Existence of Equilibria in Economies with Externalities and Nonconvexities

We consider a general equilibrium model of an economy in which the production possibilities, the consumption sets and the preferences of the consumers are represented by set-valued mappings which depend on the environment to take into account the possibility of external effect. In order to encompass all kinds of nonconvexities, we do not put any convexity assumption either on the graph of the set-valued mapping which describes the technological possibilities or on the production set for a given environment. The firms are instructed to set their prices according to general pricing rules which may depend on the production plans of other producers and on consumption plans.We report an existence result of general equilibria. As in the model without external effects, the key hypotheses are bounded loss and survival assumptions. Nevertheless, we also assume that the set-valued mappings which describe the fundamentals of the economy are lower semi-continuous and have a closed graph.Our framework is sufficiently large to generalize previous works on the existence of competitive equilibria with externalities when the firms have convex production sets and on the existence of equilibria with general pricing rule without externality.     

Nanostructured silicon as a photonic material

Photonics applications of silicon are presented. In particular it is demonstrated that silicon when rendered low dimensional, e.g. in form of nanocrystals or quantum wires, can be turned into an active photonic materials which shows light amplification characteristics, non-linear optical effects, photon confinement in both one and two dimensions, photon trapping with evidences of light localization, and gas sensing properties.     

Atom optics with rotating Bose-Einstein condensates

The atom optics of Bose-Einstein condensates containing a vortex of circulation one is discussed. We first analyze in detail the reflection of such a condensate falling on an atomic mirror. In a second part, we consider a rotating condensate in the case of attractive interactions. We show that for sufficiently large nonlinearity the rotational symmetry of the rotating condensate is broken. Received 16 September 2002 / Received in final form 17 November 2002 Published online 11 February 2003     

Effect of molecular architecture and size of mesogen on phase behavior and photoactive properties of photoactive liquid crystalline hyperbranched polyester epoxies containing benzylidene moiety

A series of photoactive liquid crystalline linear and hyperbranched polyester epoxies were synthesized by polyaddition of photoactive bis benzylidene alkanone diol monomers and terephthalic acid and trimesic acid respectively with good yield. The effect of molecular architecture (linear and hyperbranched), size of mesogenic unit (cyclic and acyclic units) on the physicochemical, thermal, mesogenic, and photoactive properties of hyperbranched polymers were studied and compared. Degree of branching of hyperbranched polymers was found to be in the range of 0.46–0.49. Monomers containing cyclic moieties only exhibited nematic mesophase, while all polymers exhibited typical nematic mesophase. Intermolecular photo cycloaddition reaction was studied by ultraviolet–visible spectra (UV–vis) and NMR spectroscopy and photo viscosity measurement of UV irradiated polymer solutions. Faster photo induced behavior of hyperbranched polymers containing acyclic alkanone moiety, as compared to polymers containing cycloalkanone moieties, was observed. The change in the refractive index was found to be in the range of 0.02–0.024. Substantial variation of refractive index indicates that this polymer could be used for optical recording. All the polymers were also found to be fluorescent in nature. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 552–563, 2008     

Thermally enhanced photoinduced in‐plane reorientation in photo‐cross‐linkable polymer liquid crystalline films and its application to linear polarizer

Thermally enhanced photoinduced in‐plane molecular reorientation in new photo‐cross‐linkable polymer liquid crystalline (PPLC) films comprising 4‐[ω‐(4‐methoxycinnamoyloxy)alkyloxy]biphenyl side groups is explored using linearly polarized ultraviolet (LPUV) light exposure and subsequent annealing. The influence of the alkylene spacer length between the photo‐cross‐linkable group and the biphenyl mesogenic moiety is investigated. The straight‐line characteristics of the photoreactive mesogenic side group and the 4‐methoxycinnamoyl group play important roles in the high photoreactivity and the large thermally enhanced molecular reorientation, where the in‐plane order and the birefringence of the reoriented film are 0.61 and 0.18 are obtained. Finally, cooperative molecular reorientation of dichroic dyes doped in PPLC films is also achieved to fabricate a linear polarizer. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 4712–4718, 2008     

Stimulation of E. coli growth by laser and incoherent red light

Summary The effect of low-intensity He−Ne laser radiation (λ=632.8 nm) and incoherent red light on DNA synthesis and cell division in Escherichia coli has been studied. It has been shown that the radiations of He−Ne laser (λ=632.8 nm) and filament lamp (λ=(631±4) nm) stimulate DNA synthesis and cell growth at doses of 10³ to 10⁴ J/m². The highest level of DNA synthesis is observed 10 min after irradiation and the difference in the numbers of irradiated and control cells is maximum 1 or 2 h after irradiation. The action spectrum of visible light on the growth rate of E. coli cells (from 560 nm to 640 nm) has been measured. The action spectrum has its maximum at (620±7) nm.

---

Riassunto Si è studiato l'effetto della radiazione laser He−Ne a bassa intensità e della luce rossa incoerente sulla sintesi del DNA e sulla divisione della cellula in Escherichia coli. Si è mostrato che le radiazioni del laser He−Ne (λ=632.8 nm) e della lampada con filamento (λ=(631±4) nm) stimolano la sintesi del DNA e la crescita cellulare a dose di (10³⋎10⁴) J/m². Il piú alto livello di sintesi del DNA è osservato 10 min dopo l'irradiazione e la differenza nei numeri di cellule irradiate e di controllo è massima 1 o 2 ore dopo irradiazione. Si è misurato lo spettro d'azione della luce visibile sul rapporto di crescita delle cellule di E. coli (da 560 nm a 640 nm). Lo spettro d'azione ha il suo massimo a (620±7) nm.

---

Резюме Изучалось влияние низконтенсивного излучения He−Ne лазэра (λ=632.8 нм) и некогерентного красного света на синтез ДНК и клеточное деление в клэтках Escherichia coli. Показано, что как излучение He−Ne лазера, так и лампьи накаливания (λ=(631±4) нм) стимулирует синтез ДНК и клетпчное леление в дозах (10⁻²⋎10⁻³) Джм². Наиболее вьисокий уровень синтеза ДНК наблюлаеттся чурез 10 минут после облучения, скорость клеточногхого делэния максимальна через (1⋎2) часа после облучения. Измерен спектр действия видимого света на скрость деления клеток E. coli от λ=560 нм до λ=640 нм. Спектр действия имеет максимум при (620±7) нм.

     

Kinetics and mechanism of the addition of iodine monochloride to some alkenes in nitrobenzene solvent. Effect of polarity of the solvent

The kinetics of the addition of iodine monochloride (ICl) to some vinyl compounds in nitrobenzene solvent was investigated. In all cases the reaction follows second order dependence on ICl and first order on the substrate, making the total order three. Rate constants were measured for each substrate at 20°, 30°, 40° and 50°C.Arrhenius plots were made from which activation energies were evaluated. Other kinetic and thermodynamic parameters are reported. A suitable mechanism is proposed for the reaction and based on this, the various parameters are discussed. Solvent effects are discussed and the data with nitrobenzene and acetic acid solvents are compared.

---

Kinetik und Mechanismus der Addition vonICl zu einigen Alkenen in Nitrobenzol als Lösungsmittel. Effekt der Polarität des Lösungsmittels

Zusammenfassung Die Kinetik der Addition von ICl zu einigen Vinylverbindungen in Nitrobenzol als Lösungsmittel wurde untersucht. In allen Fällen ist die Reaktion von zweiter Ordnung hinsichtlich ICl und von erster Ordnung hinsichtlich des Substrats, d. h. mit einer Gesamtordnung von drei. Geschwindigkeitskonstanten wurden für jedes Substrat bei 20°, 30°, 40° und 50°C gemessen. AusArrhenius-Diagrammen wurden Aktivierungsenergien ermittelt und auch andere kinetische und thermodynamische Parameter wurden bestimmt. Ein Mechanismus wird vorgeschlagen, wobei die verschiedenen Parameter diskutiert werden. Lösungsmitteleffekte werden ebenfalls diskutiert und die Daten mit Nitrobenzol und Essigsäure als Lösungsmittel miteinander verglichen.

     

Substituent effect on ionisation potential in a series of related molecules: A theoretical study in a molecular orbital framework

The effect of replacing the hydrogen atoms in thioformaldehyde by halogen atoms (F, Cl) on the ionisation potential of the non-bonding electron is analysed by using the Hellman-Feynman theorem, regarding the nuclear charge of the substituent as a parameter in the many-electron Hamiltonian. The trends predicted by our theory nicely agree with the relevant ionisation potentials computed either by applying Koopmans’ theorem or by the ΔE _SCF method. For the carbonyls, avaible experimental data indicate the reliability of our prediction.     

Refractive index and nonlinear optical properties of polyaniline derivatives

An investigation of the refractive index and third-order nonlinear optical susceptibility χ⁽³⁾ of two polypernigraniline derivatives, poly (4,4'-diphenylimine methine) (PDPIM) and poly (4,4'-diphenylimine p-heptyloxybenzylidene) (PDPIHB) reveals effects of molecular structure on the linear optical and nonlinear optical properties of conjugated polymers. The χ⁽³⁾ (?3ωω,ω,ω) of PDPIM was found to decrease relative to polypernigraniline, reflecting the observed decrease of the oscillator strength of the 2.2 eV absorption band when a methine carbon replaces one of the nitrogen atoms of pernigraniline repeat unti. The alkoxyphenylene side group substitution at the methine carbon in PDPIHB, however, significantly enhances the nonlinear optical response of PDPIHB while reducing the refractive index compared to PDPIM and polypernigraniline. The present results suggest that structural changes in conjugated polymers can be made in such a way as to enhance the nonlinear optical properties while modulating the linear optical properties. © 1994 John Wiley & Sons, Inc.