Absolute Stability of Neutral Systems with Lurie Type Nonlinearity

The paper studies absolute stability of neutral differential nonlinear systems x ˙ ( t ) = A x t + B x t − τ + D x ˙ t − τ + b f ( σ ( t ) ) , σ ( t ) = c T x ( t ) , t ⩾ 0 $$ \begin{align}\dot x(t)=Ax\left ( t \right )+Bx\left ( {t-\tau} \right ) +D\dot x\left ( {t-\tau} \right ) +bf({\sigma (t)}),\,\, \sigma (t)=c^Tx(t), \,\, t\geqslant 0 \end{align} $$ where x is an unknown vector, A, B and D are constant matrices, b and c are column constant vectors, 𝜏 > 0 is a constant delay and f is a Lurie-type nonlinear function satisfying Lipschitz condition. Absolute stability is analyzed by a general Lyapunov-Krasovskii functional with the results compared with those previously known.

Complex Phase Retrieval from Subgaussian Measurements

Phase retrieval refers to the problem of reconstructing an unknown vector $$x_0 \in {\mathbb {C}}^n$$ x 0 ∈ C n or $$x_0 \in {\mathbb {R}}^n $$ x 0 ∈ R n from m measurements of the form $$y_i = \big \vert \langle \xi ^{\left( i\right) }, x_0 \rangle \big \vert ^2 $$ y i = | ⟨ ξ i , x 0 ⟩ | 2 , where $$ \left\{ \xi ^{\left( i\right) } \right\} ^m_{i=1} \subset {\mathbb {C}}^m $$ ξ i i = 1 m ⊂ C m are known measurement vectors. While Gaussian measurements allow for recovery of arbitrary signals provided the number of measurements scales at least linearly in the number of dimensions, it has been shown that ambiguities may arise for certain other classes of measurements $$ \left\{ \xi ^{\left( i\right) } \right\} ^{m}_{i=1}$$ ξ i i = 1 m such as Bernoulli measurements or Fourier measurements. In this paper, we will prove that even when a subgaussian vector $$ \xi ^{\left( i\right) } \in {\mathbb {C}}^m $$ ξ i ∈ C m does not fulfill a small-ball probability assumption, the PhaseLift method is still able to reconstruct a large class of signals $$x_0 \in {\mathbb {R}}^n$$ x 0 ∈ R n from the measurements. This extends recent work by Krahmer and Liu from the real-valued to the complex-valued case. However, our proof strategy is quite different and we expect some of the new proof ideas to be useful in several other measurement scenarios as well. We then extend our results $$x_0 \in {\mathbb {C}}^n $$ x 0 ∈ C n up to an additional assumption which, as we show, is necessary.

The vertical stratification of potential bridge vectors of mosquito-borne viruses in a central Amazonian forest bordering Manaus, Brazil

The emergence of Zika virus (ZIKV) in Latin America brought to the fore longstanding concerns that forests bordering urban areas may provide a gateway for arbovirus spillback from humans to wildlife. To bridge urban and sylvatic transmission cycles, mosquitoes must co-occur with both humans and potential wildlife hosts, such as monkeys, in space and time. We deployed BG-Sentinel traps at heights of 0, 5, 10, and 15 m in trees in a rainforest reserve bordering Manaus, Brazil, to characterize the vertical stratification of mosquitoes and their associations with microclimate and to identify potential bridge vectors. Haemagogus janthinomys and Sabethes chloropterus, two known flavivirus vectors, showed significant stratification, occurring most frequently above the ground. Psorophora amazonica, a poorly studied anthropophilic species of unknown vector status, showed no stratification and was the most abundant species at all heights sampled. High temperatures and low humidity are common features of forest edges and microclimate analyses revealed negative associations between minimum relative humidity, which was inversely correlated with maximum temperature, and the occurrence of Haemagogus and Sabethes mosquitoes. In this reserve, human habitations border the forest while tamarin and capuchin monkeys are also common to edge habitats, creating opportunities for the spillback of mosquito-borne viruses.

Trace finite element methods for surface vector-Laplace equations

In this paper we analyze a class of trace finite element methods for the discretization of vector-Laplace equations. A key issue in the finite element discretization of such problems is the treatment of the constraint that the unknown vector field must be tangential to the surface (‘tangent condition’). We study three different natural techniques for treating the tangent condition, namely a consistent penalty method, a simpler inconsistent penalty method and a Lagrange multiplier method. The main goal of the paper is to present an analysis that reveals important properties of these three different techniques for treating the tangent constraint. A detailed error analysis is presented that takes the approximation of both the geometry of the surface and the solution of the partial differential equation into account. Error bounds in the energy norm are derived that show how the discretization error depends on relevant parameters such as the degree of the polynomials used for the approximation of the solution, the degree of the polynomials used for the approximation of the level set function that characterizes the surface, the penalty parameter and the degree of the polynomials used for the approximation of the Lagrange multiplier.

Solution of Fault Accommodation Problem in Nonlinear Systems by Methods of Linear Algebra

Solution of the problem of fault accommodation in nonlinear dynamic systems is related to constructing the control law which provides full decoupling with respect to fault effects. The possibility of this solution is strictly limited by the demand on the system state vector availability (this vector is immediately included into control law description). As a rule, not all components of the state vector are immediately measurable at practice. Also, it is impossible to estimate full state vector for the system with unknown (affected by the faults) dynamics. The purpose of this article is to solve the problem of full decoupling by constructing a compensator that is independent of the fault effects a nd is based on a new control law. A solution is based on so-called logic-dynamic approach using only linear methods to solve the problem for nonlinear systems. The implementation of this method does not require a preliminary estimation of the parameters. It is assumed that fault detection and isolation procedure is performed by known methods. Assume the fault occurred and detected, then a solution of the control problem is performed on the basis of additional system that corresponding in a definite sense to the initial model. To solve the problem of accommodation, an efficient algorithm based on a logical-dynamic approach is presented, as a result of which a compensator is constructed. Additional system does not contain unknown vector that describes defects. As a result, fault accommodation effect is achieved. Theoretical results are demonstrated by illustrative and illustrative example.

Boundary least squares method with three-dimensional harmonic basis of higher order for solving linear div-curl systems with Dirichlet conditions

Solving linear divergence-curl system with Dirichlet conditions is reduced to finding an unknown vector function in the space of piecewise-polynomial gradients of harmonic functions. In this approach one can use the boundary least squares method with a harmonic basis of a high order of approximation formulated by the authors previously. The justification of this method is given. The properties of the bilinear form and approximating properties of the basis are investigated. Convergence of approximate solutions is proved. A numerical example with estimates of experimental orders of convergence in $\begin{array}{} {\bf V}_h^p \end{array}$-norm for different parameters h, p (p ⩽ 10) is presented. The method does not require specification of penalty weight function.

On the analytical approach to the linear analysis of an arbitrarily curved spatial Bernoulli-Euler beam

The equilibrium and kinematic equations of an arbitrarily curved spatial Bernoulli-Euler beam are derived with respect to a parametric coordinate and compared with those of the Timoshenko beam. It is shown that the beam analogy follows from the fact that the left-hand side in all the four sets of those equations are the covariant derivatives of unknown vector. Furthermore, an elegant primal form of the equilibrium equations is composed. No additional assumptions, besides those of the linear Bernoulli-Euler theory, are introduced, which makes the theory ideally suited for the analytical assessment of big-curvature beams. The curvature change is derived with respect to both convective and material/spatial coordinates, and some aspects of its definition are discussed. Additionally, the stiffness matrix of an arbitrarily curved spatial beam is calculated with the flexibility approach utilizing the relative coordinate system. The numerical analysis of the carefully selected set of examples proved that the present analytical formulation can deliver valid benchmark results for testing of the purely numeric methods.

A New Analytical Approach for Free Vibration, Buckling and Forced Vibration of Rectangular Nanoplates Based on Nonlocal Elasticity Theory

In this paper, an analytical Hamiltonian-based model for the dynamic analysis of rectangular nanoplates is proposed using the Kirchhoff plate theory and Eringen’s nonlocal theory. In a symplectic space, the dynamic problem is reduced to solving a unified Hamiltonian dual equation formed by a total unknown vector consisting of displacements, rotation angles, bending moments and generalized shear forces. The exact solutions for free vibration, buckling and steady state forced vibration are established by the eigenvalue analysis and expansion of eigenfunction without any trial functions. In addition, the explicit expressions of the characteristic equations, mode functions and steady state response of the nanoplate with two opposite edges that are simply supported or guided supported are obtained. To verify the accuracy and reliability of the present method, numerical results are compared with published solutions and excellent agreement is obtained. Comprehensive benchmark results that consider the nonlocal effect on the dynamic behaviors of rectangular nanoplates are also presented in dimensionless tabular and graphical forms.

Excited vector mesons: phenomenology and predictions for a yet unknown vector ss state with a mass of about 1.93 GeV

The firm understanding of standard quark-antiquark states (including excited states) is necessary to search for non-conventional mesons with the same quantum numbers. In this work, we study the phenomenology of two nonets of excited vector mesons, which predominantly correspond to radially excited vector mesons with quantum numbers n2S+1LJ = 23S1 and to orbitally excited vector mesons with quantum numbers n2S+1LJ = 13D1. We evaluate the decays of these mesons into two pseudoscalar mesons and into a pseudoscalar and a ground-state vector meson by making use of a relativistic quantum field theoretical model based on flavor symmetry. Moreover, we also study the radiative decays into a photon and a pseudoscalar meson by using vector meson dominance. We compare our results to the PDG and comment on open issues concerning the corresponding measured resonances. Within our approach, we are also able to make predictions for a not-yet discovered ss state in the n2S+1LJ = 13D1 nonet, which has a mass of about 1.93 GeV. This resonance can be searched in the upcoming GlueX and CLAS12 experiments which take place at the Jefferson Lab.