One of the most striking and interesting of the many traditions and current beliefs regarding venomous serpents is that a power may be acquired of freely handling them without injury, and even of successfully resisting the poisonous effects of their bites.

Early in September of this year I received from the Falkland Islands a box, dispatched by Mr G. Millen Coughtrey, a former student of the University, now an employé in the New Zealand Whaling Company. It contained a number of specimens which illustrated the anatomy of the auditory apparatus in the Cetacea. The whales were caught in the South Atlantic, mostly at South Shetland, though some were from Graham's Land, at which place he had been whaling last season.

If the marked divergence of ethnological opinion concerning the degree of racial purity or admixture of the Australian aboriginal affords evidence of anything at all, it can only be of the fact that the problems of his origin, as of his degree of racial purity, are not yet solved. Not only are there the most conflicting opinions on these points, but the cognate subjects of the origin, and degree of purity of the Tasmanian, and of his relationship, if any, to the Australian, are equally undetermined, whilst there is lastly the debatable point of the relation of both those primitive peoples to the Papuan.

The late Professor Gratiolet, in his elaborate and beautifully illustrated memoir, “Sur les Plis Cérébraux de l'Homme et des Primates,” attaches great weight in his differential diagnosis of their cerebral characters to the presence or absence of one or more members of a series of convolutions, which he designates as the plis de passage. When present, these convolutions bridge over the external perpendicular fissure of the hemisphere, and connect the parietal and temporal with the occipital lobes. By various anatomists in this country they are called bridging, connecting, or annectent convolutions. In the brain of the Chimpanzee M. Gratiolet states that the first bridging convolution is altogether wanting; that the second is present, but concealed under the operculum of the occipital lobe; that the third and fourth are superficial.

It is shown that the fine structure of the asymptotic estimates for the eigenvalues of a large class of ordinary differential operators, can be described in terms of the Fourier coefficients of a function of class L2.

We study sufficient conditions under which a nowhere scattered $\mathrm {C}^*$-algebra $A$ has a nowhere scattered multiplier algebra $\mathcal {M}(A)$, that is, we study when $\mathcal {M}(A)$ has no nonzero, elementary ideal-quotients. In particular, we prove that a $\sigma$-unital $\mathrm {C}^*$-algebra $A$ of

1. (i) finite nuclear dimension, or

2. (ii) real rank zero, or

3. (iii) stable rank one with $k$-comparison,

$\mathcal {M}(A)$

Skew left braces arise naturally from the study of non-degenerate set-theoretic solutions of the Yang–Baxter equation. To understand the algebraic structure of skew left braces, a study of the decomposition into minimal substructures is relevant. We introduce chief series and prove a strengthened form of the Jordan–Hölder theorem for finite skew left braces. A characterization of right nilpotency and an application to multipermutation solutions are also given.

We use new methods, specific for non-locally convex quasi-Banach spaces, to investigate when the quasi-greedy bases of a $p$-Banach space for $0< p<1$ are democratic. The novel techniques we obtain permit to show in particular that all quasi-greedy bases of the Hardy space $H_p({\mathbb {D}})$ for $0< p<1$ are democratic while, in contrast, no quasi-greedy basis of $H_p({\mathbb {D}}^d)$ for $d\ge 2$ is, solving thus a problem that was raised in [7]. Applications of our results to other spaces of interest both in functional analysis and approximation theory are also provided.

In this communication the mode of experimenting was described by which the experimental results quoted in the theoretical paper were obtained; and the principal parts of the special apparatus which had been constructed and used in the investigation, were laid before the Royal Society.

Interaction equations of long and short water wave are considered. It is shown that the Cauchy problem for

is locally well posed in the largest space where the three conservations

can be justified. Here E(u,v) is the energy functional associated to the system. By these conservation laws, we establish the global well-posedness of the system in the largest class of initial data.

The Laplacian operator Δ on a bounded domain Ω in ℝn containing 0, with Dirichlet boundary condition, is perturbed by a pseudopotential δ, the Dirac measure at 0. Such a perturbation will be defined in Lp(ℝ) for n = 2, 1 <lt; p < ∞, and for n = 3, < p < 3, and is shown to be the generator of an analytic semigroup. Thus solutions of the corresponding evolutionary system are well defined. The necessary estimates involve the Gagliardo– Nirenberg inequality and the Kato inequality.

We give an alternative proof of the theorem of Alikakos and Fusco concerning existence of heteroclinic solutions U : ℝ → ℝN to the system

Here a± are local minima of a potential W ∈ C2(ℝN) with W(a±) = 0. This system arises in the theory of phase transitions. Our method is variational but differs from the original artificial constraint method of Alikakos and Fusco and establishes existence by analysing the loss of compactness in minimizing sequences of the action in the appropriate functional space. Our assumptions are slightly different from those considered previously and also imply a priori estimates for the solution.

This paper is concerned with a neutral differential equation with four constant coefficients, one delay and one advancement. By means of the theory of envelopes, we consider all possible values of the parameters involved in the equation and obtain a complete set of necessary and sufficient conditions for all solutions to be oscillatory.

By using a monotonic functional on a suitable matrix space, some new oscillation criteria for self-adjoint matrix Hamiltonian systems are obtained. They are different from most known results in the sense that the results of this paper are based on information only for a sequence of subintervals of [t0, ∞), rather than for the whole half-line. We develop new criteria for oscillations involving monotonic functionals instead of positive linear functionals or the largest eigenvalue. The results are new, even for the particular case of self-adjoint second-differential systems which can be applied to extreme cases such as

We give here a group extension sequence for calculating, for a non-simply-connected space X, the group of self-homotopy-equivalence classes which induce the identity automorphism of the fundamental group, that is the kernel of the representation → aut (π1(X)). This group extension sequence gives in terms of , where Xn is the n-th stage of a Postnikov decomposition. As special cases, we calculate for non-simply-connected spaces having at most two non-trivial homotopy groups, in dimensions 1 and n, as the unit group of a semigroup structure on ; and we calculate up to extension for non-simply-connected spaces having at most three non-trivial homotopy groups. The group is, for nice spaces, isomorphic to the groups and of self-homotopy-equivalence classes of X in the categories top*M and top M, respectively, where X→M = K1(π1(X)) is a top fibration which determines an isomorphism of the fundamental group; and our results are obtained initially in topM.

(1) An attempt has been made to prove experimentally that there is definite localisation of translocation in the plant.

(2) This localisation is brought about by the almost complete absence of easy cross-transfer of materials in the plant tissues. It affects the movement of both salts and elaborated food-materials.

(3) The fact that movement upwards and downwards is easy while lateral movement is almost completely absent is clearly demonstrated where it is shown that the materials which are elaborated in the leaves on one side of. the swede plant are stored as reserved food-materials in the portion of the bulb on the same side.

(4) It is also shown that this localisation is found in the case of other plants, and that it offers a new method of attacking a variety of problems which at the present time present some difficulty of interpretation.

A construction is given for a trace function on the semigroup algebra of a certain type of E-unitary inverse semigroup over any subfield of the complex field that is closed under complex conjugation. In particular, the method applies to the semigroup algebras of free inverse semigroups of arbitrary rank.

Cardinal interpolation by integer translates of shifted three-directional box splines is studied. It is shown that, for arbitrary orders, k, l, m ∈ N of the directional vectors, this problem is correct if and only if the shift vector is taken from the hexagonal shift region (modulo translation with respect to the lattice Z2). This confirms a conjecture of S. D. Riemenschneider [9], and settles the problem studied in [5] for the special case k = l = m in full generality. The method of proof is from homotopy theory.

The Cauchy problem for the time-dependent Ginzburg–Landau equations of superconductivity in Rd (d = 2, 3) is investigated in this paper. When d = 2, we show that the Cauchy problem for this model is well posed in L2. When d = 3, we establish the existence result of solutions for L3 initial data and the uniqueness result for L4 initial data.