For example if f h h then this is

For example, if f(h)=h, then (this is a rough estimate). We should note here that Varin announced an unprecedented exact value of α=0.33205… (by 32 digits!), with an unlimited accuracy [1,3] (see also a brief summary in Ref. [4]). Aside from the above-described, the Pade approximation [5] is applied to the power series related to the Crocco boundary problem (the questions of the convergence of the interpolation process are outside the scope of this study and are not discussed here). The Pade approximation as applied to solving the problems of strong approximations of the power series intervals, of the analytical extension and the solutions of boundary problems is studied in detail, aside from Gonchar and Suetin\'s classical monographs, in Refs. [7,8]. Finally, the extensive study in Ref. [9] examines the differential equations with quadratic nonlinearity in the context of nonlinear problems (the study also contains the history of the problem and cites numerous works for further reference). Ref. [10] is a similar study on this subject, discussing Lie groups of transformations for Crocco\'s equation of a boundary layer with gradient (nonuniform) external flow, and the solutions corresponding to these groups.
Conclusion For the approximate solution estimates of the Crocco boundary problems (1) – (4) in general (i.e., on the 0 < h <1 interval) it mct2 inhibitor is sufficient to use the integral identities obtained from the limiting conditions. These estimates can be considered as rough, since the values of the solution constants are calculated with an error no less than 1.5%. It has been shown that the integral identities are related to the extremum condition of a certain distribution. The solutions obtained by Varin were used as model ones; Using the integral identities turns out to be sufficient for finding the binomial approximation constants for various Crocco boundary problems, i.e., (1), (2) and (1), (3), with a modest accuracy (the error is about 1 %). The maximum disagreement between the exact solution of the boundary problem and the binomial approximation is expectedly observed near the singularity h=1 – 0 for the derivative. This is a regular singularity of a ‘stripping’ (logarithmic) order; Crocco\'s equation is related to the necessary minimum condition for a positive distribution (functional). The respective Hamiltonian is alternating. The solution of the distribution minimum problem is equivalent to finding the binomial constants from the integral identities; the uniform boundary problem (1), (3) falls into two typical Crocco boundary problems for the intervals to the left and to the right of the critical point (the maximum) of φ(h). The integral identities in the boundary problem (1), (3) can be also used for obtaining rough estimates of constants.
Introduction The photodynamic therapy (PDT) is currently rapidly developing as a method for treating cancers of various sites. This method is based on generating active oxygen as a result of a photochemical reaction at a cellular level using a photosensitizer. The pharmacokinetics of the photosensitizer determines its selective accumulation in mitochondria and membranes of pathological cells. When photosensitized tissues are exposed to optical radiation, non-toxic triplet oxygen is transformed into a singlet form that has a pronounced cytotoxic effect leading to the disruption of cellular membranes in tumor cells [1,2]. The efficiency of PDT is largely due to the physicochemical, the pharmacodynamical and the pharmacokinetic properties of the photosensitizer. There are currently several groups of photosensitizing compounds, in particular, those based on porphyrins and chlorins. Photosensitizers based on the derivatives of chlorin e6, including the commercially available Russian compound Photoditazin®[3], are among the most viable due to their biomedical, optical and physical properties. At the same time, the efficiency of the PDT method depends to a great extent on the spectral content of the optical radiation exciting the photochemical reaction of the photosensitizer. Obtaining agreement between the spectral content of the radiation and the absorption spectrum of the photosensitizer could significantly improve the efficiency of the photosensitizer\'s optical excitation and reduce the side effects from the irradiation of healthy tissues. The recent advances in semiconductor optoelectronics allow to reach this agreement for virtually any photosensitizer, as cheap compact high-power sources of laser radiation based on semiconductor laser diodes have been developed [4].