Lobe envelope

Figure 3.7 Interruptions between the end parts of the windowed portion can be remedied by using a lobe envelope to smooth both sides of fhe window...

Lobe envelopes, however, have their own unwanted side-effects. Note that the amplitude of the whole signal now rises and falls periodically. This is a clear case of ring modulation (see Chapter 2) in which the windowing frequency acts as the modulating frequency. Enveloped windowing also may distort the analysis process, but the result is still more accurate than with windowing without envelopes. 

The spectral frequency range covered by the central lobe of this sinc fiinction increases as the piilselength decreases. For a spectrum to be undistorted it should really be confined to the middle portion of this central lobe (figure B 1.12.2). There are a number of examples in the literature of solid-state NMR where the resonances are in fact broader than the central lobe so that the spectrum reported is only effectively providing infonnation about the RF-irradiation envelope, not the shape of the signal from the sample itself... 

A sine-shape has side lobes which impair the excitation of a distinct slice. Other pulse envelopes are therefore more commonly used. Ideally, one would like a rectangular excitation profile which results from a sine-shaped pulse with an infinite number of side lobes. In practice, a finite pulse duration is required and therefore the pulse has to be truncated, which causes oscillations in the excitation profile. Another frequently used pulse envelope is a Gaussian frmction ... 

An alternative channel for the formation of sdB stars considers the ultimate fate of binary systems which are so evolved as to comprise two white dwarfs in a close binary orbit. This predicates a binary system which has passed through several stages of mass transfer (whether common-envelope or stable Roche-lobe overflow) to leave these remnants. 

Early models suggest at least two phases of mass transfer necessary to explain the very low surface hydrogen abundances e.g. [J27]. The current best model for the evolution of v Sgr [9] is that it began as a f 0+3 Mq, f 50 d binary in which the envelope was blown to infinity, with little change of orbit, as the more massive star approached both Roche Lobe overflow and the Cepheid instability strip simultaneously. 

Of course, this is really tantamount to apodizing with a step function, and unless the signal has already decayed to the noise level by the cutoff time, it will naturally introduce side-lobes about each peak. This spectral distortion can be alleviated by use of apodization functions of "intermediate smoothness," i.e., in between the discontinuous extreme of the sharp cutoff and the gentle extreme of the exponential decay. A typical example would be an envelope function in the shape of a quarter-cycle of a sine function, so phased that it reaches zero just at the end of the desired time region. (For further discussion of these and related points see Ref. 14-16). 

The three 2p orbitals are directed along the. v, y and r axes and are described respectively as 2p., 2p, and 2p. They each consist of two lobes, one of which has positive tj/ values, the other having negative tj/ values. The envelopes of the five 3d orbitals are shown in Figure 2,8. Those of the seven 4f orbitals are shown in Figure 2.9. 

Figure 4.6 The bonding C—H orbital is the orbital where one lobe of a single phase (represented by one color) envelops the C—H atoms. The adjacent unfilled antibonding orbital is the orbital where the phase changes between the carbon and its hydrogen atom. The staggered conformation of ethane (a) has greater overlap between the bonding C—H orbital and the adjacent antibonding orbital than in the eclipsed conformation (b).

COROLLA. Inner circle or second whorl of floral envelopes if the parts are separate, they are petals and the corolla is said to be poly-petalous if not separate, they are teeth, lobes, divisions, or undifferentiated, and the corolla is said to be gamopetalous or sympetalous CORYMB. Short and broad, more or less flat-topped indeterminate inflorescence, the outer flowers opening first... 

When an arbitrary pattern is generated by the FT of a hologram, it is contained within a sine envelope based on the dimensions of the smaller or fundamental pixel. For each lobe in the sine there is an associated replication of the pattern. There is also a replication of the pattern at each zero in the sine, even though the central value of the pattern is suppressed by the zero. With holograms, we are only interested in the central lobe of the sine function. The other orders or lobes merely repeat the desired pattern in the replay field and waste the available intensity which can be placed into that desired pattern. The area of interest in the replay field must be limited to half of the area of the central lobe to prevent overlap of orders. As the pixel pitch decreases, the central lobe of the sine envelope broadens, easing the restrictions that are placed on the replay field pattern. 

Fig. 3. Electron micrograph of a replica obtained from the fracture surface of an open cell prepared as described by Wallach et al. Note the preservation of the chloroplast cupshaped form. The outer chloroplast envelope (ce) shows numerous particles on its fractured surface. A deep fracture breaks through the distal chloroplast lobes and exposes the well preserved grana (g). The plasma membrane (p) is open (arrow) and remote from the cell wall (cw). (15,000x) (For experimental details see ref. 51.)...

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