Integration by Parts Formula for Regional Fractional Laplacian

We obtain the integration by parts formula for the regional fractional Laplacian which are generators of symmetric α-stable processes on a subset of (0 < α < 2). In this formula, a local operator appears on the boundary connected with the regional fractional Laplacian on domain. Hence this formula can be understood as the Green formula for the regional fractional Laplacian. The similar integration by parts formula is also given for more general nonlocal operators. The reflected stable-like processes are studied.Research partially supported by NSFC 10501048     

Gaussian Integral Formula for Quaternions Based on Class Operator＇s Formula of Rotation Group

Abstract There exists rare integration formulas over quaternions due to the noncommutativity of quarternions multplication. Based on the class operator＇s formula of rotation group we derive a Gaussian integral formula for quaternions, which is similar in form to the integration for coherent state＇s completeness relation.     

Weyl-Ordered Operator Product Formula Derived by Technique of Integration Within Weyl-Ordered Product of Operators

Based on the explicit Weyl-ordered form of Wigner operator and the technique of integration within Weylordered product of operators we derive the Weyl-ordered operator product formula. The formula is then generalized to the entangled form with the help of entangled state representations.     

Weyl Ordering Operator Formula Derived by IWOP Technique and ItsApplication for Fresnel Operator

Based on the technique of integration within an ordered product ofoperators, the Weyl ordering operator formula is derived and the Fresneloperators' Weyl ordering is also obtained, which together with the Weyltransformation can immediately lead to Fresnel transformation kernel inclassical optics.     

Schwinger Formula Revisited

We apply the formal W.K.B. method in the complex plane to the quantum field theory to obtain the Schwinger formula for spin and spinless particles; i.e., we obtain the probability that the vacuum state remains unchanged in presence of a constant electric field. Finally, from Schwinger formula we calculate the probability that n pairs are produced.     

高能质子照相的成像方程

与X射线闪光照相相比,GeV级质子照相因质子的穿透能力更强而更能满足流体动力学最佳光程、更小不确定度的要求。质子照相用于提取阴影客体信息的过程比X射线闪光照相复杂。为了便于分析质子照相过程及其特性,以质子照相的输运过程为基础,逐步考虑了质子与物质相互作用的各种过程——核反应、多次库仑散射、准弹性散射和弹性散射,并获得含各种过程的质子照相理论计算表达式。在含准直的系统中,理论计算公式中包含了多次弹性散射和准弹性散射项。通过与QMCPrad计算结果的对比得知弹性散射高斯近似下的理论计算结果与蒙特卡罗方法(MC)计算结果一致,与更准确的"黑体"模型的相对误差为3%~5%。这意味着在某种程序上,当研究质子照相规律或设计系统时,高能质子照相的理论计算公式能够替代MC模拟。     

q形变三参数吴曾公式

结合微扰论的结果详细分析了描述偶偶核基带能谱三参数吴曾公式的q形变形式. 运用阻危非线性最小二乘法对大部分稀土区和锕系区的偶偶核基带能谱进行了拟合. 计算结果表明,q形变三参数吴曾公式比原来从微扰论导出的三参数吴曾公式更为精确,并能较好地描述回弯现象.     

质子放射性寿命的新规律

对球形核和变形核质子放射性的半衰期进行了系统的分析和研究,提出了新的计算质子放射性寿命的解析公式。 通过对公式计算寿命和实验测量值的系统比较,发现两者之间符合得非常好,说明新公式十分准确并具有良好的预言能力。 Systematic calculations on proton radioactivity half lives of both spherical and deformed nuclei are carried out. A new formula with only four parameters is proposed for proton radioactivity half lives. The half lives calculated by using the new formula are in good agreement with the experimental ones. The new formula is simple but accurate, which is very useful for further experiments.     

时空中子倍增公式解法研究

通过将空间概念引入中子倍增公式, 建立了时空中子倍增公式, 针对时空中子倍增公式计算时间效率过低的缺点, 对时空倍增公式的计算方法进行了研究, 新解法在保证精确性的基础上, 又提高了计算效率。新的计算方法可以应用于研究反应堆反应性发生动态变化的情况, 例如反应堆启堆或停堆以及变功率运行的过程, 对具有很强机动性要求的小型反应堆的安全分析有一定的理论意义和实用价值。 The space time neutron multiplication formula was established by introducing the concept of space time to the neutron multiplication formula. Because of the rather long computing time by using the formula, the solution of space time neutron multiplication formula is optimized which is efficient and accurate. The new method can be used to study the reactor with dynamic change in reactivity. It can be also used for studying the process of startup, outage and power drawn operation, which is of great importance to the safety analysis of the mini nuclear reactor.     

用推广的Viola-Seaborg公式计算α衰变寿命

根据Audi等编评的最新核数据表, 对Z≥84, N≥128的核的α衰变实验寿命用Viola-Seaborg公式进行最小方差拟合, 得到一套新参数. 用新拟合参数计算的偶偶核的衰变寿命与实验寿命很好地符合, 平均偏差1.3倍.而对奇A和奇奇核理论寿命与实验寿命相差较远. 考虑到处于基态时奇A和奇奇核与偶偶核的主要区别在于自旋和宇称, 对Viola-Seaborg公式做了推广. 在公式中引入了离心势垒(即α粒子轨道角动量)对衰变寿命的影响. 由推广公式计算的奇A和奇奇核的寿命与实验寿命平均偏差2.5倍,最大偏差5—6倍.     

柯林斯公式的D-FFT计算

将柯林斯公式及其逆运算表示为卷积形式,导出对应的传递函数,讨论使用快速傅里叶变换(FFT)计算柯林斯公式时满足取样定理的条件,基于研究结果,给出光波通过一光学系统的衍射场计算及根据衍射场重建入射平面光波场的实例。     

Bohr-Mottelson转动谱公式参数之间的新关系式

在利用Harris两参数公式研究Bohr-Mottelson转动谱公式参数之间的关系的基础上,改用Harris三参数公式,并由此提出了Bohr-Mottelson转动谱公式参数之间的新关系式,进而用I(I+1)四参数展开式计算了A～60,80,130,140,150,190区超形变偶偶核的基带和锕系和稀土区正常形变核基带,讨论了参数之间的关系,发现新关系式与实验较好地符合.     

Simplified Formula of Bending Loss for Optical Fiber Sensors

A simple fiber-optic bending loss formula is achieved for optical fiber sensors. This simple formula considers various bending radii, number of turns, extra bending angle, and wavelength and has good agreement with theoretical and experimental data. We also propose a simplified formula for sensitivity of the fiber-optic bending loss in this article. The defined sensitivity formula has the benefit of showing parameters for fiber-optic bending sensor systems.     

Simplified Formula of Bending Loss for Optical Fiber Sensors

A simple fiber-optic bending loss formula is achieved for optical fiber sensors. This simple formula considers various bending radii, number of turns, extra bending angle, and wavelength and has good agreement with theoretical and experimental data. We also propose a simplified formula for sensitivity of the fiber-optic bending loss in this article. The defined sensitivity formula has the benefit of showing parameters for fiber-optic bending sensor systems.     

金属二次电子发射系数表达式

根据二次电子发射的主要物理过程,推导出二次电子发射系数和单位背散射电子产生的内二次电子数与原电子产生的内二次电子数之比、原电子入射能量、参数、最大二次电子发射系数、背散射系数之间的关系式。根据实验结果,给出了2~10 keV比率的表达式。根据推导的关系式,用实验数据分别计算出6种金属的平均参数。发现6种金属的平均参数都近似为一个常数11.89(eV)0.5。根据推导的关系式和计算的参数,推导出以背散射系数、原电子入射能量和最大二次电子发射系数为变量的二次电子发射系数通式。用该通式计算出二次电子发射系数,并与相应的实验值进行了比较,最后成功地推导出金属2~10 keV的二次电子发射系数通式。     

q-Taylor's Formula with Its -Remainder

We derive the q-Taylor's formula with its q-remainder through the q-differentiation approach. Comparison between q-Taylor's expansion with the ordinary Taylor's formula is made, which shows that the q-remainder is different from the ordinary one.     

Amended Formula for the Decay of Radioactive Material for Cosmic Times

An amended formula for the decay of radioactivematerial is presented. It is a modification of thestandard exponential formula. The new formula appliesfor long cosmic times comparable to the Hubble time. It reduces to the standard formula for shorttimes. It is shown that the material decays faster thanexpected. The application of the new formula to directmeasurements of the age of the universe and its implications are briefly discussed.     

菲涅耳公式的研究及数值模拟

菲涅耳公式阐述了光在两种不同透明介质的分界面上,发生反射和折射现象时,反射光、折射光的振幅变化规律。本文通过对菲涅尔公式的变形处理,得到了新的表达形式,并且应用Matlab软件进行了数值模拟,使菲涅耳公式的物理意义更清晰明了。     

Trace Formula for Noisy Flows

A trace formula is derived for the Fokker–Planck equation associated with Itô stochastic differential equations describing noisy time-continuous nonlinear dynamical systems. In the weak-noise limit, the trace formula provides estimations of the eigenvalues of the Fokker–Planck operator on the basis of the Pollicott–Ruelle resonances of the noiseless deterministic system, which is assumed to be non-bifurcating. At first order in the noise amplitude, the effect of noise on a periodic orbit is given in terms of the period and the derivative of the period with respect to the pseudo-energy of the Onsager–Machlup–Freidlin–Wentzell scheme.     

Analytical Dielectric Spectrum Formula Based on Representative Frequencies

基于电介质复折射率的实验数据,采用最小二乘法结合选取的代表频率拟合得到了电介质的介电谱解析表达式,可以得到电介质在全频段的光频常数和介电常数. 研究了三个典型液态电介质,水、乙醇和甲苯的介电谱. 在实验数据可以获取的频率范围内,采用解析表达式得到的光频常数与采用Kramers-Kronig转换得到的折射率实部和实验得到的折射率虚部吻合得很好. 基于介电谱解析表达式可以预测目前实验无法测量的区域的介电谱.