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2019年01月20日

【期刊论文】Defense Resource Allocation Against Sequential Unintentional and Intentional Impacts

彭锐

IEEE TRANSACTIONS ON RELIABILITY,2019,0(0):1-11

2019年01月01日

摘要

This paper studies the defense strategy for a parallel system subject to an unintentional impact and an intentional impact. Existing research assumes that system damage is caused by either natural disasters (unintentional impacts) or strategic attackers (intentional impacts). However, in practice, the defender may encounter diverse scenarios, where these two kinds of impacts can happen in a sequential order.Without knowing the precise occurrence sequence, the defender must allocate its limited resources against two successive impacts. In each contest, the defender can construct redundant elements and protect them from damage, to minimize the expected loss from system destructions. Illustrative examples of the optimal strategy are presented in three cases: first, where the unintentional impact comes first; second, where the intentional impact comes first; and third, where the two impacts come in an uncertain order. Supplemental protection is considered in the model extension, where the defender can allocate additional protection resources to those elements that have survived after the first impact.

关键词: Defense strategy,, expected damage,, intentional impact,, system vulnerability,, unintentional impact.,

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2019年03月21日

【期刊论文】The Theory of Dove-like Particles

Zuodong Sun

Journal of US-China Medical Science,2019,16(2):73-99

2019年03月15日

摘要

Alzheimer’s disease (AD) has been reported for more than 100 years since its first discovery in 1906. There has been no significant progress in the study of its real causes and pathogenesis. The viewpoint of this paper is a heuristic viewpoint based on brain cell activation theory under such background. In this paper, the pathogenesis of sporadic AD is discussed at molecular level by applying the principles of cell physics and biology. The purpose of this paper is to harmonize the existing theories of etiology of AD and to solve the source problems that have plagued the research field of neurodegenerative diseases for a long time. Conclusion: (1) Basic contents: excess cations are transferred from extracellular to intracellular. They compete position with potassium ions on the inner surface of cell membranes, thus abatementing the membrane potential, making action potential unable to activate calcium channels normally, which eventually leads to abnormal apoptosis of brain cells. Amyloid plaque is the remains of abnormal apoptotic brain cells. Amyloid plaque is the aggregation of amyloid spots by van der Waals force and electrostatic attraction, and its interstitium is amyloid protein. Brain cells consist of neurons, microglia and astrocytes in turn. Most of the spotted nuclei in the remains are cations. (2) Solutions: physical means, especially transcranial magnetoelectricity stimulation, should be the first choice for treatment. (3) Naming principles: because of the core point of view in this paper—The position of cation occupying potassium is the initiating factor of AD, so the etiology theory is named theory of dove-like particles. Take the Chinese idiom “Turtledove occupies the nest of magpies”. “Turtledove” represents the non-essential cation, “magpie” refers to the effective potassium ion, and “nest” refers to the position of the effective potassium ion.

关键词: Alzheimer,, etiology,, cationic placement,, amyloid plaque,, cell remains,, physical mean

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2019年09月12日

【期刊论文】Effect of Extrusion and Heat Treatment on Microstructure and Mechanical Properties of Hypereutectic A390-0.3wt%Nd Alloy

Jidong He, Bo Gao

Materials Research,2019,22(2):1-4

2019年07月29日

摘要

An hypereutectic aluminium alloy with a composition of 16-18wt%Si, 4-5wt%Cu, 0.45-0.65wt%Mg, 0.3wt%Nd and Al balance (A390-0.3wt%Nd alloy) was processed by extrusion and aging at 200ºC for 10 hours. The effect of the thermomechanical processing and heat treatment on microstructure and mechanical properties was investigated for A390-0.3wt%Nd alloy. It was shown that the eutectic structure disappeared after the processing and heat treatment. In the meantime, the morphology of Al(Si,Mg) solid solution was transformed from dendritic to equiaxed and the Si particles were refned to have fne sizes of 1-10µm and dispersed in the Al(Si,Mg) matrix. Some of the Si particles became globular in shape, which can reduce stress concentration. The tensile strength of the A390-0.3wt%Nd alloy increased by 14.8% (211MPa to 242MPa) after extrusion and aging, and the elongation to fracture increased signifcantly from 0.5% to 13.3%. Thus, the mechanical properties of extruded and heat-treated A390-0.3wt%Nd alloy were improved after the extrusion and aging. The fracture mode is transformed from brittle fracture of as-cast alloy to ductile fracture of extruded and heat-treated alloy.

关键词: Aluminium alloy,, thermomechanical processing,, heat treatment,, mechanical properties.,

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2019年10月09日

【期刊论文】Forward self-similar solutions of the fractional Navier-Stokes equations

Baishun Lai, Changxing Miao, Xiaoxin Zheng

Advances in Mathematics,2019,352(2):981–1043

2019年06月28日

摘要

We study forward self-similar solutions to the 3-D Navier-Stokes equations with the fractional diffusion (−Δ)^α. First, we construct a global-time forward self-similar solutions to the fractional Navier-Stokes equations with 5/6 <α ≤1for arbitrarily large self-similar initial data by making use of the so called blow-up argument. Moreover, we prove that this so-lution is smooth in R^3×(0, +∞). In particular, when α =1, we prove that the solution constructed by Korobkov and Tsai (2016) [16]satisfies the decay estimate by establishing regu-larity of solution for the corresponding elliptic system, which implies this solution has the same properties as a solution which was constructed in Jia and Šverák (2014) [13].

关键词: Self-similar solution,, Nonlocal smoothing effect,, Blowup argument,, The weighted estimate

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2019年11月13日

【期刊论文】On the regularity issues of a class of drift-diffusion equations with nonlocal diffusion

Changxing Miao, Liutang Xue

SIAM J. Math. Anal.,2019,51(4): 2927-2970

2019年02月15日

摘要

In this paper we address the regularity issues of drift-diffusion equation with nonlocal diffusion, where the diffusion operator is in the realm of stable-type L\'evy operator and the velocity field is defined from the considered quantity by a zero-order pseudo-differential operator. Through using the method of nonlocal maximum principle in a unified way, we prove the eventual regularity result in the supercritical type cases and the global regularity at some logarithmically supercritical cases. The feature of these results is that the time after which the solution is smoothly regular in the supercritical type cases can be evaluated explicitly.

关键词: Drift-diffusion equation,, surface quasi-geostrophic equation,, nonlocal maximum principle, Levy operator,, regularity

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2019年11月13日

【期刊论文】The two-dimensional Euler equation in Yudovich and bmo-type spaces

Qionglei Chen, Changxing Miao, Xiaoxin Zheng

Rev. Mat. Iberoam. ,2019,35(1):195–240

2019年01月01日

摘要

We construct global-in-time, unique solutions of the two-dimensional Euler equations in a Yudovich type space and a $\rm bmo$-type space. First, we show the regularity of solutions for the two-dimensional Euler equations in the Spanne space involving an unbounded and non-decaying vorticity. Next, we establish an estimate with a logarithmic loss of regularity for the transport equation in a bmo-type space by developing classical analysis tool such as the John-Nirenberg inequality. We also optimize estimates of solutions to the vorticity-stream formulation of the two-dimensional Euler equations with a bi-Lipschitz vector field in bmo-type space by combining an observation introduced in \cite{Y1} by Yodovich with the so-called ``quasi-conformal property" of the incompressible flow.

关键词: Two-dimensional incompressible Euler equations,, Yudovich type data, John– Nirenberg inequality,, global existence and uniqueness of solutions.,

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2019年11月13日

【期刊论文】Linear adjoint restriction estimates for paraboloid

Changxing Miao, Junyong Zhang, Jiqiang Zheng

Mathematische Zeitschrift ,2019,292(2):427-451

2019年02月10日

摘要

We prove a class of modified paraboloid restriction estimates with a loss of angular derivatives for the full set of paraboloid restriction conjecture indices. This result generalizes the paraboloid restriction estimate in radial case from [Shao, Rev. Mat. Iberoam. 25(2009), 1127-1168], as well as the result from [Miao et al. Proc. AMS 140(2012), 2091-2102]. As an application, we show a local smoothing estimate for a solution of the linear Schr\"odinger equation under the assumption that the initial datum has additional angular regularity.

关键词: Linear adjoint restriction estimate,, local restriction estimate,, Bessel function,, spherical harmonics,, local smoothing.,

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2019年11月18日

【期刊论文】A phenomenological constitutive modelling of polyethylene foam under multiple impact conditions

卢富德, 卢富德

Packaging Technology and Science,2019,32(7):367-379

2019年04月01日

摘要

This paper extends the knowledge into the mechanical behaviour characterizations and constitutive modelling of polyethylene (PE) foam under multiple loading and unloading. The mechanical properties of PE foam subjected to single loading cases can be obtained by uniaxial compressive tests at quasi‐static and dynamic states.And the multiple loading and unloading behaviours of the foam can be revealed by consecutive drop tests. The major objective of this research is to propose a phenomenological model consists of shape function and modulus function, which can be predicted compressive response of PE foam for single loading cases. The constitutivemodels of foamed PE under multiple loading and unloading conditions are established by both using hyperbolic function, where the relations between coefficients and residual strain are introduced. And then, experiments are conducted to validate the proposed model by comparing the constitutive models proposed in this paper and those predicting by finite element software ABAQUS with those by experiments, showing that the proposed models are more accurate for predicting accelerationtimes curves of multiple drop scenarios.

关键词: polyethylene foam,,

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2021年01月09日

【期刊论文】Mathematical Elements on Natural Reality

毛林繁, 毛林繁

Bulletin of the Calcutta Mathematical Society,2019,Vol.111(NO.6):597-618

2019年11月30日

摘要

Actually, one establishes mathematicalmodel for understanding a natural thing or matter $T$ by its mathematical property $\widehat{T}$ characterized by model, called mathematical reality. {\it Could we always conclude the equality $\widehat{T}=T$ in nature}? The answer is disappointing by Godel's incomplete theorem which claims that any formal mathematical axiom system is incomplete because it always has one proposition that can neither be proved, nor disproved in this system. Thus, we can not determine $\widehat{T}=T$ or $\not=T$ sometimes by the boundary of mathematics. Generally, a natural thing or matter is complex, even hybrid with other things. Unlike purely thinking, physics and life science determine natural things by subdividing them into irreducible but detectable units such as those of quarks, gluons or cells, i.e., the composition theory of $T$ in the microcosmic level, which concludes the reality of $T$ is the whole behavior of a complex network induced by local units. However, all mathematical elements can only determines the character of $T$ locally and usually brings about a contradictory system in mathematics. {\it Could we establish a mathematics on complex networks avoiding Godel's incomplete theorem for science, i.e., mathematical combinatorics}? The answer is positive motivated by the traditional Chinese medicine, in which a living person is completely reflected by $12$ meridians with balance of Yin ($Y^-$) and Yang ($Y^+$) on his body, which alludes that there is a new kind of mathematical elements, called {\it harmonic flows} $\overrightarrow{G}^{L^2}$ with edge labeled by $L^2:(v,u)\in E\left(\overrightarrow{G}\right)\rightarrow L(v,u)-iL(v,u))$, where $i^2=-1$, $L(v,u)\in\mathscr{B}$ and $2$ end-operators $A_{vu}^+, A_{vu}^-$ on Banach space $\mathscr{B}$ holding with the continuity equation on vertices $v\in V\left(\overrightarrow{G}\right)$ with dynamic behavior characterized by Euler-Lagrange equations.

关键词: Mathematical element,, harmonic flow,, dynamics,, Smarandache multispace,, mathematical combinatorics,, C

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