A remarkable relation between the mass of the proton and the lifetime of the ρ-meson

1977 ◽  
Vol 18 (6) ◽  
pp. 183-184 ◽  
Author(s):  
F. Schwarz ◽  
P. Volk
Keyword(s):  
Remarkable Relation

scholarly journals The figure of the earth from gravity observations and the precision obtainable

1935 ◽  
Vol 234 (743) ◽  
pp. 377-431 ◽  
Keyword(s):  
External Potential ◽  
Higher Harmonics ◽  
The Earth ◽  
Figure Of The Earth ◽  
Remarkable Relation

In 1849 Stokes published a remarkable relation between the form of the geoid and the values of gravity. He neglected terms involving the square of the ellipticity. The validity of his expression for the external potential has been doubted by some later writers, particularly for purposes of a higher approximation. Sir George Darwin, ignoring the departure of the geoid from spheroidal form, derived expressions for the internal and external potentials of the earth, keeping terms of the order of the square of the ellipticity. He justified his results for the region between two spheres concentric with the earth of radii equal to the earth’s minimum and maximum radii. But again some doubted the validity of his expressions for this very region. In the present paper the external potential is derived directly (§§ 1-13) from an extension of a theorem due to Green, without any assumption as to its form. The expression includes terms involving the square of the ellipticity and also the higher harmonics representing the departure of the geoid from a spheroid; but products of these departures and the ellipticity are neglected.

scholarly journals Study of Relations between Computer Experience and Readiness to Access Internet Resources

10.28945/3162 ◽  
2007 ◽  
Author(s):  
Andrzej Malachowski
Keyword(s):  
Service Providers ◽  
Regional Scale ◽  
Internet Access ◽  
Computer Users ◽  
Computer Experience ◽  
Information Structures ◽  
Internet Service ◽  
Internet Resources ◽  
History Of ◽  
Remarkable Relation

The paper presents results of studies among computer users, demonstrating a remarkable relation between history of computer use (computer experience) and readiness to access Internet resources (Internet access). The observed relation, referred to as ‘Internet entry delay syndrome’, may be described as follows: the greater the user’s computer experience, the longer it takes him/her to decide on accessing Internet and using it on a regular basis. The delay is markedly shorter for inexperienced computer users. The results of the study can be invaluable for Internet Service Providers (ISPs), allowing for more precise design of network infrastructure, as well as for local administration authorities striving to implement the policy of information society through development of information structures and services and improving Internet access on local and regional scale.

Quantum spin chains and classical integrable systems

2018 ◽  
Author(s):  
Anton Zabrodin
Keyword(s):  
Integrable Systems ◽  
Quantum Spin ◽  
Spin Chains ◽  
Algebraic Equations ◽  
Quantum Spin Chains ◽  
Many Body ◽  
Finite Dimensional ◽  
The Family ◽  
Classical Correspondence ◽  
Remarkable Relation

This chapter is a review of the recently established quantum-classical correspondence for integrable systems based on the construction of the master T-operator. For integrable inhomogeneous quantum spin chains with gl(N)-invariant R-matrices in finite-dimensional representations, the master T-operator is a sort of generating function for the family of commuting quantum transfer matrices depending on an infinite number of parameters. Any eigenvalue of the master T-operator is the tau-function of the classical modified KP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0th time of the hierarchy. This implies a remarkable relation between the quantum spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, a system of algebraic equations can be obtained for the spectrum of the spin chain Hamiltonians.

scholarly journals Classical extension of quantum-correlated separable states

2015 ◽  
Vol 13 (02) ◽  
pp. 1550015 ◽  
Author(s):  
G. Bellomo ◽  
A. Plastino ◽  
A. R. Plastino
Keyword(s):  
Separable State ◽  
Separable States ◽  
Classical State ◽  
Classical Extension ◽  
Low Dimensional ◽  
Remarkable Relation

Li and Luo [Phys. Rev. A 78 (2008) 024303] discovered a remarkable relation between discord and entanglement. It establishes that all separable states can be obtained via reduction of a classically-correlated state "living" in a space of larger dimension. Starting from this result, we discuss here an optimal classical extension of separable states and explore this notion for low-dimensional systems. We find that the larger the dimension of the classical extension, the larger the discord in the original separable state. Further, we analyze separable states of maximum discord in ℂ2 ⊗ ℂ2 and their associated classical extensions showing that, from the reduction of a classical state in (ℂ2 ⊗ ℂ3) ⊗ ℂ2, one can obtain a separable state of maximum discord in ℂ2 ⊗ ℂ2.

On a Remarkable Relation between Atomic and Universal Constants

1957 ◽  
Vol 25 (5) ◽  
pp. 324-325 ◽  
Author(s):  
Raimondo Baggiolini
Keyword(s):  
Remarkable Relation

III. On some remarkable relations which obtain among the roots of the four squares into which a number may be divided, as compared with the corresponding roots of certain other numbers

1859 ◽  
Vol 149 ◽  
pp. 49-59
Keyword(s):  
The Other ◽  
The Subject ◽  
Remarkable Relation

The property of numbers, which is the subject of this paper, first presented itself to my attention in the case of the odd squares 1, 9, 25, 49, &c. (2 n ∓ 1) 2 ; any two adjoining odd squares may be divided (each of them) into 4 square numbers, whose roots will have this remarkable relation to each other: two of them will be identically the same; and as to the other two, one of them will be 2 less, and the other will be 2 more than the roots of the preceding or subsequent odd square; for example, 25 and 49 may be divided into squares, the roots of which being placed below, will appear thus: — 25 49 so 49 81 -2, 1, 4, 2 -4, 1, 4,4 0, 2, 3, 6 -2, 2, 3, 8 or thus 0, 0, 3, 4 -2, 0, 3, 6. In comparing the roots of the adjoining odd squares, 2 roots (placed in the middle) are the same; of the others, one is 2 more, the other 2 less than the corresponding roots of the other.

VI. The diurnal variations of the wind and barometric pressure at Bombay

1873 ◽  
Vol 21 (139-147) ◽  
pp. 384-385
Keyword(s):  
Barometric Pressure ◽  
Diurnal Variations ◽  
The Government ◽  
Remarkable Relation

The object of this paper is to bring to notice a remarkable relation that has been found to exist between the diurnal variations of the wind and the barometer at Bombay. The observations made use of are the records of a Robinson’s anemograph during the first three years of its performance, viz. from June 1867 to May 1870, and the corresponding hourly observations of the barometer and the dry- and wet-bulb thermometer made at the Government Observatory, Bombay.

scholarly journals Generalised Algebraic Continued Fractions related to Definite Integrals

1958 ◽  
Vol 9 (4) ◽  
pp. 170-182
Author(s):  
L. R. Shenton
Keyword(s):  
Recurrence Relation ◽  
Fourth Order ◽  
Continued Fractions ◽  
Recurrence Formula ◽  
Second Order ◽  
Third Order ◽  
First Order ◽  
Definite Integrals ◽  
Image Position ◽  
Remarkable Relation

The present paper is a continuation of the work initiated in [l]-[5]. In [5] I gave an expansion of the formfor the second order C.F. associated withwhere U8, V8, W8 satisfy a fourth-order recurrence relation, there being a similar expansion for third order C.F.'s. I shall now give simple expressions for U8, V8, W8 (or related forms) in terms of χ2s(Z1), χ2s (Z2), ω2s(Z1), ω2s(Z2), whereand show that there is a remarkable relation between the recurrence formula for the first order C.F. and that satisfied by U3, V3, W3. The generalised form of these results will be stated and proved.

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