Muhammad Kabil Djafar, La Ode Safiuddin, Lilis Laome
et al.
This paper discusses about arc length of circles that connected any two points on a sphere. On a sphere, there are infinitely many circles that connect any two points. Using a monotone sequence of functions, we can show that the shortest arc length of circle that connect any two points on sphere is the circle with its center at the origin.
If we go through the literature, one can find many matrices that are derived for a given simple graph. The one among them is the anti-adjacency matrix which is given as follows; The anti-adjacency matrix of a simple undirected graph $G$ with vertex set $V (G) \,= \,\{\,v_1,\,v_2,\\ \dots, v_n\}$ is an $n \times n$ matrix $B(G) = (b_{ij} )$, where $b_{ij} = 0$ if there exists an edge between $v_i$ and $v_j$ and $1$ otherwise. In this paper, we try to bring out an expression, which establishes a connection between the anti-adjacency matrices of the two graphs $G_1$ and $G_2$ and the anti-adjacency matrix of their tensor product, $G_1 \otimes G_2$. In addition, an expression for the anti-adjacency matrix of the disjunction of two graphs, $G_1\lor G_2$, is obtained in a similar way. Finally, we obtain an expression for the anti-adjacency matrix for the generalized tensor product and generalized disjunction of two graphs. Adjacency and anti-adjacency matrices are square matrices that are used to represent a finite graph in graph theory and computer science. The matrix elements show whether a pair of vertices in the graph are adjacent or not.
M. Fikar Papalia, Solimun Solimun, Nurjannah Nurjannah
The assumption of normality is often not fulfilled, this causes the estimation of the resulting parameters to be less efficient. The problem with assuming that normality is not satisfied can be overcome by resampling. The use of resampling allows data to be applied free of distributional assumptions. In this study, a research simulation was carried out by applying Jackknife resampling and Double Jackknife resampling in path analysis with the assumption that the normality of the residuals was not fulfilled and the number of resampling was set at 100 with the degree of closeness level of relationship between variables consisting of low closeness, medium closeness, and high closeness. Based on the simulation results, resampling with a power of 100 can overcome the problem of unfulfilled normality assumptions. In addition, the comparison of the relative efficiency level of the resampling jackknife and double jackknife in the path analysis obtained by the resampling double jackknife has more efficiency than the resampling jackknife
In this paper, we find the best proximity point in G-metric spaces for G-generalized ζ-β-T contraction mappings and verify the existence and uniqueness of the best proximity point in the complete G metric space using the idea of an approximatively compact set. In addition, an example is provided to illustrate the outcome.
The work reported in this article studies the equivalence relationship between fractional integral equation and Ψ-Hilfer Hybrid Langevin Differential Equations of fractional order with nonlocal initial conditions, and then we use this relationship to establish the existence of the results by means of Banach algebra and Schauder’s fixed point theorem. We then demonstrate the uniform local attractiveness of all the solutions.
Experiments on the living environment of vertebrate ecosystems, it has been shown that predators have a massive influence on the demographic growth rate of prey. The proposed fear effect is a mathematical model that affects the reproductive growth rate of prey with the Holling Type I interaction model. Mathematical analysis of the prey-predator model shows that a strong anti-predator response can provide stability for prey-predator interactions. The parameter area taken will be shown for the extinction of the prey population, the balance of population survival, and the balance between the prey birth rate and the predator death rate. Numerical simulations were given to investigate the biological parameters of the population (birth rate, natural mortality of prey, and predators). Another numerical illustration that is seen is the behavior of prey which is less sensitive in considering the risk of predators with the growth rate of prey.
Ahmed CHABLI, Youssef El Madhi, Abdelmounim Qarbous
et al.
Abstract. The study of the epistemological obstacles linked to the teaching of geology at Moroccan middle schools has been the subject of numerous studies in science teaching. All the studies show that students come to class with personal conceptions, which, in most cases, constitute obstacles to the acquisition of geological concepts. The present work aims initially to highlight these obstacles in Moroccan students of the third year of middle school in five topics in geology appearing in the official program of Life and Earth Sciences of the school level concerned. The methodology used is based on a questionnaire sent to a sample of 230 pupils and interviews conducted with 30 pupils on the same themes of the questionnaire. The results obtained show that most students present essentially three epistemological obstacles that oppose the acquisition of scientific knowledge in geology: the obstacle of the first experience, the verbal obstacle, and the obstacle of general knowledge. Subsequently, we suggest some solutions to teachers to overcome this problem and deal with these epistemological obstacles related to geology’s teaching.
Dengue Hemorrhagic Fever (DHF) is a dangerous disease transmitted by the Dengue virus. In 2020, along with the occurrence of the Covid-19 pandemic in Indonesia, the number of dengue cases in Indonesia was high. One of the provinces recorded as the highest suspected dengue fever area is North Sumatra. This is evidenced in October 2019 North Sumatra became the province with the highest suspected dengue fever in Indonesia with a total of 250 cases. Based on the medical record data of patients with DHF at the Dr. Pirngadi General Hospital, Medan in 2019, the factors thought to affect the rate of survival of DHF patients were age, gender, platelet count, and hematocrit levels. Furthermore, survival analysis was carried out using the Kaplan-Meier method and Cox Proportional Hazard Regression with the suspected factors to determine the estimated survival function for patients with DHF and to determine the factors that affect the recovery rate of patients with DHF. Based on the survival function curve, it was found that the curve decreased slowly because many patients with DHF were censored and it was found that the chances of survival of patients with DHF were relatively high, ranging from 1 to 0.6352. Based on the selection of the best model, it was found that only the age variable had a significant effect on the model.
This review paper discusses advances of statistical inference in modeling extreme observations from multiple sources and heterogeneous populations. The paper starts briefly reviewing classical univariate/multivariate extreme value theory, tail equivalence, and tail (in)dependence. New extreme value theory for heterogeneous populations is then introduced. Time series models for maxima and extreme observations are the focus of the review. These models naturally form a new system with similar structures. They can be used as alternatives to the widely used ARMA models and GARCH models. Applications of these time series models can be in many fields. The paper discusses two important applications: systematic risks and extreme co-movements/large scale contagions.
Some aspects of the brain change volume at a fairly constant rate across the life span, i.e., linear maturation rate with respect to age, whereas other aspects of the brain change volume at different rates for younger vs. older age ranges, i.e., non-linear changes. Various forms of non-linear maturation likely reflect different biological mechanisms such that theoretical distinctions between maturation patterns ought to be considered. Simulated data with known maturation patterns and a single critical age characterizing a qualitative change in maturation were used to establish the validity of a non-parametric fitting method, the smoothing spline, combined with processing steps for determining the form of the pattern and the associated critical age. Multiple classes of models were assessed, including model-free, bottom up approaches. Three categories of maturation patterns were explored: U-shaped, with a change in direction; sigmoidal, with an isolated period of change; accelerating, with changes in amplitude but not direction. As noise is a limiting factor in curve fitting, smoothing splines were fit to data with idealized low and realistic noise levels. The smoothing spline was shown to contain the relevant information to extract the critical ages of all maturation patterns in the form of derivative zero points, but the previously proposed method of using third derivative zero points worked only for the accelerating category. Therefore, an additional classification step was included to first determine the category of maturation pattern. Classification accuracy and identification of the calculated critical age within 5 years of the actual critical age was found to be perfect for low noise and high for realistic noise levels. To demonstrate the applicability of the method, a reevaluation of published biological data previously analyzed using third derivative zero points to determine critical ages was carried out for 17 aspects of MRI scans from 1,100 subjects. For a majority of non-linear areas, new critical ages were identified. Further modifications to the analysis procedure could include a wider set of maturation patterns and the inclusion of multiple critical ages to help determine distinctions between brain areas in the timing of developmental or degenerative events that influence their volume.
Concentration inequalities have been the subject of exciting developments during the last two decades, and have been intensively studied and used as a powerful tool in various areas. These include convex geometry, functional analysis, statistical physics, mathematical statistics, pure and applied probability theory, information theory, theoretical computer science, learning theory, and dynamical systems. Concentration of Measure Inequalities in Information Theory, Communications, and Coding focuses on some of the key modern mathematical tools that are used for the derivation of concentration inequalities, on their links to information theory, and on their various applications to communications and coding. In addition to being a survey, this monograph also includes various new recent results derived by the authors. This third edition of the bestselling book introduces the reader to the martingale method and the Efron-Stein-Steele inequalities in completely new sections. A new application of lossless source coding with side information is described in detail. Finally, the references have been updated and ones included that have been published since the original publication. Concentration of Measure Inequalities in Information Theory, Communications, and Coding is essential reading for all researchers and scientists in information theory and coding.
Tasadduq Niaz, Khuram Ali Khan, Dilda Pecaric
et al.
In this work, we estimated the different entropies like Shannon entropy, Renyi divergences, Csiszar divergence by using the Jensen’s type functionals. The Zipf’s mandelbrot law and hybrid Zipf’s mandelbrot law are used to estimate the Shannon entropy. Further the Taylor one point and Taylor two points interpolations are used to generalize the new inequalities for m-convex function.