scholarly journals The Convergence of Calderón Reproducing Formulae of Two Parameters in $L^p$, in $\mathscr S$ and in $\mathscr S'$

2017 ◽  
Vol 9 (4) ◽  
pp. 87
Author(s):  
Jiang-Wei Huang ◽  
Kunchuan Wang

The Calderón reproducing formula is the most important in the study of harmonic analysis, which has the same property as the one of approximate identity in many special function spaces. In this note, we use the idea of separation variables and atomic decomposition to extend single parameter to two-parameters and discuss the convergence of Calderón reproducing formulae of two-parameters in $L^p(\mathbb R^{n_1} \times \mathbb R^{n_2})$, in $\mathscr S(\mathbb R^{n_1} \times \mathbb R^{n_2})$ and in $\mathscr S'(\mathbb R^{n_1} \times \mathbb R^{n_2})$.

2012 ◽  
Vol 04 (01n02) ◽  
pp. 1250012 ◽  
Author(s):  
XUEMING WU ◽  
DEJIE YU

We propose an atomic decomposition method (AD) based on adaptive chirplet dictionary for decomposing multicomponent nonstationary signals with polygonal instantaneous frequencies (IFs). These signals are waveforms of the very general form ∑ Ai(t) cos (φi(t)), where the phase φi(t) is time-varying and the amplitude Ai(t) is slowly varying. Different from the traditional four-parameters chirplet, the one applied in this paper only contains two parameters (chirp offset and chirp rate) and its IF can be regarded as a line on the time–frequency (TF) plane. The idea is to use matching pursuit (MP) algorithm to search for the chirplets, which provide the best trade-off between complexity and goodness of fitting and chain the chirplets together adaptively as to form the desired signals. Our particular application in conjunction with this problem is the decomposition of meshing frequency component and its modulating frequency components in gear fault diagnosis. This strategy is general and may be applied in many other problems. We complement our study with numerical experiments showing that our algorithm boasts of many advantages, such as favorable TF resolution, strong noise robust property (NRP), good decomposition precision, and acceptable algorithm efficiency and is highly competitive compared to the current TF analysis methods.


Galaxies ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 55 ◽  
Author(s):  
Rajendra P. Gupta

We have developed a cosmological model by allowing the speed of light c, gravitational constant G and cosmological constant Λ in the Einstein filed equation to vary in time, and solved them for Robertson-Walker metric. Assuming the universe is flat and matter dominant at present, we obtain a simple model that can fit the supernovae 1a data with a single parameter almost as well as the standard ΛCDM model with two parameters, and which has the predictive capability superior to the latter. The model, together with the null results for the variation of G from the analysis of lunar laser ranging data determines that at the current time G and c both increase as dG/dt = 5.4GH0 and dc/dt = 1.8cH0 with H0 as the Hubble constant, and Λ decreases as dΛ/dt = −1.2ΛH0. This variation of G and c is all what is needed to account for the Pioneer anomaly, the anomalous secular increase of the moon eccentricity, and the anomalous secular increase of the astronomical unit. We also show that the Planck’s constant ħ increases as dħ/dt = 1.8ħH0 and the ratio D of any Hubble unit to the corresponding Planck unit increases as dD/dt = 1.5DH0. We have shown that it is essential to consider the variation of all the physical constants that may be involved directly or indirectly in a measurement rather than only the one whose variation is of interest.


Author(s):  
Duangui Wang

Formulation of the problem. In the chamber-vocal genre, the composer exists in two images: he is both the interpreter of the poetic composition and the author of a new synthetic music and poetic composition. The experience of the style analysis of one of the best examples of Ukrainian vocal lyrics of the first third of the 20th century shows that the cycle op. 20 characterizes the mature style of the composer, which was formed, on the one hand, under the influence of European Romanticism. On the other hand, the essence of the Ukrainian “branch” of the Western European song-romance (“solo-singing”) is revealed by the prominent national song-romance intonation, filled with not only a romantic worldview, but also with some personal sincerity, chastity, intimate involvement with the great in depth and simplicity poetry line, read from the individual position of the musician. The paradox is as follows. Although Pushkin’s poetry is embodied in a “holistic adequacy” (A. Khutorskaya), and the composer found the fullest semantic analogue of the poetic source, however, in terms of translating the text into the Ukrainian language, the musical semantics changes its intonation immanence, which naturally leads to inconsistency of the listeners’ position and ideas about the style of Russian romance. We are dealing with inter-specific literary translation: Pushkin’s discourse creates the Ukrainian romance style and system of figurative thinking. The purpose of the article is to reveal the principle of re-semantization of the intonation-figurative concept of the vocal composition by V. Kosenko (in the context of translating Pushkin’s poetry into the Ukrainian language) in light of the theory of interspecific art translation. Analysis of recent publications on the topic. Among the most recent studies of Ukrainian musicology, one should point out the dissertation by G. Khafizova (Kyiv, 2017), in which the theory of modelling of the stylistic system of the vocal composition as an expression of Pushkin’s discourse is described. The basis for the further stylistic analysis of V. Kosenko’s compositions is the points from A. Hutorska’s candidate’s thesis; she develops the theory of interspecific art translation. The types of translation of poetry into music are classified according to two parameters. The exact translation creates integral adequacy, which involves the composer’s finding a maximally full semantic analogue of the poetic source. The free translation is characterized by compensatory, fragmentary, generalized-genre adequacy. Presenting the main material. The Zhitomir period for Viktor Kosenko was the time of the formation of his creative style. Alongside the lyrical imagery line, the composer acquired one more – dramatic, after his mother’s death. It is possible that the romances on the poems of A. Pushkin are more late reflection of this tragic experience (op. 20 was created in 1930). “I Loved You” opens the vocal cycle and has been dedicated by A. V. Kosenko. The short piano introduction contains the intonation emblem of the love-feeling wave. The form of the composition is a two part reprising (А А1) with the piano Introduction and Postlude. The semantic culmination is emphasized by the change of metro-rhythmic organization 5/4 (instead of 4) and the plastic phrase “as I wish, that the other will love you” sounding in the text. Due to these melodies (with national segments in melo-types, rhythm formulas and harmony) V. Kosenko should be considered as “Ukrainian Glinka”, the composer who introduced new forms and “figures” of the love language into the romantic “intonation dictionary”. In general, V. Kosenko’s solo-singing represents the Ukrainian analogue of Pushkin’s discourse – the theme of love. The melos of vocal piece “I Lived through My Desires” is remembered by the broad breath, bright expression of the syntactic deployment of emotion. On the background of bass ostinato, the song intonation acquires a noble courage. This solo-singing most intermediately appeal to the typical examples of the urban romance of Russian culture of the 19th century. “The Raven to the Raven” – a Scottish folk ballad in the translation by A. Pushkin. V. Kosenko as a profound psychologist, delicately transmits the techniques of versification, following each movement of a poetic phrase, builds stages of the musical drama by purely intonation means. The semantics of a death is embodied through the sound imaging of a black bird: a marching-like tempo and rhythm of the accompaniment, with a characteristic dotted pattern in a descending motion (like a raven is beating its wings). The middle section is dominated by a slow-motion perception of time space (Andante), meditative “freeze” (size 6/4). The melody contrasts with the previous section, its profile is built on the principle of descending move: from “h1” to “h” of the small octave (with a stop on S-harmony), which creates a psychologically immersed state, filled by premonition of an unexpected tragedy. In general, the Ukrainian melodic intonation intensified the tragic content of the ballad by Pushkin. The musical semantics of V. Kosenko’s romances is marked by the dependence on the romantic “musical vocabulary”, however, it is possible to indicate and national characteristics (ascending little-sixth and fifth intervals, which is filled with a gradual anti-movement; syllabic tonic versification, and other). Conclusion. The romances (“solo-singings”) by V. Kosenko belongs to the type of a free art translation with generalized-genre adequacy. There is a re-semantization of poetic images due to the national-mental intonation. Melos, rhythm, textural presentation (repetitions), stylization of different genre formulas testify to the rare beauty of Kosenko’s vocal style, spiritual strength and maturity of the master of Ukrainian vocal culture. Entering the “Slavic song area”, the style of Ukrainian romance, however, is differenced from the Russian and common European style system of figurative and intonation thinking (the picture of the world).


Universe ◽  
2018 ◽  
Vol 4 (10) ◽  
pp. 104 ◽  
Author(s):  
Rajendra Gupta

By relaxing the constraint of adiabatic universe used in most cosmological models, we have shown that the new approach provides a better fit to the supernovae Ia redshift data with a single parameter, the Hubble constant H0, than the standard ΛCDM model with two parameters, H0 and the cosmological constant Λ related density, ΩΛ. The new approach is compliant with the cosmological principle. It yields the H0 = 68.28 (±0.53) km s−1 Mpc−1 with an analytical value of the deceleration parameter q0 = −0.4. The analysis presented is for a matter-only, flat universe. The cosmological constant Λ may thus be considered as a manifestation of a nonadiabatic universe that is treated as an adiabatic universe.


Geosciences ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 353
Author(s):  
Katarzyna Dołżyk-Szypcio

Analyzing the results of triaxial compression tests under drained conditions for Erksak sand published in the literature, the stress–dilatancy relationships were described using the frictional state concept. At all phases of shearing, the linear stress ratio–plastic dilatancy relationship can be expressed by the critical frictional state angle and two parameters of the frictional state concept. At failure, dense sand exhibits purely frictional behavior (α = 0, β = 1) and the stress ratio–dilatancy relationship may be correctly described by the Rowe, Bolton, and frictional state concept relationships. Very loose Erksak sand sheared under drained triaxial compression at the ultimate state reaches a stable condition, but the reached stress ratio is significantly smaller than the one at a critical state.


1985 ◽  
Vol 62 (2) ◽  
pp. 304-335 ◽  
Author(s):  
R.R Coifman ◽  
Y Meyer ◽  
E.M Stein

1993 ◽  
Vol 25 (03) ◽  
pp. 714-716
Author(s):  
K. D. Glazebrook

We propose a two-parameter family of conjugate prior distributions for the number of undiscovered objects in a class of Bayesian search models. The family contains the one-parameter Euler and Heine families as special cases. The two parameters may be interpreted respectively as an overall success rate and a rate of depletion of the source of objects. The new family gives enhanced flexibility in modelling.


1993 ◽  
Vol 25 (3) ◽  
pp. 714-716 ◽  
Author(s):  
K. D. Glazebrook

We propose a two-parameter family of conjugate prior distributions for the number of undiscovered objects in a class of Bayesian search models. The family contains the one-parameter Euler and Heine families as special cases. The two parameters may be interpreted respectively as an overall success rate and a rate of depletion of the source of objects. The new family gives enhanced flexibility in modelling.


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