31,431 research outputs found

    Small Business and Government Procurement

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    A quickest detection problem with an observation cost

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    In the classical quickest detection problem, one must detect as quickly as possible when a Brownian motion without drift "changes" into a Brownian motion with positive drift. The change occurs at an unknown "disorder" time with exponential distribution. There is a penalty for declaring too early that the change has occurred, and a cost for late detection proportional to the time between occurrence of the change and the time when the change is declared. Here, we consider the case where there is also a cost for observing the process. This stochastic control problem can be formulated using either the notion of strong solution or of weak solution of the s.d.e. that defines the observation process. We show that the value function is the same in both cases, even though no optimal strategy exists in the strong formulation. We determine the optimal strategy in the weak formulation and show, using a form of the "principle of smooth fit" and under natural hypotheses on the parameters of the problem, that the optimal strategy takes the form of a two-threshold policy: observe only when the posterior probability that the change has already occurred, given the observations, is larger than a threshold A≥0A\geq0, and declare that the disorder time has occurred when this posterior probability exceeds a threshold B≥AB\geq A. The constants AA and BB are determined explicitly from the parameters of the problem.Comment: Published at http://dx.doi.org/10.1214/14-AAP1028 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Optimal treatment planning governed by kinetic equations

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    In this paper we study a problem in radiotherapy treatment planning, where the evolution of the radiation field is governed by a deterministic Boltzmann transport equation. We show existence, uniqueness and regularity of solutions to an optimal dose distribution problem constrained by the Boltzmann Continuous Slowing-Down equation in an appropriate function space. The main new difficulty is the treatment of the stopping power term. Furthermore, we characterize optimal controls for problems governed by this transport equation.Comment: 15 pages, 1 figur

    Esscher transform and the duality principle for multidimensional semimartingales

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    The duality principle in option pricing aims at simplifying valuation problems that depend on several variables by associating them to the corresponding dual option pricing problem. Here, we analyze the duality principle for options that depend on several assets. The asset price processes are driven by general semimartingales, and the dual measures are constructed via an Esscher transformation. As an application, we can relate swap and quanto options to standard call and put options. Explicit calculations for jump models are also provided.Comment: Published in at http://dx.doi.org/10.1214/09-AAP600 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Development of Women Education in India

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    Women constitute almost half of the population of the world. Education for women is the best way to improve the health, nutrition and economic status of a household that constitute a micro unit of a nation economy. In this context, it can be argued that lack of woman education can be an impediment to the country’s economic development. In India, women achieve far less education that of men. As per the Census report 2001, the literacy rate of women is 54.16 per cent and that of men is 65.38 per cent. There has been a sincere effort to improve the education attainment of women by both government and voluntary organizations. The changes in the policies and infrastructural supports on primary, secondary and higher education reflect the initiatives of the Government of India towards women education. This paper examined the trends in women education, the investments on education and infrastructural supports in India. The study revealed that there had been significant progress in the performance of women education revealed from female literacy levels and its change over time. It was also observed that the gaps between rural and urban female literacy rates are narrowing down. It was observed that rural poverty acts as a push factors for women’s education rather than as an obstacle to women’s education. The significant influence of urbanization on women’s education implied that urbanization had been playing a beneficial role in the attainment of women’s education in India. At the same time, the drop-out rate had a negative effect on women’s education. It revealed that that reduction of girl’s drop-out rates is necessary for achieving women’s education. The initiatives of the government through investment and infrastructure in developing education in India were examined. With regard to facilities in schools, it had improved significantly, but a lot more need to be done. In sum, the study revealed that there have been concerted efforts to encourage girls to attend schools, which would lead to higher literacy in future. The study also revealed that there are several infrastructural barriers to women education in India. The study calls for focused approach towards increasing women centred educational infrastructure so as to reduce the women drop-out rates and to improve female literacy levels in India.Women Development, women education, women literacy, education infrastructure, Female literacy rate, women in India, Indian women, primary education, secondary education, higher education, India

    Microphase separation in thin block copolymer films: a weak segregation mean-field approach

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    In this paper we consider thin films of AB block copolymer melts confined between two parallel plates. The plates are identical and may have a preference for one of the monomer types over the other. The system is characterized by four parameters: the Flory-Huggins chi-parameter, the fraction f of A-monomers in the block copolymer molecules, the film thickness d, and a parameter h quantifying the preference of the plates for the monomers of type A. In certain regions of parameter space, the film will be microphase separated. Various structures have been observed experimentally, each of them characterized by a certain symmetry, orientation, and periodicity. We study the system theoretically using the weak segregation approximation to mean field theory. We restrict our analysis to the region of the parameter space where the film thickness d is close to a small multiple of the natural periodicity. We will present our results in the form of phase diagrams in which the absolute value of the deviation of the film thickness from a multiple of the bulk periodicity is placed along the horizontal axis, and the chi-parameter is placed along the vertical axis; both axes are rescaled with a factor which depends on the A-monomer fraction f. We present a series of such phase diagrams for increasing values of the surface affinity for the A-monomers. We find that if the film thickness is almost commensurate with the bulk periodicity, parallel orientations of the structures are favoured over perpendicular orientations. We also predict that on increasing the surface affinity, the region of stability of the bcc phase shrinks.Comment: 35 pages, 20 figure
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