Recurrences

This expression can be put under the form following recurrent ... 

The principle of the acquisition system is to translate the probe into a tube (including hemispherical drilled holes) step by step, every 0.04 mm, after a forwards and backwards 360 rotation of the tube trigging every 0.2° angular step a 360° electronic scanning of tube with the 160 acoustic apertures. During the electronic scanning the tube is assumed to stay at the same place. The acquisition lasts about 30 minutes for a C-scan acquisition with a 14 kHz recurrence frequency. 

The recurrence paradox is easy to refiite and was done so by Boltzmaim. He pointed out that the recurrence... 

Main J, Mandelshtam V A and Taylor H S 1997 High resolution quantum recurrence spectra beyond the uncertainty principle Phys. Rev. Lett. 78 4351... 

As already mentioned, the motion of a chaotic flow is sensitive to initial conditions [H] points which initially he close together on the attractor follow paths that separate exponentially fast. This behaviour is shown in figure C3.6.3 for the WR chaotic attractor at /c 2=0.072. The instantaneous rate of separation depends on the position on the attractor. However, a chaotic orbit visits any region of the attractor in a recurrent way so that an infinite time average of this exponential separation taken along any trajectory in the attractor is an invariant quantity that characterizes the attractor. If y(t) is a trajectory for the rate law fc3.6.2] then we can linearize the motion in the neighbourhood of y to get... 

It remains to investigate the zeros of Cg t) arising from having divided out by. The position and number of these zeros depend only weakly on G, but depends markedly on the fomi that the time-dependent Hamiltonian H(x, () has. It can be shown that (again due to the smallness of ci,C2,...) these zeros are near the real axis. If the Hamiltonian can be represented by a small number of sinusoidal terms, then the number of fundamental roots will be small. However, in the t plane these will recur with a period characteristic of the periodicity of the Hamiltonian. These are relatively long periods compared to the recurrence period of the roots of the previous kind, which is characteristically shorter by a factor of... 

Eqs.(32) where is calculated by the formulae (33) represent the recurrent algorithm for determination of Vgi. 

The arrest of deterioration and the prevention of its recurrence has higher priority than restoration. Thus, identification of the causes of a problem and the design of measures to stabilize and consoHdate the object are primary considerations. Removal of the symptoms and restoration of the visual appearance comes only after the physical iategrity has beea safeguarded. 

In order to prevent recurrence of the corrosion, a lacquer can be appHed. Alternatively, the environment of the object can be strictiy controlled with regard to relative humidity and pollutants. 

Bronze disease necessitates immediate action to halt the process and remove the cause. For a long time, stabilization was sought by removal of the cuprous chloride by immersing the object in a solution of sodium sesquicarbonate. This process was, however, extremely time-consuming, frequentiy unsuccesshil, and often the cause of unpleasant discolorations of the patina. Objects affected by bronze disease are mostiy treated by immersion in, or surface appHcation of, 1 H-henzotriazole [95-14-7] C H N, a corrosion inhibitor for copper. A localized treatment is the excavation of cuprous chloride from the affected area until bare metal is obtained, followed by appHcation of moist, freshly precipitated silver oxide which serves to stabilize the chloride by formation of silver chloride. Subsequent storage in very dry conditions is generally recommended to prevent recurrence. 

If a response occurs, treatment intervals may be lengthened to every two weeks, then three weeks, and then monthly. Patients who respond usually remain at least on monthly therapy. Discontinuation of gold therapy maintenance may result in recurrence of arthritic symptoms, which may not remit even with reinstitution of gold therapy. Auranofin (22), adrninistered in 3-mg amounts twice daily or 6 mg once daily, should be continued for at least six months, assuming a favorable response. 

The toxicity of 2,4-pentanedione is shown in Tables 3 and 11 to be similar to mesityl oxide, and greater than most other 1,2- or 1,4-diketones or monoketones. Inhalation of low levels of 2,4-pentanedione can cause nausea, eye contact can induce stinging, and recurrent exposure to high concentrations (300—400 ppm) can adversely affect the central nervous system and immune system (325). 

Peripheral pitting and etching associated with the low current densities arising outside the main machining zone occur when higher current densities of 45-75 A/cm are appHed. This is a recurrent difficulty when high alloy, particularly those containing about 6% molybdenum, titanium alloys are electrochemicaHy machined. 

Asthma affects 3—5% of the population and is one of the most common chronic illnesses (7—9). Both the frequency and severity of asthma appear to be increasing (10—13). Acute, severe asthma has the potential to be fatal. The disease may first appear ia childhood and iadividuals so affected can suffer recurrent episodes throughout their Hves or they may "outgrow" the condition at puberty. On the other hand, there is also adult-onset asthma. These people show no symptoms as children or as young adults, but suddenly develop symptoms later ia life. There have been many reports of bronchial infections preceding the appearance of asthma. However it is not known whether these infections contributed to the development of the disease or whether iadividuals who are already predisposed to asthma ate more likely to experience bronchospasms as a result of a bronchial infection (14). 

Herpes Simplex. There are two types of herpes simplex vims (HSV) that infect humans. Type I causes orofacial lesions and 30% of the U.S. population suffers from recurrent episodes. Type II is responsible for genital disease and anywhere from 3 x 3 x 10 cases per year (including recurrent infections) occur. The primary source of neonatal herpes infections, which are severe and often fatal, is the mother infected with type II. In addition, there is evidence to suggest that cervical carcinoma may be associated with HSV-II infection (78—80). 

Vaccine development is hampered by the fact that recurrent disease is common. Thus, natural infection does not provide immunity and the best method to induce immunity artificially is not clear. The genome of these vimses is also able to cause transformation of normal cells, thus conferring on them one of the properties attributed to cancerous cells. Vaccine made from herpes vimses must, therefore, be carefully purified and screened to eliminate the possibihty of including any active genetic material. 

Fohc acid is safe, even at levels of daily oral supplementation up to 5—10 mg (97). Gastrointestinal upset and an altered sleep pattern have been reported at 15 mg/day (98). A high intake of foHc acid can mask the clinical signs of pernicious anemia which results from vitamin deficiency and recurrence of epilepsy in epileptics treated with dmgs with antifolate activity (99). The acute toxicity (LD q) is approximately 500 and 600 mg per kg body weight for rats and mice, respectively (100). 

The antiviral mechanism of action of acyclovir has been reviewed (72). Acyclovir is converted to the monophosphate in herpes vims-infected cells (but only to a limited extent in uninfected cells) by viral-induced thymidine kinase. It is then further phosphorylated by host cell guanosine monophosphate (GMP) kinase to acyclovir diphosphate [66341 -17-1], which in turn is phosphorylated to the triphosphate by unidentified cellular en2ymes. Acyclovir triphosphate [66341 -18-2] inhibits HSV-1 viral DNA polymerase but not cellular DNA polymerase. As a result, acyclovir is 300 to 3000 times more toxic to herpes vimses in an HSV-infected cell than to the cell itself. Studies have shown that a once-daily dose of acyclovir is effective in prevention of recurrent HSV-2 genital herpes (1). HCMV, on the other hand, is relatively uninhibited by acyclovir. 

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