Spectral extremal results on edge blow-up of graphs

The edge blow-up $F^{p+1}$ of a graph $F$ for an integer $p\geq 2$ is obtained by replacing each edge in $F$ with a $K_{p+1}$ containing the edge, where the new vertices of $K_{p+1}$ are all distinct. Let $ex(n,F)$ and $spex(n,F)$ be the maximum size and maximum spectral radius of an $F$-free graph of order $n$, respectively. In this paper, we determine the range of $spex(n,F^{p+1})$ when $F$ is bipartite and the exact value of $spex(n,F^{p+1})$ when $F$ is non-bipartite for sufficiently large $n$, which are the spectral versions of Tur\'{a}n's problems on $ex(n,F^{p+1})$ solved by Yuan [J. Combin. Theory Ser. B 152 (2022) 379--398]. This generalizes several previous results on $F^{p+1}$ for $F$ being a matching, or a star. Additionally, we also give some other interesting results on $F^{p+1}$ for $F$ being a path, a cycle, or a complete graph. To obtain the aforementioned spectral results, we utilize a combination of the spectral version of the Stability Lemma and structural analyses. These approaches and tools give a new exploration of spectral extremal problems on non-bipartite graphs

Spectral extremal problem on tt copies of ℓ\ell-cycle

Denote by $tC_\ell$ the disjoint union of $t$ cycles of length $\ell$. Let $ex(n,F)$ and $spex(n,F)$ be the maximum size and spectral radius over all $n$-vertex $F$-free graphs, respectively. In this paper, we shall pay attention to the study of both $ex(n,tC_\ell)$ and $spex(n,tC_\ell)$. On the one hand, we determine $ex(n,tC_{2\ell+1})$ and characterize the extremal graph for any integers $t,\ell$ and $n\ge f(t,\ell)$, where $f(t,\ell)=O(t\ell^2)$. This generalizes the result on $ex(n,tC_3)$ of Erd\H{o}s [Arch. Math. 13 (1962) 222--227] as well as the research on $ex(n,C_{2\ell+1})$ of F\"{u}redi and Gunderson [Combin. Probab. Comput. 24 (2015) 641--645]. On the other hand, we focus on the spectral Tur\'{a}n-type function $spex(n,tC_{\ell})$, and determine the extremal graph for any fixed $t,\ell$ and large enough $n$. Our results not only extend some classic spectral extremal results on triangles, quadrilaterals and general odd cycles due to Nikiforov, but also develop the famous spectral even cycle conjecture proposed by Nikiforov (2010) and confirmed by Cioab\u{a}, Desai and Tait (2022).Comment: 25 pages, one figur

Salt Content Distribution and Paleoclimatic Significance of the Lop Nur “Ear” Feature: Results from Analysis of EO-1 Hyperion Imagery

Lop Nur, a playa lake located on the eastern margin of Tarim Basin in northwestern China, is famous for the “Ear” feature of its salt crust, which appears in remote-sensing images. In this study, partial least squares (PLS) regression was used to estimated Lop Nur playa salt-crust properties, including total salt, Ca2+, Mg2+, Na+, Si2+, and Fe2+ using laboratory hyperspectral data. PLS results for laboratory-measured spectra were compared with those for resampled laboratory spectra with the same spectral resolution as Hyperion using the coefficient of determination (R2) and the ratio of standard deviation of sample chemical concentration to root mean squared error (RPD). Based on R2 and RPD, the results suggest that PLS can predict Ca2+ using Hyperion reflectance spectra. The Ca2+ distribution was compared to the “Ear area” shown in a Landsat Thematic Mapper (TM) 5 image. The mean value of reflectance from visible bands for a 14 km transversal profile to the “Ear area” rings was extracted with the TM 5 image. The reflectance was used to build a correlation with Ca2+ content estimated with PLS using Hyperion. Results show that the correlation between Ca2+ content and reflectance is in accordance with the evolution of the salt lake. Ca2+ content variation was consistent with salt deposition. Some areas show a negative correlation between Ca2+ content and reflectance, indicating that there could have been a small-scale temporary runoff event under an arid environmental background. Further work is needed to determine whether these areas of small-scale runoff are due to natural (climate events) or human factors (upstream channel changes

Temperature and magnetism bi-responsive molecularly imprinted polymers: Preparation, adsorption mechanism and properties as drug delivery system for sustained release of 5-fluorouracil

This document is the Accepted Manuscript version of the following article: Longfei Li, Lin Chen, Huan Zhang, Yongshen Yang, Xuguang Liu, and Yongkang Chen, ‘Temperature and magnetism bi-responsive molecularly imprinted polymers: Preparation, adsorption mechanism and properties as drug delivery system for sustained release of 5-fluorouracil’, Materials Science and Engineering: C, Vol. 61: 158-168, April 2016, made available under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License CC BY NC-ND 4.0 (http://creativecommons.org/licenses/by-nc-nd/4.0/).Temperature and magnetism bi-responsive molecularly imprinted polymers (TMMIPs) based on Fe3O4-encapsulating carbon nanospheres were prepared by free radical polymerization, and applied to selective adsorption and controlled release of 5-fluorouracil (5-FU) from an aqueous solution. Characterization results show that the as-synthesized TMMIPs have an average diameter of about 150 nm with a typical core–shell structure, and the thickness of the coating layer is approximately 50 nm. TMMIPs also displayed obvious magnetic properties and thermo-sensitivity. The adsorption results show that the prepared TMMIPs exhibit good adsorption capacity (up to 96.53 mg/g at 25 °C) and recognition towards 5-FU. The studies on 5-FU loading and release in vitro suggest that the release rate increases with increasing temperature. Meanwhile, adsorption mechanisms were explored by using a computational analysis to simulate the imprinted site towards 5-FU. The interaction energy between the imprinted site and 5-FU is − 112.24 kJ/mol, originating from a hydrogen bond, Van der Waals forces and a hydrophobic interaction between functional groups located on 5-FU and a NIPAM monomer. The electrostatic potential charges and population analysis results suggest that the imprinted site of 5-FU can be introduced on the surface of TMMIPs, confirming their selective adsorption behavior for 5-FU.Peer reviewe

Corrected Navier-Stokes equations for compressible flows

For gas flows, the Navier-Stokes (NS) equations are established by mathematically expressing conservations of mass, momentum and energy. The advantage of the NS equations over the Euler equations is that the NS equations have taken into account the viscous stress caused by the thermal motion of molecules. The viscous stress arises from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress is proportional to the gradient of velocity1. Thus, the assumption is the only empirical element in the NS equations, and this is actually the reason why the NS equations perform poorly under special circumstances. For example, the NS equations cannot describe rarefied gas flows and shock structure. This work proposed a correction to the NS equations with an argument that the viscous stress is proportional to the gradient of momentum when the flow is under compression, with zero additional empirical parameters. For the first time, the NS equations have been capable of accurately solving shock structure and rarefied gas flows. In addition, even for perfect gas, the accuracy of the prediction of heat flux rate is greatly improved. The corrected NS equations can readily be used to improve the accuracy in the computation of flows with density variations which is common in nature.Comment: 13 pages, 7 figure

Single snapshot multiple frequency modulated imaging of subsurface optical properties of turbid media with structured light

We report a novel demodulation method that enables single snapshot wide field imaging of optical properties of turbid media in the Spatial Frequency Domain (SFD). This Single Snapshot Multiple frequency Demodulation (SSMD) method makes use of the orthogonality of harmonic functions to extract the modulation transfer function (MTF) at multiple modulation frequencies simultaneously from a single structured-illuminated image at once. The orientation, frequency, and amplitude of each modulation can be set arbitrarily subject to the limitation of the implementation device. We first validate and compare SSMD to the existing demodulation methods by numerical simulations. The performance of SSMD is then demonstrated with experiments on both tissue mimicking phantoms and in vivo for recovering optical properties by comparing to the standard three-phase demodulation approach. The results show that SSMD increases significantly the data acquisition speed and reduces motion artefacts. SSMD exhibits excellent noise suppression in imaging as well at the rate proportional to the square root of the number of pixels contained in its kernel. SSMD is ideal in the implementation of a real-time spatial frequency domain imaging platform and will open up SFDI for vast applications in imaging and monitoring dynamic turbid medium and processes