Fair income tax with endogenous productivities and a fresh start

This paper considers a model in which agents have heterogeneous preferences over labour and consumption. Additionally, they also differ in their earning skills, which are a function of both an innate ability and an early investment decision. In this framework we axiomatically derive a social ordering function that, besides compensating agents for their unequal productivities, grants a fresh start to those who regret their initial choices. Next, by assuming a second-best context we characterise the income tax scheme that satisfies this social ordering. This analysis permits us to present an explicit criterion for the assessment of social welfare under different tax policies. We obtain that the optimal scheme aims to compensate those endowed with the lowest marginal productivity. More importantly, on account of the forgiveness ideal positive social marginal weights are assigned to those who earn the lowest income levels, something that induces a progressivity tendency at the bottom of the earnings distribution.

A Stopping Criterion for the Training Process of the Specific Signal Generator

Mathematical description of a complex signal is very important in engineering but nearly impossible in many occasions. The emergence of the Generative Adversarial Network (GAN) shows the possibility to train a single neural network to be a Specific Signal Generator (SSG), which is only controlled by a random vector with several elements. However, there is no explicit criterion for the GAN training process to stop, and in real applications the training always stops after a certain big iteration. In this paper, a serious issue was discussed during the process to use GAN as a SSG. And, an explicit criterion for the GAN as a SSG to stop the training process were proposed. Several experiments were carried out to illustrate the issues mentioned above and the effectiveness of the stopping criterion proposed in this paper.

A Novel Methodology to Calculate the Probability of Volatility Clusters in Financial Series: An Application to Cryptocurrency Markets

One of the main characteristics of cryptocurrencies is the high volatility of their exchange rates. In a previous work, the authors found that a process with volatility clusters displays a volatility series with a high Hurst exponent. In this paper, we provide a novel methodology to calculate the probability of volatility clusters with a special emphasis on cryptocurrencies. With this aim, we calculate the Hurst exponent of a volatility series by means of the FD4 approach. An explicit criterion to computationally determine whether there exist volatility clusters of a fixed size is described. We found that the probabilities of volatility clusters of an index (S&P500) and a stock (Apple) showed a similar profile, whereas the probability of volatility clusters of a forex pair (Euro/USD) became quite lower. On the other hand, a similar profile appeared for Bitcoin/USD, Ethereum/USD, and Ripple/USD cryptocurrencies, with the probabilities of volatility clusters of all such cryptocurrencies being much greater than the ones of the three traditional assets. Our results suggest that the volatility in cryptocurrencies changes faster than in traditional assets, and much faster than in forex pairs.

Hopf Bifurcation of the Higher Dimensional Hénon Map

In this paper, the discrete time generalized Hénon map is considered and the existence of Hopf bifurcation via an explicit criterion for N≥3, in particular for N=4 and N=5 has given. The relation between the parameters a and b as well as the range of the values of the parameters for N=3,4,5 has driven and the existence of Hopf bifurcation is demonstrated for the values of the parameters calculated from their relations. The results of numerical simulations for different values of the parameters are also presented. Dhaka Univ. J. Sci. 67(1): 73-78, 2019 (January)

On the number of bound states of semirelativistic Hamiltonian with Dirac delta potentials in one dimension

We study the bound state problem for semirelativistic N attractive Dirac δ-potentials in one dimension. We give a sufficient condition for the Hamiltonian to have N bound states and give an explicit criterion for it.

Regulators of an Infinite Family of the Simplest Quartic Function Fields

We explicitly find regulators of an infinite family {Lm} of the simplest quartic function fields with a parameter m in a polynomial ring [t], where is the finite field of order q with odd characteristic. In fact, this infinite family of the simplest quartic function fields are subfields of maximal real subfields of cyclotomic function fields having the same conductors. We obtain a lower bound on the class numbers of the family {Lm} and some result on the divisibility of the divisor class numbers of cyclotomic function fields that contain {Lm} as their subfields. Furthermore, we find an explicit criterion for the characterization of splitting types of all the primes of the rational function field (t) in {Lm}.

Paradigms in information science

Purpose – The purpose of this paper is the conceptual expansion of the science-theoretical foundations of information science, i.e. to develop new thought schemes for information science. Design/methodology/approach – The design of the paper is as follows: first, the paper will discuss the foundation of the systemic paradigm (SP). Then the authors will consider the history of information science related to the philosophy of science. In the remaining part of the paper, the authors will investigate information science and its relation to the philosophy of science, focusing on SP. Findings – In conclusion, the authors will summarise the seven criteria for the application of SP in information science. Research limitations/implications – Paradigms in information science have rarely reflected upon the use of a SP in information science. Practical implications – The practical use of the seven criteria in information science Criterion 1: make your premises, suppositions, prerequisites and motives explicit. Criterion 2: make your moral/ethical results and consequences explicit. Criterion 3: research should be evaluated in relation to the transcendence of knowledge. Criterion 4: emphasise methodical pluralism, i.e. empirical generalisations and conceptual generalisations. Criterion 5: emphasise proximity and in-depth studies. Criterion 6: look for patterns and patterns which combine. Criterion 7: look for the power behind the patterns. Social implications – The opinion is that scientists to a great extent should seek knowledge on the basis of a belief, a specific way of thinking, and by means of specific methods. To make the authors belief explicit makes the way of thinking visible. What the authors achieve, and possibly the only thing the authors can achieve, is to reaffirm the conscious belief. This does not make reality more real, but it could put the authors in a better position to see through the authors way of thinking when faced with scientific problems. This indicates that a scientific study should emphasise all three entities: “The Context of Discovery”, “The Context of Justification” and “The Context of Solution”. These three entities, according to SP, make up the unity of the scientific process. Originality/value – The seven criteria entail that Kuhn’s argumentative chain (where he tries to find out why theory A is preferred to theory B on a rational pretext) does not concur with SP. This indicates that a scientific study should emphasise all three entities: “The Context of Discovery”, “The Context of Justification” and “The Context of Solution”. These three entities, according to SP, make up the unity of the scientific process.

Rational criterion testing the density of additive subgroups of R^n and C^n

<p>In this paper, we give an explicit criterion to decide the<br />density of finitely generated additive subgroups of R^n and C^n.</p>