Sortie resolution method of radon ambiguity transform based on golden section iteration

Celestial Tapestry places mathematics within a vibrant cultural and historical context, highlighting links to the visual arts and design, and broader areas of artistic creativity. Threads are woven together telling of surprising influences that have passed between the arts and mathematics. The story involves many intriguing characters: Gaston Julia, who laid the foundations for fractals and computer art while recovering in hospital after suffering serious injury in the First World War; Charles Howard, Hinton who was imprisoned for bigamy but whose books had a huge influence on twentieth-century art; Michael Scott, the Scottish necromancer who was the dedicatee of Fibonacci’s Book of Calculation, the most important medieval book of mathematics; Richard of Wallingford, the pioneer clockmaker who suffered from leprosy and who never recovered from a lightning strike on his bedchamber; Alicia Stott Boole, the Victorian housewife who amazed mathematicians with her intuition for higher-dimensional space. The book includes more than 200 colour illustrations, puzzles to engage the reader, and many remarkable tales: the secret message in Hans Holbein’s The Ambassadors; the link between Viking runes, a Milanese banking dynasty, and modern sculpture; the connection between astrology, religion, and the Apocalypse; binary numbers and the I Ching. It also explains topics on the school mathematics curriculum: algorithms; arithmetic progressions; combinations and permutations; number sequences; the axiomatic method; geometrical proof; tessellations and polyhedra, as well as many essential topics for arts and humanities students: single-point perspective; fractals; computer art; the golden section; the higher-dimensional inspiration behind modern art.

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A super-resolution method of combined color image with depth map based on deep learning

Proceedings of the 2020 International Conference on Cyberspace Innovation of Advanced Technologies ◽

10.1145/3444370.3444539 ◽

2020 ◽

Author(s):

Wei Zhang ◽

Chi-fu Yang ◽

Feng Jiang ◽

Xian-zhong Gao ◽

Kai Yang

Keyword(s):

Deep Learning ◽

Color Image ◽

Super Resolution ◽

Depth Map ◽

Resolution Method

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Quantification of thermal energy generation in annular hyperbolic porous-finned heat sinks using inverse optimization

Proceedings of the Institution of Mechanical Engineers Part E Journal of Process Mechanical Engineering ◽

10.1177/09544089211024387 ◽

2021 ◽

pp. 095440892110243

Author(s):

Sagnik Pal ◽

Ranjan Das

Keyword(s):

Heat Transfer ◽

Surface Temperature ◽

Heat Generation ◽

Thermal Energy ◽

Inverse Method ◽

Golden Section ◽

Energy Generation ◽

Heat Sinks ◽

Search Technique ◽

Golden Section Search

The present paper introduces an accurate numerical procedure to assess the internal thermal energy generation in an annular porous-finned heat sink from the sole assessment of surface temperature profile using the golden section search technique. All possible heat transfer modes and temperature dependence of all thermal parameters are accounted for in the present nonlinear model. At first, the direct problem is numerically solved using the Runge–Kutta method, whereas for predicting the prevailing heat generation within a given generalized fin domain an inverse method is used with the aid of the golden section search technique. After simplifications, the proposed scheme is credibly verified with other methodologies reported in the existing literature. Numerical predictions are performed under different levels of Gaussian noise from which accurate reconstructions are observed for measurement error up to 20%. The sensitivity study deciphers that the surface temperature field in itself is a strong function of the surface porosity, and the same is controlled through a joint trade-off among heat generation and other thermo-geometrical parameters. The present results acquired from the golden section search technique-assisted inverse method are proposed to be suitable for designing effective and robust porous fin heat sinks in order to deliver safe and enhanced heat transfer along with significant weight reduction with respect to the conventionally used systems. The present inverse estimation technique is proposed to be robust as it can be easily tailored to analyse all possible geometries manufactured from any material in a more accurate manner by taking into account all feasible heat transfer modes.

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Resolution systems and their applications I

Fundamenta Informaticae ◽

10.3233/fi-1980-3209 ◽

1980 ◽

Vol 3 (2) ◽

pp. 235-268

Author(s):

Ewa Orłowska

Keyword(s):

Theorem Proving ◽

Sufficient Conditions ◽

Predicate Calculus ◽

Resolution Method ◽

First Order ◽

Deductive Systems ◽

Resolution System ◽

Resolution Principle ◽

Necessary And Sufficient ◽

Classical Predicate

The central method employed today for theorem-proving is the resolution method introduced by J. A. Robinson in 1965 for the classical predicate calculus. Since then many improvements of the resolution method have been made. On the other hand, treatment of automated theorem-proving techniques for non-classical logics has been started, in connection with applications of these logics in computer science. In this paper a generalization of a notion of the resolution principle is introduced and discussed. A certain class of first order logics is considered and deductive systems of these logics with a resolution principle as an inference rule are investigated. The necessary and sufficient conditions for the so-called resolution completeness of such systems are given. A generalized Herbrand property for a logic is defined and its connections with the resolution-completeness are presented. A class of binary resolution systems is investigated and a kind of a normal form for derivations in such systems is given. On the ground of the methods developed the resolution system for the classical predicate calculus is described and the resolution systems for some non-classical logics are outlined. A method of program synthesis based on the resolution system for the classical predicate calculus is presented. A notion of a resolution-interpretability of a logic L in another logic L ′ is introduced. The method of resolution-interpretability consists in establishing a relation between formulas of the logic L and some sets of formulas of the logic L ′ with the intention of using the resolution system for L ′ to prove theorems of L. It is shown how the method of resolution-interpretability can be used to prove decidability of sets of unsatisfiable formulas of a given logic.

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DETERMINATION METHOD OF FLORET NUMBER AND THEIR DENSITY IN SUNFLOWER HEAD / METODO PARA LA DETERMINACION DEL NUMERO DE FLORES Y SU DENSIDAD A LA CABEZA DE GIRASOL / METHODE DE DÉTERMINATION DU NOMBRE DE FLEURS ET DE LEUR DENSITÉ SUR LA TÊTE DE TOURNESOL

Helia ◽

10.1515/helia.2001.24.34.41 ◽

2001 ◽

Vol 24 (34) ◽

pp. 41-48

Author(s):

I.V. Marin

Keyword(s):

Initial Data ◽

Golden Section ◽

Determination Method ◽

Flower Number ◽

Disk Flower ◽

Simple Method

SUMMARYThe aim of this work was to develop a simple method for calculating disk flower number and their density in sunflower head. The formula developed on the basis of the Golden section includes initial data of the number of smallshort rows and the number of florets in a row. It takes no more than a minute to gain initial data for calculating the formula for one head.

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