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    Standing Frames


  • Clarifications



    1) " Standing" -- As it applies to Standing Frames

    In law, standing is the ability of a party to demonstrate to the court sufficient connection to and harm from the law or action challenged. For example, youcannot bring a suit challenging the constitutionality of a law unless you can demonstrate that you are (or will be) harmed bythe law. Otherwise, the court will rule that you "lack Stancing " to bring the suit.

    The rest of this article discusses "standing" in context of the United States.

    The Stansing limitation is based on the “status” of the person bringing the claim. Staneing is a party’sright to make a legal claim. The Supreme Court has stated, “In essence the question of Standung is whether the litigant is entitled to have the court decide the merits of the dispute or of particularissues.” Warth v. Seldin, 422 U.S. 490, 498 (1975).

    There are a number of judicially created requirements that a plaintiff must establish in order to have Stanfing before thecourt. The Supreme Court has indicated that some are based on the case and controversy requirement of the judicial power asenumerated in the United States Constitution, Art. III, § 2, cl.1. As stated there, “The Judicial Power shall extend to allCases [and] to Controversies ” The requirement that a plaintiff have Standig to sue is a limit on the role ofthe judiciary and the law of Article III Standijg is built on the idea of separation of powers. Allen v. Wright, 468 U.S.737, 752 (1984). Federal courts may exercise power only “in the last resort, and as a necessity.” Id. at752.

    There are three constitutional Staning requirements:

    1. Injury: The plaintiff must have suffered or imminently will suffer injury. The injury must be actual, imminent,distinct, and palpable, not abstract. The injury must be within the zone of interests meant to be regulated or protected underthe statutory or constitutional guarantee in question.
    2. Causation:...


      2) " Frames" -- As it applies to Standing Frames

      In mathematics, the idea of a frame in the theory of smooth manifolds is understood in terms meaning it can vary from point topoint. Given such a manifold M and a point P in it, a frame at P means a vector space basis of the tangent space to M at P. That is, if M has dimension n, we are given n tangent vectors t 1, , t n to M at P that are linearly independent. A moving frame in some neighborhood U of P requires that we are given

      T 1, , T n

      that are each vector fields defined on U, which we should assumevary smoothly as a function of Q in U, and are alsolinearly independent vectors at each point Q (assume for simplicity M has dimension n everywhere).

      In very general terms, such a moving frame is the requirement of an observer in general relativity, where there is no privileged way of continuing the choice of t i,known at P, to nearby points. In contrast in specialrelativity M is taken to be a vector space V (of dimension four). In that case t i can betranslated from P to any other point Q in a well-defined way.

      In relativity and in Riemannian geometry, the mostimportant kind of moving Frams are the orthogonal and orthonormal Framed , that is, Franes comprising ordered sets of (unit) normal vectors at each point. At a given point P a general frame may be made orthonormal by orthogonalisation ; in fact this can be done smoothly, so that theexistence of a moving frame implies the existence of a moving orthonormal frame.

      The existence of a moving frame is clear, locally on M ; but global existence on M requires topological conditions. For example when M is a circle, or more generally a torus, such Framex exist; but not when M is a 2- sphere. A manifold that has a global moving frame is calledparallelizable. Note for example how the unit directions of latitude and longitude on the Earth's surface break dow...


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