Tug and Basar  and Tug  have introduced and studied the new double sequence spaces B([M.sub.u]), B([C.sub.p]), B([C.sub.bp]), B([C.sub.r]), and B([L.sub.q]) as the domain of four-dimensional
generalized difference matrix B(r, s, t, u) in the spaces [M.sub.u], [C.sub.p], [C.sub.bp], [C.sub.r], and [L.sub.q], respectively That is,
Approaching the Planck epoch is therefore associated with the signature change from Lorentzian space-time to Euclidean four-dimensional
modified Lorenz-Stenflo system can be modeled by an electronic circuit [16-19].
To have a better understanding of the four-dimensional
Lorenz-Stenflo system, we use an innovative technique to present the three-dimensional phase portraits shown in Figure 2.
Examination of the fetal heart by four-dimensional
ultrasound with spatiotemporal image correlation during routine second-trimester examination: The 'three-steps technique'.
The negative spacetime dimensions -[x.sup.*], -[y.sup.*], -[z.sup.*] and -c[t.sup.*] are inversions in the origin (or four-dimensional
inversion) of the positive spacetime dimensions x, y, z and ct.
Just as a two-dimensional drawing of a cube has serious shortcomings in depicting all the properties of a real cube, so does the three-dimensional model of a tesseract fail to capture all the characteristics of a real four-dimensional
ultrasound, which combines many three-dimensional pictures of unborn babies to show movement in real time, is a relatively new technology in Britain.
Among many other topics, the book summarizes the last decade of assessment instrument development; provides seven ways to gauge attitudes, beliefs, skills, competencies and technology integration proficiencies of educators; offers methods for analyzing teacher-student interaction patterns in a distance-learning setting; examines the best uses of computerized testing; sets out a four-dimensional
model to assess student learning in instructional technology courses; and outlines three models for assessing the significance of information technology in education from a teacher's perspective.
Since the (111) plane of the primitive cubic lattice is the two-dimensional hexagonal lattice, the three-dimensional hexagonal lattice can be considered as the (1110) plane of a four-dimensional
cubic lattice (19).
Instead it may be just one of many three-dimensional, or 'three-brane' universes within a 'mother dimension' - a thin four-dimensional
A new four-dimensional
Ab Initio potential energy surface will be reported for the long-range interaction of [H.sub.2] with the open-shell CN diatomic in the its first electronic state [A.sup.2][pi].