text:
Sharia-based Stocks: Do Muslim Investors Prefer Metaphysical or Materialistic Returns?

• MAHASTANTI, Linda Ariany (Management Department, Faculty of Economics and Business, Universitas Kristen Satya Wacana) ;
• Accepted : 2020.12.14
• Published : 2021.01.30

Abstract

Faith-based investment instruments, such as sharia-based stocks, have developed rapidly in recent years. When investing in these instruments, investors tend to emphasize materialistic returns as measured with monetary returns and metaphysical returns, such as blessings from God (Allah) because of their observance of Islamic teachings. In this respect, it is important to investigate the role of individuals' religiosity in investment decision making in Sharia-based financial products. An equally crucial research question is whether individuals' religiosity levels affect expected material returns as measured by the tolerable negative returns of sharia-based stocks. This study relies on a survey method that involves university students in Java island who actively invest through the Investment Gallery of their faculties/ universities as the sample. Data is then analysed with the multinomial regression analysis technique. The results show that individuals who are more observant of their religious teachings are more likely to fully invest their funds in Sharia-based stocks and exhibit greater tolerance towards the negative returns of Sharia-based stocks. The findings indicate that Muslim investors who are more observant of Islamic teachings emphasize metaphysical returns from their investment decisions.

1. Introduction

The last several years have witnessed the rapid growth of the sharia-based capital market in Indonesia, as indicated by the data of the Indonesian Stock Exchange (IDX) that records an increase of sharia-based investors. In particular, during the last five years, the number of Sharia-based investors has increased from 2,705 investors in late 2014 to 62,480 investors per October 2019, with a level of activity of 32 percent. The data suggest that Sharia-based stocks have been a major investment instrument for Indonesians.

Increases in Sharia-based stock investments in recent years show that investors do not solely search for the return factor in making investment decisions but also consider the investment products’ social values. This view is in line with Akerlof (1980), Romer (1984) and Arfah et al. (2020). They proposed that individuals are motivated by social norms and motives when making decisions because they are unwilling to lose reputations in their social environments. This perspective is also consistent with Kubler (2001) who argues that social norms generally affect an individual’s behaviour, while Kim and Venkatachaman and Rajgopal (2011) and Baker and Nofsinger (2012) reveal the impact of social norms on individuals’ preferences and investment decisions. Hence, investors’ preferences in making investment decisions align with their norms and ethical values obtained from their social environments or religious teachings. Consequently, investors tend to abandon investments in stocks that are considered as not consistent with their perspectives. In this respect, Muslim societies manage to clearly identify stocks that violate their norms derived from Islamic religious teachings as non-Islamic (conventional) stocks and stocks that adhere to Islamic religious norms as Islamic (Sharia- based) stocks. Besides, Muslim retail investors will follow Islamic trade rules because of their high religiosity levels (Awadhi and Dempsey, 2017) and trust for Islamic product (Islamic bank) Usman (2015).

Sharia-based stocks are stocks with specific segments because they are based on Islamic religious teachings. Merton (1987) proposes a market segmentation theory that argues that stocks neglected in segmented markets will outperform other stocks. However, the findings still leave several unanswered questions, including 1) to what extent do religion-based segmented markets increase or inhibit overall market behavior, and 2) to what extent does religious faith interact with stock investments, stock returns, stock trade, and liquidity decisions? These issues motivate further studies in investments. The classical investment theories, such as portfolio theory (Markowitz, 1954), suggest that investors consider expected risks and returns in making investment decisions but overlook non-economic factors such as beliefs derived from social norms or religious teachings. In this regard, it is crucial to analyze non-economic factors in investment decisions because classical finance theories emphasize risk and return factors that maximize individuals’ utilities but overlook other factors related to non-economic returns (Higgins, 1998). Non-economic returns result from individuals’ evaluation process on their social, cultural, and religious values (Kutschera, 1977). These values arguably satisfy individuals’ personal values and not only maximize monetary values. Individuals’ personal values refer to non-monetary/metaphysical returns, such as having spiritual satisfaction or obtaining blessings because of their observance of religious teachings. On the other hand, these individuals also search for monetary/materialistic factors, such as returns from their investments.

Several follow-up studies have considered non-economic factors that affect individuals’ decision-making processes including psychological factors. This paradigm involves the belief factors derived from Islamic religious teachings that potentially affect individuals’ financial decisions. In particular, scholars argue that religious beliefs lead to a self-categorization process that forms individuals’ identities (Benjamin et al., 2016). Barro and McCleary (2003) established that religions offer moral and ethical teachings for their adherents and encourage them to act according to certain ways. Religiosity forms individuals’ norms and values and affects their tendency to take risks. Consequently, it also affects their personal finance-related behaviors, including investment decisions (León & Pfeifer, 2013; Mahdzan et al., 2016).

The above discussion indicates that beliefs from religious teachings is likely to affect sharia-based stock investments (León & Pfeifer, 2013; Hess, 2012; Mahdzan et al., 2016). However, it is crucial to observe whether highly religious investors are also highly loyal to sharia-based financial products, i.e., whether they still buy or hold their sharia-based investment products although the returns of these products decline sharply because these products are considered consistent with their religious teachings. In other words, it is important to analyze the alignment of religious norms-motivated and economic-driven needs fulfillment.

It is interesting to evaluate the above discussion because prior studies find that more religious individuals are less willing to take risks (Leon & Pfeifer, 2013; Mahdzan et al., 2017). When investors align their economic (materialistic) with non-economic (metaphysical) factors, religiosity will motivate them to prefer sharia-based stocks to conventional ones. After selecting Sharia-based stocks, individuals will evaluate the returns of sharia-based stocks and sell the stocks when the returns decline sharply. Hence, it is interesting to investigate whether highly religious Muslim investors exhibit greater loyalty towards sharia-based stocks, i.e., they will continue to buy or hold sharia-based stocks, although the returns of these stocks decline sharply. It is also crucial to analyze whether religiosity levels affect Muslim investors’ adjustment decisions when determining the thresholds of return decreases to reduce losses. This is important because Indonesian Sharia capital market has volatility risk (Rahmi et al., 2016)

Thus, this study examines whether individuals’ religiosity levels affect sharia-based stock investments and whether religiosity affects investors’ decisions to set the thresholds for tolerable return declines of sharia-based stocks to balance their economic needs. Accordingly, this study administers a survey to students of economics and business faculties in Jogjakarta Special Region, Central Java, and Jakarta, who actively make investment activities through the investment galleries of their faculties/ universities.

The contribution of this study to the faith-based investment literature is twofold. First, we investigate the role of religiosity in Sharia-based stock investment decisions and the determination of the thresholds of tolerable return decreases of Sharia-based stocks. The analysis is important in observing whether the metaphysical or materialistic returns are more dominant in investment decisions. Thus, this paper analyzes whether Muslim investors align their metaphysical and materialistic needs in their investment decisions. Second, this study employs the psychometric approach in measuring religiosity to analyze differences in individuals’ responses from the psychological perspective.

This article is organized into several sections. The first section contains the introduction, followed by the second section that discusses the theoretical analysis and hypothesis development. Next, the third section presents the research methods, while the fourth section discusses the results. Lastly, the fifth section presents the conclusion.

2. Hypothesis Development

2.1. Rationality in Islam

Theories of decision making in highly uncertain environments are largely based on utility theory. Several classical finance theories (the 1950-1980 period), such as portfolio theory (Markowitz, 1952) and Capital Asset Pricing Model (CAPM) by Sharpe (1964) and Lintner (1965), employ Expected Utility Theory (EUT) as the underlying theory. EUT proposes that individuals think rationally in making investment decisions by considering the expected risks and returns of each investment choice to maximize investors’ utilities subject to their risk preferences.

The development of faith-based investment products motivates individuals to consider their religious teachings when buying these investment products. According to the explanation of Islamic rationality, Islamic economics has its own view in explaining consumers’ behavior. Unlike conventional economics, Hossain (2014) illustrates a concept commonly known as Islamic Economic Rationalism (IER). In a similar vein, Ramli and Mirza (2007) classify Islamic rationality into two components, namely worldview and personal interests. In the personal interest component, individuals will fulfill their interests by adhering to sharia principles. Similarly, IER also establishes religion as the main determinant, while sharia is based on religion.

Based on the above discussion, individuals will form unique utilities according to the preferences of their religions. Individuals have different utilities depending on their beliefs, creating subjective preferences toward Sharia-based financial products. This phase is accomplished through all activities, including consumption that adheres to sharia-based ethical and religious values (Ghassan, 2015). Further, Ghassan explains that materialistic and metaphysical satisfaction represent the benefits of satisfaction. Consumption-based Islamic teachings such as using halal goods/ services will deliver utilities or benefits (Ramli & Mirza, 2007) that enable Falah maximization (individuals do not solely search for returns but also worldly and afterlife triumph).

However, on the other hand, rational Muslim investors also maximize their worldly success. As suggested by Ghassan (2015), Muslim investors channel their satisfaction benefits both materialistically and metaphysically. Hence, in making investment decisions, Muslim investors do not solely consider subjective rationality based on Islamic teachings, but they also consider objective rationality as represented by risks and returns to obtain worldly returns.

The above explanations suggest that understanding investors’ behavior when buying sharia-based products involves both financial and non-financial perspectives. Particularly, the financial perspective focuses on worldly (monetary/ materialistic) needs, while the non-financial perspective emphasizes heavenly interests based on Islamic teachings (non-monetary/ metaphysical needs).

2.2. Religiosity and Investment Portfolio

Muslims adhere to the practices of virtue and ethics when making investments that likely affect their financial behaviour. In Arabic terms, these practices are labelled as akhlaq. Some investors do not solely seek returns and wealth accumulation from their investments but also the fulfilment of moral obligations (Shakeel, 2015; Anas & Mounira, 2009). Scientific literature also demonstrates that religiosity affects ones’ risk-taking and portfolio allocation behaviours. As a cultural dimension embedded into individuals’ identities, religion plays a major role in individuals’ economic and financial behaviors (Arora & Marwaha 2014; Benjamin et al., 2016; Yusuff & Mansor, 2016). Empirical studies support the idea and have documented evidence that religion and religiosity affect individuals’ financial and investment behaviours.

The literature generally demonstrates the positive relationship between religiosity and decision making. For example, Tabellini (2010) reveal that values, culture, and norms directly affect attitudes and preferences and, eventually, decision making. Hence, religion-derived values will result in preferences in the decision-making process, particularly when individuals choose financial products that comply with Islamic religious teachings. Canepa and Ibnrubbian (2014) study in Saudi Arabia observes that religious teachings affect individuals’ portfolio formation.

Prior studies have found that religion and religiosity play a major role in decision-making behaviour which indicates that the religiosity factor likely affects the allocation of financial assets in portfolio formation. Thus, this study predicts that higher Islamic religiosity levels will positively affect asset allocation into sharia-based stocks.

H1: Religiosity positively affects investments in sharia-based financial products.

2.3. Religiosity and Declines in Sharia-based Stocks’ Returns

Empirical studies reveal that religion and religiosity affect individuals’ financial and investment decisions and risk- taking behaviour. The literature generally shows a positive association between religiosity and risk-averse behaviour where more religious individuals are more risk-averse (Renneboog & Spaenjers, 2012; Lu & Chan, 2012; León & Pfeifer, 2013; Jiang et al., 2015; Chen et al., 2016; Mahdzan et al., 2017). Because they are more risk-averse, religious people do not tend to participate in risky investments (Tahir & Brimble, 2011; Davutyan & Öztürkkal, 2016; Yusuf & Mansor, 2016).

Based on these studies, besides considering metaphysical factors, highly religious individuals also account for materialistic factors when making investment decisions, as indicated by their reluctance to invest in risky assets. Hence, after choosing sharia-based financial products that adhering to Islamic religious teachings, individuals will evaluate their tolerable risks and returns. Highly religious Muslim investors are arguably less willing to take the risks of declines of their sharia-based investments, as indicated by their tolerable percentage of return declines.

H2: Religiosity negatively affects the willingness to take the risks of the declines of sharia-based stocks’ returns.

3. Methods

This study relies on a survey method to generate data by distributing questionnaires to Muslim students who actively invest through the Investment Gallery of economics and business faculties in Java Island, Indonesia. We use students as the sample to analyse the investment behaviour of retail investors, especially young ones. Using students as the sample is important because younger investors tend to make investment decisions to maximize monetary returns. Additionally, whether they also seek religion-derived permanent returns from their investments is relatively understudied. Hence, it is crucial to determine whether young investors are still attracted to Sharia-based financial products when they are offered both conventional and Sharia-based financial products as alternative investment instruments. The sample is generated with non-probability convenience sampling. Before the pilot test, three Islamic scholars who also actively participated in Islamic financial organizations have validated the questionnaire’s content to analyse whether each question item conforms to Islamic religious teachings. After the question items are validated, we distribute the questionnaires to 90 respondents in the pilot test and subsequently run the Exploratory Factor Analysis to classify the question items into several dimensions.

The Exploratory Factor Analysis (EFA) test results are revalidated by three Islamic scholars to examine whether the dimension formation of the EFA analysis can explain Islamic religious teachings comprehensively. Based on the revised and validated questionnaire, we distribute 250 questionnaires to the targeted respondents, resulting in 184 usable responses or a response rate of 73.6 percent, a considerably high rate for statistical validity. The questionnaire is presented in Indonesian language and consists of three parts. The first part focuses on respondents’ demographic profile. The second part measures Islamic religiosity based on the psychometric approach, as developed by Masri and Priester (2007) and Olufadi (2016). Lastly, the third part involves portfolio selection choices based on Tung et al., (2014), Van Rooij et al., (2011), and Mahdzan et al., (2017).

3.1. Dependent Variables: Investment Portfolio

The dependent variable of this paper is portfolio allocation. A simple quantitative measurement is developed to indicate the tendency to allocate risky assets into portfolios. We ask the following question to the respondents, “Which financial asset combination below that best represents your investment?” This study enables respondents to provide a simple estimation of fund allocation in their portfolios. In particular, they have five possible answers to choose: (1) 100 percent in Sharia-based stocks, (2) 75 percent in Sharia- based stocks and 25 percent in conventional stocks, (3) 50 percent in Sharia-based stocks and 50 percent in conventional stocks, (4) 75 percent in conventional stocks and 25 percent in Sharia-based stocks, and (5) 100 percent in conventional stocks. This categorization follows prior studies (Bertaut & Starr-McCluer, 2002; Duasa & Yusof, 2013; Mahdzan et al., 2017).

Next, the questionnaire also asked respondents’ tolerable declines in Sharia-based stocks’ returns with the following question: What is your tolerable percentage of decline in Sharia-based stocks’ returns that you decide still to buy or hold the stocks? The alternative answers are (1) < 25%, (2) 25%-50%, (3) 50%-75%, and (4) I will continue to hold Sharia-based stocks regardless of the declines of Sharia- based stocks’ returns. The responses reflect the ordinal measure of the tendency to invest in Sharia-based stocks relative to conventional stocks to obtain metaphysical returns that adhere to Islamic religious teachings. Next, investors will justify the percentage of the return declines of Sharia-based stocks selected before to achieve materialistic returns.

3.2. Independent Variable

Islamic Religiosity

Religiosity is a comprehensive sociological term that refers to individuals’ involvement, interests, or participation in various aspects of dedication, belief, and religious activities (Delener, 1990b; Azari et al., 2005 and can be classified into two dimensions: extrinsic and intrinsic religiosity (Allport & Ross, 1967; Vitell et al., 2006). We adapt the measurement scale of Masri and Priester (2007) and Olufadi (2016) to capture various religiosity domains, including Muslims’ faith, beliefs, and practices, by using 29 question items. Next, this study employs the Exploratory Factor Analysis (EFA) to test the internal consistency and form the latent constructs that underlie religiosity. In this case, as suggested by Hair et al. (2014), we use the threshold of 0.6 to develop factors from EFA. Consequently, we have to leave out ten items because of low factor loadings. EFA for the remaining 19 items produces the five solution factors. Further, this study runs the reliability test by using Cronbach’s alpha with Cronbach’s alpha values between 0.668 and 0.805. The following Table 1 below displays the results of EFA and Cronbach’s Alpha.

Islamic Religiosity as Measured with Two Methods

In the first method, following Wan Ahmad et al. (2008) and Mahdzan et al., (2017), respondents are separated into three groups that reflect the relative strength of their religiosity levels: relaxed, moderate, and observant. The categorization process starts with calculating the average and standard deviation values of 19 items that contain the above factors for all respondents. Table III displays the descriptive statistics of religiosity levels.

Religiosity Dimensions

The second method is to measure how religiosity involves the five dimensions of Islamic religiosity produced by the factor analysis procedure in Section 3.1.3. Table I shows that factor analysis produces five reliable dimensions. Based on the discussions with Islamic scholars, the grouping process of the factor analysis produces five dimensions, namely (1) belief in Allah, (2) belief in Islamic Sharia teachings, (3) interaction with fellow human beings (hablum minannash), (4) morals (Akhlaq), and (5) worshiping behaviour.

3.3. Control Variables

Sociodemographic Variables

The control variables of this study are the demographic variables of the respondents, namely gender, pocket money/ income, age, and participation in Islamic financial organizations. These variables are measured with dummy variables (Gender: male =1, female = 0; Age: 0= 17-20, 1 = 21-24, 2: 25-28, 3=>28; Monthly income/ pocket money: 0=<1,000,000, 1 = 1,000,000 – 2,500,000, 2 = 2,500,001- 4,000,000, 3 > 4,000,001; Participation in Islamic financial organizations: 1 = active 0 = not active).

4. Results and Discussions

4.1. Descriptive Statistics

This section discusses the descriptive statistics of the religiosity measure and respondents’ characteristics. Table 2 below explains the results of the measurement of religiosity.

Table 2 above informs that the respondents exhibit relatively balanced religiosity levels (observant, moderate, and relaxed). The highest proportion of religiosity levels is the moderate level (37%), followed by the observant level (36%). Next, women dominate our respondents (60% of total respondents), and men constitute the rest (40%). Most respondents earn monthly income or pocket money less than 1,000,000 rupiahs and are between 17 and 24 years old. Further, most respondents (58%) actively participate in Islamic financial organizations and are highly loyal to sharia- based financial products, as indicated by their willingness to hold sharia-based stocks regardless of the magnitude of the return declines (46%).

4.2. Multivariate Analysis

We then run the multivariate analysis using the multiple multinomial regression method after the descriptive analysis and bivariate analyses. This method belongs to logistic regression used when the dependent variable has a polychotomous or multinomial scale. The multinomial scale is a measure that is categorized into more than two categories. Hosmer and Lemeshow (2000) suggest using logistic regression when the response variable is categorical (nominal or ordinal), and the predictor variables are continuous or categorical. The following is the logistic regression model:

$\pi(x) \frac {e^{g(x)}} {1+e^{g(x)}}$       ...(1)

With g(x) = β0 + β1 X1 + βp Zp

Table 2: The Descriptive Statistics of Research Variables

g j (x) is investment decisions as the dependent variable with a multinomial scale (five possible decisions) and the decline in Sharia-based stocks’ returns with four possible answers. Next, X is religiosity as the independent variable (total or per dimension), and Z is the control variables (gender, income, age, and participation in Islamic financial organizations). Table 3 below demonstrates the results of the multiple multinomial regression analysis between religiosity and investments.

Table 3: Multinomial Regression Analysis – The Effect of Religiosity on Investment Portfolios

Table 3: Continued

a. The reference category is: 100% Sharia-based stocks.

Explanation: significance levels 10 %(*), 5% (**), and 1% (***)

The above multivariate analysis shows the effect of religiosity (total or per dimension) on stock investment choices controlled by the sociodemographic variables (gender, age, income/ pocket money, and participation in Islamic financial organizations). The results demonstrate that the total religiosity variable has significant and consistent effects on every investment decision. Particularly, individuals with observant religiosity levels are less likely to select 100% conventional stocks than 100% sharia-based stocks. Hence, more religious individuals are less likely to select 100% conventional stocks than invest 100% of their funds in sharia-based stocks. We also find similar results for other investment choices (70% conventional 30% sharia, 50% conventional 50% sharia, and 30% conventional 70% sharia) compared with the reference value (100% sharia- based stocks).

Next, from each religiosity dimension’s perspectives, individuals with the highest score for belief in Allah are less likely to invest in 70% conventional stocks and 30% sharia-based stocks than in 100% sharia-based stocks with the probability value of 0.006. Similarly, individuals with higher scores for their worshiping behavior are less likely to invest in 70% conventional stocks and 30% sharia-based stocks than in 100% sharia-based stocks with the probability value of 0.333.

Belief in Islamic sharia is significant for the investment choice of 50% conventional stocks-50% sharia-based stocks with 100% investment in sharia-based stocks as the comparison. Thus, individuals with higher belief in Islamic sharia are less likely to invest in 50% conventional stocks and 50% sharia-based stocks than in 100% sharia- based stocks with the probability value of 0.142. Several demographic variables exhibit significant values in model 1 (total religiosity), such as age and participation in Islamic financial organizations. Meanwhile, in model 2 (religiosity dimensions), income/ pocket money and participation in Islamic financial organizations are the significant sociodemographic variables.

Based on the above statistical results, religiosity generally affects investment decisions (Mahdzan et al., 2017). More observant individuals (those with higher religiosity scores) prefer 100% sharia-based stocks to other proportions in their investment portfolios. The results demonstrate that Islamic societies have strong desire to avoid conventional stocks that their Islamic religious teachings consider sinful (Fabozzi et al., 2008). The investors avoid firms whose activities conflict with Islamic religious teachings, such as firms who sale products that contain pork, alcohol, and casino contradict Islamic religious teachings (Durand et al., 2013). Canepa and Ibnrubbian (2014) document that religious teachings affect individuals’ portfolio formation in Saudi Arabia. Hence, our findings support prior studies (Fabozzi et al., 2008; Durand et al., 2013; Canepa & Ibnrubbian, 2014; Mahdzan et al., 2017).

Next, the religiosity measurement dimensions that play crucial roles in investment decisions are belief in Allah, belief in Islamic sharia, and worshiping behaviour. Muslim investors consider sharia-based stocks important because they have strong beliefs in their religious teachings. Consequently, they are highly loyal to sharia-based financial products. These results show that observant Muslim investors will maximize metaphysical returns to obtain blessings (barakah) from Allah when making investment decisions by investing more in sharia-based stocks than conventional ones (Ghassan, 2015). Hence, the risk and return variables are insufficient in analysing the investment patterns of sharia-based financial products because other significant variables that are based on individuals’ values affect investment decisions such as religiosity.

Figure 1: Investment Reasons in Sharia-based Stocks

Our findings also highlight that participation in Islamic financial organizations strengthens further the decisions to buy sharia-based stocks for both model 1 and model 2. Thus, Islamic financial organizations in Indonesia play a crucial role in socializing Islamic finance in Indonesia. This study also include an open-ended question that asks the reasons for the respondents’ choices of investment portfolios. The following figure illustrates the results:

Figure 1 above indicates that more respondents invest in sharia-based stocks based on Islamic religious reasons (57%) than based on economic reasons (43%). Thus, the religiosity factor is more dominant in affecting investment decisions than the economic factor. Next, we analyse further the Islamic religious teachings on which Muslim investors base their investment decisions.

Muslim investors choose sharia-based stocks because they need to avoid riba, invest in halal products that comply with Islamic religious teachings (46%). Next, Muslim investors also expect other returns in the form of blessings (barakah) from Allah because they adhere to Islamic religious teachings (29%). After empirically underscoring the importance of metaphysical returns, we then investigate whether Muslim investors also consider materialistic returns as indicated by the returns of sharia- based stocks, especially when the returns of these stocks continue declining. Particularly, this study asks the percentage of the decline in sharia-based stocks’ returns that are still tolerable by Muslim investors. Table 4 below demonstrates the results.

Table 4 informs that individuals’ religiosity levels likely affect willingness to bear the declines in sharia-based stocks’ returns. In model 1, more religious individuals are less willing to bear the declines in sharia-based stocks’ returns of less than 25% than any percentage of decline in sharia-based stocks’ returns with the probability of 0.300 times. We find similar results for other percentages of return declines (25%- 50%, 50%-75%) as compared with any percentage of return decline. If analysed per religiosity dimension, belief in Allah and Islamic sharia have greater impacts on willingness to bear any percentage of decline in sharia-based stocks’ returns than other dimensions.

Next, for both model 1 and model 2, ages of level 0= 17-20 and 1=21-24 as the control variable significantly affect willingness to bear the return decline. In particular, respondents in these age groups are less willing to bear any percentage of the decline of sharia-based stocks’ returns, and they tend to accept a 25%-75% return decline.

The statistical results above suggest that highly observant Muslim investors tend to hold their sharia-based stocks although these stocks offer significant return declines (they are willing to bear any percentage of return decline). These findings demonstrate that more observant individuals are more loyal to sharia-based stocks and are more willing to sacrifice materialistic returns for metaphysical returns. However, the association is affected by individuals’ age. Specifically, younger individuals are less willing to bear any percentage of declines in sharia-based stocks’ returns. Thus, they still consider materialistic returns important, while older investors tend to prioritize metaphysical returns.

Overall, these findings do not support hypothesis 2 that predicts that individuals who adhere to their religious teachings more strongly are less willing to take risks. This study even documents the opposite results. Higher religiosity levels are associated with risk-taking behaviour, as indicated by the willingness to bear any percentage of the decline in sharia-based stocks’ returns. Thus, sharia-based stocks have a highly loyal market segment, especially for Muslim investors.

Table 4: Multinomial Regression Analysis – The Effect of Religiosity on Tolerable Declines in Sharia-based Stocks’ Returns

a. The reference category is: Any percentage of decline in sharia-based stocks’ returns.

Explanation: significance levels 10%(*), 5% (**), and 1% (***)

5. Conclusions

This paper concludes that individuals’ religiosity levels affect investment portfolio choices. Individuals with higher piety towards Islamic teachings are more likely to have investment portfolios that entirely (100%) consist of sharia- based stocks. The belief dimensions of religiosity measure (belief in Allah and belief in Islamic sharia) strengthen the results. Further, more observant Muslim investors will bear any decline in sharia-based stocks’ returns, implying that they are highly loyal to sharia products because they believe in Allah and Islamic sharia. The above discussions indicate that individuals’ adherence to religious teachings positions metaphysical returns to be more important than materialistic returns. However, younger investors exhibit different tendencies because they consider both metaphysical and materialistic returns in their investment decisions. Besides, Islamic financial organizations also play crucial roles in socializing Islamic finance to Muslim investors. This study highlights the importance of religiosity in sharia-based stock investments. Hence, future studies can use archival data to investigate the optimal prices for sharia-based stocks by involving the religiosity factor in the analysis.

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24. Hosmer, D. W., & Lemeshow, S. (2000) Applied logistic regression (2nd ed.). New York, NY: John Wiley & Sons, Inc.
25. Jiang, F., Jiang, Z., Kim, K. A., & Zhang, M. (2015). Family-firm risk-taking: does religion matter. Journal of Corporate Finance, 33, 260-278. https://doi.org/10.1016/j.jcorpfin.2015.01.007
26. Kim, I., & Venkatachalam, M. (2011). Are sin stocks paying the price for accounting sins?. Journal of Accounting, Auditing & Finance 26(2), 415-442. https://doi.org/10.1177/0148558x11401222
27. Kubler, D. (2001). On the regulation of social norms. Journal of Law, Economics, and Organization 17(2), 449-476. https://doi.org/10.1093/jleo/17.2.449
28. Kutschera, F. (1977). Subjective Preference, Rationality, and Justice. Social Ethics, 11(1), 97-111. https://doi.org/10.1007/bf00169846
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30. Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. The Review of Economics and Statistics, 47(1), 13-37. https://doi.org/10.2307/1924119
31. Lu, J., & Chan, C. (2012). Religious-based portfolio selection. Review of Financial Economics, 21(1), 31-38. https://doi.org/10.1016/j.rfe.2011.12.004
32. Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77-91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
33. Masri Jana, A., & Priester, P. E. (2007). The development and validation of a Qur'an-based instrument to assess Islamic religiosity: The Religiosity of Islam Scale. Journal of Muslim Mental Health, 2(2), 177-188. https://doi.org/10.1080/15564900701624436
34. Merton, R. C. (1987). A simple model of capital market equilibrium within 670 complete information, The Journal of Finance 42(3), 483-510. https://doi.org/10.1111/j.1540-6261.1987.tb04565.x
35. Olufadi, Y. (2017). Muslim Daily Religiosity Assessment Scale (MUDRAS): A new instrument for Muslim religiosity research and practice. Psychology of Religion and Spirituality, 9(2), 165-179. https://doi.org/10.1037/rel0000074
36. Rahmi, M., Azma, N., Muttaqin, A. A., Jazil, T., & Rahman, M. (2016). Risk Volatility Measurement: Evidence from Indonesian Stock Market, Journal of Asian Finance, Economics and Business, 3(3), 57-65. https://doi.org/10.13106/jafeb.2016.vol3.no3.57.
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text:
# OOP paradigm in python - Extend class functionalities

I am a novice of Python and I am trying to understand how to use OOP paradigm to improve my scripts. My scripts usually read some data from a formatted csv file and perform some numerical analysis. Here is a short example:

SIMPLY SUPPORTED BEAM
NNODES <NNnodes><Node,X,Y>
2
1,0,0
2,1,0

This input is for a script for solving a structural analysis problem. Generally one may want to extend the functionalities of the script adding new features, for instance adding elements, materials, section properties and so on.

My idea is to set up the code in such way one can include those functionalities in the easiest possible way.

My solution is to create a class, and then extend it using inheritance. Here what I wrote so far:

• A class for the properties of the problem, named Mesh
• Two initial instance variables storing the name of the input file and the title (first row of the csv file)
• A method for reading information from the file, named read_input
class Mesh() :
'class defining the property of the problem'

def __init__(self) :
self.name = None
self.title = None

self.name = input_name
with open(self.name) as file :

Let's say that one may want to improve the script including the number of nodes (NNODES in the csv file). First I create a class for node, storing ID and coordinates:

class Node() :
'class for defining a node'

def __init__(self, input1 , input2 , input3) :
self.ID = int(input1)
self.x = float(input2)
self.y = float(input3)

Then I add "functionalities" to the class defining a new child class (with the same name of the parent class, because I don't actually need a new child class, just a redefinition of the initial Mesh class ). The new class reads:

• New constructor, using super() to include the parent class constructor and new instance variables.
• Redefinition of the read_input method to include the new lines of the csv file.
class Mesh(Mesh) :

def __init__ (self) :
super().__init__()
self.Nnodes = None
self.nodes = list()

with open(self.name) as file :
for node in range(0,self.Nnodes) :
ID , x, y = file.readline().split(',')
self.nodes.append( Node( ID , x, y ) )

Finally, the initialization of the class and the use of the method to read the file:

input = Mesh()

Here my doubts:

• Is it a good application of the OOP paradigm or I have totally misunderstood the concept?
• Does it have any sense to call the child class with the same name of the parent class? (I did not find any examples in previous questions)
• Is it a good way to structure the code? Maybe other people than me will modify the code in future, and I would like to simplifies this procedure as much as possible.

I have always used procedural languages, such as C and FORTRAN, and I don't have any experience in OOP paradigm.

EDIT I modified the code with suggestions from StackOverflow

1. Modification of the class Mesh, in this way it should be self-contained.
2. Child class name different from the parent one.
3. Use of dataclass for defining the Node class.

Code:

from dataclasses import dataclass

class Mesh() :
'class defining the property of the problem'

def __init__(self , input1) :
self.title = input1

name = 'input_short.txt'''
with open(name) as file :

@dataclass
class Node:
'class for defining a node'

ID: int
x: float
y: float

class Mesh_nodes(Mesh) :
'Extend Mesh class to account for nodes'

def __init__(self , input1, input2, input3) :
super().__init__(input1)
self.Nnodes = input2
self.nodes = input3

name = 'input_short.txt'''
with open(name) as file :
nodes = list()
for node in range(0,Nnodes) :
ID , x, y = file.readline().split(',')
nodes.append( Node( int(ID) , float(x), float(y) ) )

mesh1 = Mesh_nodes(name,Nnodes,nodes)

Anyway, my original questions are still valid:

• Is it a good application of the OOP paradigm or I have totally misunderstood the concept?

• Is it a good way to structure the code? Maybe other people than me will modify the code in future, and I would like to simplifies this procedure as much as possible.

• The edit makes it apparent that the code doesn't work as intended. SECTIONS is not handled by the provided code. Feb 15 '20 at 15:09
• "I am just wondering if this is possible or not." Yes, it's possible. The answer isn't super(). Get the code working with "Edit 2" and then add another object and get it working with that. Once you have it working with 3 objects move them around and see how you can get it to work - you'll notice the while ignore loop is a problem. Feb 15 '20 at 15:56

Your code can probably utilize OOP. However, the way you're currently using objects is not what I'd call good.

But before we start adding in complicated objects, it looks like we can do everything you want with a couple of functions:

1. Read the title of the document:

self.title = file.readline()

2. You read until you get to NNODES:

while not file.readline().startswith('NNODES') : continue

self.Nnodes = int( file.readline() )

for node in range(0,self.Nnodes) :
ID , x, y = file.readline().split(',')
self.nodes.append( Node( ID , x, y ) )

All of 2-4 seems to be related to how you read NNODES objects, so we can just call them in the same function.

def load(file):
return {
}

_NNODE_KEYS = ['ID', 'x', 'y']

continue
values = []
for node in range(amount):
values.append(dict(zip(
_NNODE_KEYS,
)))
return values

with open('input_short.txt') as f:
import pprint
pprint.pprint(data)

{
'title': 'SIMPLY SUPPORTED BEAM',
'nnodes': [
{'ID': '1', 'x': '0', 'y': '0'},
{'ID': '2', 'x': '1', 'y': '0'},
]
}

I can understand how OOP would help here, but your current method isn't great.

Inheritance isn't really going to help here. All you need to do is make your objects have a load method like the above. This load method should be a staticmethod so that it's in charge of instantiating the objects. It seriously just needs to be that simple.

from __future__ import annotations
from dataclasses import dataclass

@dataclass
class Mesh:
title: str
nnode: NNode

@classmethod
return cls(
)

@dataclass
class NNode:
nodes: List[dict]

@classmethod
continue
values = []
for node in range(amount):
values.append(dict(zip(
_NNODE_KEYS,
)))
return cls(values)

Now this could be a cool little file reader project you have. But the thing is, that you've not really implemented much.

1. You ignore vital data with a while ignore loop.
2. You ignore what the data should look like, you don't parse NNODES <NNnodes><Node,X,Y>.
3. You assume everything is the exact same format, you haven't implemented a way to allow different classes.

Overall I'm not going to write these things for you. I suggest you try your arm at them with the above code.

• Your code for sure is better than mine, but that's not exactly what i'm looking for. I made a small edit to the question. Feb 15 '20 at 15:06
• @Stefano As addressed at the bottom of my answer, you have not written that and so I'm not going to create something you can't be arsed to implement yourself. Feb 15 '20 at 15:08
• Of course you are right, but I don't want you to write the code for me. Probably my edit 2 is bad written Feb 15 '20 at 15:20
• @Stefano "but I don't know how to start to find a solution." shows the code not working as you intend, and all you're asking is "give me a solution to my problem". That is off-topic here, as your code should be working the way you intend it to; it's clear it's not. Feb 15 '20 at 15:28
• The problem is that I don't really know where to find something. I looked at previous questions, I looked in the manuals, I looked at some guides on internet. I'll try to make a code that does not work as I would like Feb 15 '20 at 15:49

format: plain


text:
# For an earth station transmitter input power of 40 dBW (10,000 W), with a backoff loss of 3 dB, a total branching and feeder loss of 3 dB, and a transmit antenna gain of 40 dB, determine the EIRP.

Free Practice With Testbook Mock Tests

## Options:

1. 40 dBW

2. 74 dBW

3. 34 dBW

4. 80 dBW

### Correct Answer: Option 2 (Solution Below)

This question was previously asked in

ISRO Scientist EC 2011 Official Paper

## Solution:

Concept:

EIRP: It stands for Effective isotropic Radiated power. It is defined as in dB.

EIRP = transmit power + transmitting Antenna gain - cable loss

$$Cable\;loss \Rightarrow \underbrace {Branching\;loss + feeder\;loss + Backoff\;loss}_{loss\;in\;power\;due\;to\;external\;devices}$$

Calculation:

Given = Pt = 40 dBW; backoff loss = 3 dB; feederloss = 3 dB

Antenna gain (Gt) = 40 dBW

EIRP = 40 + 40 - 3 - 3 = 74 dBW


text:
##### Question Info

This question is public and is used in 115 tests or worksheets.

Type: Multiple-Choice
Category: Functions and Relations
Standards: HSF-IF.A.2
Tags: functions

# Functions and Relations Question

View this question.

Add this question to a group or test by clicking the appropriate button below.

## Grade 9 Functions and Relations CCSS: HSF-IF.A.2

The function $f(x)=50(1.2)^x$ gives the number of bacteria in a science experiment, where x is the number days after the start of the experiment. To the nearest whole number, how many bacteria will there be after 5 days?
1. 124
2. 375,000,000
3. 300
4. 777,600,000
You need to have at least 5 reputation to vote a question down. Learn How To Earn Badges.


text:
International Association for Cryptologic Research

# IACR News Central

Get an update on changes of the IACR web-page here. For questions, contact newsletter (at) iacr.org. You can also receive updates via:

To receive your credentials via mail again, please click here.

You can also access the full news archive.

Further sources to find out about changes are CryptoDB, ePrint RSS, ePrint Web, Event calender (iCal).

2013-11-30
04:17 [Pub][ePrint]

Recently, researchers have proposed many non-interactive deniable authentication (NIDA) protocols. Most of them claim that their protocols possess full deniability. However, after reviewing, we found that they either cannot achieve full deniability, or suffer KCI or SKCI attack; moreover, lack efficiency, because they are mainly based on DLP, factoring problem, or bilinear pairings. Due to this observation, and that ECC provides the security equivalence to RSA and DSA by using much smaller key size, we used Fiat-Shamir heuristic to propose a novel ECC-based NIDA protocol for achieving full deniability as well as getting more efficient than the previous schemes. After security analyses and efficiency comparisons, we confirmed the success of the usage. Therefore, the proposed scheme was more suitable to be implemented in low power mobile devices than the others.

04:17 [Pub][ePrint]

itCoin is a decentralized digital currency, introduced in 2008, that has recently gained noticeable popularity. Its main features are: (a) it lacks a central authority that controls the transactions, (b) the list of transactions is publicly available, and (c) its syntax allows more advanced transactions than simply transferring the money. The goal of this paper is to show how these properties of BitCoin can be used in the area of secure multiparty computation protocols (MPCs).

Firstly, we show that the BitCoin system provides an attractive way to construct a version of \"timed commitments\", where the committer has to reveal his secret within a certain time frame, or to pay a fine. This, in turn, can be used to obtain fairness in some multiparty protocols. Secondly, we introduce a concept of multiparty protocols that work \"directly on BitCoin\". Recall that the standard definition of the MPCs guarantees only that the protocol \"emulates the trusted third party\". Hence ensuring that the inputs are correct, and the outcome is respected is beyond the scope of the definition. Our observation is that the BitCoin system can be used to go beyond the standard \"emulation-based\" definition, by constructing protocols that link their inputs and the outputs with the real BitCoin transactions.

As an instantiation of this idea we construct protocols for secure multiparty lotteries using the BitCoin currency, without relying on a trusted authority (one of these protocols uses the BitCoin-based timed commitments mentioned above). Our protocols guarantee fairness for the honest parties no matter how the looser behaves. For example: if one party interrupts the protocol then her money is lost and transferred to the honest participants. Our protocols are practical (to demonstrate it we performed their transactions in the actual BitCoin system), and can be used in real life as a replacement for the online gambling sites. We think that this paradigm can have also other applications. We discuss some of them.

04:17 [Pub][ePrint]

We extend the techniques of Kiltz et al. (in ASIACRYPT 2010) and Galindo et al. (in SAC 2012) to construct two efficient leakage-resilient signature schemes. Our schemes based on Boneh-Lynn-Shacham (BLS) short signature and Waters signature schemes, respectively. Both of them are more efficient than Galindo et al.\'s scheme, and can tolerate leakage of (1-o(1))/2 of the secret key at every signature invocation. The security of the proposed schemes are proved in the generic bilinear group model (additionally, in our first scheme which based on the BLS short signature, a random oracle is needed for the proof).

2013-11-28
13:44 [Event][New]

Submission: 3 March 2014
Notification: 14 April 2014
From June 5 to June 6
Location: Moscow, Russia
More Information: http://www.tc26.ru/en/CTCryptEN/CTCrypt2014/

2013-11-26
10:25 [Event][New]

Submission: 3 February 2014
Notification: 11 April 2014
From July 19 to July 22
Location: Vienna, Austria
More Information: http://csf2014.di.univr.it/index

10:24 [Job][New]

A 4 year position as Senior Assistant (postdoc) is available at the Mathematics Department in Neuchatel (Switzerland). Little teaching duties (in French). Preference will be given to candidates who reinforce one of the research directions of the department (among which we have coding theory and cryptography). The starting date is Aug-Sept 2014.

Further information soon available at http://www2.unine.ch/sciences/cms/op/edit/lang/fr/emploi

10:23 [Job][New]

The Information Security Group at Royal Holloway, University of London is seeking to recruit a post-doctoral research assistant to work in the area of “Cryptography: Bridging Theory and Practice”. The position is available immediately and will run until February 28th 2015.

The post-doc will join a team of post-docs and PhD students working under the leadership of Prof. Kenny Paterson. The aim of the project is to find weaknesses in cryptographic specifications and implementations, to understand how these weaknesses can be addressed in practical ways, and to develop extensions of current cryptographic theory that permit more realistic modelling of cryptographic primitives as they are used in fielded systems. The position will also involve activities designed to engage both the theory community and practitioners in the research.

Applicants should have already completed, or be close to completing, a PhD in a relevant discipline. Applicants should have an outstanding research track record in Cryptography, in either theoretical or applied aspects of the subject, and, ideally, in both aspects. Applicants should be able to demonstrate scientific creativity, research independence, and the ability to communicate their ideas effectively in written and verbal form.

Salary is in the range £32,862 to £34,724 per annum inclusive of London Allowance

Informal enquiries can be made to Kenny Paterson at kenny.paterson (at) rhul.ac.uk.

To view further details of this post and to apply please visit http://www.rhul.ac.uk/aboutus/jobvacancies/home.aspx . The RHUL Recruitment Team can be contacted with queries by email at: recruitment (at) rhul.ac.uk or via telephone on: +44 (0)1784 41 4241.

Please quote the reference: X1113/7450

Closing Date: Midnight, Sunday 22nd December 2013

Interview Date: To be confirmed

08:03 [News]

The Ethics Committee of the IACR is responsible for providing recommendations to editors, program chairs, program-committee members, and reviewers concerning fairness and ethical aspects of all matters under the influence of the IACR, such as its operations, its events, and its publications.

The mission of the Ethics Committee is described in the "IACR Policy for the Ethics Committee", available at http://www.iacr.org/docs/

The Ethics committee has discussed only a handful of cases in 2013. In the interest of raising awareness for ethical matters among the researchers in cryptology, the Ethics Committee may occasionally inform the IACR members about its work. An account of one case follows.

A team of authors submitted a paper to a non-IACR conference in the field of cryptology and information security. After submitting the work, the authors developed their method further and discovered other ways to attack the problem. Before receiving an acceptance or rejection notification from the conference, the authors had written another paper on the second method and submitted this to a second conference, this one sponsored by the IACR. The second paper did not cite or mention the first paper.

Some reviewers in the overlap of the two program committees spotted a similarity of the works, and, in line with the IACR Policy on Irregular Submissions, they shared this information with the program chairs of the two venues. The program chair of the first conference then rejected the first paper declaring that it was a "potential double submission" and informed the program chair of the IACR conference about this. The authors then reached out to the IACR Ethics Committee and explained their case. They wanted to obtain a clarification that there was no double submission.

The Ethics Committee reviewed the situation and examined the submitted papers superficially. The committee then concluded that there was no obvious case of "parallel submissions" as described in the IACR Policy and that the second paper should enter the regular reviewing process of the IACR conference. The committee also remarked that it cannot make any statement towards the first conference because it is not an IACR venue. To the committee, it seemed that there was a misunderstanding because the existence and nature of technical links between the contributions of the two papers were not mentioned by the authors.

Last but not least, the committee recommended to the authors that, in the interest of being transparent in scientific work, authors should always cite existing known related work, even when a new contribution would not directly build on it. Furthermore, considering the delicate issues around double submissions, this point was particularly important with related work from the same authors.

#### IACR Ethics Committee (2013)

• Josh Benaloh
• Thomas Berson
• Christian Cachin (chair)

07:58 [Event][New]

Submission: 14 April 2014
Notification: 9 June 2014
From September 3 to September 5
Location: Amalfi, Italy
More Information: http://scn.dia.unisa.it/

2013-11-25
22:17 [Pub][ePrint]

The authenticated encryptions which resist misuse of initial value (or nonce) at some desired level of privacy are two-pass or Mac-then-Encrypt constructions (inherently inefficient but provide full privacy) and online constructions, e.g., McOE, sponge-type authenticated encryptions (such as duplex, AEGIS) and COPA. Only the last one is almost parallelizable with some bottleneck in processing associated data. In this paper, {\\em we design a new online secure authenticated encryption, called \\tx{ELmE} or Encrypt-Linear mix-Encrypt, which is completely (two-stage) {\\bf parallel} (even in associated data) and {\\bf pipeline implementable}}. It also provides full privacy when associated data (which includes initial value) is not repeated. The basic idea of our construction and COPA are based on \\tx{EME}, an Encrypt-Mix-Encrypt type SPRP constructions (secure against chosen plaintext and ciphertext). Unlike \\tx{EME}, we consider (so does COPA) online computable {\\bf linear mixing}. In addition with getting rid of bottleneck, our construction optionally supports {\\bf intermediate tags} which can be verified faster with less buffer size. Intermediate tag provides security against block-wise adversaries which is meaningful in low-end device implementation.

22:17 [Pub][ePrint]

We present a new Cryptographically Secure Pseudo-Random Number Generator. It uses permutations as its internal state, similarly to the RC4 stream cipher. We describe a statistical test which revealed non-random patterns in a sample of $2^{16.6}$ outputs of a 3-bit RC4.

Our new algorithm produced $2^{46.8}$ undistinguishable from random 3-bit outputs in the same test. We probed $2^{51}$ outputs of the algorithm in different statistical tests with different word sizes

and found no way of distinguishing the keystream from a random source. The size of the algorithm\'s internal state is $2^{3424}$ (for an 8-bit implementation). The algorithm is cryptographically secure to the extent we were able to analyse it. Its design is simple and easy to implement. We present the generator along with a key scheduling algorithm processing both keys and initialization vectors.


text:
# Finding the second derivative of an integral function

I have a continuous function $f:[0,1] \rightarrow \mathbb R$ and I would like to find the second derivative of $$G(x) = \int_x^1(t-x)f(t)dt$$

I started off by using partial integration and got:

$$G(x) = [(t-x)\int_0^tf(s)ds]|_x^1 - \int_x^1\Big ( \int_0^tf(s)ds\Big )dt=$$ $$(1-x)\int_0^1f(s)ds-\int_x^1\Big ( \int_0^tf(s)ds\Big )dt$$

This is where I get stuck. If, what I have so far is correct, I would move on trying to take the derivative of $G$ now with the Fundamental theorem of calculus. However, since I am using it for the first time, I do not quite know what to do, especially with the limits of my integral being switched up ($x$ is the lower limit instead of the upper limit). How do I proceed here? Any help is greatly appreciated!

• You can just swap the limits by putting in a $-$ sign in front. Also you could use $\frac{d}{dx}\int_a^x f(t)dt=f(x)$. – John Doe Apr 21 '17 at 16:19
• @JohnDoe Then is the answer $G''(x) = f'(x)$ correct? – AxiomaticApproach Apr 21 '17 at 16:23
• Not quite - see my answer – John Doe Apr 21 '17 at 16:26
• @JohnDoe got it, will approve the answer once I can. Thanks! – AxiomaticApproach Apr 21 '17 at 16:26

$$G(x)=(1-x)\int_0^1f(s)ds-\int_x^1\Big ( \int_0^tf(s)ds\Big )dt$$

$$G'(x)=-\int_0^1f(s)ds+\frac{d}{dx}\int_1^x\Big ( \int_0^tf(s)ds\Big )dt$$

$$=-\int_0^1f(s)ds+\int_0^xf(s)ds$$

$$\Rightarrow G''(x)=f(x)$$

You can use the Leibniz integral rule: $$\frac{d}{dx}\int_{a(x)}^{b(x)} c(x,t)\,dt = \int_{a(x)}^{b(x)}\frac{dc}{dx}(x,s)\,ds + c[x,b(x)]\frac{db}{dx} - c[(x,a(x)]\frac{da}{dx}.$$

This will give $$G'(x) = \int_{x}^1 -f(t)\,dt + 0 - 0$$ $$G''(x) = 0+0+f(x).$$


text:
### Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

### Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

### Dice and Spinner Numbers

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

# Lemons and Oranges

##### Stage: 2 Challenge Level:

(If you are working with metric measures go here )

On the table there is a pile of oranges and lemons that weighs exactly two and a half pounds.

The oranges all weigh $4$ oz. The lemons are also all the same weight, which is less than $\frac{3}{4}$ of the weight of an orange.

There are twice as many lemons as oranges in the pile.

How many lemons are there and how much does each one weigh?


text:
Questions on concepts with multiple definitions

Recently, I've seen several questions on measure theory in which an answer must prove a set is measurable. To several of these questions, for example this, someone replies in the comments or an answer something to the effect of "$\sigma$-algebras are closed under [some set theoretic operation] so this set is measurable." These answers often strike me as not very useful to the OP as many measure theory classes begin with a construction of the Lebesgue measure and then later discuss abstract measure theory. Thus, it is unlikely that they have already proven the set of Lebesgue measurable sets form a $\sigma$-algebra, so these answers are not helpful to them.

The problem is further complicated by the many logically equivalent definitions of measurability (e.g. Caratheodory, approximation by open sets, etc.), which can also lead to answers that are unhelpful to the OP as they use a different definition of measurability that they may not yet have proved is equivalent to the one they are familiar with.

Similar problems occur in other subjects. For example, I have seen users trying to prove $\bar{A}$ is closed. Using one definition of the closure (the intersection of all closed sets containing $A$), this statement is trivial; using the other common definition ($\bar{A} = A \cup A'$) this question is less trivial.

As I see it, the problem is two-fold:

• Questioners not specifying which of the many equivalent definitions of concept they are using, thus making it hard for answerers to provide helpful answers.
• Answerers assuming the OP is using a logically equivalent definition of a concept which they would be unfamiliar with and then providing answers to the question that aren't helpful to the OP. (Of course, these answers may still be useful to the OP in the future and to other users.)

I'm not really sure there is a fix to this problem, but I thought I would bring it up in meta. Have others seen situations like this? Other than requesting feedback in the comments, is there a way we can make it clear to new users that there often many equivalent definitions of concepts they are using and suggest they include which one they are using in their questions?

• Personally, I find it handy to keep a list of links to TFAE theorems for big definitions in my field. Then I can point OP in the right direction if it turns out he's using a definition that's different from mine. – Alexander Gruber Nov 27 '17 at 4:13
• This is one of the reasons why it is good to provide context in questions, and definitions being used are often part of the relevant context. – Michael Greinecker Nov 27 '17 at 8:32
• Answerers can not read the minds of askers to discern precisely which of perhaps many definitions the asker has been exposed to. So I agree with @MichaelGreinecker, that it is the asker's responsibility to define the terms they are asking about. Of course, many such questions receive comments to that effect, so the asker often has prompts to define concepts/definitions as they are currently familiar with. – Namaste Nov 27 '17 at 17:49
• I normally ask for context from the OP and sometimes get a reply about the definition being used. When no such context is provided even after request I generally preface the answer with the definition being used. And the option to downvote for lack of context is always available. – Paramanand Singh Nov 29 '17 at 12:25
• Of course you have to be aware that there are different definition in order to take that possibility in account. I for one had not been aware before reading your question that anyone defines $\overline A$ not as the smallest closed set containing $A$ (the intersection is just another formulation of the same definition, of course). – celtschk Nov 30 '17 at 6:59
• @AlexanderGruber: What are TFAE theorems? – celtschk Nov 30 '17 at 7:02
• @celtschk TFAW stands for The following are equivalent" – eepperly16 Nov 30 '17 at 7:51
• It is obvious that answerers cannot read the questioner's mind. In some cases, though, if an answerer happens to be aware that multiple definitions are used in various contexts, they might indicate this awareness rather than blithely answering from a particular perspective. That's only if they happen to be aware of other perspectives, and happen to remember about them at the time, of course. – G Tony Jacobs Dec 2 '17 at 21:09