The number of software failures, software reliability, and failure rates can be measured and predicted by the software reliability growth model (SRGM). SRGM is developed and tested in a controlled environment where the operating environment is different. Many SRGMs have developed, assuming that the working and developing environments are the same. In this paper, we have developed a new SRGM incorporating the imperfect debugging and testing coverage function in the presence of a random environment. The proposed model’s parameters are estimated from two real data sets and compared with some existing SRGMs based on five goodness-of-fit criteria. The results show that the proposed model gives better descriptive and predictive performance than the existing model.

Solving various real-life problems ultimately requires solving systems of linear equations. However, the parameters involved in such real-life problems may be pervaded with uncertainty, which result in fuzzy parameters rather than crisp parameters. Intuitionistic fuzzy parameters are more suitable for some cases since they allow to deal with the feeling of fear or hesitation when making a decision, which are characteristics of human being in applying knowledge and skills. Intuitionistic fuzzy linear system (IFLS) resulting from the real-life problem involves large number of equations and equally large number of unknowns. When IFLS is in matrix-vector form the resulting coefficient matrix will have a sparse structure, which makes iterative methods necessary for their solution. In this paper, the known Gauss-Seidel and SOR iterative methods for solving linear system of equations are discussed, to the best of our knowledge for the first time, to solve (IFLS). The single parametric form representation of intuitionistic fuzzy numbers (IFN) makes it possible to apply these iterative techniques to IFLS. Finally a problem of voltage input output in electric circuit has been considered to show the applicability and the efficiency of these methods.

This article discusses the class of Periodic Generalized Poisson Integer-Valued Generalized Autoregressive Conditional Heteroscedastic (PGPINGARCH) models. The model, in addition to properly capture the periodic feature in the autocovariance structure, encompasses different types of dispersions, with this conditional marginal distribution. The main theoretical properties of this model are developed, in particular, the first two moment periodically stationary conditions, while the closed form of these moments are derived. Moreover, the existence of the higher order moment and their closed forms are established. The periodic autocovariance structure is studied. The estimation is done by the Yule Walker and the Conditional Maximum Likelihood methods and their performance is shown via an simulation study. Moreover, an application on Campylobacteriosis time series is provided, which indicates that the proposed models performs better than other models in the literature.

The aim of this research is to generalize the famous Lyapunov theorem concerning the classical explicit differential systems (Continuous or Discrete) described by two abstract forms: x’(t) = Px(t) or xn+1 = Pxn, where P is an operator or a matrix if the space has finite dimension, in order to study the spectrum of the degenerate differential systems: Ax(t) = Bx(t), for all t≥0. Here A and B are two bounded operators acting in Banach spaces also the operator A is not invertible. Using some properties of the spectral theory for the operator pencil of the corresponding systems which is obtained by substituting x(t) = e^(λt).v into the homogenous above equation, and an appropriate conformal mapping we obtain important results can be applied to study the stabilizability and controllability of certain degenerate controlled systems.

Determining the isothermal and adiabatic nonlinearity parameters of liquids and the soft matter is crucially important for a variety of engineering applications requiring operations under high pressures, nondestructive testing, exploring propagation of finite amplitude and shock waves, etc. It is shown recently [Postnikov et al., J. Mol. Liq. 310 (2020) 113016; Belenkov & Postnikov, . Izv. VUZ. Appl. Nonlin. Dyn. 31 (2023) 1] that mathematically this problem can be reduced to the initial value problem for an ODE built based on the linear response theory for thermodynamic equalities. The required initial conditions should be determined from thermodynamic measurements at ambient pressure (or along the saturation curve). From the physical point of view, the required regression leading to the determining nonlinearity parameters originates from certain regularities in the response of molecular oscillations to the density changes. In this work, we explore, how this regression procedure should be optimised computationally respectively to temperature ranges, which exclude anomalies affecting parameters of equations used for the required predictive calculations under high pressures. The validity of the proposed approach is tested by case studies of the propagation of weakly non-linear waves with finite amplitudes and density changes due to shock waves under the Rankine-Hugoniot jump conditions.

In this paper, we present a two-component Weibull mixture model. An important property is that this new model accommodates bimodality, which can appear in data representing phenomena in some heterogeneous populations. We provide some useful statistical properties, such as quantile function and moments. Also, the Expectation-Maximization (EM) algorithm used to find maximum-likelihood estimates of the model parameters is discussed. Further, a Monte Carlo study is carried out to evaluate the performance of the estimators on finite samples. The new model's relevance is shown with an application referring to vote proportion for the Brazilian presidential elections runoff in 2018. The proportion of votes is an important measure to analyze electoral data, and since it is a variable limited to the unitary interval, unit distributions should be considered to analyze its probabilistic behavior. Thus, the introduced model is suitable for describing the characteristics detected in these data, such as the asymmetric behavior, bimodality, and the unit interval as support. In the application, the superiority of the proposed model is verified when comparing the fit with the two-component beta mixture models.

One of the applicable concepts in metric fixed point theory is the notion of hybrid functional equations. In the same vein, the role of graphs in computational sciences and nonlinear functional analysis is currently well known. However, as duly revealed from the available literature, we understand that hybrid fixed point notions in metric space endowed with graph have not been well considered. In this note, therefore, a general class of contractive inequality, namely admissible hybrid (H-α-ϕ)-contraction is proposed in metric space endowed with a graph and new criteria for which the mapping is a Picard operator are examined. The significance of this type of contraction is connected with the possibility that its inequality can be particularized in more than one way, depending on the provided constants. Relevant examples are designed to support the assumptions of our obtained notions and to show how they are different from the known ones. A corollary which reduces our obtained result to some recently announced results in the literature is pointed out and discussed.

We give a logarithmic estimate in small time for big order generators on a compact manifold. We do a mixture between Malliavin Calculus we got for big order generators and large deviation estimates we got for big order generators. We follow the strategy we have used for diffusion, when there is a stochastic process besides, in order to get logarithmic estimates for hypoelliptic operators under the Hoemander's hypothesis where we were mixing large deviation estimates of Wentzel freidlin estimates (P.T.R.F. 1987)

Target setting and optimal allocation of limited resources are critical for sustainability and competitiveness of organizations. The process of resource distribution and targeting is usually implemented through a central unit that decides for the resources supplied to the subordinate decision-making units (DMUs) along with DMUs lower bounds of desired efficiency. Moreover, the central unit has the authority to set the overall expected output targets so as to maximize the organizational effectiveness. In this paper, we evaluate the efficiency of organizations using a bilevel network data envelopment analysis (DEA) approach in a stochastic framework. The proposed bilevel DEA model with stochastic conditions optimizes centralized resource allocation and target setting imposing lower bounds on the efficiencies of all DMUs belonging to the organization. Consequently, the total input consumption is minimized and the total output production is maximized at the same time while considering additional bounds and availability constraints for inputs. In the stochastic bilevel model, uncertainty is introduced through the upper level (leader) problem that attempts to maximize organizational effectiveness while in the lower level (follower) problem it evaluates the efficiency of the DMUs. A solution methodology for the bilevel network DEA-based model is presented and numerical results are obtained using data from the literature. The obtained results are compared with those published in other case studies for centralized resource allocation DEA models.

In this paper we solve numerically a parabolic-parabolic chemotaxis model with Lokta-Volterra type logistic sources chemotaxis in heterogeneous environments using Deep Neural Network (DNN) based models and study the convergence of numerical solutions to corresponding theoretical solutions and find a priori estimates of predictor error. In addition, we compare our deep learning-based model to the classical numerical methods and obtained similar results. However, the advantages of deep learning-based methods on numerical methods include solutions obtained that are not restricted to the grid points and we can predict the future dynamical behavior of the system.