Some remarks on the decomposition properties of the single machine total tardiness problem

The note extends Lawler’s [E.L. Lawler, A pseudopolynomial algorithm for sequencing jobs to minimize total tardiness, Annals of Discrete Mathematics, 1 (1977) 331–342] fundamental decomposition theorem. This extension serves as a basis for alternate criteria that recognize when the problem is non-decomposable. It also shows that even relaxing a single criterion to a weak inequality may contradict Lawler’s (1977) decomposition theorem.     

A counterexample concerning Whitney reversible properties

Two properties of continua are shown which are strong Whitney reversible while not sequential strong Whitney reversible. This answers an old question of S. B. Nadler, Jr.

     

Photosensitized degradation of polyethylene glycols in aqueous solutions. I. Viscosimetric measurements

Investigations were performed on acetone and benzene-sensitized degradation of triethylene glycol (TEG), polyethylene glycol 400 (PEG 400), and polyethylene glycol 4000 (PEG 4000) in aqueous solutions exposed to irradiation at λ = 254 nm and λ ～ 313 nm. The systems investigated were exposed at 20°C (±1°C) in both deaerated and undeaerated solutions. The course of the photosensitized degradation was examined viscosimetrically. The determined quantum yield (?) of chain scission decreases distinctly as the molecular weight of the polymer rises, irrespective of the wavelength of the light absorbed and deaeration of system exposed.     

Derivations of differential forms on jet bundles

Summary The theory of derivations of differential forms, originally formulated by Frölicher and Nijenhuis [2], is generalized to include derivations which connect differential forms on two different manifolds. This generalized theory is then used to analyze derivations of direct limits of exterior algebras of forms on jet bundles. Such derivations have found applications in the analysis of Lie equations [3], [4] and in the inverse problem of the calculus of variations [6], [7], [8], [9].

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Résumé On présente une généralization de la théorie des dérivations des formes extérieures, formulée par Frölicher et Nijenhuis [2], au cas des dérivations qui relient les formes extérieurs sur deux variétés différentes. On utilize ensuite cette théorie généralizée pour étudier les dérivations des limites directes des algèbres des formes extérieures sur les fibrés des jets. Ces dérivations ont été appliquées dans l'analyse des équations de Lie [3], [4] et dans le problème inverse du calcul des variations [6], [7], [8], [9].

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This work is a part of a program conducted jointly with ProfessorBenenti at Istituto di Fisica Matematica «J. L. Lagrange» of Torino. The authors are greatly indebted to the Director of the Institute Professor D.Galletto for his interest and encouragement.This work has been supported by Gruppo Nazionale per la Fisica Matematica del Consiglio Nazionale delle Ricerche.     

Structural studies on lactarius sesquiterpenes: structure elucidation of lactarorufins D and E and conformational analysis of lactaran-5-olides

The structures of lactarorufins D and E, two new sesquiterpenes from Lactarius necator, have been elucidated. Conformational analysis of lactarorufins and blennins is discussed.     

Novel Polyhedral Silsesquioxanes [POSS(OH)32] as Anthracycline Nanocarriers—Potential Anticancer Prodrugs

Anthracyclines belong to the anticancer drugs that are widely used in chemotherapy. However, due to their systemic toxicity they also exert dangerous side effects associated mainly with cardiovascular risks. The pathway that is currently often developed is their chemical and physical modification via formation of conjugated or complexed prodrug systems with a variety of nanocarriers that can selectively release the active species in cancer cells. In this study, six new nanoconjugates were synthesized with the use of polyhedral oligosilsesquioxanes [POSS(OH)₃₂] as nanocarriers of the anticancer drugs anthracyclines—doxorubicin (DOX) and daunorubicin (DAU). These prodrug conjugates are also equipped with poly(ethylene glycol) (PEG) moieties of different structure and molecular weight. Water-soluble POSS, succinic anhydride modified (SAMDOX and SAMDAU) with carboxylic function, and PEGs (PEG1, PEG2 and PEGB3) were used for the synthesis. New nanoconjugates were formed via ester bonds and their structure was confirmed by NMR spectroscopy (¹H-NMR, ¹³C-NMR, ¹H-¹³C HSQC, DOSY and ¹H-¹H COSY), FTIR and DLS. Drug release rate was evaluated using UV-Vis spectroscopy at pH of 5.5. Release profiles of anthracyclines from conjugates 4–9 point to a range of 10 to 75% (after 42 h). Additionally, model NMR tests as well as diffusion ordered spectroscopy (DOSY) confirmed formation of the relevant prodrugs. The POSS-anthracycline conjugates exhibited prolonged active drug release time that can lead to the possibility of lowering administered doses and thus giving them high potential in chemotherapy. Drug release from conjugate 7 after 42 h was approx. 10%, 33% for conjugate 4, 47% for conjugate 5, 6, 8 and 75% for conjugate 9.     

NMR analysis of antitumor drugs: Doxorubicin,daunorubicin and their functionalized derivatives

¹H, ¹H–¹H COSY and ¹³C NMR techniques were proven as effective methods for the analysis of functionalized doxorubicin (DOX) and daunorubicin (DAU) derivatives. These compounds represent important drug conjugate intermediates that can be coupled to a variety of nanocarriers. NMR spectroscopy was shown to be an efficient method for following the progress of drug modification and can also be useful for evaluation of the functionalized structures purity. Additionally, a correction of the chemical shifts reported in the literature for the relevant drugs e.g. DOX·HCl and DAU·HCl is presented.     

Probabilistic aspects of Al-Salam--Chihara polynomials

We solve the connection coefficient problem between the Al-Salam--Chihara polynomials and the -Hermite polynomials, and we use the resulting identity to answer a question from probability theory. We also derive the distribution of some Al-Salam--Chihara polynomials, and compute determinants of related Hankel matrices.

     

Two families of affine projectively flat surfaces

The aim of this paper is to classify affine projectively flat surfaces with nondiagonalizable (over the field ) shape operator.