THE CHARACTERISTIC POLYNOMIAL ANDEIGENVALUES OF FINILE RIODAN MATRIXTHE CHARACTERISTIC POLYNOMIAL ANDEIGENVALUES OF FINILE RIODAN MATRIX

In this paper we deal with the characteristic polynomial of finite Riodan matix. We giveseveral forms of its explicit expressions. Its applications to combinatorial identities, specially to F-Lidentities, are stated.

E-characteristic Polynomials of Real Rectangular Tensor

By the resultant theory, the E-characteristic polynomial of a real rectangular tensor is defined. It is proved that an E-singular value of a real rectangular tensor is always a root of the E-characteristic polynomial. The definition of the regularity of square tensors is generalized to the rectangular tensors, and in the regular case, a root of the Echaracteristic polynomial of a special rectangular tensor is an E-singular value of the rectangular tensor. Moreover, the best rank-one approximation of a real partially symmetric rectangular tensor is investigated.

Trace Formulae of Characteristic Polynomial and Cayley-HamUton's Theorem, and Applications to Chiral Perturbation Theory and General Relativity

由使用组合数学，我们为典型多项式系数的复发关系给一个新证明，并且我们进一步获得明确的表情系数顺序的通用术语，它与明确地给的所有系数产出凯利·哈密尔顿的定理的踪迹公式。这暗示一个副产品，为任何有限维的矩阵的决定因素的完全的表情以它的连续力量的踪迹。并且我们讨论一些他们的应用到 chiral 不安理论和一般相关性。

Research on the Stability Analysis Method of DC Microgrid Based on Bifurcation and Strobe Theory

During the operation of a DC microgrid,the nonlinearity and low damping characteristics of the DC bus make it prone to oscillatory instability.In this paper,we first establish a discrete nonlinear system dynamic model of a DC microgrid,study the effects of the converter sag coefficient,input voltage,and load resistance on the microgrid stability,and reveal the oscillation mechanism of a DC microgrid caused by a single source.Then,a DC microgrid stability analysis method based on the combination of bifurcation and strobe is used to analyze how the aforementioned parameters influence the oscillation characteristics of the system.Finally,the stability region of the system is obtained by the Jacobi matrix eigenvalue method.Grid simulation verifies the feasibility and effectiveness of the proposed method.

Lattices Generated by Joins of the Flats in Orbits under Finite Affine-singular Symplectic Group and its Characteristic Polynomials

Let ASG（2v ＋ l, v; Fq） be the （2v ＋l）-dimensional affine-singular symplectic space over the finite field Fq and ASp2v＋l,v（Fq） be the affine-singular symplectic group of degree 2v ＋ l over Fq. Let O be any orbit of flats under ASp2v＋l,v（Fq）. Denote by J the set of all flats which are joins of flats in O such that O LJ and assume the join of the empty set of flats in ASG（2v ＋ l, v;Fq） is φ. Ordering LJ by ordinary or reverse inclusion, then two lattices axe obtained. This paper firstly studies the inclusion relations between different lattices, then determines a characterization of flats contained in a given lattice LJ, when the lattices form geometric lattice, lastly gives the characteristic polynomial of LJ.

RITT-WU'S CHARACTERISTIC SET METHOD FOR ORDINARY DIFFERENCE POLYNOMIAL SYSTEMS WITH ARBITRARY ORDERING

In this paper, a Ritt-Wu＇s characteristic set method for ordinary difference systems is proposed, which is valid for any admissible ordering. New definition for irreducible chains and new zero decomposition algorithms are also proposed.

Spatiotemporal Characteristics of Rural Labor Migration in China: Evidence from the Migration Stability under New-type Urbanization

Although the factors affecting rural-to-urban migration have been discussed and analyzed in detail, few studies have examined the spatiotemporal dynamic characteristics of rural migrants’ employment and working-cities in the post-immigrate era, which is essential for the citizenization and social integration of new-type urbanization in China. This study uses survey data from rural migration laborers across the eastern, central, and western China to construct a comprehensive labor migration stability index, and compares the determinants of the migration stability of rural labor among cities and industries using Geodetector. The results are as follows: 1) Compared with the midwestern cities, eastern cities have attracted younger and more skilled rural labor, and industries with higher technical content have higher migration stability among rural laborers. 2) Rural laborers more often adapt to changes by changing employment instead of changing working-cities. 3) The individual experiences of rural laborers and urban characteristics have significant impacts on the stability of migration, and family and societal guanxi(Chinese interpersonal relationships) enhance migration stability. 4) A unified labor market and convenient transportation have somewhat slowed industrial transfers and labor backflow. This study enhances our understanding of the roles of industrial transfer and new-type urbanization in shaping the labor geography landscape and provides policy implications for the promotion of people-oriented urbanization.

Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay

One of challenging issues on stability analysis of time-delay systems is how to obtain a stability criterion from a matrix-valued polynomial on a time-varying delay.The first contribution of this paper is to establish a necessary and sufficient condition on a matrix-valued polynomial inequality over a certain closed interval.The degree of such a matrix-valued polynomial can be an arbitrary finite positive integer.The second contribution of this paper is to introduce a novel LyapunovKrasovskii functional,which includes a cubic polynomial on a time-varying delay,in stability analysis of time-delay systems.Based on the novel Lyapunov-Krasovskii functional and the necessary and sufficient condition on matrix-valued polynomial inequalities,two stability criteria are derived for two cases of the time-varying delay.A well-studied numerical example is given to show that the proposed stability criteria are of less conservativeness than some existing ones.

Circular β ensembles,CMV representation,characteristic polynomials

In this note we first briefly review some recent progress in the study of the circular β ensemble on the unit circle,where β > 0 is a model parameter.In the special cases β = 1,2 and 4,this ensemble describes the joint probability density of eigenvalues of random orthogonal,unitary and sympletic matrices,respectively.For general β,Killip and Nenciu discovered a five-diagonal sparse matrix model,the CMV representation.This representation is new even in the case β = 2;and it has become a powerful tool for studying the circular β ensemble.We then give an elegant derivation for the moment identities of characteristic polynomials via the link with orthogonal polynomials on the unit circle.

Effects of pH on rheological characteristics and stability of petroleum coke water slurry

In this study, the effects of pH on slurrying properties of petroleum coke water slurry（PCWS） were investigated. The slurrying concentration, rheological characteristics and stability of PCWS were studied with four different types of additives at pH varying from 5 to 11.The results showed that the slurrying concentration, rheological characteristics and stability of PCWS all increased at first and then decreased with increasing pH from 5 to 11,and a pH of around 9 was found to be the most favorable acid–alkali environment to all these three slurrying properties. It was also indicated that only in a moderate alkaline environment can the additives be active enough to react with particle surfaces sufficiently to obtain good slurrying concentration and form a stable three-dimensional network structure, which can support strong pseudoplastic characteristics and good stability. An acid environment was a very unfavorable factor to the slurrying properties of PCWS.

THE CHARACTERISTIC POLYNOMIAL OF A GEOMETRIC LATTICE IN SYMPLECTIC GEOMETRY OVER FINITE FIELDS

Let F be a field and V= Vn（F）={（a1,…, an）|ai∈F} be the row vector space of finite dimension n over F. Let be a finite set ofsubspaces of Vsuch that U=（0）. And let L= L（（?）） be the set of intersections of dements of. Partial order L by reverse inclusion has V as its minimal element and as its set of atoms. We denote the partial order-

Sphere-cone-polynomial special window with good aberration characteristic

Optical windows with external surfaces shaped to satisfy operational environment needs are known as special windows. A novel special window, a sphere-cone-polynomial （SCP） window, is proposed. The formulas of this window shape are given. An SCP MgF2 window with a fineness ratio of 1.33 is designed as an example. The field-of-regard （FOR） angle is ±75°. From the window system simulation results obtained with the calculated fluid dynamics （CFD） and optical design software, we find that compared to the conventional window forms, the SCP shape can not only introduce relatively less drag in the airflow, but also have the minimal effect on imaging. So the SCP window optical system can achieve a high image quality across a super wide FOR without adding extra aberration correctors. The tolerance analysis results show that the optical performance can be maintained with a reasonable fabricating tolerance to manufacturing errors.

Characteristic polynomial and higher order traces of third order three dimensional tensors

Eigenvalues of tensors play an increasingly important role in many aspects of applied mathematics. The characteristic polynomial provides one of a very few ways that shed lights on intrinsic understanding of the eigenvalues. It is known that the characteristic polynomial of a third order three dimensional tensor has a stunning expression with more than 20000 terms, thus prohibits an effective analysis. In this article, we are trying to make a concise representation of this characteristic polynomial in terms of certain basic determinants. With this, we can successfully write out explicitly the characteristic polynomial of a third order three dimensional tensor in a reasonable length. An immediate benefit is that we can compute out the third and fourth order traces of a third order three dimensional tensor symbolically, which is impossible in the literature.

Stability characteristics of ring-stiffened cylindrical shells under different longitudinal and transverse external pressures

Because ring-stiffened cylindrical shell structures have many merits, they are widely used in many areas. However, as the strength of steel increase continuously, ensuring of the structure stability is becoming more and more important. Therefore, it is necessary to carry on a more particular analysis. Based on the understanding and analysis of the characteristics of stability for a ring-stiffened cylindrical shell under uniform external pressure and under external single pressure, the characteristics under different cross uniform external pressures are analyzed, and the regularity of it is also gotten. The curve of stability given various geometrical parameters under different cross uniform external pressures is protracted by the analysis of the theory. The conclusion not only improves the theory structural mechanics, it also was important effects on engineering calculation and design.

STABILITY AND STRICT POSITIVE REALNESS OF CONVEX POLYTOPES OF INTERVAL POLYNOMIALS

For an uncertain system described by convex combination of interval polynomials, its Hurwitz-stability can be guaranteed by, certain subset composed of vertices and edges. Furthermore, the testing set does not increase when the order of given system increases.

Characteristics of Sb6Te4/VO2 Multilayer Thin Films for Good Stability and Ultrafast Speed Applied in Phase Change Memory

The Sb6 Te4/VO2 multilayer thin films are prepared by magnetron sputtering and the potential application in phase change memory is investigated in detail. Compared with Sb6 Te4, Sb6 Te4/VO2 multilayer composite thin films have higher phase change temperature and crystallization resistance, indicating better thermal stability and less power consumption. Also, Sb6 Te4/VO2 has a broader energy band of 1.58 eV and better data retention （125℃ for 103/）. The crystallization is suppressed by the multilayer interfaces in Sbf Te4/VO2 thin film with a smaller rms surface roughness for Sbf Te4/VO2 than monolayer Sb4Te6. The picosecond laser technology is applied to study the phase change speed. A short crystallization time of 5.21 ns is realized for the Sb6Te4 （2nm）/VO2 （8nm） thin film. The Sb6 Te4/VO2 multilayer thin film is a potential and competitive phase change material for its good thermal stability and fast phase change speed.

Chebyshev Polynomial-Based Analytic Solution Algorithm with Efficiency, Stability and Sensitivity for Classic Vibrational Constant Coefficient Homogeneous IVPs with Derivative Orders n, n-1, n-2

The Chebyshev polynomials are harnessed as functions of the one parameter of the nondimensionalized differential equation for trinomial homogeneous linear differential equations of arbitrary order n that have constant coefficients and exhibit vibration. The use of the Chebyshev polynomials allows calculation of the analytic solutions for arbitrary n in terms of the orthogonal Chebyshev polynomials to provide a more stable solution form and natural sensitivity analysis in terms of one parameter and the initial conditions in 6n + 7 arithmetic operations and one square root.

Increasing grain weight and yield stability by increasing pre-heading non-structural carbohydrate reserves per spikelet in short-growth duration rice

Rice yield stability is a breeding goal,particularly for short-growth duration rice,but its underlying mechanisms remain unclear.In an attempt to identify the relationship between yield stability and source–sink characteristics in short-growth duration rice,a field experiment was conducted at three sites(Yueyang,Liuyang,and Hengyang)in 2021 and 2022.This study compared yield,yield components,source–sink characteristics,and their stability between two stable-yielding short-growth duration rice cultivars,Zhongzao 39(Z-39)and Lingliangyou 268(L-268),and two unstable-yielding short-growth duration rice cultivars,Zhongjiazao 17(Z-17)and Zhuliangyou 819(Z-819).The stability of agronomic parameters was represented by the coefficient of variation(CV).The respective CVs of yield in Z-17,Z-819,Z-39,and L-268 were 10.2%,10.1%,4.5%,and 5.7%in 2021 and 19.7%,15.0%,5.4%,and 6.5%in 2022.The respective CVs of grain weight were 6.3%,5.7%,3.4%,and 4.5%in Z-17,Z-819,Z-39,and L-268 in 2021,and 8.1%,6.3%,1.5%,and 0.8%in 2022.The mean source capacity per spikelet and pre-heading non-structural carbohydrate reserves per spikelet(NSC_(pre))were 7%–43%and7%–72%lower in Z-819 and Z-17than in L-268 and Z-39 in 2021 and 2022.The mean quantum yield of photosystem II photochemistry of leaf,leaf area index,and specific leaf weight of L-268 and Z-39 were higher than those of Z-819 and Z-17 at the heading stage.This study suggests that high NSC_(pre),caused by great leaf traits before heading,increases source capacity per spikelet and its stability,thereby increasing the stability of grain weight and yield.Increasing NSC_(pre)is critical for achieving grain weight and yield stability in short-growth duration rice.

Physical modeling of long-term dynamic characteristics of the subgrade for medium-low-speed maglevs

To investigate the dynamic characteristics and long-term dynamic stability of the new subgrade structure of medium-low-speed(MLS)maglevs,cyclic vibration tests were performed under natural and rainfall conditions,and the dynamic response of the subgrade structure was monitored.The dynamic response attenuation characteristics along the depth direction of the subgrade were compared,and the distribution characteristics of the dynamic stress on the surface of the subgrade along the longitudinal direction of the line were analyzed.The critical dynamic stress and cumulative deformation were used as indicators to evaluate the long-term dynamic stability of the subgrade.Results show that water has a certain effect on the dynamic characteristics of the subgrade,and the dynamic stress and acceleration increase with the water content.With the dowel steel structure set between the rail-bearing beams,stress concentration at the end of the loaded beam can be prevented,and the diffusion distance of the dynamic stress along the longitudinal direction increases.The dynamic stress measured in the subgrade bed range is less than 1/5 of the critical dynamic stress.The postconstruction settlement of the subgrade after similarity ratio conversion is 3.94 mm and 7.72 mm under natural and rainfall conditions,respectively,and both values are less than the 30 mm limit,indicating that the MLS maglev subgrade structure has good long-term dynamic stability.

Influence of the characteristics of fault gouge on the stability of a borehole wall

How to find more effective way to stabilize the borehole wall in the fault gouge section is the key technical challenge to control the stability of the borehole wall in the Wenchuan fault gouge section during the process of core drilling.Here we try to describe the characters of deep fault gouge in fracture zones from the undisturbed fault gouge samples which are obtained during the core drilling.The XRay Diffraction(XRD),X-Ray Fluorescence(XRF) and Scanning Electron Microscope(SEM) provided the detailed information of the fault gouge's microscopic characteristics on the density,moisture content,expansibility,dispersity,permeability,tensile strength and other main physical-mechanical properties.Based on these systematic experimental studies above and analysis of the fault gouge instability mechanism,a new technical procedure to stabilize the borehole wall is proposed — a low water and a low loss low permeability drilling fluid system that consists of 4% clay + 0.5% CMC-HV + 2% S-1 + 3%sulfonated asphalt + 1% SMC + 0.5% X-1 + 0.5% T type lubricant + barite for core drilling in fault gouge sections.