Algebroid Functions Research Articles

On the characteristic of an algebroid function

On the characteristic of an algebroid function

Open Riemann Surface with Null Boundary

Recently the writer has obtained some results concerning meromorphic or algebroidal functions with the set of essential singularities of capacity zero, with an aid of a theorem of Evans. In the present paper, suggested from recent interesting papers of Sario and Pfluger, the writer will extend his results to single-valued analytic functions defined on open abstract Riemann surfaces with null boundary in the sense of Nevanlinna, using a lemma instead of Evans’ theorem.

The Riemann Multiple-Space and Algebroid Functions

The Riemann Multiple-Space and Algebroid Functions

Societies and Academies

PARIS. Academy of Sciences, September 17.—M. Joseph Boussinesq in the chair.—The president announced the death of M. J. Violle.—P. Villard: The true colour of clouds. It is generally admitted that the true colour of clouds is white, and that the colour effects observed are due to the coloured rays of the sun at sunrise and sunset. From the results of twenty years' observations the author believes that this is not always the case and that clouds may possess a colour of their own, not necessarily white, although illuminated with pure white light. Variations of colour have been noted during the disappearance and re-formation of light cumulus clouds.—P. Sergesco: The distribution of the characteristic values of the nuclei of Marty N(x, y) =A(x)K(x, y).—Antoine Zygmund: The Riemann theory of trigonometrical series.—Georges J. Remoundos: A property of elimination and algebroid functions.—O. M. Tino: The passage from the theory of the fundamental Fredholm functions to that of the fundamental Schmidt functions.—Serge Bernstein: The mathematical demonstration of Mendel's law of heredity.—o A. Petot: A characteristic difference between the modes of action of front and back brakes. It is shown that there is a fundamental difference between the action of front and back braking on a motor-car. The latter arrests only the motion of translation of the car; in the former the brake also affects the car's movement of rotation round the vertical.—L. J. Simon and M. Frerejacque:. The action of dimethyl sulphate on salicylic acid, methyl sali-cylate, and methoxysalicylic acid. Sulph'onation and methylation. In the absence of water, methyl sulphate and salicylic react, giving three substances, C6H3(OH) (CO2CH3)SO3H, C6H3(OH)(CO2CH3)SO3CH3, and C6H3(OCH3)(CO2CH3)SO3H. The trimethyl sulphonated derivative is not produced.—Ch. Courtot and A. Dondelinger: Some new secondary bases of the indene series.—Paul Dumanois: A method of air-drying. A scheme for preventing the moisture in air reaching absolute alcohol or petrol stored in bulk.—F. Vincens: The aspergillomycosis of bees.—R. Herpin: Ethology and development of Nereis caudata.