SCIENTIFIC ABSTRACT YEGOROV, Y. V. - YEGOROVA, A. M.

Document Type: 
Document Number (FOIA) /ESDN (CREST): 
CIA-RDP86-00513R001962510013-3
Release Decision: 
RIF
Original Classification: 
S
Document Page Count: 
100
Document Creation Date: 
November 2, 2016
Document Release Date: 
September 1, 2001
Sequence Number: 
13
Case Number: 
Publication Date: 
December 31, 1967
Content Type: 
SCIENTIFIC ABSTRACT
File: 
AttachmentSize
PDF icon CIA-RDP86-00513R001962510013-3.pdf4.11 MB
Body: 
4F ;ACCESSIONI,NRI AP4037551 uniqueness of the optimal control -is proved.,for a series of example so, OrLga art# hass 20 formulas* ASSOCIATIONt none OSUBMITTEDs 23Apr63 DATE ACQt 09Jun64 ENCLI 00 3 US COD19 I NA NO REF SM 008 OTHEM 002 Card 859-3r S10201601134100310221033xx C 111/ C 333 AUTHOR: Yegorov, Yu. V. 7~ TITLEs Hyperbolic Equations With Discontinuous Coefficients PERIODICALs Doklady Akademii nauk SSSR, 1960, V01,134P Nr,3, PP-514- ~515 TEXTt In the domain x CO'T] , where dl is a domain of the s.pace x - (XII "" Xn) And is bounded by-S, the author considers the hyperbolic equation 2u n 9 n ID u -~-7 - Z (t,x) ~Lu) + bi(t,x) -5- + (1) 3 (t,x) t oxi x + e(t,x)u + f(t,x) where ~ S~~ 0, a ij - a ji is subdivided into domains JI it . .1 mby (n-l)-dimensional ail faces Y . The g , a ij are continuous in Qr r x (0,T] can, however, show discontinuities Card 1/ 6 8593Z S102U1601134100310221033XX C ill/ C-333 Hyperbolic Equations With Discontinuous Coefficients of the first kind on-the surfaces F 5 Y x: [0,T] . The author in- vestigates the classical and the generalized solution of the mixed 'problem for (1) with conditions (2 9 u(t,x) (x) u(t,x) 0 ) u(t,x) It=0 = TOW, 0 t I t-0 1 IV - where fS!~_'r Sx: [ 0,T] . The classical solution is to be twice con- tinuously differentiable in Qr and satisfy (1) + (2) in and on r"it is to verify (3) Lu(t,x)lr - 0, 1 K t , x) (,), u I r- 0- Here K(t,x) 2_! K > 0 is a piecewise smooth function with discon- tinuities of the ?irst kind on T" ; ajj't,x) Cos (Y Ox'. u TX_j i,j-l Card 2/ 6 85932 3/020/60/134/003/022/033Y-% 0 ill/ G 333 Hyperbolic Equations With Discontinuous Coefficients V is the normal to r; -and the symbol [vj denotes the jump of v on r . A generalized solution of (1), (2), C3) is defined to be an element u(tjx) E W2 (1)(Q) (see (Ref-4)) for which u/t.0 T 0, u/,, - 0 and ~u 'IF I U __ _ 7 K. ij 4) 9t rd jj..l i a x (Kbi 0 IL a K K U + Kcu + Kf] F dx dt + ij ~x ~Xi r6 t t J-1 I (K ~)It=0 P(o,x) q~,(x) dx 0 Card 3/6 8593Z ;~Iiic.1~60/134/03/022/04ZXX C 1 C 333 Hyperbolic Equations With Discontinuous Coefficients is satisfied for every F E: W2(1)(q) which vanishes on V and for t tio t, E- (0,T). Theorem-li Let _T 9 a , bi, c and the generalized derivatives QN19t, (?S /Qt 29 id a ii /a t, Ob,/r6t be measurable and bounded in 7~ 1 K(t,x) G C(2)( Ft ) ; f (t, x) C- L - W2(1)(Jl) r r 2((Z); q)o(x) C (Po (x) Is -0; q51 (x) C- L2(a) . Let S and ? be piecewise smooth. Then there exists a unique generalized aolution of (1), (2), M- The proof is carried out according to 0. A. Oleynik (Ref.2,3) by replacing the coefficients T(t,x) etc. by functions 3hG C (Co ) (Q) etc. which for h --> 0 converge in the mean to kS etc. According to (Ref-5) there exists a solution uh E- coo (Qh Card 4/ 6 85932 3/020/60/1 4/003/022/033XX C 3 Hyperbolic Equations With Discontinuous 0 --Rs of the corresponding-problem. The author gives-an estimalion of "uhl' from which there follow the-weak compactness of { u I an3 thereby the existence of the solutions. The-uniqueness is P#oved a~c,.irding to (Ref.5). The6rem 21 ~f S and are continuousli differentiable up-to tne order I + 2(l 2: n + 1~ if the V are c osed and do not intersect t emselves and S, if K,.? , a E C bi, cE C(l)( t h U+2 ('+')(~r f E W 2(1) (q\ r W2 J^L \ q)l W2(1+')r(a\, and if Oc n P P (6) %/S - 0 0, 1 a P Kai M POO i1J-1 Tt J Ituo Y,,, _P Cos( x M 0 04 - 0'. o 1) jx CPV toe, where it is and is determined for V. > 2 I . 0 with the aid of (1) from' 9,0 anl Yi, then the generalized Card 5/6 8593Z s/o-o/,6o/i34/003/022/033XX C 1117 0 333 Hyperbolic Equations With Discontinuous Coefficients solution of (1)p (2)p (3) is aIRI(Lhe claaBical solution. For 1 2~ 1 + I + X it is u(t,x) e C Itf The Cauchy Rroblem can-be similarly treated,for-a-linear.hyperbolic systemIPof-first order-with discontinuous-coefficient On-the plane as well as for some symmetric problems-in (tj-xjFV.. xn). The author mentions S. M. Nikollskiy, L. K. 310bodotok y-and,Q,._L. Sobolevt he thanks 0. A.'Olenik fo -advices. There are 8 Soviet references. ASSOCIATIONs Moskovskiy gosudarstvennyy-universitet'imeni M. V. Lomonosova-(Moscow-State University-imeni M. V. Lomonosov)- PRESEITEDs MaY 7, 1960, by J. 0. Petrovskiy-,~Academician SUBMITTEDs May 6, 1960 Card 6/6 23662 3/186/61/003/001/015/020 AO-51/AI29 C) AUTHORSt Yegorov, Yu,V.j Pushkarev, V.V., Tkachenko, Ye.V. TITLE: Copreoipitation of mioro-quantities of Sr go with active manganese dioxide in the presence of macro-quantities of barium and potassium PERIODICALt Radiokhimiya, V 3, no 1, 1961t 87-89 TEXTs The authors-have established that the competition of mioro-quantities of Sr90 with macro-quantities of calcium &nd barium in their copreoipitation with active manganese dioxide obaygoan equation, whereby the logarithm of the distribution coefficient of Sr is linearly dependent on the logarithm of the molar ratio of the total quantity of the analogue to the sorbent. The given equation is said to be derived from the law of active masses. The authors further show that barium is stronger than calcium in suppressing the sorption of SOO with active manganese dioxide; this fact leads to the con- clusion that the formed sorbing compounds of the calcium and barium manganate Card 1/4 23882 Coprecipitation of micro-quantities of Sr go 000 311861611003100110151020 A051/A129 type have varying stability, i.e., the corresponding compound of calcium is more subjected to hydrolysis then -the other. The relationship described above was derived from the following oonsiderationst 1) the sorbent is lo- cated in the range of saturation b the analogue (barium or calcium), 2) the pH of the aolution is cpstant, 3~ the ratio of the activity coefficients of the analogues and Sr in the solid phase is conotantp which is the same as the absence of a noticeable interaction between the adsorbed cations (Ref 7). The factors used whores A the quantity of the analogue in the solid phase (in moles), Aliquid the qWantity of the analogue in the liquid phase (in moles), Ao M AT + Aliquid the total quantitiy of the analogue in the system (in moles), 6 the distribution coefficient of Sr 90 equal to the ratio of the adsorbed part to the equilibrium part, m the mass of the s?6bent (in mole S)fzIand Z2 the charges of the ions of the analogues and Sr The following relationships are designated by A and Gi A Ao G AT (2) m M then on the basis of the law of active masses the expressions Card 2/4 23882 go 5/186/61/OC3/001/015/020 Coprecipitation of micro-quantities of Sr A051/A129 1/z 1 o M - %U-111 K li uid . '/z2 (3) is found, where Ko M const under A ocnditions of constancy of the temperature; in the given case the volume of solution and sorbent mass are also constant. Z1 ZI/'2 A if K Kf and transforming (3) we obtain K W .6 (--2 - 1) (4)- 0 A Taking into consideration (1) and (2) and taking the ldg&rTthm of (4),'the following uquation in obtainedt Ig B - z 1g (L-0) (5), where B lg(KG) 22/z, z An analysis of the obtained relationship showed that under the given oondi- tions the sorbent has a capacity of 0,38 mX Sr/mM KnO . For sufficiently high values of Ap formula (5) in written approximatelis z ig E . B - lgA (6), The experimental data obtained agree favorably with this 4pression. The absolute value of the angle oo- Card 3/4 23882 go SliS61611003100110151020 Coprecipitation, of micro-quantities of Sr ... 1051/A129 z efficient z in this range is equal to I for both analogues. This proves the equality of the ion charges of these analogues and Sr go during the exchange process. Tho macro-quantitiee of barium have a s;6onger depressing action on the sorption of the micro-concentrations of Sr than equimolar quantities of calcium. -This is thought to be due to the different relationship of the analogues to the sorbent. There are 6 formulae and 2 graphs. Figure Is Coprooipitation of strontium with active manganese dioxide. Longmuir's isotherm. 0 t ,17-190C, strontium chloride was labelled with WO. Experiments without access of air. Card 4/4 PUSHKAREV, V.V.; YEGOROV,__Lu!_Y.; TKAGHENKO, YeV,; FUZAKO, V.D. Sorption of microquantities of strontium-;90 by ferric hydroxide in the presence of alkaline earth metals. Izv.vys.ucheb.zav.; khim.i khim.tekh. 4 no.l.-60-63 161. (KERA 14:6) 1. Ural'skiy politakhnichookiy institut imeni S.M.Kirova, Mfedrs, radiokhimii, (Strontium-isotopes) (Sorption) 33183 s/186/61/003/oo6/oO2/010 WjD E040/E185 AUTHORS: Yegorov, Yu.V.1 Krylov, Ye.I., and Tkachenko, Ye.V. TITLEs Contribution to the theory of the distribution of micro-quantities of radioactive strontium between hydrated oxides and the solution PERIODICALi Radiokhimiya, v-3. no.6, 1961, 654-661 TEXT: In spite of the considerable scientific and technical importance of the processes of radioisotope adsorption on metal hydroxide, the mechanism of the process is still far from being elucidated, especially at micro-concentrations of radioisotopes, and no unified ideas have so far been formulated for the co-precipitation of radioisotopes with the hydrates. These problems are analysed theoretically and a series of equations is derived for the absorption of-micro-quantities of the cations of radioisotopes (which do not form radiocolloids) by the precipitates of metal hydroxides capable of behaving as cationites in acid media. The following assumptions were made in the derivation of the equations: 1) the hydrated oxides have ion-exchange properties and, under certain definite conditions, behave as a cationite in Card l/ 3 33183 Contribution to the theory of s/i86/61/003/006/002/010 E040/E185 acid mediumi 2) the law of active mass is applicable to the systemi and 3) the radioactive isotope behaves as an electrolyte at infinite dilution. The equations were checked by plotting experimental data obtained for the absorption of radioactive strontium (Sr90) by ferric hydroxide and active Mn02 an a function of the p11 of the medium. The S-shaped curves obtained represent a general function of the type y = C + mpH and thereby confirm the correctness of the assumptions made, especially with regard to the ion-exchange character of the sorption of strontium by metallic hydroxides. I.Ye. Starik, A.I. Novikov, L.G. Kuz'mina and Yu.V. Morachevskly are mentioned in the article in connection with their contributions in this field. There are 3 figures and 22 referenceal 12 Soviet-bloc, I Russian translation from non- Soviet-bloc publication, and 9 non-Soviet-bloc. The four most recent Englifih language references read as followst Ref.3j M.H. Xurbatov, G.B. Wood, J.D. Kurbatov~ J. Chem. Phys., v.19, 2, 258 (1951). Card 2/3 33183 ContrIbution to the theory of s/186/61/003/006/oO2/010 E040/E185 RefAt M.H. Kurbatov, G.B. Wood, J.D. Kurbatov. J. Phys. a. Coll. Chem., v-55, 7, 1170 (1951). Ref.5s M.H. Kurbatov, G.B. Wood, J. Phys. Chem., V.56, 6, 698 (1952). Ref.16s A. Kozawa, J. Electrochem. Soc., v.106, 7, 552 (1959). SUBMITTED: October 31, 1960 Card 3/3 AUTHORS: TITLE: S/121/62/000/004/005/008 D040/DU3 Kupershmidt, Sh. N., and Yegoroy, Yu. V. Automatic reader for co-ordinate Jig boring machines PERIODICAL: Stanki i instrument, no. 4, 1962~ 33-36 TEXT: The described new reader developed and tested at the Moskovskiy zavod koordinatno-rastochnykh stankov (Moscow Co-Ordinate Jig Boring Machine Plant) for program-controlled jig borers is an improvement on existing optical readers used by this pUnt, the Leningradsidy stankozavod im. Sverdlova (Leningrad Machine Tool Plant im. Sverdlov) and other plants. The existing device with a 65- or 125-fold amplification has 0,001-0.002 mm scale divisions and produces inadequate' line shadow on the screen because the illuminance of the latter is too weak (0.5-2 lx). The new system has an improved photoelectric transducer with 3-ight' modulation produced by a diagram oscillating at 50 cps, so that the appearance of a dark line in the field of view of the photocell causes a pulse signal on the amplifier output. The diagram is oscillated by an electromagnet connected to! Card V2 5/121/62/000/004/005/009 Automatic reader for co-ordinate lig .... D040/DU3 the electric network. The system includes an amplifier, a phase-sensitive stage,! and a phase regulator. It has been stated in tests that the optimum diaphragm slot width is 1.3 m, that the slot length must be smaller than the sensitive layer of the photoresistor, that the slot must be placed precisely opposite the center of the photoresistor, and that the oscillation amplitude must not extend -r tha- beyond the sensitive layer. The new reader has a reading accuracy highe n 11.4,, a simple design, and stable characteristics. Mathematical formula for the modulAtor motion, and diagrams of the system and of the photoelectric transducer,! are given. There are 9 figures. Card 2/2 PUSHKAREV) V.V.; TKAGHENKO, Ye.V.; )(KGOKQY,-XU.L ; LYUBIMOV, A.S. Sorption of some radioactive isotopes from aqueous solutions by active manganese dioxide. Radiokhimia 4 n0-1:49-54 162. (MIRA 15:4) (Radioisotopes) (Sorption) (Manganese oxides) s/i86/62/004/003/019/022 E075/E436 AUTHORS: Pushkarev, V.V., Tkachenko, Ye. V. TITLE: On the influence of ethyl alcohol on the sorption of strontium ions with an active manganese dioxide PERIODICAL: 11adiokhimiya, v.14, no-3, 1962, 37.1-373 TEXT: The object or the work wits to elucidate the nature of the connection between the parameter of sorption affinity a from the Lingmuir isotherm, and the solution properties. The Langmuir isotherm is given as CT) 1 1 C cc r -a r p where Cp - equilibrium concentration of Sr2+ in solution; Cc - adsorption of Sr2+, f' - capacity of sorbent. An active MnO2 was used as a sorbent. The compound undergoing distribution was SrC12 labelled with Sr89, and the non-aqueous solvent ethyl alcohol, The latter was added to the solution of SrC12 in water containing a-coagulated INW02 sOl- It was found Card 1/2 S/186/62/oo4/003/0-19/022 On the influence of ethyl ... E075/E436 that the capacity of the sorbent is the same in all the experiments. Parameter a incroases with the decreasing dielectric constant of the medium, It was shown that when the dielectric con5tant of the solution changes from 58.0 to 75.5, there exists a linear dependence of 1g a. on the reciprocal of dielectric constant of the alcohol-water solution. There are and 1 table. S'UBMITTED: May 12, 1961 Card 2/2 "Y YEGCRCIV. Y NIKOLAYEV, V.M.; MYLOVv YO.I.,- TKACHEWO, Ye.V. Fojaibi~6ty of using a mixture of isotopes of Sr89 and Sr 0 7 in direct radiometry, Radiokhimia /+ no.4:516-518 162. (MIM 15:1-1) (Strontium-Isotopes) (Yttrium-Io-otopea) (Radiometry) Y"; TKACHENKO, Yo.v.; FUSHKAREV, V.V.;J~OROVI YU,Y, Adsorption of strontium bY manganese dioxide from water-ethanol solutions. Izv.vys.ucneb.zav.; khim-i khim-tokli- 5 no.l.,172- 174 162. (MDU 15 ~4) 1. Ural'skiy politekhnicheskiy institut, imeni Kirova, kafedra radiokhimiia (Strontium) (Adsorption) (Manganese oxides) Ygamov, Yu. V.; KRYLOVj Ye. 1. Yature of absorption of electrolytes by some preolpItates. Izv. vys. ucheb. sa-r.; khim. i khim. takh. 5 no.5:749-752 162. (MIRA 16:1) 1. Urailiskiy politekhnicheskiy institut imeni S. M. Kirova. kafedra khimii i takhnologii rodkikh elementov. (Adsorption) (Electrolytes) YEGOROV, Yu.V.; KRYIDVj Ye.I.; TKACHENKOp Ye.V. Analysis of the sorption capacity ofdron hydrbxide. Trady Ural. politekh.ins~,no.1210%~" 162. (MIRA 1625) (Iron'~ydroxidos) (Porption) win PUSHKAREV, V.V.; TKACHENKO, Ye.V.; YEGOROV, Yu.V. IKARIDV, V.A. Adsorption of strontium by active manganese dioxide from water- alcohol solutions. Trudy Ural,politekh.inat.no.121:45-48 162. (MIRA 160) (Strontium) (Adsorption) (Manganese oxides) S/020/62/145/004/002/v-24 ILI roov B112/B102 AUTHOR; Yegorov, Yu. V. TITLE: Certain Drobloms in the optimum control theory, PERIODICAL: Akademiya nauk SSSR. Dokladyo V-1145, no- 4, 1962, 720 - 723 TEX': A controlling function p(t) (1p(t)1-"- 1) is-said to.be I-optimal if. 2 2 the solution of the boundary value problem au(t,x)/at,; a u(t,x)/ax U(O,x) 0, au(t,O)/ax - 0, au(t,l)/8x -.a[p(t) - u(t )], corresponds to 1 2 the minimum value of the functional I(P) - f[u(T,x).-.u OWI dx, where 0 u 0(x) is a given function. It is demonstrated that an I-optimal co*ntrol exists every'ahere. 1. few other versions of this problem are considere!. Their solvability and uniqueness are shorm, and convenient methods of solving them are derived. AS SOCIATIO"Vi Moskovskiy gosudarstvennyy universitet im. M. V. Lomonosova (Moscow State University imeni X. V. Lomonosov) Card 1/2 3/020/62/145/004/002/024 Certain problems in the optimuei ... B112/BI02 PRESENTED: 14.14arch 15, 1962, by L. S. ?ontryagin, Academician 14, SUBMITTZD: "larch 14, 1962 Card 2/2 non 5~ r .31MOEDVt Xu.V. (tbakva) Some Ijibblems in the theory of optimum oatml. Zhar. vychs mats i mat. fiz. 3 no;'.~:887-904 S-0 163. (MJRA 16:11) Yu.V.;IKRYIkV, Ye.I. Effect of the mass of a collector (hydrated oxide) on the sorption of trace amotint3 of certain radionatiye isotopes. Radiokhiniia 5 no.2:205-211 163. Characteristics of the sorption of strontium 90 by active manganese dioxide. 23-1-215 (MM 16:10) t ~-B075/M6---- V AUTHORS: Yegorov and Krylov,-Ye.l. TITLE: some peculiarities of sorption of strontium-90 on active manganese dioxide. :PERIODICAL: Radiokhimiya, v.5, no.2, 1963, 211-215 -TEXT: Sorption of micro-quantitioa-of.9OSr was studied on an active MnO2 resulting.from the action of H202 On K MnO4 under conditionL of free coagulation, wheroby the precipitate (Mn02) sorbed a proportion or K+ ions and the pH of the system remained constant. The dependence of ~OH-3 on the mass "concentration" of the sorbent ~Ms] was determined aciclimetrically. The following equations were obtained: ~m,:j ,f o.64 1 68 ~O H -3 0.42 * (2) where ~ms3er - effective MA65 of sorbent, The quantity of 9OSr x-emoved-by-M 'nO2--ia- gJ-ven--by-l--- Card 1/2- s/i86/63/005/002/001/005 Some peculiarities of sorption of E075/2,136- K 2 92 (4) --t--' -t- -Eq-(4)-w&s-confirmed-experimentallyfora fli-er- -K, cons an - solution of IC Mn02 (0.192 to 1.15 ira-11t), KCZ (8 g/t) and about .10 microcurios/~ 905r precipitated by H202. K1 was found to be The amount of coagulant (KCV affects strongly the distribution of 90sr between 11n02 and the solution. There are 3 figures and I table. SUBMITTED: March 26, 1962 Card 2/2 ACCESSION NRs AT4017556 0/3074/62/000/047/0073/0085 AUTHORs Yegorov# YU* Ve (Assistant) TITLE: Efficient controlled ferrite phase ihifter, SOURCE: Leningrad. Elektrotekhnicheakiy institut. Xzv., no* 47, TOPIC TAGS: phase abifter, ferrite Phase ohifter, controlled ferrite phase shifter, LSE mode, LSM mode, longitudinal transverse waves, field concentratlon in-ferrite ABSTRACT: The paper deals i;ith the case of a ferrite slab of arbi- trary dimension-located near any of the-walls of a rectangular wave- guide, magnetized along an arbitrary axis, for an arbitrary wave propagation mode. The solution is obtained by'the perturbation metbod, using the solutions of the unperturbed problem in the form of LSE and LSX modesi the behavior of which was investigated under Card ----------- a ACCESSION NRt AT4017556 the corresponding cases by the'author earlier (Xzvestiya LETI,. No. 47, 1962). Allowance is made for the concentration of the field in the ferrite, which plays the decisive role in the theory of opera- tion of efficient phase shifters. Simple formulas are proposed for the ferrite-slab calculations so as to ensure.maximum utilization of this effect. The calculations are confirmed by experiment. -The good agreement between the calculations and the experiment for the case of a single slab leads to the conclusion that'the proposed cal- culation procedure is valid also for other ferrite structures with analogous physical phenomena. -This applies also to-the phase shifter of Reggia and Spencer (Proc. of'IRE, v. 45, 11, 1957). j,Orig. art. hass 6 figures and 20 formulas* ASSOCIATIONs Leningradakiy elektrotekbnicheskiy institut (Leningrad Electrotechnical Institute) BU13MXTTEDs OOKay6l DATS ACQs 20Kar64 ZSCLI 00 BUBCODEs G3# SD NR,.REF SOVs 003 OTHER2 0" CaM 2/2 'j- T, L ioo4g-63 ACCESS= HH: A83000388 8/0OW/63/000/004/023/tO23 SOUME: RZhe Mika.. Abe. 4zhi36 XMOR., TME: - LOngitudinalmtransverse vaves in rectangular vaveguide filled vith two different media CI= SOURCE: Izvo. Leningr# elektrotekhne in,-tap vyp, 47t 1962; 86-97 TOPIC TAGS: waveguldes, loaded, field components TRAMIATION: The propagation of vaves in a layered rectangular vaveguide is considered. A~,system of two transverse electrccegnatic vaves is introduced, equivalent to the system of electric wA magnetic vaves. For each of these types, a characteristic equation is obtained in the case of two layers of a dielectric in the waveguide. Plots are made for the dependence of the propgation constant in a partially filled-wavegulde as a function of the couposition and thickness of the filling dielectric, 0. Postnoy Card 14/ ------------------------------------------------- A- -A NIKOLAYEVP V.M.; KRYLOV, Y().I.; BAGILF,7SOV,, V.F.; YEWROV, Yu.V. Behavior of radiocolloids of cerium in sorption systems. Radiokhimlia 5 no.5:622-626 163. (MIPA 17:3) 3t AFF-1C IMESSIO"I NRI AP3000509 S/0020/6)/l 9~/002/OZ~1/02/A 11LUTHORs Yegorov, Yu. V, TITLEs Optimal control in a Banach spacej~ SOURQEt~ AN SSSR. Do'klady*,, v. 150, no. 29 19630 241-244 TOPIC TAGSt optimal controls Banach space JABSTRAM Given the differential equation f (X (t), a (1)), X (a) X6 (a