In 2021 Almetwally introduced a new lifetime distribution named theodd Weibull inverted Topp-Leone (OWITL) distribution. In this note we study oneof the important characteristics “saturation” of this new cumulative function to thehorizontal asymptote with respect to Hausdorff metric as we prove some estimates. Inadditional we consider a new adaptive model with “polynomial variable transfer”. Theapplicability of the model is proved in simulation study to “COVID-19 data”. Somenumerical examples and software modules within the programming environment CASMATHEMATICA are presented.
In this paper we improve the efficiency of the simple matrix-multiplicationalgorithm using parallelism and hardware instrinsics with C# and .Net Task ParallelLibrary. We demonstrate how additional processing can result the overall shorterexecution times. We present an algorithm in C# that achieves up to five times performanceimprovement on midrange hardware, using single-instruction-multiple-datainstructions and unsafe code foo direct access to memory where other techniques arenot possible in the .Net managed environment.
Our research is a natural continuation of previous results in [1]. Theideas given in [1] can be extended for other models of SIRD-type. From a method-ological point of view, we recommend the specialists working in this scientific field tostudy the possibility of using input functions lambda(t) and k_d(t) of polynomial type (forthe MSIRD model [2]). A similar modifications are proposed for the modified modelproposed in [3]. The specialists working in the field of ”reaction-kinetic mechanisms”have the word. Numerical examples, illustrating our results are given using CAS Math-ematica.
In this note we study properties of some inverted cumulative distri-bution functions (CDFs). More precisely, we prove estimates for the “saturation” –d about Hausdorff metric using two–parameters generalized inverted exponential c.d.f.The technique used can be successfully applied to other commonly used CDFs in prac-tice. We consider also modified families of adaptive functions with “polynomial variabletransfer” with applications to the Antenna–feeder Analysis. Numerical examples, illus-trating our results using CAS MATHEMATICA are given.
Ricci-like solitons with potential Reeb vector field are introduced and studied on almost contact B-metric manifolds. The cases of Sasaki-like manifolds and torse-forming potentials have been considered. In these cases, it is proved that the manifold admits a Ricci-like soliton if and only if the structure is Einstein-like. Explicit examples of Lie groups as 3- and 5-dimensional manifolds with the structures studied are provided.
In this article we study properties of a generalized G family of cu-mulative distribution functions (CDFs) proposed by Altun et all. [1]. More precisely,we prove estimates for the ”saturation” - d about Hausdorff metric. The techniqueused can be successfully applied to other commonly used CDFs in practice. Also weconstruct and study families of recurrence generated adaptive functions based on theG–family. We consider modified families of adaptive functions with ”polynomial vari-able transfer” with applications to the Antenna–feeder Analysis. Numerical examples,illustrating our results using CAS MATHEMATICA are given.
The recent paper presents automatic retrieval of publicly available in-formation about products on the Internet, analysis and aggregation of this informationand sending the relevant notifications to the users. A Telegram bot has been deve-loped, which periodically checks the information for certain products and analyzes theretrieved data. This saves customers periodic visits to online stores. A number of com-mands have been developed and integrated in the bot that can be used by the users.We give examples of using the developed application for retrieving information aboutproduct availability, increasing or decreasing price, product reviews, posting new adson sales sites. Due to the lack of a unified standard for presenting product informationin e-commerce, it was necessary to develop adapters for each site. The application isbased on techniques for web data extraction, microservices and cron jobs. Possibilitiesfor further development of the presented application are also considered.A
In this article we study some general classes of trigonometric cumulative distribution functions.We consider also modified families of ''adaptive functions'' with ''polynomial variable transfer'' with applications to the Antenna--feeder Analysis.We study the ''saturation'' - $d$ in the Hausdorff sense for some special cases of the families.Numerical examples, illustrating our results using {\it CAS MATHEMATICA} are given. Numerical examples using {\it CAS Mathematica}, illustrating our results are given.
The current state of available software tools for near-rings over finitecyclic groups is such that the final steps of the research into new theorems that describegroups of these near-rings must be done manually. We propose an approach and havedeveloped an algorithm for automatically matching groups of near-rings over finitecyclic groups to already existing theorems. Additional parts of the developed softwaremodule filter out the already described near-rings and group the remaining ones intobatches of items with similar or same dependencies between the elements inside them.The final step is outputting these groups into a human-readable format, which aidsmathematicians’ investigation into new theorems and hypotheses.
In this article we study some general classes of trigonometric cumu-lative distribution functions with baseline inverted exponential (cdf). We consideralso modified families of ”adaptive functions” with ”polynomial variable transfer” withapplications to the Antenna–feeder Analysis. We study the ”saturation” - d in theHausdorff sense for some special cases of the families. Numerical examples, illustratingour results using CAS MATHEMATICA are given.Numerical examples using CAS Mathematica, illustrating our results are given.
In this article we study some general classes of trigonometric cumulative distribution functions.We consider also modified families of ''adaptive functions'' with ''fractional linear correction''.Here we will also focus on a hypothetical adaptive function, which we will call the ''difference adaptive function'' (DAF).We study the ''saturation'' - $d$ in the Hausdorff sense for some special cases of the families.Numerical examples, illustrating our results using CAS MATHEMATICA are given.
Difference equations with a special type of delay is studied. Thistype of delay is characterized by the maximum value of the unknown function onthe past time interval with a constant length. It is studied the exponential stability.Some sufficient conditions are theoretically proved and computer simulated on severalexamples. The influence of the type of the coefficients is illustrated.
In the present article is considered a modification of the classicalLotka–Volterra model. The ’input functions alpha(t) and gamma(t) are algebraic polynomi-als of degree n, alpha(t) is monotonically increasing (with ”saturation”) and gamma(t) > 0 ismonotonically decreasing in the considered interval. This model is very sensitive withrespect to the coefficients of the polynomials ai and bi. Therefore it is attractive forconducting computer simulations, including other modified predator-prey models andactivator-inhibitor mechanisms. Numerical examples, illustrating our results are givenusing CAS Mathematica.
Training is an incremental process involving slow and methodicalachievement of small goals over a given period. Each step in the process involvesthe assimilation of matter by accepting a set of errors, the correction of which leadsto the improvement of knowledge and deeper understanding of the problem area andmatter as a whole. The classical learning approach, where the facilitator is part of the learning processand has the technical ability to test the work of trained agents, allows for easy andeffective classification of a set of errors to serve as the basis for changing and improvingthe material. One major disadvantage of the e-learning is that the process supervisordoes not have this ability due to the lack of real-time action as well as the large scaleof those training sessions. In this article, we will look at a mechanism for classifying a set of errors usedin the UniPlayground project to categorize the behavior of trained agents based ontheir omissions, errors, or failure to conform to the particulars of the course material.The article examines learning in the context of programming courses and softwaredevelopment.
One of the main tasks of modern education is to form in studentsthe knowledge and competencies applicable in different fields, to increase their interestin learning, to form and develop their cognitive motivation. The variety of appliedteaching methods has a strong motivating potential in this respect, with an emphasison interactive teaching methods in a digital environment. This article presents somepedagogical strategies for development of various cognitive skills for learners. Differentmethodological approaches to learning through the application of innovative educa-tional tools are discussed. The advantages they offer in the learning process are pointedout. In the research we focus on pedagogical approaches, which create conditions forprovoking students’ thinking, for free expression of opinions and defense of one’s ownposition, for provoking creative thinking rather than reproduction of information.
In this article we study the Hausdorff approximation of the Haarscaling function by sigmoidal scaling functions. We prove upper and lower estimatesfor the value of the Hausdorff distance d. A simple dynamic software module usingCAS Mathematica and Wolfram Cloud Open Access is developed. Numerical examplesare given to illustrate our results.
Generalized Mittag-Leffler stability of neural networks modeled by anonlinear Caputo fractional differential equations with baounded delay and impulses isstudied. We study the case whenn the lower limit of the Caputo derivative is equal tothe impulsive time point, i.e. it is changeable.
In this note we study some properties of an new inverse Weibull cu-mulative function proposed by Afify, Shawky and Nassar [1]. More precisely, we proveestimates for the ”saturation” - d about Hausdorff metric. A new activation functionsare defined. We consider also modified families of functions with ”polynomial vari-able transfer” with applications to the Antenna–feeder Analysis. Numerical examples,illustrating our results using CAS MATHEMATICA are given.
Verhulst model [1] makes an extensive use of the logistic sigmoidal function S(t) = a 1+e . Studying ”Canteloup growth”, Pearl et al. [2]–[3] empirically found that one should generalized the logistic map in order to reproduce better the data. We consider a new class of growth curves, generated by reaction networks, based on the insertion of ”correcting amendments” of polynomial–type: M(t) = 1 1+e (t) where F (t) = ∑n i=0 ait . We will call this family the ”Verhulst curve of growth with polynomial variable transfer” (VCGPVT). The new coronavirus [29], SARSCoV-2, is the reason for a new disease, Covid-19. As of 22th February, there have been more than 77,977 cases, including 54,298 laboratory confirmed cases. There have been 2,366 deaths [28]. Below we look at some comparisons between the Verhulst model and the new model (VCGPVT), as well as the ability to approximate specific population dynamics data, including ”Data Corona Virus”. Some numerical examples with real data, using CAS MATHEMATICA illustrating our results are given. AMS Subject Classification: 41A46
The paper deals with integral variants of a seven-point triangular finiteelement. This is an enriched quadratic element constructed by adding a non-negativebasis bulb-function which vanishes on the element boundary. The polynomial spacewhich seven-point element uses is P 2 + span{x 2 y + xy 2 }. The main goal here is to determine two-sided bounds of eigenvalues for a second-order elliptic operator. The method consists of finite element solving of the problemby means of seven-point conforming element and then constructing an nonconforminginterpolant of the approximate conforming eigendunctions. Thus, solving only oncethe eigenvalue problem, we get upper and lower bounds for the exact eigenvalues.Furthermore, the fact that the nonconforming interpolants uses the nodal values of theconforming approximate eigenfunctions gives an obvious computational advantage.Finally, numerical experiments confirming the efficiency of the proposed algorithmare also provided.
