Real Functions Research Articles

Developing statistical literacy in high school through real data and exponential functions: an educational evaluation

The use of real data for the interpretation of statistical graphs encompassing exponential function was investigated. The goal was to develop, apply and assess an educational product composed of a website that simulates exponential functions, using real data for the interpretation of statistical graphs. The issue of how to develop statistical literacy for the interpretation of graphs involving exponential function in high school students using real data was addressed. The theoretical basis of Vygotsky's socio-interactionism was used. The application of the product, which was contextualized in a didactic sequence, was carried out in a class of the first year of high school. The collected data were treated qualitatively, based on the presuppositions of Bardin's content analysis; texts resulting from the application of the didactic sequence served as sources of analysis. Four categories were generated from the analysis of the texts: students' difficulty, students' protagonist, mathematics and exponential functions, and educational product and didactic sequence.

Constructing a Network Digital Twin through formal modeling: Tackling the virtual–real mapping challenge in IIoT networks

The Industrial Internet of Things (IIoT) presents numerous requirements, such as reliability, energy efficiency, and real-time performance, among others. Digital Twins technology addresses these needs by enabling the simulation, monitoring, and optimization of such systems. Specifically, Network Digital Twins (NDTs) have recently attracted significant attention from both the industrial and academic networking communities. Numerous research efforts focus on the challenge of network modeling in this context, as simulation tools can increase cost and computational complexity. In this paper, we explore the integration of the formal modeling technique, Petri-nets, within the context of NDTs to model the IIoT, enabling data-driven Petri-nets. We present an architecture based on open-source tools as a framework to encourage researchers to investigate this research direction. Furthermore, we validate the proposed architecture through a case study involving a small-scale network modeled with Timed Petri-Nets. The results demonstrate the model’s effectiveness in executing what-if scenarios based on the network’s operational parameters to predict the Packet Delivery Ratio and enable real-time fault detection. Lastly, we conduct a study on the IIoT observability by the NDT to address the challenge of virtual–real systems mapping in such a context.

Extensions of Functions with a Closed Graph and Quasi-continuous Functions with a Closed Graph from Dense Subspaces

In this paper, we prove some conditions for existence of an extension of a real (quasi-continuous) function with a closed graph defined on a given dense subset D of a topological space X to a (quasi-continuous) function with a closed graph on whole X.

A Comprehensive Investigation into the Money Demand Function in Cambodia: An Empirical Analysis

The objective of this study is to establish a money demand function in Cambodia. The findings obtained through the ARDL approach to cointegration indicate that real income, consumer price index, and interest rate are cointegrated with real money demand. In terms of the estimated results derived from the long-run model, it is observed that real income has a statistically significant positive impact on real money demand, while the general price level and interest rate have a negative impact. The short-run dynamic model, known as the error correction model, demonstrates that all explanatory variables collectively account for the growth rate of real money balances. In the short-run, the growth rate of real income exhibits a positive relationship with the demand for real money, whereas the inflation rate and changes in interest rate have a significant negative effect on the demand for real money balances. The estimated slope coefficient of the short-run dynamic model, which measures the speed of adjustment, is projected to be 60.67%. This outcome suggests that the real money balance model takes no more than two quarters to adjust towards long-run equilibrium in response to short-run dynamic shocks. Stability tests, such as the CUSUM and CUSUMSQ tests, indicate that the real money demand function in Cambodia remains stable in the long-term. The findings derived from this study provide empirical evidence in favor of the quantity theory of money.

Measuring law's normative force

AbstractAn important question in legal theory and policy is when people are willing to put aside their policy preferences to uphold higher‐order legal values. That is, when does constitutional or international law, for instance, have “normative force”? Around two‐dozen experimental studies have attempted to measure this question empirically, but their designs contain an inherent limitation. While they are interested in gauging the effect of internalizing a norm, they measure only the effect of exposure to that norm. This is significant because subjects in the treatment group whose priors are strongly contrary to the treatment message on the legality of a policy may effectively be “treatment resistant”: it is difficult to successfully treat them because their prior beliefs on the issue are entrenched; as a result, they simply do not believe the treatment message. This treatment failure attenuates any effects, and where a significant portion of the treatment and/or control group is not successfully treated, the results will be biased toward small, null, or even backfire findings. This article first formally models the mechanism underlying experiments on law's normative force. I then demonstrate a methodological solution to the problem of treatment resistance. By using the experimental treatment as an instrumental variable and employing a post‐treatment treatment‐uptake test, the researcher can estimate the causal effect of the real explanatory variable of interest: sincerely holding a belief about a policy's higher‐order lawfulness. Using new data from a 2022 survey experiment conducted on US residents, I illustrate this method for three constitutional or international law issues. The theoretical and empirical results together suggest that backfire effects documented by some studies do not reflect a tepid or negative response against the legal source per se, but rather reflect treatment resistance. These findings suggest that we should re‐evaluate the existing body of experimental studies on law's normative force, and they should prompt researchers to reconsider how we conduct future research in this domain.

Efficient Optical OFDM System Resilience to Indoor Wireless Multipath Channels

This article presents a developed intensity modulation/direct detection (IM/DD) optical orthogonal frequency division multiplexing (O-OFDM). More precisely, the presented C-O-OFDM is based on the C-transform as a unitary orthogonal transform instead of the state-of-the-art discrete Fourier transform (DFT). Due to the properties of the real C-transform, Hermitian symmetry (HS) is not required to produce real OFDM samples. Therefore, the proposed scheme supports twice the input symbols compared to conventional DFT-based OFDM system. Real data mapping and DC bias technology is considered to evaluate the performance of the presented scheme over optical wireless multipath. The simulation results shows that the proposed C-O-OFDM is more resilience to multipath phenomena than the competitive DFT-O-OFDM and DHT-O-OFDM schemes for similar bit rate. The proposed scheme achieves about 22 dB signal-to-noise ratio (SNR) gain in comparison with the DFT-O-OFDM and about 2.5 dB SNR gain in comparison with the DHT-O-OFDM scheme.

Complex turbulent exchange coefficient in Akerblom–Ekman model

Abstract The turbulent exchange in boundary layer models is usually characterized by a scalar eddy viscosity coefficient assumed to be a positive function of the vertical variable. We introduce a more general form for the turbulence exchange description, which includes two functions that describe the turbulence without any assumption about their positivity. We construct a model of the Akerblom–Ekman type, but with a complex coefficient of turbulent exchange. The basic quality criterion for these models and algorithms is the maximal agreement with meteorological observations. We optimize the agreement between the global meteorological archive of high-resolution wind observations that are provided by World Meteorological Organization (WMO) in Binary Universal Form for the Representation (BUFR). The main result of our work is that agreement between model solutions and observations will be much better if the turbulent exchange coefficient is optimized in the space of all complex-valued functions, and not limited to the cone of real positive functions.

Multipliers of Variationally Mcshane Integrable Functions in Locally Convex Space

Abstract We study measurable real valued multipliers of variationally McShane (resp. McShane) integrable functions defined on a σ-finite outer regular quasi-Radon measure space and taking values in a complete locally convex topological vector space X. We also show: in case X is representable by semi-norm then essentially bounded real measurable functions are multipliers of functions which are Pettis integrable as well as integrable by semi-norm. The space of real valued measurable and essentially bounded functions turn out to be precisely the multipliers of variationally McShane (resp. McShane) integrable functions in case X is representable by semi-norm.

On Strong Porosity of Some Families of Functions

Abstract The paper deals with the strong porosity of some families of real functions continuous with respect to a given topology 𝒯 or 𝒜-continuous (i.e., continuous with respect to some special family 𝒜 of sets of the real line). Particularly, porosity of those families is investigated in space of the Baire 1 functions or in the space of the Baire 1 and Darboux functions.

PENERAPAN PELAYANAN HOLISTIK GEREJA DALAM KEBHINNEKAAN UMAT BERAGAMA DI INDONESIA

This study aims to provide an understanding of the church's responsibility for holistic service in society, nation and state and to create a harmonious life so that the unity and integrity of Indonesia can be maintained. Republik Indonesia is the largest archipelagic country in the world with more than 17,000 islands. Through its uniqueness and diversity, Indonesia is known as a country with pluralistic society. This can be seen in the Indonesian value "Bhinneka Tunggal Ika", the word "bhinneka" means "different", an acknowledgment that the Indonesia is a nation with pluralism. Behavior that reflects the values ​​of unity and integrity in the social community is very much needed to maintain the nation. The Indonesian need to have solidarity based on the spirit of unity and unity in diversity in order to achieve a common goal, for the unity and welfare of Indonesia, for that the role of the church is very important in giving impact in the form of holistic services. The current study uses qualitative method, sourced from various literatures and journal articles related to the topic of discussion. The results of the study state that a church can carry out a holistic service function and have an impact on improving social welfare for a harmonious life in the unity and integrity Indonesia. The final conclusion states that the church should be able to have a real impact and function to play a holistic ministry such as koinonia, marturia, diakonia within the framework of Indonesian unity and integrity.

Keys to the weakening of the real social function of the union. Approach to the barriers to the formation of branch/industry unions and the exercise of solidarity strikes in three Latin American labor models

En este trabajo desarrollaremos un estudio comparativo de modelos laborales que categorizaremos como coherentes, incoherentes y mixtos a partir de la compenetración que estos tengan con los postulados del derecho de libertad sindical devenidos de los convenios 87 y 98 de la OIT, y la efectivización de dos objetos de análisis: la libertad de constitución, tamaño y organización estructural del sindicato y la interacción gremial a partir de la huelga por solidaridad. Para este fin, se realiza una investigación descriptiva y explicativa, empleándose la metodología dogmática ?clásica de las ciencias jurídicas? y los submétodos sistemático, analítico y de enjuiciamiento de hecho. En tal medida, concluiremos cuáles son los principales errores de los modelos laborales en la búsqueda de los principios e ideales de la sindicalización y algunos comentarios respecto a las razones por las cuales superviven ciertos instrumentos jurídicos enquistados en el siglo XIX en momentos en los que debería encontrarse el auge del reconocimiento y amparo del sujeto colectivo laboral.

Forecasting and stress testing with quantile vector autoregression

SummaryA quantile vector autoregressive (VAR) model, unlike standard VAR, traces the interaction among the endogenous random variables at any quantile. Quantile forecasts are obtained by factorizing the joint distribution in a recursive structure but cannot be obtained from reduced form estimation. Identification strategies and structural quantile impulse response functions are derived as generalization of the VAR model. The model is estimated using real and financial variables for the euro area. The dynamic properties of the system change across quantiles. This is relevant for stress testing exercises, whose goal is to forecast the tail behavior of the economy when hit by large financial and real shocks.

Aggregate Skewness and the Business Cycle

Abstract We develop a data-rich measure of expected macroeconomic skewness in the US economy. Expected macroeconomic skewness is strongly procyclical, mainly reflects the cyclicality in the skewness of real variables, is highly correlated with the cross-sectional skewness of firm-level employment growth, and is distinct from financial market skewness. Revisions in expected skewness lead to business cycle fluctuations nearly indistinguishable from those induced by the main business cycle shock of Angeletos et al. (2020). This result is robust to controlling for macroeconomic volatility and uncertainty, and alternative macroeconomic shocks. Our findings suggest an important role of higher-order dynamics for business cycle theories.

Eigenvalues bifurcating from the continuum in two-dimensional potentials generating non-Hermitian gauge fields

It has been recently shown that complex two-dimensional (2D) potentials Vɛ(x,y)=V(y+iɛη(x)) can be used to emulate non-Hermitian matrix gauge fields in optical waveguides. Here x and y are the transverse coordinates, V(y) and η(x) are real functions, ɛ>0 is a small parameter, and i is the imaginary unit. The real potential V(y) is required to have at least two discrete eigenvalues in the corresponding 1D Schrödinger operator. When both transverse directions are taken into account, these eigenvalues become thresholds embedded in the continuous spectrum of the 2D operator. Small nonzero ɛ corresponds to a non-Hermitian perturbation which can result in a bifurcation of each threshold into an eigenvalue. Accurate analysis of these eigenvalues is important for understanding the behavior and stability of optical waves propagating in the artificial non-Hermitian gauge potential. Bifurcations of complex eigenvalues out of the continuum is the main object of the present study. Using recent mathematical results from the rigorous analysis of elliptic operators, we obtain simple asymptotic expansions in ɛ that describe the behavior of bifurcating eigenvalues. The lowest threshold can bifurcate into a single eigenvalue, while every other threshold can bifurcate into a pair of complex eigenvalues. These bifurcations can be controlled by the Fourier transform of function η(x) evaluated at certain isolated points of the reciprocal space. When the bifurcation does not occur, the continuous spectrum of 2D operator contains a quasi-bound-state which is characterized by a strongly localized central peak coupled to small-amplitude but nondecaying tails. The analysis is applied to the case examples of parabolic and double-well potentials V(y). In the latter case, the bifurcation of complex eigenvalues can be dampened if the two wells are widely separated.

Exploring the Relationship Between Attribute Discrepancy and Avatar Embodiment in Immersive Social Virtual Reality.

Social virtual reality (VR) is an emerging set of platforms where users interact while embodying avatars. Given that VR headsets track real physical movements and map them onto one's avatar body, the nature of one's digital representation is an important aspect of social VR. However, little is known about how the visual proximity of an avatar to the self shapes user experience in naturalistic, social VR environments. In this article, we use this context to explore how embodiment is influenced by the perceived differences between the physical attributes of a user and the virtual attributes of their avatar. We selected a number of attributes for this measure that have been shown to be important for customization and representation in VR. Participants created an avatar, spent time in social VR, and reported on their experience in a questionnaire. Our results demonstrate a significant negative association between attribute discrepancy and avatar embodiment, the psychological experience of one's virtual body as their own body. We discuss implications for theories of self-representation and suggest urgency on the part of games and VR designers to improve the methods of creating avatars.

Optimizing experimental parameters for orbital mapping

A new material characterization technique is emerging for the transmission electron microscope (TEM). Using electron energy-loss spectroscopy, real space mappings of the underlying electronic transitions in the sample, so called orbital maps, can be produced. Thus, unprecedented insight into the electronic orbitals responsible for most of the electrical, magnetic and optical properties of bulk materials can be gained. However, the incredibly demanding requirements on spatial as well as spectral resolution paired with the low signal-to-noise ratio severely limits the day-to-day use of this new technique. With the use of simulations, we strive to alleviate these challenges as much as possible by identifying optimal experimental parameters. In this manner, we investigate representative examples of a transition metal oxide, a material consisting entirely of light elements, and an interface between two different materials to find and compare acceptable ranges for sample thickness, acceleration voltage and electron dose for a scanning probe as well as for parallel illumination.

Structural estimates of the South African sacrifice ratio

This paper estimates the output cost of fighting inflation—the sacrifice ratio—for the South African economy using quarterly data spanning the period 1998:1–2019:3. To compute the sacrifice ratio, the structural vector autoregressive (SVAR) model developed by Cecchetti and Rich (2001) based on Cecchetti (1994) is employed. Our findings show us a small sacrifice ratio, which lies within the range 0.00002–0.231 percent with an average of 0.031 percent, indicating a low level of output to be sacrificed while fighting inflation. Hence, the reserve bank is recommended to sustain an inflation rate within the target range and reap the benefits of a predictable and stable price path, as restrictive monetary policy has only a transitory effect on real variables like output.

Inverse scattering problem for a third-order operator with local potential

Inverse scattering problem for the operator representing sum of the operator of the third derivative on semi-axis and of the operator of multiplication by a real function is studied in this paper. Properties of Jost solutions of such an operator are studied and it is shown that these Jost solutions are solutions of the Riemann boundary value problem on a system of rays. The main system of linear singular integral equations is derived. This system is equivalent to the solution of inverse scattering problem.

Association between the ESR1 and ESR2 polymorphisms and osteoporosis risk: An updated meta-analysis.

Gene polymorphisms of estrogen receptor (ESR) 1 PvuII (rs2234693), XbaI (rs9340799), G2014A (rs2228480), ESR2 AluI (rs4986938), and RsaI (rs1256049) had been reported to be associated with the risk of osteoporosis. However, these conclusions were inconsistent, therefore, an updated meta-analysis was conducted to further explore these issues. To evaluate the association between gene polymorphisms of ESR1 PvuII (rs2234693), XbaI (rs9340799), G2014A (rs2228480), ESR2 AluI (rs4986938), RsaI (rs1256049), and osteoporosis risk. PubMed, Medline, Ovid, Embase, CNKI, and China Wanfang databases were searched. Association was assessed using odds ratio with 95% confidence interval. Moreover, the false-positive reporting probability, Bayesian false-finding probability, and Venetian criteria were used to assess the credibility of statistically significant associations. Overall, ESR1 PvuII (rs2234693) and XbaI (rs9340799) were associated with the risk of osteoporosis in Indians. Moreover, ESR1 G2014A (rs2228480) was associated with the decreased risk of osteoporosis in East Asians. Moreover, ESR2 Alul (rs4986938) was associated with the increased risk of osteoporosis in East Asians and Caucasians. There was a significant association between ESR2 Rsal (rs1256049) and osteoporosis risk in overall population. When only high-quality and Hardy-Weinberg equilibrium studies were included in the sensitivity analysis, all results did not change in the present study. When the credibility was evaluated applying false-positive reporting probability, Bayesian false-finding probability, and Venetian criteria, all significant associations were considered as false positive results. In summary, this study shows that all substantial associations between gene polymorphisms of ESR1 (PvuII, XbaI, and G2014A) and ESR 2 (AluI and RsaI) and osteoporosis risk are possibly false positive results instead of real associations or biological variables.

Three-Dimensional Graph Drawing Procedures for Functions of Two and Several Variables

Many functions depend on more than one independent variable. For instance, the volume of a right circular cylinder is a function of its radius and its height, so it is a function V(r, h) of two variables r and h.
 Real valued functions of several independent real variables are defined similarly to functions in the single-variable case. In this article, we define functions of more than one independent variable and discuss ways to graph them. But their graph is impossible in the two-dimensional system and the MATLAB program is the language that guarantees computer implementation at a high level in mathematics, easily presenting calculations, images, graphs, and writing programs in its environment.
 For achieving this goal, we first explained the plot3 procedure in the three-dimensional coordinate system to draw the graph of two dependent subordinates on the MATLAB program environment, followed by the surf procedure as well as the mesh procedure. Then we explained the procedures mentioned in the polar coordinates. We have provided examples to better understand each procedure.