Application of GM (1,1) and EXGM (1,1) forecasting models to Turkey's research and development expenditures

Disiplinler arası bir bilim alanı olan Gri sistem Teorisi az sayıda veri kullanarak bilinmeyen sistemlerin davranışını tahmin etmektedir ve birçok alana başarı ile uygulanmıştır. Bu çalışmada ise Gri Sistem Teorisi Türkiye’nin Araştırma ve Geliştirme (Ar-Ge) harcamalarını tahmin etmek için kullanılmıştır. 2011-2020 yılları arasındaki Ar-Ge harcamaları verileri Türkiye İstatistik Kurumu’ndan alınarak 2021-2030 yıllarının tahmini Standart Gri Model (GM (1,1)) ve Üstel Gri Model (EXGM (1,1)) kullanılarak yapılmıştır. Her iki modelin tahmin değerlerindeki hata ve korelasyon sonuçları karşılaştırılmıştır. 2011-2020 yılları arasındaki verileri kullanarak, gerçek ve tahmin değeri arasındaki yüzde bağıl hata (RPE) ve ortalama yüzde bağıl hata (MAPE) belirlenmiştir.Grey system theory, which is an interdisciplinary field of science, predicts the behaviour of unknown systems using a small amount of data and has been successfully applied to many fields. In this study, the Grey System Theory is used to estimate Turkey's Research and Development (R&D) expenditures. Turkey's R&D expenditure datas were taken from the Turkish Statistical Institute for the years 2011-2020 and estimated for the years 2021-2030 using Standard Gray Model (GM (1,1)) and Exponential Gray Model (EXGM (1,1)). The error and correlation results in the prediction values of both models were compared. The percentage relative error (RPE) between the actual and predicted values and mean absolute percentage error (MAPE) were determined using the data from 2011-2020

Application of Fractional SPRSPR Psychological Disease Model in Turkey and Stability Analysis

Psychological diseases and their treatment are problems related to public health. According to data from the World Health Organization, about a billion people have either mental illness or substance use disorder problems in 2017. Mental, neurological diseases and substance use disorders account for 30 percent of the global non-fatal disease burden and 10 percent of the global disease burden. It is noted that in the world Dec 2005 and 2015, the incidence of mental health diseases increased by about 16 percent. In this study, we have created a fractional-order mathematical modeling for the population of individuals suering from psychological diseases in a society. In this model, the total population was divided into three compartments: individuals who did not receive psychological treatment (S), individuals who received psychological support (P) and individuals who recovered after completing psychological treatment (R). As a fractional derivative, we used the Caputo derivative definitions. Numerical solutions were obtained with the help of Euler method by performing stability analysis related to the fractional SPR model created for the mathematical model of psychological patients. Thus, it was interpreted by creating dynamics for the number of individuals with psychological problems in a population

An application of khuri’s biorthogonality condition on stokes flow in a rectangular cavity

The paper present a different semi-analytical solutions for the Stokes flow in a rectangular cavity by using the biorthogonality condition of the eigenfunctions. Firstly, the biorthogonality condition for rectangular cavity is applied on Stokes Flow problem. Secondly, the biorthogonality condition and the new solution is verified against results available in the literature. Further, it has been found that this solution mechanism is effi cient and it can be successfully used to obtain flow structures and bifurcations

New grey forecasting model with its application and computer code

Grey theory is an approach that can be used to construct a model with limited samples to provide better forecasting advantage for short-term problems. In some cases, a grey forecasting model may yield unacceptable forecasting errors. In this work, a new exponential grey prediction model, which is called as EXGM (1,1), is proposed. By using this model, new cases, deaths and recovered cases of COVID-19 in Turkey is forecast. Numerical results show that EXGM (1,1) is a model that performs more accurately than the comparison models

Effect of the Reynolds number on flow bifurcations and eddy genesis in a lid-driven sectorial cavity

WOS: 000379036300003This paper presents the two-dimensional (2D) steady incompressible flow in a lid-driven sectorial cavity. In order to analyze the flow structures, the 2D Navier-Stokes equations are solved by using the finite element method. Different cases of the cavity aspect ratio A and three cases of the speed ratios of the upper and the lower lids are considered. The finite element formulation for the governing equations is adopted via the velocity-pressure formulation. By varying A for each S, the effect of the Reynolds number on the streamline patterns and their bifurcations are investigated in range . A comparison between the obtained results and some earlier studies is presented

Bifurcations and eddy genesis of Stokes flow within a sectorial cavity

This work analyzes the Stokes flow generated in a sectorial driven cavity formed by a pair of curved stationary side walls capped by straight translating lids

Gri modelleme ile Türkiye sağlık sektöründe harcamaların matematiksel tahmini

Grey theory is an effective theory that deals with systems that lack weak information and / or information. With this theory, effective and very accurate estimates can be created for future times by utilizing a small number of data. The grey modeling method is a sub-branch of the theory of grey systems and the modeling process is carried out with the help of differences equations and differential equations. The least squares approach plays a role in the precise results of the method. Using the GM (1,1) modeling method, which is the basis of grey prediction models with its accuracy and usefulness, health expenditures in Turkey that will be achieved in the coming years were estimated.These estimates are particularly useful for health and economic policies.Gri teorisi, zayıf bilgi ve / veya bilgi içermeyen sistemlerle ilgilenen etkili bir teoridir. Bu teoriyle, az sayıda veri kullanılarak gelecek zamanlar için etkili ve çok doğru tahminler oluşturulabilir. Gri modelleme yöntemi, gri sistem teorisinin bir alt dalıdır ve modelleme işlemi, denklemler ve diferansiyel denklemler yardımıyla gerçekleştirilir. En küçük kareler yaklaşımı, yöntemin kesin sonuçlarında rol oynar. Gri tahmin modellerinin temeli olan GM (1,1) modelleme yönteminin doğruluğu ve kullanışlılığı ile Türkiye’de önümüzdeki yıllarda sağlanacak sağlık harcamaları tahmin edilmiştir. Bu tahminler özellikle sağlık ve ekonomi politikaları için faydalıdır

An optimized continuous fractional grey model for forecasting of the time dependent real world cases

The new priority in the grey modelling is to build new models that have more accurate forecasting power than the previous ones. This paper aims to develop the prediction performance of the existing continuous grey models. Therefore, a novel continuous grey model (OCCFGM(1,1)) is proposed with conformable fractional derivative. The numerical results of three case studies show that the novel model's prediction accuracy is higher than other competitive models, and the proposed model is more reasonable for practical cases

Optical soliton solutions for the variable coefficient modified Kawahara equation

WOS: 000365457700056In this paper, we obtain the 1-soliton solutions of the variable-coefficient modified Kawahara equation (VCMKE). The dark optical as well as bright optical soliton solutions were found related to the model considered in this study. The solitary wave ansatz method is used to carry out the integration

Analytical solution and flow topology in a lid-driven S-shaped cavity

In this study, the Stokes flow problem in an S-shaped double lid-driven cavity filled with fluid was analyzed. Side edges of the cavity were considered as immovable walls. The flow region was divided into two sub-regions, and the streamfunction in each sub-region was considered as an extension of Papkovich-Faddle eigenfunctions. Parameters in the analytical solution were obtained using biorthogonality conditions. The Newton iteration method was used to obtain the eigenvalues of the problem, and integrals were calculated with the Gaussian quadrature method. It was ensured that solutions made separately for the two sub-regions converge on the interface, which is the intersection of these sub-regions. The two parameters controlling the flow structure were determined as the speed ratio of movable lids (S) and the aspect ratio of the cavity (A). The effects of these parameters on flow structures were shown. New eddy formation mechanisms and bifurcations were observed in the cavity by keeping the speed ratio of the lids constant and slowly changing the aspect ratio