ON ENTIRE SOLUTIONS OF SOME TYPE OF NONLINEAR DIFFERENCE EQUATIONS

In this article, the existence of finite order entire solutions of nonlinear difference equations fn＋ Pd（z, f） = p1 eα1 z＋ p2 eα2 z are studied, where n ≥ 2 is an integer, Pd（z, f） is a difference polynomial in f of degree d（≤ n-2）, p1, p2 are small meromorphic functions of ez, and α1, α2 are nonzero constants. Some necessary conditions are given to guarantee that the above equation has an entire solution of finite order. As its applications, we also find some type of nonlinear difference equations having no finite order entire solutions.

Structural Domain Imaging and Direct Determination of Crystallographic Orientation in Noncentrosymmetric Ca3 Ru2O7 Using Polarized Light Reflectance

The noncentrosymmetricity of a prototypical correlated electron system Ca3Ru2O7 renders extensive interest in the possible polar metallic state,along with multiple other closely competing interactions.However,the structural domain formation in this material often complicates the study of intrinsic material properties.It is crucial to fully characterize the structural domains for unrevealing underlying physics.Here,we report the domain imaging on Ca3Ru2O7 crystal using the reflection of polarized light at normal incidence.The reflection anisotropy measurement utilizes the relative orientation between electric field component of the incident polarized light and the principal axis of the crystal,and gives rise to a peculiar contrast.The domain walls are found to be the interfaces between 90° rotated twin crystals by complementary magnetization measurements.A distinct contrast in reflectance is also found in the opposite cleavage surfaces,owing to the polar mode of the RuO6 octahedra.More importantly,the analysis of the contrast between all inequivalent cleavage surfaces enables a direct determination of the crystallographic orientation of each domain.Such an approach provides an efficient yet feasible method for structural domain characterization,which can also find applications in noncentrosymmetric crystals in general.

A Novel Model of Predicting Archie's Cementation Factor from Nuclear Magnetic Resonance(NMR) Logs in Low Permeability Reservoirs

The resistivity experimental measurements of core samples drilled from low permeability reservoirs of Ordos Basin, Northwest China, illustrate that the cementation factors are not agminate, but vary from 1.335 to 1.749. This leads to a challenge for the estimation of water and hydrocarbon sa- turation. Based on the analysis of Purcell equation and assumption that rock resistivity is determined by the parallel connection of numerous capillary resistances, a theoretical expression of cementation factor in terms of porosity and permeability is established. Then, cementation factor can be calculated if the parameters of porosity and permeability are determined. In the field application, porosity can be easily obtained by conventional logs. However, it is a tough challenge to estimate permeability due to the strong heterogeneity of low permeability reservoirs. Thus, the Schlumberger Doll Research （SDR） model derived from NMR logs has been proposed to estimate permeability. Based on the analysis of the theoretical expressions of cementation factor and SDR model, a novel cementation factor prediction model, which is relevant to porosity and logarithmic mean of NMR T2 spectrum （T21m）, is derived. The advantage of this model is that all the input information can be acquired from NMR logs accurately. In order to confirm the credibility of the novel model, the resistivity and corresponding laboratory NMR measurements of 27 core samples are conducted. The credibility of the model is confirmed by compar- ing the predicted cementation factors with the core analyzed results. The absolute errors for all core samples are lower than 0.071. Once this model is extended to field application, the accuracy of water and hydrocarbon saturation estimation will be significantly improved.

Recent advances in the development of activatable multifunctional probes for in vivo imaging of caspase-3

Caspases are a family of proteases that play critical roles in controlling inflammation and cell death.Apoptosis is a caspase-3 mainly controlled behavior to avoid inflammation and damage to surrounding cells,whereas anomalistic cell apoptosis may be associated with many diseases.The detection and imaging of caspase-3 will be of great significance in evaluating the early therapeutic effect of tumors.Developing smart fluorescent probes may be helpful for the visualization of the rapeutic effect compared with "always on" probes.Thus,more and more works toward activatable fluorescent probes for caspase-3 imaging have been reported.In addition,multifunctional probes have also been designed to further improve the imaging of caspase-3.Herein,this review systematically summarized the representative wo rk of caspase-3 from the perspective of molecular design that it will play a guiding role in the design of probes that respond to caspase-3.Also,challenges and perspectives toward the field for imaging of cell apoptosis(caspase-3) are also discussed.

Revealing Formaldehyde Fluxes in Alzheimer's Disease Brain by an Activity-Based Fluorescence Probe

Formaldehyde(FA)plays critical roles in Alzheimer's disease and the associations between FA and Alzheimer's disease(AD)are still obscure.To reveal FA fluxes in the Alzheimer's disease brain,an activity-based fluorescence probe NP-FA with superb blood-brain barrier permeable abilities was exquisitely designed.The probe responded to FA with significant fluorescence increases(F/F0=81),thus laying the foundation for the sensitive detection of FA in cuvette and in vivo.Moreover,the probe also possessed some fasci-nating performances,including endoplasmic reticulum(ER)-targeting abilities,good one-photon/two-photon absorption properties,and appropriate hydrophobicity property(log P=2.34±0.05).As a result,the probe can readily reflect the overproduction of FA con-tent in live cells under ER stress by high-fidelity two-photon imaging.More interestingly,ex vivo imaging of AD brains and two-photon imaging of AD slice tissues visually disclosed that the FA level of AD brain is much higher than that of the normal brain.This work afforded a specific activity-based probe for the imaging of FA in the AD mouse brains,which could be further extended to FA-related studies in Alzheimer's disease.

Subtle metastability of the layered magnetic topological insulator MnBi_(2)Te_(4) from weak interactions

Layered quantum materials can host interesting properties,including magnetic and topological,for which enormous computational predictions have been done.Their thermodynamic stability is much less visited computationally,which however determines the existence of materials and can be used to guide experimental synthesis.MnBi_(2)Te_(4) is one of such layered quantum materials that was predicted to be an intrinsic antiferromagnetic topological insulator,and later experimentally realized but in a thermodynamically metastable state.

A New Empirical Method for Constructing Capillary Pressure Curves from Conventional Logs in Low-Permeability Sandstones

Pore structure reflected from capillary pressure curves plays an important role in low-permeability formation evaluation. It is a common way to construct capillary pressure curves by Nuclear Magnetic Resonance（NMR） log. However, the method＇s efficiency will be severely affected if there is no NMR log data or it cannot reflect pore structure well. Therefore, on the basis of J function and diagenetic facies classification, a new empirical model for constructing capillary pressure curves from conventional logs is proposed here as a solution to the problem. This model includes porosity and the relative value of natural gamma rays as independent variables and the saturation of mercury injection as a dependent variable. According to the 51 core experimental data sets of three diagenetic facies from the bottom of the Upper Triassic in the western Ordos Basin, China, the model＇s parameters in each diagenetic facies are calibrated. Both self-checking and extrapolation tests show a positive effect, which demonstrates the high reliability of the proposed capillary pressure curve construction model. Based on the constructed capillary pressure curves, NMR T_2 spectra under fully brine-saturated conditions are mapped by a piecewise power function. A field study is then presented. Agreement can be seen between the mapped NMR T_2 spectra and the MRIL-Plog data in the location of the major peak, right boundary, distribution characteristics and T_2 logarithmic mean value. In addition, the capillary pressure curve construction model proposed in this paper is not affected by special log data or formation condition. It is of great importance in evaluating pore structure, predicting oil production and identifying oil layers through NMR log data in low-permeability sandstones.

Optical spectroscopy study of Ca_3(Ru_(0.91)Mn_(0.09))_2O_7 single crystal in high magnetic fields

The magneto-optical spectrum, with magnetic fields up to 42 T, of double layered ruthenates Ca_3(Ru_(0.91)Mn_(0.09))_2O_7(CRMO) single crystal is studied. Both the temperature and magnetic field induced insulator-to-metal transitions(IMTs) are observed via magneto-optical properties of the crystal. The critical magnetic field(H//c) of IMT for CRMO is found to be as large as 35 T at 5 K. The fine structure of optical spectra identified the antiferromagnetic/ferro-orbital-ordering configurations of Ru 4d orbitals at low temperatures. Meanwhile, the configuration of orbital polarization of such double-layer CRMO single crystal is discussed. These results suggest that the orbital degree of freedom plays an important role in the field induced IMT of multi-orbital system.

High yield production of ultrathin fibroid semiconducting nanowire of Ta2Pd3Se8

Immediately after the demonstration of the high-quality electronic properties in various two dimensional(2D)van der Waals(vdW)crystals fabricated with mechanical exfoliation,many methods have been reported to explore and control large scale fabrications.Comparing with recent advancements in fabricating 2D atomic layered crystals,large scale production of one dimensional(1D)nanowires with thickness approaching molecular or atomic level still remains stagnant.Here,we demonstrate the high yield production of a 1D vdW material,semiconducting Ta2Pd3Se8 nanowires,by means of liquid-phase exfoliation.The thinnest nanowire we have readily achieved is around 1 nm,corresponding to a bundle of one or two molecular ribbons.Transmission electron microscopy(TEM)and transport measurements reveal the as-fabricated Ta2Pd3Se8 nanowires exhibit unexpected high crystallinity and chemical stability.Our low-frequency Raman spectroscopy reveals clear evidence of the existing of weak inter-ribbon bindings.The fabricated nanowire transistors exhibit high switching performance and promising applications for photodetectors.

Unusually strong lateral interaction in the CO overlayer in phosphorene-based systems

By means of vibrational spectroscopy and density functional theory (DFT), we investigate CO adsorption on phosphorene-based systems. We find stable CO adsorption at room temperature on both phosphorene and bulk black phosphorus. The adsorption energy and vibrational spectrum are calculated for several possible configurations of the CO overlayer. We find that the vibrational spectrum is characterized by two different C–O stretching energies. The experimental data are in good agreement with the prediction of the DFT model and reveal the unusual C–O vibrational band at 165–180 meV, activated by the lateral interactions in the CO overlayer. [Figure not available: see fulltext.] © 2016, Tsinghua University Press and Springer-Verlag Berlin Heidelberg.