ON THE EXISTENCE OF ZERO POINTS OF A CONTINUOUS FUNCTION

A sufficient condition is given to assert that a continuous mapping between Rm and Rn has a zero. The constructive proof of the result is based upon continuation methods and supplies the existence of a path leading to the zero point.

On the Cosmical Zero Point Energy Density

The frequency spectrum of the cosmical Zero Point Energy (ZPE) and its total density are so far unknown in their details. In the present complementary investigation, a revised theory forms the basis for studies of this concept in two respects. It first applies to the observable universe considered as an entity, as well as to included subregions such as the galaxies with supermassive black holes. Second, experiments are proposed on the maximum Casimir force arising between two metal plates of different materials and with a vanishing air gap in their spacing. This serves the purpose of making an indirect determination of the ZPE energy density in the laboratory, i.e. at the Earth’s orbit. The ZPE energy density is interpreted as dark matter density and its pressure gradient as dark energy force density.

Mode Interaction at a Triple Zero Point of O(2) symmetric Nonlinear Systems with Two Parameters

We consider a triple zero point of nonlinear equations with O(2 symmetry, where the Jacobian has a zero eigenvalue of geometric multiplicity one and algebraic multiplicity three. We show that this triple zero point exhibits a new bifurcation phenomenon, that is, a mode interaction of the following three paths: bifurcation points from steady states, steady states and rotating waves to standing waves, rotating waves and modulated rotating waves respectively.

The ~3.6 to 3.7 M Paucity in Global Earthquake Frequency: Potential Coupling to Zero Point Fluctuation Force and Quantum Energies

There has been protracted historical evidence of a relative paucity in the distribution frequency of global earthquakes within the M = 3.5 to 4.0 range. We observed a similar phenomenon for all recently recorded earthquakes from January 2009 through August 2013. Frequency distributions with increments of M = 0.1 verified the trough of the diminished incidence to be between M = 3.6 and 3.7 with an abrupt increase between M = 3.9 and 4.0. The calculated equivalent photon wavelength for the energies associated with M = 3.6 approaches Planck’s Length while the related time increment is the cutoff frequency for the Zero Point Fluctuation force coupled to gravity. The conspicuous congruence between Planck’s time and length and the lower than expected frequency based upon Gaussian assumptions of distribution for the discrete band of energy associated with this magnitude range of earthquakes suggests a conduit may exist between intrinsic features of Planck space-time and geophysical processes. The existence of such a connection would encourage alternative explanations for sun-seismic activities as due to solar instabilities. Instead, it may reflect influence upon both from alterations in the structure of space being traversed by the solar system as it moves through the galaxy.

Zero Point of Charge of Organo—Mineral Complexes

Five soil sapmles collected from China and two soil samples from Pakistan with widely different origin and characterstics were used to study the zero point of charge(ZPC) of soil colloids.The results showed that the value of zero point of charge of H-clay complexes was lower than that of H-clays in all the samples.Natural clay complexes had the highest ZPC as compared to -Hclay complex and H-clay in alfisol,closer to H-clays rather than H-clay complexes in oxisol and udult.The Delta Value of ZPT(zero point of titration )to ZPC was higher in H-Clay complexes than in H-Clays.

Some Consequences of Zero Point Energy

Both theory and experiments indicate that the vacuum is not a state of empty space, but is populated by electromagnetic fluctuations at a lowest nonzero level, the Zero Point Energy (ZPE). This debouches into considerable changes of fundamental physics, as shown by a revised quantum electrodynamic theory (RQED) applied to elementary particles, and by a revised ZPE frequency spectrum applied to the expanding universe. The Standard Model based on a vacuum state of empty space is thus replaced by RQED, thereby resulting in massive elementary particles from the beginning, independently of the theory by Higgs. Also the basic properties of the Higgs-like particle detected at CERN can be reproduced by RQED. It further leads to new fundamental results beyond the theories by Dirac and Higgs, such as to a deduced value of the elementary net charge, magnetic confinement of charged particle configurations, intrinsic local particle charges, photon spin with a very small but nonzero photon rest mass, and needle-like particle-wave properties which contribute to the understanding of the photoelectric effect and two-slit experiments. The real macroscopic pressure due to the revised ZPE frequency distribution further influences the dynamics of the expanding universe, by the ZPE photon pressure gradient acting as dark energy, and the ZPE photon energy density acting as dark matter. This results in a model being consistent with the observed scale, the rate of expansion, and the stability of a flat expanding observable universe.

Zero Point Energy Effects on Quantum Electrodynamics

The vacuum is not a state of empty space, but is populated by electromagnetic fluctuations at a lowest nonzero level, the Zero Point Energy (ZPE). As distinguished from conventional theories, such as that of the Standard Model, the present revised quantum electrodynamic theory (RQED) includes the ZPE in its field equations. This leads to new results far beyond those obtained from conventional theories such as those by Dirac and Higgs. Thus, the present theory results in massive elementary particles from the beginning, being independent of the theory by Higgs. This paper describes the background and results of RQED, summarizing the weak points of conventional theories, the unification of included fundamental concepts, the present basic field equations, new obtained results, and special points of experimental support. In other words, the new points stressed in this paper are in particular the relation between a nonzero electric field divergence in the vacuum and the ZPE, and a number of new experimentally supported results due to a nonzero ZPE energy density in the same state.

A SIMPLICIAL ALGORITHM FOR COMPUTING AN INTEGER ZERO POINT OF A MAPPING WITH THE DIRECTION PRESERVING PROPERTY

A mapping f ： Z^n → Rn is said to possess the direction preserving property if fi（x） 〉 0 implies fi（y） ≥ 0 for any integer points x and y with ｜｜x - y｜｜∞≤ 1. In this paper, a simplicial algorithm is developed for computing an integer zero point of a mapping with the direction preserving property. We assume that there is an integer point x^0 with c ≤ x^0≤d satisfying that maxl≤i≤（xi - xi^0）fi（x） 〉 0 for any integer point x with f（x） ≠ 0 on the boundary of H = {x ∈R^n [c-e ≤ x〈d＋e},wherecanddaretwo finite integer points with c 〈 d and e = （1, 1,... , 1）^T E R^n. This assumption is implied by one of two conditions for the existence of an integer zero point of a mapping with the preserving property in van der Laan et al. （2004）. Under this assumption, starting at x^0, the algorithm follows a finite simplicial path and terminates at an integer zero point of the mapping. This result has applications in general economic equilibrium models with indivisible commodities.

A SIMPLICIAL HOMOTOPY ALGORITHM FOR COMPUTING ZERO POINTS ON POLYTOPES

In this paper a triangulation of continuous and arbitrary refinement of grid sizes is proposed for simplicial homotopy algorithms to compute zero points on a polytope P. The proposed algorithm generates a piecewise linear path in P × [1,∞) from any chosen interior point x0 of P on level {1} to a solution of the underlying problem. The path is followed by making linear programming pivot steps in a linear system and replacement steps in the triangnlation.The starting point x0 is left in a direction to one vertex of P. The direction in which x0 leaves depends on the function value at x0 and the polytope P. Moreover, we also give a new equivalent form of the Brouwer fixed point theorem on polytopes. This form has many important applications in mathematical programming and the theory of differential equations.

ZEROS AND FIXED POINTS OF DIFFERENCE OPERATORS OF MEROMORPHIC FUNCTIONS

Let f be a transcendental meromorphic function and △f（z） = f（z ＋ 1） -- f（z） A number of results are proved concerning the existences of zeros and fixed points of Af（z） and △f（z）/f（z） when f（z） is of order σ（f）=1. Examples show that some of the results are sharp.

Number of zero point for a polynomial in real field

IT is well known that for any real coefficient polynomial f(x) of degree n,how to determineits number of real zero points is a very important problem in theory of polynomial,as well as inapplications in mathematics,mechanics,physics and other subjects.The way to solve thisproblem by using Euclidean mutual division as pointed out by Sturm is not simple and conve-nient for us to use the theoretic analyses for the above problem because the relation

The Isoelectric Point and the Points of Zero Charge of Fe-Al-Mg Hydrotalcite-like Compounds

The relation of the isoelectric point (IEP) and the point of zero net charge (PZNC) of the hydrotalcite-like compounds was discussed. It was found that the IEP does not equal to the PZNC and the IEP is higher than the PZNC. The structural positive charges existing in the HTlc, which cause the difference between the IEP and the PZNC. The effects of the structural positive charges of the HTlc on its IEP and PZNC are the same as the specific adsorption of metal cations.

Indelible Rules of Josephson Coupling Energy and Zero-Point Energy in High-Tc Cuprates

This paper shows that the Josephson coupling energy and the zero-point energy have indelible rules on the superfluid density and the superconductivity in the high-Tc cuprates.This paper also shows that the values of Tc at underdoped and overdoped regions are determined by the damage conditions of the phase coherence in the classical and the quantum XY-models,respectively.

A Note on Modified Mann Accretive Iterations for Zero Points of Operators

A more general form of modified Mann iterations which converges strongly to a zero point of an m-accretive operator is given.The work in this paper is an extension and complement of the corresponding result of Kim T.H.and Xu H.K in

A Measure System of Zero Moment Point Using Wearable Inertial Sensors

Keeping balance is the premise of human walking. ZMP(zero moment point) is a point where total torque achieves balance. It is an important evaluation parameter of balance ability in walking, since it can be used to better reflect the dynamic balance during walking. ZMP can be used in many applications, such as medical rehabilitation, disease diagnosis, treatment and etc. In this paper, wearable inertial sensors system based on MEMS is used to measure ZMP(zero moment point) during walking, which is cheap, convenient, and free from the restriction of lab. Our wearable ZMP measurement system consists of inertial measurement subsystem and PC real-time monitoring station. Inertial measurement subsystem includes 9-axis inertial sensing nodes, the body communication network and the central node. Inertial sensing nodes are mounted on different parts of the body to collect body posture information in real-time, and then the best estimation of current posture are obtained by Kalman filter. The data from sensors is aggregated to the central node through the CAN bus, and then ZMP is calculated. Finally, it can be showed in the PC monitoring station. Experiments prove the system can achieve real-time ZMP detection during walking.

Superconductivity, Superfluidity and Zero-Point Oscillations

It is shown that both super phenomena-superconductivity and superfluidity are based on the same mechanism of streamline of zero-point oscillations. Proof of this is the agreement of obtained theoretical estimations with measured data.

An Analogy between the Properties of “Dark Energy” and Physical Vacuum Consisting of Quantum Harmonic Oscillators Characterized by Zero-Point Energy

In quantum field theory, the physical vacuum, free from magnetic and electric fields (without regard to gravitational energy), is defined not as an empty space but as the ground state of the field consisting of quantum harmonic oscillators (QHOs) characterized by zero-point energy. The aim of this work is to show that such physical vacuum may possess the properties similar to the properties of dark energy: the positive density, the negative pressure, and the possibility of so-called accelerated expansion. In the model discussed, the mass of QHOs determines the positive density of dark energy. The observed electric polarization of physical vacuum in an electric field means the existence of electric dipole moment of QHO, which, in turn, suggests the existence inside the QHO of a repulsive force between unlike charges compensating the attractive Coulomb force between the charges. The existence of such repulsive force may be treated as the existence of omniradial tensions inside every QHO. In terms of hydrodynamics, it means that the vacuum with this property may be regarded as a medium with negative pressure. The electric dipole-dipole interaction of QHOs under some condition may result in the expansion of physical vacuum consisting of QHOs. It is shown also that the physical vacuum consisting of QHOs is a luminiferous medium, and based on this concept the conditions are discussed for the emergence of invisiblity of any objects (in particular, dark matter). The existence of luminiferous medium does not contradict the second postulate of special relativity (the principle of constancy of the velocity of light in inertial systems), if to take into account the interaction of photons with QHOs and with virtual photons (the virtual particles pairs) created by quantum entities that constitute the inertial systems.

基于零点有效缺口应力的薄板焊接接头疲劳评估

文中采用零点有效缺口应力进行了薄板焊接接头的疲劳评估研究.该方法综合考虑整体结构应力以及缺口根部到零点位置的非线性峰值应力的影响,以临界距离法和零点结构应力法为基础,将零点应力位置作为缺口对结构疲劳影响的临界距离对焊接结构进行疲劳强度评估.通过对两种不同类型的焊接接头试样(T形单面焊接头和不同厚度组合搭接接头)的疲劳试验结果进行拟合.结果表明,在对焊根失效的试样进行疲劳评估时,焊根位置不同截面应力线性化之后得到零点有效缺口应力存在较大差异;其中,焊脚截面应力线性化得到的S-N曲线分散带宽度最小;再者,同时考虑焊趾和焊根失效的零点有效缺口应力S-N曲线,与分别考虑焊趾或焊根失效的零点有效缺口应力S-N曲线分散带相差不大,证明该方法可同时用于焊接接头焊趾和焊根疲劳评估.

应用于半导体激光器的高精度温控系统设计

面向半导体激光器温控系统的高精度、高速与高集成化的需求,设计了一款高精度、快速响应、高集成化、低成本的数模混合架构温控系统。该系统以FPGA为控制核心,硬件部分包括由三线制惠斯通电桥、仪表放大器、模数转换器组成的温度信号采集与调理模块,全桥降压电路驱动模块,热电制冷器模块等。针对热敏电阻和电桥的非线性误差,提出了一种可变控温零点的温度信号调理方法,该方法基于迭代与多目标最优化算法,提高了控温精度,同时降低了仪表放大器与模数转换器的指标要求,从而降低了系统成本。针对温度滞后大、延迟高的特点,控温策略采用了抗饱和积分的PID(AWPID)自动控制方法,从而降低超调,加快收敛速度。测试结果表明,该温控系统在-45~75℃的温度范围内,实现了±0.02℃的控温精度,相较于固定控温零点的温控系统最大0.1951℃的控温精度提高了89.7%。与传统PID控制算法相比,AWPID控制算法将超调从9.13%降低到1.5%,将稳定时间从41 s降低到30 s。稳定性测试表明,该温控系统能够在长时间内保持±0.02℃的控温精度,满足稳定性要求。该系统具有高精度、快速响应、高集成化、低成本的特点,为半导体激光器的复杂应用场景提供了高精度的温度保障。

一种求解包含问题的算法研究

一种实希尔伯特空间中求解包含问题的算法被提出,所提出的算法基于向前向后方法、压缩方法、惯性方法和无需搜索的自适应步长。算法的特点为迭代中多次使用惯性加速方法,且自适应步长随着迭代次数增加可能增大。在包含问题解集非空、一个映射极大单调、另一个映射单调且利普希茨连续的假设下,算法的强收敛性被证明。