On classification of singular matrix difference equations of mixed order

This paper is concerned with singular matrix difference equations of mixed order. The existence and uniqueness of initial value problems for these equations are derived, and then the classification of them is obtained with a similar classical Weyl's method by selecting a suitable quasi-difference. An equivalent characterization of this classification is given in terms of the number of linearly independent square summable solutions of the equation. The influence of off-diagonal coefficients on the classification is illustrated by two examples. In particular, two limit point criteria are established in terms of coefficients of the equation.Comment: 27 page

A Review on Nanofluids: Preparation, Stability Mechanisms, and Applications

Nanofluids, the fluid suspensions of nanomaterials, have shown many interesting properties, and the distinctive features offer unprecedented potential for many applications. This paper summarizes the recent progress on the study of nanofluids, such as the preparation methods, the evaluation methods for the stability of nanofluids, and the ways to enhance the stability for nanofluids, the stability mechanisms of nanofluids, and presents the broad range of current and future applications in various fields including energy and mechanical and biomedical fields. At last, the paper identifies the opportunities for future research

Large Language Models at Work in China's Labor Market

This paper explores the potential impacts of large language models (LLMs) on the Chinese labor market. We analyze occupational exposure to LLM capabilities by incorporating human expertise and LLM classifications, following Eloundou et al. (2023)'s methodology. We then aggregate occupation exposure to the industry level to obtain industry exposure scores. The results indicate a positive correlation between occupation exposure and wage levels/experience premiums, suggesting higher-paying and experience-intensive jobs may face greater displacement risks from LLM-powered software. The industry exposure scores align with expert assessments and economic intuitions. We also develop an economic growth model incorporating industry exposure to quantify the productivity-employment trade-off from AI adoption. Overall, this study provides an analytical basis for understanding the labor market impacts of increasingly capable AI systems in China. Key innovations include the occupation-level exposure analysis, industry aggregation approach, and economic modeling incorporating AI adoption and labor market effects. The findings will inform policymakers and businesses on strategies for maximizing the benefits of AI while mitigating adverse disruption risks

Enhanced Thermal Conductivity for Nanofluids Containing Silver Nanowires with Different Shapes

Nanofluids are the special agents to enhance the heat transfer property of the common fluids, and most of the thermal additives are the spherical nanoparticles. Up to now, the 1D thermal additives are not well exploited. In this paper, a kind of silver nanowires (AgNWs) with well-distributed shape and aspect ratio is synthesized. The results show that when we use the AgNWs prepared by the poly-vinyl-pyrrolidone (PVP) with a specific molecular weight of 40000, the thermal conductivity enhancement of nanofluids prepared by that kind of silver nanowires is as high as 13.42% when loading 0.46 vol.% AgNWs, and the value of the thermal conductivity is 0.2843 W/m·K, which is far more than the case when loading the same volume of spherical silver particles. Besides, we use H&C model to fit the experimental results and the experimental results are consistent with the model

Promoted electron transport and sustained phonon transport by DNA down to 10 K

a b s t r a c t This work reports on a pioneering study of the electron transport in nanometer-thick Ir film supported by a DNA fiber, and the phonon transport sustained by the DNA itself. By evaluating the electrical resistivity (r e )~temperature relation based on the Block-Grüneisen theory, we find the Ir film has weak phonon softening indicated by 7e15% Debye temperature reduction. The Ir film's intrinsic r e is promoted by DNA electron thermal hopping and quantum tunneling, and is identical to that of bulk Ir. Although the nanocrystalline structure in ultrathin metallic films intends to give a higher Lorenz number since it reduces the electrical conductivity more than thermal conductivity, the DNA-promoted electron transport in the Ir film preserves a Lorenz number close to that of bulk crystalline Ir. By defining a new physical parameter entitled "thermal reffusivity", the residual phonon thermal resistivity of DNA is identified and evaluated for the first time. The thermal reffusivity concept can be widely used to predict the phonon thermal transport potential of defect-free materials. We predict that the thermal diffusivity of defect-free DNA fiber could be 36e61% higher than the samples studied herein. The structure domain size for phonon diffusion/scattering is determined as 0.8 nm in DNA

Non-real eigenvalues of symmetric Sturm–Liouville problems with indefinite weight functions

The present paper deals with non-real eigenvalues of regular Sturm–Liouville problems with odd symmetry indefinite weight functions applying the two-parameter method. Sufficient conditions for the existence and non-existence of non-real eigenvalues are obtained. Furthermore, an explicit expression of the bound of non-real eigenvalues will be given in the paper

Surface Chemical Modification of Multiwalled Carbon Nanotubes by a Wet-Mechanochemical Reaction

A wet-mechanochemical reaction for surface modification of multiwalled carbon nanotubes (CNTs) has been developed. In the treatment, CNTs reacted with potassium hydroxide in alcohol solvent at room temperature under mechanical milling. The results from Fourier transmission infrared spectroscopy demonstrate that the nonreactive surfaces of CNTs have been modified successfully by multiple hydroxyl groups. Functionalized carbon nanotubes exhibit higher zeta potential values indicating their high dispersibility in polar solvents. XRD studies corroborate that the surface functionalization does not affect the basic crystal domain size of CNTs. TEM observations reveal that CNTs have been cut into shorter ones by the milling. Shortened CNTs with functionalized surfaces show good dispersion properties