A distributional theory for asymptotic expansions

1990 ◽  
Vol 428 (1875) ◽  
pp. 399-430 ◽  
Keyword(s):  
Asymptotic Expansions ◽  
Asymptotic Series ◽  
Generalized Functions ◽  
The Moment ◽  
The One ◽  
Topological Tensor Products ◽  
Multidimensional Integrals ◽  
Vector Valued ◽  
Selection Of ◽  
Mathematics And Physics

We present various techniques for the asymptotic expansions of generalized functions. We show that the moment asymptotic expansions hold for a very wide variety of kernels such as generalized functions of rapid decay and rapid oscillations. We do not use Mellin transform techniques as done by previous authors in the field. Instead, we introduce a direct approach that not only solves the one-dimensional problems but also applies to various multidimensional integrals and oscillatory kernels as well. This approach also helps in the development of various asymptotic series arising in diverse fields of mathematics and physics. We find that the asymptotic expansions of generalized functions depend on the selection of suitable spaces of test functions. Accordingly, we have exercised special care in classifying the spaces and the distributions defined on them. Furthermore, we use the theory of topological tensor products to obtain the expansions of vector-valued distributions. We present several examples to illustrate that many classical results follow in a simple manner. For instance, we derive from our results the asymptotic expansions of certain series considered by Ramanujan.

scholarly journals The impact of viewer’s emotional tension on the choice of films

2016 ◽  
Vol 7 (3) ◽  
pp. 121-134 ◽  
Author(s):  
N.G. Voskresenskaya
Keyword(s):  
Time Perspective ◽  
Social Needs ◽  
Subjective Perception ◽  
Voluntary Attention ◽  
Temporal Perspective ◽  
The Moment ◽  
The One ◽  
The Impact ◽  
Selection Of ◽  
Stimulation Of

The author analyses peculiarities of choices of motion pictures with different dy- namic characteristics, taking into consideration spectator’s subjective perception of in- tenseness of his or her life in time perspective. The student participants were offered a choice of 16 films from which they were required to select the one they would prefer to watch at the moment. The film set was formed based on the ratings of films that are popular amongst students, in which survey 187 students participated. The selected films differed in terms of temporal and dynamic characteristics, and they were famil- iar to all the 60 participants in the sample. The students were also required to rate the fullness of their life in temporal perspective. The analysis of the data revealed that the film preference appears to be compensatory in nature. The perception of one’s life as boring and barren determines the choice of dynamic films with stimulation of forced attention by means of attention reflex and actualization of basic needs. The percep- tion of one's life as dynamic and full of new experiences contributes to the selection of circumstantial cinematic narrative and stimulation of voluntary attention through actualization of social needs.

scholarly journals Myśli Jana Jakuba Rousseau o wychowaniu i muzyce – ich reminiscencje w rytmice Emila Jaques-Dalcroze’a

2015 ◽  
Vol 30 (3) ◽  
pp. 87-103
Author(s):  
Ewa Szatan
Keyword(s):  
Music Education ◽  
Learning Process ◽  
Musical Education ◽  
The Moment ◽  
The One ◽  
Selection Of

The text is an attempt to analyze and interpret a selection of Jean-Jacques Rousseau’s thoughts about education relating to music education, the thoughts that I find as reminiscences of assumptions and methods of Emil Jaques-Dalcroze. He focuses his discourse on the issues related to the moment when the musical education of the child takes form and also on the quality of the child’s first contacts with music, and the role of parent and teacher in the child’s appreciation of music. A comparison of the assumptions regarding musical education of Rousseau and Jaques-Dalcroze may seem interesting, because, despite the passage of successive decades, they seem to be still valid, as, for example, the one that speaks of the joy of discovery that should accompany the child in the learning process.

Note on Selection of Coordinate Systems for Geodynamics

1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen
Keyword(s):  
Sea Level ◽  
The Other ◽  
Coordinate Systems ◽  
Mean Sea Level ◽  
The Earth ◽  
The One ◽  
Static Systems ◽  
Selection Of

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.

Costumes and Choreography from Bodenwieser's Trunk: The Coat as Affective Memory

2019 ◽  
Vol 37 (1) ◽  
pp. 89-110
Author(s):  
Rachel Fensham
Keyword(s):  
Modern Dance ◽  
Human Condition ◽  
Personal Life ◽  
Creative Thought ◽  
Cain And Abel ◽  
Embodied Research ◽  
The Many ◽  
The One ◽  
Material Evidence ◽  
Selection Of

The Viennese modern choreographer Gertrud Bodenwieser's black coat leads to an analysis of her choreography in four main phases – the early European career; the rise of Nazism; war's brutality; and postwar attempts at reconciliation. Utilising archival and embodied research, the article focuses on a selection of Bodenwieser costumes that survived her journey from Vienna, or were remade in Australia, and their role in the dramaturgy of works such as Swinging Bells (1926), The Masks of Lucifer (1936, 1944), Cain and Abel (1940) and The One and the Many (1946). In addition to dance history, costume studies provides a distinctive way to engage with the question of what remains of performance, and what survives of the historical conditions and experience of modern dance-drama. Throughout, Hannah Arendt's book The Human Condition (1958) provides a critical guide to the acts of reconstruction undertaken by Bodenwieser as an émigré choreographer in the practice of her craft, and its ‘materializing reification’ of creative thought. As a study in affective memory, information regarding Bodenwieser's personal life becomes interwoven with the author's response to the material evidence of costumes, oral histories and documents located in various Australian archives. By resurrecting the ‘dead letters’ of this choreography, the article therefore considers how dance costumes offer the trace of an artistic resistance to totalitarianism.

The Munich conference of Minister-Presidents of German lands in 1947

2020 ◽  
Vol 2020 (10-2) ◽  
pp. 86-98
Author(s):  
Ivan Popov
Keyword(s):  
The State ◽  
State Governments ◽  
The West ◽  
Constitutional Development ◽  
The Moment ◽  
The One

The paper deals with the organization and decisions of the conference of the Minister-Presidents of German lands in Munich on June 6-7, 1947, which became the one and only meeting of the heads of the state governments of the western and eastern occupation zones before the division of Germany. The conference was the first experience of national positioning of the regional elite and clearly demonstrated that by the middle of 1947, not only between the allies, but also among German politicians, the incompatibility of perspectives of further constitutional development was existent and all the basic conditions for the division of Germany became ripe. Munich was the last significant demonstration of this disunity and the moment of the final turn towards the three-zone orientation of the West German elite.

PROMETHEE-based ranking of project managers based on the five personality traits

Kybernetes ◽  
2019 ◽  
Vol 49 (4) ◽  
pp. 1083-1102
Author(s):  
Georgios N. Aretoulis ◽  
Jason Papathanasiou ◽  
Fani Antoniou
Keyword(s):  
Personality Traits ◽  
Questionnaire Survey ◽  
Multicriteria Decision Making ◽  
Project Managers ◽  
Preference Ranking ◽  
Infrastructure Projects ◽  
Public Infrastructure ◽  
Content Type ◽  
The One ◽  
Selection Of

Purpose This paper aims to rank and identify the most efficient project managers (PMs) based on personality traits, using Preference Ranking Organization METHod for Enrichment Evaluations (PROMETHEE) methodology. Design/methodology/approach The proposed methodology relies on the five personality traits. These were used as the selection criteria. A questionnaire survey among 82 experienced engineers was used to estimate the required weights per personality trait. A second two-part questionnaire survey aimed at recording the PMs profile and assess the performance of personality traits per PM. PMs with the most years of experience are selected to be ranked through Visual PROMETHEE. Findings The findings suggest that a competent PM is the one that scores low on the “Neuroticism” trait and high especially on the “Conscientiousness” trait. Research limitations/implications The research applied a psychometric test specifically designed for Greek people. Furthermore, the proposed methodology is based on the personality characteristics to rank the PMs and does not consider the technical skills. Furthermore, the type of project is not considered in the process of ranking PMs. Practical implications The findings could contribute in the selection of the best PM that maximizes the project team’s performance. Social implications Improved project team communication and collaboration leading to improved project performance through better communication and collaboration. This is an additional benefit for the society, especially in the delivery of public infrastructure projects. A lot of public infrastructure projects deviate largely as far as cost and schedule is concerned and this is an additional burden for public and society. Proper project management through efficient PMs would save people’s money and time. Originality/value Identification of the best PMbased on a combination of multicriteria decision-making and psychometric tests, which focus on personality traits.

scholarly journals Asymptotic Expansions and Strategies in the Online Increasing Subsequence Problem

2021 ◽  
Vol 174 (1) ◽  
Author(s):  
Amirlan Seksenbayev
Keyword(s):  
Dynamic Programming ◽  
Asymptotic Expansions ◽  
Dual Problem ◽  
Infinite Length ◽  
Expected Time ◽  
Selection Strategies ◽  
Dynamic Programming Equation ◽  
Optimal Values ◽  
Design Selection ◽  
Selection Of

AbstractWe study two closely related problems in the online selection of increasing subsequence. In the first problem, introduced by Samuels and Steele (Ann. Probab. 9(6):937–947, 1981), the objective is to maximise the length of a subsequence selected by a nonanticipating strategy from a random sample of given size $n$ n . In the dual problem, recently studied by Arlotto et al. (Random Struct. Algorithms 49:235–252, 2016), the objective is to minimise the expected time needed to choose an increasing subsequence of given length $k$ k from a sequence of infinite length. Developing a method based on the monotonicity of the dynamic programming equation, we derive the two-term asymptotic expansions for the optimal values, with $O(1)$ O ( 1 ) remainder in the first problem and $O(k)$ O ( k ) in the second. Settling a conjecture in Arlotto et al. (Random Struct. Algorithms 52:41–53, 2018), we also design selection strategies to achieve optimality within these bounds, that are, in a sense, best possible.

scholarly journals Gradient boosting for linear mixed models

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Colin Griesbach ◽  
Benjamin Säfken ◽  
Elisabeth Waldmann
Keyword(s):  
Random Effects ◽  
Mixed Models ◽  
Selection Procedure ◽  
Classification Theory ◽  
Gradient Boosting ◽  
Random Structure ◽  
Boosting Algorithm ◽  
The One ◽  
Biased Estimates ◽  
Selection Of

Abstract Gradient boosting from the field of statistical learning is widely known as a powerful framework for estimation and selection of predictor effects in various regression models by adapting concepts from classification theory. Current boosting approaches also offer methods accounting for random effects and thus enable prediction of mixed models for longitudinal and clustered data. However, these approaches include several flaws resulting in unbalanced effect selection with falsely induced shrinkage and a low convergence rate on the one hand and biased estimates of the random effects on the other hand. We therefore propose a new boosting algorithm which explicitly accounts for the random structure by excluding it from the selection procedure, properly correcting the random effects estimates and in addition providing likelihood-based estimation of the random effects variance structure. The new algorithm offers an organic and unbiased fitting approach, which is shown via simulations and data examples.

scholarly journals Helium, [Fe/H] Abundances and the HR (Log TEFF, MBol) Diagram With Hipparcos Data of The Four Nearest Open Clusters: Hyades, Coma Berenices, The Pleiades and Praesepe

1998 ◽  
Vol 11 (1) ◽  
pp. 565-565
Author(s):  
G. Cayrel de Strobel ◽  
R. Cayrel ◽  
Y. Lebreton
Keyword(s):  
Main Sequence ◽  
Open Clusters ◽  
Main Sequence Stars ◽  
Spectroscopic Analyses ◽  
Solar Metallicity ◽  
Metal Abundances ◽  
The Mean ◽  
The Moment ◽  
The One ◽  
Best Fit

After having studied in great detail the observational HR diagram (log Teff, Mbol) composed by 40 main sequence stars of the Hyades (Perryman et al.,1997, A&A., in press), we have tried to apply the same method to the observational main sequences of the three next nearest open clusters: Coma Berenices, the Pleiades, and Praesepe. This method consists in comparing the observational main sequence of the clusters with a grid of theoretical ZAMSs. The stars composing the observational main sequences had to have reliable absolute bolometric magnitudes, coming all from individual Hipparcos parallaxes, precise bolometric corrections, effective temperatures and metal abundances from high resolution detailed spectroscopic analyses. If we assume, following the work by Fernandez et al. (1996, A&A,311,127), that the mixing-lenth parameter is solar, the position of a theoretical ZAMS, in the (log Teff, Mbol) plane, computed with given input physics, only depends on two free parameters: the He content Y by mass, and the metallicity Z by mass. If effective temperature and metallicity of the constituting stars of the 4 clusters are previously known by means of detailed analyses, one can deduce their helium abundances by means of an appropriate grid of theoretical ZAMS’s. The comparison between the empirical (log Teff, Mbol) main sequence of the Hyades and the computed ZAMS corresponding to the observed metallicity Z of the Hyades (Z= 0.0240 ± 0.0085) gives a He abundance for the Hyades, Y= 0.26 ± 0.02. Our interpretation, concerning the observational position of the main sequence of the three nearest clusters after the Hyades, is still under way and appears to be greatly more difficult than for the Hyades. For the moment we can say that: ‒ The 15 dwarfs analysed in detailed in Coma have a solar metallicity: [Fe/H] = -0.05 ± 0.06. However, their observational main sequence fit better with the Hyades ZAMS. ‒ The mean metallicity of 13 Pleiades dwarfs analysed in detail is solar. A metal deficient and He normal ZAMS would fit better. But, a warning for absorption in the Pleiades has to be recalled. ‒ The upper main sequence of Praesepe, (the more distant cluster: 180 pc) composed by 11 stars, analysed in detail, is the one which has the best fit with the Hyades ZAMS. The deduced ‘turnoff age’ of the cluster is slightly higher than that of the Hyades: 0.8 Gyr instead of 0.63 Gyr.

scholarly journals A comparison of two methods for predicting changes in the distribution of gene frequency when selection is applied repeatedly to a finite population

1969 ◽  
Vol 13 (2) ◽  
pp. 117-126 ◽  
Author(s):  
Derek J. Pike
Keyword(s):  
Iterative Procedure ◽  
Gene Frequency ◽  
Finite Population ◽  
Transition Matrices ◽  
Single Cycle ◽  
Gene Frequencies ◽  
Mean And Variance ◽  
The Mean ◽  
The One ◽  
Selection Of

Robertson (1960) used probability transition matrices to estimate changes in gene frequency when sampling and selection are applied to a finite population. Curnow & Baker (1968) used Kojima's (1961) approximate formulae for the mean and variance of the change in gene frequency from a single cycle of selection applied to a finite population to develop an iterative procedure for studying the effects of repeated cycles of selection and regeneration. To do this they assumed a beta distribution for the unfixed gene frequencies at each generation.These two methods are discussed and a result used in Kojima's paper is proved. A number of sets of calculations are carried out using both methods and the results are compared to assess the accuracy of Curnow & Baker's method in relation to Robertson's approach.It is found that the one real fault in the Curnow-Baker method is its tendency to fix too high a proportion of the genes, particularly when the initial gene frequency is near to a fixation point. This fault is largely overcome when more individuals are selected. For selection of eight or more individuals the Curnow-Baker method is very accurate and appreciably faster than the transition matrix method.

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