THE EQUIVALENT CHARACTERIZATION OF F(p,q,s)SPACE ON BOUNDED SYMMETRIC DOMAINS OF Cn

LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F（p, q, s） space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F（p, q, s） space and Bloch type space on Ω too.

ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE

The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize the Carleman＇s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna＇s representation for harmonic functions in the half sphere by using HSrmander＇s theorem.

Analytical solutions for constant-rate test in bounded confined aquifers with non-Darcian effect

This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge boundaries.The mathematical modelling for the pumping-induced flow in aquifers with different boundaries is developed by employing image-well theory with the superposition principle,of which the non-Darcian effect is characterized by Izbash’s equation.The solutions are derived by Boltzmann and dimensionless transformations.Then,the non-Darcian effect and wellbore storage are especially investigated according to the proposed solution.The results show that the aquifer boundaries have non-negligible effects on pumping,and ignoring the wellbore storage can lead to an over-estimation of the drawdown in the first 10 minutes of pumping.The higher the degree of non-Darcian,the smaller the drawdown.

Estimated Bounds for Zeros of Polynomials from Traces of Graeffe Matrices

In this paper, we combine Graeffe matrices with the classical numerical method of Dandelin-Graeffe to estimate bounds for the moduli of the zeros of polynomials. Furthermore, we give some examples showing significant gain for the convergence towards the polynomials dominant zeros moduli.

Bounds for Polynomial’s Roots from Fiedler and Sparse Companion Matrices for Submultiplicative Matrix Norms

We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial P(X) over the field C[X]. From a n×n Fiedler companion matrix C, sparse companion matrices and triangular Hessenberg matrices are introduced. Then, we identify a special triangular Hessenberg matrix Lr, supposed to provide a good estimation of the roots. By application of Gershgorin’s theorems to this special matrix in case of submultiplicative matrix norms, some estimations of bounds for roots are made. The obtained bounds have been compared to known ones from the literature precisely Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds. According to the starting formel of Lr, we see that the more we have coefficients closed to zero with a norm less than 1, the more the Sparse method is useful.

ELEMENTARY DENSITY BOUNDS FOR SELF-SIMILAR SETS AND APPLICATION

Falconer[1] used the relationship between upper convex density and upper spherical density to obtain elementary density bounds for s-sets at H S-almost all points of the sets. In this paper, following Falconer[1], we first provide a basic method to estimate the lower bounds of these two classes of set densities for the self-similar s-sets satisfying the open set condition （OSC）, and then obtain elementary density bounds for such fractals at all of their points. In addition, we apply the main results to the famous classical fractals and get some new density bounds.

Impulsive stabilization of a class of nonlinear system with bounded gain error

Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua＇s circuit.

Six-Dimensional ab initio Potential Energy Surface and Bound States for He-H2S Complex

We present a new six-dimensional potential energy surface for He-H2S including the intramolecular Q1,Q2,and Q3 normal modes for theν1 symmetric stretching,ν2 bending andν3 asymmetric stretching of H2S.The potential was calculated at the coupled-cluster singles and doubles with noniterative inclusion of connected triples[CCSD(T)]-F12a level with augmented correlation-consistent polarized-valence triple-zeta(aug-cc-p VTZ)basis set plus the midpoint bond function(3s3p2d1f1g).Three vibrationally averaged potentials with H2S at the vibrational ground stateν1 as well as the excited statesν2 andν3 were generated from the integration of the six-dimensional potential over the Q1,Q2 and Q3 coordinates.Each potential has a planar T-shaped global minimum,a planar local minimum,two inplane saddle points as well as an out-plane saddle point.The global minimum is located at R=3.46A,θ=109.9° andφ=0.0° with a well depth of 35.301 cm^-1.The radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm were employed to calculate the rovibrational energy levels.The calculated band origins are blue-shifted(0.025 cm^-1 and 0.031 cm^-1)and(0.041 cm^-1 and 0.060 cm^-1)for He-(paraH2S)and He-(ortho-H2S)in theν2 andν3 region of the H2S molecule,respectively.

Detection of spin current through a quantum dot with Majorana bound states

The spin transport properties are theoretically investigated when a quantum dot(QD)is side-coupled to Majorana bound states(MBSs)driven by a symmetric dipolar spin battery.It is found that MBSs have a great effect on spin transport properties.The peak-to-valley ratio of the spin current decreases as the coupling strength between the MBS and the QD increases.Moreover,a non-zero charge current with two resonance peaks appears in the system.In the extreme case where the dot-MBS coupling strength is strong enough,the spin current and the charge current are both constants in the non-resonance peak range.When considering the effect of the Zeeman energy,it is interesting that the resonance peak at the higher energy appears one shoulder.And the shoulder turns into a peak when the Zeeman energy is big enough.In addition,the coupling strength between the two MBSs weakens their effects on the currents of the system.These results are helpful for understanding the MBSs signature in the transport spectra.

Quantum Mechanics of Moving Bound States

The quantum mechanics of bound states with discrete energy levels is well understood. The quantum mechanics of scattering processes is also well understood. However, the quantum mechanics of moving bound states is still debatable. When it is at rest, the space-like separation between the constituent particles is the primary variable. When the bound state moves, this space-like separation picks up the time-like separation. The time-separation is not a measurable variable in the present form of quantum mechanics. The only way to deal with this un-observable variable is to treat it statistically. This leads to rise of the statistical variables such entropy and temperature. Paul A. M. Dirac made efforts to construct bound-state wave functions in Einstein’s Lorentz-covariant world. In 1927, he noted that the c-number time-energy relation should be incorporated in the relativistic world. In 1945, he constructed four-dimensional oscillator wave functions with one time coordinate in addition to the three-dimensional space. In 1949, Dirac introduced the light-cone coordinate system for Lorentz transformations. It is then possible to integrate these contributions made by Dirac to construct the Lorentz-covariant harmonic oscillator wave functions. This oscillator system can explain the proton as a bound state of the quarks when it is at rest, and explain the Feynman’s parton picture when it moves with a speed close to that of light. While the un-measurable time-like separation becomes equal to the space-like separation at this speed, the statistical variables become prominent. The entropy and the temperature of this covariant harmonic oscillator are calculated. It is shown that they rise rapidly as the proton speed approaches that of light.

Alternative Error Bounds for Some Numerical Quadrature Rules

Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson＇s quadrature rule involving n-time（1 ≤ n ≤ 4） differentiable mappings and then to the estimations of error bounds for the adaptive Simpson＇s quadrature rule.

REMARKS ON BOUNDS ON THE DISCREPANCY OF APPROXIMATE SOLUTIONS CONSTRUCTED BY GODUNOV'S SCHEME

The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with small jumps for general quasilinear hyperbolic systems of conservation laws are extended to shock waves for isentropic equations of gas dynamics in a bounded invariant region with ρ=0 as one of boundries of the region. Two counterexamples are given to show that two iuequalities given by Godunov do not hold for all rational numbers γ∈(1, 3]. It seems that the approach by Godunov to obtain the forementioned bounds may not be possible.

From Black Holes to Information Erasure: Uniting Bekenstein’s Bound and Landauer’s Principle

This research aims to integrate Bekenstein’s bound and Landauer’s principle, providing a unified framework to understand the limits of information and energy in physical systems. By combining these principles, we explore the implications for black hole thermodynamics, astrophysics, astronomy, information theory, and the search for new laws of nature. The result includes an estimation of the number of bits stored in a black hole (less than 1.4 × 1030 bits/m3), enhancing our understanding of information storage in extreme gravitational environments. This integration offers valuable insights into the fundamental nature of information and energy, impacting scientific advancements in multiple disciplines.

Glycosidically Bound Volatile Compounds of Satureja montana L.,S.cuneifolia Ten.,S.subspicata Vis.and Endemic S.visianii SiliC

In this paper, the glycoconjugated volatile compounds of four Croatian Satureja species (Satureja montana L., S. cuneifolia Ten., S. subspicata Vis. and endemic S. visianii Silic) were investigated. Content and composition of these compounds were examined depending on the stage of plant development. GC and GC–MS analysis of volatile aglycones revealed twenty-one compounds. Thymoquinone, geraniol and carvacrol were detected in all vegetative phases of the investigated plants. Other quantitatively important aglycones were eugenol and thymol of S. montana, phenyl ethyl alcohol, benzene acetaldehyde, borneol, α-terpineol, thymol and eugenol of S. cuneifolia, phenyl ethyl alcohol, benzene acet-aldehyde, terpinen-4-ol, α-terpineol and β-ionone of S. subspicata and camphor, thymol and 8a-acetoxylemolol of S. visianii. Moderate similarity in the chemical composition of essential oils and volatile aglycones of investigated plant species indicate that many biologically active compounds are glycosylated and accumulate as non-volatile glycosides.

T-S模糊系统的自触发有限时间H∞控制

为克服事件触发控制对硬件设备的依赖以及控制策略频繁更新的局限,针对一类不确定Takagi-Sugeno(T-S)模糊系统的有限时间H∞控制问题,引入自触发机制,提出一种基于此机制下只与触发时刻状态有关的模糊控制器设计方法;基于自触发机制并结合有限时间控制的思想,通过设计触发间隔函数、推导并求解线性矩阵不等式(LMI),使得系统在保障稳定性的前提下,系统运动轨迹不会超过一定的界限,并达到所期望H∞性能水平;同时相较于事件触发机制,自触发机制位于系统内部,无需额外硬件设备接收触发信号且只需利用当前的触发状态信息来预测下一触发时刻,在一定程度上进一步降低系统资源成本;此外,利用李亚普诺夫函数对系统稳定性进行了严格分析,并提供一个确保能够防止芝诺现象发生的证明;最后,通过数值仿真、单连杆刚性机器人系统实例仿真两个实验说明所提方法的有效性。

直角坐标系下无向双环网络G(N;±1,±s)直径的研究

提出将直角坐标系引入无向双环网络的研究,通过直角坐标系,系统研究无向双环网络G(N;±1,±s)的直径、平均直径,验证直径的下界,得出平均直径的下界。最后给出直角坐标系下无向双环网络的仿真方法,该方法克服了传统L型瓦方法在无向双环网络研究中的不足,大大提升了无向双环网络的研究水平。

两类新的基于T/S范数的模糊神经元模型及其应用

基于T范数和S范数提出了F1型和F2型两类神经元模型 ,并研究了它们的性质和应用 (F1型灵敏性强而鲁棒性弱 ,而F2型神经元灵敏性弱而鲁棒性强 ) ;给出了一个基于F1型神经元的广义AND/OR运算为T/S范数簇的充分必要条件 ;首先提出了弱界三角范数的概念 ,并发现F2型的一个特例模型能实现弱界三角范数 .经分析 ,F1型更适合用于工业控制系统 ,而F2型更适合用于面向用语言描述知识的医学和人文社会领域的计算机应用系统 .该文把一个由特殊的F2型神经元组成的神经网络用于模糊推理 ,发现该推理方法是Zadeh的CRI法的推广 ,且能满足假言推理 .通过权值的调整 ,该推理法能满足若干推理原则的要求 .

S-Nekrasov矩阵的逆矩阵无穷范数的上界

在不改变矩阵性质的情况下,通过引入恰当的参数,首先构造了S-SDD矩阵,其次利用S-SDD矩阵与SNekrasov矩阵的逆矩阵无穷范数的关系,得到了S-Nekrasov矩阵的逆矩阵无穷范数的新上界.数值算例不仅说明了新上界的有效性和可行性,也说明了该结果改进了现有的结果.

Stirling公式中参数θ的改进上界

本文应用级数理论证明了一个关于阶乘的不等式 ,从而给出Stirling公式中参数θ的一个改进上界 。

最优非单位步长无向双环网络G(N;±r,±s)的构造

创造性地将直角坐标系引入无向双环网络的研究,通过直角坐标系,系统地研究无向双环网络G(N;±r,±s)的直径、平均直径,得出平均直径的下界。提出最优无向双环网络BestG(N;±r,±s)(直径、平均直径均达到下界)的构造方法,并研究步长r、s与其直径之间的关系。与传统L型瓦方法在无向双环网络研究中相比,该方法克服了其不足,大大提升了无向双环网络的研究水平。