Nonzero Point Research Articles

Nonlinearly Parametrized Modeling and Adaptive Control for a Generic Hypersonic Vehicle

This paper constructs a nonlinearly parametrized hypersonic cruise vehicle model on the basis of the existing on-orbit flight data using a curve-fitting technique. The hypersonic cruise vehicle system is separated into two interconnected subsystem: an attitude subsystem with rotational dynamics and a velocity subsystem with engine dynamics. The continuous adaptive controllers are designed for two subsystems using a novel function bounding technique and appropriate coordinate transformations, respectively, which ensure the global boundedness of all signals and achieve the non-zero equilibrium point regulation of nonlinearly parametrized hypersonic vehicle systems. One of the implications of this result is that growing nonlinearities in the uncertain model of the hypersonic vehicle system may be allowed for global stabilization. A simulation result verifies the effectiveness of the proposed adaptive control scheme.

Non-trivial solutions for a partial discrete Dirichlet nonlinear problem with $ p $-Laplacian

<abstract><p>We investigate the non-trivial solutions for a partial discrete Dirichlet nonlinear problem with $ p $-Laplacian by applying Ricceri's variational principle and a two non-zero critical points theorem. In addition, we identify open intervals of the parameter $ \lambda $ under appropriate constraints imposed on the nonlinear term. This allows us to ensure that the nonlinear problem has at least one or two non-trivial solutions.</p></abstract>

Improved parameter optimization method for measurement device independent protocol

The optimal selection of parameters in practical quantum key distribution can greatly improve the key generation rate and maximum transmission distance of the system. Owing to the high cost of global search algorithm, local search algorithm is widely used. However, there are two shortcomings in local search algorithm. One is that the solution obtained is not always the global optimal solution, and the other is that the effectiveness of the algorithm is greatly dependent on the choice of initial value. This paper uses the Monte Carlo method to prove whether the key generation rate function is convex, and also simulates and analyzes the projection of the key generation rate function on each dimension of the parameter, in contrast to the approach in previous article. In order to eliminate the effect of the initial value, this paper proposes the particle swarm local search optimization algorithm which integrates particle swarm optimization algorithm and local search algorithm. The first step is to use the particle swarm optimization to find a valid parameter which leads to nonzero key generation rate, and the second step is to adopt the parameter as the initial value of local search algorithm to derive the global optimal solution. Then, the two algorithms are used to conduct simulation and their results are compared. The results show that the key generation rate function is non-convex because it does not satisfy the definition of a convex function, however, since the key generation rate function has only one non-zero stagnation point, the LSA algorithm can still obtain the global optimal solution with an appropriate initial value. When the transmission distance is relatively long, the local search algorithm is invalid because it is difficult to obtain an effective initial value by random value method. The particle swarm optimization algorithm can overcome this shortcoming and improve the maximum transmission distance of the system at the cost of slightly increasing the complexity of the algorithm.

An accelerated conjugate gradient method for the Z-eigenvalues of symmetric tensors

<abstract><p>We transform the Z-eigenvalues of symmetric tensors into unconstrained optimization problems with a shifted parameter. An accelerated conjugate gradient method is proposed for solving these unconstrained optimization problems. If solving problem results in a nonzero critical point, then it is a Z-eigenvector corresponding to the Z-eigenvalue. Otherwise, we solve the shifted problem to find a Z-eigenvalue. In our method, the new conjugate gradient parameter is a modified CD conjugate gradient parameter, and an accelerated parameter is presented by using the quasi-Newton direction. The global convergence of new method is proved. Numerical experiments are listed to illustrate the efficiency of the proposed method.</p></abstract>

Modeling and adaptive control of air vehicles with partial nonlinear parametrization

This paper studies the control of a generic longitudinal air vehicle dynamic model during the cruise phase with nonlinearly parametrized uncertain aerodynamic functions. Verified by the improved coefficient precision of the aerodynamic forces and moments, using a curve fitting technique on available flight data, it is demonstrated that a nonlinearly parametrized model can more accurately capture the vehicle dynamics than a linearly parametrized model. For control design, the air vehicle model is decomposed into a flight-path angle subsystem with rotational dynamics and a speed subsystem with engine actuation dynamics. An adaptive control scheme is developed using the combination of a function bounding technique and a modified backstepping control method for two interconnected subsystems. The designed adaptive control laws ensure both global stabilization and adaptive non-zero equilibrium point regulation of the closed-loop control system. A thorough simulation study is presented to show the effectiveness of the developed adaptive control scheme for a nonlinearly parametrized air vehicle system model.

ENRIQUES INVOLUTIONS AND BRAUER CLASSES

AbstractWe prove that every element of order 2 in the Brauer group of a complex Kummer surface X descends to an Enriques quotient of X. In generic cases, this gives a bijection between the set ${\mathcal Enr}(X)$ of Enriques quotients of X up to isomorphism and the set of Brauer classes of X of order 2. For some K3 surfaces of Picard rank $20,$ we prove that the fibers of ${\mathcal Enr}(X)\to \mathrm {{Br}}(X)[2]$ above the nonzero points have the same cardinality.

Formula omitted]-free lattice points in random walks

Let Z2 be the two-dimensional integer lattice. For an integer k≥1, a non-zero lattice point is k-free if the greatest common divisor of its coordinates is a k-free number. We consider the proportions of k-free and twin k-free lattice points on a path of an α-random walker in Z2. Using the second-moment method and tools from analytic number theory, we prove that these two proportions are 1/ζ(2k) and ∏p(1−2p−2k), respectively, where ζ is the Riemann zeta function and the infinite product takes over all primes.

A three-phase power flow algorithm for ungrounded network based on constraints of zero-sequence components

The existing research on three-phase power flow in ungrounded distribution networks primarily adopts the methods of presetting zero-sequence reference voltages and neutral point reference voltages. This makes it impossible to calculate the power flow in ungrounded network with non-zero neutral point voltages or zero-sequence voltages. Furthermore, a unified zero-sequence components constraint method of ungrounded distribution network does not exist. In this paper, a three-phase power flow algorithm is proposed to calculate three-phase power flow in an ungrounded distribution network. First, power flow equation variables, transformer admittance matrices and zero-sequence components are used to analyze the characteristic of three-phase power flow in an ungrounded distribution network. Second, a three-phase power flow algorithm for ungrounded distribution network is designed by constraining the zero-sequence currents of the ungrounded winding nodes to zero. Third, theoretical analyses and mathematical derivations are used to prove the applicability of the two methods, one of which constrains zero-sequence voltages of ungrounded winding nodes to zero and the other constrains squares of zero-sequence voltages and currents to zero. Last, a five-nodes network, modified IEEE123 network and practical network are used to demonstrate that the proposed method has a high accuracy and good applicability in calculating the three-phase power flow of ungrounded distribution networks.

Ferromagnetic Weyl semimetals and Quantum Anomalous Hall effect in 2D half-metallic Mn2NT2

Using the first-principles calculations, we predict the 2D monolayer MXene Mn2NT2 (T=-OH, -F, =O) is a half-metallic Weyl semimetal. Without spin–orbit coupling, multiple types Weyl fermions and Fermi arc edge state are observed, and there are abundant topological phases under biaxial strain in the a–b plane. Considering the spin–orbit coupling, the Weyl points are gapped, and the quantum anomalous Hall effect is observed, which is also proved by the chiral edge state in the gap and Chern number. In addition, a tight-binding model is applied to understand the origin of the non-trivial electronic properties of the quantum anomalous Hall phase. Finally, we calculate the Berry curvature and abnormal Hall conductivity of Mn2NT2, and find that they are a non-zero energy point near the Fermi level. Our results indicate that monolayer Mn2NT2 have a potential application in magnetoelectronic devices.

Effect of time-lag on two mutually competing plant populations under allelochemicals

This paper examines a bionomic model of competing organisms in the presence of allelochemicals with differing time-dependent densities. A competition mathematical model is proposed in this paper. It is shown that when one plant produces an allelochemical, it gives stimulatory effect to itself and inhibitory effect to the other plant. Equilibrium points are calculated and stability analysis is performed about non-zero equilibrium point. Hopf-bifuraction is observed with the help of delay parameter introducing in term of allelochemicals. Model is verified with already existing data for the effect of allelochemical on plant growth by Zahid et.al (2016). The numerical results are substantiated using MATLAB.

Nearest neighbor control for practical stabilization of passive nonlinear systems

This paper studies static output feedback stabilization of continuous-time (incrementally) passive nonlinear systems where the control actions can only be chosen from a discrete (and possibly finite) set of points. For this purpose, we are working under the assumption that the system under consideration is large-time norm observable and the convex hull of the realizable control actions contains the target constant input (which corresponds to the equilibrium point) in its interior. We propose a nearest-neighbor based static feedback mapping from the output space to the finite set of control actions, that is able to practically stabilize the closed-loop systems. Consequently, we show that for such systems with m-dimensional input space, it is sufficient to have m+1 discrete input points (other than zero for general passive systems or the target constant input for constant-incrementally passive systems). Furthermore, we present a constructive algorithm to design such m+1 nonzero input points that satisfy the conditions for practical stability using our proposed nearest-neighbor control.

Coexistence of multiple Weyl fermions and quantum anomalous Hall effect in 2D half-metallic Cr2NT2

Topological state in two-dimensional (2D) magnetic system has attracted widespread attention due to its potential application in spintronics and quantum computing fields. As a novel topological states of matter, Weyl semimetals with multiple topological phases have been studied. However, realizing multiple topological phases in 2D magnetic system and studying their entanglement still face great challenges. In this work, using first-principles calculations, we predict that 2D monolayer Cr2NT2 (T = -OH, -F, =O) has multiple Weyl fermions (WFs) and large spin-down gap. Ferromagnetic ground states of monolayer Cr2NT2meet the dynamic, thermal and mechanical stabilities. Without spin-orbit coupling (SOC), these WPs are fully spin-polarized. When considering SOC, apart from WP3 in Cr2NO2, all WPs are opened the gap, and the chiral edge states are observed in Cr2NT2. In particular, there is a quantum anomalous Hall effect in Cr2NF2. Further, a biaxial strain in the a-b plane leads to the emergence of rich topological phases without SOC. In addtion, an effective four-band tight-binding model is constructed to clarify the origin of WFs in the non-trivial band topology. Finally, we calculate the Berry curvature and abnormal Hall conductivity of Cr2NT2, and find that they are a non-zero energy points around the Fermi level, indicating that monolayer Cr2NT2 are promising candidates for spintronic applications. Therefore, it is necessary to explore 2D magnetic materials with multiple types of WFs and QAH phases.

Distribution of values of quadratic forms at integral points

The number of lattice points in d-dimensional hyperbolic or elliptic shells {m : a<Q[m]<b}, which are restricted to rescaled and growing domains r,Omega , is approximated by the volume. An effective error bound of order o(r^{d-2}) for this approximation is proved based on Diophantine approximation properties of the quadratic form Q. These results allow to show effective variants of previous non-effective results in the quantitative Oppenheim problem and extend known effective results in dimension d ge 9 to dimension d ge 5. They apply to wide shells when b-a is growing with r and to positive definite forms Q. For indefinite forms they provide explicit bounds (depending on the signature or Diophantine properties of Q) for the size of non-zero integral points m in dimension dge 5 solving the Diophantine inequality |Q[m] |< varepsilon and provide error bounds comparable with those for positive forms up to powers of log r.

A Fuzzy Qualitative Simulation Study of College Student’s Mental Health Status

The fuzzy qualitative approach used in this paper provides an in-depth study and analysis of the simulation of the mental health state of college students, which is continued from another perspective using structural equation modeling, in which sufficient conditions for the equation to satisfy local asymptotic stability, instability, and global attraction at the zero equilibrium point and sufficient conditions for the existence and instability of nonzero equilibrium points are discussed, respectively. In addition, the paper proves the boundedness of the solutions of the equation by mathematical induction and obtains sufficient conditions to ensure that the solutions are bounded. The intrinsic causes of college students’ psychological problems lie in the lack of social support in the family and outside the family and the influence of the overall social environment on college students. Finally, this paper puts forward some suggestions and countermeasures based on this research finding from three levels: family, school, and society, giving full play to the role of family support; schools should expand the main body of support, enrich the form of support, and provide comprehensive and multifaceted social support for college students. Finally, the simulation of the equation is carried out to verify the correctness of its conclusion. The rate of mental subhealth is 1.605 times that of college students admitted to ideal universities, which is consistent with our actual situation. At the level of condition guarantee, the hardware facilities, management system, and professional team of mental health education for college students are evaluated; from the specific content, the teaching work, educational activities, psychological counseling, and crisis intervention of mental health education for college students are evaluated; from the perspective of effect, the degree of goal achievement, social adaptation, and result satisfaction of the effect of mental health education for college students are evaluated. The final part analyzes and elaborates on the construction of evaluation indexes of mental health education for college students, the design of weight of guiding indexes, and the content and optimization path of the evaluation test. The results of the study show that personal ability and external pressure are important factors influencing college students’ mental health, and the influence of external pressure is greater. Logistic regression and structural equation modeling methods complement each other, and the findings of structural equation modeling are more comprehensive and integrated, while logistic regression illustrates the degree of each influencing factor.

A Heuristic Method to Approximate the Closest Vector Problem

The closest vector problem, or CVP for short, is a fundamental lattice problem. The purpose of this challenge is to identify a lattice point in its ambient space that is closest to a given point. This is a provably hard problem to solve, as it is an NP-hard problem. It is considered to be more difficult than the shortest vector problem (SVP), in which the shortest nonzero lattice point is required. There are three types of algorithms that can be used to solve CVP: Enumeration algorithms, Voronoi cell computation and seiving algorithms. Many algorithms for solving the relaxed variant, APPROX-CVP, have been proposed: The Babai nearest algorithm or the embedding technique. In this work we will give a heuristic method to approximate the closest vector problem to a given vector using the embeding technique and the reduced centered law.

On the distribution of $ k $-full lattice points in $ \mathbb{Z}^2 $

&lt;abstract&gt;&lt;p&gt;Let $ \mathbb{Z}^2 $ be the two-dimensional integer lattice. For an integer $ k\geq 2 $, we say a non-zero lattice point in $ \mathbb{Z}^2 $ is $ k $-full if the greatest common divisor of its coordinates is a $ k $-full number. In this paper, we first prove that the density of $ k $-full lattice points in $ \mathbb{Z}^2 $ is $ c_k = \prod_{p}(1-p^{-2}+p^{-2k}) $, where the product runs over all primes. Then we show that the density of $ k $-full lattice points on a path of an $ \alpha $-random walk in $ \mathbb{Z}^2 $ is almost surely $ c_k $, which is independent on $ \alpha $.&lt;/p&gt;&lt;/abstract&gt;

Population Dynamic Study of Prey‐Predator Interactions with Weak Allee Effect, Fear Effect, and Delay

In this study, a predator‐prey model with the Allee effect and fear effect is established. We use the comparison principle to prove boundedness. The zero equilibrium point and nonzero equilibrium point of the model are calculated, and the local stability conditions are obtained. Next, according to the Sotomayor theorem, the cross‐sectional conditions of transcritical bifurcation and Hopf bifurcation are obtained. The conditions for the Hopf bifurcation to be supercritical or subcritical can be calculated by the normal form theory. Then, to make the model more realistic, we introduce the gestation delay in the proposed mathematical model. Stability and Hopf bifurcation are also analyzed. Finally, several numerical simulations are presented to verify the conclusions. Our results demonstrate that the Allee effect, fear effect, and delay play significant roles in population dynamics. The Allee effect and delay destabilize the originally stable model, after which Hopf bifurcation occurs. However, the fear effect can enhance stable coexistence.

Modelling and analysis of prey-predator model involving predation of mature prey using delay differential equations

&lt;p style='text-indent:20px;'&gt;In this paper, the modelling and analysis of prey-predator model involving predation of mature prey is done using DDE. Equilibrium points are calculated and stability analysis is performed about non-zero equilibrium point. Delay parameter destabilizes the system and triggers asymptotic stability when value of delay parameter is below the critical point. Hopf bifurcation is observed when the value of delay parameter crosses the critical point. Sensitivity analysis has also been performed to look into the effect of other parameters on the state variables. The numerical results are substantiated using MATLAB.&lt;/p&gt;

Generalized Drazin-1-meromorphic invertible operators and generalized Kato-1-meromorphic decomposition

In this paper we generalize the concept of Koliha-Drazin invertible operators by introducing generalized Drazin-1-meromorphic invertible operators. A bounded linear operator T on a Banach space X is said to be 1-meromorphic if every non-zero point of its spectrum is an isolated point. For T we say that it is generalized Drazin-1-meromorphic invertible if there exists a bounded linear operator S acting on X such that TS = ST, STS = S, TST ? T is 1-meromorphic, while T admits a generalized Kato-1-meromorphic decomposition if there exists a pair of T-invariant closed subspaces (M,N) such that X = M?N, the reduction TM is Kato and TN is 1-meromorphic.

Analysis of "big data" and mathematical modeling of the covid-19 epidemic in Europe

The regularities of the dynamics of the covid-19 pandemic in Ukraine and other European countries are studied by using the methods of analyzing "big data" in the form of time series and related information from open online sources. Statistical analysis of smoothed curves of new cases I (t), dead D (t), recovered R (t) and other time series has shown different types of dynamics: wave (i), quasi-wave with time shift (ii), stepwise (iii), with abnormally high or low amplitudes of local oscillations. The appropriate similarity trees have been constructed by using the nearest neighbor method. It is shown that the countries with different types of dynamics (i, ii, iii) are located in separate branches of the trees. The stability of zero and nonzero stationary points have been investigated on the basis of the popular mathematical model SIRS. The solutions of the linearized system have been obtained and the influence of the model parameters on the eigenvalues of the system matrix has been investigated. The presence of different types of dynamics is shown: with three negative real (a), one positive real (b), one real and a pair of complex conjugate(c) eigenvalues. The phase portraits have been constructed and the connection of the types of time series (i, ii, iii) and solutions (a, b, c) of the SIRS equations is shown. The obtained results allow us to estimate the dynamic behavior of the system, its stability or instability with the possibility of chaotic dynamics on the basis of the analysis of time series on any current day.