A direct proof of uniqueness of square-root of a positive semi-definite tensor

Understanding of the basic properties of the positive semi-definite tensor is a prerequisite for its extensive applications in theoretical and practical fields, especially for its square-root. Uniqueness of the square-root of a positive semi-definite tensor is proven in this paper without resorting to the notion of eigenvalues, eigenvectors and the spectral decomposition of the second-order symmetric tensor.

SNWPM:A Siamese Network Based Wireless Positioning Model Resilient to Partial Base Stations Unavailable

Artificial intelligence(AI)models are promising to improve the accuracy of wireless positioning systems,particularly in indoor environments where unpredictable radio propagation channel is a great challenge.Although great efforts have been made to explore the effectiveness of different AI models,it is still an open problem whether these models,trained with the data collected from all base stations(BSs),could work when some BSs are unavailable.In this paper,we make the first effort to enhance the generalization ability of AI wireless positioning model to adapt to the scenario where only partial BSs work.Particularly,a Siamese Network based Wireless Positioning Model(SNWPM)is proposed to predict the location of mobile user equipment from channel state information(CSI)collected from 5G BSs.Furthermore,a Feature Aware Attention Module(FAAM)is introduced to reinforce the capability of feature extraction from CSI data.Experiments are conducted on the 2022 Wireless Communication AI Competition(WAIC)dataset.The proposed SNWPM achieves decimeter-level positioning accuracy even if the data of partial BSs are unavailable.Compared with other AI models,the proposed SNWPM can reduce the positioning error by nearly 50%to more than 60%while using less parameters and lower computation resources.

Existence for positive steady states of an eco-epidemiological model

An eco-epidemiological model with an epidemic in the predator and with a Holling type Ⅱ function is considered.A system with diffusion under the homogeneous Neumann boundary condition is studied.The existence for a positive solution of the corresponding steady state problem is mainly discussed.First,a prior estimates（positive upper and lower bounds） of the positive steady states of the reaction-diffusion system is given by the maximum principle and the Harnack inequation.Then,the non-existence of non-constant positive steady states by using the energy method is given.Finally,the existence of non-constant positive steady states is obtained by using the topological degree.

Interpretation,Construction and Exhibition-Seeking the Positive Significance of Ancient Architecture Model Making in the Teaching of History of Chinese Architecture

On the basis of a special project for teaching reform, in order to change the boring and dull situation of History of Chinese Architecture in students, ancient architecture model was introduced in the teaching process of the pure history course. Through the interpretation, construction, and exhibition stages,the ability of students in grasping the knowledge of architecture history can be strengthened. Then, from the historical background, physical composition, artistic conception of space, structural system, detailed structure, and architectural evolution, the positive significance of ancient architecture model to the teaching of the History of Chinese Architecture was discussed, in the hope of providing certain theoretical basis for the teaching of the History of Chinese Architecture.

Hybrid Dynamic Variables-Dependent Event-Triggered Fuzzy Model Predictive Control

This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative dynamic variable and an additive dynamic variable.The addressed DETM-based fuzzy MPC issue is described as a “min-max” optimization problem(OP).To facilitate the co-design of the MPC controller and the weighting matrix of the DETM,an auxiliary OP is proposed based on a new Lyapunov function and a new robust positive invariant(RPI) set that contain the membership functions and the hybrid dynamic variables.A dynamic event-triggered fuzzy MPC algorithm is developed accordingly,whose recursive feasibility is analysed by employing the RPI set.With the designed controller,the involved fuzzy system is ensured to be asymptotically stable.Two examples show that the new DETM and DETM-based MPC algorithm have the advantages of reducing resource consumption while yielding the anticipated performance.

Positive Almost Periodic Solution on a Nonlinear Logistic Biological Model with Grazing Rates

In this paper, we study the following nonlinear biological modeldx(t)/dt = x(t)[a(t)-b(t)x α (t)] + f(t, xt),by using fixed pointed theorem, the sufficient conditions of the existence of unique positive almost periodic solution for the above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the positive almost periodic solution are derived.

Hybrid pedestrian positioning system using wearable inertial sensors and ultrasonic ranging

Pedestrian positioning system(PPS)using wearable inertial sensors has wide applications towards various emerging fields such as smart healthcare,emergency rescue,soldier positioning,etc.The performance of traditional PPS is limited by the cumulative error of inertial sensors,complex motion modes of pedestrians,and the low robustness of the multi-sensor collaboration structure.This paper presents a hybrid pedestrian positioning system using the combination of wearable inertial sensors and ultrasonic ranging(H-PPS).A robust two nodes integration structure is developed to adaptively combine the motion data acquired from the single waist-mounted and foot-mounted node,and enhanced by a novel ellipsoid constraint model.In addition,a deep-learning-based walking speed estimator is proposed by considering all the motion features provided by different nodes,which effectively reduces the cumulative error originating from inertial sensors.Finally,a comprehensive data and model dual-driven model is presented to effectively combine the motion data provided by different sensor nodes and walking speed estimator,and multi-level constraints are extracted to further improve the performance of the overall system.Experimental results indicate that the proposed H-PPS significantly improves the performance of the single PPS and outperforms existing algorithms in accuracy index under complex indoor scenarios.

A New Interpretation of the Higgs Vacuum Potential Energy Based on a Planckion Composite Model for the Higgs

We present a new interpretation of the Higgs field as a composite particle made up of a positive, with, a negative mass Planck particle. According to the Winterberg hypothesis, space, i.e., the vacuum, consists of both positive and negative physical massive particles, which he called planckions, interacting through strong superfluid forces. In our composite model for the Higgs boson, there is an intrinsic length scale associated with the vacuum, different from the one introduced by Winterberg, where, when the vacuum is in a perfectly balanced state, the number density of positive Planck particles equals the number density of negative Planck particles. Due to the mass compensating effect, the vacuum thus appears massless, chargeless, without pressure, energy density, or entropy. However, a situation can arise where there is an effective mass density imbalance due to the two species of Planck particle not matching in terms of populations, within their respective excited energy states. This does not require the physical addition or removal of either positive or negative Planck particles, within a given region of space, as originally thought. Ordinary matter, dark matter, and dark energy can thus be given a new interpretation as residual vacuum energies within the context of a greater vacuum, where the populations of the positive and negative energy states exactly balance. In the present epoch, it is estimated that the dark energy number density imbalance amounts to, , per cubic meter, when cosmic distance scales in excess of, 100 Mpc, are considered. Compared to a strictly balanced vacuum, where we estimate that the positive, and the negative Planck number density, is of the order, 7.85E54 particles per cubic meter, the above is a very small perturbation. This slight imbalance, we argue, would dramatically alleviate, if not altogether eliminate, the long standing cosmological constant problem.

On capped Higgs positivity cone

The Wilson coefficients of the standard model effective field theory are subject to a series of positivity bounds.It has been shown that while the positivity part of the ultraviolet(UV)partial wave unitarity leads to the Wilson coefficients living in a convex cone,further including the nonpositivity part caps the cone from above.For Higgs scattering,a capped positivity cone was obtained using a simplified,linear unitarity condition without utilizing the full internal symmetries of Higgs scattering.Here,we further implement stronger nonlinear unitarity conditions from the UV,which generically gives rise to better bounds.We show that,for the Higgs case in particular,while the nonlinear unitarity conditions per se do not enhance the bounds,the fuller use of the internal symmetries do shrink the capped positivity cone significantly.

THE POSITIVE SOLUTION OF CLASSICAL GELFAND MODEL WITH COEFFICIENT THAT CHANGE SIGN

The existence and iteration of positive solution for classical Gelfand models are considered, where the coefficient of nonlinear term is allowed to change sign in [0, 1]. By using the monotone iterative technique, an existence theorem of positive solution is obtained, corresponding iterative process and convergence rate are given. This iterative process starts off with zero function, hence the process is simple, feasible and effective.

A Dynamic Modeling Analysis of Loom Dobbies and a Converted Positive Dobby Introduced

There are two different types of dobbies used for weavingmachines,i.e.the negative and the positive ones.In or-der to compare them,a dynamic modeling analysis ishere dealt with.Since the dynamic behavior of the posi-tive dobby is better,an electronic positive dobby conve-rted from the negative one(Staubli 2500 series)is prop-osed at the end of the paper.

Implementation of positive-operator-value measurements for single spin qubit via Heisenberg model

This paper shows that a proposal for implementing all possible two-operator positive-operator-value measurements of single spin qubit can be obtained via introducing another spin qubit as ancilla. The realization process is accomplished from the free evolution of the Heisenberg XX model by considering nearest-neighbour spin interaction. A controlled- NOT gate, which is a significant operator for this scheme is also constructed and the generalisation to multiple-operator is considered finally.

Global asymptotic stability of positive equilibrium in a 3-species cooperating model with time delay

The asymptotic behavior of the time-dependent solution for a 3-species cooperating model was investigated with the effects of both diffusion and time delay taken into consideration. We proved the global asymptotic stability of a positive steady-state solution to the model problem by using coupled upper and lower solutions for a more general reaction-diffusion system that gives a common framework for 3-species cooperating model problems. The result of global asymptotic stability implies that the model system coexistence is permanent. Some global asymptotic stability results for 2-species cooperating reaction-diffusion systems are included in the discussion, and some known results are extended.

The Existence of Positive Solutions for Volterra-Lotka Cooperating Model with Diffusion

In this paper,using the existence and comparison result for the quasi-monotone increasing system developed by C V Pao,the upper and lower solutions principle and an iterative method,we investigate the existence of the positive solutions of the Volterra-Lotka cooperating model.

An interacting multiple model-based two-stage Kalman filter for vehicle positioning

To address the problem that a general augmented state Kalman filter or a two-stage Kalman filter cannot achieve satisfactory positioning performance when facing uncertain noise of the micro-electro-mechanical system（MEMS） inertial sensors, a novel interacting multiple model-based two-stage Kalman filter（IMM-TSKF） is proposed to adapt to the uncertain inertial sensor noise. Three bias filters are developed based on different noise characteristics to cover a wide range of noise levels. Then, an accurate estimation of biases is calculated by the interacting multiple model algorithm to correct the bias-free filter. Thus, the vehicle positioning system can achieve good performance when suffering from uncertain inertial sensor noise. The experimental results indicate that the average position error of the proposed IMMTSKF is 25% lower than that of the general TSKF.

Single Point Positioning with Sequential Least-Squares Filter and Estimated Real-Time Stochastic Model

To obtain higher accurate position estimates, the stochastic model is estimated by using residual of observations, hence, the stochastic model describes the noise and bias in measurements more realistically. By using GPS data and broadcast ephemeris, the numerical results indicating the accurate position estimates at sub-meter level are obtainable.

Model Predictive Controller Design for the Dynamic Positioning System of a Semi-submersible Platform

This paper researches how to apply the advanced control technology of model predictive control （MPC） to the design of the dynamic positioning system （DPS） of a semi-submersible platform. First, a linear low-frequency motion model with three degrees of freedom was established in the context of a semi-submersible platform. Second, a model predictive controller was designed based on a model which took the constraints of the system into account. Third, simulation was carried out to demonstrate the feasibility of the controller. The results show that the model predictive controller has good performance and good at dealing with the constraints or the system.

Effects of positive acceleration(+Gz stress) on liver enzymes,energy metabolism,and liver histology in rats

BACKGROUND Exposure to high sustained +Gz(head-to-foot inertial load) is known to have harmful effects on pilots' body in flight. Although clinical data have shown that liver dysfunction occurs in pilots, the precise cause has not been well defined.AIM To investigate rat liver function changes in response to repeated +Gz exposure.METHODS Ninety male Wistar rats were randomly divided into a blank control group(BC group, n = 30), a +6 Gz/5 min stress group(6 GS group, n = 30), and a +10 Gz/5 min stress group(10 GS group, n = 30). The 6 GS and 10 GS groups were exposed to +6 Gz and +10 Gz, respectively, in an animal centrifuge. The onset rate of +Gz was 0.5 G/s. The sustained time at peak +Gz was 5 min for each exposure(for 5 exposures, and 5-min intervals between exposures for a total exposure and non-exposure time of 50 min). We assessed liver injury bymeasuring the portal venous flow volume, serum alanine aminotransferase(ALT)and aspartate aminotransferase(AST), liver tissue malondialdehyde(MDA), Na+-K+-ATPase, and changes in liver histology. These parameters were recorded at 0 h, 6 h, and 24 h after repeated +Gz exposures.RESULTS After repeated +Gz exposures in the 6 GS and the 10 GS groups, the velocity and flow signal in the portal vein(PV) were significantly decreased as compared to the BC group at 0 h after exposure. Meanwhile, we found that the PV diameter did not change significantly. However, rats in the 6 GS group had a much higher portal venous flow volume than the 10 GS group at 0 h after exposure. The 6 GS group had significantly lower ALT, AST, and MDA values than the 10 GS group 0 h and 6 h post exposure. The Na^+-K^+-ATPase activity in the 6 GS group was significantly higher than that in the 10 GS group 0 h and 6 h post exposure.Hepatocyte injury, determined pathologically, was significantly lower in the 6 GS group than in the 10 GS group.CONCLUSION Repeated +Gz exposures transiently cause hepatocyte injury and affect liver metabolism and morphological structure.

Adaptive high precision position control of servo actuator with friction compensation using LuGre model

Adaptive control of servo actuator with nonlinear friction compensation is addressed. LuGre dynamic friction model is adopted to characterize the nonlinear friction and a new kind of slid ing mode observer is designed to estimate the internal immeasurable state of LuGre model. Based on the estimated friction state, adaptive laws are designed to identify the unknown model parameters and the external disturbances, and the system stability and asymptotic trajectory tracking perform ance are guaranteed by Lyapunov function. The position tracking performance is verified by the ex perimental results.