Tangent Lines

In [1] Leibniz published the first treatment of the subject of calculus. An English translation can be found in [2]; he says that to find a tangent is to draw a right line, which joins two points of the curve having an infinitely small difference, or the side of an infinite angled polygon produced, which is equivalent to the curve for us. Today, according to [3], a straight line is said to be a tangent line of a curve y = f(x) at a point x = c on the curve if the line passes through the point (c, f (c)) on the curve and has slope f\u27(c) where f\u27 is the derivative of f. At first glance, it would appear that this second definition is simply a more precise version of the first; indeed, the cited Wikipedia article states this sentiment explicitly. In this paper we examine cases where Wikipedia\u27s definition is more strict than Leibniz\u27s original one, and present two attempts at formulating a more general, but still precise, definition

Elliptic Curves

Elliptic curves have found widespread use in number theory and applications thereof, such as cryptography. In this paper we will first examine the basic theory of elliptic curves and then look specifically at how they can be used to construct cryptographic systems more efficient than their counterparts, and how they can be used to generate proofs for or against primality

The Legislative Process and the Rule of Law: Attempts to Legislate Taste in Moral and Political Beliefs

In a nutshell, the topic of this paper is Comstockery and the Bowdlerizing of Ideas. The thesis here asserted is that the Rule of Law is violated when legislatures succumb to modern attempts by the often pathologically-motivated zealot legally to freeze current tastes in moral and political beliefs. The relationship between taste statutes and the seemingly esoteric topic, The Legislative Process and the Rule of Law, is based on the premise that the maximum possible degree of intellectual freedom for each individual is an essential ingredient in the legal system of a civilized society

Federal Control of Health and Safety Standards in Peacetime Private Atomic Energy Activities

This article is directed to the question of the power of Congress to provide for such regulation of those who handle radioactive materials in private industry and not to the policy question of whether Congress ought to attempt such regulation

Introduction: Legislative, Administrative, and Judicial Nonscience

This symposium deals with the legal issues, or rather some of them, that are created by scientific research. Anyone remotely interested in scientific developments should be aware that even the existence of new scientific facts, let alone the application of such discoveries to everyday activities, gives rise to a host of human value judgments that should be faced and resolved by society. Although these problems are often left in purgatory forever, it is the legal system, broadly defined, that attempts to resolve the conflict of interests (or the balancing of values) when a decision is made. Making this type of balancing of values judgments is the overriding-or perhaps even sole-function of the legal system. This is true whether we act through administrative regulations, legislative enactments, or judicial decisions

Radiation Injuries and Statistics: The Need for a New Approach to Injury Litigation

The emphasis given by the mass media of communication to some of the dramatic problems arising from the use of nuclear energy unfortunately has diverted attention from some of the matters about which something can be done by lawyers, administrators, and legislators without the necessity of complicated international negotiations between various parties to the Cold War. The headlines leave the uninformed, and perhaps often also the informed, public with the impression that even for radiation injuries the important problems all deal with such questions as: (1) Will only a few or many millions of people survive an all-out nuclear war? (2) Will the fallout from nuclear weapons testing cause no, a few, or hundreds of thousands of cases of leukemia and similar diseases among the populations of the world

BANKRUPTCY--SIX MONTHS RULE--APPLICATION OF THE RULE TO PRIVATE CORPORATIONS

The debtor, being reorganized under chapter 10 of the Bankruptcy Act, was a hotel corporation which owned and operated a hotel in Albany. The reorganization plan which was approved below is being challenged for the reason, among others, that the plan gives preference to certain unsecured creditors. These creditors had furnished supplies to the hotel for a short time before the receiver was appointed in the foreclosure suit which precipitated the bankruptcy proceeding. The trustee allowed the priority on the ground that the supplies were necessary to keep the hotel a going concern and that the six months rule, applicable to railroads and other public service companies, applied. Held, in so far as the supplies were furnished within six months of the receivership and so far as they were necessary to keep the hotel open, they were proper preferred claims. Dudley v. Mealey, (C.C.A. 2d, 1945) 147 F. (2d) 268

TORTS-DAMAGES FROM SHOCK-LIABILITY FOR MENTAL INJURY CAUSED BY DEFENDANT\u27S SUICIDE IN PLAINTIFF\u27S HOME

Decedent was the close neighbor of the plaintiff and her husband. While they were absent from home, decedent, at that time a guest in the home, committed suicide in plaintiff\u27s kitchen. When plaintiff opened the door she saw the body, and started to fall but was caught by her husband. A physician to whom she was taken pronounced her condition as one of shock. Subsequently she was restless, nervous and found difficulty in sleeping. She now sues the estate of decedent for damages resulting from what she alleges was the willful act of decedent. The trial court gave a directed verdict for defendant on the ground that the cause of action did not arise before decedent\u27s death and, therefore, there could be no action against the estate under the survival statue. Held: For purposes of the survival statute the cause of action arose before, and survived, decedent\u27s death; therefore, the jury must decide if decedent\u27s act was willful, since if it was, there can be recovery for mental injury caused by fright, even in the absence of other physical injury. Blakeley v. Shortal\u27s Estate, (Iowa 1945) 20 N.W. (2d) 28 (1945)