STABILITY CRITERIA IN TERMS OF TWO MEASURES FOR DELAY DIFFERENTIAL EQUATIONS

By using the variational Liapunov method, stability properties in terms of two measures for delay differential equations are discussed. In the case that the unperturbed systems are ordinary differential systems, employing auxiliary measure h*(t, x), criteria on nonuniform and uniform stability in terms of two measures for delay differential equations are established.

Stability and boundedness in terms of two measures for nonlinear impulsive control systems

In this paper we study stability and boundedness in terms of two measures for impulsive control systems. By using variational Lyapunov method, a new variational comparison principle and some criteria on stability and boundedness are obtained. An example is presented to illustrate the efficiency of proposed result.

Study on creep deformation and energy development of underground surrounding rock under four‐dimensional support

There is an urgent need to develop optimal solutions for deformation control of deep high‐stress roadways,one of the critical problems in underground engineering.The previously proposed four‐dimensional support(hereinafter 4D support),as a new support technology,can set the roadway surrounding rock under three‐dimensional pressure in the new balanced structure,and prevent instability of surrounding rock in underground engineering.However,the influence of roadway depth and creep deformation on the surrounding rock supported by 4D support is still unknown.This study investigated the influence of roadway depth and creep deformation time on the instability of surrounding rock by analyzing the energy development.The elastic strain energy was analyzed using the program redeveloped in FLAC3D.The numerical simulation results indicate that the combined support mode of 4D roof supports and conventional side supports is highly applicable to the stability control of surrounding rock with a roadway depth exceeding 520 m.With the increase of roadway depth,4D support can effectively restrain the area and depth of plastic deformation in the surrounding rock.Further,4D support limits the accumulation range and rate of elastic strain energy as the creep deformation time increases.4D support can effectively reduce the plastic deformation of roadway surrounding rock and maintain the stability for a long deformation period of 6 months.As confirmed by in situ monitoring results,4D support is more effective for the long‐term stability control of surrounding rock than conventional support.

Analysis of the SBP-SAT Stabilization for Finite Element Methods Part Ⅱ:Entropy Stability

In the hyperbolic research community,there exists the strong belief that a continuous Galerkin scheme is notoriously unstable and additional stabilization terms have to be added to guarantee stability.In the first part of the series[6],the application of simultaneous approximation terms for linear problems is investigated where the boundary conditions are imposed weakly.By applying this technique,the authors demonstrate that a pure continu-ous Galerkin scheme is indeed linearly stable if the boundary conditions are imposed in the correct way.In this work,we extend this investigation to the nonlinear case and focus on entropy conservation.By switching to entropy variables,we provide an estimation of the boundary operators also for nonlinear problems,that guarantee conservation.In numerical simulations,we verify our theoretical analysis.

Dynamic Analysis of Fractional-Order Fuzzy BAM Neural Networks with Delays in the Leakage Terms

In this paper, based on the theory of fractional-order calculus, we obtain some sufficient conditions for the uniform stability of fractional-order fuzzy BAM neural networks with delays in the leakage terms. Moreover, the existence, uniqueness and stability of its equilibrium point are also proved. A numerical example is presented to demonstrate the validity and feasibility of the proposed results.

Effects of anti-pull ties on the bearing behaviors of shallow tunnel-type anchorages in soft rock

Tunnel-type anchorages(TTAs)installed in human gathering areas are characterized by a shallow burial depth,and in many instances,they utilize soft rock as the bearing stratum.However,the stability control measures and the principle of shallow TTAs in soft rock have not been fully studied.Hence,a structure suitable for improving the stability of shallow TTAs in soft rock strata,named the anti-pull tie(APT),was added to the floor of the back face.Physical tests and numerical models were established to study the influence of the APT on the load transfer of TTAs,the mechanical response of the surrounding rock,the stress distribution of the interface,and the failure model.The mechanical characteristics of APTs were also studied.The results show that the ultimate bearing capacity of TTAs with an APT is increased by approximately 11.8%,as compared to the TTAs without an APT.Also,the bearing capacity of TTAs increases approximately linearly with increasing height,width,length,and quantity of APTs,and decreases approximately linearly with increasing distance from the back face and slope angle of the tie slope.The normal squeezing between the tie slope and the surrounding rock increases the shear resistance of the interface and expands the range of the surrounding rock participating in bearing sharing.Both tension and compression zones exist in the APT during loading.The tension zone extends from the tie toe to the tie bottom along the tie slope.The range of the tie body tension zone constantly expands to the deep part of the APT with an increasing load.The peak tensile stress value is located at the tie toe.The distribution of compressive stress in the tie body is the largest at the tie top,followed by the tie slope,and then the tie bottom.

Climate change and permafrost stability in the eastern Canada Cordillera:The results of 33 years of measurements

Over the last 33 years,a network of climate stations has been set up at high altitude mountain permafrost sites from Plateau Mountain near Claresholm,Alberta,north to Sheldon Lake on the North Canol Road in the Yukon.Taken together with the data from the US National Weather Service and the Canadian Atmospheric Environment Service,the results indicate a cooling of mean annual air temperature south of Calgary,no significant change in Calgary,a slight warming at Jasper,and a major warming at Summit Lake,west of Fort Nelson.In contrast,the south eastern and central Yukon show only a minor warming trend that lies well within the limits of a sixty-year record measured by the Canadian Atmospheric Environment Service.Along the Mackenzie valley and on the North Slope of Alaska,the mean annual air temperature is rising.Permafrost is aggrading on Plateau Mountain,degrading at Summit Lake,and appears to be stable in southern Yukon and southern Alaska.This is in contrast to the warming occurring on the Arctic coastal plain and along the Mackenzie valley.It therefore appears that changes in climate vary considera-bly from place to place,and even where warming may occur,it may not continue indefinitely.There has been a northward shift of the arctic front due to a weakening of air pressure in the Yukon and Alaska relative to the continental tropical(cT) and maritime polar(mT) air masses to the south.Any actual changes that may be occurring appear to undergo amplification along the Mackenzie valley and Arctic coastal plain and reduction by buffering in the interior Yukon and Alaskan mountains,a result of mi-cro-environmental factors.Continued,careful monitoring of the climate is required and needs to be expanded in the National Parks in the mountains in order to provide data on the changes that may be taking place.Such measurements can provide a sound basis for interpreting ecological and other climate-related data.The existing climate models are not working satisfactorily because we do not know enough about the causes and processes involved in climate change.Improved results can indicate where best to site structures such as pipelines so as to minimize maintenance costs.Models may also help explain why certain areas such as Beringia,which saw reduced climate change,acted as important refugia during the glaciations.

Information Security Evaluation of Industrial Control Systems Using Probabilistic Linguistic MCDM Method

Industrial control systems(ICSs)are widely used in various fields,and the information security problems of ICSs are increasingly serious.The existing evaluation methods fail to describe the uncertain evaluation information and group evaluation information of experts.Thus,this paper introduces the probabilistic linguistic term sets(PLTSs)to model the evaluation information of experts.Meanwhile,we propose a probabilistic linguistic multi-criteria decision-making(PL-MCDM)method to solve the information security assessment problem of ICSs.Firstly,we propose a novel subscript equivalence distance measure of PLTSs to improve the existing methods.Secondly,we use the Best Worst Method(BWM)method and Criteria Importance Through Inter-criteria Correlation(CRITIC)method to obtain the subjective weights and objective weights,which are used to derive the combined weights.Thirdly,we use the subscript equivalence distance measure method and the combined weight method to improve the probabilistic linguistic Visekriterijumska Optimizacija I Kompromisno Resenje(PL-VIKOR)method.Finally,we apply the proposed method to solve the information security assessment problem of ICSs.When comparing with the existing methods such as the probabilistic linguistic Tomada deDecisão Iterativa Multicritério(PL-TODIM)method and probabilistic linguistic Technique for Order Preference by Similarity to Ideal Solution(PL-TOPSIS)method,the case example shows that the proposed method can provide more reasonable ranking results.By evaluating and ranking the information security level of different ICSs,managers can identify problems in time and guide their work better.

Network Structure-Based Critical Bus Identification for Power System Considering Line Voltage Stability Margin

Voltage security assessment of power system is an important and all-inclusive aspect of power system operation and preventive control actions. Fast and accurate detection of critical components of the power system is one essential approach for preventing the occurrence of voltage collapse phenomenon. Over the years, several approaches for voltage collapse point identification and prevention have been widely studied using the continuous power flow approach, minimum singular value of eigenvalues, Jacobian matrices, and power transfer concept. In this work, critical node (bus) identification based on power system network structure is proposed. In this approach, the power system is treated as a multidimensional graph with several nodes (buses) linked together by the transmission lines. An improved line voltage stability margin estimator which is based on active and reactive power changes in a power system is used as the weight of each transmission line and an adaptation of the degree of centrality approach is used to determine the criticality of the system buses. A comparative analysis with other bus voltage stability indices is presented to test the suitability of the proposed approach using the IEEE 14, 30, 57 and 118 bus test systems.

Estimation of unloading relaxation depth of Baihetan Arch Dam foundation using long-short term memory network

The unloading relaxation caused by excavation for construction of high arch dams is an important factor influencing the foundation’s integrity and strength.To evaluate the degree of unloading relaxation,the long-short term memory(LSTM)network was used to estimate the depth of unloading relaxation zones on the left bank foundation of the Baihetan Arch Dam.Principal component analysis indicates that rock charac-teristics,the structural plane,the protection layer,lithology,and time are the main factors.The LSTM network results demonstrate the unloading relaxation characteristics of the left bank,and the relationships with the factors were also analyzed.The structural plane has the most significant influence on the distribution of unloading relaxation zones.Compared with massive basalt,the columnar jointed basalt experiences a more significant unloading relaxation phenomenon with a clear time effect,with the average unloading relaxation period being 50 d.The protection layer can effectively reduce the unloading relaxation depth by approximately 20%.

Global Stability of SEIRS Model in Epidemiology

In this article, an infectious model with saturation effect is considered. By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Muldowney and Micheal Li, we study globally stable problem of the model.

Long-term inorganic plus organic fertilization increases yield and yield stability of winter wheat

An understanding of wheat yield and yield stability response to fertilization is important for sustainable wheat production. A 36-year long-term fertilization experiment was employed to evaluate the yield and yield stability of winter wheat. Five fertilization regimes were compared,including(1) CK, no fertilizer;(2) NPK, inorganic fertilizer only;(3) O, organic fertilizer only;(4)NPKO, 50% of NPK plus 50% of O, and(5) HNPKO, 80% of NPK plus 80% of O. The greatest yield increase was recorded in HNPKO, followed by NPKO, with O producing the lowest mean yield increase. Over the 36 years, the rate of wheat yield increase in fertilized plots ranged from95.31 kg ha-1 year-1 in the HNPKO to 138.65 kg ha-1 year-1 in the O. Yield stability analysis using the additive main effects and multiplicative interactions(AMMI) method assigned 62.3%, 26.3%,and 11.4% of sums of squares to fertilization effect, environmental effect, and fertilization ×environment interaction effect, respectively. The combination of inorganic and organic fertilization(NPKO and HNPKO) appeared to produce more stable yields than O or NPK, with lower coefficients of variation and AMMI stability value. However, wheat grown with O seemed to be the most susceptible to climate change and the least productive among the fertilized plots.Significant correlations of grain yield with soil properties and with mean air temperature were observed. These findings suggest that inorganic + organic fertilizer can increase wheat yield and its stability by improvement in soil fertility and reduction in variability to climate change.

Thermal Stability and Thermal Decomposition Kinetics of 1-Butyl-3-methylimidazolium Dicyanamide

Thermal stability and thermal decomposition kinetics of 1-butyl-3-methylimidazolium dicyanamide ([bmin+][N(CN) ]2-) were investigated using both isothermal and non-isothermal thermogravimetric analyses (TGA) under high pure nitrogen as carrier gas. The long-term thermogravimetric studies revealed that the highest temperature used should be 110 °C, at which [bmin+][N(CN)2-] lost less than 10% by mass in 10 hours. The non-isothermal activation energy values determined using Friedman and ASTM methods were (150±13) and (147±2) kJ·mol –1 , respectively. Multivariate non-linear-regression methods showed that expanded Fn and CnB models were the best fit models with highest correlation coefficient of 0.9994, and the apparent activation energies were consistent with iso-conversional methods.

THE STABILITY OF INTERVAL MATRICES

In this paper,the authors discuss the measure of interval matrices and its applications.The authors give a new method of the stability of interval matrices and get some sufficient and neessary conditions for it.These results are contained in work [4-9].

Ground stability of new surface buildings erected on site above worked-out area

The subsided area caused by mining is expanding gradually in coal mining areas. In order to occupy less or no farmland, many mining areas are constructing or intend to erect new buildings (structures) on the ground sites above the worked-out areas. The long-term safety of the new buildings is of great importance. This matter should be, therefore, handled with great care. Following an analysis of the different conditions of the worked-out areas, and the characteristics of the failure of different types of worked-out areas and their overlying strata, the cause for the occurrence of residual deformation of the surface above the worked-out area was explained. The techniques for (evaluating) the stability of ground site for erecting new buildings above worked-out area, and the technical measures for protecting such buildings were proposed. The ground stability evaluation techniques were introduced by reference to specific cases.

EXPONENTIAL STABILITY OF INTERVAL DYNAMICAL SYSTEM WITH MULTIDELAY

Using the matrix measure and delay differential inequality, the sufficient conditions were obtained for exponential stability of interval dynamical system with multidelay. These conditions are an improvement and extension of the results achieved in earlier papers presented by LIAO, LIU, ZHANG, SUN, et al.

Examine the Stability Margin of Cascade Circuits

This paper proposes an engineering approach to examine the stability margin of cascade circuits. The proposed measurement injects an external perturbation current into the cascade interface and measures the load-side response current. The system stability margin can be figured out by comparing the magnitudes of the perturbation current and the response current. The proposed measurement is strictly derived in theory, implemented with details, and demonstrated by experiment.