Egg and math: introducing a universal formula for egg shape

2021 ◽  
Author(s):  
Valeriy G. Narushin ◽  
Michael N. Romanov ◽  
Darren K. Griffin
Keyword(s):  
Universal Formula ◽  
Egg Shape

scholarly journals A universal formula for avian egg shape

2020 ◽  
Author(s):  
Valeriy G. Narushin ◽  
Michael N. Romanov ◽  
Darren K. Griffin
Keyword(s):  
Mathematical Model ◽  
Mathematical Formulation ◽  
Additional Function ◽  
Geometric Figures ◽  
Universal Formula ◽  
Egg Shape ◽  
Significant Step ◽  
Last Stage ◽  
Pointed End ◽  
Avian Egg

AbstractThe bird’s oomorphology has far escaped mathematical formulation universally applicable. All bird egg shapes can be laid in four basic geometric figures: sphere, ellipsoid, ovoid, and pyriform (conical/pear-shaped). The first three have a clear mathematical definition, each derived from expression of the previous, but a formula for the pyriform profile has yet to be inferred. To rectify this, we introduced an additional function into the ovoid formula. The subsequent mathematical model fits a completely novel geometric shape that can be characterized as the last stage in the evolution of the sphere—ellipsoid—Hügelschäffer’s ovoid transformation applicable to any avian egg shape geometry. Required measurements are the egg length, maximum breadth, and diameter at the terminus from the pointed end. This mathematical description is invariably a significant step in understanding not only the egg shape itself, but how and why it evolved, thus making widespread biological and technological applications theoretically possible.

scholarly journals Does Every Calculation Formula Fit for All Types of Intraocular Lenses? Optimization of Constants for Tecnis ZA9003 and ZCB00 Is Necessary

Medicina ◽  
2021 ◽  
Vol 57 (4) ◽  
pp. 319
Author(s):  
Ivajlo Popov ◽  
Veronika Popova ◽  
Juraj Sekac ◽  
Vladimir Krasnik
Keyword(s):  
Prediction Error ◽  
Poor Performance ◽  
Intraocular Lenses ◽  
Power Calculation ◽  
Universal Formula ◽  
Aspheric Iol ◽  
Different Types ◽  
The Mean ◽  
Clinically Significant ◽  
Mean Prediction Error

Background and Objectives: To evaluate the performance of intraocular lenses (IOLs) using power calculation formulas on different types of IOL. Materials and Methods: 120 eyes and four IOL types (BioLine Yellow Accurate Aspheric IOL (i-Medical), TECNIS ZCB00, TECNIS ZA9003 (Johnson & Johnson) (3-piece IOL) and Softec HD (Lenstec)) were analyzed. The performance of Haigis, Barret Universal II and SKR-II formulas were compared between IOL types. The mean prediction error (ME) and mean absolute prediction error (MAE) were analyzed. Results: The overall percentage of eyes predicted within ±0.25 diopters (D) was 40.8% for Barret; 39.2% Haigis and 31.7% for SRK-II. Barret and Haigis had a significantly lower MAE than SRK-II (p < 0.05). The results differed among IOL types. The largest portion of eyes predicted within ±0.25 D was with the Barret formula in ZCB00 (33.3%) and ZA9003 (43.3%). Haigis was the most accurate in Softec HD (50%) and SRK-II in Biolline Yellow IOL (50%). ZCB00 showed a clinically significant hypermetropic ME compared to other IOLs. Conclusions: In general, Barret formulas had the best performance as a universal formula. However, the formula should be chosen according to the type of IOL in order to obtain the best results. Constant optimizations are necessary for the Tecnis IOL ZCB00 and ZA9003, as all of the analyzed formulas achieved a clinically significant poor performance in this type of IOL. ZCB00 also showed a hypermetropic shift in ME in all the formulas.

Use of various keratometry data (ring and zone) in trifocal IOL calculation

2021 ◽  
pp. 53-56
Author(s):  
A.D. Loginova ◽  
◽  
S.V. Shukhaev ◽  
S.S. Kudlakhmedov ◽  
E.V. Boiko ◽  
...  
Keyword(s):  
Power Distribution ◽  
Optical Power ◽  
Iol Implantation ◽  
Universal Formula ◽  
Significant Difference ◽  
Trifocal Iol ◽  
Iol Calculation ◽  
Km Value ◽  
Tomographic Data ◽  
Corneal Refractive Power

Purpose. To compare the results of trifocal IOL calculation using various corneal tomographic data (ring and zone). Methods. This retrospective study involved 46 patients (46 eyes), underwent cataract surgery with trifocal IOL implantation (AcrySof IQ PanOptix). The calculation was performed using Tomey OA-2000 according to 2 formulas (Barrett II Universal, Olsen). Keratometry values included Km (the average of two main meridians of a cornea) provided by Pentacam HR Power Distribution Apex map, which describes total corneal refractive power (TCRP) with diameter of 3.0, 4.0 and 5.0 mm on a ring and zone. Mean (MAE) and median (MedAE) predicted postoperative refraction errors were assessed after surgery. Results. Mean Km value on 3 mm zone and ring was: 42.75±1,46 D and 42,91±1,43 D, respectively (p<0,0001). Mean Km on 4 mm zone and ring was: 42.6±1.5 D and 43.3 ± 1.5 D, respectively (p <0.005). Mean Km value on 5 mm zone and ring was: 43,09±1,5 D and 43,55±1,48 D, respectively (p<0,0001). Calculations using the Barrett II Universal formula revealed significant difference between MAE and MedAE of the predicted postoperative refraction on 5mm zone and ring (p=0.045). When using the Olsen formula in the calculations, significant difference was revealed using the Km data with a diameter of 3 mm and 5 mm (p=0.001 и p=0.009, respectively). The calculation on 3 mm ring was more accurate than for 3 mm zone. With a 5 mm diameter, the calculation is more accurate according to the zone data. Conclusion. Mean Km value on Power Distribution Apex map according to ring is significantly greater then according to zone. 1) The calculation of the trifocal IOL based on the TCRP zone data is reliably more accurate than the ring data according to both formulas (Barrett II Universal and Olsen) with a diameter of 5 mm. 2) According to the Olsen formula with a diameter of 3 mm, the calculation of the optical power of trifocal IOL based on TCRP ring data is more accurate. Key words: IOL calculation, Trifocal IOL, corneal topography

scholarly journals Egg shape mimicry in parasitic cuckoos

2017 ◽  
Vol 30 (11) ◽  
pp. 2079-2084 ◽  
Author(s):  
M. R. G. Attard ◽  
I. Medina ◽  
N. E. Langmore ◽  
E. Sherratt
Keyword(s):  
Egg Shape

scholarly journals KONTSEVICH'S UNIVERSAL FORMULA FOR DEFORMATION QUANTIZATION AND THE CAMPBELL–BAKER–HAUSDORFF FORMULA

2000 ◽  
Vol 11 (04) ◽  
pp. 523-551 ◽  
Author(s):  
VINAY KATHOTIA
Keyword(s):  
Lie Algebras ◽  
Deformation Quantization ◽  
Differential Operators ◽  
Main Tool ◽  
Graphical Analysis ◽  
Poisson Structures ◽  
Nilpotent Lie Algebras ◽  
Enveloping Algebra ◽  
Universal Formula ◽  
The Given

We relate a universal formula for the deformation quantization of Poisson structures (⋆-products) on ℝd proposed by Maxim Kontsevich to the Campbell–Baker–Hausdorff (CBH) formula. We show that Kontsevich's formula can be viewed as exp (P) where P is a bi-differential operator that is a deformation of the given Poisson structure. For linear Poisson structures (duals of Lie algebras) his product takes the form exp (C+L) where exp (C) is the ⋆-product given by the universal enveloping algebra via symmetrization, essentially the CBH formula. This is established by showing that the two products are identical on duals of nilpotent Lie algebras where the operator L vanishes. This completely determines part of Kontsevich's formula and leads to a new scheme for computing the CBH formula. The main tool is a graphical analysis for bi-differential operators and the computation of certain iterated integrals that yield the Bernoulli numbers.

MAXIMUM SECONDARY ELECTRON YIELDS FROM SEMICONDUCTORS AND INSULATORS

2016 ◽  
Vol 24 (04) ◽  
pp. 1750045 ◽  
Author(s):  
A. G. XIE ◽  
Z. H. LIU ◽  
Y. Q. XIA ◽  
M. M. ZHU
Keyword(s):  
Electron Emission ◽  
Secondary Electron ◽  
Maximum Yield ◽  
Secondary Electron Emission ◽  
High Energy ◽  
Secondary Electrons ◽  
Backscattered Electrons ◽  
Universal Formula ◽  
Yield Formula ◽  
Primary Electrons

Based on the processes and characteristics of secondary electron emission and the formula for the yield due to primary electrons hitting on semiconductors and insulators, the universal formula for maximum yield [Formula: see text] due to primary electrons hitting on semiconductors and insulators was deduced, where [Formula: see text] is the maximum ratio of the number of secondary electrons produced by primary electrons to the number of primary electrons. On the basis of the formulae for primary range in different energy ranges of [Formula: see text], characteristics of secondary electron emission and the deduced universal formula for [Formula: see text], the formulae for [Formula: see text] in different energy ranges of [Formula: see text] were deduced, where [Formula: see text] is the primary incident energy at which secondary electron yields from semiconductors and insulators, [Formula: see text], are maximized to maximum secondary electron yields from semiconductors and insulators, [Formula: see text]; and [Formula: see text] is the maximum ratio of the number of total secondary electrons produced by primary electrons and backscattered electrons to the number of primary electrons. According to the deduced formulae for [Formula: see text], the relationship among [Formula: see text], [Formula: see text] and high-energy back-scattering coefficient [Formula: see text], the formulae for parameters of [Formula: see text] and the experimental data as well as the formulae for [Formula: see text] in different energy ranges of [Formula: see text] as a function of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] were deduced, where [Formula: see text] and [Formula: see text] are the original electron affinity and the width of forbidden band, respectively. The scattering of [Formula: see text] was analyzed, and calculated [Formula: see text] values were compared with the values measured experimentally. It was concluded that the deduced formulae for [Formula: see text] were found to be universal for [Formula: see text].

scholarly journals On the evaluation of chicken egg shape variability

2008 ◽  
Vol 56 (5) ◽  
pp. 69-74 ◽  
Author(s):  
Miroslav Havlíček ◽  
Šárka Nedomová ◽  
Jana Simeonovová ◽  
Libor Severa ◽  
Ivo Křivánek
Keyword(s):  
Shape Index ◽  
Width Ratio ◽  
Geometrical Parameters ◽  
Fourier Descriptors ◽  
Shape Variation ◽  
Egg Volume ◽  
Maximum Width ◽  
Chicken Egg ◽  
Egg Shape ◽  
Elliptic Fourier Descriptors

Although recently reported models for determining egg shape are highly accurate, certain com­pli­ca­ted measurements or computations are to be performed. Thus relatively simple and attainable analysis methods of chicken egg shape variability were chosen and used for the purpose of presented research. Sample of 250 eggs of ISA BROWN strain was examined. Geometrical parameters were measured and calculated with following expression of their coefficient of variation – namely egg length 3.56 %, egg maximum width 2.84 %, shape index 3.80 %, surface area 5.08 %, and egg volume 7.23 %. The second method consisted in shape quantitative measuring by the score of the principal components of elliptic Fourier descriptors (EFDs). The first four principles components which could explain over 99 % of the egg shape variations were found to be very good measures of the monitored phenomenon. It was found that 87.41 % of the total shape variation can be accounted to length to width ratio. Usefulness and relevance of the shape index usage was confirmed.

scholarly journals Produksi Telur Ayam Persilangan Merawang dengan Arab

2019 ◽  
Vol 7 (3) ◽  
pp. 120-122
Author(s):  
N. Widayanti ◽  
S. Darwati ◽  
R. Afnan
Keyword(s):  
Egg Production ◽  
Shape Index ◽  
Feed Conversion ◽  
Egg Weight ◽  
Egg Shape

The egg production of local chiken can be increased by crossing of arab and merawang chicken. This study aimed to observed egg production performances of crossing between merawang x merawangarab (M-MA), merawangarab x merawang (MA-M), merawangarab x merawangarab (MA-MA), arabmerawang x arabmerawang (AM-AM), merawangarab x arab (MA-A), and arab x merawangarab (A-MA). Parameters in this study were egg weight, egg shape index, hen day production and feed conversion. The result showed that the egg weight of MA-M chicken was significantly greater (P<0.05). than M-MA, MA-MA, AM-AM, MA-A, and A-MA chicken. The MA-A egg index was significantly larger (P<0.05) than other crossing. Hen day production of M-MA chicken was significantly greater (P<0.05) and feed convertion was significantly efficient (P<0.05) than other crossing. MA hens had better production than other hens.

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