Continuum limit for lattice Schrödinger operators

We study the behavior of solutions of the Helmholtz equation [Formula: see text] on a periodic lattice as the mesh size [Formula: see text] tends to 0. Projecting to the eigenspace of a characteristic root [Formula: see text] and using a gauge transformation associated with the Dirac point, we show that the gauge transformed solution [Formula: see text] converges to that for the equation [Formula: see text] for a continuous model on [Formula: see text], where [Formula: see text]. For the case of the hexagonal and related lattices, in a suitable energy region, it converges to that for the Dirac equation. For the case of the square lattice, triangular lattice, hexagonal lattice (in another energy region) and subdivision of a square lattice, one can add a scalar potential, and the solution of the lattice Schrödinger equation [Formula: see text] converges to that of the continuum Schrödinger equation [Formula: see text].

Criteria for minimization of spectral abscissa of time-delay systems

Spectral abscissa (SA) is defined as the real part of the rightmost characteristic root(s) of a dynamical system, and it can be regarded as the decaying rate of the system, the smaller the better from the viewpoint of fast stabilization. Based on the Puiseux series expansion of complex-valued functions, this paper shows that the SA can be minimized within a given delay interval at values where the characteristic equation has repeated roots with multiplicity 2 or 3. Four sufficient conditions in terms of the partial derivatives of the characteristic function are established for testing whether the SA is minimized or not, and they can be tested directly and easily.

Big Data Business Actual Analysis: Stock Price Prediction Based on Time Series Model

This paper selects the daily closing price data of the Shanghai Composite Index from January 1, 2016 to December 31, 2017, excluding holidays, and preprocesses the data. After taking the logarithm and converting it into the rate of return data, the first-order difference is performed to make it into a stable time series, and then the ARMA(p,q) model is constructed. Through parameter significance test, residual test and characteristic root test, according to the minimum principle of AIC, the optimal model is finally determined to be ARMA(2,5) of sparse coefficient, and the expression of the model is obtained. The GARCH(1,1) model is established for the residual of ARMA(2,5), and the model expression is obtained. In order to directly predict the return rate of the Shanghai Composite Index, the ARIMA(2,1,5) model of the sparse coefficient is constructed for the return rate of the Shanghai Composite Index, and the model expression is obtained. By predicting the Shanghai Composite Index return data on January 2, 2018, it is found that the prediction error of the model is small, and it can be used for subsequent predictions.

Ni-Doped ZnO Thin Films: Deposition, Characterization and Photocatalytic Applications

Root like structured Ni-doped zinc oxide [Zn(1-x)NixO (x = 0.09)] thin films were deposited on a non-conducting glass substrate by indigenously developed spray pyrolysis system at optimized substrate hotness of 573±5 K. Thus obtained Ni-doped ZnO thin films were characterized by UV-visible spectroscopy, X-ray diffraction (XRD), scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), Atomic Force Microscopy (AFM). XRD result revealed that Ni-doped ZnO has a polycrystalline nature with a hexagonal wurtzite structure. For pure ZnO and Ni-doped ZnO thin films, the particle sizes were 60.9 and 53.3 nm while lattice strain values were 1.56×10−3 and 1.14×10−3, respectively. The film surface showed characteristic root-like structure as observed by the SEM. It was observed that the Ni-doped ZnO thin films were grown in high density along with more extent of branching as compared to pure ZnO thin films but retained the root-like morphologies, however, the branches were more-thinner and of shorter lengths. AFM analysis showed that the surface grains of the Ni-doped samples are homogeneous with less RMS roughness values compared with the undoped ZnO samples. The photocatalytic activity of the prepared thin films was evaluated by the degradation of methyl orange (MO) dye under UV light irradiation. Pure ZnO and Ni-doped ZnO thin films took 150 min and 100 min to degrade about 60% MO dye, respectively.

Stability analysis of connected vehicles with V2V communication and time delays: CTCR method via Bézout’s resultant

This paper is focused on the distributed control of connected vehicles via vehicle-to-vehicle (V2V) communication. A mixed predecessor following topology with a virtual leader under constant time headway policy is analysed in case of communication and input delays. The longitudinal dynamics of each vehicle in the platoon is represented by a third-order linear model. Unavoidable communication and input delays are introduced into the platoon structure which converts the characteristic equation of the system into a transcendental type. The stability regions of the system in delay space are obtained by utilizing the cluster treatment of characteristic root (CTCR) method in the case of single and multiple time delays. A new Bézout resultant matrix-based approach is proposed to determine the kernel and offspring hypersurfaces of the CTCR method. The determination of these kernel and offspring hypersurfaces becomes computational costly as the number of vehicles increases in the platoon due to the increasing degree of characteristic equation. However, the proposed method reduces the dimensions of the coefficient matrix which is created by using the characteristic equation. It is concluded that the proposed method confirms the internal stability of the connected vehicles with both generic information flow topologies and formation between vehicles under single and multiple time delays. Thereafter, a local string stability definition is proposed in terms of spacing errors. Sufficient conditions to obtain string stability under mixed predecessor following topology for the existence and nonexistence of time delay are given. Finally, several simulation studies with different scenarios are conducted to display the effectiveness of the proposed model and method for internal and string stabilities.

Reduction to a Canonical Form of a Third-Order Polynomial Matrix with One Characteristic Root by means of Semiscalarly Equivalent Transformations

For the selected class of polynomial matrices of order three with one characteristic root with respect to the transformation of semiscalar equivalence, special triangular forms are established. The theorems of their uniqueness are proved. This gives reason to consider such canonical forms.

Root system architecture analysis in Mesembryanthemum crystallinum (ice plant) seedlings reveals characteristic root halotropic response

One of the major environmental stress factors that affect root growth is salinity. Arabidopsis thaliana, a glycophyte, shows halotropism, whereby it alters the direction of root growth in a non-gravitropic pattern to evade high soil salinity. Asymmetric auxin distribution regulated by the relocation of auxin-efflux carrier proteins is a key cellular event in the halotropic response. However, there are no reports of halotropism in halophytes. Here, we investigated root growth traits in Mesembryanthemum crystallinum, ice plant, under high salinity conditions. We hypothesized that ice plant roots would show halotropic responses different from those of Arabidopsis. Notably, similar to halotropism observed in Arabidopsis, ice plant roots showed continuous root bending under salinity stress. However, the root elongation rate did not change in ice plants. Expression analyses of several genes revealed that auxin transport might be partially involved in ice plant halotropism. This study enhances our understanding of halophyte root adaptation to high salinity stress.

Dynamic cell wall modifications in brassicas during clubroot disease

Biotic interactions of plants and microbial pathogens can cause drastic changes in cell wall composition in response to developmental reprogramming caused as consequence of an infection. Clubroot disease, caused by the biotrophic plant pathogen Plasmodiophora brassicae (Phytomyxea, Rhizaria), is the economically most important disease of Brassica crops worldwide. The disease is best known by the characteristic hypertrophied roots (root galls, clubroots). Amongst a series of physiological changes of the host tissue, the formation of the characteristic root galls leads to cell wall modification and reorganization. Cell wall chemistry and the hosts genetic repertoire are discussed to play a role in the resilience of plants against clubroot disease. Plant cells infected with P. brassicae are markedly enlarged, and look very differently from uninfected, healthy cells. Here we systematically review cell wall related processes that lead to the typical clubroot phenotype and provide novel insights how P. brassicae uses these modifications to benefit its own development. An infection with P. brassicae impacts on nearly all cell wall related processes, but all alterations are meaningful for successful growth and development of P. brassicae. Processes related to cell wall stability and rigidity (e.g. cellulose, pectin or lignin synthesis) are down-regulated, while cell wall degrading enzymes or processes that increase the flexibility of the host cell wall (e.g. expansin) are up-regulated. The here presented findings indicate that P. brassicae weakens the structural stability of its host cell while it increases its elasticity, which in consequence allows P. brassicae to grow bigger and ultimately to develop more resting spores. Consequently, the understanding of the modification of the host cell wall is important for the formation of the characteristic root galls but also to better understand clubroot disease.

The mechanism: how dental resorptions occur in ameloblastoma

ABSTRACT Knife-edge or blunt root resorptions characterize ameloblastomas and are pathognomonic for this tumor, because they differentiate ameloblastomas from simple bone cysts, odontogenic keratocysts and nasopalatine duct cysts, which do not lead to resorption of involved teeth. Despite the very high frequency and importance of these characteristics for a differential diagnosis, a microscopic examination should also be conducted before defining the diagnosis and the treatment plan for these cases. This paper describes a six-step hypothesis to explain the mechanism by which ameloblastomas promote the characteristic root resorptions found in association with these benign epithelial tumors, which have a fibrous capsule formed by islands and epithelial cords that mimic the dental lamina, invade neighboring tissues and release mediators (IL-1, EGF) of tooth and root resorption. This hypothesis may be one more explanation for the tooth resorptions sometimes found in orthodontic records, and may help differentiate the root resorptions that are specific to the orthodontic practice.

Canonical Form of Reduced 3-by-3 Matrix with One Characteristic Root and with Some Zero Subdiagonal Elements

A canonical form for a reduced matrix of order 3 with one characteristic root and with some zero subdiagonal elements is constructed. Thus, the problem of classification with respect to semiscalar equivalence of a selected set of polynomial matrices is solved.