Historical review of missile aerodynamic developments

The development of missiles from early history up to about 1970 is discussed. Early unpowered missiles beyond the rock include the spear, the bow and arrow, the gun and bullet, and the cannon and projectile. Combining gunpowder with projectiles resulted in the first powered missiles. In the early 1900's, the development of guided missiles was begun. Significant advances in missile technology were made by German scientists during World War II. The dispersion of these advances to other countries following the war resulted in accelerating the development of guided missiles. In the late 1940's and early 1950's there was a proliferation in the development of missile systems in many countries. These developments were based primarily on experimental work and on relatively crude analytical techniques. Discussed here are some of the missile systems that were developed up to about 1970; some of the problems encountered; the development of an experimental data base for use with missiles; and early efforts to develop analytical methods applicable to missiles

Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions

Starting from equations obeyed by functions involving the first or the second derivatives of the biconfluent Heun function, we construct two expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta functions. The first series applies single Beta functions as expansion functions, while the second one involves a combination of two Beta functions. The coefficients of expansions obey four- and five-term recurrence relations, respectively. It is shown that the proposed technique is potent to produce series solutions in terms of other special functions. Two examples of such expansions in terms of the incomplete Gamma functions are presente

The Historical, Jurisprudential, and Empirical Wisdom of Parental Responsibility Laws

The parent-child relationship is woven deep within historical and contemporary culture, but strong retributive ideals have led to blaming parents because of their presumed vicarious role in juvenile crime. The current article will discuss the history, forms, legal challenges, and empirical research related to parental involvement laws in the United States. The parent-child relationship provides the historical framework behind the separate juvenile justice parens patriae system; however, with the juvenile justice system not as successful as originally imagined, blame has shifted to the parents. We examine the potential constitutional implications of enacting and enforcing parental involvement statutes and ordinances and also the potential efficacy of parental involvement laws in reducing juvenile delinquency. In addition, we propose empirical research to test the underlying assumptions about blame made by parental involvement laws

Continuous monitor for gas ratios in a mixture

Fluidic oscillator, incorporating piezoelectric transducer to sense molecular weight of gas mixture, is used to continuously monitor ratio of a mixture of two gases in a flowing system. Device is lightweight, compact, reliable, easy to install, and also produces a simple output signal for controller. Frequency of oscillation is measured and signal converted to ac output

A Characterization of Infinite LSP Words

G. Fici proved that a finite word has a minimal suffix automaton if and only if all its left special factors occur as prefixes. He called LSP all finite and infinite words having this latter property. We characterize here infinite LSP words in terms of $S$-adicity. More precisely we provide a finite set of morphisms $S$ and an automaton ${\cal A}$ such that an infinite word is LSP if and only if it is $S$-adic and all its directive words are recognizable by ${\cal A}$