Threshold dynamics type approximation schemes for propagating fronts

Upon prior investigation on statistical convergence of fuzzy sequences, we study the notion of pointwise ??-statistical convergence of fuzzy mappings of order ?. Also, we establish the concept of strongly ??-summable sequences of fuzzy mappings and investigate some inclusion relations. Further, we get an analogue of Korovkin-type approximation theorem for fuzzy positive linear operators with respect to ??-statistical convergence. Lastly, we apply fuzzy Bernstein operator to construct an example in support of our result.

Download Full-text

Improvement Dependability of Offshore Horizontal-Axis Wind Turbines by Applying New Mathematical Methods for Calculation the Excess Speed in Case of Wind Gusts

Energies ◽

10.3390/en14113085 ◽

2021 ◽

Vol 14 (11) ◽

pp. 3085

Author(s):

Konstantin Osintsev ◽

Seregei Aliukov ◽

Alexander Shishkov

Keyword(s):

Computer Simulation ◽

Wind Turbines ◽

Experimental Studies ◽

Offshore Wind ◽

Approximation Schemes ◽

Calculation Error ◽

Strong Wind ◽

Mathematical Methods ◽

Wind Gusts ◽

Gas Dynamic

The problem of increasing the reliability of wind turbines exists in the development of new offshore oil and natural gas fields. Reducing emergency situations is necessary due to the autonomous operation of drilling rigs and bulk seaports in the subarctic and Arctic climate. The relevance of the topic is linked with the development of a methodology for theoretical and practical studies of gas dynamics when gas flows in a pipe, based on a mathematical model using new mathematical methods for calculation of excess speeds in case of wind gusts. Problems in the operation of offshore wind turbines arise with storm gusts of wind, which is comparable to the wave movement of the gas flow. Thus, the scientific problem of increasing the reliability of wind turbines in conditions of strong wind gusts is solved. The authors indicate a gross error in the calculations when approximating through the use of the Fourier series. The obtained results will allow us to solve one of the essential problems of modeling at this stage of its development, namely: to reduce the calculation time and the adequacy of the model built for similar installations and devices. Experimental studies of gas-dynamic flows are carried out on the example of a physical model of a wind turbine. In addition, a computer simulation of the gas-dynamic flow process was carried out. The use of new approximation schemes in processing the results of experiments and computer simulation can reduce the calculation error by 1.2 percent.

Download Full-text

Common Fixed Point and Invariant Approximation Results on Non-Starshaped Domains

Georgian Mathematical Journal ◽

10.1515/gmj.2005.659 ◽

2005 ◽

Vol 12 (4) ◽

pp. 659-669

Author(s):

Nawab Hussain ◽

Donal O'Regan ◽

Ravi P. Agarwal

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Fréchet Spaces ◽

Approximation Theorems ◽

Type Approximation ◽

Invariant Approximation ◽

Commuting Maps

Abstract We extend the concept of 𝑅-subweakly commuting maps due to Shahzad [J. Math. Anal. Appl. 257: 39–45, 2001] to the case of non-starshaped domains and obtain common fixed point results for this class of maps on non-starshaped domains in the setup of Fréchet spaces. As applications, we establish Brosowski–Meinardus type approximation theorems. Our results unify and extend the results of Al-Thagafi, Dotson, Habiniak, Jungck and Sessa, Sahab, Khan and Sessa and Shahzad.

Download Full-text

Threshold Dynamics in a Model for Zika Virus Disease with Seasonality

Bulletin of Mathematical Biology ◽

10.1007/s11538-020-00844-6 ◽

2021 ◽

Vol 83 (4) ◽

Cited By ~ 1

Author(s):

Mahmoud A. Ibrahim ◽

Attila Dénes

Keyword(s):

Zika Virus ◽

Reproduction Number ◽

Virus Disease ◽

Threshold Dynamics ◽

Global Dynamics ◽

Threshold Parameter ◽

Globally Asymptotically Stable ◽

Linear Integral ◽

The Impact ◽

Disease Free

AbstractWe present a compartmental population model for the spread of Zika virus disease including sexual and vectorial transmission as well as asymptomatic carriers. We apply a non-autonomous model with time-dependent mosquito birth, death and biting rates to integrate the impact of the periodicity of weather on the spread of Zika. We define the basic reproduction number $${\mathscr {R}}_{0}$$ R 0 as the spectral radius of a linear integral operator and show that the global dynamics is determined by this threshold parameter: If $${\mathscr {R}}_0 < 1,$$ R 0 < 1 , then the disease-free periodic solution is globally asymptotically stable, while if $${\mathscr {R}}_0 > 1,$$ R 0 > 1 , then the disease persists. We show numerical examples to study what kind of parameter changes might lead to a periodic recurrence of Zika.

Download Full-text

Weak Convergence in Poisson and Lévy Approximation Schemes

10.1002/9781119851257.ch2 ◽

2021 ◽

pp. 57-106

Keyword(s):

Weak Convergence ◽

Approximation Schemes

Download Full-text

A two-dimensional matrix Padé-type approximation in the inner product space

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2009.04.013 ◽

2009 ◽

Vol 231 (2) ◽

pp. 680-695 ◽

Cited By ~ 2

Author(s):

Youtian Tao ◽

Chuanqing Gu

Keyword(s):

Product Space ◽

Inner Product Space ◽

Inner Product ◽

Two Dimensional ◽

Type Approximation ◽

Dimensional Matrix

Download Full-text

DENSE STABLE RANK AND RUNGE-TYPE APPROXIMATION THEOREMS FOR MAPS

Journal of the Australian Mathematical Society ◽

10.1017/s1446788721000045 ◽

2021 ◽

pp. 1-29

Author(s):

ALEXANDER BRUDNYI

Keyword(s):

Disjoint Union ◽

A Priori ◽

Holomorphic Functions ◽

Stable Rank ◽

Open Unit ◽

Uniform Estimates ◽

Approximation Theorems ◽

Type Approximation ◽

Similar Approximation ◽

Bounded Holomorphic

Abstract Let $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ be the Banach algebra of bounded holomorphic functions defined on the disjoint union of countably many copies of the open unit disk ${\mathbb {D}}\subset {{\mathbb C}}$ . We show that the dense stable rank of $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ is $1$ and, using this fact, prove some nonlinear Runge-type approximation theorems for $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ maps. Then we apply these results to obtain a priori uniform estimates of norms of approximating maps in similar approximation problems for the algebra $H^\infty ({\mathbb {D}})$ .

Download Full-text