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A method of measuring the positions of X-ray sources with Copernicus is described. The limitation of the accuracy achievable for bright sources is set by the uncertainty in the experiment pointing direction which is about + 0. 5' while for faint sources an additional contribution to the error of a similar magnitude arises from statistical fluctuations in the counting rates. The positions of a number of sources have been successfully measured. In addition, bright stars proposed as optical counterparts for a further four sources have been examined. Three of these associations are disproved, the results for the fourth being inconclusive. The proposed association of sources in the 2U catalogue with bright stars is found to be unlikely, the number of coincidences having been reduced by these and other observations to the level expected from random fluctuations. An important problem of X-ray astronomy is the identification of the optical and radio counterparts of the X-ray source, such counterparts having been found only for a small fraction of the known sources. Of course, once a counterpart has been found, the total amount of information which can be obtained about the source is very greatly increased, as the examples of the Crab Nebula and Scorpius X-1 show. In each of these cases, an understanding of the emission mechanisms could not be reliably based on the X-ray measurements alone, but followed on the identification of the counterpart. The first step in making an identification is an accurate measurement of the position of the source. The accuracy required depends of course on the star density, which is much greater in the plane of the Galaxy than elsewhere. For a galactic source, which will usually lie near the plane, an accuracy of the order of 10-20' is required. In fact, the identifications made thus far have been based on positions of much lower accuracy - usually 1-2'. Such an error box contains a few tens of candidate stars which must be examined for evidence of spectrum or other peculiarity to complete the identification. The most powerful kind of additional evidence to date has come from observations of variability. Scorpius X-I is irregularly variable and the optical and X-ray variations are correlated. The Crab pulsar, and the important class of eclipsing binary X-ray sources such as Hercules X-1, are other examples. Variability is in fact a common feature of the galactic X-ray sources. The starting point of the Copernicus observations was the error boxes of the 2U catalogue produced from the observations of the Uhuru satellite. Where practic

The efficiency of an information storage technique based on binary comparisons is analyzed. Generating functions are applied to finding the mean and variance of the number of comparisons needed to retrieve one item from a store of n items. Surprisingly, the variance approaches 7 - 2/3π 2 for large n .

Results are presented for the density of states of binary alloys from a calculation using the matrix coherent potential approximation. A form of the density of states with realistic features was obtained even though the quasicrystalline assumption for the off-diagonal elements was not employed. These features arise solely from the local information about small clusters of atoms. However, it is felt from these results that a proper density of state can only be calculated from information of larger clusters.

The coherent-potential approximation for phonons in disordered binary alloys has been used to interpret the observed Raman spectra of the substitutionally disordered Si-Ge alloys. The spectral density function is calculated for the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}=0$ optical phonons.

Molar excess volumes and ultrasonic velocities were determined for the systems cyclopentanol + cyclohexanol, cyclopentanol + cycloheptanol, and cyclohexanol + cycloheptanol at 25 °C. Values of the adiabatic compressibilities were calculated from the experimental results.

The viscosity of binary systems of incompatible polymers is lower than that of the individual rubbers. In the case of compatible polymers, the viscosity of the systems changes additively with its composition or may increase somewhat. The degree of compatibility of the polymers affects the size of the entrance effect and the character of its dependence on strain rate.

A theoretical and experimental investigation of adaptive digital elements suitable for use as an output interface for digital stochastic computers is presented. An adaptive digital element using a binary rate multiplier is demonstrated to provide a significant improvement in accuracy without reduction in bandwidth characteristics. The experimental results are shown to be in close agreement with the various theoretical predictions.

Upper and lower bounds to the probability of error in a binary communication system with intersymbol interference and independent noise are computed. The symbols may be dependent or independent. The bounds are tight and practically coincide for a proper choice of certain parameters.

The purpose of this study was to determine the effect of different sorts of feedback upon performance in a multiple-cue probability learning task with binary cues and binary events. In addition to traditional outcome feedback, subjects were given periodic feedback messages throughout the experiment. Different types of feedback included percentage of correct responses, cue-event validity coefficients, cue-response utilization coefficients, and a combination of both of the last two types. Feedback was based upon either all previous trials (long-term feedback) or the last 20 trials (short-term feedback) or both. Two different tasks were used. Nine hundred seventy-two subjects were assigned to 32 groups in a 4 (feedback type) by 2 (short-term feedback) by 2 (long-term feedback) by 2 (task) design, and were individually run for 300 noncontingent trials. In general, the results were that no type of feedback enhanced performance, but all feedback types except percentage correct feedback resulted in a decrement in performance. Long-term and short-term feedback interaction effects were found.

The work functions of the binary alloys potassium-rubidium, cesium-rbidium, potassium-cesium, sodium-rubidium, sodium-potassium, sodium-cesium, mercury-potassium, mercury-rubidium and mercury-cesium have been investigated in a vacuum of 10 −9 torr. The shape of the curves of work function versus concentration depends on the kind of phase equilibrium diagram and on the adsorption process.

This paper describes several tactics (including batch branching) for employing a directed tree search strategy to find a binary vector slated to optimize a linear function. Certain tactics are especially useful when interfacing with an LP system to guide the tree search.

A matrix-flushing method for quantitative multicomponent analysis by X-ray diffraction is reported. It is simpler and faster than, yet as reliable as, the conventional internal-standard method. In this new method, the calibration-curve procedure is shunted; a more fundamental `matrix-flushing' concept is introduced. The matrix-flushing theory gives an exact relationship between intensity and concentration free from matrix effect. Contrary to most theoretical methods the working equation is very simple, no complicated calculations are involved. The matrix-flushing theory and the analytical procedure are presented. Eight illustrative examples are drawn to demonstrate how this theory is applied to multicomponent analysis and amorphous-content determination. A novel `auto-flushing' phenomenon of binary systems was observed which appears to make the analysis of any binary system a simple matter.

SUMMARY A Bayesian approach is taken to the problem of estimating a multivariate discrete density. Prior distributions on the space of multivariate densities are formulated to reflect the idea that the density is near a particular one, or near one which has independent variates. Given a sample of multivariate observations, an approximation to the posterior distribution of the unknown density is developed, and simple formulae for a density which approximates the mode of this posterior distribution are given. The estimate is developed in particular when the variates are binary and the prior distribution reflects that the variates are nearly but not exactly independent. The degree of apparent lack of independence in the sample determines how far from the usual estimate assuming independence this estimate will be. The proposed estimate can be thought of as interpolating between the histogram or 'cell frequency' estimate and an estimate assuming independence.

Coefficients of association have been widely employed in cluster analysis. However, their use has been, for the most part, restricted to binary data. This limitation can be overcome by redefining positive and negative matches and mismatches in terms of minimum and maximum values of paired elements of parallel vector arrays. Rewriting the algorithms of coefficients of association with these new components gives the new “quantified” coefficients general utility for binary, ordered multistate, and quantitative data, while retaining their original analytic properties. Quantified coefficients of association avoid several problems of shape and size that are associated with correlation coefficients and measures of Euclidean distance. However, when measuring similarity, quantified coefficients weight each attribute of an object by that attribute's magnitude. A related set of similarity indices termed “mean ratios” is introduced; these indices give each attribute equal weight in all situations. Both quantified coefficients of association and mean ratios are related to a number of measures of similarity introduced to various fields of scientific research during the past 50 years. A review of this literature is included in an attempt to consolidate methodology and simplify nomenclature.

The electron cell model is used to calculate the thermodynamic and elastic properties of ternary noble metal alloys. The thermodynamic properties so calculated compare favorably with experimental values. Since previous calculations on the basis of the model have given consistent descriptions of the thermodynamic and elastic properties of binary alloys, the calculated elastic moduli of ternary noble metalsalloys may be expected to be good approximations to the actual values.

A theory for combined Doppler and pressure broadening has recently been proposed by Nienhuis [Physica 66 (1973) 245]. We show that his dynamical classical limit can obtained as a result of binary collisions in which the radiator returns to its initial translational state after every collision, and thus the Doppler effect is not fully incorporated.

Eighteen binary metal oxides consisting of TiO2–MmOn, ZnO–MmOn and Al2O3–MmOn (MmOn: metal oxide) were prepared by the usual co-precipitation method, their acid amounts and strengths being determined by n-butylamine titration using various acid-base indicators. The acid strengths of fourteen of the tested binary oxides of molar ratio 1 : 1 were found to be remarkably higher than those of the component single oxides. High acid strengths were as follows: H0≤−8.2 for TiO2–SiO2, H0≤−5.6 for TiO2–Al2O3 and Al2O3–ZrO2 and H0≤−3 for TiO2–CdO, TiO2–SnO2 and ZnO–SiO2. The acid amounts of sixteen binary oxides were larger than those of the component oxides. The effect of the composition of binary oxides on acidity was examined for TiO2–Al2O3, ZnO–Al2O3 and Al2O3–ZrO2. The acidity maxima appearing for TiO2–Al2O3 and ZnO–Al2O3 were found to be of molar ratio\simeq9:1 and for Al2O3–ZrO2\simeq3:2. A fairly good correlation has been demonstrated between the observed highest acid strengths and the average electronegativi...

The weak nonexponential relaxation $\ensuremath{\propto}{t}^{\ensuremath{-}{a}^{\ensuremath{'}}}$ recently found in computer experiments on the phase separation of alloys is explained in terms of a cluster reaction and diffusion process. The nonlinear features of this process can be accounted for by a time-dependent diffusion constant. Estimates for the resulting exponents [${a}^{\ensuremath{'}}=\frac{1}{(3+d)}$] are consistent with the computer simulations. The experimental observability of this slowing down is discussed.

Color images can be produced from three computer-generated holograms, one for each of the primary colors. Two basic problems must be solved: scaling the images according to wavelength and avoiding false images. The former can be solved by a computational step, during synthesis of he holograms, or during reconstruction. The latter problem, false images, can be solved by the reconstruction geometry or by using multi-emulsion color film. The wavelentgh-selective absorption of the different layers in color film can be used to selectively absorb light of an undesired color while transmitting light of the desired color at a given point on the film. This effect allows the spatial multiplexing of binary detour-phase holograms. In addition to density variations, there exist corresponding phase variations in color film, particularly Kodachrome II, making onaxis holograms possible. Furthermore, the phase variations can be used to eliminate an undesired color by selectively diffracting it off to the sides. Experimental results are presented.

A new semiempirical model for predicting the work function of binary compounds is proposed. The model is a modification of the Gordy and Thomas relation and is applicable to binary compounds. The work functions of binary compounds, φAB are found to be primarily determined by the properties of the element of low work function, A, perturbed by the other element of high work function, B, according to φAB=φA + (1.41/dA)[(2φA − φB − 0.34)/(φA + φB − 0.68)]. Experimental values tabulated by Fomenko are compared with the predicted work functions, and the quantitative agreement is good in spite of the simplicity of the model.

A method entitled "analytical potentiometry" is described which permits the accurate determination of the stability constants and of the distribution of simultaneously existing complex species in multi-component systems. A series of computer programs are introduced to facilitate the otherwise tedious mathematical analysis of data. Besides simple binary systems, this method is capable of dealing with mixed ligand coordination complexes and can be adapted to polynuclear systems. For many metal ions, there are no electrodes permitting the accurate determination of those ions over a wide enough concentration range. This method eliminates the need for metal ion specific electrodes. The concentration of free metal ions is determined indirectly by the use of a weak base and the glass electrode. These features bear great significance in resolving complex systems containing multiple species simultaneously which cannot be solved by the commonly known classical methods.

The products of the cocondensation reactions of Rh atoms with N2 and N2/Ar mixtures at 10 °K are investigated by matrix isolation infrared spectroscopy and are shown to be binary dinitrogen complexes of the form Rh(N2)n. Examination of the reaction products in pure 14N2, 15N2, 14N2/15N2, and in dilute Ar/14N2, Ar/14N2/15N2, and Ar/14N2/14N15N/15N2 matrices establish the values of n to be 1–4. Isotopic frequencies are computed for the NN stretching modes of the individual dinitrogen complexes on the basis of the Cotton–Kraihanzel (C.K.) force field approximation and are found to be in close agreement with observed values. Trends in the best fit C.K. force constants for Rh(N2)n (n = 1–4) and the thermodynamic stabilities of the individual complexes as indicated by the function ΔHcn, a measure of the enthalpy of decomposition, are discussed. Comparisons are made between Ni(N2)n and Rh(N2)n (where n = 1–4). The structure of Rh(N2)4 in solid nitrogen is shown to be that of a distorted tetrahedron. Calculations show that a site symmetry of D2d for Rh(N2)4 satisfactorily accounts for all of the spectral lines observed for the complex in nitrogen. In solid argon, Rh(N2)4 appears to have an approximately regular tetrahedral structure. The relationship between RhN2 and N2 chemisorbed on Rh metal is discussed and compared with the analogous Ni–, Pd–, and Pt–nitrogen systems.

Using the theory of distorted components in very close binaries the semi-axes are computed for several possible models. The coefficients of limb-darkening and gravity effect are found as weighted mean values of the results of several theoretical investigations. A simple linear relation is found between the coefficient of limb-darkening and the logarithm of the effective temperature in the spectral interval A0 to K0. The Fourier series for the intrinsic light variation of such distorted components is given for any polytropic index. The influence of the tidal bulge is described in detail.

We consider a set of static files or inventories, each consisting of the same number of entries, each entry a binary word of the same fixed length selected (with replacement) from the set of all binary sequences of that length, and the entries in each file sorted into lexical order. We also consider several retrieval questions of interest for each such file. One is to find the value of the j th entry, another to find the number of entries of value less than k . When a binary representation of such a file is stored in computer memory and an algorithm or machine which knows only the file parameters (i.e. number of entries, number of possible values per entry) accesses some of the stored bits to answer a retrieval question, the number of bits stored and the number of bits accessed per retrieval question are two cost measures for the storage and retrieval task which have been used by Minsky and Papert. Bits stored depends on the representation chosen: bits accessed also depends on the retrieval question asked and on the algorithm used. We give firm lower bounds to minimax measures of bits stored and bits accessed for each of four retrieval questions, and construct representations and algorithms for a bit-addressable machine which come within factors of two or three of attaining all four bounds at once for files of any size. All four factors approach one for large enough files.

We suggest that the Pauli-force model potential defines a new electronegativity scale consisting of explicit orbital components. These are determined algebraically from atomic spectral data. We find that these components distinguish quantitatively the most stable crystal structures of 34 nontransition elemental solids and $59{A}^{N}{B}^{8\ensuremath{-}N}$ binary compounds.

The variation of the line width of the rotational components in the pressure-induced infrared spectra of H2–inert-gas mixtures is calculated. At low densities, the contribution of the R-modulation effect to the line shape is calculated assuming quadrupolar induction and neglecting intercollisional interference effects. The observed line narrowing at high densities is interpreted in terms of a model for the stochastic modification of the binary dynamics resulting from multiple collisions, and described in terms of the diffusion coefficient of the gas mixture. The width at high densities is shown to be proportional to the diffusion coefficient, in agreement with a previous simplified analysis.

The authors present a method which improves the results of the coherent potential approximation (CPA) generally used to study the electronic properties of disordered alloys. They replace the disordered medium by an effective one characterized by a local coherent potential which varies from place to place and depends on the particular alloy configuration. The local electronic density of states is determined by equations similar to that found in the CPA, and then conveniently averaged over all the possible configurations in order to obtain the alloy density of states. As opposed to the CPA, this method yields tails in the allowed energy bands. As an illustration for the method, the authors calculate the electronic density of states of a simple one-dimensional model and compare it to the exact density of states and to the results of CPA calculation.

The coherent-potential approximation has been employed to discuss itinerant-electron magnetism of binary alloys by use of diagram techniques, which make clear the meanings of, and the differences between, the formulations by Hasegawa and Kanamori (HK), Levin etal. and Harris and Zuckermann. These diagram techniques make it easy to obtain the wave-vector and frequency-dependent susceptibility for the Wolff model at finite impurity concentrations. The results reduce to that of HK in the uniform and static limit. The formula enables us to discuss on the same footing both local exchange enhancement and paramagnons by changing the concentration of magnetic atoms. It is also shown that the charge transfer has some important consequences. By use of this susceptibility, the possibility of the spin-density-wave state has been discussed in similar ways as Penn's argument for pure systems. It is found that the occurrence of magnetic states is essentially related not to the total density of states but to the local density of states. In addition to the static properties, the diffusion constant of spin fluctuations is discussed in relation to the electronic specific heat.

Unstable 4-body systems with negative energy can ultimately decay to (1) a binary plus two single stars, (2) two separate binaries, or (3) a stable triple plus a single star. One hundred random 2-dimensional and one hundred random 3-dimensional 4-body systems have been numerically integrated to determine the statistics of the end products. Of the final stable triples and binaries, 19% were triples, which agrees well with observational estimates of the ratio of triples to binaries. The results were essentially the same for 2- and 3- dimensional systems.

We suppose that prior to partitioning a set of experimental units into experimental blocks of size t, each unit is classified with respect to k different binary variables or attributes. The 2k cells of this classification are then used as building blocks to form experimental blocks of t homogeneous experimental units.In our attempt to achieve within-block homogeneity we first order the 2⊃ cells in a sequence so that any two adjacent cells differwith respect to exactly one attribute. The contents of each cell are then partitioned into blocks and, where necessary, units from adjacent cells are combined to form blocks. In the ease of standardized quantitative variables which have been dichotomized at zero, a within-cell partition is based upon an ordering of the experimental units with respect to that particular quantitative variable which changes its sign in the next cell of the sequence.

This correspondence defines a new set of precision tone frequencies for digitally generating normal progress tones in a PCM switching environment. The technique of generating the progress tones is similar to the one described for digital multiple frequency (MF) tone senders in which the tone is generated by reading a memory store that contains the binary words representing a presynthesized waveform [1]. New frequency combinations are derived that minimize storage requirements by taking advantage of the allowable frequency tolerances to force waveform symmetry with respect to the sampling period.

A Turing machine multiplies binary integers on-line if it receives its inputs, low-order digit first, and produces the jth digit of the product before reading in the (j+1)st digits of the two inputs. We present a general method for converting any off-line multiplication algorithm which forms the product of two n-digit binary numbers in time F(n) into an on-line method which uses time only O(F(n) log n), assuming that F is monotone and satisfies n@?F(n)@?F(2n)/2@?kF(n) for some constant k. Applying this technique to the fast multiplication algorithm of Schonhage and Strassen gives an upper bound of O(n (log n)^2 loglog n) for on-line multiplication of integers. A refinement of the technique yields an optimal method for on-line multiplication by certain sparse integers. Other applications are to the on-line computation of products of polynomials, recognition of palindromes, and multiplication by a constant.

We live in a binary world of computers, accepting the inevitability of dealing with strings of O's and l's, simply because this is dictated by the two-valued nature of switching primitives which make up the machines. Yet there is little doubt that most of us would prefer decimal machines if they were available. Present technology is unlikely to result in such machines in the near future, at least not the kind where basic building blocks are inherently 10-valued. However, this does not mean that the binary approach must continue to be the only alternative. Considerable advantages may be gained by considering higher-radix systems, even if decimal schemes are presently out of reach.

The distribution functions of penetrable-sphere models are expressed in terms of those of the related binary mixtures of species a and b. The transcription takes a simple form for approximations, such as the mean-field (MF) or Percus-Yevick (PY), in which the direct correlation functions caa (r) and cbb (r) are zero. For the MF the equation of state and the distribution functions are classical at the critical point, and it is shown that these results become exact at infinite dimensionality for the two most widely studied versions of the penetrable-sphere model. The transcription of the PY approximation leads to an inconsistency in the correlation functions at the critical point, but the equation of state is still classical. The hyper-netted chain (HNC) approximation leads to a pressure equation of state (for any mixture) which is symmetrical in the two components a and b, but to a compressibility equation which is not. For one of the models studied here, however, both lead to a thermodynamically non-class...

In this paper a method is proposed for the determination of the correctable and detectable errors number, which ensures an optimum compromise between the incorrect decoding probability and the transmission rate. The method is based on the fact that by decreasing the correctable errors number and increasing the detectable errors number, both the incorrect decoding probability and transmission rate are reduced. Among the types of problems which can be solved by this method the most interesting is that of adapting the decoder to the transmission channel. In this paper the binary symmetrical channel is considered, but for other types of channels similar results can also be obtained.

Recursion relations correct to lowest order in $\ensuremath{\epsilon}=4\ensuremath{-}d$ are obtained for simple models representing the critical dynamics of a binary liquid, a Heisenberg antiferromagnet, superfluid helium, and related systems. The exponents for the divergences of the transport coefficients satisfy the "scaling" relations predicted by mode-mode coupling theory. The viscosity of the binary liquid is predicted to diverge as ${k}^{\ensuremath{-}\frac{\ensuremath{\epsilon}}{19}}$ near $d=4$, which is a new result.

A rapid method for a quantitative analysis of a multielement alloy is discussed. This method is independent of surface-roughness and contaminations. Co

The regular solution model is used to compute the surface enrichment in the (111)- and (100)-faces of silver-gold alloys. Surface enrichment by silver is predicted to increase if the surface plane becomes less saturated and decreases if one raises the temperature. The possible implications of these findings are considered in the light of the recently reported mechanism of the epoxidation of ethylene over silver catalysts.