Positive Mental Attitude, or PMA, is largely referred to by The Combined Insurance Company of America, as being a creation of W. Clement Stone, despite the fact that similar ideas have been in existence far before Stone claimed it as his own.

In physics, an inertial frame of reference (also inertial reference frame or inertial frame or Galilean reference frame) is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time independent manner. All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not accelerating (in the sense of proper acceleration that would be detected by an accelerometer). Measurements in one inertial frame can be converted to measurements in another by a simple transformation (the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity). In general relativity, an inertial reference frame is only an approximation that applies in a region that is small enough for the curvature of space to be negligible.

Physical laws take the same form in all inertial frames. In a non-inertial reference frame the laws of physics depend upon the particular frame of reference, and the usual physical forces must be supplemented by fictitious forces.

For example, a ball dropped towards the ground does not go exactly straight down because the Earth is rotating. Someone rotating with the Earth must include the Coriolis force to predict the horizontal motion. Another example of a fictitious force associated with rotating reference frames is the centrifugal force.

Introduction

The motion of a body can only be described relative to something else - other bodies, observers, or a set of space-time coordinates. These are called frames of reference. If the coordinates are chosen badly, the laws of motion may be more complex than necessary. For example, suppose a free body (one having no external forces on it) is at rest at some instant. In many coordinate systems, it would begin to move at the next instant, even though there are no forces on it. However, a frame of reference can always be chosen in which it remains stationary. Similarly, if space is not described uniformly or time independently, a coordinate system could describe the simple flight of a free body in space as a complicated zig-zag in its coordinate system. Indeed, an intuitive summary of inertial frames can be given as: In an inertial reference frame, the laws of mechanics take their simplest form.

In an inertial frame, Newton's first law (the law of inertia) is satisfied: Any free motion has a constant magnitude and direction. Newton's second law for a particle takes the form:

\mathbf{F} = m \mathbf{a} \ ,

with F the net force (a vector), m the mass of a particle and a the acceleration of the particle (also a vector) which would be measured by an observer at rest in the frame. The force F is the vector sum of all "real" forces on the particle, such as electromagnetic, gravitational, nuclear and so forth. In contrast, Newton's second law in a rotating frame of reference, rotating at angular rate Ω about an axis, takes the form:

\mathbf{F}' = m \mathbf{a} \ ,

which looks the same as in an inertial frame, but now the force F′ is the resultant of not only F, but also additional terms (the paragraph following this equation presents the main points without detailed mathematics):

\mathbf{F}' = \mathbf{F} - 2m \mathbf{\Omega} \times \mathbf{v}_{B} - m \mathbf{\Omega} \times (\mathbf{\Omega} \times \mathbf{x}_B ) - m \frac{d \mathbf{\Omega}}{dt} \times \mathbf{x}_B \ ,

where the angular rotation of the frame is expressed by the vector Ω pointing in the direction of the axis of rotation, and with magnitude equal to the angular rate of rotation Ω, symbol × denotes the vector cross product, vector x_B locates the body and vector v_B is the velocity of the body according to a rotating observer (different from the velocity seen by the inertial observer).

The extra terms in the force F′ are the "fictitious" forces for this frame. (The first extra term is the Coriolis force, the second the centrifugal force, and the third the Euler force.) These terms all have these properties: they vanish when Ω = 0; that is, they are zero for an inertial frame (which, of course, does not rotate); they take on a different magnitude and direction in every rotating frame, depending upon its particular value of Ω; they are ubiquitous in the rotating frame (affect every particle, regardless of circumstance); and they have no apparent source in identifiable physical sources, in particular, matter. Also, fictitious forces do not drop off with distance (unlike, for example, nuclear forces or electrical forces). For example, the centrifugal force that appears to emanate from the axis of rotation in a rotating frame increases with distance from the axis.

All observers agree on the real forces, F; only non-inertial observers need fictitious forces. The laws of physics in the inertial frame are simpler because unnecessary forces are not present.

In Newton's time the fixed stars were invoked as a

Reference management software, citation management software or personal bibliographic management software is software for scholars and authors to use for recording and utilising bibliographic citations (references). Once a citation has been recorded, it can be used time and again in generating bibliographies, such as lists of references in scholarly books, articles and essays. The development of reference management packages has been driven by the rapid expansion of scientific literature.

These software packages normally consist of a database in which full bibliographic references can be entered, plus a system for generating selective lists of articles in the different formats required by publishers and scholarly journals. Modern reference management packages can usually be integrated with word processors so that a reference list in the appropriate format is produced automatically as an article is written, reducing the risk that a cited source is not included in the reference list. They will also have a facility for importing the details of publications from bibliographic databases.

Reference management software does not do the same job as a bibliographic database, which tries to list all articles published in a particular discipline or group of disciplines; examples are those provided by Ovid Technologies (e.g. Medline), the Institute for Scientific Information (e.g. Web of Knowledge) or monodisciplinary learned societies e.g. the American Psychological Association (PsycINFO). These databases are large and have to be housed on major server installations. Reference management software collects a much smaller database, of the publications that have been used or are likely to be used by a particular author or group, and such a database can easily be housed on an individual's personal computer.

Apart from managing references, most reference management software also enables users to search references from online libraries. These online libraries are usually based on Z39.50 public protocol. Users just need to specify the IP address, database name and keywords to start a Z39.50 search. It is quicker and more efficient than a web browser. However, Z39.50 is a little out of date. Some popular scientific websites, such as Google Scholar, IEEE Xplore and arXiv, do not support the Z39.50 protocol.