Studies of distributed parameter systems: Decoupling the state-parameter estimation problem

The problem of state-parameter estimation is considered in terms of decoupling the estimation procedure. First, the theoretical preliminaries necessary for the mathematical statement of the problem are defined. Then using the extended Kalman filter (EKF) approach, the state and parameter are estimated by applying the solution techniques to a distributed parameter system. Next, the state estimation problem is decoupled from the parameter estimation problem and by using a numerical example, the advantage of this decoupling procedure is demonstrated. The numerical results show that convergence can be improved when this decoupling procedure is employed. The effect of the location of the measurements on the estimation problem is also analysed in this work. The results show that the convergence of the problem depends on the location as well as the number of measurements.     

Evaporation of polymer-solvent mixtures

Summary The Stefan-Winkelmann diffusion technique has been used to determine vapor pressures of high boiling point compound-solvents mixtures. Data are reported at a temperature of 67°C for the mixtures polyphenyl ether (6 rings) — benzene and carbowax 1500 — benzene and at a temperature of 100°C for the mixtures polyphenyl ether (6 rings) — toluene and tricresylphosphate-toluene. The range of concentration is only limited by the appearance of a solid phase, and results are in good agreement with those determined by vapor pressure osmometry.Nomenclature A Vapour source - B Flowing gas phase - c Concentration, g-mol/cm³ - D_AB Molecular diffusion coefficient, cm₂/s - h_i Total interface depth, cm - K Parameter defined by equation (6), dimensionless - I Polymer or high boiling point compound - M_A Molecular weight - N_AZ Molar flux, g-mol/(cm₂) (s) - P_A Partial pressure at the interface, atm - P Total pressure, atm - R Gas constant, (atm) (cm₃) / (°K) (g-mol) - T Temperature, °K - t Time, s - Y_A Molar fraction at the interface, dimensionless - z_o Initial interface depth, cm - z_i Drop of the interface depth, cm - z Interface position Greek Letters _A Density of the liquid phase, g/cm³     

Thermal analysis of styrene–alkyl methacrylate polymers. I. Glass transition temperatures

The glass transition temperatures (T_g's) of several polystyrenes and styrene–alkyl methacrylate copolymers and terpolymers were measured using thermomechanical analysis (TMA) and differential scanning calorimetry (DSC). The polymers studied had number-average molecular weights from 3000 to 250,000 g/mole. The results indicate that the composition dependence of the T_g's for the copolymers and terpolymers can be satisfactorily described by a general Fox equation. In general, the measured T_g's of the copolymer and terpolymer samples depend more on the steric effects of the constituent pendent groups than on their molecular weights. The chain flexibility rather than the size of the pendent group is the determining factor in the glass transition properties of the styrene polymers.     

X-ray crystal structure of the dye 2-cyano-4-bromo-4′-N,N-diethylaminoazobenzene

The crystal structure and molecular conformation of 2-cyano-4-bromo-4′-N,N-diethylaminoazobenzene (C₁₇H₁₇N₄Br, mol. wt. = 357·2 a.m.u) has been determined from X-ray diffraction data; triclinic, P$\text{1}$ (No. 2), a = 10·132(11) Å, b = 12·216(16) Å, c = 6·966(11) Å, α = 104·21(9)°, β = 92·67(12)°, γ = 97·22(7)°, V = 826·5(9) ų, Z = 2, D_c = 1·436 g cm^?3, F(000) = 378, λ(MoKα) = 0·71069 Å, μ(MoKα) = 26·0 cm^?1. The structure was solved by the multiple solution direct method and refined by full-matrix least-squares to R = 0·059 for 1538 independent observed reflections. The azobenzene skeleton is planar to within 0·06 Å. Most significant bonding data are: NN, 1·290(8) Å; BrC, 1·866(6) Å; mean CN (azo) 1·380(8) Å; NNC, 113·6(4) and 115·3(4)°; NCC (cis relative to NN) 125·9(4)° and 126·7(4)°; NCC (trans) 116·8°(5)° and 116·1(4)°.     

An NMR study of the dissociation of N,N′-(2-propyloximino)-4,4′-methylenebis(phenylcarbamate) and its crosslinking of polymers containing labile hydrogens. II

Nuclear magnetic resonance spectroscopy has been used to study the dissociation and reaction of N,N′-(2-propyloximino)-4,4′-methylenebis(phenylcarbamate), as a crosslinking agent for polymers containing labile hydrogens. The crosslinking of poly(acrylic acid), polyacrylamide, and poly(vinyl alcohol) was found to result upon heating each to 150°C for 10 min with this component at 2–10 wt %.     

ABSORPTION AND DESORPTION TO AND FROM LIQUID FILMS ON INCLINED PLANES

Two published theoretical models are examined and applied to experimental results for absorption and desorption. The system used was CO₂/H₂O and studies were made for liquid film flow down inclined planes. Experimental results give “Reduced” values of mass ransfer rates.

Interferometric studies give interfacial concentration, penetration and film depths, and take-up of carbon dioxide. In the case of desorption the interferograms are distorted by “deflections.”

All the experimental values for absorption and desorption differ from those calculated from theoretical models.

Desorption is not a mirror image of absorption, and it is approximately 75% of the transfer rate of absorption over a wide operating range.

A comparison is made of the behaviour of static pools and flowing liquid films.     

A linear algebra approach to OLAP

Inspired by the relational algebra of data processing, this paper addresses the foundations of data analytical processing from a linear algebra perspective. The paper investigates, in particular, how aggregation operations such as cross tabulations and data cubes essential to quantitative analysis of data can be expressed solely in terms of matrix multiplication, transposition and the Khatri–Rao variant of the Kronecker product. The approach offers a basis for deriving an algebraic theory of data consolidation, handling the quantitative as well as qualitative sides of data science in a natural, elegant and typed way. It also shows potential for parallel analytical processing, as the parallelization theory of such matrix operations is well acknowledged.