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For spatially dependent functional data, a generalized Karhunen-Lo\`{e}ve expansion is commonly used to decompose data into an additive form of temporal components and spatially correlated coefficients. This structure provides a convenient model to investigate the space-time interactions, but may not hold for complex spatio-temporal processes. In this work, we introduce the concept of weak separability, and propose a formal test to examine its validity for non-replicated spatially stationary functional field. The asymptotic distribution of the test statistic that adapts to potentially diverging ranks is derived by constructing lag covariance estimation, which is easy to compute for practical implementation. We demonstrate the efficacy of the proposed test via simulations and illustrate its usefulness in two real examples: China PM$_{2.5}$ data and Harvard Forest data.

Based on measurements of rubber hysteresis curves, the relationship between the network structure of elastomers and their mechanical behavior is analyzed. On the basis of the classical theory of ru...

Two-level fractional factorial designs are often used in screening scenarios to identify active factors. This article investigates the block diagonal structure of the information matrix of nonregul...

A coupled multiphysics vibroacoustic model is developed for axisymmetric scattering of plane progressive time-harmonic sound waves from a fluid-filled and submerged smart hybrid double concentric c...

This note deals with the leader-following formation problem for multiple underactuated ships in the presence of structure uncertainties and the time-varying parameterized disturbances. Following this ideology, a novel robust fuzzy dynamic surface formation control algorithm is proposed by fusing of the dynamic surface control (DSC), minimal learning parameter (MLP) and low frequency gain-learning (LFG). In the control algorithm, the intermediate virtual control laws do not appear in the finally actual control effort, and only two fuzzy type approximators are introduced to compensate the model uncertainties and the external disturbances, which can effectively overcome the constraints of ‘explosion of complexity’ and ‘curse of dimensionality’ in the traditional approximation-based algorithm. Unlike the current DSC technique, no filter errors are required to be stabilized in the Lyapunov function by virtue of the filter compensation signal, which could optimize the calculation of stabilization analysis. Furthermore, benefiting from the LFG technique, the robustness and applicability of the proposed control algorithm can be improved. Based on the Lyapunov theory analysis, all signals of the closed-loop control system can be guaranteed to be semi-global uniformly ultimately bounded (SGUUB). Finally, the simulated experiment is provided to verify the effectiveness and superiority of the proposed control scheme.

To a very good approximation, particularly for hadron machines, charged-particle trajectories in accelerators obey Hamiltonian mechanics. During routine storage times of eight hours or more, such particles execute some $10^{8}$ revolutions about the machine, $10^{10}$ oscillations about the design orbit, and $10^{13}$ passages through various bending and focusing elements. Prior to building, or modifying, such a machine, we seek to identify accurately the long-term behavior and stability of particle orbits over such large numbers of interactions. This demanding computational effort does not yield easily to traditional methods of symplectic numerical integration, including both explicit Yoshida-type and implicit Runge-Kutta or Gaussian methods. As an alternative, one may compute an approximate one-turn map and then iterate that map. We describe some of the essential considerations and techniques for constructing such maps to high order and for realistic magnetic field models. Particular attention is given to preserving the symplectic condition characteristic of Hamiltonian mechanics., 28 pages, 5 figures

This article uses Gaussian copula marginal regression and tail dependence estimation by copula to explore COVID-19’s effects on the dependence structure of the US stock market. Specifically, we inv...

Tubular thin-walled structure has attracted more and more attention because of its light weight and energy absorption characteristic, and has been widely applied to the fields of aerospace and auto...

The estimation algebra plays an important role in classification of finite dimensional filters. When finite dimensional estimation algebra has maximal rank, Yau et al. [Yau (2003). Complete classif...

This article presents crack repair in the structure by piezoelectric material and predict the fatigue life of the structure. The extended finite element method is applied to model the crack discont...

We introduce forward-backward stochastic equations (FBSEs) that incorporate fully-coupled forward-backward structure into backward stochastic equations (BSEs) introduced in Cheridito and Nam (Ann. ...

There exist many bivariate parametric copulas to model bivariate data with different dependence features. We propose a new bivariate parametric copula family that cannot only handle various dependence patterns that appear in the existing parametric bivariate copula families, but also provides a more enriched dependence structure. The proposed copula construction exploits finite mixtures of bivariate normal distributions. The mixing operation, the distinct correlation and mean parameters at each mixture component introduce quite a flexible dependence. The new parametric copula is theoretically investigated, compared with a set of classical bivariate parametric copulas and illustrated on two empirical examples from astrophysics and agriculture where some of the variables have peculiar and asymmetric dependence, respectively.

This study aims to extend the spectral element technique to the three-dimensional (3D) mechanical response of the multi-layered transversely isotropic structure under a moving vehicular load and im...

In this paper, we study partial group actions on Lie algebras. We describe the structure of the inverse semigroup of all partial automorphisms (isomorphisms between ideals) of a finite-dimensional ...

Recently, a new layered-ternary compound V2SnC was successfully synthesised by reacting V, Sn, and C powder mixture at 1000°C. Its space group was identified as P63/mmc. In this work, the structura...

The inverse motion concept is used to optimize thermo-hyperelastic structures using an exact description of the deformed geometry. This method prescribes the shape of the structure in the deformed ...

This paper deals with some probabilistic and statistical properties of a periodic generalized integer-valued autoregressive PINAR(1) model. The autocovariance structure is studied while establishin...

In this paper, G-majorization inequalities are proven for the gradients of two Gateaux differentiable G-increasing functions defined on a real linear space endowed with the structure of an Eaton tr...

This communication presents a small size, planar, and two-port wideband multiple-input-multiple-output (MIMO) antenna operating from 2.08 GHz to 5.81 GHz with 94.55% fractional bandwidth. It satisf...

We introduce a new subgroup embedding property, namely S*-embedded subgroup and study the structure of a finite group G under the assumption that some subgroups of prime order are S*-embedded in G....

MAX phase materials a new family of ternary layered carbide and nitride compounds are represented by the general formula of Mn+1AXn, where n = 1 ∼ 3, M stands for early transition metal, A express ...

The additional confinement loss caused by external loads has so far restricted the wide applications of photonic crystal fibers (PCFs). With the rapid development of metamaterials, there is an incr...

Groups of structure 2.O8+(2) have an irreducible representation of degree 8 which can be realized over Z and any prime field Fp. This representation extends to a group of structure 2.O8+(2).2. Any ...

In contrast to symmetric cone optimization, there has no unified framework for non-symmetric cone optimization. One main reason is that the structure of various non-symmetric cone differs case by c...

Topology optimization with classical mechanics has already made tremendous advances for macroscopic structure in the last few decades. However, size effects are detected from small-scale structures...

In this article, we study Lie hyperalgebras and compare them with Lie algebras. We introduce the L-relation on a Lie hyperalgebra such that the quotient structure by its transitive closure is a Lie...

The structure of Maxwell's equations is reproduced for the potentials introducing a second vector potential c, in addition to the usual vector potential A. These in turn can be described in terms o...

Reconfigurable architectures are more prominent in modern-day multi-band radio systems. This work has been conceptualized for a flexible 8-bit digitally controlled oscillator (DCO) design to suit r...

It is well known that superderivation of a Lie superalgebra is certain generalization of derivation of a Lie algebra. This paper is devoted to investigate the structure and dimension of superderiva...

In this study, we have analyzed twist angles between layers at which the bilayer graphene (BLG) layer structure is periodic. In addition, the dependence of interlayer binding energies on the BLG la...

In the present paper, we introduce the notion of non-abelian tensor product of a given precrossed module by one of its ideals. We use this concept to study the second homology and the nilpotent mul...

We introduce two classes of point processes: a fractional non-homogeneous Poisson process of order k and a fractional non-homogeneous Pólya-Aeppli process of order k: We characterize these processes by deriving their non-local governing equations. We further study the covariance structure of the processes and investigate the long-range dependence property.

Most of the scientific and industrial experiments usually involve small number of factors, especially biomedical experiments and computer based experiments. We construct some highly useful designs ...

Structure is the key to understanding the properties of metal nanoclusters. Finding a globally optimal structure on an extremely complex potential energy surface is a great challenge for theoretica...

The research of damping is an important and urgent topic in the research of structural vibration. Concrete material is one of the main bulk materials in civil engineering. The purpose of this study...

Despite the importance and complexity of Poisson’s effect in tubular braids, it has been overlooked in researches investigating the mechanical properties. In this study, the effect of structural pa...

Cities are spatially evolving complex systems. The order and pattern beneath the apparent chaos and diverse physical forms of cities are still unclear. How the form and structure of a city evolve t...

The calculation of the three-dimensional structure of crystals of fifteen polymorphic varieties of graphene functionalized with fluorine was carried out by the atom-atom potential method. The energ...

In this paper, it is shown that most guidance methods can be considered as a specific form of the cross-product steering law which is based on aligning two physical vectors along with each other, a...

This research proposes a surrogate model to predict the seismic response of individual structural elements in structures whose inherent vertical and horizontal irregularities result in components w...

The third or organismic view of space states that space is neither lifeless nor neutral, but a living structure capable of being more living or less living, thus different fundamentally from the first two mechanistic views of space: Newtonian absolute space and Leibnizian relational space. The living structure is defined as a physical and mathematical structure or simply characterized by the recurring notion (or inherent hierarchy) of far more small substructures than large ones. This paper seeks to lay out a new geography as a science of the Earth's surface founded on the third view of space. The new geography aims not only to better understand geographic forms and processes but also - maybe more importantly - to make geographic space or the Earth?s surface to be living or more living. After introducing two fundamental laws of geography: Tobler's law on spatial dependence (or homogeneity) and scaling law on spatial heterogeneity, we argue that these two laws are fundamental laws of living structure that favour statistics over exactitude, because the former (or statistics) tends to make a structure more living than the latter (or exactitude). We present the concept of living structure through some working examples and make it clear how a living structure differs from a non-living structure, under the organismic worldview that was first conceived by the British philosopher Alfred Whitehead (1861-1947). In order to make a structure or space living or more living, we illustrate two design principles - differentiation and adaptation - using two paintings and two city plans. The new geography is a science of living structure, dealing with a wide range of scales, from the smallest scale of ornaments on walls to the scale of the entire Earth's surface.

In this research article, a high-performance and compact 2-port slotted hexagonal structure multiple-input multiple-output (MIMO) system is presented. This structure is designed by using novel tech...

Silicon semiconductors with excellent thermoelectric characteristics have been widely used in integrated electronic systems. Thermal rectification has important potential applications in semiconduc...

TPMS (triply periodic minimal surface) sheet structure consists of a spatially continuous surface, which forms a periodic porous structure, and has outstanding mechanical performance and ultralight...