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关键词： Moore-Penrose inverse   Signless Laplacian   Incidence matrix   Tree   Unicyclic graph  

摘要： The signless Laplacian Q and signless edge-Laplacian S of a given graph may or may not be invertible. The Moore-Penrose inverses of Q and Sare studied. In particular, using the incidence matrix, we find combinatorial formulas of the Moore-Penrose inverses of Q and S for trees. Also, we present combinatorial formulas of the inverses of Q and S for odd unicyclic graphs. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Fractional Laplacian   full waveform inversion (FWI)   pseudo-spectral time-domain (PSTD)   viscoacoustic   wave-field reconstruction  

摘要： We develop a fractional Laplacian viscoacoustic wave equation-based full waveform inversion (FWI) method. The main novelty is efficient reconstruction of the source wavefields in gradient computation by the adjoint state method. Our FW1 is based on Fourier pseudo-spectral time-domain (PSTD) numerical solutions of the fractional Laplacian viscoacoustic wave equation, which can describe the frequency independent Q (quality factor) behaviors of seismic waves accurately. The presented wavefield reconstruction strategy utilizes reverse time-marching formulae to compute the source wavefields backward in time, including an implicit formula in the interior domain and an explicit one in the perfectly matched layer (PML) absorbing domains. Since the wavefields in the entire domain are recovered, our method does not require storing massive boundary values like conventional reconstruction methods. To avoid numerical instability in reverse time reconstruction, we design a global-local checkpointing technique. When reverse time reconstruction encounters numerical instability, the forward propagation restarts from the nearest global checkpoint and proceeds to the unstable time step. Then, the reverse time reconstruction continues. The local checkpoints help to delay the numerical instability in the PML domains. Numerical examples verify the feasibility of our reconstruction strategy and the efficiency gain achieved by using this strategy in FWI.

关键词： Photon   DKP equation   Rainbow gravity   Maxwell equations  

摘要： In the present article, quantum dynamics of the photon is investigated in the cosmic string spacetime via gravity's rainbow. We solve the mDKP (massless Duffin-Kemmer-Petiau) equation exactly and obtain the energy spectrum of photon. Then, we solve the Maxwell equations in the same gravity's rainbow background and show that the solutions obtained are equivalent to the results of the photon equation. The energy spectrum of the photon is analyzed for three different rainbow functions. (C) 2021 Elsevier Inc. All rights reserved.

关键词： Periodically forced oscillators   Force transmissibility   Circular spring-mass systems   Stiffness matrix   Negative stiffness   Inverse vibration problem   Minimization problem involving matrices   Circulant matrices   Asymptotic limit for matrices   One-dimensional discrete bi-harmonic operator   Eigenpair   Trace Jansen Inequality  

摘要： We optimize the spring constants k(i,j) (stiffness) of circular spring-mass systems with nearest-neighbour (NN) and next-nearest-neighbour (NNN) springs only. In this optimization problem, such systems are also subjected to damping and periodic external forces. The function to be minimized is the average ratio of the square norm of the on-site internal forces (response) to the square norm of the external on-site forces (input). Under the average of this response/input ratio is meant the average over time and over all configurations of external forces. As main result, it is established that the optimum stiffness matrix converges to the discrete and periodic bi-Laplacian operator as the size n of the system increases. Such a result is obtained under the following assumptions: (a) the system has the natural mode shape (eigenvector) of alternating 1s and -1s;and (b) the (external) forcing frequency is at least 1.095 times higher than the highest natural frequency. It is remarkable that this optimum stiffness matrix exhibits negative stiffness for the springs linking NNN point masses. More specifically, as n increases, 0 > k(i,i+2) = -1/4 k(i,i+1) is the relation between the optimum NNN spring constant and the optimum NN spring constant. Such systems illustrate that the introduction of negative stiffness springs in some specific positions does in fact reduce the average response/input ratio. Numerical tables illustrating the main result are given.

关键词： nonlinear partial equations   Sobolev-type equations   exact solutions  

摘要： Since the second half of the twentieth century, wide studies of Sobolev-type equations are undertaken. These equations contain items that are derivatives with respect to time of the second order derivatives of the unknown function with respect to space variables. They can describe nonstationary processes in semiconductors, in plasm, phenomena in hydrodinamics and other ones. Notice that wide studies of qualitative properties of solutions of Sobolev-type equations exist. Namely, results about existence and uniqueness of solutions, their asymptotics and blow-up are known. But there are few results about exact solutions of Sobolev-type equations. There are books and papers about exact solutions of partial equations, but they are devoted mainly to classical equations, where the first or second order derivative with respect to time or the derivative with respect to time of the first order derivative of the unknown function with respect to the space variable is equal to a stationary expression. Therefore it is interesting to study exact solutions of Sobolev-type equations. In the present paper, a third order nonlinear partial equation containing a p-Laplacian is studied. Six classes of its exact solutions are built. They are expressed in terms of elementary functions, quadratures and special functions (solutions of some ordinary differential equations).

关键词： ammonia   quantum molecular dynamics   quantum Hamilton mechanics   tunneling dynamics   quantum trajectory  

摘要： Ammonia is a well-known example of a two-state system and must be described in quantum-mechanical terms. In this article, we will explain the tunneling phenomenon that occurs in ammonia molecules from the perspective of trajectory-based quantum dynamics, rather than the usual quantum probability perspective. The tunneling of the nitrogen atom through the potential barrier in ammonia is not merely a probability problem;there are underlying reasons and mechanisms explaining why and how the tunneling in ammonia can happen. Under the framework of quantum Hamilton mechanics, the tunneling motion of the nitrogen atom in ammonia can be described deterministically in terms of the quantum trajectories of the nitrogen atom and the quantum forces applied. The vibrations of the nitrogen atom about its two equilibrium positions are analyzed in terms of its quantum trajectories, which are solved from the Hamilton equations of motion. The vibration periods are then computed by the quantum trajectories and compared with the experimental measurements.

关键词： Condensed Matter Physics   Materials Science   general   Atomic   Molecular   Optical and Plasma Physics   Physics   Measurement Science and Instrumentation   Classical and Continuum Physics  

摘要： In this paper, a five-dimensional (5-D) two-memristor-based Colpitts system is constructed by introducing two ideal memristors with cosine memductance into the classical three-dimensional (3-D) Colpitts oscillator model. The proposed memristive Colpitts system possesses a plane equilibrium set and their stabilities are periodically varied on the memristor initial plane. Moreover, the stability distribution patterns are evolved with the change of system control parameters. The parameter- and initial-dependent behaviors are investigated by employing several numerical methods. The numerically simulated results indicate that the system trajectories are confined by several unstable stability regions around the initiating point, leading to the generation of parameter and initial offset boosting dynamics. Furthermore, a dimensionality reduction model with determined equilibrium is formulated through integral transformation of state variables. The parameter and initial offset boosting dynamics is reconstituted theoretically and expounded numerically. Finally, circuit synthesis and PSIM (power simulation) simulations are carried out to validate the abovementioned dynamical behaviors.

关键词： zinc oxide   quantum dot   polyvinylpyrrolidone   photodynamic therapy   photosensitizers   reactive oxygen species   nanoparticle   SW480 cancer cell  

摘要： Despite the numerous available treatments for cancer, many patients succumb to side effects and reoccurrence. Zinc oxide (ZnO) quantum dots (QDs) are inexpensive inorganic nanomaterials with potential applications in photodynamic therapy. To verify the photoluminescence of ZnO QDs and determine their inhibitory effect on tumors, we synthesized and characterized ZnO QDs modified with polyvinylpyrrolidone. The photoluminescent properties and reactive oxygen species levels of these ZnO/PVP QDs were also measured. Finally, in vitro and in vivo experiments were performed to test their photodynamic therapeutic effects in SW480 cancer cells and female nude mice. Our results indicate that the ZnO QDs had good photoluminescence and exerted an obvious inhibitory effect on SW480 tumor cells. These findings illustrate the potential applications of ZnO QDs in the fields of photoluminescence and photodynamic therapy.

关键词： Environmental trace evidence   Diatom analysis   Persistence   Clothing   Seasonal variability   Forensic ecology  

摘要： Freshwater diatoms offer valuable circumstantial forensic indicators, with a growing empirical research base aiming to identify and understand some of the spatial and temporal factors affecting their validity as trace evidence. Previous studies demonstrated that recipient surface characteristics, environmental variability, and individual species traits influence the initial transfer of freshwater diatoms to clothing. However, no previous research has sought to consider the impact of these and other variables on the persistence of transferred diatoms over investigative timescales. Therefore, this study aimed to identify and explore diatom retention dynamics on clothing following wear over time (hours to weeks). A series of experiments were designed to examine the impact of clothing material, seasonality, and time since wear (persistence interval) on the total number and species-richness of diatoms recovered and their relative retention (%) over time. Nine clothing swatches were immersed in a freshwater environment and then worn for one month in the spring. Subsamples were retrieved at regular intervals (e.g. 30 mins, 1 h, 8 h, 24 h) up to one month, diatoms were extracted using a H2O2 method, and examined microscopically. Three clothing materials were subject to the same experiment in the winter to generate a seasonal comparison. The results broadly identified three stages of diatom persistence on clothing - rapid initial loss, variable intermediate decay, and sustained long-term presence. Clothing material significantly impacted the number of diatoms recovered and retention dynamics over time, with complex interactions identified with seasonality. Although fewer diatoms were recovered in the winter, overall retention trends were consistent at the different times of year. The findings demonstrate that diatoms can be recovered from clothing, even weeks or months after an initial transfer, yielding a useful environmental trace indicator for forensic reconstructions ove

关键词： patterned ground   ice wedges   degradation   computer vision   graph analysis   remote sensing   permafrost   image processing  

摘要： In response to increasing Arctic temperatures, ice-rich permafrost landscapes are undergoing rapid changes. In permafrost lowlands, polygonal ice wedges are especially prone to degradation. Melting of ice wedges results in deepening troughs and the transition from low-centered to high-centered ice-wedge polygons. This process has important implications for surface hydrology, as the connectivity of such troughs determines the rate of drainage for these lowland landscapes. In this study, we present a comprehensive, modular, and highly automated workflow to extract, to represent, and to analyze remotely sensed ice-wedge polygonal trough networks as a graph (i.e., network structure). With computer vision methods, we efficiently extract the trough locations as well as their geomorphometric information on trough depth and width from high-resolution digital elevation models and link these data within the graph. Further, we present and discuss the benefits of graph analysis algorithms for characterizing the erosional development of such thaw-affected landscapes. Based on our graph analysis, we show how thaw subsidence has progressed between 2009 and 2019 following burning at the Anaktuvuk River fire scar in northern Alaska, USA. We observed a considerable increase in the number of discernible troughs within the study area, while simultaneously the number of disconnected networks decreased from 54 small networks in 2009 to only six considerably larger disconnected networks in 2019. On average, the width of the troughs has increased by 13.86%, while the average depth has slightly decreased by 10.31%. Overall, our new automated approach allows for monitoring ice-wedge dynamics in unprecedented spatial detail, while simultaneously reducing the data to quantifiable geometric measures and spatial relationships.