International Journal of Mathematics and Mathematical Sciences

Fitting a time series model to the process data before applying a control chart to the residuals is essential to fulfill the basic assumptions of statistical process control (SPC). Autoregressive integrated moving average (ARIMA) model has been one of the well-established time series modeling approaches that is extensively used for this purpose and is widely recognized for its accuracy and efficiency. Nevertheless, the research community commented that its iterative stages are laborious and time-consuming. In addressing this gap, a novel time series modeling technique with its conceptual assumptions of attributes that was derived from the geometric Brownian motion (GBM) law was developed in this study. It was termed as the logarithmic return (LR) model. Then, the model was employed and tested on a real-world autocorrelated data, whereby the results were assessed and benchmarked with the ARIMA model. The findings for LR model reported a mean average percentage error that ranged between 1.5851% and 3.3793% (less than 10%), which were as accurate as the ARIMA model. The running time (in second of CPU time) taken by the LR model was at least 96.2% faster than the ARIMA model. Interestingly, the corresponding multivariate control chart constructed from the LR model also portrayed a similar general conclusion as that of its counterpart. The LR model was obviously parsimonious and easier to compute and took a shorter running time than the ARIMA model. Therefore, it possessed the potential as an alternative time series modeling methodology for the ARIMA model in the procedures of SPC.

The article describes a new thought on the chromatic polynomial of an intuitionistic fuzzy graph which is illustrated based on -level graphs. Besides, the alpha-beta fundamental set of an intuitionistic fuzzy graph is also defined with a vivid description. In addition to that, some characterizations of the chromatic polynomial of an intuitionistic fuzzy graph are specified as well verified. Furthermore, some untouched properties of the -level graph are also projected and proved.

The concept of state has been considered in commutative and noncommutative logical systems, and their properties are at the center for the development of an algebraic investigation of probabilistic models for those algebras. This article mainly focuses on the study of the lattice of state ideals in De Morgan state residuated lattices (DMSRLs). First, we prove that the lattice of all state ideals of a DMSRL is a coherent frame. Then, we characterize the DMSRL for which the lattice is a Boolean algebra. In addition, we bring in the concept of state relative annihilator of a given nonempty subset with respect to a state ideal in DMSRL and investigate various properties. We prove that state relative annihilators are a particular kind of state ideals. Finally, we investigate the notion of prime state ideal in DMSRL and establish the prime state ideal theorem.

In this paper, we discuss a well known class studied by Ramesha in 1995 and later by Janteng in 2006, and we then extend the class to a wider class of functions denoted by which are normalized and univalent, in the unit disk satisfying the condition where is analytic function in , such that , with a new condition that is introduced. The main purpose of this paper is to give an estimate for the same when belongs to the class .

We fully describe the envelope of all line segments that divide the perimeter of a triangle into the ratio as varies from 0 to . If is larger than the ratio of the longest side length to the perimeter, then the envelope is a 12-sided closed curve consisting of six line segments and six parabolic arcs. For other values of , the envelope is the union of one to three parabolic arcs and possibly a 5- or 9-sided nonclosed curve consisting of line segments and parabolic arcs.

In this paper, we propose a new method for estimating trends in extreme spatiotemporal processes using both information from marginal distributions and dependence structure. We combine two statistical approaches of an extreme value theory: the temporal and spatial nonstationarities are handled via a tail trend function in the marginal distributions. The spatial dependence structure is modeled by a latent spatial process using generalized -Pareto processes. This methodology for trend analysis of extreme events is applied to precipitation data from Burkina Faso. We show that a significant increasing trend for the 50 and 100 year return levels in some parts of the country. We also show that extreme precipitation is spatially correlated with distance for a radius of approximately 200 km.