Like a Sum Is Generalized into an Integral, a Product May Be Generalized into an Inteduct

It is well known that an integral is nothing but a continuous form of a sum. Is it possible to do the same thing with a product? The answer is yes and done for the first time in this publication. The new operator is called inteduct. As an integral is a proper tool to calculate the arithmetic mean of a function, the inteduct gives the geometric mean of a function. This defines a new branch of mathematics. Most applications may lay way ahead. Only some are discussed here. One is applying the inteduct to probability theory. There it is possible e.g., to determine a function for a life expectation rather than just a numerical value. Another application is to distinguish chaos from randomness within numerically given values. At least for the logistic map there exists a direct connection between Lyapunov exponent and inteduct. To distinguish between chaos and randomness is particularly important in finance. While randomness implies ergodicity, chaos is non-ergodic. And many fundamental financial theories from portfolio theory to market efficiency require ergodicity.

Wrong Use of Averages Implies Wrong Results from Many Heuristic Models

In a linear world, averages make perfect sense. Something too big is compensated by something too small. We show, however that the underlying differential equations (e.g. unlimited growth) rather than the equations themselves (e.g. exponential growth) need to be linear. Especially in finance and economics non-linear differential equations are used although the input parameters are average quantities (e.g. average spending). It leads to the sad conclusion that almost all results are at least doubtful. Within one model (diffusion model of marketing) we show that the error is tremendous. We also compare chaotic results to random ones. Though these data are hardly distinguishable, certain limits prove to be very different. Implications for finance can be important because e.g. stock prices vary generally, chaotically, though the evaluation assumes quite often randomness.

Scrutinizing Distributions Proves That IQ Is Inherited and Explains the Fat Tail

The motivation of this paper is to show how to use the information from given distributions and to fit distributions in order to confirm models. Our examples are especially for disciplines slightly away from mathematics. One minor result is that standard deviation and mean are at most a more or less good approximation to determine the best Gaussian fit. In our first example we scrutinize the distribution of the intelligence quotient (IQ). Because it is an almost perfect Gaussian distribution and correlated to the parents’ IQ, we conclude with mathematical arguments that IQ is inherited only which is assumed by mainstream psychologists. Our second example is income distributions. The number of rich people is much higher than any Gaussian distribution would allow. We present a new distribution consisting of a Gaussian plus a modified exponential distribution. It fits the fat tail perfectly. It is also suitable to explain the old problem of fat tails in stock returns.

A Statistical Analysis of Games with No Certain Nash Equilibrium Make Many Results Doubtful

Some games may have a Nash equilibrium if the parameters (e.g. probabilities for success) take certain values but no equilibrium for other values. So there is a transition from Nash equilibrium to no Nash equilibrium in parameter space. However, in real games in business and economics, the input parameters are not given. They are typically observed in several similar occasions of the past. Therefore they have a distribution and the average is used. Even if the averages are in an area of Nash equilibrium, some values may be outside making the entire result meaningless. As the averages are sometimes just guessed, the distribution cannot be known. The main focus of this article is to show this effect in an example, and to explain the surprising result by topological explanations. We give an example of two players having three strategies each (e.g. player and keeper in penalty shooting) where we demonstrate the effect explicitly. As the transition of Nash equilibrium to no equilibrium is sharp, there may be a special form of chaos which we suggest to call topological chaos.

Intercultural Trust in Global Contexts:Synthesizing a Western Nomological Approach with a Chinese Systems Approach

Intercultural trust in global contexts plays a central role in helping people from different cultures to communicate comfortably,which is essential for cooperation.Attempting to construct a framework that might foster international cooperation,and thus be helpful for coping with global emergencies,we relate a Western nomological approach to an Eastern systems approach to analyse intercultural trust in global contexts.Considering cultural impacts on intercultural trust and the nomological framework of cultural differences,we propose an intercultural trust model to interpret how cultural differences influence trust.A qualitative study of Chinese-Irish interactions was conducted to interpret this model.We organized 10 seminars on intercultural trust,and interviewed 16 people to further explore the respondents'deeper feelings and experiences about intercultural trust in global contexts.Through this study,we have identified factors impacting on intercultural trust,and found that intercultural trust can be developed and improved in various ways.To llustrate these ways,we have provided tactics and methods for building intercultural trust in global contexts.Implications are highlighted for organizations to avoid cultural clashes and relevant political or economic risks.