The effective geometry Monte Carlo algorithm: Applications to molecular communication

In this work, we address the systematic biases and random errors stemming from finite step sizes encountered in diffusion simulations. We introduce the Effective Geometry Monte Carlo (EG-MC) simulation algorithm which modifies the geometry of the receiver. We motivate our approach in a 1D toy model and then apply our findings to a spherical absorbing receiver in a 3D unbounded environment. We show that with minimal computational cost the impulse response of this receiver can be precisely simulated using EG-MC. Afterwards, we demonstrate the accuracy of our simulations and give tight constraints on the single free parameter in EG-MC. Finally, we comment on the range of applicability of our results. While we present the EG-MC algorithm for the specific case of molecular diffusion, we believe that analogous methods with effective geometry manipulations can be utilized to approach a variety of problems in other branches of physics such as condensed matter physics and cosmological large scale structure simulations.     

Measuring the Polarization Parameters of Rain by Inverse Scattering

The theory is presented for one method of determining the effective polarization parameters of the rain medium in the problem of polarization information processing of detecting target. The determination of the effective polarization parameters of the propagation medium is from the data of propagation measurements over a line-of-sight link. The polarization parameters the effective average value, the effective standard deviation and F the effective shape parameter of the propagation medium are obtained by means of the method of inverse scattering, showing a good agreement with the data from direct measurements.     

稀磁半导体Cd_（1－x）Fe_xTe的磁光光谱

在７０－３００Ｋ温度范围内测量了组分ｘ为０．０１和０．０４的Ｃｄ１－ｘＦｅｘＴｅ及ＣｄＴｅ的法拉第效应随入射光子能量的变化，首次获得了Ｃｄ１－ｘＦｅｘＴｅ在布里渊区Γ点和Ｌ点的有效ｇ因子及其与温度的关系。给出了Ｆｅ２＋离子与载流子间的ｓｐ－ｄ交换作用常数Ｎ０（β－α）＝（－１．５７±０．０３）ｅＶ。     

Parallel Implementation of Successive Convex Relaxation Methods for Quadratic Optimization Problems

As computing resources continue to improve, global solutions for larger size quadrically constrained optimization problems become more achievable. In this paper, we focus on larger size problems and get accurate bounds for optimal values of such problems with the successive use of SDP relaxations on a parallel computing system called Ninf (Network-based Information Library for high performance computing).     

En route to Background Independence: Broken split-symmetry,and how to restore it with bi-metric average actions

The most momentous requirement a quantum theory of gravity must satisfy is Background Independence, necessitating in particular an ab initio derivation of the arena all non-gravitational physics takes place in, namely spacetime. Using the background field technique, this requirement translates into the condition of an unbroken split-symmetry connecting the (quantized) metric fluctuations to the (classical) background metric. If the regularization scheme used violates split-symmetry during the quantization process it is mandatory to restore it in the end at the level of observable physics. In this paper we present a detailed investigation of split-symmetry breaking and restoration within the Effective Average Action (EAA) approach to Quantum Einstein Gravity (QEG) with a special emphasis on the Asymptotic Safety conjecture. In particular we demonstrate for the first time in a non-trivial setting that the two key requirements of Background Independence and Asymptotic Safety can be satisfied simultaneously. Carefully disentangling fluctuation and background fields, we employ a ‘bi-metric’ ansatz for the EAA and project the flow generated by its functional renormalization group equation on a truncated theory space spanned by two separate Einstein–Hilbert actions for the dynamical and the background metric, respectively. A new powerful method is used to derive the corresponding renormalization group (RG) equations for the Newton- and cosmological constant, both in the dynamical and the background sector. We classify and analyze their solutions in detail, determine their fixed point structure, and identify an attractor mechanism which turns out instrumental in the split-symmetry restoration. We show that there exists a subset of RG trajectories which are both asymptotically safe and split-symmetry restoring: In the ultraviolet they emanate from a non-Gaussian fixed point, and in the infrared they loose all symmetry violating contributions inflicted on them by the non-invariant functional RG equation. As an application, we compute the scale dependent spectral dimension which governs the fractal properties of the effective QEG spacetimes at the bi-metric level. Earlier tests of the Asymptotic Safety conjecture almost exclusively employed ‘single-metric truncations’ which are blind towards the difference between quantum and background fields. We explore in detail under which conditions they can be reliable, and we discuss how the single-metric based picture of Asymptotic Safety needs to be revised in the light of the new results. We shall conclude that the next generation of truncations for quantitatively precise predictions (of critical exponents, for instance) is bound to be of the bi-metric type.     

Modular forms and effective Diophantine approximation

After the work of G. Frey, it is known that an appropriate bound for the Faltings height of elliptic curves in terms of the conductor (Frey?s height conjecture) would give a version of the ABC conjecture. In this paper we prove a partial result towards Frey?s height conjecture which applies to all elliptic curves over $\mathbb{Q}$, not only Frey curves. Our bound is completely effective and the technique is based in the theory of modular forms. As a consequence, we prove effective explicit bounds towards the ABC conjecture of similar strength to what can be obtained by linear forms in logarithms, without using the latter technique. The main application is a new effective proof of the finiteness of solutions to the S-unit equation (that is, S-integral points of ${\mathbb{P}}^1?\{0,1,\infty \}$), with a completely explicit and effective bound, without using any variant of Baker?s theory or the Thue–Bombieri method.     

Orbital deletion procedure and its applications

The orbital deletion procedure is introduced, which is suited to quantitatively investigating the electronic delocalization effiect in earboeations and boranes. While the routine, ab initio molecular orbital methods can generate wavefunetions for real systems where all electrons are delocalized, the present orbital deletion procedure can generate wavefunctions for hypothetical reference molecules where electronic delocalization effect is deactivated. The latter wavefunetion normlly corresponds In the most stable resonance structure in terms of the resonance theory. By comparing and analyzing the delocalized and the localized wavefunetions, one can obtain a quantitative and instinct pieture to show how electronic deloealizalion inside a molecule affects the molecular structure, energy as well as other physical properties. Two examples are detailedly discussed. The first is related to the hypercoujugation of alkyl groups in carbocations and a comparison of the order of stability of carbocations is made, T     

A photo-oxidation procedure using UV radiation/H2O2 for decomposition of wine samples — Determination of iron and manganese content by flame atomic absorption spectrometry

This paper proposes the use of photo-oxidation with UV radiation/H₂O₂ as sample pretreatment for the determination of iron and manganese in wines by flame atomic absorption spectrometry (FAAS). The optimization involved the study of the following variables: pH and concentration of buffer solution, concentrated hydrogen peroxide volume and irradiation time. The evaluation of sample degradation was monitored by measuring the absorbance at the maximum wavelength of red wine (530 nm). Using the experimental conditions established during the optimization (irradiation time of 30 min, oxidant volume of 2.5 mL, pH 10, and a buffer concentration of 0.15 mol L^− 1), this procedure allows the determination of iron and manganese with limits of detection of 30 and 22 μg L^− 1, respectively, for a 5 mL volume of digested sample. The precision levels, expressed as relative standard deviation (RSD), were 2.8% and 0.65% for iron and 2.7% and 0.54% for manganese for concentrations of 0.5 and 2.0 mg L^− 1, respectively. Addition/recovery tests for evaluation of the accuracy were in the ranges of 90%–111% and 95%–107% for iron and manganese, respectively. This digestion procedure has been applied for the determination of iron and manganese in six wine samples. The concentrations varied from 1.58 to 2.77 mg L^− 1 for iron and from 1.30 to 1.91 mg L^− 1 for manganese. The results were compared with those obtained by an acid digestion procedure and determination of the elements by FAAS. There was no significant difference between the results obtained by the two methods based on a paired t-test (at 95% confidence level).     

糠醛系氮配位螯合树脂对贵金属元素的吸附性能

呋喃衍生物糠醛与二乙烯三胺反应制得了含有Schiff碱基,胺基及大共轭π键地的氮配位螯合树脂,应用电感耦合等离子体发射光谱研究了所得螯合树脂对贵金属元素Au,Pd,Pt,Rh,Ru,Ir及重金属元素Hg的吸附性能。结果表明,所得螯合树脂在较宽的酸度范围内能很好地吸附Au,Pd,Pt,Rh,Ru元素,具有优良的吸附选择性及较高的富集倍数,特别是对Au能达到定量吸附与洗脱,同时,在一定酸度条件下亦对Pt,Ir及Hg显示良好的吸附性能。