Continuous-Time Channel Prediction Based on Tensor Neural Ordinary Differential Equation

Channel prediction is critical to address the channel aging issue in mobile scenarios.Existing channel prediction techniques are mainly designed for discrete channel prediction,which can only predict the future channel in a fixed time slot per frame,while the other intra-frame channels are usually recovered by interpolation.However,these approaches suffer from a serious interpolation loss,especially for mobile millimeter-wave communications.To solve this challenging problem,we propose a tensor neural ordinary differential equation(TN-ODE)based continuous-time channel prediction scheme to realize the direct prediction of intra-frame channels.Specifically,inspired by the recently developed continuous mapping model named neural ODE in the field of machine learning,we first utilize the neural ODE model to predict future continuous-time channels.To improve the channel prediction accuracy and reduce computational complexity,we then propose the TN-ODE scheme to learn the structural characteristics of the high-dimensional channel by low-dimensional learnable transform.Simulation results show that the proposed scheme is able to achieve higher intra-frame channel prediction accuracy than existing schemes.

The Boundary Element Method for Ordinary State-Based Peridynamics

The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous problems.Up to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic finite element method(PD-FEM),and peridynamic boundary element method(PD-BEM),have been proposed.PD-BEM,in particular,outperforms other methods by eliminating spurious boundary softening,efficiently handling infinite problems,and ensuring high computational accuracy.However,the existing PD-BEM is constructed exclusively for bond-based peridynamics(BBPD)with fixed Poisson’s ratio,limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems.In this paper,we address these limitations by introducing the boundary element method(BEM)for ordinary state-based peridynamics(OSPD-BEM).Additionally,we present a crack propagationmodel embeddedwithin the framework ofOSPD-BEM to simulate crack propagations.To validate the effectiveness of OSPD-BEM,we conduct four numerical examples:deformation under uniaxial loading,crack initiation in a double-notched specimen,wedge-splitting test,and threepoint bending test.The results demonstrate the accuracy and efficiency of OSPD-BEM,highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson’s ratios.Moreover,OSPDBEMsignificantly reduces computational time and exhibits greater consistencywith experimental results compared to PD-MPM.

New Numerical Integration Formulations for Ordinary Differential Equations

An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, unconventional base-functions with trigonometric and exponential terms satisfying different conditions are employed to generate a number of formulations. Performances of the new schemes are tested against well-known numerical integrators for selected test cases with quite satisfactory results. Convergence and stability issues of the new formulations are not addressed as the treatment of these aspects requires a separate work. The general approach introduced herein opens a wide vista for producing virtually unlimited number of formulations.

Classification of 24 New Ordinary Chondrites from the Grove Mountains, Antarctica

Petrography and mineral chemistry of 24 ordinary chondrites from the Grove Mountains, Antarctica, have been studied in order to identify their chemical-petrographic types. These samples were selected from a total of 4448 Grove Mountains (GRV) meteorites collected during the 19th Chinese Antarctic Research Expedition so as to make an estimation of the large GRV meteorite collection. The chemical-petrographic types of these meteorites are presented below: 1 H3,2 H4, 4 H5, 2 H6, 1 L4, 7 L5, 5 L6, 1 LL4 and 1 LL6. The new data weaken the previous report that unequilibrated ordinary chondrites are unusually abundant in the Grove Mountains region. However, this work confirms significant differences in distribution patterns of chemical-petrographic types between the Grove Mountains and other regions in Antarctica. Many of these meteorites show significant terrestrial weathering, probably due to a high abundance ratio of meteorites found in moraines to those on blue ice. Nine meteorites experienced severe shock metamorphism, as evidenced by undulose extinction and intense fracturing of silicates and presence of shock-induced melt veins and pockets. These heavily shocked meteorites provided us with natural samples for the study of high-pressure polymorphs of minerals.

New Derivation of Ordinary Differential Equations for Transient Free-Surface Green Functions

Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics.

Mapping Soil Electrical Conductivity Using Ordinary Kriging Combined with Back-propagation Network

Accurate mapping of soil salinity and recognition of its influencing factors are essential for sustainable crop production and soil health. Although the influencing factors have been used to improve the mapping accuracy of soil salinity, few studies have considered both aspects of spatial variation caused by the influencing factors and spatial autocorrelations for mapping. The objective of this study was to demonstrate that the ordinary kriging combined with back-propagation network(OK_BP), considering the two aspects of spatial variation, which can benefit the improvement of the mapping accuracy of soil salinity. To test the effectiveness of this approach, 70 sites were sampled at two depths(0–30 and 30–50 cm) in Ningxia Hui Autonomous Region, China. Ordinary kriging(OK), back-propagation network(BP) and regression kriging(RK) were used in comparison analysis; the root mean square error(RMSE), relative improvement(RI) and the decrease in estimation imprecision(DIP) were used to judge the mapping quality. Results showed that OK_BP avoided the both underestimation and overestimation of the higher and lower values of interpolation surfaces. OK_BP revealed more details of the spatial variation responding to influencing factors, and provided more flexibility for incorporating various correlated factors in the mapping. Moreover, OK_BP obtained better results with respect to the reference methods(i.e., OK, BP, and RK) in terms of the lowest RMSE, the highest RI and DIP. Thus, it is concluded that OK_BP is an effective method for mapping soil salinity with a high accuracy.

Refraction of extraordinary rays and ordinary rays in the Savart polariscope

The refraction of rays in the Savart polariscope is different from the isotropic medium. We have analysed and discussed the refraction of rays in the Savart polariscope on the basis of the Snell law. The refraction formulae of the extraordinary rays and ordinary rays were derived. Results obtained may provide theoretical and practical guide lines for studying, developing and engineering of polarization interference imaging spectrometer.

Effects of fibers on expansive shotcrete mixtures consisting of calcium sulfoaluminate cement,ordinary Portland cement,and calcium sulfate

The mining industry often uses shotcrete for ground stabilization. However, cracking within shotcrete is commonly observed, which delays production schedules and increases maintenance costs. A possible crack reduction method is using expansive shotcrete mixture consisting of calcium sulfoaluminate cement(CSA), ordinary Portland cement(OPC), and calcium sulfate(CS) to reduce shrinkage. Furthermore, fibers can be added to the mixture to restrain expansion and impede cracking. The objective of this paper is to study the effects of nylon fiber, glass fiber, and steel fiber on an expansive shotcrete mixture that can better resist cracking. In this study, parameters such as density, water absorption, volume of permeable voids, unconfined compressive strength(UCS), splitting tensile strength(STS), and volume change of fiber-added expansive mixtures were determined at different time periods(i.e. the strengths on the 28 th day, and the volume changes on the 1 st, 7 th, 14 th, 21 st, and 28 th days). The results show that addition of fibers can improve mixture durability, in the form of decreased water absorption and reduced permeable pore space content. Moreover, the expansion of the CSA-OPC-CS mixture was restrained up to50% by glass fiber, up to 43% by nylon fiber, and up to 28% by steel fiber. The results show that the STS was improved by 57% with glass fiber addition, 43% with steel fiber addition, and 38% with nylon fiber addition. The UCS was also increased by 31% after steel fiber addition, 26% after nylon fiber addition, and16% after glass fiber addition. These results suggest that fiber additions to the expansive shotcrete mixtures can improve durability and strengths while controlling expansion.

Sonocatalytic degradation of methyl orange in the presence of (nanometer and ordinary) anatase TiO_2 powders

The nanometer and ordinary anatase titanium dioxide(TiO_2) powders were adopted as the sonocatalysts for the degradation of methyl orange used as a model compound for the first time. It was found that the sonocatalytic degradation effect of methyl orange in the presence of TiO_2 powder were much better than that without TiO_2, but the sonocatalytic activity of the nanometer anatase TiO_2 particle was obviously higher than that of ordinary anatase TiO_2 particle. Although there are many factors influencing sonocatalytic degradation of methyl orange, the experimental results showed that the best degradation ratio of methyl orange could be obtained when the experimental conditions were: initial concentration 15 mg/L, nanometer anatase TiO_2 adding amount 750 mg/L, ultrasonic frequency 40 kHz, output power 50 W, pH = 3.0 and temperature 40℃ within 150 min. In addition, the catalytic activity of reused nanometer anatase TiO_2 catalyst was also studied and found to decline gradually comparing with initial nanometer anatase TiO_2 catalyst. All experiments indicated that the method of the sonocatalytic degradation of organic pollutants in the presence of TiO_2 powder was an advisable choice for non- or low-transparent organic wastewaters.

HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.

The Durability of Alkali-Activated Materials in Comparison with Ordinary Portland Cements and Concretes:A Review

China is the largest producer and user of ordinary Portland cement(OPC),and the rapid growth of infrastructure development demands more sustainable building materials for concrete structures.Alkali-activated materials(AAMs)are a new type of energy-saving and environmentally friendly building material with a wide range of potential applications.This paper compares the durability of AAMs and 0 PC-based materials un der sulfate attack,acid corrosion,carb on ation,and chloride penetratio n.Different AAMs have shown distinct durability properties due to different compositions being formed when different raw materials are used.According to the calcium(Ca)concentration of the raw materials,this paper interprets the deterioration mechanisms of three categories of AAMs:calcium-free,low-calcium,and calcium-rich.Conflicts found in the most recent research are highlighted,as they raise concerns regarding the consistenee and long-term properties of AAMs.Nevertheless,AAMs show better durability performances than OPC-based materials in general.

On Exact Solutions of Second Order Nonlinear Ordinary Differential Equations

In this paper, a new approach for solving the second order nonlinear ordinary differential equation y’’ + p(x;y)y’ = G(x;y) is considered. The results obtained by this approach are illustrated by examples and show that this method is powerful for this type of equations.

The vanadium isotopic composition of L ordinary chondrites

Stable isotopic data of meteorites are critical for understanding the evolution of terrestrial planets. In this study, we report high-precision vanadium （V） isotopic compositions of 11 unequilibrated and equilibrated L chondrites. Our samples show an average δ^51v of -1.25‰ ±0.38‰ （2SD, n = 11）, which is ,- 0.5‰ lighter than that of the bulk silicate Earth constrained by mantle peridotites. Isotopic fractionation in type 3 ordinary chondrites vary from - 1.76‰ to - 1.29‰, whereas the δ^51V of equilibrated chondrites vary from - 1.37‰ to -1.08‰. 551V of L chondrites do not correlate with thermal metamorphism, shock stage, or weathering degree. Future studies are required to explore the reason for V isotope variation in the solar system.

A New Circulant Preconditioned GMRES Method for Solving Ordinary Differential Equation

The preconditioned generalized minimal residual(GMRES) method is a common method for solving non-symmetric,large and sparse linear systems which originated in discrete ordinary differential equations by Boundary value methods.In this paper,we propose a new circulant preconditioner to speed up the convergence rate of the GMRES method, which is a convex linear combination of P-circulant and Strang-type circulant preconditioners. Theoretical and practical arguments are given to show that this preconditioner is feasible and effective in some cases.

Weathering,shock metamorphism and type distribution patterns of 98 ordinary chondrites from the Grove Mountains,Antarctica

Petrography and mineral chemistry of ninety-eight ordinary chondrites from Grove Mountains （GRV）, Antarctica, were presented and their. Weathering effect, shock metamorphism and type distribution patterns were discussed in this study. Among them, six are unequilibrated ordinary chondrites, including 3 H3 and 3 L3 ; and 92 meteorites are equilibrated ordinary chondrites, including 24 H-group （ 13 H4, 10 H5, 1 H6）, 64 L-group （2 L4, 44 L5, 18 L6） and 4 LL-group （3 LL4, 1 LL5）. Most GRV ehondrites （ 〉 90% ） displayed minor weathering effect （ W1 and W2）. About half of the meteorites experienced severe shock metamorphism. They commonly contain shock-induced melt veins and pockets. These heavily shocked meteorites provide us with natural samples for study of high-pressure polymorphs of minerals. In addition, the Grove Mountains collection seems to have more abundant unequilibrated and L group ordinary ehondrites compared to the US Antarctic meteorite collection which were mainly found along the Transantarctic Mountains.

Role of detection of microsatellite instability in Chinese with hereditary nonpolyposis colorectal cancer or ordinary hereditary colorectal cancer

AIM： To detect microsatellite instability （MSI） in patients with hereditary nonpolyposis colorectal cancer or ordinary hereditary colorectal cancer and to provide criteria for screening the kindreds with hereditary nonpolyposis colorectal cancer at molecular level.METHODS： MSI was detected in the specimens from 20 cases with HNPCC, 20 cases with ordinary hereditary colorectal cancer and 20 cases with sporadic colorectal cancer by means of polymerase chain reaction-single strand conformation polymorphism. RESULTS： The positive rate of MSI was 85% （17/20） in HNPCC group, 40% （8/20） in ordinary hereditary colorectal cancer group and 10% （2/20） in the sporadic colorectal cancer group respectively. The differences were significant. The mean ages of the three groups were 43.6, 52.2, and 61.8 years respectively, which increased gradually. The incidence of right hemicolon cancer was 64.7%, 37.5%, and 0% respectively, which decreased gradually and had significant difference. The expression ratio of BAT26 and BAT25 was 94.1% respectively, which was highest in the 5 gene sites studied. The incidence of poorly differentiated adenocarcinoma was 70.6% in HNPCC group among high frequency microsatellite instability （MSI-H）, which was higher than the other two groups, which had 50% and 50% respectively. CONCLUSION： The incidence of MSI-H is higher in HNPCC group. The detection of MSI is simple and economical and has high correlation with the clinicopathologic feature of HNPCC and can be used as a screening method to detect the germ line mutation of the mismatch repair gene.

Stochastic Computational Approach for Complex Nonlinear Ordinary Differential Equations

We present an evolutionary computational approach for the solution of nonlinear ordinary differential equations(NLODEs).The mathematical modeling is performed by a feed-forward artificial neural network that defines an unsupervised error.The training of these networks is achieved by a hybrid intelligent algorithm,a combination of global search with genetic algorithm and local search by pattern search technique.The applicability of this approach ranges from single order NLODEs,to systems of coupled differential equations.We illustrate the method by solving a variety of model problems and present comparisons with solutions obtained by exact methods and classical numerical methods.The solution is provided on a continuous finite time interval unlike the other numerical techniques with comparable accuracy.With the advent of neuroprocessors and digital signal processors the method becomes particularly interesting due to the expected essential gains in the execution speed.

Comparative Study on Energy Consumption Structure of Ordinary Rural Households and Rural Tourism Households in Zhejiang Province, China

With the rapid development of rural tourism in China, more and more rural households operate a rural tourism business. The purpose of this study is to understand the energy consumption characteristic of ordinary rural households (ORHs) and rural tourism households (RTHs) in the mountainous area and islands area in Zhejiang province. 225 households were surveyed, including 185 ORHs and 40 RTHs, based on a field survey in Quzhou (mountainous area) and Zhoushan (islands area). Results reveal that energy consumption of ORHs is low, but energy comsumption of RTHs is high, about 3 to 5 times higher than that of ORHs. Given the results, the government and RTHs should pay more attention to take measures to reduce energy comsumption. Meanwhile, the factors affecting households’ energy consumption are also analyzed. Energy consumption of ORHs is affected by frequently used area, family income level and permanent population. Then energy consumption of RTHs is mainly related to the total building area, number of air conditioner (AC), number of guestrooms and family income level.

Nonlinear Acoustic-Optical Effect and Extraordinary Diffraction Distribution in Liquid Surface

Nonlinear acoustic-optical effect is discovered by using a low-frequency liquid surface acoustic wave with great amplitude.There are higher harmonics in diffracted light and the intensity of the higher harmonic has the relation of Bessel's function with the amplitude.The light patterns diffracted by the wave can be classified into the ordinary and extraordinary beams which are corresponding to small and great amplitudes of the waves.The ordinary and extraordinary patterns are observed experimentally and the critical amplitude value is found.

Cantorian-Fractal Kinetic Energy and Potential Energy as the Ordinary and Dark Energy Density of the Cosmos Respectively

In a one-dimension Mauldin-Williams Random Cantor Set Universe, the Sigalotti topological speed of light is where . It follows then that the corresponding topological acceleration must be a golden mean downscaling of c namely . Since the maximal height in the one-dimensional universe must be where is the unit interval length and note that the topological mass (m) and topological dimension (D) where m = D = 5 are that of the largest unit sphere volume, we can conclude that the potential energy of classical mechanics translates to . Remembering that the kinetic energy is , then by the same logic we see that when m = 5 is replaced by for reasons which are explained in the main body of the present work. Adding both expressions together, we find Einstein’s maximal energy . As a general conclusion, we note that within high energy cosmology, the sharp distinction between potential energy and kinetic energy of classical mechanics is blurred on the cosmic scale. Apart of being an original contribution, the article presents an almost complete bibliography on the Cantorian-fractal spacetime theory.