Binary Chain Research Articles

Notes on the main band fine structure of a dilute, disordered binary chain

It is shown that fine structure exists in the main band of the frequency spectrum of spectrum of a dilute, disordered binary chain and that an approximate theory of Wu accounts for the general features of this structure.

Application of infinite order perturbation theory in linear systems. II. The frequency spectrum of disordered chains

A formulation is presented such that the ensemble average of the diagonal elements of the Green's function for a one-dimensional disordered system can be calculated to arbitrary accuracy. The method is illustrated with an application to an isotopically disordered chain. An approximate solution to the frequency spectrum of a disordered binary chain is also discussed.

The Joint Probability Generating Function for Run-Lengths in Regenerative Binary Markov Chains, with Applications

Gontcharov obtained the joint probability generating function for the numbers of runs of all lengths, both of successes and failures, in a Bernoulli sequence. This is here generalized to a class of regenerative binary Markov processes. For an allied class of Markov processes, the probability generating function is obtained for a "total score" defined in terms of runs of successes only, and asymptotic formulas are derived for the expectation and variance of the score.

Sur la formation de chalcogenures vitreux ternaires

The formation, from simple structure units, of binary chains using mostly the p-orbitals, the rules governing the insertion of a third element in these chains and the possible inclusion of foreign units give a rather good account of the limits for obtaining the vitreous state in the ternary chalcogenides. Examples are given in the AsSeGe, SbSeGe, AsSeTl, AsSe*z.sbnd;Br and AsTeI systems.

Cell division in marine Ceratium. I.

The binary fission of 3 forms of marine Ceratium, C.gibberum, C.gibberum f.sinsitra and C.tripos f.atlantica was observed in culture. In either of the 3 forms, it is possible to make cell division take place under the condition of single cell culture. Both binary fission and chain formation have been observed. Concerning the relationship between binary fission and chain formation, light intensity may be considered as a controlling factor.

Vibrational modes of disordered chains in next-nearest-neighbour interaction

The vibrational modes of an isotopic, disordered binary chain in harmonic approximation including next-nearest neighbour interaction have been studied. The chain and the nearest-neighbour force constant λ are taken to be the same as those chosen by Dean and Bacon to facilitate comparison. The modes at intermediate and high frequencies though remaining localized show a tendency to spread out which increases with increasing next-nearest-neighbour force constant μ. This tendency is particularly marked at intermediate frequencies. The localized modes of the binary chain are found to be directly related to the clusters of light atoms appearing in the chain. To determine the effect of neighbours more distant than the next-nearest, harmonic forces due to all neighbours were introduced. The force constant due to the kth neighbour was assumed to be λ 2 k−1 . The intermediate- and and high-frequency modes continue to be localized in this long-range interaction.

Wide dynamic range logarithmic count rate meter

The developed solid state, logarithmic, count rate meter, having eight decades of dynamic range (10 1 to 10 8 counts/min) and applicable in fast nuclear counting systems, incorporates a high-speed integrated circuit binary chain and provides a maximum deviation of ±16% of reading from the desired logarithmic characteristic over the entire range of the instrument.

Design Equations for the Finitely and Infinitesimally Separated Position Synthesis of Binary Links and Combined Link Chains

A general method for synthesizing spatial linkages (derived in a previous paper [1]) is applied to the design of various types of binary links and combined link chains. Equations governing those special points and lines which define the link dimensions are derived. Types and order of loci of such special points and lines and the maximum number of design positions for each link are given. Numerical method for computing these special points and lines are discussed, and a numerical example is presented.

A Unified Theory for the Finitely and Infinitesimally Separated Position Problems of Kinematic Synthesis

A rigid body is studied in a series of different positions. These positions can be finitely separated, infinitesimally separated, or a combination of the two. A general method for determining the locations of points or lines (in the rigid body) which have their different multiple positions satisfying the constraints of binary links or combined link chains is developed. In a companion paper [10] equations governing the locations of these special points and lines are derived.

Kinetics of replication of copolymeric DNA

The theory of crystallization of binary chains ( Chernov, 1965) has been used to study the kinetics of replication of copolymeric DNA. The importance of the stacking and bond energies in the process of replication is emphasized. The dependence of rate of replication on the distribution of base pairs for the same ratio of ( G + C) and ( A + T) bases in DNA is established. Analytic formulae are given for the rate of replication for copolymeric DNA with regular and random distribution of base pairs in terms of frequencies of the addition and dissolution of hydrogen bonds. A comparison is made with the observed rates of replications for synthetic and natural DNA.

Rearrangement of a flat surface without altering the number of broken bonds : J. F. Nicholas, J. Phys. Chem. Solids, Vol. 24, 1963, pp. 1279–1284

The vibrational modes of an isotopic, disordered binary chain in harmonic approximation including next-nearest neighbour interaction have been studied. The chain and the nearest-neighbour force constant λ are taken to be the same as those chosen by Dean and Bacon to facilitate comparison. The modes at intermediate and high frequencies though remaining localized show a tendency to spread out which increases with increasing next-nearest-neighbour force constant μ. This tendency is particularly marked at intermediate frequencies.The localized modes of the binary chain are found to be directly related to the clusters of light atoms appearing in the chain.To determine the effect of neighbours more distant than the next-nearest, harmonic forces due to all neighbours were introduced. The force constant due to the kth neighbour was assumed to be λ2k−1. The intermediate- and and high-frequency modes continue to be localized in this long-range interaction.

Quadratics in Markov-Chain Frequencies, and the Binary Chain of Order 2

SUMMARY Let nr be the frequency of the state r in a segment of a regular ergodic Markov chain. It is shown how to obtain the asymptotic distribution of any quadratic expression in the nr’s. The method is especially convenient where the Markov chain is produced by a random motion on a circle. An explicit formula is given for the asymptotic variance of the number of 0’s in a binary Markov chain of order 2.

An automatic test set for FM/FM telemetry systems

Techniques of automation are applied to the problem of preflight check-out of airborne telemetry systems. The result is a test set that measures and analyzes key system parameters without operator participation. Operation of the subcarrier analyzer portion of the test set is described. Circuit details of pre-set binary counter chain, counter readout matrix, and GO/NO-GO voltmeter are given. An example of typical test set packaging is shown.

Periodic Impurities in a Periodic Lattice

Because binary delta-function lattices of the Kronig-Penney type which have been previously studied are incapable of describing several important features of real crystals, the eigenvalue problem for a periodic linear chain $\ensuremath{\cdots}A(BB\ensuremath{\cdots}BB)A(BB\ensuremath{\cdots}BB)\ensuremath{\cdots}$ of arbitrary square-well, $A$ and $B$ atoms of an arbitrary concentration is taken up and solved. The methods used are generalizable to other binary or multi-nary chains. It is shown that a theorem of Saxon and Hutner and of Luttinger relating to the preservation of the common forbidden energies of pure $A$ and pure $B$ lattices in a mixed $A$, $B$ lattice is peculiar to their deltafunction representations of $A$ and $B$, and is without general validity.