Golden Ratio Rule Research Articles

ПРИМЕНЕНИЕ ПРАВИЛА ЗОЛОТОГО СЕЧЕНИЯ В ЮРИСПРУДЕНЦИИ: АНАЛИЗ И ПЕРСПЕКТИВЫ

This article examines the application of the golden ratio, also known as the golden proportion, in jurisprudence. The golden ratio is a mathematical and aesthetic principle that has been known since ancient times, and its application in various fields of knowledge has attracted the interest of researchers. The article explores examples of the use of the golden ratio in legal practice, including the analysis of legal texts, argumentation, and the making of judicial decisions. Drawing on existing research and theoretical concepts, the article also discusses the prospects of applying the golden ratio rule to enhance effectiveness and fairness in jurisprudence. The author was inspired by the monograph "The Golden Ratio and Evolution: An Introduction to the General Theory of Non-local Evolution" by Kokin A. V. and Kokin A. A., published in 2022, where the authors examined the theory of the golden ratio through the lens of the synergistic paradigm.

Psychology of ustoychivost': numerical scale for assessing human’s ustoychivost' according to the golden ratio rule

Exploring man, the modern psychology of Europe and America began to actively apply the concepts stability and/or resistance that, in Russia psychology, are combined into one concept — ustoychivost’. In modern psychology, there is no methodology for numerically assessing human ustoychivost’. The article presents the author’s scale of numerical evaluation of ustoychivost ’person and outlines an approach to the formation of its road map. Human ustoychivost ’refers to his ability to maintain health at the psychophysiological, psychological and psychosocial levels of life, forming the unity of the individual, personality and the subject of work in a person. Three hypotheses are put forward. Hypothesis 1: it is possible to numerically establish human ustoychivost ' if you create a scale for assessing it by applying the golden ratio rule — the stability scale for the golden ratio (SUGP). Hypothesis 2: if a person subjectively evaluates his ustoychivost ’in the range from 0.382 to 0.618, then objectively he is stability; if a person subjectively evaluates his ustoychivost ’in the intervals from 0.382 to 0 or from 0.618 to 1, then objectively he is resistance. To test the hypotheses put forward, an experiment on a sample of firefighters is presented, which confirms their fidelity, and also indicates the appropriateness of using SUGP in extreme psychology, labor psychology.

A novel optimally weighted framework of piecewise gamma corrected fractional order masking for satellite image enhancement

A novel image quality enhancement framework is proposed here through a collective inspiration of the exponential, differential and linear operational behavior of pixel intensities. Here, a new mask framing strategy (based on uniformity principle) is presented for harvesting the benefits of optimally ordered fractional differential (FD) unsharp masking, which is consequently counter-corrected by piecewise gamma correction (PGC) through a robustly framed weighted summation framework. PGC is imparted by the constructive involvement of reciprocal gamma values (γ1=γandγ2=1/γ,∀γ>1), which leads to interim compressed as well as interim expanded images. Golden-ratio rule inspired gradient-free, modified Cuckoo Search (MCS) optimization model, utilizing a newly framed Grey-Level Co-occurrence Matrix (GLCM) features based objective-function is proposed here. Experimentation highlights the outperformance of the proposed approach by desired increment in contrast, entropy, colorfulness and sharpness along with least values of correlation, energy and homogeneity, for parallel texture enhancement along with dark image enhancement.

Design of Band Stop Filter with Frequency Selective Surfaces Analysis by Implementing the Golden Ratio Rule

Design of Band Stop Filter with Frequency Selective Surfaces Analysis by Implementing the Golden Ratio Rule

The Fibonacci recurrence with harmonic inhomogeneity

In this paper, a non-homogeneous version of the classical Fibonacci recurrence relation is investigated. The inhomogeneity is defined by a harmonic sequence , with real-valued parameters . It turns out that the golden ratio rule carries over to the solution of the non-homogeneous recurrence for almost all parameter values. The exceptional set is a one-dimensional submanifold in –-space, which is related to the graph of the Lerch transcendent.

‘Selfies’ Reveal Systematic Deviations from Known Principles of Photographic Composition

We used ‘selfies’, self-portraits taken with a hand-held smartphone camera, to test three known principles of photographic composition: The rule of thirds, the golden ratio rule, and the eye centering principle. Although they are often taught and discussed, the origin of these principles remains unclear. It is possible that they stem from constraints on human perceptual processes. Alternatively, these principles might serve more practical purposes, such as forcing photographers to explore all quadrants of the image. Selfies provide an ideal test bed for these questions due to the control they give self-photographers when they compose the photograph. We used a database of images created by non-professional photographers (). After analysis, we conclude that there little support for any of the three principles, suggesting that none is strongly rooted in spontaneous perceptual preferences.

Aplicability of golden ratio rule in modern product design

This paper presents research regarding application of golden ratio rule in field of product design. The rule was applied to the design on vacuum cleaner, as it is a common and widely spread product. The aim of this paper is to research possibilities of applications of the rule in modern design. In order to determine consumer’s subjective aesthetic judgment of products designed by directly applying golden ratio rule, one vacuum cleaner was designed in that manner. Results for consumer’s subjective aesthetic preference were compared to results for other differently designed vacuum cleaner models present in the market today. Factors used were age, gender and level of education of participants (typical consumer). The results showed no statistical influence of age or gender factors. Statistically significant differences were noticed for level of education factor, between participants with high school diploma and university diploma. It was observed that product de-signed using golden ratio rule received higher marks regarding aesthetics in case of participants with university diploma. It can be concluded that golden ratio rule can be applied in field of product design, equally successful as in the other art fields where it is commonly used, but consumer demographics must be taken in to consideration, especially education level.

Three-dimensional Brownian motion and the golden ratio rule

Let $X=(X_t)_{t\ge0}$ be a transient diffusion process in $(0,\infty)$ with the diffusion coefficient $\sigma>0$ and the scale function $L$ such that $X_t\rightarrow\infty$ as $t\rightarrow \infty$, let $I_t$ denote its running minimum for $t\ge0$, and let $\theta$ denote the time of its ultimate minimum $I_{\infty}$. Setting $c(i,x)=1-2L(x)/L(i)$ we show that the stopping time \[\tau_*=\inf\{t\ge0\vert X_t\ge f_*(I_t)\}\] minimizes $\mathsf{E}(\vert\theta-\tau\vert-\theta)$ over all stopping times $\tau$ of $X$ (with finite mean) where the optimal boundary $f_*$ can be characterized as the minimal solution to \[f'(i)=-\frac{\sigma^2(f(i))L'(f(i))}{c(i,f(i))[L(f(i))-L(i)]}\int_i^{f(i)}\frac{c_i'(i,y)[L(y) -L(i)]}{\sigma^2(y)L'(y)}\,dy\] staying strictly above the curve $h(i)=L^{-1}(L(i)/2)$ for $i>0$. In particular, when $X$ is the radial part of three-dimensional Brownian motion, we find that \[\tau_ *=\inf\biggl\{t\ge0\Big\vert\frac{X_t-I_t}{I_t}\ge\varphi\biggr\},\] where $\varphi=(1+\sqrt{5})/2=1.61\ldots$ is the golden ratio. The derived results are applied to problems of optimal trading in the presence of bubbles where we show that the golden ratio rule offers a rigorous optimality argument for the choice of the well-known golden retracement in technical analysis of asset prices.

A subjective supply–demand model: the maximum Boltzmann/Shannon entropysolution

The present authors have put forward a projective geometry model of rational trading. Theexpected (mean) value of the time that is necessary to strike a deal and the profit stronglydepend on the strategies adopted. A frequent trader often prefers maximal profit intensityto the maximization of profit resulting from a separate transaction because the grossprofit/income is the adopted/recommended benchmark. To investigate activities that havedifferent periods of duration we define, following the queuing theory, the profit intensity asa measure of this economic category. The profit intensity in repeated trading has a uniqueproperty of attaining its maximum at a fixed point regardless of the shape ofdemand curves for a wide class of probability distributions of random reversetransactions (i.e. closing of the position). These conclusions remain valid for ananalogous model based on supply analysis. This type of market game is oftenconsidered in research aiming at finding an algorithm that maximizes profit of atrader who negotiates prices with the Rest of the World (a collective opponent),possessing a definite and objective supply profile. Such idealization neglects thesometimes important influence of an individual trader on the demand/supplyprofile of the Rest of the World and in extreme cases questions the very idea ofdemand/supply profile. Therefore we put forward a trading model in which thedemand/supply profile of the Rest of the World induces the (rational) trader to(subjectively) presume that he/she lacks (almost) all knowledge concerning themarket but his/her average frequency of trade. This point of view introducesmaximum entropy principles into the model and broadens the range of economicphenomena that can be perceived as a sort of thermodynamical system. As aconsequence, the profit intensity has a fixed point with an astonishing connection withFibonacci classical works and looking for the quickest algorithm for obtainingthe extremum of a convex function: the profit intensity reaches its maximumwhen the probability of transaction is given by the golden ratio rule . This condition sets a sharp criterion of validity of the model and can be tested with realmarket data.

Algorithms for generalized round robin routing

This paper presents new algorithms to construct a Generalized Round Robin (GRR) routing sequence for distributing one stream of traffic to multiple queues. The performance objective is to minimize the expected delay. Given a target allocation in terms of the fraction of jobs that should be routed to each queue, the algorithms scan the queues in order of descending fraction and assign the next job to the first queue with current allocation not exceeding an easilycomputed threshold. We prove that the constructed sequence has properties related to Hajek's most regular sequence; in particular, it is optimal for the case of two queues. Simulation results show improvement over Itai-Rosberg's Golden Ratio Rule and come very close to a lower bound obtained by Hajek.