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В статье приводятся разложения в ряд для фрактальных броуновских движений на единичном шаре и единичной сфере по ультрасферическим многочленам и сферическим гармоникам. Устанавливается сильный локальный недетерминизм изотропных гауссовских случайных полей на единичной сфере, а также то же свойство для фрактального и бифрактального броуновских движений на единичном шаре и единичной сфере.

This paper introduces a power-law subordinator and a power-law Lévy process whose Laplace transform and characteristic function are simply made up of power functions or the ratio of power functions, respectively, and proposes a power-law vector random field whose finite-dimensional characteristic functions consist merely of a power function or the ratio of two power functions. They may or may not have first-order moment, and contain Linnik, variance Gamma, and Laplace Lévy processes (vector random fields) as special cases. For a second-order power-law vector random field, it is fully characterized by its mean vector function and its covariance matrix function, just like a Gaussian vector random field. An important feature of the power-law Lévy processes (random fields) is that they can be used as the building blocks to construct other Lévy processes (random fields), such as hyperbolic secant, cosine ratio, and sine ratio Lévy processes (random fields).

A novel method for type synthesis of lower-mobility decoupled parallel mechanism with redundant constraints is proposed. Firstly, the definition of the redundant constraints is put forward. Then, number and topology structure synthesis is carried out based on the redundant constraints between the closed loop structure of parallel configuration. Next, the specific procedure for type synthesis of lower-mobility decoupled parallel mechanism is derived. Furthermore, the local freedom of the limbs was established through the relationship of motion-screw and constraint-screw between limbs. Finally, type synthesis of 2R1T decoupled parallel mechanism is established. The synthesized configuration theoretical output characteristics is a decoupled Jacobin matrix. The output characteristics are analyzed based on theoretical calculation and ADAMS simulation software. The simulation results and the theoretical calculation results are consistent. The proposed method can be applied to type synthesis of lower-mobility decoupled parallel mechanisms.

This paper introduces the K-combined vector random field, whose finite-dimensional characteristic functions are made up of certain power functions and whose finite-dimensional density functions are...

Distribution network reconfiguration technology is the key technology of distribution network fault treatment and power supply recovery. Given the problem that the traditional distribution network reconfiguration algorithm needs a lot of power flow calculation and low efficiency to find the optimal target, the simulated annealing algorithm is proposed to optimize the computing speed and searching ability of the distribution network reconfiguration algorithm. Firstly, the information interaction technology of distribution network protection and control equipment is studied, and the real-time data rapid peer-to-peer exchange and data and information interaction model is built, which improves the fault detection and timely removal ability of the distribution network. Secondly, the simulated annealing algorithm is used to reduce the number of power flow calculations, reduce the calculation time, improve the calculation speed of network reconstruction problems, and ensure that the optimal or better network topology can be obtained. Finally, the simulation analysis of the IEEE37 node system verifies the effectiveness of the proposed reconfiguration protection method in a complex environment with massive access to distributed energy.

This paper studies the properties of l 1 -symmetric vector random fields in R d , whose direct/cross covariances are functions of l 1 -norm. The spectral representation and a turning bands expression of the covariance matrix function are derived for an l 1 -symmetric vector random field that is mean square continuous. We also establish an integral relationship between an l 1 -symmetric covariance matrix function and an isotropic one. In addition, a simple but efficient approach is proposed to construct the l 1 -symmetric random field in R d , whose univariate marginal distributions may be taken as arbitrary infinitely divisible distribution with finite variance.

The covariance matrix function is characterized in this paper for a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the compact two-point homogeneous space. Necessary and sufficient conditions are derived for a symmetric and continuous matrix function to be an isotropic covariance matrix function on all compact two-point homogeneous spaces. It is also shown that, for a symmetric and continuous matrix function with compact support, if it makes an isotropic covariance matrix function in the Euclidean space, then it makes an isotropic covariance matrix function on the sphere or the real projective space.

In this thesis, author have reviewed the classical characterizations of isotropic positive definite functions on Euclidean spaces and spheres, and had applied them to develop a construction of isotropic positive de nite functions on spheres. However, this construction only works when the dimension of the sphere is odd. The next work is to develop isotropic positive de nite functions on all spheres.

For the peakedness comparison between two Gaussian random fields about their mean functions, a necessary and sufficient condition is derived in this paper in terms of their covariance functions. Interestingly, such a condition is also necessary and sufficient for the convex ordering between the two Gaussian random fields having identical mean functions. The relation to the equivalence of two Gaussian random fields is illustrated through some parametric examples. Necessary and/or sufficient conditions are given for the peakedness comparison and convex ordering between two elliptically contoured random fields. These conditions are applied to examine how certain parameters affect the peakedness of some Gaussian or elliptically contoured random fields.

It is shown in this paper that the probability measures generated by selfsimilar Gaussian random fields are mutually singular, whenever they have different scaling parameters. So are those ...

The Berezinskii-Kosterlitz-Thouless (BKT) mechanism, building upon proliferation of topological defects in 2D systems, is the first example of phase transition beyond the Landau-Ginzburg paradigm of symmetry breaking. Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. Here, we pin down two transitions that bound a BKT phase in an ideal 2D frustrated magnet TmMgGaO$_4$, via nuclear magnetic resonance under in-plane magnetic fields, which do not disturb the low-energy electronic states and allow BKT fluctuations to be detected sensitively. Moreover, by applying out-of-plane fields, we find a critical scaling behaviour of the magnetic susceptibility expected for the BKT transition. The experimental findings can be explained by quantum Monte Carlo simulations applied on an accurate triangular-lattice Ising model of the compound which hosts a BKT phase. These results provide a concrete example for the BKT phase and offer an ideal platform for future investigations on the BKT physics in magnetic materials., Comment: Version as accepted by Nature Communications, main text: 7 pages, 3 figures; supplementary information: 5 pages, 7 figures

In recent years, the development and research of flexible sensors have gradually deepened, and the performance of wearable, flexible devices for monitoring body temperature has also improved. For the human body, body temperature changes reflect much information about human health, and abnormal body temperature changes usually indicate poor health. Although body temperature is independent of the environment, the body surface temperature is easily affected by the surrounding environment, bringing challenges to body temperature monitoring equipment. To achieve real-time and sensitive detection of various parts temperature of the human body, researchers have developed many different types of high-sensitivity flexible temperature sensors, perfecting the function of electronic skin, and also proposed many practical applications. This article reviews the current research status of highly sensitive patterned flexible temperature sensors used to monitor body temperature changes. First, commonly used substrates and active materials for flexible temperature sensors have been summarized. Second, patterned fabricating methods and processes of flexible temperature sensors are introduced. Then, flexible temperature sensing performance are comprehensively discussed, including temperature measurement range, sensitivity, response time, temperature resolution. Finally, the application of flexible temperature sensors based on highly delicate patterning are demonstrated, and the future challenges of flexible temperature sensors have prospected.

A thin-tailed vector random field, referred to as a $K$-differenced vector random field, is introduced. Its finite-dimensional densities are the differences of two Bessel functions of second order,...

This paper introduces several vector random fields whose finite-dimensional characteristic functions are of hyperbolic type, including generalized logistic, hyperbolic secant, hyperbolic tangent, hyperbolic cosine ratio, and hyperbolic sine ratio vector random fields. They are elliptically contoured vector random fields with all orders of moments, and are infinitely divisible. In the scalar case, we make the peakedness comparison among these random fields. Hyperbolic cosine ratio and hyperbolic since ratio Levy processes are formulated as well.

A simple but efficient approach is proposed in this paper to construct the isotropic random field in (d ⩾ 2), whose univariate marginal distributions may be taken as any infinitely divisible distri...

We introduce a new class of non-Gaussian vector random fields in space and/or time, which are termed binomial-$\chi^2$ vector random fields and include $\chi^2$ vector random fields as special case...

Summary This paper introduces a simple method to construct a stationary process on the real line with a Polya-type covariance function and with any infinitely divisible marginal distribution, by randomising the timescale of the increment of a second-order Levy process with an appropriate positive random variable. With the construction method extended to the multivariate case, we construct vector stochastic processes with Polya-type direct covariance functions and with any specified infinitely divisible marginal distributions. This makes available a new class of non-Gaussian vector stochastic processes with flexible correlation structure for use in modelling and simulation.

A general form of the covariance matrix function is derived in this paper for a vector random field that is isotropic and mean square continuous on a compact connected two-point homogeneous space and stationary on a temporal domain. A series representation is presented for such a vector random field, which involve Jacobi polynomials and the distance defined on the compact two-point homogeneous space., 17 pages, no figures

This article characterizes the covariance matrix function of a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the sphere. By applying the characterization to examine the validity of a matrix function whose entries are polynomials of degrees up to 4, we obtain a necessary and sufficient condition for the polynomial matrix to be an isotropic covariance matrix function on the sphere.

For a vector random field that is isotropic and mean square continuous on a sphere and stationary on a temporal domain, this paper derives a general form of its covariance matrix function and provides a series representation for the random field, which involve the ultraspherical polynomials. The series representation is somehow an imitator of the covariance matrix function, but differs from the spectral representation in terms of the ordinary spherical harmonics, and is useful for modeling and simulation. Some semiparametric models are also illustrated.

This paper deals with a class of second-order vector random fields in the unit ball of Rd , whose direct/cross covariances are invariant or isotropic with respect to a distance defined on the ball, and gives a series representation of such an isotropic vector random field. A necessary format of covariance matrix functions is also derived for isotropic and mean square continuous vector random fields on the ball.