In this paper, we study the existence of periodic solutions for the following piecewise third-order differential equation:
$$
\dddot{x}+\dot{x}-\varepsilon\sum\limits_{i=1}^{2}c_i|x|^i=0,
$$
with $\varepsilon$ a real parameter sufficiently small, $c_1$ and $c_2$ real numbers. By applying new results from the averaging theory for continuous differential systems, we prove the existence of at most one periodic solution for the differential equation. An example is given to illustrate the established result.
Probabilities. Mathematical statistics, Instruments and machines
According to The Indonesian Earthquake Map, Padang City in West Sumatra is in Earthquake zone 6. This indicates that Padang City is very vulnerable to earthquakes. Meanwhile, developments in the construction of high buildings also continue to show progress all the time. The main problem that is often faced is the issue of structural damage due to earthquakes. Efforts are needed in earthquake engineering on buildings so that collapse can be minimized. The earthquake damping system used is FVD (Fluid Viscous Dampers) with different types. The Type-A damper is FVD-750 kN and the Type-B damper is FVD-1000 kN, and without using a damper. This research aims to analyze the efficiency of reducing earthquake loads such as floor displacement and vibration period of an 18-story building structure 18 meters high from the base.The analysis method used is a numerical method by calculating earthquake load reduction based on numerical error analysis from the two types of dampers used on structures without using dampers. Building planning refers to SNI 1727-2013, SNI 1726-2019, and SNI 2847-2019, and is assisted by ETABS software. Based on SNI 1726-2019, earthquake risk category II, soft soil condition type (SE), earthquake acceleration response value SDS = 0.745g and SD1 = 0.784g are obtained. The earthquake load used is a dynamic load, taking into account that the condition of the building is irregular. Based on the results of the analysis, it was found that the displacement between floors using the Type-AFVD Damper could reduce the displacement by up to 45.72% and with the Type-B FVD Damper it could reduce the displacement by up to 92.72%. Meanwhile, the period of vibration natural using a Type-A FVD Damper can be reduced by up to 12.34% and using a Type-B FVD Damper can be reduced by up to 33.21%.
Norwaziah Mahmud, Nur Syuhada Muhammat Pazil, Nur Syakirah Rosli
et al.
Predicting students' academic performance plays an important role in academics. Mathematics is a science concerned with the logic of shape, quantity, and order. This subject holds a crucial role in the school curriculum. Mathematics is a basic knowledge that students should have the expertise in order for them to score in the other subjects. However, most students find Mathematics a difficult subject, they will have difficulty scoring in this subject. Therefore, this paper aims to determine the factors that affect students’ performance in Mathematics subject which is the pre-calculus subject among students of Diploma in Computer Sciences (CS110) in UiTM Cawangan Melaka Kampus Jasin. During the analysis, gender, assessment marks, place of students, time spent studying pre-calculus subject per week, whether the student took additional mathematics in SPM, act as independent variables whereas grade for pre-calculus subject as the dependent variable, were examined. The assessments refer to test 1, test 2, lab assignment, quiz 1, quiz 2 and written assignment. The logistic regression model was applied, and the results showed that the gender, test 2 and quiz 2 are variables that are significant to the model with the p-value 0.031,0.014 and 0.03 respectively. When examining the variables influencing the academic performance of CS110 students at UiTM Cawangan Melaka Kampus Jasin, there are certain knowledge gaps and restrictions. It is advised that future studies should collect data from more respondents and keep the question simple but clear in order to get more accurate results.
Abdullah Hasan Hassan, Dipo Aldila, Muhamad Hifzhudin Noor Aziz
This study presents a comprehensive analysis of the transmission dynamics of monkeypox, considering contaminated surfaces using a deterministic mathematical model. The study begins by calculating the basic reproduction number and the stability properties of equilibrium states, specifically focusing on the disease-free equilibrium and the endemic equilibrium. Our analytical investigation reveals the occurrence of a forward bifurcation when the basic reproduction number equals unity, indicating a critical threshold for disease spread. The non-existence of backward bifurcation indicates that the basic reproduction number is the single endemic indicator in our model. To further understand the dynamics and control strategies, sensitivity analysis is conducted to identify influential parameters. Based on these findings, the model is reconstructed as an optimal control problem, allowing for the formulation of effective control strategies. Numerical simulations are then performed to assess the impact of these control measures on the spread of monkeypox. The study contributes to the field by providing insights into the optimal control and stability analysis of monkeypox transmission dynamics. The results emphasize the significance of contaminated surfaces in disease transmission and highlight the importance of implementing targeted control measures to contain and prevent outbreaks. The findings of this research can aid in the development of evidence-based strategies for mitigating the impact of monkeypox and other similar infectious diseases.
Hansen Juni Lieus, Devin Tedja, Vanessa Joewita
et al.
Transferring credit risk to an insurance company is a way to mitigate risk. Premiums should be calculated accurately to attain economic value for both the lender and the guarantor. The aim of this study was to determine the net single premium (NSP) values for an unsecured credit insurance product using the expected credit loss (ECL) method from IFRS 9. This study used data generated through simulation of insurance policies issued in 2015 or 2016. Their state classifications were monthly observed from 2016 to 2020. The probability of disbursed claim (PDC) parameter replaced the probability of default parameter on the ECL model, whereas the PDC model was constructed based on the components of a state-transition probability matrix, obtained with the Markov chain approach using the cohort method: = 0.999181, = 0.000130, and = 0.000689. The PDC model validation showed relatively decent results, whereas MSE = 2.457% and zs = 0.608 with a = 5%. These results indicated that the PDC model was a good fit to calculate ECL. 5,000 iterations were done as part of the cash flow simulation process, whereas debtors’ loan amounts were randomly generated during each iteration, and the average NPV of these iterations was -Rp564.419.305. Based on model sensitivity analysis, cash flow values were most sensitive to the variable used to construct the PDC model (). Thus, the 5,000-iteration process was repeated with the newly adjusted PDC value, which were = 0.998924 and = 0.000946. The new average NPV of these iterations was Rp409,877,840, indicating that the constructed ECL model was a good fit to calculate NSP values for unsecured credit insurance products.
In this article, strongly minimal geometries of fragment hybrids are considered. In this article, a new concept was introduced as a family of Jonsson definable subsets of the semantic model of the Jonsson theory T, denoted by JDef(CT ). The classes of the Robinson spectrum and the geometry of hybrids of central types of a fixed RSp(A) are considered. Using the construction of a central type for theories from the Robinson spectrum, we formulate and prove results for hybrids of Jonsson theories. A criterion for the uncountable categoricity of a hereditary hybrid of Jonsson theories is proved in the language of central types. The results obtained can be useful for continuing research on various Jonsson theories, in particular, for hybrids of Jonsson theories.
The paper investigates integro-differential equations in Banach spaces with operators, which are a composition of convolution and differentiation operators. Depending on the order of action of these two operators, we talk about integro-differential operators of the Riemann-Liouville type, when the convolution operator acts first, and integro-differential operators of the Gerasimov type otherwise. Special cases of the operators under consideration are the fractional derivatives of Riemann-Liouville and Gerasimov, respectively. The classes of integro-differential operators under study also include those in which the convolution has an integral kernel without singularities. The conditions of the unique solvability of the Cauchy type problem for a linear integro-differential equation of the Riemann-Liouville type and the Cauchy problem for a linear integrodifferential equation of the Gerasimov type with a bounded operator at the unknown function are obtained. These results are used in the study of similar equations with a degenerate operator at an integro-differential operator under the condition of relative boundedness of the pair of operators from the equation. Abstract results are applied to the study of initial boundary value problems for partial differential equations with an integro-differential operator, the convolution in which is given by the Mittag-Leffler function multiplied by a power function.
For centuries, mathematicians and, later, statisticians, have found natural research and employment opportunities in the realm of insurance. By definition, insurance offers financial cover against unforeseen events that involve an important component of randomness, and consequently, probability theory and mathematical statistics enter insurance modeling in a fundamental way. In recent years, a data deluge, coupled with ever-advancing information technology and the birth of data science, has revolutionized or is about to revolutionize most areas of actuarial science as well as insurance practice. We discuss parts of this evolution and, in the case of non-life insurance, show how a combination of classical tools from statistics, such as generalized linear models and, e.g., neural networks contribute to better understanding and analysis of actuarial data. We further review areas of actuarial science where the cross fertilization between stochastics and insurance holds promise for both sides. Of course, the vastness of the field of insurance limits our choice of topics; we mainly focus on topics closer to our main areas of research. Expected final online publication date for the Annual Review of Statistics, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
M.A. Bobodzhanova, B.T. Kalimbetov, G.M. Bekmakhanbet
In this paper, the regularization method of S.A.Lomov is generalized to the singularly perturbed integrodifferential fractional-order derivative equation with rapidly oscillating coefficients. The main goal of the work is to reveal the influence of the oscillating components on the structure of the asymptotics of the solution to this problem. The case of the absence of resonance is considered, i.e. the case when an integer linear combination of a rapidly oscillating inhomogeneity does not coincide with a point in the spectrum of the limiting operator at all points of the considered time interval. The case of coincidence of the frequency of a rapidly oscillating inhomogeneity with a point in the spectrum of the limiting operator is called the resonance case. This case is supposed to be studied in our subsequent works. More complex cases of resonance (for example, point resonance) require more careful analysis and are not considered in this work.
Forecasting the foreign currency exchange is a challenging task since it is influenced by political, economic and psychological factors. This paper focuses on the forecasting Malaysian Ringgit (MYR) exchange rate against the United States Dollar (USD) using Exponential Smoothing Techniques which are Single Exponential Smoothing, Double Exponential Smoothing, and Holt’s method. The objectives of this paper are to identify the best Exponential Smoothing Technique that describes MYR for 5 years period and to forecast MYR 12 months ahead by using the best Exponential Smoothing Technique. The comparison between these techniques is also made and the best one will be selected to forecast the MYR exchange rate against USD. The result showed that Holt’s method has the smallest value of error measure which depending on the Mean Square Error (MSE) and Mean Absolute Percentage Error (MAPE) for the evaluation part. The MSE is 1.43915x10-14 and MAPE is 2.5413 x 10-6. Meanwhile, the forecast value of MYR in August 2019 is RM 4.30226.
Sample surveys are often affected by nonresponse. These surveys have in common that their outcomes depend at least partly on a human decision whether or not to participate. If it would be completely clear how this decision mechanism works, estimates could be corrected. An often used approach is to introduce the concept of the response probability. Of course, these probabilities are a theoretical concept and therefore unknown. The idea is to estimate them by using the available data. If it is possible to obtain good estimates of the response probabilities, they can be used to improve estimators of population characteristics. Estimating response probabilities relies heavily on the use of models. An often used model is the logit model. In the article, this model is compared with the simple linear model. Estimation of response probabilities models requires the individual values of the auxiliary variables to be available for both the respondents and the nonrespondents of the survey. Unfortunately, this is often not the case. This article explores some approaches for estimating response probabilities that have less heavy data requirements. The estimated response probabilities were also used to measure possible deviations from representativity of the survey response. The indicator used is the coefficient of variation (CV) of the response probabilities.
In most of the longitudinal studies, involving count responses, excess zeros are common in practice. Usually, the current response measurement in a longitudinal sequence is a function of previous outcomes. For example, in a study about acute renal allograft rejection, the number of acute rejection episodes for a patient in current time is a function of this outcome at previous follow-up times. In this paper, we consider a transition model for accounting the dependence of current outcome on the previous outcomes in the presence of excess zeros. We propose the use of the generalized Poisson distribution as a flexible distribution for considering overdispersion (or underdispersion). The maximum likelihood estimates of the parameters are obtained using the EM algorithm. Some simulation studies are performed for illustration of the proposed methods. Also, analysis of a real data set of a kidney allograft rejection study illustrates the application of the proposed model.
Stefan Fleck, Thomas Karner, Sabine Schuster
et al.
The European road freight transport statistics (RFTS) result from surveys, which are conducted by several states on the basis of EU-legislation. As there is no strict methodology for the implementation of these surveys, they are slightly different regarding the individual states.
This article analyses the additional use of toll data to improve the European RFTS and to impute transport volume and performance of third states affecting the Austrian territory. First, it was attempted to derive journeys as defined in the RFTS from the toll data and assign them to their type of transport. These analyses were very elaborate but showed no satisfying results. The number of journeys from the RFTS data and toll data were too different to allow a reliable interpretation. Hence, this approach was rejected.
A comparison of vehicle-kilometres on the higher road network between the two data sources proved to be more successful, as the differences were in an explainable and acceptable scope. Two thirds of them could be derived from methodological reasons regarding the survey in the respective member states and due to missing third states. On the basis of the vehicle-kilometres from the toll data a correction factor for the RFTS results of the individual member states and a procedure for the imputation of third states were developed and applied to publish weighted results.
In this paper we study the existence of continuous solutions of an integro-differential equation in unbounded interval depending on derivative This paper extend some results obtained by the authors using the technique developed in their previous paper. This technique consists in introducing, in the given problems, a function q, belonging to a suitable space, instead of the state variable x. The fixed points of this function are the solutions of the original problem. In this investigation we use a fixed point theorem in Fréchet spaces.
In this paper, we construct q-parametric Szász-Mirakjan operators generated by the q-Dunkl generalization of the exponential function. We obtain Korovkin’s type approximation theorem and compute convergence of these operators by using the modulus of continuity. Furthermore, we obtain the rate of convergence of these operators for functions belonging to the Lipschitz class.