Evaluation of natural recharge of Chingshui geothermal reservoir using tritium as a tracer

Naturally existing tritium in groundwater was applied as a tracer to evaluate the natural recharge of the Chingshui geothermal reservoir. The residence time (or, age) of Chingshui geothermal water was first determined with tritium data at 15.2 and 11.3 year using the plug flow and dispersive model, respectively. The annual natural recharge was then estimated by combining the use of the residence time and the fluid-in-place of the Chingshui geothermal reservoir. The natural recharge for Chingshui geothermal reservoir was estimated at 5.0 × 10⁵ and 6.7 × 10⁵ m³ year^?1 using the plug flow and dispersive model, respectively. Chingshui geothermal water is largely from a fractured zone in the Jentse Member of the Miocene Lushan Formation. The dispersive model more adequately represents the fracture flow system than the simple plug flow model.     

Using a partially observable Markov chain model to assess colonoscopy screening strategies – A cohort study

Colorectal cancer (CRC) is notoriously hard to combat for its high incidence and mortality rates. However, with improved screening technology and better understanding of disease pathways, CRC is more likely to be detected at early stage and thus more likely to be cured. Among the available screening methods, colonoscopy is most commonly used in the U.S. because of its capability of visualizing the entire colon and removing the polyps it detected. The current national guideline for colonoscopy screening recommends an observation-based screening strategy. Nevertheless, there is scant research studying the cost-effectiveness of the recommended observation-based strategy and its variants. In this paper, we describe a partially observable Markov chain (POMC) model which allows us to assess the cost-effectiveness of both fixed-interval and observation-based colonoscopy screening strategies. In our model, we consider detailed adenomatous polyp states and estimate state transition probabilities based on longitudinal clinical data from a specific population cohort. We conduct a comprehensive numerical study which investigates several key factors in screening strategy design, including screening frequency, initial screening age, screening end age, and screening compliance rate. We also conduct sensitivity analyses on the cost and quality of life parameters. Our numerical result demonstrates the usability of our model in assessing colonoscopy screening strategies with consideration of partial observation of true health states. This research facilitates future design of better colonoscopy screening strategies.     

Congruences of multipartition functions modulo powers of primes

Let p _r (n) denote the number of r-component multipartitions of n, and let S _γ,λ be the space spanned by η(24z) ^γ ?(24z), where η(z) is the Dedekind’s eta function and ?(z) is a holomorphic modular form in \(M_{\lambda}(\mathrm{SL}_{2}(\mathbb{Z}))\) . In this paper, we show that the generating function of \(p_{r}(\frac{m^{k} n +r}{24})\) with respect to n is congruent to a function in the space S _γ,λ modulo m ^k . As special cases, this relation leads to many well known congruences including the Ramanujan congruences of p(n) modulo 5,7,11 and Gandhi’s congruences of p ₂(n) modulo 5 and p ₈(n) modulo 11. Furthermore, using the invariance property of S _γ,λ under the Hecke operator \(T_{\ell^{2}}\) , we obtain two classes of congruences pertaining to the m ^k -adic property of p _r (n).     

Room-temperature ferromagnetism of Cu-doped ZnO films probed by soft X-ray magnetic circular dichroism

We report direct evidence of room-temperature ferromagnetic ordering in O-deficient ZnO:Cu films by using soft x-ray magnetic circular dichroism and x-ray absorption. Our measurements have revealed unambiguously two distinct features of Cu atoms associated with (i) magnetically ordered Cu ions present only in the oxygen-deficient samples and (ii) magnetically disordered regular Cu2+ ions present in all the samples. We find that a sufficient amount of both oxygen vacancies (V(O)) and Cu impurities is essential to the observed ferromagnetism, and a non-negligible portion of Cu impurities is uninvolved in the magnetic order. Based on first-principles calculations, we propose a microscopic "indirect double-exchange" model, in which alignments of localized large moments of Cu in the vicinity of the V(O) are mediated by the large-sized vacancy orbitals.     

A diffractive study of optical parametric interactions in nonlinear photonic crystals

With the nonlinear diffraction concept, we present a diffractive study of optical parametric interactions in nonlinear photonic crystals. The nonlinear diffraction concept enables the design of complicated nonlinear photonic crystal structures in an intuitive way. We show that there are two basic linear sequences, the anti-stacking and the para-stacking sequences, existing in a one-dimensional structure; and we present the realization of multiple phase-matching resonances in the combination of the two basic sequences. The parameters affecting the structure factor of a two-dimensional nonlinear photonic crystal are investigated, which indicate that not only the Ewald construction but also the relative domain size determines two-dimensional nonlinear diffractions.     

Distributions of Poles to Painlevé Transcendents via Padé Approximations

A version of the Fair–Luke algorithm has been used to find the Padé approximate solutions to the Painlevé I, II, and IV equations. The distributions of poles in the complex plane are studied to check the dynamics of movable poles and the emergence of rational and truncated solutions, as well as various patterns formed by the poles. The high-order approximations allow us to check asymptotic expansions at infinity and estimate the range of asymptotic domains. The Coulomb gas interpretation of the pole ensembles is discussed in view of the patterns arising in Painlevé IV transcendents.