Linearized maximum principle for neutral-type,variable-structure optimal problems with delays in controls

The authors state and study an optimal problem for variable-structure systems described by neutral-type quasilinear differential equations with discontinuous initial condition and incommensurable delays. The variation of the system structure means that in the process of motion, at a certain instant of time not known in advance, the object considered can pass from one law of motion to another, and, moreover, the initial condition for each of the subsequent states of the system depends on the state of the next to the last. The discontinuity of the initial condition means that at the initial instant of time, the value of the initial function and that of the trajectory do not coincide in general. The necessary optimality conditions are proved in the form of the linearized integral maximum principle for controls and initial functions and in the form of inequalities and equalities for the initial and final instants of structure change. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 42, Optimal Control, 2006.     

On the well-posedness of the Cauchy problem for quasilinear differential equations of neutral type

This paper proves the theorems on the continuous dependence of solutions when perturbations of the initial moment, the initial vector, the initial functions, the matrix coefficients, and the nonlinear summand on the right-hand side are small in the Euclidean and integral topologies, respectively. __________ Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 19, Optimal Control, 2006.     

Catalytic conversions of linalool and linalyl acetate over large-pore zeolites and mesoporous MCM-41

The dehydration, condensation, and isomerization of linalool and linalyl acetate occur over the H-and dealuminated forms of zeolites FAU(Y), BEA, MOR, and OFF and mesoporous aluminosilicate MCM-41 at 373–453 K. The yields of linalool isomerization to geraniol and α-and β-terpineols are low. The use of linalyl acetate enhances isomerization; the highest yields of the products of linalyl acetate rearrangement (geranyl acetate and terpinyl acetate) are achieved over DeAlBEA(277). Dehydration produces various C₁₀H₁₆ terpenic hydrocarbon isomers.     

The mechanism of phenol methylation on acid and basic zeolite catalysts

The alkylation of phenol with methanol on HY and CsY/CsOH catalysts was studied in situ under static conditions by ¹³C NMR spectroscopy. Attention was largely given to the identification of intermediate compounds and mechanisms of anisole, cresol, and xylenol formation. The mechanisms of phenol methylation were found to be different on acid and basic catalysts. The primary process on acid catalysts was the dehydration of methanol to dimethyl ether and methoxy groups. This resulted in the formation of anisole and dimethyl ether, the ratio between which depended on the reagent ratio, which was evidence of similar mechanisms of their formation. Subsequent reactions with phenol gave cresols and anisoles. Cresols formed at higher temperatures both in the direct alkylation of phenol and in the rearrangement of anisole. The main alkylation product on basic catalysts was anisole formed in the interaction of phenolate anions with methanol; no cresol formation was observed. The deactivation of acid catalysts was caused by the formation of condensed aromatic hydrocarbons that blocked zeolite pores. The deactivation of basic catalysts resulted from the condensation of phenol and formaldehyde with the formation of phenol-formaldehyde resins.     

Thermostability of rat sarcoma M1 procollagen solutions,procollagen fibers and whole tissues

In close to equilibrium conditions (1° per 400 min), the DSC measurements demonstrated that the melting parameters of white rat sarcoma M1 procollagen equaled to T_m?=?34.4 °C and ΔT_m?=?2.7°, and the same parameters of fibers reconstructed from those solutions of procollagen were T_m?=?38.5 °C and ΔT?=?3.1°. These values were by 1.0° lower and 0.8° wider, and by 1.7° lower and 0.7° wider in comparison with the parameters of procollagen and fibers of healthy rat tissue, accordingly. The simultaneous increase in melting temperature and melting width, and a weak decrease in melting enthalpy demonstrated that sarcoma M1 procollagen had some defects. The considerable decrease by 7° in melting temperature and decrease in thermostability of procollagen fibrils in case of sarcoma M1 in comparison to the healthy norm gives a good prospective potential of using this approach as a quick DSC test to detect various sarcomas, including human sarcomas, by comparing the biopsy material or postsurgical tissues with the normal samples.