Cyclic phenomenon

First, they cannot be used for the evaluation of volumes of individual bubbles. Only an average bubble volume is obtained. Bubble formation is generally a cyclic phenomenon, and for a definite flow rate in a particular system, the frequency and the bubble volume are time-independent. However, there are situations where each bubble is followed by smaller secondary bubbles. In such cases, the above methods cannot yield reliable values and photographic methods have to be resorted to. 

Disease progress refers to the evolution ot a disease over time. Specifically, it can be used to describe the time course ot a biomarker or clinical outcome, reflecting the status of a disease. The status is a reflection ot the state ot the disease at a point in time. The disease status may improve or worsen over time, or may be a cyclical phenomenon (e.g., malarial quartan fever or seasonal affective disorder). Therefore, a model ot disease progress is a mathematical expression that describes the expected changes in status over time. 

Another way of looking at it starts from the periodic nature of the basis functions. As far as the sines and cosines are concerned, the signal could be just one period of a cyclic phenomenon. When we plot the concatenated signal (Fig. 22(a)), we see that it is dominated by a triangular oscillation, a saw-tooth as it is called. The Fourier transform of the signal will be equally dominated by the transform of that saw-tooth, which, due to the sharp edges in the saw-tooth, contains a lot of high frequencies. To illustrate this, the saw-tooth and its power spectrum have been plotted in Fig. 22(b) and (c). 

During electrochemical fluorination retention of important functional groups or atoms in molecules is essential. Acyl fluorides and chlorides, but not carboxylic acids and anhydrides (which decarboxylate), survive perfluorination to the perfluorinated acid fluorides, albeit with some cyclization in longer chain (>C4) species [73]. Electrochemical fluorination of acetyl fluoride produces perfluoro-acetyl fluoride in 36-45% yields [85]. Electrochemical fluorination of octanoyl chloride results in perfluorinated cyclic ethers as well as perfluorinated octanoyl fluonde. Cyclization decreases as initial substrate concentration increases and has been linked to hydrogen-bonded onium polycations [73]. Cyclization is a common phenomenon involving longer (>C4) and branched chains. a-Alkyl-substituted carboxylic acid chlorides, fluorides, and methyl esters produce both the perfluorinated cyclic five- and six-membered ring ethers as well as the perfluorinated acid... 

The ethylenediamine derivative [31] possesses higher promoting activities than other diamines. This phenomenon may be ascribed to the copromoting effect of the two amino groups on the decomposition of persulfate through a CCT (contact charge transfer complex) formation. So we proposed the initiation mechanism via CCT as the intimate ion pair and deprotonation via CTS (cyclic transition state) as follows ... 

Using dilatometry in parallel with cyclic voltammetry (CV) measurements in lmolL 1 LiC104 EC-l,2-dimethoxy-ethane (DME), Besenhard et al. [87] found that over the voltage range of about 0.8-0.3 V (vs. Li/Li+), the HOPG crystal expands by up to 150 percent. Some of this expansion seems to be reversible, as up to 50 percent contraction due to partial deintercalation of solvated lithium cations was observed on the return step of the CV. It was concluded [87] that film formation occurs via chemical reduction of a solvated graphite intercalation compound (GIC) and that the permselective film (SEI) in fact penetrates into the bulk of the HOPG. It is important to repeat the tests conducted by Besenhard et al. [87] in other EC-based electrolytes in order to determine the severity of this phenomenon. 

A long-range proton coupling, which was found to be transmitted by a sulfone group in thiolane dioxide systems292, is apparently facilitated by a nonbonding p-orbital on one of the sulfone oxygen atoms. This phenomenon is of interest for saturated cyclic systems. 

The pentagon stabilization has been found in a biochemical phenomenon [80], The hydrogen on the thiazolium ring 9 (Scheme 7) is easily ionized to afford the corresponding carbene 10, a key catalyst in enzymatic reactions for which thiamine (vitamin B-1,11) pyrophosphate is the cofactor. The pentagon stability is expected to contribute to this unusual deprotonation. A lone pair generated on the carbon atom in 10 can similarly delocalize through the vicinal C-N and C-S a bonds in a cyclic manner. 

The results of our calculations based on both the static and dynamic theories show that most of the nonbenzenoid cyclic conjugated systems examined exhibit in a greater or lesser degree a marked double-bond fixation. The static theory indicates that even in benzene there exists a hidden tendency to distort into a skewed structure and that such a tendency is actually realized in [4n-f-2] annulenes larger than a certain critical size. In nonalternant hydrocarbons bond distortion is a rather common phenomenon. Fulvenes, fulvalenes and certain peri-condensed nonalternant hydrocarbons undergo a first-order bond distortion, and... 

Porphyrin is a multi-detectable molecule, that is, a number of its properties are detectable by many physical methods. Not only the most popular nuclear magnetic resonance and light absorption and emission spectroscopic methods, but also the electron spin resonance method for paramagnetic metallopor-phyrins and Mossbauer spectroscopy for iron and tin porphyrins are frequently used to estimate the electronic structure of porphyrins. By using these multi-detectable properties of the porphyrins of CPOs, a novel physical phenomenon is expected to be found. In particular, the topology of the cyclic shape is an ideal one-dimensional state of the materials used in quantum physics [ 16]. The concept of aromaticity found in fuUerenes, spherical aromaticity, will be revised using TT-conjugated CPOs [17]. 

Some of the investigations carried out in the first half of the twentieth century were related to CL associated with thermal decomposition of aromatic cyclic peroxides [75, 76] and the extremely low-level ultraviolet emission produced in different reaction systems such as neutralization and redox reactions involving oxidants (permanganate, halogens, and chromic acid in combination with oxalates, glucose, or bisulfite) [77], In this period some papers appeared in which the bright luminescence emitted when alkali metals were exposed to oxygen was reported. The phenomenon was described for derivatives of zinc [78], boron [79], and sodium, potassium, and aluminum [80]. 

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