Word spacing

Revealed by wide letter/word spaces andloug final endings or ostentatious strokes. This person tends to overdo things. One may first notice this trait in the style of clothes she wears. It is a combination of desire for attention and generosity to one s self... 

Each operation has a result, and just naming that result is sometimes more convenient than going into a big explanation as to what you want done. You can economize with words, space, time, and ink. The following are results of operations most commonly used. 

Now we come to a totally different method for producing matrix representations of a point group a method which involves the concept of a function space. The word space is used in this context in a mathematical sense and should not be confused with the more familiar three-dimensional physical space. A function space is a collection or family of mathematical functions which obeys certain rules. These rules are a generalization of those which apply to the family of position vectors in physical space and in order to help in understanding them, the corresponding vector rule will be put in square brackets after each function rule. 

Key words space weather, cosmic rays, radiation hazard, monitoring, forecasting... 

Steimning It is a process to find the root of a word to achieve reduction in the word space. For example, the root for keywords connection, connections, connective, connected, and coimecting all relate to coimect. Stemming allows reduction in data dimension and data overload [22]. 

The collection of all column vectors with n real components is Euclidean n-space, and is denoted R". The collection of column vectors with n complex components is denoted C . We shall use vector space to mean either 1 or C . In discussing the space R", the word scalar will mean a real number, and in discussing the space C", it will mean a complex number. A subset S of a vector space is a subspace such that if u and V are vectors in S, and if c is any scalar, then u + v and cu are in S. We shall sometimes use the word space to mean a subspace. If B = vi, V2,..., Vjt is a collection of vectors in a vector space, then the set S consisting of aU vectors ciVi + C2V2 + —h c v for aU scalars ci,C2,...,c is a subspace, called the span... 

Most metal surfaces have the same atomic structure as in the bulk, except that the interlayer spaciugs of the outenuost few atomic layers differ from the bulk values. In other words, entire atomic layers are shifted as a whole in a direction perpendicular to the surface. This is called relaxation, and it can be either inward or outward. Relaxation is usually reported as a percentage of the value of the bulk interlayer spacing. Relaxation does not affect the two-dimensional surface unit cell synuuetry, so surfaces that are purely relaxed have (1 x 1) synuuetry. 

Geometrically, Liouville s theorem means that if one follows the motion of a small phase volume in Y space, it may change its shape but its volume is invariant. In other words the motion of this volume in T space is like that of an incompressible fluid. Liouville s theorem, being a restatement of mechanics, is an important ingredient in the fomuilation of the theory of statistical ensembles, which is considered next. 

In other words, if we look at any phase-space volume element, the rate of incoming state points should equal the rate of outflow. This requires that be a fiinction of the constants of the motion, and especially Q=Q i). Equilibrium also implies d(/)/dt = 0 for any /. The extension of the above equations to nonequilibriiim ensembles requires a consideration of entropy production, the method of controlling energy dissipation (diennostatting) and the consequent non-Liouville nature of the time evolution [35]. 

In Section IV.A, the adiabatic-to-diabatic transformation matrix as well as the diabatic potentials were derived for the relevant sub-space without running into theoretical conflicts. In other words, the conditions in Eqs. (10) led to a.finite sub-Hilbert space which, for all practical purposes, behaves like a full (infinite) Hilbert space. However it is inconceivable that such strict conditions as presented in Eq. (10) are fulfilled for real molecular systems. Thus the question is to what extent the results of the present approach, namely, the adiabatic-to-diabatic transformation matrix, the curl equation, and first and foremost, the diabatic potentials, are affected if the conditions in Eq. (10) are replaced by more realistic ones This subject will be treated next. 

All Np states belonging to the Pth sub-space interact strongly with each other in the sense that each pair of consecutive states have at least one point where they form a Landau-Zener type interaction. In other words, all j = I,... At/> — I form at least at one point in configuration space, a conical (parabolical) intersection. 

The general formula and the individual cases as presented in Eq. (97) indicate that indeed the number of conical intersections in a given snb-space and the number of possible sign flips within this sub-sub-Hilbert space are interrelated, similar to a spin J with respect to its magnetic components Mj. In other words, each decoupled sub-space is now characterized by a spin quantum number J that connects between the number of conical intersections in this system and the topological effects which characterize it. 

The symmetry T p) = T[—p) implies that reversing the order of these three steps and changing the sign of r and p results in exactly the same method. In other words, Verlet is time-reversible. (In practice, the equations are usually reduced to equations for the positions at time-steps and the momenta at halfsteps, only, but for consideration of time-reversibility or symplecticness, the method should be formulated as a mapping of phase space.)... 

Many of the species involved in the endogenous metabolism can undergo a multitude of transformations, have many reaction channels open, and by the same token, can be produced in many reactions. In other words, biochemical pathways represent a multi-dimensional space that has to be explored with novel techniques to appreciate and elucidate the full scope of this dynamic reaction system. 

Because ol Lhe use of Lwo double-precision words for each in tegral. IlyperCbem needs, for example, ahoiil 44 MByles of computer mam memory and/or disk space Lo store the elecLroii repulsion inlejrrals for benzene wilh a double-zeta 6-i lG basis set. 

SpartanView uses the word density to identify size density surfaces The size density surface is similar in size and shape to a space filling model... 

The text form for parameters uses white space or commas to separate the fields (columns) of the parameter files. They can be read by ordinary text editors, word processors, etc. In the text form, parameters are easy to modify but not easy to compare, study, etc. Many database programs are capable of reading columns of text as a database, however. While spreadsheets are not, per se, databases, they can be useful for examining parameter sets. Microsoft Excel, for example, can read the text form of a parameter file and put the data in a form easily manipulated as a matrix or a database. The text form of parameters are stored, by default only, in. txt files. 

Because of the use of two double-precision words for each integral, HyperChem needs, for example, about 44 MBytes of computer main memory and/or disk space to store the electron repulsion integrals for benzene with a double-zeta 6-3IG basis set. 

There is potential confusion in the use of the word array in mass spectrometry. Historically, array has been used to describe an assemblage of small single-point ion detectors (elements), each of which acts as a separate ion current generator. Thus, arrival of ions in one of the array elements generates an ion current specifically from that element. An ion of any given m/z value is collected by one of the elements of the array. An ion of different m/z value is collected by another element. Ions of different m/z value are dispersed in space over the face of the array, and the ions are detected by m/z value at different elements (Figure 30.4). 

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