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In this paper, we present the notion of a magic pair of digits in a number system with an arbitrary basis b, and we study its equivalent definitions. In particular, we determine all pairs of magic digits in decimal, octal, hexadecimal, and binary number system. We use magic pairs of digits to derive a new multiplication formula. In the end, we give an application of a well-known formula related to magic pairs. [ABSTRACT FROM AUTHOR]

This paper is an initial attempt to make an empirical evaluation of what happened in Chile after the 2004 enactment of the new Civil Marriage Act (Law 19,947), which included absolute divorce for the first time in Chilean law. Until that moment, the way that a marriage could formally be ended was by an annulment due to incompetence of the Civil Registry officer, possible only provided there was mutual consent of the spouses and the resources to hire an attorney. The analysis says that although the divorce rate has increased considerably with respect to the annulment rate prior to the law, it is not high in relation to other countries, despite an accumulation of couples who wanted to be divorced at the time the law was enacted. The study concludes that the new Civil Marriage Act has extended and equalized the possibility of a legal dissolution of the bond of marriage. Although no changes are seen in birth rates and the percentage of infants born outside of marriage, marriages have increased, even when controlling for some variables and discounting second marriages. Also, under the new law divorced women and their children would be more protected than women who are merely separated as the former would receive more alimony from their ex-husbands. At the end, some policy measures are discussed. [ABSTRACT FROM AUTHOR]

To what extent was the Great Financial Crisis of 2007-2009 similar to previous crises, and what were the main causes behind it? The purpose of this paper is to explore these questions, presenting the traditional pattern followed by financial crises in the past, a chronology of the recent crisis, and an in-depth analysis of its causes. We distinguish between three different classes of causes in our analysis: those which created the opportunity for severe distortions to arise in the financial system, those which explain the desire of the financial system to take advantage of them, and those responsible for the neglect shown by our regulatory and supervisory frameworks to rein them in and avoid a catastrophic event. The crisis was caused by a complex series of factors, some of which are traditional, and others are new to our experience. Distinguishing clearly between main causes and mere symptoms of the crisis is essential for the design of adequate regulatory policy. [ABSTRACT FROM AUTHOR]