Poly(hydroxyisobutyrate) by ring‐opening polymerizations of 5,5‐dimethyl‐1,3,2‐dioxithiolan‐4‐one‐2‐oxide

α‐Hydroxyisobutyric acid anhydrosulfate HiBAS (5,5‐dimethyl‐1,3,2‐dioxithiolan‐4‐one‐2‐oxide) was polymerized under various reaction conditions and the solid reaction products were characterized by ¹H NMR spectroscopy, MALDI‐TOF mass spectrometry (MT m.s.), fast atom bombardment mass spectrometry (FAB m.s.), viscosity, and SEC measurements. Thermal polymerizations at 100 °C mainly yielded cyclic oligo polyesters presumably resulting from a zwitterionic polymerization. Cycles were also detected when pyridine was used as catalyst at 20 °C. When triethylamine was used as catalyst traces of H₂O played the role of initiators. Benzyl alcohol initiated the polymerization of HiBAS at 100 °C and yielded a polyester terminated by one benzylester and one OH endgroup. The SEC measurements indicated that all samples possess relatively low molar masses with number–average molecular weights ≤ 10,000 Da (in contrast to the literature data). © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6229–6237, 2008     

Finite-dimensional time-invariant linear dynamical systems: Algebraic theory

Willems' approach to dynamical systems without a priori distinguishing between inputs and outputs is accepted, and with this as a starting point, new linear dynamical systems are introduced and studied. It is proved in particular that (in the complex case) the set of isomorphism classes of completely observable (or completely reachable) linear systems with given input and output numbers and McMillan degree, has a natural structure of a compact algebraic variety. This variety is closely connected to the one constructed by Hazewinkel using the Rosenbrock linear systems % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabeiEayaaca% aaaa!35DB!\[{\rm{\dot x}}\]=Ax+Bu, v=Cx+D(·)u, where D is a polynomial matrix, and may be regarded as the most natural compactification of it. (The connection is very similar to that of Grass_m,mx+p() and Mat_m.p(). Input/output linear systems, i.e. linear systems equipped with an extra structure which distinguishes input and output signals, are also considered. It is shown that each of them may be represented by the equations K% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabeiEayaaca% aaaa!35DB!\[{\rm{\dot x}}\]+L% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabeyDayaaca% aaaa!35D8!\[{\rm{\dot u}}\]=Fx+Gu, v=Hx+Ju (det(K–sF)0). Such systems clearly contain the so-called generalized linear systems. They also contain the Rosenbrock linear systems mentioned above and essentially coincide with them.     

Ternary complex formation inducing large expansions of chemomechanical polymers by metal chelators, aminoacids and peptides as effectors

Formation of supramolecular ternary complexes within a functionalized hydrogel are shown for the first time to lead to large macroscopic motions with biologically important effectors such as aminoacids and peptides. The mechanical motions can be made reversible by the addition of external metal ion complexing agents, and represent also chemical logical gate functions, operating without external devices or power supply.     

On Some Entire Modular Forms of an Integral Weight for the Congruence subgroup Γ0(4N)

Four types of entire modular forms of weight are constructed for the congruence subgroup ₀(4N) when s is even. One can find these forms helpful in revealing the arithmetical meaning of additional terms in the formulas for the number of representations of positive integers by positive quadratic forms with integral coefficients in an even number of variables.     

Synthesis of noval benzoylated indoles

It has been shown that Friedel-Crafts p-nitrobenzoylation of 2,2-dicarbethoxybis(5-indoyl)methane occurs at the bridging group. From the products of p-nitrobenzoylation of 2-carbethoxy-5-methylindole, 2-carbethoxy-5-hydroxy-indole and 2,7-dicarbethoxy-1H,6H-pyrrolo[2,3-e]indole there were obtained corresponding amines and an oxime.Iv. Dzhavakhishvili State University, Tbilisi 380028. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1202–1205, September, 1994. Original article submitted September 15, 1994.     

Cyclic polypeptides by thermal polymerization of α‐amino acid N‐carboxyanhydrides

The NCAs of the following five amino acids were polymerized in bulk at 120 °C without addition of a catalyst or initiator: sarcosine (Sar), L ‐alanine (L ‐Ala), D ,L ‐phenylalanine (D ,L ‐Phe), D ,L ‐leucine (D ,L ‐Leu) and D ,L ‐valine (D,L ‐Val). The virgin reaction products were characterized by viscosity measurements ¹³C NMR spectroscopy and MALDI‐TOF mass spectrometry. In addition to numerous low molar mass byproducts cyclic polypeptides were formed as the main reaction products in the mass range above 800 Da. Two types of cyclic oligo‐ and polypeptides were detected in all cases with exception of sarcosine NCA, which only yielded one class of cyclic polypeptides. The efficient formation of cyclic oligo‐ and polypeptides explains why high molar mass polymers cannot be obtained by thermal polymerizations of α‐amino acid NCAs. Various polymerization mechanisms were discussed. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 4012–4020, 2008     

Lifting discrete trajectories

It is shown that every discrete trajectory of a polynomial matrix can be lifted to a continuous one.     

Structuring of photosensitive material below diffraction limit using far field irradiation

In this paper, we report on in-situ atomic force microscopy (AFM) studies of topographical changes in azobenzene-containing photosensitive polymer films that are irradiated with light interference patterns. We have developed an experimental setup consisting of an AFM combined with two-beam interferometry that permits us to switch between different polarization states of the two interfering beams while scanning the illuminated area of the polymer film, acquiring corresponding changes in topography in-situ. This way, we are able to analyze how the change in topography is related to the variation of the electrical field vector within the interference pattern. It is for the first time that with a rather simple experimental approach a rigorous assignment can be achieved. By performing in-situ measurements we found that for a certain polarization combination of two interfering beams [namely for the SP (?, ?) polarization pattern] the topography forms surface relief grating with only half the period of the interference patterns. Exploiting this phenomenon we are able to fabricate surface relief structures with characteristic features measuring only 140 nm, by using far field optics with a wavelength of 491 nm. We believe that this relatively simple method could be extremely valuable to, for instance, produce structural features below the diffraction limit at high-throughput, and this could significantly contribute to the search of new fabrication strategies in electronics and photonics industry.