81 research outputs found

    Powers of generalized binomial edge ideals of path graphs

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    In this article, we study the powers of the generalized binomial edge ideal JKm,Pn\mathcal{J}_{K_m,P_n} of a path graph PnP_n. We explicitly compute their regularities and determine the limit of their depths. We also show that these ordinary powers coincide with their symbolic powers. Additionally, we study the Rees algebra and the special fiber ring of JKm,Pn\mathcal{J}_{K_m,P_n} via Sagbi basis theory. In particular, we obtain exact formulas for the regularity of these blowup algebras

    Least Squares Estimation for α

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    We consider a fractional bridge defined as dXt=-α(Xt/(T-t))dt+dBtH,  0≤t1/2 and parameter α>0 is unknown. We are interested in the problem of estimating the unknown parameter α>0. Assume that the process is observed at discrete time ti=iΔn,  i=0,…,n, and Tn=nΔn denotes the length of the “observation window.” We construct a least squares estimator α^n of α which is consistent; namely, α^n converges to α in probability as n→∞

    Pricing of Equity Indexed Annuity under Fractional Brownian Motion Model

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    Fractional Brownian motion with Hurst exponent H∈(1/2,1) is a good candidate for modeling financial time series with long-range dependence and self-similarity. The main purpose of this paper is to address the valuation of equity indexed annuity (EIA) designs under the market driven by fractional Brownian motion. As a result, this paper presents an explicit pricing expression for point-to-point EIA design and bounds for the pricing of high-water-marked EIA design. Some numerical examples are given to illustrate the impact of the parameters involved in the pricing problems

    UV/Ozone treatment to reduce metal-graphene contact resistance

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    We report reduced contact resistance of single-layer graphene devices by using ultraviolet ozone (UVO) treatment to modify the metal/graphene contact interface. The devices were fabricated from mechanically transferred, chemical vapor deposition (CVD) grown, single layer graphene. UVO treatment of graphene in the contact regions as defined by photolithography and prior to metal deposition was found to reduce interface contamination originating from incomplete removal of poly(methyl methacrylate) (PMMA) and photoresist. Our control experiment shows that exposure times up to 10 minutes did not introduce significant disorder in the graphene as characterized by Raman spectroscopy. By using the described approach, contact resistance of less than 200 {\Omega} {\mu}m was achieved, while not significantly altering the electrical properties of the graphene channel region of devices.Comment: 17 pages, 5 figure