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have magnitudes (lengths) and directions (the way the arrows are pointing) Not all physical entities can be expressed as four-vectors, however Some quantities such as temperature don t point in any direction It would be silly for a weather forecaster to say it s going to be a northwesterly 30 degrees outside The wind velocity could shift in such a manner, but not the temperature itself Therefore temperature is an example of a directionless mathematical object known as a scalar Scalars don t have components, they are just single numbers A third type of entity, the workhorse of the field of differential (calculus-based) geometry, is called a tensor A tensor is essentially a rule sheet, or rulebook, delineating a particular way of transforming one mathematical object into another For instance, a tensor applied to a four-vector might render it a different four-vector, or, alternatively, a scalar.

Bank customers asking for investment advice were referred to the affiliates and then sold inappropriate securities by salesmen they thought they could trust as much as their commercial banker The element of trust between banker and customer had been broken Many bank customers testified before the committee about being fleeced by salesmen who assured them that the securities they purchased were of good quality, when many in fact were those of companies near bankruptcy..

Figure 31 shows pacing performed from the high right atrium, so atrial activation at the His bundle area and the left atrium (as represented by the coronary sinus) electrograms have the same general temporal relationship Notice, however, that the pattern of activation in the coronary sinus electrograms (ellipses) is different than during sinus rhythm This can occur because of two possibilities First, pacing is performed at a right atrial site that is near but not at the sinus node, which leads to a different pattern of left atrial activation Second, with more rapid atrial activation the pattern of atrial activation can change due to the development of regions of tissue that exhibit slower conduction or refractoriness Finally, an issue on pacing nomenclature in the electrophysiology laboratory should be discussed here.

Not all rules are possible; mathematicians restrict these to certain kinds of transformations Nevertheless, tensors offer a great deal of flexibility, rendering them essential tools for modern geometric description Tensors are often depicted in arrays, with rows and columns like a spreadsheet or a checkerboard For example a tensor transforming one four-vector into another would be a four-by-four checkerboard Each column represents one of the dimensions of the old fourvector (x, y, z, or t), and each row, one of the dimensions of the new four-vector Placed in each square of the checkerboard is a function (mathematical rule) showing the part the old vector components play during their transformation into the new By applying these rules, the tensor acts as a well-programmed machine, precisely carrying out its transformational duties One of the most important operations in Minkowskian relativity involves a four-vector, a scalar, and a tensor.

The unsignedLong datatype, which is derived from nonNegativeInteger, represents a number with an upper bound of 18446744073709551615. The unsignedInt datatype is derived from the unsignedLong datatype. The following list contains the facets available in the unsignedLong datatype:

Although with implanted pacemakers that pace at constant rates it is easier to think of pacing rates and beats per minute, in the electrophysiology laboratory, where pacing is often not performed at constant rates and premature extrastimuli are delivered, it is easier to think of intervals between pacing stimuli So delivering constant stimuli at 600 ms intervals is pacing at a rate of 100 beats per minute, at 500 ms intervals the pacing rate is 120 beats per minute, and at 400 ms intervals the pacing rate is 150 beats per minute..

Suppose one wishes to measure the distance between two events in space-time, for example, the amount of space-time traversed by Hans and Peter s football This differs from the conventional spatial distance, calculated by use of the Pythagorean theorem According to the Pythagorean theorem, the square of the distance between two objects is the sum of the squares of their x, y, and z coordinate differences But Minkowski space-time is not exactly a Euclidean geometry, so one must amend this formula..

The elections of 1932 displayed wide discontent with Republicans and ushered in a Democratic Congress. The new faces brought with them a new attitude toward economic conditions and an even harsher view of Wall Street than existed before. Many of the radicals in the Senate and the House lost their committee jobs as the Democrats swept control of both houses. Norbeck was replaced by Duncan Fletcher, a long-sitting Democrat from