Exponential sum approximations of finite completely monotonic functions

Bernstein's theorem (also called Hausdorff--Bernstein--Widder theorem) enables the integral representation of a completely monotonic function. We introduce a finite completely monotonic function, which is a completely monotonic function with a finite positive integral interval of the integral representation. We consider the exponential sum approximation of a finite completely monotonic function based on the Gaussian quadrature with a variable transformation. If the variable transformation is analytic on an open Bernstein ellipse, the maximum absolute error decreases at least geometrically with respect to the number of exponential functions. The error of the Gaussian quadrature is also expanded by basis functions associated with the variable transformation. The basis functions form a Chebyshev system on the positive real axis. The maximization of the decreasing rate of the error bound can be achieved by constructing a one-to-one mapping of an open Bernstein ellipse onto the right half-plane. The mapping is realized by the composition of Jacobi's delta amplitude function (also called dn function) and the multivalued inverse cosine function. The function is single-valued, meromorphic, and strictly absolutely monotonic function. The corresponding basis functions are eigenfunctions of a fourth order differential operator, satisfy orthogonality conditions, and have the interlacing property of zeros by Kellogg's theorem. We also analyze the initialization method of the Remez algorithm based on a Gaussian quadrature to compute the best exponential sum approximation of a finite completely monotonic function. The numerical experiments are conducted by using finite completely monotonic functions related to the inverse power function

生体分子シミュレーションの摂動解析

要旨あり生体高分子の揺らぎとダイナミクス－シミュレーションと実験の統計解析－研究詳

On the weights of end-pairs in n-end catenoids of genus zero

First principles calculations are carried out to analyze adsorption of CO and H2 molecules on a Pt (111) surface and the effect of surface strain on the adsorption energy. A CO molecule is more adsorptive on the Pt (111) surface than a H2 molecule under an ordinary condition. Surface expansion enhances CO poisoning on a Pt (111) surface. On the contrary, a compressive strain reduces adsorptive strength of a CO molecule. Similar tendency is also found in adsorption of a H2 molecule on the bridge, fcc-hollow, and hcp-hollow sites. However, H2 adsorption on the top site is less affected by the strain. As a consequence, the difference of adsorption energies between CO and H2 molecules becomes smaller when compressive strain is introduced into the Pt (111) surface. Based on thermodynamics, surface coverage ratio is quantitatively evaluated with taking into account the effect of surface strain and partial pressure of gas phase. It is revealed that compressive strain improves probability of H2 adsorption on Pt surface

Prediction of transcriptional regulatory elements for plant hormone responses based on microarray data

<p>Abstract</p> <p>Background</p> <p>Phytohormones organize plant development and environmental adaptation through cell-to-cell signal transduction, and their action involves transcriptional activation. Recent international efforts to establish and maintain public databases of <it>Arabidopsis </it>microarray data have enabled the utilization of this data in the analysis of various phytohormone responses, providing genome-wide identification of promoters targeted by phytohormones.</p> <p>Results</p> <p>We utilized such microarray data for prediction of <it>cis</it>-regulatory elements with an octamer-based approach. Our test prediction of a drought-responsive RD29A promoter with the aid of microarray data for response to drought, ABA and overexpression of DREB1A, a key regulator of cold and drought response, provided reasonable results that fit with the experimentally identified regulatory elements. With this succession, we expanded the prediction to various phytohormone responses, including those for abscisic acid, auxin, cytokinin, ethylene, brassinosteroid, jasmonic acid, and salicylic acid, as well as for hydrogen peroxide, drought and DREB1A overexpression. Totally 622 promoters that are activated by phytohormones were subjected to the prediction. In addition, we have assigned putative functions to 53 octamers of the Regulatory Element Group (REG) that have been extracted as position-dependent <it>cis</it>-regulatory elements with the aid of their feature of preferential appearance in the promoter region.</p> <p>Conclusions</p> <p>Our prediction of <it>Arabidopsis cis</it>-regulatory elements for phytohormone responses provides guidance for experimental analysis of promoters to reveal the basis of the transcriptional network of phytohormone responses.</p

Logical design of oral glucose ingestion pattern minimizing blood glucose in humans

Excessive increase in blood glucose level after eating increases the risk of macroangiopathy, and a method for not increasing the postprandial blood glucose level is desired. However, a logical design method of the dietary ingestion pattern controlling the postprandial blood glucose level has not yet been established. We constructed a mathematical model of blood glucose control by oral glucose ingestion in three healthy human subjects, and predicted that intermittent ingestion 30 min apart was the optimal glucose ingestion patterns that minimized the peak value of blood glucose level. We confirmed with subjects that this intermittent pattern consistently decreased the peak value of blood glucose level. We also predicted insulin minimization pattern, and found that the intermittent ingestion 30 min apart was optimal, which is similar to that of glucose minimization pattern. Taken together, these results suggest that the glucose minimization is achieved by suppressing the peak value of insulin concentration, rather than by enhancing insulin concentration. This approach could be applied to design optimal dietary ingestion patterns

Witnessing the Hierarchical Assembly of the Brightest Cluster Galaxy in a Cluster at z=1.26

We have obtained a new high-resolution K'-band image of the central region of the rich X-ray cluster RX J0848.9+4452 at z=1.26. We found that the brightest cluster galaxy (BCG) in the cluster is clearly separated into two distinct objects. Whereas the optical to near-infrared colors of the objects are consistent with the predictions of passive evolution models for galaxies formed at high redshift, the luminosities of the two galaxies are both considerably fainter than predicted by passive evolution of BCG's in low and intermediate redshift clusters. We argue that this is evidence of an on-going merger of normal cluster ellipticals to form the dominant galaxy in the core of RX J0848.9+4452. The two galaxies appear to point towards the nearby cluster ClG J0848+4453 and are aligned with the outer X-ray contour of their parent cluster, supporting a model of BCG formation by collimated infall along the surrounding large-scale structure.Comment: 14 pages, 5 figures, to be appeared in ApJ Letter

A Shock-Induced Pair of Superbubbles in the High-Redshift Powerful Radio Galaxy MRC 0406-244

We present new optical spectroscopy of the high-redshift powerful radio galaxy MRC 0406$-$244 at redshift of 2.429. We find that the two extensions toward NW and SE probed in the rest-frame ultraviolet image are heated mainly by the nonthermal continuum of the active galactic nucleus. However, each extension shows a shell-like morphology, suggesting that they are a pair of superbubbles induced by the superwind activity rather than by the interaction between the radio jet and the ambient gas clouds. If this is the case, the intense starburst responsible for the formation of superbubbles could occur $\sim 1 \times 10^9$ yr ago. On the other hand, the age of the radio jets may be of the order of $\sim 10^6$ yr, being much shorter than the starburst age. Therefore, the two events, i.e., the starburst and the radio-jet activities, are independent phenomena. However, their directions of the expanding motions could be governed by the rotational motion of the gaseous component in the host galaxy. This idea appears to explain the alignment effect of MRC 0406$-$244.Comment: 4 pages (emulateapj.sty), Fig. 1 (jpeg) + Fig.2 (eps). Accepted for publications in ApJ (Letters

Isotope production in proton-, deuteron-, and carbon-induced reactions on Nb 93 at 113 MeV/nucleon

Isotope-production cross sections for p-, d-, and C-induced spallation reactions on Nb93 at 113 MeV/nucleon were measured using the inverse-kinematics method employing secondary targets of CH2, CD2, and C. The measured cross sections for Mo90, Nb90, Y86,88 produced by p-induced reactions were found to be consistent with those measured by the conventional activation method. We performed benchmark tests of the reaction models INCL-4.6, JQMD, and JQMD-2.0 implemented in the Particle and Heavy Ion Transport code System (PHITS) and of the nuclear data libraries JENDL-4.0/HE, TENDL-2017, and ENDF/B-VIII.0. The model calculations also showed generally good agreement with the measured isotope-production cross sections for p-, d-, and C-induced reactions. It also turns out that, among the three nuclear data libraries, JENDL-4.0/HE provides the best agreement with the measured data for the p-induced reactions. We compared the present Nb93 data with the Zr93 data, that were measured previously by the same inverse kinematics method (Kawase et al., Prog. Theor. Exp. Phys. 2017, 093D03 (2017)2050-391110.1093/ptep/ptx110), with particular attention to the effect of neutron-shell closure on isotope production in p- and d-induced spallation reactions. The isotopic distributions of the measured production cross sections in the Zr93 data showed noticeable jumps at neutron number N=50 in the isotopic chains of ΔZ=0 and -1, whereas no such jump appeared in isotopic chain of ΔZ=0 in the Nb93 data. From INCL-4.6 + GEM calculations, we found that the jump formed in the evaporation process is smeared out by the intranuclear cascade component in Nb91 produced by the Nb93(p,p2n) and (d,d2n) reactions on Nb93. Moreover, for Nb93, the distribution of the element-production cross sections as a function of the change in proton number ΔZ is shifted to smaller ΔZ than for Zr93, because the excited Nb prefragments generated by the cascade process are more likely to emit protons than the excited Zr prefragments, due to the smaller proton-separation energies of the Nb isotopes

Coulomb breakup reactions of 93,94 Zr in inverse kinematics

Coulomb breakup reactions of 93,94 Zr have been studied in inverse kinematics at incident beam energies of about 200 MeV/nucleon in order to evaluate neutron capture reaction methods. The 93 Zr(n,γ) 94 Zr reaction is particularly important as a candidate nuclear transmutation reaction for the long-lived fission product 93 Zr in nuclear power plants. One- and two-neutron removal cross sections on Pb and C targets were measured to deduce the inclusive Coulomb breakup cross sections, 375 ± 29 (stat.) ± 30 (syst.) and 403 ± 26 (stat.) ± 31 (syst.) mb for 93 Zr and 94 Zr, respectively. The results are compared with estimates using the standard Lorentzian model and microscopic calculations. The results reveal a possible contribution of the pygmy dipole resonance or giant quadrupole resonance in the Coulomb breakup reactions of 94 Zr

Cross sections for nuclide production in proton- and deuteron-induced reactions on 93

Isotopic production cross sections were measured for proton- and deuteron-induced reactions on 93Nb by means of the inverse kinematics method at RIKEN Radioactive Isotope Beam Factory. The measured production cross sections of residual nuclei in the reaction 93Nb + p at 113 MeV/u were compared with previous data measured by the conventional activation method in the proton energy range between 46 and 249 MeV. The present inverse kinematics data of four reaction products (90Mo, 90Nb, 88Y, and 86Y) were in good agreement with the data of activation measurement. Also, the model calculations with PHITS describing the intra-nuclear cascade and evaporation processes generally well reproduced the measured isotopic production cross sections