An interesting application of Bohr theory

1988 ◽  
Vol 56 (8) ◽  
pp. 746-747 ◽  
Author(s):  
B. Bagchi ◽  
Paul Holody
Keyword(s):  
Interesting Application ◽  
Bohr Theory

The (α, β)-ramification invariants of a number field

2021 ◽  
Vol 71 (1) ◽  
pp. 251-263
Author(s):  
Guillermo Mantilla-Soler
Keyword(s):  
Zeta Function ◽  
Number Field ◽  
Residue Class ◽  
Interesting Application ◽  
Dedekind Zeta Function ◽  
Arithmetic Properties

Abstract Let L be a number field. For a given prime p, we define integers α p L $ \alpha_{p}^{L} $ and β p L $ \beta_{p}^{L} $ with some interesting arithmetic properties. For instance, β p L $ \beta_{p}^{L} $ is equal to 1 whenever p does not ramify in L and α p L $ \alpha_{p}^{L} $ is divisible by p whenever p is wildly ramified in L. The aforementioned properties, although interesting, follow easily from definitions; however a more interesting application of these invariants is the fact that they completely characterize the Dedekind zeta function of L. Moreover, if the residue class mod p of α p L $ \alpha_{p}^{L} $ is not zero for all p then such residues determine the genus of the integral trace.

scholarly journals A Review of Current Research in Subscale Flight Testing and Analysis of Its Main Practical Challenges

Aerospace ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 74
Author(s):  
Alejandro Sobron ◽  
David Lundström ◽  
Petter Krus
Keyword(s):  
Literature Review ◽  
Research And Development ◽  
Rapid Prototyping ◽  
Experimental Method ◽  
Low Cost ◽  
Full Scale ◽  
Interesting Application ◽  
Flight Testing ◽  
Scale Characteristics ◽  
Vehicle Technologies

Testing of untethered subscale models, often referred to as subscale flight testing, has traditionally had a relatively minor, yet relevant use in aeronautical research and development. As recent advances in electronics, rapid prototyping and unmanned-vehicle technologies expand its capabilities and lower its cost, this experimental method is seeing growing interest across academia and the industry. However, subscale models cannot meet all similarity conditions required for simulating full-scale flight. This leads to a variety of approaches to scaling and to other alternative applications. Through a literature review and analysis of different scaling strategies, this study presents an overall picture of how subscale flight testing has been used in recent years and synthesises its main issues and practical limitations. Results show that, while the estimation of full-scale characteristics is still an interesting application within certain flight conditions, subscale models are progressively taking a broader role as low-cost technology-testing platforms with relaxed similarity constraints. Different approaches to tackle the identified practical challenges, implemented both by the authors and by other organisations, are discussed and evaluated through flight experiments.

GAP SEQUENCES OF GRAPH-DIRECTED SETS

Fractals ◽  
2016 ◽  
Vol 24 (03) ◽  
pp. 1650036
Author(s):  
JUAN DENG ◽  
LIFENG XI
Keyword(s):  
Separation Condition ◽  
Interesting Application ◽  
Strong Separation ◽  
Self Similar ◽  
Strong Separation Condition ◽  
Directed Sets ◽  
Gap Sequences

This paper studies the gap sequences of graph-directed sets satisfying the strong separation condition. An interesting application is to investigate the gap sequences of self-similar sets with overlaps.

scholarly journals Vibration Analysis by the Wigner-Ville Transformation Method

2018 ◽  
Vol 20 (4) ◽  
pp. 24-28 ◽  
Author(s):  
Jaroslav Smutny ◽  
Viktor Nohal ◽  
Daniela Vukusicova ◽  
Herbert Seelmann
Keyword(s):  
Mathematical Analysis ◽  
Vibration Analysis ◽  
Linear Time ◽  
Practical Experience ◽  
Transformation Method ◽  
Application Area ◽  
Interesting Application ◽  
Time Frequency ◽  
Natural Processes

This paper deals with description and application of the Wigner-Ville transformation for vibration analysis. This transformation belongs to the group of non-linear time-frequency processes. Thanks to its properties, it may be successfully used in the area of non-stationary and transitional signals describing various natural processes. The use in the field of the railway constructions testing represents a quite an interesting application area of the transformation. This paper contains mathematical analysis of the transformation, a case study and practical experience obtained and recommendations for its practical use.

On the equivalence of certain Markov chains

1976 ◽  
Vol 13 (02) ◽  
pp. 357-360
Author(s):  
Pedro Vit
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Simple Proof ◽  
Interesting Application ◽  
Null Recurrence ◽  
A Chain

It is shown that an irreducible and aperiodic Markov chain can be altered preserving irreducibility without altering the nature of the chain in the sense that, the modified chain is transient (recurrent) if and only if the original chain is transient (recurrent). Furthermore, it is shown by means of a counterexample that ergodicity (null-recurrence) is not preserved. An interesting application of this result is a simple proof of Pakes's generalization of Foster's criterion for a chain to be recurrent.

scholarly journals XVI.—On the Path of a Rotating Spherical Projectile. II.

1900 ◽  
Vol 39 (2) ◽  
pp. 491-506 ◽  
Author(s):  
Tait
Keyword(s):  
Great Part ◽  
Numerical Data ◽  
Terminal Velocity ◽  
Considerable Improvement ◽  
Golf Ball ◽  
Initial Speed ◽  
Interesting Application ◽  
A Value ◽  
Special Case

The first instalment of this paper was devoted in great part to the general subject involved in its title, but many of the illustrations were derived from the special case of the flight of a golf-ball. Since it was read I have endeavoured, alike by observation and by experiment, to improve my numerical data for this interesting application, particularly as regards the important question of the coefficient of resistance of the air. As will be seen, I now find a value intermediate to those derived (by taking average estimates of the mass and diameter of a golf-ball) from the results of Robins and of Bashforth. This has been obtained indirectly by means of a considerable improvement in the apparatus by which I had attempted to measure the initial speed of a golf-ball. I have, still, little doubt that the speed may, occasionally, amount to the 300, or perhaps even the 350, foot-seconds which I assumed provisionally in my former paper:—but even the first of these is a somewhat extravagant estimate; and I am now of opinion that, even with very good driving, an initial speed of about 240 is not often an underestimate, at least in careful play. From this, and the fact that six seconds at least are required for a long carry (say 180 yards), I reckon the “terminal velocity” at about 108, giving v2/360 as the resistance-acceleration.

Energetic Analysis of Solar-Supplied Processes for Methane, Biogas and Wood Chip Production

2013 ◽  
Vol 772 ◽  
pp. 720-724 ◽  
Author(s):  
Franco Cotana ◽  
Federico Rossi ◽  
Andrea Nicolini ◽  
Mirko Filipponi ◽  
Anna Laura Pisello
Keyword(s):  
Solar Energy ◽  
Methane Production ◽  
Production Systems ◽  
Wood Chip ◽  
Energetic Efficiency ◽  
Interesting Application ◽  
Energetic Analysis

An interesting application of solar energy for methane production is here analysed in terms of energetic efficiency. The application (called Solargas) is constituted by photovoltaic (PV) panels, an electrolyser and a Sabatier reactor. PV panels pick up the solar energy to supply the electrolyser. The electrolyser produces hydrogen from water; the produced hydrogen is used in a Sabatier reactor to obtain methane. Solargas system is here compared to typical biogas and wood chip production systems in terms of the ratio between the output fuel energy and the input solar energy.

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