Academic literature on the topic 'Fibonacci Box'

Benoit Mandelbrot coined the word “fractal” in the late 1970s, but an object is now defined as fractals in form known to artists and mathematicians for centuries. A fractal object is self-similar in that the subsections of the object are somewhat similar to the whole object. No matter how small the subdivision is, the subsection contains no less detail than the whole. Atypical example of a fractal body is the “snowflake curve” (invented by Helga von Koch (1870-1924) in 1904. There are as many relationships between architecture, the arts, and mathematics as symmetry. The golden ratio, the Fibonacci sequence in this paper explain the method of counting box and measuring the roughness ratio. And small scale analysis after calculating the box to understand fractal concepts, we must know two dimensions. Through analyzing the samples in the research, it has been proven that fractal geometry is present everywhere in our lives in nature, in buildings, and even in plants and its role in architecture is to find fractal systems that appeal to our inclinations for dynamic vitality. Therefore, finding such fractals enables us to create high-performance structures that achieve psychological, aesthetic and environmental aspects in an integrated design. Therefore, Self- Similarity Dimension (Ds) Box-counting Dimension (Db.) All of these dimensions are directly related to the fractional dimension of Mandelbrot (D). In all similar constructions there is a relationship between the scale factor and the number of the smaller pieces the original construction is divided into.

TPS778 Background: Phosphorylated p68 may play a vital role in cell proliferation and tumor/cancer progression. RX-5902 is a novel compound that targets phosphorylated p68 RNA helicase (also known as DDX5), a member of the DEAD box family of RNA helicases. As a single agent, RX-5902 inhibits tumor growth and enhances survival in a variety of xenograft tumor models (e.g., pancreatic, renal, ovarian, melanoma). Methods: This Phase 1, open-label, multicenter study evaluates the efficacy and safety of RX-5902 in subjects with solid tumors. RX-5902 is administered orally 1, 3 or 5 times per week for 3 weeks with 1 week of rest in each 4 week cycle. Dose escalation starts with an accelerated design treating 1 subject per dose followed by a standard 3 + 3 design using a modified Fibonacci sequence after the occurrence of a single Grade 2 or greater adverse event that is considered at related to RX-5902. The primary endpoint is the overall safety profile characterized by the type, frequency, severity, timing of onset, duration and relationship to study therapy of any adverse events, or abnormalities of laboratory tests or electrocardiograms as well as the description of any dose limiting toxicities that occur during Cycle 1, serious adverse events, or adverse events leading to discontinuation of study treatment. Secondary endpoints include pharmacokinetic parameters (e.g., time to maximum observed concentration [Tmax], maximum observed plasma concentration [Cmax], trough concentration [Ctrough], area under the concentration-time curve [AUC]) and Indices of anti-tumor activity (e.g., overall response rate, time to response, duration of response, and progression-free survival during treatment. Exploratory endpoints are biochemical levels of drug targets in blood and tumor samples. Eligible subjects must have confirmed histologic or cytologic evidence of metastatic or locally advanced solid neoplasm that has failed to respond to standard therapy, progressed despite standard therapy or for which standard therapy does not exist. There is no limit on the number of prior treatment regimens. Clinical trial information: NCT02003092.

Mack and Czernezkyj (2010) have given an interesting account of primitive Pythagorean triples (PPTs) from a geometrical perspective. In this article, the authors wish to enlarge on the role of the equicircles (incircle and three excircles), and show there is yet another family tree in Pythagoras' garden. Where Mack and Czernezkyj (2010) begin with four equicircles, the authors begin with four tangent circles, attached to the corners of a rectangle based on the right triangle. Reflecting these circles in a certain line results in a congruent tangent cluster, having the same six points of tangency, orthogonal to the first four, and ultimately revealed as (jostled) equicircles! They then develop three celebrated families of triples by elementary means, and tinker with the sequencing rules until the classic Pythagorean family tree magically appears. Using a favourite set of four parameters to identify and tag triples, they find more circle secrets. (Contains 7 figures.)

Abstract We study, by means of numerical methods, new SU(N) self-dual instanton solutions on R × T3 with fractional topological charge Q = 1/N. They are obtained on a box with twisted boundary conditions with a very particular choice of twist: both the number of colours and the ’t Hooft ZN fluxes piercing the box are taken within the Fibonacci sequence, i.e. N = Fn (the nth number in the series) and $$ \left|\overrightarrow{m}\right| $$ m → = $$ \left|\overrightarrow{k}\right| $$ k → = Fn−2. Various arguments based on previous works and in particular on ref. [1], indicate that this choice of twist avoids the breakdown of volume independence in the large N limit. These solutions become relevant on a Hamiltonian formulation of the gauge theory, where they represent vacuum-to-vacuum tunneling events lifting the degeneracy between electric flux sectors present in perturbation theory. We discuss the large N scaling properties of the solutions and evaluate various gauge invariant quantities like the action density or Wilson and Polyakov loop operators.