Infinite horizon disturbance attenuation for discrete-time systems. A Popov-Yakubovich approach

It is proved that for the discrete-time linear systems with time-varying coefficients the existence of a controller which simultaneously stabilizes and provides prescribed disturbance attenuation for the resultant closed-loop system, implies the existence of global solutions to several Kalman-Szegö-Popov-Yakubovich systems. It is also proved that this fact is equivalent to the existence of the positive semidefinite stabilizing solutions to corresponding game-theoretic Riccati equations. The family of all controllers with the above mentioned properties is constructed in terms of the solutions to the cited Kalman-Szegö-Popov-Yakubovich systems. The main tool is the generalized Popov-Yakubovich theory which is essentially developed in an operator-theoretic framework.     

Studies in the field of polyethylene—V. Correlations between compressibility,crystallinity and molecular weight of high pressure natural polyethylenes

The P-V-T relations of high pressure polyethylene free of additives have been studied in a modified universal testing machine. These polymers show a rapid compression at the melting point of the crystalline phase.     

On the generators of semisimple lie algebras

It will be shown that given any element X in a simple Lie algebra $\text{Q}$ over C, there exists a Y ∈ $\text{Q}$ such that the Lie algebra generated by X and Y is $\text{Q}$. The result is extended to the real semisimple Lie algebras. In some sense the main theorem of this paper can be regarded as an extension of Morozov-Jacobson theorem concerning three dimensional simple Lie algebras (see the remark at the end of Sec. 4). A new property of a special class of regular elements, known as the cyclic elements, is given.     

Restes des formules de quadrature de Gauss et de Turán

Sans résumé Présenté par P. Turán     

Electronic spectroscopy of the A1A' <-- X1A' system of CDF

To further investigate the Renner-Teller (RT) effect and barriers to linearity and dissociation in the simplest singlet carbene, we recorded fluorescence excitation spectra of bands involving the pure bending levels 2(n)(0) with n = 0-9 and the combination states 1(1)(0)2(n)(0) with n = 1-8 and 2(n)(0)3(1)(0) with n = 0-5 in the A(1)A'<-- X(1)A' system of CDF, in addition to some weak hot bands. The spectra were measured under jet-cooled conditions using a pulsed discharge source, and rotationally analyzed to yield precise values for the band origins and rotational constants; fluorescence lifetimes were also measured to probe for lifetime lengthening effects due to the RT interaction. The derived A state parameters are compared with previous results for CHF and with predictions of ab initio electronic structure theory. The approach to linearity in the A state is evidenced in a sharp increase in the A rotational constant with bending excitation, and a minimum in the vibrational intervals near 2(9). A fit of the vibrational intervals for the pure bending levels yields an A state barrier to linearity in good agreement both with that previously derived for CHF and ab initio predictions. From the spectra and lifetime measurements, the onset of extensive RT perturbations is found to occur at a higher energy than in CHF, consistent with the smaller A constant.     

Synthesis and Biological Evaluation of Some New N1‐[4‐(4‐Chlorophenylsulfonyl)benzoyl]‐N 4‐(aryl)‐thiosemicarbazides and Products of Their Cyclization

In the present study, new 1,2,4‐triazoles, 1,3,4‐thiadiazoles, and acylthiosemicarbaz‐ides derived from 4‐(4‐chlorophenylsulfonyl)benzoic acid hydrazide were synthesized and screened for their antimicrobial and analgesic activities. Acylthiosemicarbazides 2–4 were synthesized by a reaction of 4‐(4‐chlorophenyl‐sulfonyl)benzoic acid hydrazide 1 with different arylisothiocyanates.4,5‐Disubstituted‐2,4‐dihydro‐3H‐1,2,4‐triazol‐3‐thiones 5–7 and 2,5‐disubstituted‐1,3,4‐thiadiazoles 8–10 were obtained by dehydrative cyclization of corresponding acylthiosemicarbazide derivatives 2–4 in basic media (8% aqueous sodium hydroxide) and in acidic media (sulfuric acid or phosphorous oxychloride), respectively. The structures of the newly synthesized compounds have been confirmed on the basis of elemental analysis and spectral studies (IR, ¹H NMR, ¹³C NMR, MS). Their antimicrobial activities against some bacteria and yeasts were investigated. The analgesic activity of all compounds was performed with two pharmacological tests: the writhing test induced with acetic acid and hot‐plate test. The results showed that triazole 7 had the best antimicrobial activity against Bacillus cereus. In the chemical stimulus test, triazoles 6 and 7 were the most active compounds whereas in the hot‐plate test thiadiazoles 9 and 10 exhibited the highest analgesic activity.     

Low-lying (K π = 0+) states of gadolinium isotopes

The sd-interacting boson approximation (sd-IBA) and the df-interacting boson approximation (df-IBA) can be related to each other and the states of the interacting boson approximation model can be identified with the fully symmetric states in the sdf interacting boson approximation model. A systematic study of the sdf-IBA model showed that the constructed Hamiltonian can successfully describe the strong octupole correlations in the deformed nuclei. We showed that the interacting boson approximation may account for many of these K ^π ?=?0⁺ states. It was found that the calculated energy spectra of the gadolinium isotopes agree quite well with the experimental data. The observed B(E2) values were also calculated and compared with the experimental data.