广义GrO¨tzsch环函数的精确界及应用

本文研究广义Grotzsch环函数与一些初等函数组合的单调性,并由此获得新的精确不等式。同时,将所得结果应用于Ramanujan模方程理论,获得广义Hersch-Pfluger偏差函数新的下界。

Correlation between ^99mTcO₄<sup style="margin-left:-7px;">-</sup>Thyroid Scintigraphy and Blood Test in Primary Hyperthyroidism

Background: The 99mTcO4- thyroid scintigraphy is commonly used for hyperthyroidism diagnosis. Uptake value of 99mTcO4- on thyroid scintigraphy is an indicator of hyperthyroidism activity. Although, the correlation between free T3 value and free T4 value is not necessary clear in primary hyperthyroidism. Introduction: This study investigated the correlation between results of blood test and uptake of 99mTcO4- on thyroid scintigraphy in primary hyperthyroidism. Methodlogy: In this retrspective study, uptake was calculated in patients diagnosed with primary hyperthyroidism (Graves’ disease/Basedow’s disease) based on clinical findings, blood tests, thyroid ultrasound, and 99mTcO4- thyroid scintigraphy (uptake ≥3%) at St. Marianna University School of Medicine Hospital between 1 January 2010 and 31 December 2019. This uptake of 99mTcO4- was compared with results of blood tests. Results: Fifty-four consecutively arriving patients at the hospital (12 men, 42 women;mean age 43.0 ± 14.0 years) were selected. Free T3 (n = 54) was 14.6 ± 6.8 pg/mL, free T4 (n = 53) was 5.0 ± 2.3 ng/mL, and uptake on thyroid scintigraphy was 10.0% ± 7.1%. The correlation coefficients were 0.60 (p < 0.01) between free T4 (all case), 0.39 (p < 0.01) between free T4 (under 7 ng/mL), 0.12 (p = 0.70) between free T4 (above 7 ng/mL) and 99mTcO4- thyroid scintigraphy uptake. Conclusion: In primary hyperthyroidism (Graves’ disease), there is a correlation between free T4 value and 99mTcO4- thyroid scintigraphy uptake, but there is no correlation in patients with high free T4 level.

非线性SchroO¨dinger-Kirchhoff型方程基态解的存在性

本文利用Nehari流形的方法和Lions引理,将非线性Schro?dinger-Kirchhoff型方程的基态转化为相应能量函的临界点,结合山路引理,证明了该类方程在一定条件下基态解的存在性。

α-Lu¨ roth展式若干度量性质

对于α-Lu?roth展式,在此篇文章我们研究了α-Lu?roth展式的一些度量性质,获得了该展式数字“0-1”律,基于该结果,得到了相应的重对数律,进一步完善了该展式的度量性质。作为交错Lu?roth展式的推广,该论文的结论包括了交错Lu?roth的相应的结果。

Gro¨ bner基方法验证乘法器的Maple实现

乘法器电路验证问题是一项极其重要而又极具挑战性的难题。当前主流的方法是先将其建模成交换代数中的理想成员问题,然后使用Mathematica、Singular等计算机代数系统中的Gr&#246;bner基方法进行判定。本文使用计算机代数系统Maple对这一方法给出了全新实现并在计算机上进行了对比实验。实验结果表明:Maple的实现在某种程度上具有更高的验证效率,可成为乘法器电路强有力的验证平台。

基于GrO¨bner基方法的乘法器等价性验证

乘法器的等价性验证目前仍是大规模算术集成电路设计领域内的一大难题。本文利用逻辑门与多项式之间的对应关系,构建了乘法器的代数模型,将乘法器等价性验证问题转化成理想成员判定问题,然后再用计算机代数系统中的Gr&#246;bner基方法进行求解。提出了一种对乘法器结构进行切片后再采用增量式验证的新方法。在Linux平台上的计算机代数系统Mathematica上所做的实验结果也表明了该方法的有效性。

GrO¨bner基法验证乘法器的设计与实现

当今形式化验证工具在大规模集成电路的设计过程中起着非常重要的作用。最有效的方法是以Gr&#246;bner基方法为基本原理,将乘法器电路建模为一组伪布尔多项式,通过Gr&#246;bner基来既约由多项式表示的字级规范。本文将基于Gr&#246;bner基方法,使用C++语言重新实现验证工具,将整个代码分成多个模块的形式,并利用容器类对变量进行分类存储。实验结果表明:C++语言设计的验证工具不仅可以实现成功,而且也为之后的研究提供了有利的验证工具。

MO¨bius梯状图的完美匹配的反强迫多项式和卢卡斯数

在本文中我们研究了M&#246;bius梯状图MLn的反强迫谱,并得到了一个关于MLn的反强迫多项式和Lucas数列关系的等式。

一类空间分数阶非线性SchrO¨dinger方程的李群约化

本文将李群约化方法应用于一类空间分数阶非线性Schr&#246;dinger方程,得到了方程的单参数新解,以及李对称约化方程。进一步,通过求解李对称约化方程获得了空间分数阶非线性Schr&#246;dinger方程的一些群不变解和行波解。

最小球B*的Ka¨hler相关性

在这篇文章中,我们研究了最小球B*的K&#228;hler几何性质。主要探索了赋予Bergman度量的最小球B*和复欧式空间ℂn的相关性问题。本文借助最小球B*的Bergman核函数的具体形式以及纳什代数函数的性质,发现最小球B*和ℂn不存在共同的K&#228;hler子流形,即B*和ℂn是K&#228;hler不相关的。

一类带有临界增长的广义拟线性SchrO¨dinger-Poisson系统基态变号解的存在性

在这篇文章当中,我们研究了如下Schr&#246;dinger-Poisson系统其中是边界光滑的有界区域,。对f,g施加适当的条件,若μ足够大,通过利用约束变分方法和形变引理,得到了该系统对于每一个λ】0都有相对应的基态变号解νλ,并且基态变号解的能量严格大于二倍基态解的能量。

一类SchrO¨dinger-Poisson系统基态变号解的存在性

运用Ekeland变分原理,约束变分等变分方法,研究有界光滑区域上一类Schr&#246;dinger-Poisson系统基态变号解的存在性。所得结果是前述已有工作的补充与推广。

具有井位势的非线性分阶SchrO¨dinger-Poisson 方程组的基态解的存在性和渐近性

在本文中,&#160;我们研究了如下分 阶 SchrO&#168;dinger-Poisson 方程组 其中(−∆)α是阶数为α∈(0, 1)的分数阶Laplace算子,λ 】是一个参数,是分数阶临街指数. 在 V, f满足适当条件下, 利用变分方法我们证明了基态解存在性. 及当λ → +∞ 基态解的渐近行为.

临界非线性分数阶 SchrO¨dinger 方程变号解的存在性

本文主要研究了一类临界增长的分数阶 Schr&#246;dinger 方程变号解的存在性,其中0 是分数阶临界指数,&#181;是一个正常数,,ε 】0是一个小参数, V ∈ C1(RN , R)满足a ≤ V (x) ≤ b, b 】a 】0 , ∀x ∈ RN.通过临界理论和下降流不变集法,我们得到了该方程存在k对变号解.

半经典次临界增长SchrO¨dinger-Poisson方程组变号解的存在性和集中现象

在本文中,研究半经典次临界增长 Schr&#246;dinger-Poisson 方程组, 当 |x| → ∞ 时,其中 ε 】0 是小参数,λ, &#181;】0 是参数,V : ℝ3 → ℝ 是有界位势函数且局部极小点集 M 非空, 利用下降流不变集方法和截断技巧证明无穷多变号解的存在性,当 ε → 0 时,通过构造惩罚项证明这些解集中在位势函数 V 的局部极小附近。

MO¨ bius立方体的h-好邻条件诊断度

条件诊断度是衡量互连网络可靠性能优劣的重要参数,“条件”意味着任何处理器的所有相邻处理器不能同时出现潜在故障。作为条件诊断度的一个改进参数,Peng等人通过限制要求每个无故障节点至少包含有h个无故障的邻点提出了h-好邻条件诊断度,是一种在节点失效的情况下衡量互连网络可靠性的重要指标。本文研究并证明了M&#246;bius立方体(MNQ)在PMC模型和MM*模型下的h-好邻条件诊断度是(n-h+1)2h-1(0≤h≤n-3),相比于传统诊断度成几何倍数的提高。

有限差分–配点法求解SchrO¨dinger方程

本文将重心插值配点法结合Crank-Nicolson差分格式求解线性Schr&#246;dinger方程。首先,对方程中的空间方向上采用重心插值Chebyshev配点格式进行离散,时间方向采用Crank-Nicolson差分格式,从而导出对应的代数方程组。最后,数值算例验证该计算格式具有高精度性,并且满足质量和能量守恒性。

Fixed-Bed Column Adsorption Modeling of MnO4- Ions from Acidic Aqueous Solutions on Activated Carbons Prepared with the Biomass

Activated carbons calcined at 400˚C and 600˚C (AC-400 and AC-600), prepared using palm nuts, collected in the town of Franceville in Gabon, were used to study the dynamic adsorption of MnO4- ions in acidic media on fixed bed column and on the kinetic modeling of experimental data of breakthrough curves of MnO4- ions obtained. Results on the adsorption of MnO4- ions in fixed-bed dynamics obtained on AC-400 and AC-600 adsorbents beds indicated that the AC-400 bed appears to be the most efficient in removing MnO4- ions in acidic media. Indeed, the adsorbed amounts, the adsorbed capacities at saturation and the elimination percentage of MnO4- ions obtained with AC-400 (31.24 mg;52.06 mg·g-1 and 41.65% respectively) were higher compared to those obtained with AC-600 (9.87 mg;16.45 mg·g-1 and 17.79% respectively). The breakthrough curves kinetic modeling revealed that the Thomas model and the pseudo-first-order kinetic model were the most suitable models to describe the adsorption of MnO4- ions on adsorbents studied in our experimental conditions. The results of the intraparticle diffusion model showed that intraparticle diffusion was involved in the adsorption mechanism of MnO4- ions on investigated adsorbents and was not the limiting step and the only process controlling MnO4- ions adsorption. In contrast to AC-400, the intraparticle diffusion on AC-600 bed plays an important role in the adsorption mechanism of MnO4- ions.

A-B效应中不可积相位因子的导出

目前推导A-B效应中不可积相位因子的方法主要是从路径积分的角度,物理意义仍不十分突出。本文从量子力学中最基本的Schr&#246;dinger方程出发,简洁地导出了A-B效应中的不可积相位因子。从理论分析上得到了不可积相位因子的本质是微观客体的波粒二象性的结论。

Quantization of the 1-D Forced Harmonic Oscillator in the Space (<i>x</i>, <i>v</i>)

The quantization of the forced harmonic oscillator is studied with the quantum variable (x, v∧), with the commutation relation , and using a Schrödinger’s like equation on these variable, and associating a linear operator to a constant of motion K (x, v, t) of the classical system, The comparison with the quantization in the space (x, p) is done with the usual Schrödinger’s equation for the Hamiltonian H(x, p, t), and with the commutation relation . It is found that for the non-resonant case, both forms of quantization bring about the same result. However, for the resonant case, both forms of quantization are different, and the probability for the system to be in the exited state for the (x, v∧) quantization has fewer oscillations than the (x, p∧) quantization, the average energy of the system is higher in (x, p∧) quantization than on the (x, v∧) quantization, and the Boltzmann-Shannon entropy on the (x, p∧) quantization is higher than on the (x, v∧) quantization.