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.

Solving the Three-Neutrino Problem as One of the Three-Body Problems in Physics

By using the standard PMNS (Pontecorvo-Maki-Nakagawa-Sakata) mixing matrix and applying the rule for the sum of the oscillation probabilities of three neutrinos, the equations of motion were derived in which the Dirac CP violating phase appeared as an unknown quantity. The equations of motion were separately derived for each of the three possible transitions for flavor-neutrino oscillations. Two roots of those equations were obtained in the form of two formulas for the Dirac CP violating phase with opposite signs. In the mathematical sense, the connection between those formulas was established in order to maintain the continuous process of oscillation of three neutrinos. This made it possible to calculate the numerical value for the Dirac CP violating phase, the Jarlskog invariant and to write the general form of the PMNS mixing matrix in the final form in which all its elements are defined with explicit numerical values.

Short and Simple

How stories from ordinary people hold extraordinary social value.During a two-week trip to my native Xinjiang Uygur Autonomous Region in northwest China,I contemplated the following question:Born and raised in the region until the age of 18,how can I tell the stories that unfold here to people on the outside?The stories of ordinary locals are very simple,to the point that many people feel they hold no real“news value.”But for those who have lived through Xinjiang’s difficult times,the present is hard-won.

Dark Matter Particles May Never Be Directly Detected by Instruments—A Dark Matter Mechanism That Does Not Exceed the Standard Model Framework

A dark matter mechanism within the framework of the standard model (SM) of particle physics is proposed in this article that the essence of dark matter may be the excited virtual particle field by the gravitational field of ordinary matter, which contains virtual photons, virtual positive and negative electron pairs, virtual gluons, virtual positive and negative quark pairs, virtual neutrinos etc. In this mechanism, there are two basic assumptions: 1) the stronger the gravitational field of ordinary matter, the greater the excited energy (mass) density of virtual particle field;2) The excited virtual particle field is generally very weak in self-interaction. The virtual particle field excited by gravity can exhibit the properties of dark matter and may become a dark matter candidate. Based on this new dark matter mechanism, the hydrodynamic equations and cosmic perturbation equations describing cosmic matter are improved, and this may be meaningful for solving the challenges faced by the standard cosmological model (Lambda-CDM or LCDM) and developing and perfecting LCDM model.

2022 HP special volume:Interdisciplinary high pressure science and technology

High pressure science and technology is a vast area of inter-disciplinary research that encompasses the fields of physics,chem-istry,geoscience,and materials science and in which the science of ordinary matter is only a special case under ambient condi-tions.Pressure,the physical variable of force exerted on the chem-ical bonding of a material,directly controls the material’s phys-ical and chemical properties.

Promising applications of non-invasive brain stimulation on military cognition enhancement:a long way to go

Cognitive function encompasses a wide range of brain functions,such as attention and working memory,all of which are essential for the effective functioning of ordinary people in their work and daily lives.However,military personnel constitute a unique occupational group,necessitating the ability to process complex environments and multiple critical events concurrently over extended durations.

Towards a Unified Single Analysis Framework Embedded with Multiple Spatial and Time Discretized Methods for Linear Structural Dynamics

We propose a novel computational framework that is capable of employing different time integration algorithms and different space discretized methods such as the Finite Element Method,particle methods,and other spatial methods on a single body sub-dividedintomultiple subdomains.This is in conjunctionwithimplementing thewell known Generalized Single Step Single Solve(GS4)family of algorithms which encompass the entire scope of Linear Multistep algorithms that have been developed over the past 50 years or so and are second order accurate into the Differential Algebraic Equation framework.In the current state of technology,the coupling of altogether different time integration algorithms has been limited to the same family of algorithms such as theNewmarkmethods and the coupling of different algorithms usually has resulted in reduced accuracy in one or more variables including the Lagrange multiplier.However,the robustness and versatility of the GS4 with its ability to accurately account for the numerical shifts in various time schemes it encompasses,overcomes such barriers and allows a wide variety of arbitrary implicit-implicit,implicit-explicit,and explicit-explicit pairing of the various time schemes while maintaining the second order accuracy in time for not only all primary variables such as displacement,velocity and acceleration but also the Lagrange multipliers used for coupling the subdomains.By selecting an appropriate spatialmethod and time scheme on the area with localized phenomena contrary to utilizing a single process on the entire body,the proposed work has the potential to better capture the physics of a given simulation.The method is validated by solving 2D problems for the linear second order systems with various combination of spatial methods and time schemes with great flexibility.The accuracy and efficacy of the present work have not yet been seen in the current field,and it has shown significant promise in its capabilities and effectiveness for general linear dynamics through numerical examples.

Inequalities for Sums and Products of Complex Zeros of Solutions to ODE with Polynomial Right Parts

The paper is devoted to non-homogeneous second-order differential equations with polynomial right parts and polynomial coefficients.We derive estimates for the partial sums and products of the zeros of solutions to the considered equations.These estimates give us bounds for the function counting the zeros of solutions and information about the zero-free domains.

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.

Effects of Different Proportions of Controlled Release Urea and Ordinary Urea on Peanut Yield

[Objectives]To study the effects of different proportions of controlled release urea and ordinary urea on peanut yield.[Methods]A total of 5 treatments were set up according to different proportions of controlled release urea and ordinary urea,randomly arranged in blocks and repeated 3 times.[Results]The test results of field districts showed that different proportions of controlled release urea and conventional urea had different effects on peanut yield.On the basis of applying 50 kg/666.7 m^(2)of calcium superphosphate and 17 kg/666.7 m^(2)of potassium sulfate,13.34 kg/666.7 m^(2)of pure nitrogen was applied.The optimal ratio of controlled release urea to ordinary urea was 75:25,followed by 50:50.The output was 379.83 and 371.83 kg/666.7 m^(2),separately increased by 6.74%and 4.50%compared to the application of ordinary urea.[Conclusions]The combined application of controlled release urea and ordinary urea in peanuts can significantly increase peanut yield compared to just applying ordinary urea.

Chinese Documentaries

The film series tells eight stories that cover the topics of family,physiology,law,and women.Eight life scenes are presented in four groups of opposite themes,offer­ing a glimpse into the choices and fate that ordinary people face in decisive moments.By zooming in on each unique story of second choices,it not only showcases the courage and resilience Chinese people exhibit when facing diffi­culties,but also inspires the audi­ence with courage to think about life and their future.

The Effect of Foreign Direct Investment on Air Pollution in the Economic Community of West African States region: What Influence Does Tax Expenditure Have?

Air pollution is one of the crucial environmental challenges facing the countries of the Economic Community of West African States (ECOWAS). The objective of this paper is to examine the effect of an attractive tax policy on the relationship between Foreign Direct Investment (FDI) and air pollution in ECOWAS region over the period 2000 to 2019. By using the Ordinary Least Squares (OLS) method and panel data analyses (fixed effects and random effects), the results show that, in general, FDI does not have a significant effect on air pollution in the region. However, closer analysis reveals that an interaction between FDI and an attractive tax policy has a negative effect on air quality, leading to an increase in air pollution. Thus, companies attracted by tax incentives may not meet rigorous environmental standards. These results highlight the importance for policymakers to balance economic incentives with environmental protection in ECOWAS. Attractive tax policies can stimulate investment, but they must be designed in a way that encourages environmentally friendly practices, thereby helping to improve air quality in the region.

A Filtered Milne-Simpson ODE Method with Enhanced Stability Properties

The Milne-Simpson method is a two-step implicit linear multistep method for the numerical solution of ODEs that obtains the theoretically highest order of convergence for such a method. The stability region of the method is only an interval on the imaginary axis and the method is classified as weakly stable which causes non-physical oscillations to appear in numerical solutions. For this reason, the method is seldom used in applications. This work examines filtering techniques that improve the stability properties of the Milne-Simpson method while retaining its fourth-order convergence rate. The resulting filtered Milne-Simpson method is attractive as a method of lines integrator of linear time-dependent partial differential equations.

Solution of Laguerre’s Differential Equations via Modified Adomian Decomposition Method

This paper presents a technique for obtaining an exact solution for the well-known Laguerre’s differential equations that arise in the modeling of several phenomena in quantum mechanics and engineering. We utilize an efficient procedure based on the modified Adomian decomposition method to obtain closed-form solutions of the Laguerre’s and the associated Laguerre’s differential equations. The proposed technique makes sense as the attitudes of the acquired solutions towards the neighboring singular points are correctly taken care of.

City-making,Space and Spirituality

This book is about the soul of the city,embodied in its spaces and people.It traces dynamics in inner city neighbourhoods of South Africa’s post-apartheid capital,Pretoria.Viewing the city through its most vulnerable people and places,it recognises that urban space is never neutral and shaped by competing value frameworks.The first part of the book invites planners,city-makers,and ordinary urban citizens to consider a new self-understanding,reclaiming their agency in the city-making process.

Evaluation of Different Topographic Parameters Extracted from the Digital Elevation Measurements with the Use of Geostatistical Interpolation Methods

Gradient slope, aspect slope, profiling and contourlines are important topographic parameters that can be derived from digital elevation data obtained from different sources with exploitation of different interpolation techniques. Geostatistical interpolation methods such as ordinary kriging models constitute reliable alternatives to deterministic approaches in creation of continuous surface models from discrete elevation data. This research aimed at extraction, analysis, and evaluation of different terrain parameters elevation measurements with the use of different ordinary kriging models including the linear model, the circular model, the spherical model, the exponential models, and the Gaussian model. Different ordinary kriging models under ESRI ArcView 3.3 package along with its 3D analyst and Spatial analysis extensions have been exploited in extraction of gradient slope maps, aspect slope maps, and hillshade maps in addition to contourline maps from a sample of elevation data. Visual analysis of the gradient slope maps shows great similarities between the slope maps from the linear, circular, spherical, and exponential OK models, however, that from OK Gaussian models look very different as different sizes and arrangements of the colour patches, referring to different tones and different textures where smooth tones and smooth textures dominate the gradient slope map from the OK Gaussian model. Thus, gradient slope degradation and smoothing are considerably high in the gradient slope map from Gaussian model compared to the slope maps from the other four OK models. Also, the mean slope in the Gaussian model records the lowest value with the lowest value of the standard deviation of slopes in the same map reflecting less structured and highly smoothed gradient slope map compared to the slope maps from the other OK models. Thus, similar sizes of the colour patches and similar tones and similar texture dominate the different aspect slope maps. This is not the case in Figure 2(e) which depicts the aspect slope map extracted with the use of the Gaussian OK model where the smooth colour patches, smooth tones and smooth textures can be observed. Also, the Aspect map, hillshade map and the contourline map from Gaussian OK model are visually and statistically different from their corresponding maps created with the other four OK models. Finally, analysis of extracted two groups of profiles shows that the profiles extracted with the use of linear, circular, spherical, and exponential OK models run close and show highly corrugated and varied terrain. This is different from the profiles with the use of the Gaussian model which are less corrugated and tend to smooth and approximate different parts of the terrains.

Three Neutrinos and the Formula for the Dirac CP Violation Phase

Based on the derived equations of three neutrinos, especially for motion through a physical vacuum and for space with a constant density of matter, the same formula for Dirac’s CP-violating phase was obtained. The main property of this formula is that it does not depend on mixing angles θ12, θ13, θ23 and remains unchanged for the spaces through which the neutrino beam moves. Using that formula, the final form for the Jarlskog invariant formula was formed. Knowing the Dirac CPV phase would have the following consequences: 1) By obtaining an explicit mathematical formula for the Dirac CPV phase, it would no longer be necessary to perform computer simulations to draw areas where it could be found. 2) At the same time, the Dirac CPV phase does not depend on the mixing angles θ12, θ13, θ23 that make up the elements of the PMNS matrix, but depends only on the ratio of the corresponding differences of the squares of the neutrino masses.

Testing the Results of Measurements of Neutrino Parameters Using the Dirac CPV Phase Formula

Essentially the main intention of this paper was to test the formula for the Dirac CPV phase and see if it can reflect the results of experimental measurements of neutrino parameters. By knowing the mathematical formula for the Dirac CPV phase, a connection was established with some of the residual symmetry groups, which made it possible to develop a procedure for directly determining the range in which the numerical value for the Dirac CPV phase could be found. In this sense, two different sources of information containing measured data for neutrinos were used for the corresponding calculations, and then a comparative overview of the calculated results was presented. It is particularly emphasized that the formula for the Dirac CPV phase does not depend on the mixing angles that are incorporated into the PMNS matrix, but only on the ratio between the corresponding squares of the neutrino mass difference. All the numerous results obtained from the corresponding calculations for the Dirac CPV phase point to the justified introduction of the theory that is related to three neutrinos, and thus the agreement of our results with the STEREO experiment is justified, so that the hypothesis of the possible existence of a sterile neutrino in nature should be excluded.

基于Ordinary Kriging方法的京津冀地区降水量空间分布研究

以77个国家气象站点降水量观测资料为基础,采用Ordinary Kriging方法探究逐月和年降水量空间分布差异。结果表明:(1)京津冀地区降水量空间差异有统计学意义,站点观测记录范围介于394.1~764.9mm,站点间平均值为506.7mm;(2)插值方法拟合的半方差模型R^(2)介于0.63~0.77之间,块金系数为5.54%~52.25%,区域降水量在空间分布上存在强烈和中度空间自相关性;(3)年内降水量分布呈顺时针变化,年降水量呈现自东向西地带性减少格局;(4)通Ordinary Kriding插值法得到京津冀地区逐月和年降水量空间分布数据,发展了稀疏站点数据拓展为空间连续性数据的应用经验。