Related papers: The architect Kha's protractor
The self-similarity of Indonesian Borobudur Temple is observed through the dimensionality of stupa that is hypothetically closely related to whole architectural body. Fractal dimension is calculated by using the cube counting method and…
We investigate correspondence functors, namely the functors from the category of finite sets and correspondences to the category of $k$-modules, where $k$ is a commutative ring.They have various specific properties which do not hold for…
Combinatorial $t$-designs have been an interesting topic in combinatorics for decades. It was recently reported that the image sets of a fixed size of certain special polynomials may constitute a $t$-design. Till now only a small amount of…
Several tools have been developed to enhance automation of theorem proving in the 2D plane. However, in 3D, only a few approaches have been studied, and to our knowledge, nothing has been done in higher dimensions. In this paper, we present…
Recently, Han obtained two hook length formulas for binary trees and asked for combinatorial proofs. One of Han's formulas has been generalized to k-ary trees by Yang. Sagan has found a probabilistic proof of Yang's extension. We give…
Arabia Terra is a region of Mars where signs of past-water occurrence are recorded in several landforms. Broad and local scale geomorphological, compositional and hydrological analyses point towards pervasive fluid circulation through time.…
It is well known that Al-Khay\^am, for the first time in history, formulated a complete theory to solve third degree equations using the intersection of geometric curves and moreover solved the fourteen types of equations using this method.…
The mausoleums of the emperors and of some members of the royal family of the Western Han Chinese dynasty, popularly known as Chinese pyramids, are a spectacular ensemble of tombs covered by a huge earth mounds, spread in the outskirts of…
Knitting turns yarn, a 1D material, into a 2D fabric that is flexible, durable [1], and can be patterned to adopt a wide range of 3D geometries [2]. Like other mechanical metamaterials [3], the elasticity of knitted fabrics is an emergent…
The royal Chinese mausoleums of the Tang, Ming and Qing Chinese dynasties are astounding ensables of monuments, conceived and built to assure to the Emperors immortality in the afterlife and perennial fame on earth. To this aim, a series of…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
Numerical integration of orbit trajectories for a large number of initial conditions and for long time spans is computationally expensive. Semi-analytical methods were developed to reduce the computational burden. An elegant and widely used…
We consider a subclass of tilings, the tilings obtained by cut and projection. Under somewhat standard assumptions, we show that the natural complexity function has polynomial growth. We compute its exponent \alpha in terms of the ranks of…
The depth of a simple algebraic extension $(L/K,v)$ of valued fields is the minimal length of the Mac Lane-Vaqui\'e chains of the valuations on $K[x]$ determined by the choice of different generators of the extension. In a previous paper,…
Schutzenberger's promotion operator, pro, is a fundamental map in dynamical algebraic combinatorics. At first, its action was mainly considered on standard Young tableaux. But pro was subsequently shown to have interesting properties when…
We study the transfer of (co)silting objects in derived categories of module categories via the extension functors induced by a morphism of commutative rings. It is proved that the extension functors preserve (co)silting objects of…
In 1982-83, E. Nochka proved a conjecture of Cartan on defects of holomorphic curves in $\Bbb P^n$ relative to a possibly degenerate set of hyperplanes. This was further explained by W. Chen in his 1987 thesis, and subseqently simplified by…
Ratios and coefficients are used to simplify calculations. For geometric usage these values also called function values. Like in Egypt also in Babylon such a value system can be shown. The reconstructed calculation sequence, of the Plimpton…
The properties of 5D gravitational flux tubes are considered. With the cross section and 5th dimension in the Planck region such tubes can be considered as string-like objects, namely $\Delta-$strings. A model of attachment of…
"The Lord made me a very great favor in an imaginary vision" wrote Maria de Agreda in the seventeenth century, "His Majesty put me at the foot of a beautiful Ladder, and showed me I had to climb it." These words refer to the spiritual…