In this paper the general synthesis problem of optimal control systems with the criterion of transient responses as a positive integral functional (3) is discussed.In the first part it is assumed that the motion of controlled object is described by a system of ordinary differential equations and that the final states of the system form a bounded and closed convex region in n-dimentional euclidian phase space. A method is proposed for finding all optimal control functions which lead any starting state into...

In this paper the general synthesis problem of optimal control systems with the criterion of transient responses as a positive integral functional (3) is discussed.In the first part it is assumed that the motion of controlled object is described by a system of ordinary differential equations and that the final states of the system form a bounded and closed convex region in n-dimentional euclidian phase space. A method is proposed for finding all optimal control functions which lead any starting state into the given final region of states. Some conclusions are obtained from the maximum principle by using transversal conditions of optimal trajectories in terminal points, and the particular properties of the stated problem are pointed out. The case of linear dif-ferential equations with integral quadratic functional criterion is investigated in detail.Further, in the second part the fundamental properties of isoloss regions, the rela-tions between the isoloss region and optimal control functions are indicated. As a direct result a partial differential equation determining the optimal loss-function J (x) is found and the connection between function J (x)and optimal vector control function u (x) is also stated. The methods proposed are practically the extension of the me-thods used by us for designing time optimal control systems as seen in [5, 6 ,7].Finally, an example is illustrated with optimal trajectories shown in phase plane.The necessary numerical data is calculated by an analog computer with high accuracy.

With γ-rays of various wave-lengths the number of counts produced in a Geiger-Muller counter of Pb-wall was determined in equal time intervals. The same experiment was carried out with a counter of Al-wall. Let Npb and NA1 represent the number of counts produced in the Pb-counter and Al-counter respectively by a beam of γ-rays of even wave-length in a given time interval. The ratio Nph/NA1 observed decreases at first with the wavelength of the incident beam due to the diminishing photo-electric of lead....

With γ-rays of various wave-lengths the number of counts produced in a Geiger-Muller counter of Pb-wall was determined in equal time intervals. The same experiment was carried out with a counter of Al-wall. Let Npb and NA1 represent the number of counts produced in the Pb-counter and Al-counter respectively by a beam of γ-rays of even wave-length in a given time interval. The ratio Nph/NA1 observed decreases at first with the wavelength of the incident beam due to the diminishing photo-electric of lead. It is, however, found to increase by 16% when the wavelength of the incident radiation is decreased from a value 6.6 x. u. 4.7 x. u. This rising is due to particles produced by the interaction of hard γ-rays with the Pb-nuclei.

This communication reports the results of a study of the gravimetric deter- mination of lead as normal phosphate, known as Vortmann and Bader method, which has been recently examined by Hubicki and Rys. According to our findings, tartaric acid should be added only when antimony is present. With the addition of tarearic acid unusual large excess of precipitant as suggested by Vortinann and Bader is required for complete precipitation. The suitable pH range for the precipitation of tertiary lead phosphate...

This communication reports the results of a study of the gravimetric deter- mination of lead as normal phosphate, known as Vortmann and Bader method, which has been recently examined by Hubicki and Rys. According to our findings, tartaric acid should be added only when antimony is present. With the addition of tarearic acid unusual large excess of precipitant as suggested by Vortinann and Bader is required for complete precipitation. The suitable pH range for the precipitation of tertiary lead phosphate is 6.5 to 10. Below pH 6.5, the precipitation will be incomplete, owing apparently to the formation of acid phosphate(s). Beyond pH 10, no experiment has been made, because no advantage is gained by working in such alkaline media. The concentration of the precipitant in sdlution after reaction should be within 0.00085-0.0033 molar in order to obtain good results. The precipitates may be ignited at any temperature from 650℃ up to at least 900℃. The practice of drying the pre- cipitates at 130℃ to constant weight suggested by Hubicki and Rys should be discarded, since the precipitates still contain noticeable amounts of water after drying to constant weight at that temperature. It is preferred to use the method of precipitation from homogeneous solution. With this technique in practice dense, crystalline and easily filterable precipitates are obtained; and small quantity of lead, as low as 5 mg, may be determined satisfactorily. The effect of presence of some alkali and ammonium salts has also-been studied.