graphical approach
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The paper presents the graphical approach to decomposition of APC effect in cohort studies (mainly applied to demographic phenomena) using multilevel or accelerated longitudinal design. The aim of the paper is to present and visualize the pure age, period and cohort effects based on simulated data with an increment of five for each successive age, period and cohort variation. In cohort analysis on real data all of the effects are usually interrelated. The analysis shows basic patterns of two-variate APC decomposition (age within period, age within cohort, cohort within period, period within age, cohort within age, period within cohort) and reveals the trajectory of curves for each of the pure effects. The APC plots are developed using apc library of R package.

Background: MQ-series gas sensors belong to the metal oxide semiconductor (MOS) family of sensors that can sense the presence of many gases. These sensors find their application in gas alarm systems as key components. While necessary sensor circuit output voltage value for alarm point in a stand-alone gas alarm system is desirable, but what exact combination of the sensor circuit parameters is required? Hitherto, the determination of these circuit parameters has not been given much attention in the research community. Aim: the purpose of this work is to explore a structured graphical approach of determination of MQ series gas sensor circuit parameters for a stand-alone gas alarm system that yields desired sensor circuit output voltage value for the alarm point; the main objective of the study was to develop mathematical model equations that relate the: (i) sensor resistance (RS) with the gas concentration (x) and the sensor resistance at standard calibration concentration of the sensor base gas in the clean air (Ro) and (ii) sensor circuit output voltage (VRL), load resistance (RL) and sensor resistance (RS). It is expected from the model equations developed that graphical correlations of the sensor circuits parameters will be generated. Using these graphs for a particular case of an MQ-4 gas sensor under the influence of LPG, the parameters that yield desired sensor circuit output voltage of 2V for 1000 ppm of LPG alarm point will be determined. Methods: Model equations were developed for the sensor dynamics, and based on these model equations, graphs for the determination of required sensor parameters were plotted for a case of MQ-4 gas sensor response to LPG. Results and Discussion: The results yielded optimal values for R_O,R_S and R_L of 20 kΩ, 30 kΩ and 20 kΩ respectively, for alarm settings of 1000 ppm and a desired sensor circuit output voltage of 2 V. Based on determined parameters, the calibration equation for determination of best concentration value for a given value of emulated LPG concentration was developed. Using the method proposed in this study makes the process of determining the MQ-series gas sensor circuit parameters less cumbersome as their value can easily be obtained from the resulting graphs. Conclusions: a structured graphical approach for determination of MQ-series gas sensor circuit parameters for alarm points in a stand-alone gas alarm system showed that using MQ-4 gas sensor and LPG as the target gas, and for a sensor circuit output voltage of 2 V for alarm point at 1000 ppm of LPG, the corresponding value of R_O, R_S and R_L obtained were 20 kΩ, 30 kΩ, and 20 kΩ respectively. Hence, a structured graphical approach is suitable for determining MQ series gas sensor circuit parameters for a stand-alone gas alarm system under the influence of its associated gases.

The concept of derivative is used in many areas including applied problems and requiring mathematical modelling in different disciplines. One of the most important approaches for teaching the derivative is to support students in visualizing the concept. Also, it is necessary to shift researchers and teachers’ focuses to students’ dynamic mental actions while learning derivative in order to conduct effective teaching process. With this necessity, I focused on the perspective of quantitative reasoning related to the graphical approach to the derivative. This study aims to reveal a calculus student’s mental actions related to the graphical approach to the derivative. The data were collected from a first-year calculus student engaged in the task requiring graphical interpretation of the derivative. Results showed that the student’s understanding of the slope shaped her inferences about the tangent line because the quantity of ratio is prior knowledge for learning the instantaneous rate of change. Besides, as the student had the idea of correspondence related to the concept of function, she had difficulties in interpreting the global view of the derivate. This result suggests that having global view of the derivative requires a strong understanding of function and rate.

Subject. This article explores the strengthening of the role of human capital in the socio-economic development of areas and the disproportion in its placement. Objectives. The article aims to find solutions to the problems associated with the assessment of human capital of regions and its accumulation. Methods. For the study, we used a content analysis, systematization, and a graphical approach. Results. The article presents a methodology that helps build a model of the interregional balance of human capital, a research algorithm, and the main results expected during each study phase. Conclusions. The developed methodology can be an effective tool for managing the accumulation and interregional distribution of human capital in Russia.

HVAC codes and standards mention that a cumulative effect of hazards from emitted harmful airborne substances can occur. In this case, air exchange should not be calculated based on a simple summation of contributions of those harmful substances as long as environmental safety will not be assured, what has been mathematically proven. This paper contains a numerical and graphical approach description as well as calculation of a minimally allowable supply air flow assuring safety of premises with cumulative hazards of emitted airborne substances.

Background The proposed sequential and combinatorial algorithm, suggested as a standard tool for assessing, exploring, and reporting heterogeneity in the meta-analysis, is useful but time-consuming particularly when the number of included studies is large. Metaplot is a novel graphical approach that facilitates performing sensitivity analysis to distinguish the source of substantial heterogeneity across studies with ease and speed. Method Metaplot is a Stata module based on Stata’s commands, known informally as "ado". Metaplot presents a two-way (x, y) plot in which the x-axis represents the study codes and the y-axis represents the values of I2 statistics excluding one study at a time (n-1 studies). Metaplot also produces a table in the ’Results window’ of the Stata software including details such as I2 and χ2 statistics and their P-values omitting one study in each turn. Results Metaplot allows rapid identification of studies that have a disproportionate impact on heterogeneity across studies, and communicates to what extent omission of that study may reduce the overall heterogeneity based on the I2 and χ2 statistics. Metaplot has no limitations regarding the number of studies or types of outcome data (binomial or continuous data). Conclusions Metaplot is a simple graphical approach that gives a quick and easy identification of the studies having substantial influences on overall heterogeneity at a glance.