scholarly journals Three-point functions in the 𝒩 = 4 orthogonal coset theory

2016 ◽  
Vol 31 (16) ◽  
pp. 1650090 ◽  
Author(s):  
Changhyun Ahn ◽  
Hyunsu Kim ◽  
Jinsub Paeng
Keyword(s):  
General Formula ◽  
Superconformal Algebra ◽  
The Other ◽  
Spin Currents ◽  
Hooft Limit ◽  
Higher Spin

We construct the lowest higher spin-2 current in terms of the spin-1 and the spin-[Formula: see text] currents living in the orthogonal [Formula: see text] Wolf space coset theory for general [Formula: see text]. The remaining 15 higher spin currents are determined. We obtain the three-point functions of bosonic (higher) spin currents with two scalars for finite [Formula: see text] and [Formula: see text] (the level of the spin-1 current). By multiplying [Formula: see text] into the above Wolf space coset theory, the other 15 higher spin currents together with the above lowest higher spin-2 current are realized in the extension of the large [Formula: see text] linear superconformal algebra. Similarly, the three-point functions of bosonic (higher) spin currents with two scalars for finite [Formula: see text] and [Formula: see text] are obtained. Under the large [Formula: see text] ’t Hooft limit, the two types of three-point functions in the nonlinear and linear versions coincide as in the unitary coset theory found previously.

scholarly journals The Dissociation of the Compound of Iodine and Thio-urea

1904 ◽  
Vol 24 ◽  
pp. 233-239 ◽  
Author(s):  
Hugh Marshall
Keyword(s):  
Nitric Acid ◽  
General Formula ◽  
Free Acid ◽  
The Other ◽  
Image Position

When thio-urea is treated with suitable oxidising agents in presence of acids, salts are formed corresponding to the general formula (CSN2H4)2X2:—Of these salts the di-nitrate is very sparingly soluble, and is precipitated on the addition of nitric acid or a nitrate to solutions of the other salts. The salts, as a class, are not very stable, and their solutions decompose, especially on warming, with formation of sulphur, thio-urea, cyanamide, and free acid. A corresponding decomposition results immediately on the addition of alkali, and this constitutes a very characteristic reaction for these salts.

scholarly journals Higher-spin currents and thermal flux from Hawking radiation

2007 ◽  
Vol 75 (12) ◽  
Author(s):  
Satoshi Iso ◽  
Takeshi Morita ◽  
Hiroshi Umetsu
Keyword(s):  
Hawking Radiation ◽  
Thermal Flux ◽  
Spin Currents ◽  
Higher Spin

scholarly journals XI. On the normal paraffins. Part III

1879 ◽  
Vol 29 (196-199) ◽  
pp. 364-365
Keyword(s):  
Hydrochloric Acid ◽  
General Formula ◽  
The Other ◽  
Partial Decomposition ◽  
Lower Temperature

The isomeric monochlorides, obtained from the normal paraffins existing in petroleum, yield by the abstraction of hydrochloric acid a mixture of olefines, one portion of which readily combines with hydrochloric acid in the cold, whilst the other unites with it only on heating. The chlorides formed in the cold boil with partial decomposition and at a lower temperature than the others, which distil without undergoing any change, and have the general formula CH 3 - CHCl—C n H 2 n +1 .

scholarly journals A general method of calculating the angles made by any planes of crystals, and the laws according to which they are formed

1833 ◽  
Vol 2 ◽  
pp. 227-229
Keyword(s):  
General Formula ◽  
Dihedral Angle ◽  
The Other ◽  
Plane Angle ◽  
General Process ◽  
Primitive Forms ◽  
Primary Form ◽  
General Method ◽  
Universal Application

The author, after stating the inconsistencies, inelegancies, and imperfections of the received notation for expressing the planes of a crystal, and the laws of decrement by which they arise, and of the usual methods of calculating their angles, explains the object of the present paper, which is to propose a system exempt from these inconveniencies, and adapted to reduce the mathematical portion of crystallography to a small number of simple formulae, of universal application. According to the method here followed, each plane of a crystal is represented by a symbol indicative of the laws from which it results, which, by varying only its indices, may be made to repre­sent any law whatever; and by means of these indices, and of the primary angles of the substance, we may derive a general formula expressing the dihedral angle contained between any one plane resulting from crystalline laws, and other . In the same manner we can find the angle contained between any two edges of the de­rived crystal. Conversely, having given the plane, or dihedral an­gles of any crystal, and its primary form, we can, by a direct and general process, deduce the laws of decrement according to which it is constituted. The purely mathematical part of this paper depends on two formulæ, demonstrated by the author elsewhere and here assumed as known; by means of one of which the dihedral angle included between any two planes can be calculated, when the equations of both planes are given; and by the other, the plane angle included between any two given right lines can in like manner be expressed by assigned functions of the coefficients of their equations, supposed given. These formulæ being taken for granted, nothing remains but to express by algebra­ical equations the planes which result from any assigned laws of decrement, for the different primitive forms which occur in crystallography.

scholarly journals XII. On the normal paraffins. —Part III

1880 ◽  
Vol 171 ◽  
pp. 451-454 ◽  
Keyword(s):  
Hydrochloric Acid ◽  
General Formula ◽  
The Other ◽  
Partial Decomposition ◽  
Lower Temperature ◽  
Derivatives Of

The isomeric monochlorides obtained from the normal paraffins existing in petroleum yield by the abstraction of hydrochloric acid a mixture of olefines, one portion of which readily combines with hydrochloric acid in the cold, whilst the other is not changed, even if it be left in contact with the acid for weeks, and only unites with it on heating. The chlorides which are formed in the cold boil with partial decomposition and at a lower temperature than the others, which distil without undergoing any change, and, as Morgan has shown, have the general formula, CH 3 —CHCl—C n H 2 n +1. † They are, therefore, derivatives of the olefines having the constitution CH 2 = CH —C n H 2 n +1 or CH 2 =CHR, and which, as Le Bel‡ has also shown, combine with hydrochloric acid only on heating.

Isentropic compressibilities of electrolytes in acetonitrile at 25 °C

1981 ◽  
Vol 59 (14) ◽  
pp. 2212-2217 ◽  
Author(s):  
Isobel Davidson ◽  
Gérald Perron ◽  
Jacques E. Desnoyers
Keyword(s):  
General Formula ◽  
Free Space ◽  
Infinite Dilution ◽  
Inorganic Ions ◽  
The Other ◽  
Square Root ◽  
Isentropic Compressibilities ◽  
Ionic Size ◽  
Acetonitrile Solutions ◽  
Solvent Molecules

The sound velocities of some 1:1 electrolytes in acetonitrile were measured by the "sing around" method. Apparent molal isentropic compressibilities [Formula: see text] of the electrolytes were derived from these data and from previously determined densities. Infinite dilution partial molal compressibilities [Formula: see text] were obtained by extrapolation from the plot [Formula: see text] against the square-root of the molality. Approximate ionic values are obtained on the assumption that [Formula: see text] In general, [Formula: see text] of inorganic ions are much more negative in acetonitrile than in water and, except for Li+, show little dependence on ionic size. On the other hand, [Formula: see text] of tetraalkylammonium bromides become increasingly positive as the size of the cations increases. This is again in contrast with [Formula: see text] of these electrolytes in water which remain negative. These large positive values arise from the free space between the ions and the solvent molecules, which is large in acetonitrile solutions.

Sign in / Sign up

Export Citation Format

Share Document