1. From the above it is therefore justifiable to conclude that Sirex cyaneus is typically hymenopterous, in that:

(a) the ripe male reproductive tissue is haploid (8 chromosomes), while the female oogonia are diploid (16 chromosomes);

(b) the abortive character of the first spermatocyte division is evidence that chromosome reduction does not occur during the maturation of the male gametes.

2. Support is thus afforded to the hypothesis commonly held, that the male hymenopteron is a haploid organism and is the product of an unfertilised (haploid) egg, while the female is a diploid organism arising from a fertilised egg.

3. Feulgen's “Nuclealreaktion” holds for the chromatin involved in the abortive division and for the chromosomes of the second spermatocyte; but the large chromatoid body and cytoplasmic granules seen in these same stages by the iron hæmatoxylin technique did not give the chromatin reaction. The nature of these chromatoid bodies remains to be discovered.

Consider the two-dimensional autonomous systems of differential equations

$$ \dot{x}=-y+\lambda x+P(x,y),\qquad\dot{y}=x+\lambda y+Q(x,y), $$

where $\lambda$ is a real constant and $P$ and $Q$ are $\mathcal{C}^{\infty}$-functions of order greater than or equal to two. These systems, so-called centre-focus-type systems, have either a centre or a focus at the origin. In this work, we give necessary and sufficient conditions of isochronicity using normal forms. We characterize the systems which have either an isochronous centre or an isochronous focus at the origin by means of the existence of a commutator of the field. Moreover, we prove that the maximum order of a weak isochronous focus for quadratic systems is two, and that for systems with cubic nonlinearities is three.

Hyperasymptotic expansions were recently introduced by Berry and Howls, and yield refined information by expanding remainders in asymptotic expansions. In a recent paper of Olde Daalhuis, a method was given for obtaining hyperasymptotic expansions of integrals that represent the confluent hypergeometric U-function. This paper gives an extension of that method to neighbourhoods of the so-called Stokes lines. At each level, the remainder is exponentially small compared with the previous remainders. Two numerical illustrations confirm these exponential improvements.

Present knowledge of the oogenesis of caddis-flies is scanty. Marshall's paper (17) on the ovary of Platyphylax designatus is the only detailed account of the growth and history of the ovarian elements during the larval and pupal stages, but he does not deal with the cytoplasmic inclusions.

The so–called rectal gland of Elasmobranch fishes claimed notice early in the history of scientific research, as might indeed be expected from the obviousness of its appearance and the invariability of its occurrence. But, in spite of this fact, the rectal gland remains one of those organs the knowledge of the structure of which is unsatisfactory, and the conjecture as to the function of which is consequently hazy.

We consider an inverse parabolic problem of reconstruction of the source function, together with the traditional solution. In contrast with older literature, we consider non-homogeneous and time-dependent boundary conditions. We are able to prove a general result of convergence to a stationary state, and of asymptotic expansion as t → ∞.

In commutative Banach algebras with factorisation, the existence of an identity (bounded approximate identity) modulo a topologically nilpotent radical implies the existence of a global identity (bounded approximate identity), respectively.

The albino rats used in this study were obtained originally from the Wistar Institute of Philadelphia and belong to a strain in which microphthalmia was first observed by Dr Helen Dean King in the F4 generation extracted from a cross between an albino female of this stock and a wild grey Norway male. The defect occurred only in the “S” strain which formed a small proportion of the main stock. Its inheritance was observed by King (1931) through eleven generations, and 538 rats having either both or a single eye microphthalmic were obtained in a strain comprising 1884 individuals. The greater frequency of microphthalmia in the American stock is a marked feature, since only 154 rats with eye defects have been observed in the Edinburgh branch of Wistar rats in fourteen generations comprising over 5000 rats, and this total includes animals with eyes of normal size but possessing defects such as aniridia, cataract, etc., and also rare cases of anophthalmia and buthalmos. It is probable that 80 per cent, of the total affected were microphthalmics, and apparently the defect was generally more pronounced than in the parent stock, that is if the rat illustrated in King's monograph is to be taken as typical. According to King, the eye-defect could easily be detected at birth, “since a small eye did not protrude from the socket.” In the total given here no still-borns are included, as it was found that this method of diagnosis, as also the opacity of the lens in such rats immediately or soon after birth, were unreliable criteria of abnormality. We are in agreement that prenatal mortality did not play an important role in determining the ratio of normal to abnormal individuals, because litters containing affected were of the average litter size and generally contained some normals (Table I). However, where a large number of still-born rats occurred in litters containing defectives, it is possible that the abnormality involved proved lethal, since still-births are not of common occurrence in this stock (Table II).

Transition probabilities are calculated which make the construction of diffusions on finitely ramified fractals straightforward. In contrast to former approaches using Brouwer's Fixed Point Theorem, we consider an approximation procedure based on the iteration of a nonlinear map L. Physically, this is done by ‘coarse-graining-renormalisation of finite electric resistor networks’. Mathematically, it is a convergence problem for quotients of Dirichlet forms on finite graphs. These graphs approximate finitely ramified fractals. The basic tool is a contraction theorem for the renormalisation map L which allows the use of known results about nested fractals for non-nested (p.c.f. self-similar) ones. In general, the above contraction is not strict because several linear independent fixed points occur.

Given an infinite-dimensional vector space V, we consider the semigroup GS (m, n) consisting of all injective linear α: V → V for which codim ran α = n, where dim V = m ≥ n ≥ ℵ0. This is a linear version of the well-known Baer–Levi semigroup BL (p, q) defined on an infinite set X, where |X| = p ≥ q ≥ ℵ0. We show that, although the basic properties of GS (m, n) are the same as those of BL (p, q), the two semigroups are never isomorphic. We also determine all left ideals of GS (m, n) and some of its maximal subsemigroups; in this, we follow previous work on BL (p, q) by Sutov and Sullivan as well as Levi and Wood.

We study the two-phase Stokes flow driven by surface tension with two fluids of equal viscosity, separated by an asymptotically flat interface with graph geometry. The flow is assumed to be two-dimensional with the fluids filling the entire space. We prove well-posedness and parabolic smoothing in Sobolev spaces up to critical regularity. The main technical tools are an analysis of nonlinear singular integral operators arising from the hydrodynamic single-layer potential and abstract results on nonlinear parabolic evolution equations.

The mapping properties of the finite Hilbert-transform (respectively the Hilbert transform on the half axis) are studied. Invertibility, surjectivity, injectivity and bounded ness from below of the transform are characterised in general weighted spaces. The results are applied to the restriction of the operator with logarithmic kernel.

It has long been known that yellow phosphorus is slowly oxidised in air at the ordinary temperature and that the oxidation is accompanied by a glow easily visible in a darkened room. If oxygen at atmospheric pressure is substituted for air no glow is perceived, and the oxidation, if it occurs at all, is incomparably slower than in air. If the pressure of oxygen is reduced either directly or by admixture with an indifferent gas the glow may be made to reappear. The seeming contradiction of the law of mass action involved in these phenomena has been the subject of many experiments, and the main object of the present investigation is to attempt to throw some light on this anomaly.

We consider an emulsion of two Stokes fluids, one of which is periodically distributed in the form of small spherical bubbles. The effects of surface tension on the bubble boundaries are modelled mathematically, as in the work of G. I. Taylor, by a jump only in the normal component of the traction. For a given volume fraction of bubbles, we consider the two-scale convergence, and in the fine phase limit we find that the bulk flow is described by an anisotropic Stokes fluid. The effective viscosity tensor is consistent with the bulk stress formula obtained by Batchelor [2].

Of the explanations advanced in respect of the observed inequality in the viability and longevity of the sexes in man, the sex‐linked lethal theory advocated by Lenz (1923), Gunther (1923), Geiser (1924–5), Huxley (1924), Schirmer (1929), amongst others, has attracted most support. One reason for this is undoubtedly that it is a genetic theory promulgated at a time when biological thought was being profoundly influenced by the many spectacular discoveries which had been made in this particular science.

Observations were made on the body temperature of a large number of diving and swimming birds of eighteen different species in the Orkney Islands and Firth of Forth, Scotland, and on and around Cayuga Lake, N.Y., U.S.A., immediately after they were killed by shooting.

1. In all the species examined, where the sex was determined, it was found that the rectal temperature of the male was slightly below that of the female.

2. Of the orders examined the highest temperatures were found in the Longipennes and the lowest in the Tubinares. When arranged according to body temperature the series does not run parallel with the zoological series.

In conclusion, I wish to express my indebtedness to Dr H. D. Reed and Dr A. H. Wright for help in identifying the specimens obtained from Cayuga Lake and the surrounding district.

Under appropriate conditions on b and a function g with 2k +1 simple zeros, the equation

has a maximal compact invariant set Ab,g in C([−1,0]R), consisting of the zeros of g and the one-dimensional unstable manifolds of these zeros. For k =2, it is shown that there may be a saddle connection in the flow on Ab,g for some g. This implies that the zeros of g as elements of the flow on Ab,g cannot be given the natural order of the reals.

The chemical composition of submarine glauconite is of considerable interest in view of the fact that glauconite is the only silicate which is synthesized at the bottom of the sea, and apparently nowhere else. Numerous analyses of this mineral have been published from time to time, but the results are far from uniform, because the material almost always—certainly in most of the older analyses—was anything but pure. The analysis which inspires most confidence on this score is one which was recently carried out in the Challenger laboratory by Collet and Lee on a purified granular glauconite dredged off the Californian coast by U.S.S. Tuscarora (1879).

In nearly every narrative of exploration in uncivilised tropical regions, accounts are given, often no doubt somewhat fanciful, of poisonous substances which are said to possess the most remarkable properties. Usually these poisons are of vegetable origin; and the great majority may be included in the two divisions of ordeal and of arrow poisons, according as they are applied to one or other of these purposes. Among the most remarkable of the ordeal poisons are the Tanghinia venifera of Madagascar, the Physostigma venenosum of Old Calabar, and the Akazga poison of the Gaboon; and of the arrow-poisons, the famous Curara or Wourali of South America, and the Antiaris toxicaria of Java.

We consider the compressible Navier–Stokes system on time-dependent domains with prescribed motion of the boundary. For both the no-slip boundary conditions as well as slip boundary conditions we prove local-in-time existence of strong solutions. These results are obtained using a transformation of the problem to a fixed domain and an existence theorem for Navier–Stokes like systems with lower order terms and perturbed boundary conditions. We also show the weak–strong uniqueness principle for slip boundary conditions which remained so far open question.