Beta-Function B-splines and Subdivision Schemes, a Preliminary Study

2018 ◽  
pp. 592-599
Author(s):  
Arne Lakså
Keyword(s):  
Beta Function ◽  
Subdivision Schemes ◽  
B Splines ◽  
Preliminary Study

scholarly journals A Family of Binary Approximating Subdivision Schemes based on Binomial Distribution

2019 ◽  
Vol 38 (4) ◽  
pp. 1087-1100 ◽  
Author(s):  
Muhammad Asghar ◽  
Ghulam Mustafa
Keyword(s):  
Tensor Product ◽  
Binomial Distribution ◽  
Probability Generating Function ◽  
Visual Performance ◽  
Complete Analysis ◽  
Subdivision Schemes ◽  
B Splines ◽  
Surface Subdivision ◽  
Product Surface ◽  
Tensor Product Surface

A simplest way is introduced to generate a generalized algorithm of univariate and bivariate subdivision schemes. This generalized algorithm is based on the symbol of uniform B-splines subdivision schemes and probability generating function of Binomial distribution. We present a family of binary approximating subdivision schemes which has maximum continuity and less support size. Our proposed family members P4, P5, P6, and P7, have C7, C9, C11 and C13 continuities respectively. In fact, we use Binomial probability distribution to increase the continuity of uniform B-splines subdivision schemes up to more than double. We present the complete analysis of one family member of proposed schemes and give a visual performance to check smoothness graphically. In our analysis, we present continuity, Holder regularity, degree of generation, degree of reproduction and limit stencils analysis of proposed family of subdivision schemes. We also present a survey of high continuity subdivision schemes. Comparison shows that our proposed family of subdivision schemes gives high continuity of subdivision schemes comparative to existing subdivision schemes. We have found that as complexity increases the continuity also increases. In the last, we give the general formula for tensor product surface subdivision schemes and also present the visual performance of proposed tensor product surface subdivision schemes.

scholarly journals Hermite B-Splines: n-Refinability and Mask Factorization

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2458
Author(s):  
Mariantonia Cotronei ◽  
Caroline Moosmüller
Keyword(s):  
Explicit Construction ◽  
Scaling Factor ◽  
Basis Functions ◽  
Fixed Degree ◽  
Subdivision Schemes ◽  
B Spline ◽  
B Splines ◽  
Refinement Mask ◽  
Hermite Splines ◽  
Fast Procedure

This paper deals with polynomial Hermite splines. In the first part, we provide a simple and fast procedure to compute the refinement mask of the Hermite B-splines of any order and in the case of a general scaling factor. Our procedure is solely derived from the polynomial reproduction properties satisfied by Hermite splines and it does not require the explicit construction or evaluation of the basis functions. The second part of the paper discusses the factorization properties of the Hermite B-spline masks in terms of the augmented Taylor operator, which is shown to be the minimal annihilator for the space of discrete monomial Hermite sequences of a fixed degree. All our results can be of use, in particular, in the context of Hermite subdivision schemes and multi-wavelets.

Construction of binary four and five point non-stationary subdivision schemes from hyperbolic B-splines

2016 ◽  
Vol 280 ◽  
pp. 30-38
Author(s):  
Shahid S. Siddiqi ◽  
Wardat us Salam ◽  
Kashif Rehan
Keyword(s):  
Subdivision Schemes ◽  
B Splines ◽  
Stationary Subdivision

The Ultrastructure of Metastatic Human Mammary Carcinoma After Prolonged Estrogen Therapy

1967 ◽  
Vol 25 ◽  
pp. 180-181
Author(s):  
John H.L. Watson ◽  
John L. Swedo ◽  
R.W. Talley
Keyword(s):  
Mammary Carcinoma ◽  
Osmium Tetroxide ◽  
Estrogen Therapy ◽  
Ultrastructural Level ◽  
Uranyl Acetate ◽  
Human Mammary Carcinoma ◽  
Surgical Biopsy ◽  
Lead Hydroxide ◽  
Preliminary Study ◽  
Hormonal Therapies

A preliminary study of human mammary carcinoma on the ultrastructural level is reported for a metastatic, subcutaneous nodule, obtained as a surgical biopsy. The patient's tumor had responded favorably to a series of hormonal therapies, including androgens, estrogens, progestins, and corticoids for recurring nodules over eight years. The pertinent nodule was removed from the region of the gluteal maximus, two weeks following stilbestrol therapy. It was about 1.5 cms in diameter, and was located within the dermis. Pieces from it were fixed immediately in cold fixatives: phosphate buffered osmium tetroxide, glutaraldehyde, and paraformaldehyde. Embedment in each case was in Vestopal W. Contrasting was done with combinations of uranyl acetate and lead hydroxide.

Fine structure of early degenerating myofibers in the tibialis anterior of young ‘MDX’ mouse

1988 ◽  
Vol 46 ◽  
pp. 322-323
Author(s):  
H.D. Geissinger ◽  
C.K. McDonald-Taylor
Keyword(s):  
Fine Structure ◽  
Muscle Regeneration ◽  
Tibialis Anterior ◽  
Genetic Defect ◽  
Mdx Mouse ◽  
Mdx Mice ◽  
Histopathological Changes ◽  
Electron Microscopic ◽  
Dystrophic Mouse ◽  
Preliminary Study

A new strain of mice, which had arisen by mutation from a dystrophic mouse colony was designated ‘mdx’, because the genetic defect, which manifests itself in brief periods of muscle destruction followed by episodes of muscle regeneration appears to be X-linked. Further studies of histopathological changes in muscle from ‘mdx’ mice at the light microscopic or electron microscopic levels have been published, but only one preliminary study has been on the tibialis anterior (TA) of ‘mdx’ mice less than four weeks old. Lesions in the ‘mdx’ mice vary between different muscles, and centronucleation of fibers in all muscles studied so far appears to be especially prominent in older mice. Lesions in young ‘mdx’ mice have not been studied extensively, and the results appear to be at variance with one another. The degenerative and regenerative aspects of the lesions in the TA of 23 to 26-day-old ‘mdx’ mice appear to vary quantitatively.

Ultrastructural observations of the aorta of calves implanted with a mechanical left ventricular assist device

1990 ◽  
Vol 48 (3) ◽  
pp. 834-835
Author(s):  
J P Cassella ◽  
V Salih ◽  
T R Graham
Keyword(s):  
Left Ventricular Assist Device ◽  
Ventricular Assist Device ◽  
Left Ventricular ◽  
Aortic Tissue ◽  
Assist Device ◽  
Ventricular Assist ◽  
Transmission Electron ◽  
Left Ventricular Assist ◽  
Preliminary Study

Left ventricular assist systems are being developed for eventual long term or permanent implantation as an alternative to heart transplantation in patients unsuitable for or denied the transplant option. Evaluation of the effects of these devices upon normal physiology is required. A preliminary study was conducted to evaluate the morphology of aortic tissue from calves implanted with a pneumatic Left Ventricular Assist device-LVAD. Two 3 month old heifer calves (calf 1 and calf 2) were electively explanted after 128 days and 47 days respectively. Descending thoracic aortic tissue from both animals was removed immediately post mortem and placed into karnovsky’s fixative. The tissue was subsequently processed for transmission electron microscopy (TEM). Some aortic tissue was fixed in neutral buffered formalin and processed for routine light microscopy.

A preliminary study on the potential of front face fluorescence spectroscopy for the discrimination of Moroccan virgin olive oils and the prediction of their quality

2021 ◽  
Author(s):  
Hicham Zaroual ◽  
El Mestafa El Hadrami ◽  
Romdhane Karoui
Keyword(s):  
Fluorescence Spectroscopy ◽  
Olive Oil ◽  
Virgin Olive Oil ◽  
Front Face ◽  
Virgin Olive Oils ◽  
Olive Oils ◽  
Preliminary Study

This study examines the feasibility of using front face fluorescence spectroscopy (FFFS) to authenticate 41 virgin olive oil (VOO) samples collected from 5 regions in Morocco during 2 consecutive crop seasons.

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