Coefficients A2 Research Articles

Studies on Movement of <SUP>90</SUP>Sr, <SUP>106</SUP>Ru, <SUP>137</SUP>Cs, <SUP>144</SUP>Ce in Environment, connected with the City Water Supply

In order to examine radioecologically behavior of radionuclides in environment of water supply, levels of radionuclides in the soil, raw water from river and its suspension, river bottom sediment, and water supplied for drinking were quantitatively investigated, and then various aspects on transfer of radionuclides in the land, river, and water works were hydrometeorologically analyzed. On three basins, Agano, Edo, and Yodo River, movements of 106Ru, 137Cs and 144Ce were derived from data of 90Sr. 90Sr was removable compared with other radionuclides in various samples. The following equations were established by the regression analysis between "ratio on each of the radionuclides to 90Sr" in soil (Rd) and that of river bottom sediment (RBS), between Rd and that in river water with suspension (R[W+S]), and between radionuclides concentration in the river water (C ; pCi/100 liter) and weight of the river suspension (S ; gr. of ash/100 liter). [numerical formula] Coefficients a1 and b1 were 8.46-1.35 and 2.35-0.62 for 106Ru, 4.14-0.989 and 2.58-0.31 for 144Ce, and 2.80-0.836 and 3.49-0.879 for 137Cs, respectively. The a2 and b2 for 137Cs were 0.085-0.055 and 0.26-0.19. The a3 and b3 in the Agano River were 0.00229 and 1.49 for 90Sr, and 0.0229 and 0.64 for 137Cs. These data indicated that the degree of deposition to the soil, adsorption, and absorption to the river bottom of 106Ru, 137Cs and 144Ce are higher than those of 90Sr, in the following order : 106Ru>144Ce>137Cs>90Sr. As for the pathway of contamination, part of 90Sr is soluble and most of 106Ru, 137Cs and 144Ce is insoluble in the river, and a part of these radionuclides exists in the river suspension and considerable amounts of 106Ru, 137Cs and 144Ce are precipitated on the river bottom. It was observed on the decontamination rates (DR%) of radionuclides in the water works that the greater the content of the suspension increases, the higher DR become. The correlation of DR and S was shown by the following equation. [numerical formula] The coefficient a4 was 0.0462 for 137Cs in the Niitsu City water works, Agano River basin. During 1962 to 1969, DR in the three water works were observed as 50% for 106Ru, 48% for 144Ce, 31% for 137Cs, and 15% for 90Sr in average value.

Excluded Volume Study of Potassium Polystyrenesulfonate‐Potassium Chloride Solutions

AbstractIntrinsic viscosities [η], sedimentation coefficients s, radii of gyration Rg and second virial coefficients A2, refractive index increments and apparent specific volumes were determined in aqueous solution in theta solvents and over a wide range of concentrations ms of a supporting electrolyte KCl, for five samples of potassium polystyrene sulfonate prepared by sulfonation of narrow molecular weight distribution polystyrenes. Coil expansion coefficients α as well as the Flory coefficient Φ relating [η] to coil dimensions were evaluated. Following a theory of Alexandrowicz, α2 was found to be a linear function of M1/4 m−1/3S; Φ appears to decrease with increase in α. The low values of Φ, characteristic for polyelectrolyte solutions, are consistent with the value determined for the Mandelkern‐Flory parameter β = Φ1/3 P−1.

Light scattering parameters of block copolymers by application of computer programming

AbstractA computer program has been adapted for use with the Sofica Light Scattering Photometer and extended for application to block copolymer studies. In the first part of the program, which is equally suitable for homopolymers and copolymers alike, the apparent molecular weight, Mapp, radius of gyration 〈S2〉1/2, and the virial coefficients A2, A3 are obtained in individual solvents. In the second part, M̄w and the parameters characterizing the heterogeneity in composition of the copolymer are calculated. This is achieved by solving three simultaneous equations from all combinations of experiments in six or more solvents with different refractive index increments. The first stage has been tested using data from a sample of polystyrene. The complete program has been applied to data originally treated by the usual graphical methods. Finally, the parameters derived by the two techniques are compared and discussed.

Short-range order and ordering energy in ? solid solutions of the copper-aluminum system

The ordering energy for annealed samples of α CuAl is calculated from the experimental coefficients α1 on the basis of the statistical theory for short-range order. The short-range order is studied as a function of the quenching temperature for CuAl alloys containing 11.9, 14.3, 15.9, and 17.6 at.% Al by means of diffuse scattering of x-rays. The experimental temperature dependences of the short-range order coefficient, α1(T), are compared with the theoretical curves.

Nonexponential Relaxation of Rotating Three-Spin Systems in Molecules of a Liquid

The longitudinal and transverse nuclear magnetic relaxation of a system of three identical spin-12 nuclei at the corners of an equilateral triangle which undergoes hindered rotation with respect to a molecule which undergoes rotational Brownian motion has been calculated on the assumption that the relaxation is due to dipole–dipole interactions between the three nuclei, including the effects of cross correlations. The longitudinal relaxation is in general the sum of three decaying exponentials. If the rotational Brownian motion is rapid compared to the Larmor frequency, the longitudinal and transverse relaxations are both proportional to A1exp(s1t) + A2exp(s2t). For a molecule of arbitrary shape, the expressions for the coefficients A1 and A2 and the negative exponents s1 and s2 are quite complicated. The expressions simplify somewhat for the case of a symmetric top molecule, and even more for the case of a spherical molecule. It is shown for a molecule of arbitrary shape that, if the hindered rotation is rapid compared to the rotational Brownian motion, which in turn is rapid compared to the Larmor frequency, then the predicted relaxation is distinctly nonexponential.

The valence orbital ionization potential of the first transition-metal atoms and ions

The 3d, 4s and 4p valence orbital ionization potentials (VOIP) are determined for the atoms and the ions with the electron configuration 3dα4sαpγ, using the Anno-Teruya values of the average energies of the configurations and the experimental ionization potentials. Not all the configurations of this type are treated for lack of the data. As far as the data are available, a quadratic equation in terms of the atomic number Z is fitted to the VOIP's of an isoelectronic series: VOIP=A0+A1Z+A2Z2. The coefficients A0's, A1's and A2's thus obtained are analysed in the light of Slater's simple expression for the total energy of an atom with the idea of screening effect due to inner electrons.

The Rotational Spectra and Dipole Moments of AgF and CuF by Microwave Absorption

Abstract The rotational transitions J=1→2 and 2→3 were measured for 107Ag 19F and 109Ag 19F by microwave absorption. These spectra allowed the determination of the Dunham-coefficients Y01, Y11, Y21, and Y02 and from these the potential coefficients a0 and a1 and internuclear distance re were derived. For 63Cu 19F and 65Cu 19F the hyperfine structure was observed in the J=0→1 and 1→2 rotational spectra. In addition to the Dunham coefficients the quadrupole coupling constants, e q Q, and spin-rotation coupling constant, c, for the Cu nucleus were obtained. Stark effect mea-surements on both AgF and CuF resulted in the determination of the electric dipole moment for the ground vibrational state.

Photoelectric Photomety of UV Piscium.

view Abstract Citations (1) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Photoelectric Photomety of UV Piscium. Carr, Roger B. Abstract V) colors have been obtained for the eclipsing binary UV Piscium with a 16-in. telescope at the Kitt Peak National Observatory. The 437 individual observations in each color were com- bined into 68 normal points. The truncated Fourier series representing the normal points outside the eclipses have the coefficients A0 Al A2 B1 B2 V 0.9705 -0.0009 -0.0027 0.0185 -0.0017 +0.0007 +0.0010 +0.0011 +0.0008 +0.0008 B 0.9726 0.0026 -0.0024 0.0199 -0.0020 +0.0006 +0.0009 +0.0010 +0.0007 +0.0007 U 0.9593 0.0126 -0.0077 0.0204 -0.0047 +0.0010 +0.0015 +0.0017 +0.0011 +0.0011 The light curves were rectified with the equations of Russell and Merrill (Contrib. Princeton Univ. Obs. No. 26, 1952). An asymmetry represented by the sine term dominates the rectification. No explanation is offered for the failure of the sign of Al to agree with theory in B and U. A nomographic solution is discussed. This work has been supported by NSF and NASA. Publication: The Astronomical Journal Pub Date: October 1967 DOI: 10.1086/110480 Bibcode: 1967AJ.....72R.788C full text sources ADS |

Microwave Rotational Spectrum of Indium Monochloride

With a high-temperature Stark-spectrometer the J=4←3 rotational spectrum of 115In35Cl has been observed. Quadrupole hyperfine structure has been observed for the lowest four vibrational states. In an analysis of the spectrum the following constants have been derived: the rotational—vibrational constants Y01, Be, Y11(≈—αe), Y21(≈γe), Y02(≈—De), and Y20(≈—ωexe); the quadrupole coupling constants eqQ including the dependence on the vibrational state; the coefficients a0, a1, and a2 of the internuclear potential; and the internuclear distance re. From the quadrupole hyperfine structure it is concluded that the molecule is 77% ionic, and that the antishielding factor of In+—γ∞≈65.

Formal solution in the problem of small divisors

view Abstract Citations (87) References (6) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Formal solution in the problem of small divisors Garfinkel, Boris Abstract Small divisors in mechanics arise from resonance, i.e., the near-commensurability of two of the natural frequencies of the motion. Under very general assumptions, the problem can be reduced to a canonical form of one degree of freedom, with the Hamiltonian F defined by F=Ao(y)+Ao(y) cos2z. Here z is the coordinate, y the momentum, and the coefficients A0 and A0 satisfy the relation A1/A0=O(k), where k is a small parameter. Resonance is associated with the vanishing of the derivative A 0' for some value Y=Y* In the neighborhood of Y*, the resonance problem is solved to O(k-") by the Bohlin-von Zeipel technique, and the solution is expressed in terms of elliptic functions. It is shown that the resonance solution reduces to the classical solution with a singularity at Y=Y*, when the divisor * is sufficiently large. Applications to celestial mechanics are illustrated by the problem of critical inclination and by the 24-h satellite in the artificial satellite theory. Publication: The Astronomical Journal Pub Date: October 1966 DOI: 10.1086/110171 Bibcode: 1966AJ.....71..657G full text sources ADS |

ANALYSIS OF HETEROGENEOUS REACTORS CONTAINING MODERATING FUEL ELEMENTS

The Feinberg-Galanin method for heterogeneous reactors is formulated by using a two-group model instead of an age kernel. This treatment is then extended to take into account secondary effects such as fast liasion and thermalization of neutrons inside a rod which may contain moderator. The use of single coefficient in a Feinberg-Galanin approach allows one to relate the source and sink strength of the fuel element to the thermal flux only. By defining a set of four coefficients it is possible to connect the strengths of thermal and fast neutron sources and sinks to both thermal and fast fluxes. A method of calculating these four coefficients α1, β1, α2 and β2 is presented. The critical fuel mass of liasion electric cell reactor is calculated by using the four coefficient method. A value of approximately 0.77 kg is obtained, compared to a critical mass of 1.3 kg estimated from two-group homogeneous theory.

Relation between Ultrasonically Measured Properties and the Coefficients in the Solid Equation of State

A relation is found by straight forward thermodynamic methods between the derivatives with respect to pressure of the isothermal and adiabatic bulk moduli which gives (∂BT/∂p)T at zero pressure from the experimental (∂Bs/∂p)T plus temperature-dependent-only thermodynamic properties. Although BT<Bs is required by thermodynamics, we find (∂BT/∂p)T>(∂Bs/∂p)T for Cu, Ag, Au, Al, NaCl, and Na. The coefficients a1 and a2 in the equation of state are evaluated from ultrasonic experimental data and compared with those obtained by experiments in high pressure physics. Agreement between the a1's is good but between the a2's it is poor.

Studies of the Polymerization of Vinyl Acetate in the Aqueous Solutions of Partially Acetylated Polyvinyl Alcohol. II. On the Change of Huggins' Constant k′ with the Variation of the Composition of the Mixed Solvent

AbstractThe change of Huggins' constant k′ of the graft polymer solution brought about by varying the composition of the solvent was studied. The graft polymer solution studied was prepared according to the method described in the author's previous paper,(1) and k′ was obtained from viscosity measurements of the solvent with varying methanol contents. The following results were obtained:(1) The Huggings' constant was found to change with the variation in the methanol content of solvent.(2) The minimum value for k′ was attained when the solvent contained 75% methanol.(3) The first interaction coefficients a2 were determined and the critical point was also observed under the same conditions.

Intrinsic viscosity and molecular weight of isotactic polypropylene

AbstractTwo samples of highly isotactic polypropylene prepared by a NATTA's catalysis, have been fractionated by a column fractionation technique.Fractions having M̄w/M̄n ratio very small (1.14 – 1.27) have been obtained and used for the determination of [η]−M̄n and [η]−M̄w relations. Because of the small values of M̄w/M̄n ratio, the [η]−M̄w relation may be assumed also valuable as [η]−M relation. This relation is for molecular weight range of 40,000–650,000, where [η] is measured in tetralin at 135°C. Moreover values of \documentclass{article}\pagestyle{empty}\begin{document}$\sqrt {\overline {r_z^2 } }$\end{document} and of second virial coefficients A2 are given in function of molecular weight.

Method for Numerical Evaluation of the Coefficients of Fourier Series

The coefficients a0, am, and bm of a Fourier series f(x) = a0 + Σmam cosmx + bm sinmx, where m = 1,2,3,⋯, ∞ is the harmonic order, can be evaluated by a simple formula if f(x) is a sequential trace of n straight lines. The formula makes use of the slopes Ai and the intercepts Bi of the 1 ≦i≦n lines contained within the period. If the line crossings are equidistant in the direction of the x axis, the formula will not only be more simplified by the direct use of these n sample values but the coefficients can be taken as the products am = Cmam* and bm = Cmbm*. The factor Cm decreases with increasing values of the integers m. The discrete values Cm appear within an envelope that is the picture of an attenuated square cosine wave. The harmonic order m and the subdivision number n of the period range are parameters in a tabulation of Cm. The second factors are introduced as periodic Fourier coefficients am* and bm*. These coefficients are an infinite repetition of the finite range 1 ≦ m ≦ n, if m runs from 1 to infinity. Assuming n is a multiple of 4, only n/4 periodic coefficients have to be evaluated. Multiplication with the tabulated values Cm result in an arbitrary series of coefficients am and bm. So far as any periodic function f(x)—given by an experimental observation, for instance—can be approximated by a sequential trace of straight lines, f(x) can be approximated by the Fourier series of the straight-line trace. The numerical evaluation of the coefficients of the trace is not restricted to a certain number. in the harmonic order, such as to the first 6 or first 12 harmonics, for instance. It can easily be programed for desk machine calculators or for computers. A simple schematic calculation can be made to yield either an arbitrary series or any particular order of coefficients. The method can be extended to numerical evaluation of the Fourier integral as well.

本邦各地の降水量の調和解析

In this study, the present author calculated the Fourier's coefficients a1…a5, and the phases φ1…φ5 in the formula for the amount R of rainfall, using the data of the monthly totals of rainfall reduced to those o, 30 days for 76 meteorological stations in Japan. (1) In Table 1 are given the value of Fourier's coefficients for rainfall. All the coefficients a1, a2, a31, a4 and a5 decrease with the increasing latitude.From a1φ1 figure (Fig. 4), the geographicaf distributon of these Fourier's coefficients can be classified into four different types, that is, the Formosa and Ryukyu type, Japan proper and Korea type, the Japan sea coast type and north Japan type. (2) It is seen that a close connection will exist between the amount of precipitation during the plum-rain season and the coefficients a1, a4 and a5.

觀測値の不足せる場合の調和分析法

If a periodic phenomena y shown by a functionis observed at six equidistant points throughout the period, the coefficients A0, A1, B1, A2 and B2 can be determined by the method of harmonic analysis. But, when one of the observed values, y1, for example, is unknown, the usual method can not be used. The author proposes a method of harmonic analysis for such a case. In this case' we may estimate graphically the unknown value, namely y1", and with this estimated value togather with the observed values, we can determine the coefficients provisionally. From these coefficients we can calculate the value of y1, and call it y1". Then the true value of y1, is given by the following equation, Generally, when the periodic phenomena is shown by the function, above method is applied repeatedly, and the most probable value of y1, may be determined.Similarly, when one of the observed values at 2m equidistant points throughout the period of the function is unknown, the same method may be applied, and the most probable value of the unknown one is given by the equation

Geometrical Interpretation of a few concomitants of the cubic in the Argand Plane

be the binary cubic whose coefficients a1, are complex numbers represented on the Argand Plane. Then if its roots are z1, z2, z3, the three corresponding points form the vertices of a triangle A1 A2 A3. Let this triad of points be said to represent the cubic. Then its Hessianis represented by a certain pair of other points; likewise every first polarassociates a definite pair of points (z) with any given point (y).

I. On the tides of the Arctic Seas. Part VII. Tides of port Kennedy, in Bellot Strait. (Final discussion.)

In Part VI. I have discussed McClintock’s observations on the Tides of Port Kennedy, using only the Heights and Times of High and Low Water, as I wished to follow the same method in comparing all the Tidal observations in the Arctic Seas. Although I adopted this method for the purpose of comparison, I was well aware that I had not exhausted all the information at my disposal, for McClintock’s observations were made hourly during 23 days, and I used of these observations only those in the neighbourhood of H. W. and L. W. of Diurnal and Semidiurnal Tides. I shall now discuss the observations, with the aid of Fourier’s Theorem, so that all the observations made at every hour of each day shall enter into the constants determined for that day. If F denote the height of the tide, observed at every hour of the day, we have by Fourier’s Theorem F = A 0 + A 1 cos s + A 2 cos2 s + A 3 cos3 s + &c. B 1 sin s + B 2 sin2 s + B 3 sin 3 s + &c .............................(1) where s denotes the sun’s hour angle, and where the coefficients A 0 , A 1 , B 1 , A 2 , B 2 , &c., are found from the following equations, in which F 0 , F 1 , F 2 , &c., denote the values of F at the hours 0, 1, 2, &c., 23.