The theory of legitimate expectation has been raised as one of the means of judicial review over exercising discretionary power in some European countries, including UK. This theory was initially considered by Schmidt's case, but this theory has been seriously criticized and many English lawyers and judges made serious doubts about it. In this paper, while outlining different perspectives, answers the question "What is the nature of the legitimate expectation and the challenges posed on this theory in the England Administrative Law System? Although the foundations of legitimate expectation have been based on "fairness", there is no single view on the nature and function of "legitimate expectations". Doubtful about accepting a substantive legitimate expectation in England and not accepting it in New Zealand and Australia, The concept of "prohibition of abuse of power" in the issuance of certain judicial opinions, the violation of the principle of separation of powers and rival concepts, such as the principle of proportionality, has posed legitimate expectations with serious challenges. These challenges have caused this concept to not have the characteristics of a legal principle.

We prove that the limit of a sequence of Pettis integrable bounded scalarly measurable weak random elements, of finite weak norm, with values in the dual of a non-separable Banach space is Pettis integrable. Then we provide basic properties for the Pettis conditional expectation, and prove that it is continuous. Calculus of Pettis conditional expectations in general is very different from the calculus of Bochner conditional expectations due to the lack of strong measurability and separability. In two examples, we derive the Pettis conditional expectations.

Data mining and knowledge discovery are important technologies for business and research. Despite their benefits in various areas such as marketing, business and medical analysis, the use of data mining techniques can also result in new threats to privacy and information security. Therefore, a new class of data mining methods called privacy preserving data mining (PPDM) has been developed. The aim of researches in this field is to develop techniques those could be applied to databases without violating the privacy of individuals. In this work we introduce a new approach to preserve sensitive information in databases with both numerical and categorical attributes using fuzzy logic. We map a database into a new one that conceals private information while preserving mining benefits. In our proposed method, we use fuzzy membership functions (MFs) such as Gaussian, P-shaped, Sigmoid, S-shaped and Z-shaped for private data. Then we cluster modified datasets by Expectation Maximization (EM) algorithm. Our experimental results show that using fuzzy logic for preserving data privacy guarantees valid data clustering results while protecting sensitive information. The accuracy of the clustering algorithm using fuzzy data is approximately equivalent to original data and is better than the state of the art methods in this field.

Acquiring information about expectations is difficult as individuals' beliefs are unobservable. Thus, how expectation forms and how to model expectation is an open question in economic modelling that has been addressed recently by experimental economics. In this article, in order to identify expectations, we examine the behaviour of subjects when encountering new exchange rates in an experiment.  Furthermore, in this experiment, differences of expectation formation among participants and their relation to cognitive abilities are analysed. To motivate people, incentive payments are used. In our setting, while the rational expectation hypothesis is not supported, the adaptive expectation is not rejected. Agents form their expectations in the same way regardless of their cognitive ability. In this context, individuals overreact to the new quantity of exchange rate which is assumed as a noisy perception.  This finding is considered as evidence of emotional behaviours in the exchange market.

Since the housing sector has an intricate relationship with other sectors of the economy, fluctuations in the price can be costly. Also, rising prices are either rooted in the underlying conditions of the economy or simply caused by the bubble, leading to different policies. Therefore, house price bubble can be considered as an early warning system to prevent adverse economic consequences. The present paper applies the theory of rational expectation bubble in the Iranian housing market during the years 2006-2020 using the Blanchard and Watson model. The theory implies that negative returns on house prices are less likely to occur if the bubbles exist. The risk assessment is, however, estimated by linear logistic function. The existence of bubble in housing market is confirmed based on 30 provinces.

Dear Editor, The new available coronavirus disesae COVID‑, 19 vaccine becomes the new hope for the control of the disease. A recent report showed that the vaccine could induce protection in a large group of vaccinated subjects. With the rapidly increasing demand for the COVID‑, 19 vaccine, the supply is usually insufficient and the price of the vaccines becomes greatly different among different buyers. At present, there are many brands of the COVID‑, 19 vaccine with different cost‑, effectiveness properties. Sometimes, it takes a long time to get a sufficient amount of COVID‑, 19 vaccine supplied by a manufacturer. There is a new idea for vaccine brand mixing—, different vaccine brands in different doses. As noted by Public Health England, this should be on extremely rare occasions. To date, there are no data from the trial on the newly proposed ideas. However, it might be roughly predicted using a medical mathematical prediction. Here, the authors focus on the three different available vaccines for the switching model. . .