On the methods of determining size/weight characteristics of food organisms of fish. (Determination of the length of Copepoda in larval stages by egg-laying females of the free living freshwater Copepoda). [Translation from: Voprosy Ikhtiologii 14, 182-194, 1960. ]

As is known, copepods play an important role in the nutrition of fish. Therefore with a view to facilitating research on the study of the quantitative side of feeding, there have recently appeared a considerable number of papers devoted to the development of methods for determining the wet. weight of these crustaceans. For the further facilitating of research in the nutrition of fish it would be of great interest to clarify the problem, is there not some kind of rule in the growth of the crustaceans during metamorphosis, and if there is such a rule is it not possible, to determine the length of the larvae at each stage, not by measuring them, but by using the formulae derived on the basis of these rules. This article examines the growth curves of different species of freshwater Copepoda, obtained on the basis of experimental observations in cultures or by way of measurement of mass material at all stages of development in samples from water-bodies. The authors study in particular the ratio of the mean diameter of the eggs to the mean length of the egg-bearing females.

Free algebras in Von Neumann-Bernays-Gӧdel set theory and positive elementary inductions in reasonable structures

This thesis consists of two independent chapters. The first chapter deals with universal algebra. It is shown, in von Neumann-Bernays-Gӧdel set theory, that free images of partial algebras exist in arbitrary varieties. It follows from this, as set-complete Boolean algebras form a variety, that there exist free set-complete Boolean algebras on any class of generators. This appears to contradict a well-known result of A. Hales and H. Gaifman, stating that there is no complete Boolean algebra on any infinite set of generators. However, it does not, as the algebras constructed in this chapter are allowed to be proper classes. The second chapter deals with positive elementary inductions. It is shown that, in any reasonable structure ᶆ, the inductive closure ordinal of ᶆ is admissible, by showing it is equal to an ordinal measuring the saturation of ᶆ. This is also used to show that non-recursively saturated models of the theories ACF, RCF, and DCF have inductive closure ordinals greater than _ω.

Observing the fractional Fourier transform by free-space Fresnel diffraction

The fractional Fourier transform of an object can be observed in the free-space Fresnel diffraction pattern of the object. (C) 1997 Optical Society of America

Relay lens-free birefringence-customized stackable beam-steering modules for optical interconnects

A previously suggested birefringence-customized modular optical interconnect technique is extended for lens-free relay operation. Various lens-free relay imaging models are developed. We claim that the lens-free relay system is important in simplifying an optical interconnect system whenever the imaging conditions permit. To verify the validity of various proposed concepts, we experimentally implemented some 8 x 8 optical permutation modules. High-power efficiency and low channel cross talk were experimentally observed. In general, the larger the channel spacing, the less the cross talk. A quantitative cross-talk measurement of the lens-free relay system shows that, for a fixed channel width of 0.5 mm and channel spacings of 0.5, 1, and 2 mm, a less than -20-dB cross-talk performance can be guaranteed for lens-free relay distances of 40, 280, and 430 mm, respectively. (C) 1998 Optical Society of America.

Norbornenyl- and nortricyclyl free radicals

The number, symmetry, and product-forming capabilities of the intermediates in the photoinitiated reductions of endo- and exo-5- bromonorbornene and 2-bromonortricyclene with tri-n-butyltin hydride at temperatures between -10° and 22° were investigated.

Three mechanisms were evaluated:

1. The 5-norbornenyl- and 2-nortricyclyl radicals isomerize reversibly with the former producing nortricyclene by abstraction of hydrogen from tri-n-butyltin hydride.

2. The 5-norbornenyl- and 2-nortricyclyl radicals isomerize reversibly, but some norbornene can be formed from the 2-nortricyclyl radical or some nortricyclene can be formed from the 5-norbornenyl radical by abstraction of hydrogen.

3. There is intervention of a "bridged" radical which may be for med reversibly or irreversibly from the 5-norbornenyl- and 2-nortricyclyl radicals.

Within small error limits, the ratios of norbornene to nortricyclene as a function of the concentration of tri-n-butyltin hydride are consistent with the first mechanism.

In the reductions with tri-n-butyltin deuteride, primary deuterium isotope effects of 2. 3 and 2. 1 for the abstraction of deuterium by the 2-nortricyclyl- and 5-norbornenyl radicals, respectively, were found. The primary deuterium isotope effects were invariant with the concentration of tri-n-butyltin deuteride, although the ratios of norbornene to nortricyclene changed appreciably over this range. This is consistent with the first mechanism, and can accommodate the formation of either product from more than one intermediate only if the primary kinetic deuterium isotope effects are nearly equal for all reactions leading to the single product.

The reduction of endo-5-bromonorbornene-5, 6, 6-d₃ with tri-n-butyltin hydride or tri-n-butyltin deuteride leads to both unrearranged and rearranged norbornenes. The ratios of unrearranged to rearranged norbornene require that the 5-norbornenyl-5, 6, 6-d₃ radical isomerize to an intermediate with the symmetry expected of a nortricyclyl free radical. The results are consistent with mechanism 1, but imply a surprising normal secondary kinetic deuterium isotope effect of about 1.25 for the abstraction of hydrogen by the 5-norbornenyl- 5, 6, 6-d₃ radical.

Approximate calculations show that there does not appear to be any substantial difference in the stabilities of the 5-norbornenyl and 2-nortricyclyl radicals.

Although the results can not exclude a small contribution by a mechanism other than mechanism 1, no such contribution is required to adequately explain the results.

Part I: Latent heat of vaporization of n-decane. Part II: Heat and mass transfer from a cylinder placed in a turbulent air stream - Sherwood and Frössling numbers as a function of free stream turbulence level and Reynolds number

Part I

The latent heat of vaporization of n-decane is measured calorimetrically at temperatures between 160° and 340°F. The internal energy change upon vaporization, and the specific volume of the vapor at its dew point are calculated from these data and are included in this work. The measurements are in excellent agreement with available data at 77° and also at 345°F, and are presented in graphical and tabular form.

Part II

Simultaneous material and energy transport from a one-inch adiabatic porous cylinder is studied as a function of free stream Reynolds Number and turbulence level. Experimental data is presented for Reynolds Numbers between 1600 and 15,000 based on the cylinder diameter, and for apparent turbulence levels between 1.3 and 25.0 per cent. n-heptane and n-octane are the evaporating fluids used in this investigation.

Gross Sherwood Numbers are calculated from the data and are in substantial agreement with existing correlations of the results of other workers. The Sherwood Numbers, characterizing mass transfer rates, increase approximately as the 0.55 power of the Reynolds Number. At a free stream Reynolds Number of 3700 the Sherwood Number showed a 40% increase as the apparent turbulence level of the free stream was raised from 1.3 to 25 per cent.

Within the uncertainties involved in the diffusion coefficients used for n-heptane and n-octane, the Sherwood Numbers are comparable for both materials. A dimensionless Frössling Number is computed which characterizes either heat or mass transfer rates for cylinders on a comparable basis. The calculated Frössling Numbers based on mass transfer measurements are in substantial agreement with Frössling Numbers calculated from the data of other workers in heat transfer.

Information collected in Teesdale concerning free-swimming stages of brown trout (Salmo trutta L.)

During 1978 and 1979, electrofishing surveys were made in Teesdale - both to provide background information for ecological work on the streams, and to provide data so that the influence of discharge regime on the fish population densities could be examined. The discharge regimes of the different streams were compared using the Base Flow Index (BFI) as developed by the Institute of Hydrology. (PDF contains 30 pages)

Class two p groups as fixed point free automorphism groups

Suppose that AG is a solvable group with normal subgroup G where (|A|, |G|) = 1. Assume that A is a class two odd p group all of whose irreducible representations are isomorphic to subgroups of extra special p groups. If p^c ≠ r^d + 1 for any c = 1, 2 and any prime r where r^2d+1 divides |G| and if C_G(A) = 1 then the Fitting length of G is bounded by the power of p dividing |A|.

The theorem is proved by applying a fixed point theorem to a reduction of the Fitting series of G. The fixed point theorem is proved by reducing a minimal counter example. IF R is an extra spec r subgroup of G fixed by A₁, a subgroup of A, where A₁ centralizes D(R), then all irreducible characters of A₁R which are nontrivial on Z(R) are computed. All nonlinear characters of a class two p group are computed.

Formation of jets by implusive acceleration of a curved free surface

The sudden axial acceleration of a column of liquid bounded at one end by a concave free surface has been found, experimentally, to produce a jet which issues from the free surface with a speed several times that imparted to the column.

Theoretical approximations to such flows, valid for small time, are formulated subject to the assumption that the fluid is inviscid and incompressible. In a special two-dimensional case, it is found that, for vanishingly small time, the velocity at the point on the free surface from which the jet emanates is π/2 times the velocity imparted to the column. The solutions to several problems in two and three dimensions assuming that the initial curvature of the free surface is small, lead to values for this ratio dependent upon the curvature—the initial velocity in the case of axial symmetry exceeding that of the analogous two-dimensional problem by approximately 25%.

Experiments conducted upon the phenomenon give values systematically in excess of those predicted by the theory, although theory and experiment are in qualitative agreement with respect to the displacement of the free surface. It is suggested that the discrepancy is attributable to effects of finite curvature having been imperfectly accounted for in the axially-symmetric analysis.

Photographic materials on pp. 115, 120, and 121 are essential and will not reproduce clearly on Xerox copies. Photographic copies should be ordered.

I. The effect of droplet solidification upon two-phase flow in a rocket nozzle. II. A kinetic theory investigation of some condensation-evaporation phenomena by a moment method

Part I:

The perturbation technique developed by Rannie and Marble is used to study the effect of droplet solidification upon two-phase flow in a rocket nozzle. It is shown that under certain conditions an equilibrium flow exists, where the gas and particle phases have the same velocity and temperature at each section of the nozzle. The flow is divided into three regions: the first region, where the particles are all in the form of liquid droplets; a second region, over which the droplets solidify at constant freezing temperature; and a third region, where the particles are all solid. By a perturbation about the equilibrium flow, a solution is obtained for small particle slip velocities using the Stokes drag law and the corresponding approximation for heat transfer between the particle and gas phases. Singular perturbation procedure is required to handle the problem at points where solidification first starts and where it is complete. The effects of solidification are noticeable.

Part II:

When a liquid surface, in contact with only its pure vapor, is not in the thermodynamic equilibrium with it, a net condensation or evaporation of fluid occurs. This phenomenon is studied from a kinetic theory viewpoint by means of moment method developed by Lees. The evaporation-condensation rate is calculated for a spherical droplet and for a liquid sheet, when the temperatures and pressures are not too far removed from their equilibrium values. The solutions are valid for the whole range of Knudsen numbers from the free molecule to the continuum limit. In the continuum limit, the mass flux rate is proportional to the pressure difference alone.