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.     

Differentiation of heterocyclic regioisomers: a combined tandem mass spectrometry and computational study of N-acridin-4-ylbenzylamide and N-acridin-2-yl-benzylamide

Electrospray ionization (ESI) tandem mass spectrometry (MS/MS) has been used to differentiate two positional isomers of acridine derivatives, N-acridin-4-ylbenzylamide and N-acridin-2-ylbenzylamide. The study revealed that the isomeric ion structures produced by these heterocycles could be distinguished upon collision-induced dissociations (CID). In particular, the loss of a water molecule was shown to be a regiospecific reaction of the protonated N-acridin-4-ylbenzylamide, in which the location of the benzylamide substituent with respect to the acridinic nitrogen greatly assists proton migration by allowing the creation of intramolecular hydrogen bonds. To a lesser extent, the two isomers could also be distinguished by the difference in the abundance of the benzoyl cation in the MS/MS spectra of the [M+H]+ ions, as this ion is produced with a much higher rate from N-acridin-4-ylbenzylamide. Calculations based on quantum-mechanical models have been performed to evaluate the stability of the ion structures and to support mechanisms proposed for these two dissociation reactions.     

1,1-dioxonaphtho[1,2-b]thiophene-2-methyloxycarbonyl (alpha-Nsmoc) and 3,3-dioxonaphtho[2,1-b]thiophene-2-methyloxycarbonyl (beta-Nsmoc) amino-protecting groups

Of the three theoretically possible, Bsmoc-related, naphthothiophene sulfone-based amino-protecting groups, the two most readily available derivatives, the alpha- and beta-Nsmoc analogues, have been examined as substitutes for the Bsmoc residue in cases where the latter lead to oily protected amino acids or amino acid fluorides. All of the naphtho systems gave easily handled solid amino acid derivatives. The intermediate sulfone alcohol 11 used as the key reagent for introduction of the alpha-Nsmoc protecting group was readily made from alpha-tetralone (Scheme 1). The corresponding beta-analogue 17 was made similarly on a small scale, but due to the high cost of beta-tetralone, an alternate route involving reaction of rhodanine with alpha-naphthaldehyde was used for large-scale work (Scheme 2). All proteinogenic amino acids were converted to their alpha- and beta-Nsmoc derivatives. Deblocking studies showed that the reactivity toward deblocking by piperidine followed the order alpha-Nsmoc > Bsmoc > beta-Nsmoc. 1H NMR experiments showed that deblocking of the two new systems was mechanistically similar to that previously established for the Bsmoc derivative in that the reaction is initiated by Michael addition to the beta-carbon atom of the alpha,beta-unsaturated sulfone system. Application of alpha- and beta-Nsmoc amino acids to the solid-phase synthesis of two model peptides was examined. An advantage of the alpha-Nsmoc system over the long-known Bsmoc system proved to be the milder conditions needed for the deblocking step relative to the Bsmoc case, which is itself more readily deblocked than the classic Fmoc analogue.     

Adiabatic Calorimetry of a Very Low Density Polyethylene Copolymer

The heat capacity of a very low-density polyethylene copolymer (VLDPE) was measured between 10 and 410 K. Using two sets of literature data for the fully crystalline and the fully amorphous states, crystallinities were calculated as a function of temperature. During the stabilisation periods in the melting process no equilibrium is reached, because of an exothermic process, which is attributed to (re)crystallization. Values for the enthalpy of melting and for the heat capacity of the liquid are given. This revised version was published online in August 2006 with corrections to the Cover Date.