Developing real option game models

By mixing concepts from both game theoretic analysis and real options theory, an investment decision in a competitive market can be seen as a “game” between firms, as firms implicitly take into account other firms’ reactions to their own investment actions. We review two decades of real option game models, suggesting which critical problems have been “solved” by considering game theory, and which significant problems have not been yet adequately addressed. We provide some insights on the plausible empirical applications, or shortfalls in applications to date, and suggest some promising avenues for future research.     

Bone tissue and porous media: common features and differences studied by NMR relaxation

Despite significant differences between bone tissues and other porous media such as oilfield rocks, there are common features as well as differences in the response of NMR relaxation measurements to the internal structures of the materials. Internal surfaces contribute to both transverse (T2) and longitudinal (T1) relaxation of pore fluids, and in both cases the effects depend on, among other things, local surface-to-volume ratio (S/V). In both cases variations in local S/V can lead to distributions of relaxation times, sometimes over decades. As in rocks, it is useful to take bone data under different conditions of cleaning, saturation, and desaturation. T1 and T2 distributions are computed using UPEN. In trabecular bone it is easy to see differences in dimensions of intertrabecular spaces in samples that have been de-fatted and saturated with water, with longer T1 and T2 for larger pores. Both T1 and T2 distributions for these water-saturated samples are bimodal, separating or partly separating inter- and intratrabecular water. The T1 peak times have a ratio of from 10 to 30, depending on pore size, but for the smaller separations the distributions may not have deep minima. The T2 peak times have ratios of over 1000, with intratrabecular water represented by large peaks at a fraction of a ms, which we can observe only by single spin echoes. CPMG data show peaks at about a second, tapering down to small amplitudes by a ms. In all samples the free induction decay (FID) from an inversion-recovery (IR) T1 measurement shows an approximately Gaussian (solid-like) component, exp[-1/2 (T/TGC), with TGC approximately 11.7+/-0.7 micros (GC for "Gaussian Component"), and a liquid-like component (LLC) with initially simple-exponential decay at the rate-average time T(2-FID) for the first 100 micros. Averaging and smoothing procedures are adopted to derive T(2-FID) as a function of IR time and to get T1 distributions for both the GC and the LLC. It appears that contact with the GC, which is presumed to be 1H on collagen, leads to the T2 reduction of at least part of the LLC, which is presumed to be water. Progressive drying of the cleaned and water-saturated samples confirms that the long T1 and T2 components were in the large intertrabecular spaces, since the corresponding peaks are lost. Further drying leads to further shortening of T2 for the remaining water but eventually leads to lengthening of T1 for both the collagen and the water. After the intertrabecular water is lost by drying, T1 is the same for GC and LLC. T(2-FID) is found to be roughly 320/alpha micros, where alpha is the ratio of the extrapolated GC to LLC, appearing to indicate a time tau of about 320 micros for 1H transverse magnetization in GC to exchange with that of LLC. This holds for all samples and under all conditions investigated. The role of the collagen in relaxation is confirmed by treatment to remove the mineral component, observing that the GC remains and has the same TGC and has the same effect on the relaxation times of the associated water. Measurements on cortical bone show the same collagen-related effects but do not have the long T1 and T2 components.     

Variations of the 1H spin-lattice relaxation in a fatty liver model as compared to normal liver

We report the results of an in vitro study on ethionine-injected rat liver (EI) and on normal rat liver (C) performed analyzing with iterative fitting procedures the 1H spin-lattice relaxation curves detected by IR pulse sequence at 20 MHz and at 37 degrees C on fresh excised samples. Single-exponential functions did not adequately describe the experimental curves both in EI and in C group. The analysis of the curves by two-exponential hypothesis showed a small portion of the signal characterizable by a time constant of about 80 ms, common both to EI and to C samples. A slowing of about 30% in the relaxation characterized the remaining portion of the curve (90-95%) in EI as compared to C samples. The hypothesis that the 1H of the triglycerides vacuoles present in EI livers had a relaxation curve additional to the remaining signal was checked by three-exponential analysis. The results were not in contrast with the known value of the triglycerides percentage content and with the spin-lattice relaxation time of the -CH2 group 1H obtained in different experimental conditions in the same fatty liver model. The negative results of the three-exponential analysis on normal liver curves as well as the favorable controls performed to test the analysis procedure supported further this hypothesis. The remaining signal after subtraction of the triglycerides contribution showed still the small fast portion and the increase of the relaxation time of the major portion (from approximately 300 ms up to approximately 400 ms) as compared to C samples.(ABSTRACT TRUNCATED AT 250 WORDS)     

Organic electroluminescence using polymer networks from smectic liquid crystals

We report the synthesis of a red light-emitting and photopolymerizable smectic liquid crystal (reactive mesogen). We investigate the suitability of polymer networks formed from smectic reactive mesogens for use in organic light-emitting diodes (OLEDs). The use of mixtures of smectic reactive mesogens is shown to lower the processing temperature for the fabrication of OLEDs to room temperature. We also report efficient energy transfer from a nematic polymer network host to a smectic light-emitting dopant and polarized emission from a polymer network formed from an aligned smectic reactive mesogen.     

Morphology,structure, and properties of in situ compatibilized linear low‐density polyethylene/polystyrene and linear low‐density polyethylene/high‐impact polystyrene blends

Blends of linear low‐density polyethylene (LLDPE) with polystyrene (PS) and blends of LLDPE with high‐impact polystyrene (HIPS) were prepared through a reactive extrusion method. For increased compatibility of the two blending components, a Lewis acid catalyst, aluminum chloride (AlCl₃), was adopted to initiate the Friedel–Crafts alkylation reaction between the blending components. Spectra data from Raman spectra of the LLDPE/PS/AlCl₃ blends extracted with tetrahydrofuran verified that LLDPE segments were grafted to the para position of the benzene rings of PS, and this confirmed the graft structure of the Friedel–Crafts reaction between the polyolefin and PS. Because the in situ generated LLDPE‐g‐PS and LLDPE‐g‐HIPS copolymers acted as compatibilizers in the relative blending systems, the mechanical properties of the LLDPE/PS and LLDPE/HIPS blending systems were greatly improved. For example, after compatibilization, the Izod impact strength of an LLDPE/PS blend (80/20 w/w) was increased from 88.5 to 401.6 J/m, and its elongation at break increased from 370 to 790%. For an LLDPE/HIPS (60/40 w/w) blend, its Charpy impact strength was increased from 284.2 to 495.8 kJ/m². Scanning electron microscopy micrographs showed that the size of the domains decreased from 4–5 to less than 1 μm, depending on the content of added AlCl₃. The crystallization behavior of the LLDPE/PS blend was investigated with differential scanning calorimetry. Fractionated crystallization phenomena were noticed because of the reduction in the size of the LLDPE droplets. The melt‐flow rate of the blending system depended on the competition of the grafting reaction of LLDPE with PS and the degradation of the blending components. The degradation of PS only happened during the alkylation reaction between LLDPE and PS. Gel permeation chromatography showed that the alkylation reaction increased the molecular weight of the blend polymer. The low molecular weight part disappeared with reactive blending. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1837–1849, 2003     

Polynomial Shift States of a Chaotic Map

We present a piecewise- linear map of the unit interval in which the resolvent of the Frobenius- Perron operator, considered in a polynomial basis, has an essen-tial singularity at the origin. Associated with the essential singularity are polynomial shift states, which are obtained from creation and annihilation operators in non- self- dual function spaces. Correlation functions of general polynomial observables have decay components that vanish in a finite time.     

Translation planes admitting a pair of index three homology groups

It is shown that a translation plane of order which admits two homology groups of order must in fact admit symmetric homology groups of this order. It is further shown that a plane admitting such symmetric index 3 homology groups is, with a finite number of exceptions, a generalized André plane. A list of the possibly exceptional orders is determined. Received 20 March 2000.