A method of computing the gradient and the Hessian of the quality criterion in parametric optimization of continuous-discrete stochastic systems

We propose an effective method of numerical determination of the gradient vector and the Hessian matrix of a quadratic quality criterion in parametric optimization of continuous-discrete stochastic dynamic control systems based on the application of adjoint equations. Translated fromDinamicheskie Sistemy, No. 13, 1994, pp. 20–25.     

Exciton states in In x Ga1−x As/GaAs double quantum wells: Normalized reflection spectra

Il Nuovo Cimento D - Normalized reflection spectra in GaInAs/GaAs quantum wells are shown for two sets of samples with different alloy concentration (x=9% and 18.5%) and well thickness ranging from...     

Preparation and Eh--pH diagrams of Fe(II)--Fe(III) green rust compounds; hyperfine interaction characteristics and stoichiometry of hydroxy-chloride, -sulphate and -carbonate

Fe(II)--Fe(III) hydroxy-chloride, -sulphate and -carbonate were prepared by oxidation of a ferrous hydroxide precipitate in anion-containing aqueous solutions. The compounds are characterized by monitoring the redox potential E_h and the pH of stochiometric suspension vs time with the appropriate concentration ratios. X-ray diffraction allows us to characterize the crystal structure by distinguishing “green rust one” (GR1) from “green rust two” (GR2). Since green rusts (GRs) are of a pyroaurite-sjögrenite-like structure, i.e., consisting of intercalated foreign anions and water molecules in the interlayers between the brucite-like layers of Fe(OH)₂, their chemical formulae can be determined from the Mössbauer spectra. Three quadrupole doublets are observed: D₁ and D₂ correspond to a ferrous state with isomershift IS of about 1.27 mm s^-1 and quadrupole splittings QS of about 2.85 and 2.60 mm s^-1, respectively, whereas D₃ corresponds to a ferric state with IS and QS of about 0.4 mm s^-1. The hyperfine parameters of these doublets are similar from one green rust to another but their intensity ratios vary considerably. Finally, E_h and pH equilibrium diagrams of the Fe species in the presence of chloride, sulphate and carbonate anions contained within the water solution are drawn and the thermodynamic conditions of existence and degrees of oxidation of green rusts are discussed.     

类铜离子的电子碰撞参数及其规律

用准相对论扭曲波方法系统地计算了Ｂａ、Ｎｄ、Ｇｄ、Ｙｂ、Ａｕ、Ｐｂ类铜离子组态能级之间的电子碰撞激发强度Ω（ｎｌ－ｎｌ），３≤ｎ≤７，４≤ｎ≤７，同时给出了高能极限的碰撞强度和外推到阈值的碰撞强度，用最小二乘样条方法拟合了全能域碰撞强度及热平均速率系数。对于一个激发过程，用１０个参数可以得到碰撞电子在任意能量下的碰撞强度以及任意温度下的速率系数。     

The Assessment of Reservation Prices of an Intermediate R&D Result and Patent Reward Under Oligopolistic Competitive Behaviour

One of the shortcomings of R&D evaluation is a lack of emphasis on analytical assessment of the value of an on-going R&D project. This paper addresses the problem concerning the distributive aspect of access to superior knowledge. Decision tree analysis and probability models appear to be appropriate tools for assessing the values of an intermediate result and patent reward of a firm's R&D decision in an environment of perfect information and oligopolistic competition. The assessed values are used as minimum prices acceptable to the firm when the knowledge is disseminated to the public. This paper will attempt to resolve this problem through the determination of the appropriate values of the reservation price of the first-stage invention in terms of the final reward and of a patent reward for which the inventor is willing to apply.     

Reflectionless potentials and soliton series of the KDV equation

Potentials of the Schrödinger equation, slowly decreasing at infinity, generate an infinite discrete spectrum converging to zero. The inverse scattering problem in the class of such potentials is solved in a constructive way similarly to the classical soliton theory. An infinite-dimensional system arising from Backlund transformations over soliton solutions plays the role of a determinant representation of the potential. The asymptotics at infinity is derived by use of the Poisson summation formula. An application to the long-time asymptotics of the solution of the Korteweg-de Vries equation is considered.In Memory of Prof. M. C. PolivanovInstitute of Mathematics, Urals Branch, Russian Academy of Sciences, 450000, Chernyshevsky str. 112, Ufa, Russia. Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 93, No. 2, pp. 286–301, November, 1992.     

Essential self-adjointness of operators associated with the Cauchy problem for the wave equation

A sufficient Hartman-Ismagilov type condition for the essential self-adjointness of a one-parameter family of unbounded operators that arise in the solution of a Cauchy problem for the wave equation is established. An analog of this result is stated for unbounded integral operators.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 7, pp. 940–948, July, 1992.     

Projective-type axioms for the hyperbolic plane

It is shown that the Laws of Pappus and Desargues may replace the Axiom of Projectivities in Menger's development of hyperbolic geometry from axioms of alignment.