scholarly journals Mathematical Modeling of a Class of Symmetrical Islamic Design

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 517
Author(s):  
Mostafa ZAHRI
Keyword(s):  
Mathematical Modeling ◽  
Unit Circle ◽  
Convergence Properties ◽  
Periodic Sequences ◽  
New Model ◽  
One Dimensional ◽  
Geometric Patterns ◽  
Interesting Class ◽  
The One

In this paper, we present a new model for simulating an interesting class of Islamic design. Based on periodic sequences on the one-dimensional manifolds, and from emerging numbers, we construct closed graphs with edges on the unit circle. These graphs build very nice shapes and lead to a symmetrical class of geometric patterns of so-called Islamic design. Moreover, we mathematically characterize and analyze some convergence properties of the used up-down sequences. Finally, four planar type of patterns are simulated.

Quasiconformal Contactomorphisms and Polynomial Hulls with Convex Fibers

1999 ◽  
Vol 51 (5) ◽  
pp. 915-935 ◽  
Author(s):  
Zoltán M. Balogh ◽  
Christoph Leuenberger
Keyword(s):  
Unit Circle ◽  
Complex Flow ◽  
One Dimensional ◽  
Holomorphic Motions ◽  
Strictly Convex ◽  
Fixed Domain ◽  
Polynomial Hulls ◽  
Polynomial Hull ◽  
The One ◽  
Special Case

AbstractConsider the polynomial hull of a smoothly varying family of strictly convex smooth domains fibered over the unit circle. It is well-known that the boundary of the hull is foliated by graphs of analytic discs. We prove that this foliation is smooth, and we show that it induces a complex flow of contactomorphisms. These mappings are quasiconformal in the sense of Korányi and Reimann. A similar bound on their quasiconformal distortion holds as in the one-dimensional case of holomorphic motions. The special case when the fibers are rotations of a fixed domain in C2 is studied in details.

Optimal and Greedy Algorithms for the One-Dimensional RSU Deployment Problem With New Model

2018 ◽  
Vol 67 (8) ◽  
pp. 7643-7657 ◽  
Author(s):  
Zhenguo Gao ◽  
Danjie Chen ◽  
Shaobin Cai ◽  
Hsiao-Chun Wu
Keyword(s):  
Greedy Algorithms ◽  
New Model ◽  
One Dimensional ◽  
The One

RELATION BETWEEN A CLASS OF QUASIPERIODIC LATTICES GENERATED BY THE SUBSTITUTION METHOD AND THE GENERALIZED CONTINUED FRACTION EXPANSION

1996 ◽  
Vol 10 (17) ◽  
pp. 2081-2101
Author(s):  
TOSHIO YOSHIKAWA ◽  
KAZUMOTO IGUCHI
Keyword(s):  
Continued Fraction ◽  
Positive Real Number ◽  
Real Numbers ◽  
Continued Fraction Expansion ◽  
Positive Real ◽  
Periodic Sequences ◽  
One Dimensional ◽  
Finite Period ◽  
The One ◽  
Positive Integers

The continued fraction expansion for a positive real number is generalized to that for a set of positive real numbers. For arbitrary integer n≥2, this generalized continued fraction expansion generates (n−1) sequences of positive integers {ak}, {bk}, … , {yk} from a given set of (n−1) positive real numbers α, β, …ψ. The sequences {ak}, {bk}, … ,{yk} determine a sequence of substitutions Sk: A → Aak Bbk…Yyk Z, B → A, C → B,…,Z → Y, which constructs a one-dimensional quasiperiodic lattice with n elements A, B, … , Z. If {ak}, {bk}, … , {yk} are infinite periodic sequences with an identical period, then the ratio between the numbers of n elements A, B, … , Z in the lattice becomes a : β : … : ψ : 1. Thereby the correspondence is established between all the sets of (n−1) positive real numbers represented by a periodic generalized continued fraction expansion and all the one-dimensional quasiperiodic lattices with n elements generated by a sequence of substitutions with a finite period.

Modeling of washout of a well-killing liquid after launching of an oil well

2020 ◽  
Vol 15 (3-4) ◽  
pp. 167-175
Author(s):  
A.S. Topolnikov
Keyword(s):  
Mathematical Modeling ◽  
Multicomponent Mixture ◽  
Variable Density ◽  
Oil Well ◽  
One Dimensional ◽  
Reservoir Fluid ◽  
Pump Head ◽  
Measuring Field ◽  
The One ◽  
Bottomhole Pressure

The paper presents the results of mathematical modeling of the process of launching and output to the mode of an oil well, which was uploaded by a well-killing liquid at the stage of repairs. After the launching of the electric submergible pump the drop of the bottomhole pressure occurs and the inflow of reservoir fluid begins. As a result the multicomponent mixture is generated inside the well, which consists of oil, associated water, well-killing liquid and free gas, originated from the oil during degassing, and this mixture is pumped out towards wellhead. As soon as the pump characteristics are changed, when the liquid with variable density is pumped out, it is necessary to control the speed of a shaft of the pump for providing the stable pump regime. This problem is solved in the paper for different ratios of densities of well-killing liquid and reservoir fluid by the mathematical modeling of multiphase flow in the well elements and inside the pump. As a mathematical model the one-dimensional quasi-stationary model in approach of drift for description of relative motion of the components is applied, which proved itself well for modeling of non-stationary processes lasting for several days. The comparison of calculated and measuring field parameters is presented. It is shown that the speed of washout of the well-killing liquid from the oil well and the probability of the pump stop due to its head failure depend on the ration of densities of the well-killing liquid and reservoir fluid. It is stated that the monitoring of change of parameters of the pump in time through the mathematical modeling can help to optimize the output to the mode of the well. This allows to avoid stops due to the pump head failure and to diminish the electricity costs.

scholarly journals Modeling of stochastic brain function in artificial intelligence

2019 ◽  
Vol 4 (3) ◽  
pp. 8-14
Author(s):  
Andrei N. Volobuev ◽  
Vasiliy F. Pyatin ◽  
Natalya P. Romanchuk ◽  
Petr I. Romanchuk ◽  
Svetlana V. Bulgakova
Keyword(s):  
Mathematical Modeling ◽  
Artificial Intelligence ◽  
Brain Function ◽  
Brain Activity ◽  
Necessary Condition ◽  
Alpha Wave ◽  
Brain Functioning ◽  
One Dimensional ◽  
The One ◽  
Stochastic Mode

Objectives -research of stochastic brain function in respect to creation of artificial intelligence. Material and methods. Mathematical modeling principles were used for simulation of brain functioning in a stochastic mode. Results. Two types of brain activity were considered: determinated type, usually modeled using the perceptron, and stochastic type. It is shown, that stochastic brain function modeling is the necessary condition for AI to become capable of creativity, generation of new knowledge. Mathematical modeling of a neural network of the cerebral cortex, consisting of the set of the cyclic neuronal circuits (memory units), was performed for the stochastic mode of brain functioning. Models of "two-dimensional" and "one-dimensional" brain were analyzed. The pattern of excitation in memory units was calculated in the "one-dimensional" brain model. Conclusion. Relying on the knowledge of the stochastic mode of brain function, a way of creation of AI can be offered. а-rhythm of a patient is a recommended focus of the therapist's attention in diagnostics and treatment of brain disorders. It was noted, that the alpha wave amplitude and frequency could indicate the cognitive, creative and intuitive abilities of a person.

scholarly journals Development and Experimentation of a New Mathematical Model for Teaching–Learning the Radioactive Decay Law

2019 ◽  
Vol 9 (2) ◽  
pp. 123
Author(s):  
Mamane ◽  
Benjelloun
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Analytical Model ◽  
Validation Study ◽  
Collaborative Work ◽  
Radioactive Decay ◽  
New Model ◽  
Preliminary Study ◽  
The One ◽  
Teaching Learning

Our plan is to bring professors and their Moroccan pupils to focus on the teaching–learning of physics, without adopting forced mathematical modeling in previously unknown frames and registers, as is actually the practice. The preliminary study consists of developing a new analytical model for the teaching–learning of the radioactive decay law. However, the validation study was conducted to test its pertinence. The results show that, compared to the official model, pupils are very satisfied. In fact, the proposed new model intelligibility frame facilitates the linking of the concept of space of reality, with those of registers and frames. The pupils’ performance amounted to 65.33% in the development of the analytical model of the radioactive decay law, while in terms of suitable applications, pupil performance ranged from 0% to 75%. This result is partly due to the collaborative work, which induced a very significant increase in pupil performance. They were observed between increases ranging from 33.3% to 69.5%. In fact, we attribute these good performances to the ICT resources’ mobilization, specifically SimulP200, the one that we have exclusively elaborated. These resources have also mitigated the difficulties of the experiment, and those related to the processes of elaboration of different radioactive decay law model.

Rate of convergence of the Nesterov accelerated gradient method in the subcritical case α ≤ 3

2019 ◽  
Vol 25 ◽  
pp. 2 ◽  
Author(s):  
Hedy Attouch ◽  
Zaki Chbani ◽  
Hassan Riahi
Keyword(s):  
Rate Of Convergence ◽  
Gradient Method ◽  
Similar Rate ◽  
Convergence Properties ◽  
Subcritical Case ◽  
Continuous Version ◽  
One Dimensional ◽  
Convex Minimization Problems ◽  
Accelerated Gradient ◽  
The One

In a Hilbert space setting ℋ, given Φ : ℋ → ℝ a convex continuously differentiable function, and α a positive parameter, we consider the inertial dynamic system with Asymptotic Vanishing Damping (AVD)α     ẍ(t) + α/tẋ(t) + ∇Φ(x(t)) = 0. Depending on the value of α with respect to 3, we give a complete picture of the convergence properties as t → +∞ of the trajectories generated by (AVD)α, as well as iterations of the corresponding algorithms. Indeed, as shown by Su-Boyd-Candès, the case α = 3 corresponds to a continuous version of the accelerated gradient method of Nesterov, with the rate of convergence Φ(x(t)) − min Φ = O(t−2) for α ≥ 3. Our main result concerns the subcritical case α ≤ 3, where we show that Φ(x(t)) − min Φ = O(t−⅔α). This overall picture shows a continuous variation of the rate of convergence of the values Φ(x(t)) − minℋ Φ = O(t−p(α)) with respect to α > 0: the coefficient p(α) increases linearly up to 2 when α goes from 0 to 3, then displays a plateau. Then we examine the convergence of trajectories to optimal solutions. As a new result, in the one-dimensional framework, for the critical value α = 3, we prove the convergence of the trajectories. In the second part of this paper, we study the convergence properties of the associated forward-backward inertial algorithms. They aim to solve structured convex minimization problems of the form min {Θ := Φ + Ψ}, with Φ smooth and Ψ nonsmooth. The continuous dynamics serves as a guideline for this study. We obtain a similar rate of convergence for the sequence of iterates (xk): for α ≤ 3 we have Θ(xk) − min Θ = O(k−p) for all p < 2α/3, and for α > 3 Θ(xk) − min Θ = o(k−2). Finally, we show that the results are robust with respect to external perturbations.

Modified δ expansion for nonlinear problems

1991 ◽  
Vol 435 (1893) ◽  
pp. 129-136 ◽  
Keyword(s):  
Nonlinear Term ◽  
Order Approximation ◽  
Nonlinear Problems ◽  
Expansion Method ◽  
Zero Order ◽  
Convergence Properties ◽  
Stationary Schrödinger Equation ◽  
One Dimensional ◽  
Zero Order Approximation ◽  
The One

A recently proposed perturbative technique called the δ expansion is modified to improve the convergence properties of the method considerably. The expansion method consists of replacing a nonlinear term like Φ 2 p by ℋ ( Φ/ℋ ) 2(1+ δ ) and then treating δ as a small parameter where ℋ is used to construct a suitable zero-order approximation. It is shown that excellent numerical results are obtained by starting with a properly chosen ℋ . The approach is applied to a zero-dimensional field theory and to the solution of the one-dimensional stationary Schrödinger equation.

Sign in / Sign up

Export Citation Format

Share Document