the amount of intermediate storage required. The degree of accuracy is quite adequate for selected applications.

Improvements in rectifier assemblies

Abstract: 1,245,741. Rectifier assemblies. ENGLISH ELECTRIC CO. Ltd. 16 July, 1968 [18 July, 1967], No. 32843/67. Heading H1K. [Also in Division H2] A rectifier assembly comprises, for each phase, a plurality of pairs of bus-bars each with a plurality of diode rectifiers distributed along their length and connected in parallel between them. The current inputs and outputs to the bars are positioned thereon intermediate the ends in such a way as to reduce variations in loading between individual cells to a minimum. Several externally commoned inputs and outputs to each bar may be used if required. In the thre-phase arrangement shown in Fig. 3, with 14 diodes between each pair of bus-bars and a single input and output to each bus-bar, the optimum positioning commensurate with the need to dispose the connections between pairs of diodes is as shown. The diodes are clamped to one finned bus-bar and are connected to the other, which is thinner and therefore more resistive, through individual fuses F. Conductor 5 forms a common output conductor for all phases. Where there are a plurality of input conductors for each phase these are preferably strapped together adjacent the bus-bars, especially when the rectifier banks are linearly arranged in phase order RR, YY, BB. Closer balancing of the current distribution may be achieved by inserting impedances in series with individual diodes or by varying the section of the bus-bars as by local reinforcements or sawcuts.

Atomic Physics Division

Abstract: actions with foils presented. On the theoretical side it was shown that two existing theories needed modification. The inclusion of plasma correlations into the theory of Compton scattering in a plasma was found to introduce a peak in the transmitted radiation, com­ patible with experimental results. The ponderomotive force structure was calculated with reflections included, and found to produce a periodic den­ sity distribution but no overall dyna­ mical effects in a model plasma. Various aspects of the diagnostics and interpretation of pico-second phe­ nomena associated with mode-locked lasers were discussed by D. J. Bradley (Belfast) and M. Duguay (Bell Tele­ phone Laboratories). Plasma diagnos­ tics by scattering of laser radiation was discussed for several applications including the measurement of magne­ tic fields and the observation of tur­ bulence in collision-free shocks. The first reports of CO2 laser scattering from plasmas were given by C. Yamanaka (Osaka), M. Kornherr (Garching) and A. Offenberger (Alberta). The meeting was attended by about 100 people. Representation from most of the major laboratories ensured that all the important topics were covered and that useful discussions were held on the state of the art and possible future developments. G.J. Pert

Systems of division problems for distributions

Abstract: Suppose (ftj)ist.jtr is a pxp matrix of real-valued infinitely (respectively /«-times continuously) differentiable functions on an open subset fl of R\". Then (fti)isi,isp maps the space of ^-tuples of distributions on fl (respectively distributions of order Smonfi) into itself. In the present paper, the pxp matrices (P/)isi,

Improvements in and relating to systems for the storage, handling, selection and distribution of goods

Abstract: 1,249,481. Automated warehouses. G. J. SARVARY. 13 Feb., 1969 [20 Feb., 1968; 25 March, 1968], Nos. 8123/68 and 14377/68. Heading B8E. [Also in Division A4] In a three-dimensional system for the storage and distribution of goods on pallets, order picking towers 14, Fig. 2, are provided and these have, at each storage level, platforms 16 which are movable to a selected row of pallets so that a pallet may be removed from a storage position, moved transversely to the direction of removal and transferred to an adjacent row. Elevating carriages 17 are provided in the towers 14 on which an operator stands whilst picking goods from the pallets on the platforms 16. The goods removed are placed on conveyers 18 which deliver them to carton lowerators 19 communicating via belt conveyers 20 with tilt-tray sorters 21. Indicators 23 inform the operators how many articles to remove from the pallets. Spaces equal in number to a complete row are kept empty so that pallets may be transferred thereto by the platforms 16. The warehouse comprises bulk stores 2, picking areas 3 and pallet replenishment areas 4. The whereabouts of pallets in the bulk store is known to the computer and full pallets are transferred from input elevators 6, 7 into the bulk storage areas by transfer trolleys 9, Fig. 3, which run along the aisle 5 at each level. The transfer trolleys also move pallets from the bulk store to the picking area under computer control, and empty pallets from the picking area to the empty pallet lowerators 25, Fig. 2, which remove them to a "goods'inwards " area to be refilled. Additional picking positions 27, 28 may be provided. Fig. 6 shows an alternative warehouse arrangement in which picking areas 81, 82 and bulk storage areas 83, 84 are provided. Transfer trolleys run along aisles 85, 86 and transfer pallets to a single picking tower 91. The tower has two elevator platforms 92, 93 for the handlers of a vertical carton lowerator 94 for moving cartons to a lower level.

Panel joining member

Abstract: 1,237,400. Joints. D. MAXWELL. 18 Aug., 1969 [28 Aug., 1968], No. 41132/68. Heading F2H. [Also in Division A4] A joining member 3 for releasably connecting together a pair of panels 1, 2 in side-to-edge rightangled abutting relationship comprises a pair of elements 4, 5 of constant and identical crosssection and an intermediate web 6 integral with the elements 4, 5, the elements 4, 5 having longitudinal axes at right angles to one another and the element 5 being provided with a screw receiving bore 7. The joining member may be of metal or plastics material and may be arranged to receive a self-tapping screw 8.

Multiple-article wrap-around carrier blanks

Abstract: 1,219,350. Clamps. OLINKRAFT Inc. 17 Dec., 1968 [26 March, 1968], No. 59966/68. Addition to. 1,192,265. Heading E2B. [Also in Division B8] A packaging band for securing six cans whose size may vary slightly has a uniform set of apertures 4 at one end and, at the other end, staggered sets 7 and 9 of tongues, one of which engages the apertures to secure the package.

Handle device for handling a container

Abstract: 1,221,764. Gripping tools. G. J. JOHNSON, and J. R. CHARGE. 22 Jan., 1969, No. 3664/69. Heading B4W. [Also in Division B8] A handle device for handling a container comprises an elongate rod 8 the top end of which terminates in a hook 9 and on which is slidable a handle assembly including a hook 14, the handle assembly being urged away from a limit stop 10 by resilient means. Preferably, two stops 10, 11 are provided, the upper stop 11 co-operating with a slot 11A in a tubular part 12A of the handle assembly both to align the hook 14 with hook 9 and to limit movement of the handle assembly away from the other stop 10 under the action of spring 16. In a modification (Fig. 6, not shown) the hook 9 is provided on a member slideable on the rod and selectively securable in one of a number of positions. The device may be used for handling containers having a rim at each end.

Analysis of a Model for Multiseptation in Bacteria

Abstract: The predictions of a model for multiseptation in bacteria recently proposed by Paulton are derived mathematically It is shown that independent of the growth rate, the time between septum formation and cell division is given by ts = · t, where is the average number of successive division sites and t is the generation time This result is in good agreement with the experimental data

Fast economical binary divider

Abstract: By eliminating the shift operation of a shift-and-subtract divider, array dividers speed up division. Since n+1 subtractors are required, there is a heavy equipment cost. However, since each parallel subtraction is data dependent, the subtractions are sequential and only one subtractor is operating at any one time. Here a divider is developed which speeds division by eliminating the shift cycle, but which only requires two parallel subtractors working sequentially.

Improvements in or relating to garden hand tools

Abstract: 1,235,666. Hand-tool handles. SAMUEL PARKES & CO. Ltd. 12 June, 1968 [13 June, 1967], No. 27128/67. Heading B4K. [Also in Division A1] A garden hand tool comprises a handle having a spigot 11 formed with either a spiral groove or slot 15, and a tool head 26 having a socket 27 provided with a stud 28 whereby in assembling the head to the handle the stud traverses the groove to pull the spigot into the socket. The tool head is formed with one or more notches 29 each having a longitudinally extending face 30 whereby a catch 18 mounted on the spigot and having a nose 23 slidable into engagement with a notch co-operates with the notch to prevent disassembly of the head from the handle. A range of different interchangeable tool heads may be provided. The catch 18 is retained against freely sliding movement in its housing 17 by a bowed leaf-spring (20) (Fig. 2, not shown).