Connection between type B (or C) and F factorizations and construction of algebras

In a recent paper (Del Sol Mesa A and Quesne C 2000 J. Phys. A: Math. Gen. 33 4059), we started a systematic study of the connections among different factorization types, suggested by Infeld and Hull, and of their consequences for the construction of algebras. We devised a general procedure for constructing satellite algebras for all the Hamiltonians admitting a type E factorization by using the relationship between type A and E factorizations. Here we complete our analysis by showing that for Hamiltonians admitting a type F factorization, a similar method, starting from either type B or type C ones, leads to other types of algebras. We therefore conclude that the existence of satellite algebras is a characteristic property of type E factorizable Hamiltonians. Our results are illustrated with the detailed discussion of the Coulomb problem.Comment: minor changes, 1 additional reference, final form to be published in JP

Complexity-entropy analysis at different levels of organization in written language

Written language is complex. A written text can be considered an attempt to convey a meaningful message which ends up being constrained by language rules, context dependence and highly redundant in its use of resources. Despite all these constraints, unpredictability is an essential element of natural language. Here we present the use of entropic measures to assert the balance between predictability and surprise in written text. In short, it is possible to measure innovation and context preservation in a document. It is shown that this can also be done at the different levels of organization of a text. The type of analysis presented is reasonably general, and can also be used to analyze the same balance in other complex messages such as DNA, where a hierarchy of organizational levels are known to exist

UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces

We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square functions associated with Poisson semigroups for Bessel operators are defined by using fractional derivatives. If B is a UMD Banach space we obtain for B-valued Hardy and BMO spaces equivalent norms involving $\gamma$-radonifying operators and square functions. We also establish characterizations of UMD Banach spaces by using Hardy and BMO-boundedness properties of g-functions associated to Bessel-Poisson semigroup

ACL Injuries in Female Athletes

The Anterior Cruciate Ligament has been studied in many different ways and become injured more with the increase in sports participation by both male and female athletes. “ACL injuries are 9x more common in female athletes than male athletes and over 1.4 million women have been suffered from the ACL rupture which is twice the rate of the previous decade” (Hewett, 2010). ACL injuries are known to occur more in females than males because of differences in anatomy, knee alignment, muscle strength, and conditioning. Since female athletes are more prone to injury, it is important to incorporate neuromuscular training to college workouts to help prevent injuries in competition. Therefore, female ACL injuries are still a growing problem in the nation and researchers must focus on designing special prevention programs rather than focus on discovering a cause. ACL injury is a knee ligament injury also known as anterior cruciate ligament injury. There are many different risk factors rising between both female and male athletes. According to Hewett (2010), several studies have shown that female athletes have a higher incidence of ACL injury than male athletes in certain sports. I intend more information by interviewing at least two athletes who have torn his or her ACL in the past. I would like to have he or she explain the physical and mental aspect of dealing with the injury. ACL tears can never be fully prevented but there are some things that can be done to help minimize the chances of an ACL injury but I would like to know about his or her workout plan, the recovery process and some of the rehabilitation exercise