scholarly journals IX. Combinatorial analysis. The foundations of a new theory

1900 ◽  
Vol 194 (252-261) ◽  
pp. 361-386 ◽  
Keyword(s):  
General Problem ◽  
Complete Solution ◽  
Latin Square ◽  
The Other ◽  
Combinatorial Analysis ◽  
Great Problem ◽  
Cambridge Philosophical Society ◽  
New Instrument ◽  
Similar Character ◽  
The One

In the ‘Transactions of the Cambridge Philosophical Society’ (vol. 16, Part IV., p. 262), I brought forward a new instrument of research in Combinatorial Analysis, and applied it to the complete solution of the great problem of the “Latin Square,” which had proved a stumbling block to mathematicians since the time of Euler. The method was equally successful in dealing with a general problem of which the Latin Square was but a particular case, and also with many other questions of a similar character. I propose now to submit the method to a close examination, to attempt to establish it firmly, and to ascertain the nature of the questions to which it may be successfully applied. We shall find that it is not merely an enumerating instrument but a powerful reciprocating instrument, from which a host of theorems of algebraical reciprocity can be obtained with facility. We will suppose that combinations defined by certain laws of combination have to be enumerated; the method consists in designing, on the one hand, an operation and, on the other hand, a function in such manner that when the operation is performed upon the function a number results which enumerates the combinations. If this can be carried out we, in general, obtain far more than a single enumeration; we arrive at the point of actually representing graphically all the combinations under enumeration, and solve by the way many other problems which may be regarded as leading up to the problem under consideration. In the case of the Latin Square it was necessary to design the operation and the function the combination of which was competent to yield the solution of the problem. It is a much easier process, and from my present standpoint more scientific, to start by designing the operation and the function, and then to ascertain the questions which the combination is able to deal with.

Realizations of chiral transformations: explicit forms

1970 ◽  
Vol 48 (19) ◽  
pp. 2272-2282 ◽  
Author(s):  
John M. Charap
Keyword(s):  
Pseudoscalar Meson ◽  
General Problem ◽  
The Other ◽  
Field Theories ◽  
Meson Field ◽  
Nonlinear Functions ◽  
The One ◽  
Nonlinear Realizations ◽  
Explicit Expressions

The parallel approaches to the general problem of giving nonlinear realizations of chiral SU(n) [Formula: see text]SU(n) appropriate to phenomenological field theories as derived by Callan, Coleman, Wess, and Zumino on the one hand, and by Barnes and Isham on the other, are reviewed and compared. Explicit expressions are given for the nonlinear functions of the pseudoscalar meson field variables which arise in these methods.

A Distinção Gráfico-Linguístico e a Notação Musical

2018 ◽  
Vol 74 (4) ◽  
pp. 1465-1492
Author(s):  
Fabrício Pires Fortes
Keyword(s):  
General Problem ◽  
Graphical Representation ◽  
Visual Representations ◽  
The Other ◽  
Linguistic Representation ◽  
Musical Notation ◽  
Other Hand ◽  
Linguistic Representations ◽  
The One ◽  
Pictorial Representations

This paper examines the traditional musical notation from the viewpoint of the general problem concerning the types of visual representations. More specifically, we analyze this system in relation to the distinction between graphical and linguistic representations. We start by comparing this notation with the representational systems which are most commonly associated with such categories: on the one hand, pictorial representations as an example of a graphical representation; on the other hand, verbal writing usually associated with a linguistic representation. Then, we examine the traditional musical notation in relation to different ways of drawing the distinction graphic–linguistic, and we evaluate the applicability of such criteria to the former system. Finally, we present some general remarks about the legitimacy of this distinction both with respect to representational systems in general and to the specific case of the traditional musical notation.

scholarly journals II. Spectroscopic observation of the sun, No. II., was resumed and concluded

1869 ◽  
Vol 17 ◽  
pp. 131-132 ◽  
Keyword(s):  
Gaseous Medium ◽  
Spectroscopic Observation ◽  
The Other ◽  
The Sun ◽  
New Instrument ◽  
Exact Determination ◽  
The Government ◽  
Government Grant ◽  
The One

Th e author, after referring to his ineffectual attempts since 1866 to observe the spectrum of the prominences with an instrument of small dispersive powers, gave an account of the delays which had impeded the construction of a larger one (the funds for which were supplied by the Government-Grant Committee early in 1867), in order that the coincidence in time between his results and those obtained by the Indian observers might not be misinterpreted. Details are given of the observations made by the new instrument, which was received incomplete on the 16th of October. These observations include the discovery, and exact determination of the lines, of the prominence spectrum on the 20th of October, and of the fact that the prominences are merely local aggregations of a gaseous medium which entirely envelopes the sun. The term Chromospher e is suggested for this envelope, in order to distinguish it from the cool absorbing atmosphere on the one hand, and from the white light-giving photosphere on the other. The possibility of variations in the thickness of this envelope is suggested, and the phenomena presented by the star in Corona are referred to.

scholarly journals PRODUCTION OF DELPHINIUM IN A TOBACCO TRANSPLANT GREENHOUSE

HortScience ◽  
2006 ◽  
Vol 41 (3) ◽  
pp. 513A-513
Author(s):  
Carl E. Niedziela ◽  
Stephen A. Emerson ◽  
Guochen Yang
Keyword(s):  
Production Systems ◽  
Latin Square ◽  
Dry Weight ◽  
The Other ◽  
Planting Density ◽  
Fresh Weight ◽  
Stage Of Development ◽  
Square Cells ◽  
The One ◽  
Final Harvest

Plug seedlings of delphinium (Delphinium elatum L. `Guardian') were planted on 19 Nov. 2004 in four production systems (harvest lugs, lay-flat bags, pots, and polystyrene trays). Production systems were randomized in a Latin-square design with four replications of each system. Each treatment plot was 0.7 × 1.1 m. Planting density was 31 plants/m2. The harvest lugs were 55 × 37 × 16 cm. The lay-flat bags were 114 × 30 × 3 cm. The pots were 25 cm bulb pans. The polystyrene trays were 67 × 34 × 5 cm and contained 32 square cells. All of the containers were filled with the same tobacco germination media. The plants in the harvest lugs, lay-flat bags and pots were irrigated daily with 150 mg N/kg from 20N–4.4P–16.6K. The plants in the polystyrene trays were floated on a solution of 150 mg N/kg from 20N–4.4P–16.6K. Float solutions were monitored and adjusted weekly for volume and fertilizer concentration. Individual stems were harvested at the one-third bloom stage of development. The final harvest was on 1 Apr. 2005. Fewer stems were harvested from float trays and lay-flat bags than from pots and harvest lugs. The stems harvested from float tray plots were shorter than those from the other three systems. Stem fresh weight from greatest to least was lay-flat bags, harvest lugs, pots, and float trays. Stem dry weight was less for float trays than the other three systems.

On a problem of Călugăreanu, Chekhlov and Krylov regarding pure endomorphic images of abelian groups

2020 ◽  
Vol 23 (1) ◽  
pp. 159-178
Author(s):  
Patrick W. Keef
Keyword(s):  
General Problem ◽  
Abelian Groups ◽  
Complete Solution ◽  
The Other ◽  
Other Hand ◽  
Torsion Groups

AbstractA problem of Călugăreanu, Chekhlov and Krylov asks which abelian groups have the property that all of their pure subgroups that are endomorphic images are necessarily summands. Complete answers are given for the groups in certain classes (for example, the torsion groups). On the other hand, examples are constructed that show a complete solution to the general problem is likely to be quite difficult.

scholarly journals On the distribution of intensity in the X-ray spectra of certain long-chain organic compounds

1925 ◽  
Vol 108 (748) ◽  
pp. 655-666 ◽  
Keyword(s):  
Single Molecule ◽  
Complete Solution ◽  
Point Of View ◽  
The Other ◽  
Active Group ◽  
X Rays ◽  
Simple Interpretation ◽  
X Ray ◽  
The One ◽  
Long Chain

Recently, many compounds, having as the basis of their structure a long chain of carbon atoms, have been investigated by means of X-rays. Although the complete solution of the crystal structure of these compounds presents great difficulties, certain measurements, which can readily be made, appear capable of a simple interpretation in terms of the molecular structure. It is found, for example, that there is one plane in the crystal which has a very much larger spacing than any of the others, and the magnitude of this spacing is very simply related to the number of carbon atoms in the molecule. In any series, as the molecular chain is increased by the continued addition of CH 2 groups, this spacing increases uniformly. This must mean that the molecules are oriented lengthwise between such planes, so that an increase in the length of the molecule results in a corresponding increase in the spacing. It does not follow that the molecules are so arranged that the direction of their length is perpendicular to these planes ; but, for any one series, the angle which this direction makes with the normal to the plane must remain very nearly constant; in certain series the molecules appear to be very nearly at right angles to the planes. A consideration of the results of many such measurements led to the conclusion that, from an X-ray point of view, the various series may be divided into two groups, ( a ) those in which the planes are separated by the length of a single molecule, ( b ) those in which the spacing corresponds to the length of two molecules. It is possible to predict with considerable certainty to which of these two classes a series will belong. If, at the end of the molecule, there is a group which is chemically active as in the cases of the fatty acids, alcohols, etc., series, it seems reasonable to conclude that, where the double length is found, the two molecules will be arranged end-to-end in opposite directions, the active group of the one molecule being oriented towards the active group of the other.

2. Description of the Hydrodynameter, a new instrument for shewing the rate of Sailing of Ships and Velocity of Currents, Rivers, Tides, &c

1845 ◽  
Vol 1 ◽  
pp. 206-207
Author(s):  
R. Adie
Keyword(s):  
Glass Tube ◽  
Zero Point ◽  
The Other ◽  
New Instrument ◽  
The One

The author here first refers to the differential barometer of the late Dr Wollaston, from which he derives his new instrument. He then describes the instrument, which, in its simplest form, consists of a glass-tube bent into the form of the letter U inverted, the one end open in the line of the arms downwards, the other has its point turned up at right angles to this line. A divided scale is placed between the tubes, having its zero point as the centre. When the instrument is used, the upper curve and arms are to be filled with oil, or any other fluid lighter than water, as far as the zero on the scale; the remaining parts of the tubes are to be filled with water.

Mechanism of Polymerization Reactions

1940 ◽  
Vol 13 (3) ◽  
pp. 557-565
Author(s):  
H. W. Melville
Keyword(s):  
Molecular Structure ◽  
General Problem ◽  
The Other ◽  
Large Molecules ◽  
Naturally Occurring ◽  
Absolute Certainty ◽  
The Subject ◽  
Points Of View ◽  
The One ◽  
And Behavior

Abstract The peculiar properties possessed by molecules consisting of long chains of atoms linked together by primary valence forces are as yet imperfectly understood. Both naturally occurring and synthetic substances of this type are now familiar in a large variety of forms, of which rubber and cellulose are well-known examples of the former type. The problem may be attacked from two points of view. On the one hand by an investigation of the properties of large molecules something may be learned about molecular structure; on the other an attempt may be made to build such molecules synthetically to a predetermined pattern so that a correlation between structure and behavior may be established. This article will be solely concerned with the second aspect of the subject. Here the general problem is to carry out the synthesis under rigidly controlled conditions in order that the precise mechanism of molecule building may be determined with absolute certainty.

Rotary Querns on the Continent and in the Mediterranean Basin

Antiquity ◽  
1943 ◽  
Vol 17 (65) ◽  
pp. 19-26 ◽  
Author(s):  
V. Gordon Childe
Keyword(s):  
Mediterranean Basin ◽  
The Other ◽  
Copper Age ◽  
Art Objects ◽  
Rotary Mill ◽  
New Instrument ◽  
Major Application ◽  
Water Wheel ◽  
The One ◽  
The Mediterranean Basin

In his two articles on querns (1) Dr Cecil Curwen has given us a really epoch-making contribution to prehistory and history. Not only has he provided the prehistorian with a new instrument for the establishment of chronology, but he has drawn the attention of excavators to a revolutionary but curiously neglected advance in technology. For the rotary mill is the first major application of rotary motion since the invention of the potter's wheel and the lathe in the remote Oriental Copper Age; it led on directly to the invention of geared machinery and the water-wheel and so to the first employment of inanimate motive power apart from the harnessing of the winds to the sail. Though this invention took place in the full light of history, the sole evidence for its origin, apart from a single reference in a writer so late as Pliny (2), is purely archaeological. Unfortunately it is still rather thin; excavators of classical and barbarian sites have generally been too preoccupied with statuary and art-objects on the one hand, with types accepted as chronologically significant on the other, to provide the historian of science with the data he craves. Truhelka for instance, generally so scrupulous in the full publication of all his finds, does not illustrate nor even describe a single quern from Dolja Dolina in Bosnia where he found plenty (3).

scholarly journals Combinatorial analysis.—The foundations of a new theory

1900 ◽  
Vol 66 (424-433) ◽  
pp. 336-337
Keyword(s):  
Large Class ◽  
Finite Differences ◽  
The Other ◽  
Combinatorial Analysis ◽  
Infinitesimal Calculus ◽  
Other Hand ◽  
The One

The object of the paper is to exhibit the processes of the infinitesimal calculus and of the calculus of finite differences as combinatorial processes. A large class of problems can be dealt with by designing on the one hand a function, and on the other hand an operation, in such wise that when the operation is performed upon the function a number results which enumerates the combinations with which the problem is concerned.

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