Orthonormal basis of wavelets with customizable frequency bands

2016 ◽  
Vol 14 (06) ◽  
pp. 1650050 ◽  
Author(s):  
Hiroshi Toda ◽  
Zhong Zhang
Keyword(s):  
Frequency Domain ◽  
Infinite Number ◽  
Orthonormal Basis ◽  
The Other ◽  
Just Intonation ◽  
Frequency Bands ◽  
Orthonormal Bases ◽  
Major Scale ◽  
Dilation Factor ◽  
New Type

We already proved the existence of an orthonormal basis of wavelets having an irrational dilation factor with an infinite number of wavelet shapes, and based on its theory, we proposed an orthonormal basis of wavelets with an arbitrary real dilation factor. In this paper, with the development of these fundamentals, we propose a new type of orthonormal basis of wavelets with customizable frequency bands. Its frequency bands can be freely designed with arbitrary bounds in the frequency domain. For example, we show two types of orthonormal bases of wavelets. One of them has an irrational dilation factor, and the other is designed based on the major scale in just intonation.

Orthonormal wavelet basis with arbitrary real dilation factor

2016 ◽  
Vol 14 (03) ◽  
pp. 1650010 ◽  
Author(s):  
Hiroshi Toda ◽  
Zhong Zhang
Keyword(s):  
Infinite Number ◽  
Wavelet Function ◽  
Good Time ◽  
Wavelet Basis ◽  
Orthonormal Wavelet ◽  
Time Frequency ◽  
Time Frequency Localization ◽  
Dilation Factor ◽  
New Type ◽  
Open Question

Daubechies posed the following problem in Ten Lectures on Wavelets (SIAM, Philadelphia, PA, 1992): “It is an open question whether there exist orthonormal wavelet bases (not necessarily associated with a multiresolution analysis), with good time-frequency localization, and with irrational [Formula: see text]” (that is, for an arbitrary irrational dilation factor [Formula: see text], with appropriate wavelet function [Formula: see text] and constant [Formula: see text], whether can [Formula: see text] construct an orthonormal wavelet basis with good time-frequency localization?). Our answer is “Yes”. In this paper, we introduce a new type of orthonormal wavelet basis having an arbitrary real dilation factor greater than 1. This orthonormal wavelet basis requires an infinite number of wavelet shapes when its dilation factor is irrational.

scholarly journals Cayley Graphs Without a Bounded Eigenbasis

2020 ◽  
Author(s):  
Ashwin Sah ◽  
Mehtaab Sawhney ◽  
Yufei Zhao
Keyword(s):  
Cayley Graph ◽  
Orthonormal Basis ◽  
Cayley Graphs ◽  
The Other ◽  
Transitive Graph ◽  
Classic Result ◽  
Other Hand ◽  
Small Set ◽  
Vertex Transitive ◽  
Vertex Transitive Graph

Abstract Does every $n$-vertex Cayley graph have an orthonormal eigenbasis all of whose coordinates are $O(1/\sqrt{n})$? While the answer is yes for abelian groups, we show that it is no in general. On the other hand, we show that every $n$-vertex Cayley graph (and more generally, vertex-transitive graph) has an orthonormal basis whose coordinates are all $O(\sqrt{\log n / n})$, and that this bound is nearly best possible. Our investigation is motivated by a question of Assaf Naor, who proved that random abelian Cayley graphs are small-set expanders, extending a classic result of Alon–Roichman. His proof relies on the existence of a bounded eigenbasis for abelian Cayley graphs, which we now know cannot hold for general groups. On the other hand, we navigate around this obstruction and extend Naor’s result to nonabelian groups.

Hydroxyl-containing bis(sulfonates). Reaction of 1,4-dibromo-2,3-butanedione with water, methanol and sodium sulfite

2021 ◽  
pp. 1-12
Author(s):  
Gerasimos M. Tsivgoulis ◽  
Dimitris G. Vachliotis ◽  
Golfo G. Kordopati ◽  
Panayiotis V. Ioannou
Keyword(s):  
13C Nmr ◽  
Sodium Sulfite ◽  
The Other ◽  
Carbonyl Carbon ◽  
1H And 13C Nmr ◽  
Sodium Sulfonate ◽  
Pure Product ◽  
Methylene Groups ◽  
New Type ◽  
High Yields

Sulfonates are well-known substances with a variety of applications, e.g. as surfactants. On the other hand, bis(sulfonates) bearing hydroxyl or keto group(s) in between the sulfonate groups can be used with or without further modification as starting materials for the preparation of new type of molecules capable to form either complexes or in general supramolecular structures. The synthesis of three hydroxyl-bearing bis(sulfonates), 2-hydroxypropane-1,3-bis(sodium sulfonate) 4, DL-2,3-dihydroxybutane-1,4-bis(sodium sulfonate) 8, and sodium 2,3,4-trihydroxy-1-sulfonate 7 (as by-product) via the Strecker sulfonation are described. Interestingly, under similar conditions, sulfonation of 1,4-dibromo-2,3-butanedione 9 was found to be very complicated and no pure product could be isolated, despite previously reported results on sulfonation of α-halogenated ketones in high yields. There are indications that SO3 2 -  attacks at the carbonyl carbon of 9 followed by rearrangement and expulsion of SO4 2 - . 1,4-dibromo-2,3-butanedione 9, bearing two keto groups next to methylene groups, can potentially exist as enols or in the case of its solution in hydroxylic solvents in the form of hemiketals or geminal diols. This behavior of 9 when is dissolved in CDCl3, CD3OD and D2O was studied by means of UV-Vis, 1H and 13C NMR and the nature of the adducts formed was elucidated.

Regeneration from duplicating fragments of the Drosophila wing disc

Development ◽  
1981 ◽  
Vol 66 (1) ◽  
pp. 117-126
Author(s):  
Jane Karlsson ◽  
R. J. Smith
Keyword(s):  
Imaginal Disc ◽  
General Rule ◽  
Wing Disc ◽  
The Other ◽  
Posterior Compartment ◽  
Drosophila Wing ◽  
Polar Coordinate ◽  
New Type ◽  
Coordinate Model

It is a general rule that of two complementary Drosophila imaginal disc fragments, one regenerates and the other duplicates. This paper reports an investigation of an exception to this rule. Duplicating fragments from the periphery of the wing disc which lacked presumptive notum were found to regenerate notum structures during and after duplication. The propensity for this was greatest in fragments lying close to the presumptive notum, with the exception of a fragment confined to the posterior compartment, which did not regenerate notum. Structures were added sequentially, and regeneration stopped once most of the notum was present. These results are not easily explained by the polar coordinate model, which states that regeneration cannot occur from duplicating fragments. Since compartments appear to be involved in this type of regeneration as in others, it is suggested that a new type of model is required, one which permits simultaneous regeneration and duplication, and assigns a major role to compartments.

scholarly journals A Hooked-Collar for Bridge Piers Protection: Flow Fields and Scour

Water ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 1251 ◽  
Author(s):  
Su-Chin Chen ◽  
Samkele Tfwala ◽  
Tsung-Yuan Wu ◽  
Hsun-Chuan Chan ◽  
Hsien-Ter Chou
Keyword(s):  
Laboratory Experiments ◽  
Horseshoe Vortex ◽  
Flow Fields ◽  
Bridge Pier ◽  
The Other ◽  
Bridge Piers ◽  
Vortex Strength ◽  
Numerical Tests ◽  
Scour Hole ◽  
New Type

A new type of collar, the hooked-collar, was studied through experiments and numerical methods. Tests were conducted using a hooked collar of a width of 1.25b and a height of 0.25b, where b is the bridge-pier width. The hooked-collar efficiency was evaluated by testing different hooked-collar placements within the bridge-pier, which were compared to the bridge-pier without any collar. A double hooked-collar configuration, one placed at the bed level and the other buried 0.25b, was the most efficient at reducing the scour hole. In other cases, a hooked-collar positioned 0.25b above the bed slightly reduced the scour hole and had similar scour patterns when compared to the pier without the hooked-collar. The flow fields along the vertical symmetrical plane in the experiments are also presented. Laboratory experiments and numerical tests show that maximal downflow is highly reduced along with a corresponding decrease in horseshoe vortex strength for the experiments with the hooked-collar, compared to cases without the hooked-collar. The flow fields reveal that the maximum turbulent kinetic energy decreases with the installation of the hooked-collar.

scholarly journals Some results of analysis of inverted echo-sounder records from the Atlantic equatorial region

1985 ◽  
Vol 33 (2) ◽  
pp. 213-218
Author(s):  
Alberto dos Santos Franco ◽  
Joseph Harari ◽  
Afrânio Rubens de Mesquita
Keyword(s):  
Spectral Analysis ◽  
Internal Waves ◽  
Frequency Band ◽  
Equatorial Region ◽  
Temperature Series ◽  
The Other ◽  
Tidal Analysis ◽  
Frequency Bands ◽  
Inverted Echo Sounder ◽  
Even Harmonics

The tidal analysis of data from the Equatorial region, given by inverted echo-sounders, show considerable residuals in the frequency band of approximately 2 cycles per day. In the even harmonics of 4 and 6 cycles per day, tidal components statistically not negligible are also identified. Spectral analysis of temperature series from the same area show, on the other hand, variabilities in the same frequency bands, which suggests the occurrence of internal waves with energy distributed in these frequency bands, in the Atlantic Equatorial area.

scholarly journals KARAKTERISTIK ORGANIOLEPTIK OTAK-OTAK IKAN YANG DIBERI EDIBLE COATING KARAGINAN DENGAN PENAMBAHAN ASAP CAIR

2015 ◽  
Vol 4 (2) ◽  
Author(s):  
Eka Irma Q Bariah ◽  
Siegfried Berhimpon ◽  
Eunike Louisje Mongi
Keyword(s):  
Environmentally Friendly ◽  
Food Product ◽  
Edible Coating ◽  
The Other ◽  
Liquid Smoke ◽  
Organoleptic Characteristics ◽  
Randomized Design ◽  
New Type ◽  
Completely Randomized Design

Edible coating is a new type of packaging made of biopolymer. The advantages of edible coating is enable to protect the food product, the original appearance of the product can be maintained and the product can be eaten as well as environmentally friendly. The study aim was to look at the organoleptic characteristics of fish cake coated with edible coating of carrageenan were given a liquid smoke. The treatments  given were variation of carrageenan concentration i,e. 0%, 1%, 1,5%, 2%, 2,5%, 3%. The experiment was designed using a Completely Randomized Design (CRD). To determine the effect of treatments, the data were tested using organoleptical tests consists of hedonic and texture.The results shown that hedonic test of the appearance and color of the raw sample have significant effect (p>0,05), while the other test showed no significant effect (p>0,05). However, the organoleptical score for taste, smell and texture shown a tendency that the fish cake coated, have  higher score than without coated. Keywords: Edible coating, Carrageenan, Fish cake, Liquid smoke.

The junctional complex in the intestine of Sagitta setosa (Chaetognatha): the paired septate junction

1980 ◽  
Vol 42 (1) ◽  
pp. 227-246
Author(s):  
M. Duvert ◽  
D. Gros ◽  
C. Salat
Keyword(s):  
Uranyl Acetate ◽  
The Other ◽  
Septate Junction ◽  
Junctional Complex ◽  
Outer Diameter ◽  
Central Ring ◽  
Straight Path ◽  
New Type ◽  
Pleated Sheet ◽  
Tight Formation

The junctional complex of the intestine of Sagitta setosa has been studied in tissues stained with uranyl acetate or after lanthanum impregnation, and by freeze-cleavage. All types of junctions have been characterized in both perpendicular and tangential planes. From the apex to the base of the cell the following junctions occur in this order: a zonula adhaerens; a septate junction where the septa occur in pairs; a pleated sheet septate junction; and numerous gap junctions of the A-type. From the upper part of the cells inwards to the septate junction, the membranes follow a relatively straight path. In the lower part of the cells the membranes are deeply interdigitating. At the intersection between 3 cells a very different junction is to be observed where small units, periodically disposed, bind the membranes of the 3 adjoining cells. Each unit is composed of 3 short segments which bind the cell membranes to a central ring 16.6 +/− 2.3 nm in outer diameter. The paired septate junction constitutes a new type. Its main features are that the septa are paired and occur in 2 formations, one the ‘loose formation’, with elements between the septa of each pair, and the other, a ‘tight formation’. After lanthanum impregnation, the thickness of each septum is seen to be about 3 nm and the undulation period 12.6 +/− 1.6 nm. On freeze-fractures 10-nm particles are found on crests on the PF face and in furrows on the EF face. The possible significance of this type of junction is discussed. The junctional complex described is analogous to those found in various invertebrate epithelia.

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