Enclosing a Set of Objects by Two Minimum Area Rectangles

In this paper, we face the problem of computing an enclosing pair of axis-parallel rectangles of a set of polygonal objects in the plane, serving as a simple container. We propose anO(nα(n)log n) worst-case time algorithm, where α( ) is the inverse Ackermann's function, for finding, given a setMof points, segments and polygons defined bynvertices, a pair of axis-parallel rectangles (s, t) such thats∪tencloses all objects inMand area(s)+area(t) is minimum. The algorithm works inO(nα(n) log log n) worst-case space. Moreover, we prove an Ω(n log n) lower bound for the one-dimensional version of the problem. We also show that for the special case of enclosing a set of polygons with axis-parallel sides, our algorithm runs in optimal worst-case timeO(n log n), using worst-case spaceO(n log log n).     

Testing thermodynamic constitutive equations for polymers by adiabatic deformation experiments

During adiabatic deformation experiments on polyisobutylene of various molecular weights and on polyvinylacetate, the temperature change was measured. The thermal effects occurring during the subsequent stress relaxation were also recorded. From all data, the conclusion was drawn that the entropic elasticity theory is obeyed for temperatures sufficiently above the glass transition temperature. When the value of T_g is approached, some interesting energy effects become appreciable.     

ac conductivity of anhydrous pellicular zirconium phosphate in hydrogen form

Aqueous suspensions of delaminated zirconium phosphate have been recently obtained in our laboratory by a suitable intercalation-deintercalation of alkylamines. By filtering these suspensions thin and flexible sheets or pellicles of lamellar α-zirconium phosphate, with the most part of the layers oriented parallel to the pellicle surface, can be easily prepared. ac conductivity measurements have been carried out, in the temperature range 150–300°C, on pellets made of α-Zr(HPO₄)₂ pressed pellicles, oriented both parallel and perpendicular to the electric field. Independently of the pellet orientation, a slope variation was observed in the Arrhenius plot at about 220°C. As already found for the α-Zr(HPO₄)₂ powder, this is associated with a phase transition at this temperature, which causes a discontinuous change of the interlayer distance from 7.4 Å to 6.8 Å. The conductivity of samples oriented parallel to the electric field ($\text{～10}{}^{\mathrm{?4}}\text{Ω}{}^{\mathrm{?1}}\text{cm}{}^{\mathrm{?1}}\text{at}\text{300°}\text{C}$) is about two orders higher than the conductivity of the anhydrous microcrystalline powder, which, in turn, is higher than that of perpendicularly oriented samples ($\text{～3 × 10}{}^{\mathrm{?7}}\text{Ω}{}^{\mathrm{?1}}\text{cm}{}^{\mathrm{?1}}\text{at}\text{300°}\text{C}$).     

AN ULTRASTRUCTURAL COMPARATIVE EVALUATION OF TUMORS PHOTOSENSITIZED BY PORPHYRINS ADMINISTERED IN AQUEOUS SOLUTION, BOUND TO LIPOSOMES OR TO LIPOPROTEINS

Abstract— Balb/c mice bearing a transplantedMS–2 fibrosarcoma have been injected with 2 mg kg^-1 hematoporphyrin either dissolved in phosphate-buffered saline (Hp-aq), or incorporated into unilamellar liposomes of dipalmitoyl-phosphatidylcholine (Hp-lip), or precomplexed with low density lipoproteins (Hp-LDL). At 24 h after injection, the mice received 150 J cm^-2 of600–680 nm light irradiation. Electron microscopic studies performed on tumor tissues taken from mice sacrificed at different times after the phototreatment showed that, in the presence of Hp-aq. tumor necrosis is largely the consequence of vascular damage. On the other hand, in the presence of Hp-lip and Hp-LDL, the response of the tumor to the phototreatment occurs at a faster rate and is mainly determined by direct damage of neoplastic cells. These findings are correlated with the different distribution of the various hematoporphyrin forms (Hp-aq, Hp-lip, Hp-LDL) among the serum proteins and the modalities of hematoporphyrin delivery to tissues by the possible carriers.     

Upper bounds on dynamic deformations of elastoplastic continua

Summary Suitable measures of plastic and of total deflections developed over a time interval by an elastic-perfectly plastic continuous structure in the presence of significant inertia and viscous forces, is shown to be bounded from above by a quantity which can be evaluated merely on the basis of a linear-elastic dynamic analysis. The results achieved are extended to elastic-workhardening bodies under the assumption of piecewiselinear yield surfaces. The practical use of the present results is checked comparatively by a simple example.

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Sommario Si mostra come misure opportunamente definite delle deformazioni plastiche o totali che si sviluppano in un certo intervallo di tempo in un continuo perfettamente elastoplastico soggetto ad azioni dinamiche, siano delimitate superiormente da quantità valutabili attraverso un'analisi dinamica in campo elastico-lineare. I risultati ottenuti vengono estesi a materiali incrudenti, mediante linearizzazione a tratti della superficie di snervamento. La loro utilizzabilità pratica è illustrata da unsemplice esempio.

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Paper accepted for presentation at the Second Bulgarian Congress of Theoretical and Applied Mechanics, Varna, 8–14 October 1973.     

Stereochemical characterization of some mono- and diaryl substituted ethylene oxides by NMR spectroscopy

NMR spectra of several styrene, stilbene and stilbazole oxides have been determined, and chemical shifts and coupling constants have been correlated with cis-and trans-configurations. Assignments have been made for all protons, and double resonance technique and ¹³C? H coupling constants have been used in some particular cases. An explanation is proposed for the observation that chemical shifts of oxirane protons are higher for cis than for trans isomers.