Showing papers on "Remainder published in 1977"

The Frkchet derivative for the onedimensional electromagnetic induction problem

Abstract: Summary. From consideration of the higher order terms, it is shown that the magneto-telluric response is Frechet differentiable with respect to conductivity; this result remains valid for discontinuous profiles, which is not so in the case of the corresponding free-oscdlation problem for the elastic earth. The remainder term in the FrCchet formula is shown to be 01161~11~ and a numerical estimate is made of the bounding constant for a restricted class of conductivity models.

Error Bounds for Linear Combinations of Order Statistics

Abstract: A Berry-Esseen bound is obtained for trimmed linear combinations of order statistics. These linear combinations are written as the sum of a linear and a quadratic combination of independent exponentially distributed random variables plus a remainder term. The remainder term is shown to be of negligible order and Fourier methods are then employed to handle the linear and quadratic terms. The main theorem is also given in a version that more easily lends itself to applications.

The Fréchet derivative for the one-dimensional electromagnetic induction problem

Abstract: Summary. From consideration of the higher order terms, it is shown that the magneto-telluric response is Frechet differentiable with respect to conductivity; this result remains valid for discontinuous profiles, which is not so in the case of the corresponding free-oscdlation problem for the elastic earth. The remainder term in the Frechet formula is shown to be O|δσ|2 and a numerical estimate is made of the bounding constant for a restricted class of conductivity models.

Problems of convergence of multiple trigonometric series and spectral decompositions. ii

Abstract: ContentsChapter III. A study, based on the mean-value formula, of spectral decompositions for second-order elliptic operators § 1. Basic notation and definitions § 2. Properties of fundamental functions § 3. An estimate of the remainder term of the spectral function in the L2 metric and its consequences § 4. A uniform estimate of the remainder term of the spectral function § 5. The general case of second-order elliptic operatorsReferences

Convergence and Remainder Terms in Linear Rank Statistics.

Abstract: A new approach to the asymptotic normality of simple linear rank statistics for the regression case studied earlier by Hajek (1968) is provided along with the estimation of the remainder term in the approximation to normality.

Musical note oscillator

Abstract: The disclosure describes an improved digital oscillator for use in an electronic musical system capable of converting electrical tone signals into corresponding sound waves. The oscillator includes an adder, accumulator and multiplexer for selectively transmitting either a divisor number or increment number to the adder. The oscillator cyclically performs incrementing operations by using the increment number over a variable range established by the divisor number at the beginning of each cycle. When the modulus of the adder is exceeded, the adder generates a carry pulse and a remainder. The divisor is then added to the remainder before the incrementing operations begin again. A digital calculator automatically calculates the proper values of the increment and divisor numbers so that the carry pulses occur at a predetermined frequency.

Phase locked loop frequency synthesizer using digital modulo arithmetic

Abstract: A reference source of digital pulses of a first frequency f 1 is coupled to the input of a frequency synthesizer which is capable of providing a second frequency f 2 output signal. The second frequency is related to the first frequency by a predetermined, rational fraction (e.g., as f 2 = (M/N)f 1 ). The synthesizer includes a phase control unit comprising an adder by way of which a first number N is added each sample period to a remainder, the sum output of the adder being operated upon modulo a second number M, e.g., by dividing by M and discarding a resultant quotient to obtain a remainder. The remainder, having a value between zero and M-1, is compared to a prefixed signal, illustratively the largest integer in M/2. If the remainder is less than the prefixed signal, a first logic state control signal is provided to a control system; else a second logic state signal is so provided. The alternation between the first and second logic states is such that M pulses of the second frequency occur for every N pulses of the first frequency. Thereby, the second frequency is synthesized responsive to the first.

Cascadable analog to digital converter

Abstract: A circuit for converting an input analog signal into a digital representation and a remainder signal is disclosed. The digital representation is generated by a coder that counts an integral number of clock cycles during an interval in which the magnitude of the input analog signal is compared with the magnitude of a ramp signal. The remainder signal is generated by duration-to-amplitude conversion of a pulse whose duration is the fractional remainder of the final uncounted clock cycle.

Imprinter and method of making same

Abstract: An imprinter comprising a unitary, extruded base with an elongated receptacle extending along the upper length thereof and a molded plastic print bed inserted within the receptacle. An elongated recess in the print bed may also be provided so that a portion of a credit card or the like overlying the recess can be depressed therein to raise the remainder of the card and permit easy removal thereof.

On interpolation sets for the algebra $ r(x)$

Abstract: In this paper a connection is established between the behavior of the series remainder (where is the annulus , and is analytic capacity) and the Gleason distance in the algebra , as .It is proved that if the compact set , is the set of all peak points of , , and as , then in order that as , it is necessary and sufficient that uniformly on the set as .This result is applied in the study of interpolation sets of the algebra .Bibliography: 10 titles.

Multicriteria integer zero-one programming : a tree-search type algorithm.

Abstract: : An algorithm for zero-one integer programming problems with more than one objective functions is developed, implemented and tested. For a multiobjective problem the notion of optimality must be replaced with that of efficiency. A solution is said to be efficient if it satisfies the constraints and no other solution satisfying them scores as well with respect to all objective functions and better with respect to at least one of them. In the presented algorithm, the problem variables are partitioned into two sets; those whose coefficients in the objective functions are all of the same sign, and the remainder. A tree search implicit enumeration algorithm based on this partition is developed and computational results are presented. (Author)

Method for dividing two numbers and device for effecting same

Abstract: Disclosure is made of a method for dividing two numbers, whereby the numbers are converted to the binary code, and there is formed an address code of three digits of the dividend (the or remainder) by determining the position of the highest-order significant digit in the three high-order digits of the divisor. The address thus formed serves to produce three digits of the remainder, i.e. a digit corresponding to the highest-order significant digit of the divisor code and two adjacent higher-order digits. The three digits of the remainder are analyzed and, depending upon the result of the analysis, the code of either the single, or doubled, or trebled divisor is subtracted from the remainder code, whereby the next two quotient code digits are produced. Disclosure is further made of a device for effecting the proposed method for dividing two numbers, which comprises an arithmetic unit connected to dividend (or remainder) registers, buffer registers, divisor registers and quotient registers. The device further includes a converter of the code of the three high-order divisor digits to the address code of the three remainder digits, whose information input is connected to an output of the divisor register. The output of said converter is connected to one of the information inputs of a three remainder digits selection commutator. Another information input of the commutator is connected to an output of the dividend (or remainder) register. The output of said commutator is connected to the input of a three-digit register which is connected to one of the inputs of a microprogram control unit of said division device. The output of the control unit connected to the control inputs of all the elements of said device.