Values Of Λ1 Research Articles

The theory of asymptotic behavior

The Green’s functions of renormalizable quantum field theory are shown to violate, in general, Euler’s theorem on homogeneous functions, that is to say, to violate naive dimensional analysis. The respective violations are established by explicit calculation with Feynman diagrams. These violations when incorporated into the renormalization group, then provide the basis for an entirely new approach to asymptotic behavior in renormalizable field theory. Specifically, the violations add new delta-function sources to the usual partial differential equations of the group when these equations are written in terms of the external momenta of the respective Green’s functions. The effect of these sources is illustrated by studying the real part, Re Γ(6)(λp), of the six-point 1PI vertex of the massless scalar field with quartic self-coupling—the simplest of renormalizable situations. Here, Γp is symbolic for the six-momenta of Γ(6). Briefly, it is found that the usual theory of characteristics is unable to satisfy the boundary condition attendant to the respective dimensional-analysis-violating sources. Thus, the method of characteristics is completely abandoned in favor of the method of separation of variables. A complete solution which satisfies the inhomogeneous group equation and all boundary conditions is then explicitly constructed. This solution has the following interesting properties: 1) It possesses Laurent expansions in the scale λ of its momentum arguments for all real values of λ2 except λ2=0, where it has a delta-function singularity in λ2 in addition to its Laurent expansions for λ2=0+ and λ2=0−. For |λ2|→∞ and |λ2|→0, the solution’s leading term in its respective Laurent series is proportional to λ−2, so that it behaves canonically in both limits! 2) The limits λ2→0+ and λ2→0− of λ2 RE Γ(6) are both nonzero and unequal. Further, on account of the delta-function singularity at λ2=0, the value of the solution at λ2=0 is not simply related to the value of either of these limits! Apparent divergences in the coefficients in the respective Laurent expansions are removed by the use of Heisenberg’s uncertainty principle. In this way, the new approach would appear to be operationally established.

Ab initio evaluation of the fine structure of the oxygen molecule

The electron spin dipole-dipole and spin-orbit contributions to the zero-field splitting in the O2 Σg−3 ground state are calculated using the correct microscopic Hamiltonians. The calculations are carried out using minimum, double-zeta, and double-zeta-plus polarization basis sets constructed from contracted Gaussian-lobe functions. Configuration-interaction wavefunctions are used for the ground state and all excited states that couple to the ground state via the spin-orbit Hamiltonian. Values of 1.790 and 1.928 cm−1 are obtained for the splitting parameter λ for the double-zeta and double-zeta-plus polarization bases, respectively, in good agreement with the accurate experimental value of 1.981 cm−1. The spin-orbit contribution which comes primarily from the low-lying excited Σg+1 state accounts for about 2/3 of the total splitting. It is observed that only states which are single excitations from the ground state have a significant spin-orbit contribution and that the over-all effect of electron correlation on the parameter λ is less than 10%. A value of λ1, λ1 = [R(dλ/dR)]Re, of 0.746 cm−1 was calculated in comparison to the experimental value of 0.7129±0.0012. The spin-spin and spin-orbit contributions to λ1 were, respectively, −1.478 and 2.224 cm−1.

Estimation of the filtration constant of dog submaxillary gland epithelia--an approximate value of hydraulic conductivity.

To estimate the hydraulic conductivity of dog submaxillary gland, an attempt was made to determine filtration constants of the glandular epithelium by analyzing the decay curve of the stop-flow intraluminal pressure.The time course of the decay of intraluminal pressure after cessation of the secretory stimulation was found to be expressed as an algebraic sum of two exponential functions of time, one having the rapid component and the other having the slow component:P=Ae-λ1t+Be-λ2tThe rapid component is atributable to the relaxation of the myoepithelium because the rate constant of the rapid component (λ2) is in good accordance with the rate constant of the relaxation of the myoepithelium. The rate constant of the slow component (λ1) is deduced theoretically to be a product of the filtration constant and a coefficient of volume elasticity of the gland. The value of λ1, was found experimentally to be 0.00512 sec-1, and the coefficient of volume elasticity obtained by measuring the intraluminal pressure elevated by retrograde injections of fluid was 1.52 mmHg·g-gland·μl-1. From these results, the filtration constant of dog submaxillary gland was estimated to be 0.0033 μl·sec-1·mmHg-1·g-glamd-1 on the average. Recalculating the value on the basis of the surface area of the acinus per unit gland weight, a value of the filtration constant or an approximate value of the hydraulic conductivity of the acinal surface was calculated to be 0.6×10-11 cm3·sec-1·dyne-1. The numerical values of the parameters described above may be applicable under similar experimental conditions to those used in the present study.

A Generalization of the Poisson Distribution

A new generalization of the Poisson distribution, with two parameters λ1 and λ2, is obtained as a limiting form of the generalized negative binomial distribution. The variance of the distribution is greater than, equal to or smaller than the mean according as λ2 is positive, zero or negative. The distribution gives a very close fit to supposedly binomial, Poisson and negative-binomial data and provides with a model suitable to most unimodel or reverse J-shaped distributions. Diagrams showing the variations in the form of the distribution for different values of λ1 and λ2 are given.

A Generalization of the Poisson Distribution

A new generalization of the Poisson distribution, with two parameters λ1 and λ2, is obtained as a limiting form of the generalized negative binomial distribution. The variance of the distribution is greater than, equal to or smaller than the mean according as λ2 is positive, zero or negative. The distribution gives a very close fit to supposedly binomial, Poisson and negative-binomial data and provides with a model suitable to most unimodel or reverse J-shaped distributions. Diagrams showing the variations in the form of the distribution for different values of λ1 and λ2 are given.

Synthetic studies on chalcone-flavanone groups. IV. Ultraviolet absorption spectra of 2',4'-dihydroxychalcone, 4'-(benzyloxy)-2'-hydroxychalcone, and their pyridine analogs

The ultraviolet absorption spectra of 2', 4'-dihydroxychalcone (V), 4'-(benzyloxy)-2'-hydroxychalcone (VI) and azachalcones (Ila-c, IIIa-c) corresponding to V and VI are reported. These chalcones and azachalcones show two absorption maxima in the wavelength region over 280 mμ, λ1 (345-350 mμ) and λ2 (282 -324 mμ) respectively. It was confirmed that λ1 is due to the electronic nature of the conjugation system of dihydroxybenzoyl group (IA) and λ2 is due to that of cinnamoyl group (IB). Relations between the values of λ1 and λ2, and the position of nitrogen atom in the azachalcones were also discussed.

Analytical Studies on the Dye Dilution Curves in Normal Subjects

1 It is important to secure the mathematical model of indicator dilution curves for the theoretical investigation of the dilution method. [numerical formula] Formula (1) reported by E. V. Newman in 1951, give us a clear explanation for the formation of dye dilution curves. But due to the insufficiency of its experimental proof in human subjects and the difficulty of the treatment of exponential equations, this formula has not been so available. For the purpose of the experimental proof of Newman's theory, we tried to decide the values of constants in formula (1), and to compose the dilution curve from the formula. In experiments, we used 1-2cc of 2% Coomasie blue solution, and after the injection into the Basilic vein, added the flashing by physiological NaCl solution. The dilution curves were recorded by ear-piece method. For Newman's theory, the assumption of instantaneous injection is the most important premise. When this assumption is satisfied, the author named such dilution curves the simple dilution curves. As we set the injection site on the Basilic vein, that condition was only approximately satisfied. And in such cases, adequate values of V1, V2, v3 can not be found. Hence, the dilution curve required to be corrected at analysis. From Newman's formula, following simultaneous equations (2), (3), (4) have been led. [numerical formula] From these simultaneous equations, we may find easily the following relations with geometrical considerations on λ-μ plane. Suppose tanα=C^-p/A^^, the equations mean that λ1, λ2, λ3 are the λ-ordinates of three intersections of the curve μ=e-tap/λ with a straight line, which makes an angle α with λ-axis. Simultaneously, three points on the curve μ=e-ti/λ of which λ-ordinates are λ-1, λ2, λ3, stand on a straight line. Having known the values of C^-1, A^-, tgt ti by the clinical experiment, we may obtain the values of λ1, λ2, λ3 with graphical method, using the above-mentioned relations.

Deformation of an Earth model by surface pressures

The surface displacements of a spherical earth model consisting of a homogeneous elastic shell enclosing a fluid core are considered, when the surface stress consists of a uniform pressure over equal antipodal circular caps and is zero elsewhere. On the earth, local loads are generally associated with geological structures, ice loads, or the ocean tides. In the present theory, the gravitational effects arising from the deformations are not included—such effects are small when the radius of the loaded area is small. Values of the surface displacements are listed for four values of the radius of the pressure cap, and for values of the elastic constants which correspond to a simplified representation of Bullen's [1947] model. In the shell the elastic constants λ2 and μ2 are 14/11×1012 and 1012, respectively, corresponding to a Poisson's ratio of 0.28. The value of the outer radius of the shell, r2, is 6.371×108 cm; the inner radius, r1 is 0.545r2. Within the core, μ1 = 0, and λ1 μ2−1 = 8. The computed results are easily modified for other values of λ1 and μ2 provided the value of Poisson's ratio in the shell remains unchanged. The geophysical implications of the results are discussed.

RESEARCH ON THE CREASE RESISTANCE OF CLOTH

The Tootal-Broadhurst-Lee Company's method was improved as follows: A cloth is conditioned for 2 days at 25°C and 65% R. H., from which the test pieces of 2cm long and 1cm wide are cut by means of a cutter. A test piece is folded across the narrow dimension and placed between two glass plates and loaded with a 500gm weight for 1hour. It is then allowed to recover for 10min. while hung over a horizontal wire of 0.3mm diameter, and then the distance l between the ends is read with a calipers. During the test the air is conditioned at 25±0.5°C and 65±1% R. H.The long dimension of the test piece was shortened to 2cm, in order to obtain the value of l, l=2sinθ/2 where θ is the crease angle.The process of crease recovery was followed in order to estimate the value l at equilibrium from an exact value after 5 or 10min. recovery period. It is found that l changes in the following relation for cloths. _??_ (1)where l_??_ is the value of l at t=o, a1, a2 and a3 are the constants, t the time of recovery, and λ1, λ2 and λ3 are the relaxation times.In the case of yarn two relaxation times λ1, λ2 are given for recovery, and one relaxation λ1 for filament. The values of λ1, λ2 and λ3 are 50_??_70, 10_??_20 and 1_??_2min. in the case of the viscose yarn used.In the range of t=3_??_20min., 160 samples of the cloths, which were woven variously by using the same viscose yarn, containing partly the resin-treated, are all indicated by the equation (1).