Journal of Mathematical Extension
Volume:17 Issue: 2, Feb 2023

In the present paper, a flexible skew version of the scale mixture of normal family is introduced based on the transmuted record type, called TRT-SMN, which seems suitable for handling any skewness and kurtosis in real data sets. Several properties of the TRT-SMN family are provided, including the moment generating function and r-th moments. The parameters of the new family are estimated through the ECME algorithm. Further to the elegant properties of the proposed family, the paper considers, in the time series context, a first-order autoregressive process with TRT-SMN distributed innovations. Some Monte Carlo simulation experiments are executed to assess the consistency of the ECME estimates. To further motivate its purpose, the proposed process is applied to analyze the series of COVID-19 incidence in Bavaria. The proposed AR(1) with TRT-SMN innovations yields superior fitting criteria compared to AR(1) process with Gaussian innovations.

In this paper, we dene the notion of the right independent (resp., left independent) subsets of BI-algebras. Some of the properties are investigated and get more results in BI-algebras. Moreover, we consider the notion of the right absorbent (resp., left absorbent) subset. It is proved that in a right distributive BI-algebra X, every right(left) independent subset of X absorbs X from the right. We show that these new concepts are dierent by presenting several examples. The goal and benets of our proposed extension of this study are to extend the theory of BI-algebras, and so we enlarge the eld of research.

Exact fractals are a type of self-similar fractals with a special form of self-affine fractals. Recently, algorithms have been developed to calculate the dimension of such fractals by the box-counting method. In this article, exact fractals will be investigated using the power spectrum method and wavelets. In the used algorithms, we use Daubechies and Symlet wavelets of orders 3 to 8 and show the efficiency of the Kaiser window function in the more accurate calculation of the exact fractal dimension. The comparison of the results obtained by the box-counting method on two types of accurate fractals that have been investigated recently shows that the power spectrum and wavelet method using the Kaiser window filter has higher accuracy.

In this paper, we introduced and studied the properties of weaker form of multifunctions such as upper and lower gp-continuous multifunctions. We obtain their characterizations and preservation the- orems. Further, we have investigated the properties of upper and lower gp-irresolute multifunctions.

This article aims to characterize a new class of simulation functions by extending the class of $\mathcal{Z}$ functions demonstrated by Cho in \cite{ze}, and via this novel notion, to establish some common fixed point theorems in modular $b-$metric spaces. Furthermore, some corollaries, which enlarge previously existing literature, have been procured. In conclusion, an example and an application to the nonlinear integral equations have been presented to state the applicability and validity of our outcomes.

In this paper, we present cost and revenue eciency evalu- ation models and target setting in data envelopment analysis (DEA) in the presence of fuzzy inputs and outputs that the corresponding prices of inputs and outputs are also fuzzy numbers. We proposed a fuzzy value-based technology based on fuzzy input and output data at corre- sponding prices. We provide an approach for calculating fuzzy cost (rev- enue) eciency based on value fuzzy based technology. The proposed fully fuzzy model is transformed into a four-objective model of non-fuzzy linear programming and solved by the weighted sum method. We show that the proposed approach is suitable than the previous approaches based on traditional models from a computational point of view. The innovation of this research is to present and solve a fully fuzzy model to obtain fuzzy cost (revenue) eciency score as a fuzzy number and we do not need additional comparisons to detect the ecient unit in previous approaches. We also obtain benchmark corresponding to the all DMUs. In the following, with two numerical examples, we obtain the results of the presented approach and compare it with the results of the previous approaches, and at the end, we present the results of the research.

In this article, invariant submanifolds of Lorentz-Sasakian space forms on the W₇- curvature tensor are investigated. For the W₇-curvature tensor, the pseudoparallel, 2-pseudoparallel, Ricci generalized pesudoparallel and 2-Ricci generalized pseudoparallel properties of the invariant submanifolds of the Lorentz-Sasakian space form are discussed.

In this paper we make an attempt to prove common fixed point theorem for two and three mappings in Banach algebra by using measure of non-compactness. In the second section of the paper we prove the common fixed point theorem for two continuous linear operators on Banach algebra and also an effort is made to prove common fixed point theorem for three continuous commuting operators in Banach algebra.

Congestion is one of the main problems in economic issues. In fact, congestion is a wasteful step in the production process, where outputs decrease as a result of increasing inputs. In the economy, congestion is important because its elimination reduces the cost and also increases the output. Therefore, there is a great benefit in identifying congestion and reducing it. Since it is difficult to compute congestion for DMUs with interval data, owing to the computational complexity of the existing methods, we first present a new method for computing congestion and then obtain congestion in the case of interval data. It is well known that if DEA inputs and outputs are in the form of intervals, there will be an efficiency interval for each DMU. Since we assume interval data in this paper, we obtain an interval for the amount of congestion possible in each DMU and prove that the interval indicates the upper and lower bounds of congestion for each DMU.

In this paper, the variable order time-fractional diusion equations in a nite domain are considered. A Du Fort-Frankel nite dierence method is introduced to solve these equations. The stability condition for this scheme is discussed and proved via the approach of Fourier analysis. Numerical examples are prepared to illsutrate that the numerical method is computationally ecient.