Showing papers by "Sofia University published in 1973"

Optimal rate of integration and ɛ-entropy of a class of analytic functions

Abstract: The author considers a class F of analytic functions real in the interval [-1, 1] and bounded in the unit circle. As an estimate of the optimal quadrature error R(n) over the class F it is shown that $$_e - \left( {2\sqrt 2 + \frac{1}{{\sqrt 2 }}} \right)\pi \sqrt n \leqslant R(n) \leqslant e^{ - \frac{\pi }{{\sqrt 2 }}n} .$$ With the additional condition that\(\mathop {max}\limits_{x \in [ - 1,1]}\) ¦f(x)¦⩽B, an estimate is obtained for the ɛ-entropy Hɛ(F): $$\frac{8}{{27}}\frac{{(1n2)^2 }}{{\pi ^2 }} \leqslant \mathop {\lim }\limits_{\varepsilon \to 0} \frac{{H_\varepsilon (F)}}{{\left( {\log \frac{1}{\varepsilon }} \right)^3 }} \leqslant \frac{2}{{\pi ^2 }}(1n2)^2 .$$

1-arm phase optical bridge with axial symmetry (with interference Newton fringes) for measuring small periodic displacements

Abstract: A 1-arm phase optical bridge with axial symmetry (with interference Newton fringes) is developed for the measurement of small periodic displacements of acoustic frequency. Using the synchronous detection method, a vibration with an amplitude as small as 3×10−14 m is measured.

Temperature-electrical domains moving in the cathode-anode direction in CdS monocrystals

Abstract: A moving temperature-electrical domain occuring in the negative differential conductivity region of the N-shaped current-voltage characteristics in CdS photosensitive crystals was observed. A noninertial method for measuring the temperature is proposed by means of which the main parameter of the domain are investigated. A periodical transition from a stationary or oscillating temperature-electrical domain to a moving one and vice versa was noted. Both the conditions for the occurrence of the transition and the main characteristics of the current oscillations, due to this transition, are found. The formation of the moving temperature-electrical domain is explained in terms of the model of the temperature-electrical recombination instability.

Charge-transfer complexes of phenothiazine derivatives with π-electron acceptors

Abstract: Charge-transfer complexes (CTC) of some phenothiazine derivatives with π-electron acceptors were obtained. They were used to determine the ionization potentials of the investigated donor compounds. The complexing constants of phenothiazine and some of its N-substituted derivatives were found. The experimental data obtained make it possible to draw conclusions relative to their configurations.

Periodic solutions of the set of equations governing the nonadiabatic convection of dry isolated thermals

Abstract: The changes with timet of a temperature deviation δT(t,α) and of a vertical velocityWi(t,α) of an isolated dry thermal have been investigated theoretically. Solutions for the functionWi(t, α) have been derived for stable and unstable environmental stratifications. Comparing these solutions with the corresponding ones for the rise of an adiabatic thermal yield some interesting conclusions.

Recombination waves in CdS induced by optical quenching

Abstract: Low-frequency current oscillations induced by optical quenching were observed in highly photosensitive CdS crystals No evidence of a negative differential resistivity was found The current oscillations were observed at room temperature at electric field strengths of 100–800 V/cm As shown by probe measurements, the instabilities resulted from a bulk phenomenon The oscillations are related to the excitation of recombination waves, predicted by Konstantinov and Perel

Complexometric determination of barium with copper(II)-EDTA-PAR as indicator

Abstract: A sensi t ive m e t h o d for de tec t ing the end-po in t of the d i rec t E D T A t i t r a t i on of Ba has been deve loped using a m i x e d C u ( I I ) E D T A / P A R indica tor . The exchange equi l ib r ium be tween C u ( I I ) E D T A and Ba ions was u t i l ized to employ the well de tec tab le endpo in t of Cn(I I ) wi th P A R . The m e t h o d was app l i ed to the analys is of ba r i t e concent ra te a n d to the de t e rmina t i on of su lphate . 1 -100 mg of Ba were de t e rmined wi th errors of a b o u t ~ 0.5--3~ . Er ro r s in the su lpha te de t e rmina t i on were a b o u t 0 .1 -0 .5 ~ Procedures 1. Ba Titration. To 100 ml of the sample solution containing 1--100 mg of Ba add 10 ml of 6.5 N ammonia, 5--6 drops of 0.01 M solution of Cu(II)-disodinm complex of EDTA and 3--5 drops of 0.050/0 aqueous PAR [4-(2-pyridylazo-resorcinol)] solution. Titrate with 0.01--0.05 M EDTA solution until the red-violet colour fades and continue carefully to a distinct change to pure yellow with no dark shade. 2. Barite Analysis. Fuse 0.3 g of the sample in a platinum crucible with 8 time the weight of Na2CO a and K2CO~, treat the melt as usual, collect the slight hydrochloric acid solution in a 250 ml volumetric flask and proceed as above, only add 3 ml of aqueous triethanolamine solution (1:2) before the ammonia as masking agent for Fe and A1. A turbidity of the solution can be prevented by further addition of tartaric acid, yet results are about 20/0 higher in this case due to the Ca present as Ba is usually accompanied by Ca and the similarity in their analytical properties is most troublesome in their quantitative determination. A correction for Ca will be dealt with later. 3. Sulphate Determination. Precipitate the slightly acid solution containing 15--30 mg of sulphate with an exactly measured excess of BaCI~ solution, allow to digest and filter. Aliqnots of the filtrate are treated as under 1.