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We consider nonzero-sum games where multiple players control the drift of a process, and their payoffs depend on its ergodic behaviour. We establish their connection with systems of ergodic backward stochastic differential equations, and prove the existence of a Nash equilibrium under generalised Isaac's conditions. We also study the case of interacting players of different type.
Using backward stochastic difference equations (BSDEs), this paper studies dynamic convex risk measures for risky positions in a simple discrete-time, binomial tree model. A relationship between BSDEs and dynamic convex risk measures is developed using nonlinear expectations. The time consistency of dynamic convex risk measures is discussed in the binomial tree framework. A relationship between prices and risks is also established. Two particular cases of dynamic convex risk measures, namely risk measures with stochastic distortions and entropic risk measures, and their mathematical properties are discussed.
The terminal lake systems of central Australia are key sites for the reconstruction of late Quaternary paleoenvironments. Paleoshoreline deposits around these lakes reflect repeated lake filling episodes and such landforms have enabled the establishment of a luminescence-based chronology for filling events in previous studies. Here we present a detailed documentation of the morphology and chemistry of soils developed in four well-preserved beach ridges of late Pleistocene and mid-to-late Holocene age at Lake Callabonna to assess changes in dominant pedogenic processes. All soil profiles contain evidence for the incorporation of eolian-derived material, likely via the formation of desert pavements and vesicular horizons, and limited illuviation due to generally shallow wetting fronts. Even though soil properties in the four studied profiles also provide examples of parent material influence or site-specific processes related to the geomorphic setting, there is an overall trend of increasing enrichment of eolian-derived material since at least ~ 33 ka. Compared to the Holocene profiles, the derived average accumulation rates for the late Pleistocene profiles are significantly lower and may suggest that soils record important regional changes in paleoenvironments and dust dynamics related to shifts in the Southern Hemisphere westerlies.
We consider backward stochastic differential equations in a setting where noise is generated by a countable state, continuous time Markov chain, and the terminal value is prescribed at a stopping time. We show that, given sufficient integrability of the stopping time and a growth bound on the terminal value and BSDE driver, these equations admit unique solutions satisfying the same growth bound (up to multiplication by a constant). This holds without assuming that the driver is monotone in y, that is, our results do not require that the terminal value be discounted at some uniform rate. We show that the conditions are satisfied for hitting times of states of the chain, and hence present some novel applications of the theory of these BSDEs.
Hydrogenated amorphous silicon-germanium alloy thin films (a-Si1-xGex:H) were deposited using reactive magnetron sputtering. Dual targets of silicon and germanium were sputtered in an argon + hydrogen atmosphere using rf excitation. Films with x = 0.4 were deposited as a function of substrate temperature and hydrogen partial pressure, and were evaluated by dark and photoconductivity, infrared absorption, and optical transmission. Photosensitivity reached a maximum value of about 5000 between 150 and 200 °C. Using the stretching modes in the region of 2000 cm-1, the hydrogen bonding was characterized in terms of the preferential attachment ratio (PA), which represents the ratio of H bonded to silicon to that bonded to germanium. The PA shows a systematic increase with increasing temperature, independent of hydrogen partial pressure. The interplay between thermodynamic and kinetics effects in determining PA and film quality will be discussed.
A useful result when dealing with backward stochastic differential equations is the comparison theorem of Peng (1992). When the equations are not based on Brownian motion, the comparison theorem no longer holds in general. In this paper we present a condition for a comparison theorem to hold for backward stochastic differential equations based on arbitrary martingales. This theorem applies to both vector and scalar situations. Applications to the theory of nonlinear expectations are also explored.
A three-dimensional photonic bandgap (PBG) structure was fabricated from CAD models using a method based on lost wax rapid prototyping and ceramic gelcasting. The inverse PBG mold was constructed from a low melting point thermoplastic using a high precision Sanders Rapid Toolmaker. An aqueous stable slurry (200-300 cp) containing 50-75wt% of the ceramic powders (BaSrTiO3, MgO), a 15wt% solution of monomer (Methacylamide) and crosslinker (Poly(ethylene glycol) dimethacrylate), and a free radical initiator (2,2'Azobis(2-amidino-propane) dihydrochloride) was cast into the mold. A polymerization reaction was thermally activated at 50°C to immobilize the ceramic powders. The wax mold was then removed by drying the green body in a high humidity oven at 120°C. Scanning Electron Microscopy (SEM) of the unfired part showed that atmosphere hampered the polymerization reaction at the surface of the part. The green density, sintered density, and permittivity all increased as the solids loading increased. In order to optimize the dielectric properties and minimize cracking and warping in the sintered part, the solids loading had to be greater than 80 wt%. This study investigated several steps in the lost mold / gelcasting procedure including stabilizing the ceramic suspension, the correlation between the solids loading and the green and sintered densities, binder removal, and the effect of shrinkage during sintering on the net shape.
This exploratory study compares the prevalence of personality disorders and traits in people over and under 55 years of age. The comorbidity between personality and other psychiatric disorders is also examined.
Psychiatrists examined 810 subjects in a two-stage community survey. The semi-structured Standardized Psychiatric Examination was used to diagnose all DSM-III personality disorders and other psychiatric disorders.
The older subjects were significantly less likely than the younger subjects to have any personality disorder (6.6% v. 10.5%; relative odds = 0.42, 95% confidence interval = 0.25–0.70, P<0.001). Antisocial and histrionic personality disorders were much less prevalent in the older than younger subjects (P < 0.05). The older subjects also had significantly fewer maladaptive personality traits (x2 = 88.9, d.f. = 3, P < 0.001). The patterns of comorbidity between personality disorders and other psychiatric disorders were different in the two age groups.
It is important to evaluate personality in patients of all ages. While some older patients no longer meet criteria for personality disorder, maladaptive traits may become evident during times of stress.