Dilation,discrimination and Uhlmann's theorem of link products of quantum channels

We establish the Stinespring dilation theorem of the link product of quantum channels in two different ways,discuss the discrimination of quantum channels,and show that the distinguishability can be improved by self-linking each quantum channel n times as n grows.We also find that the maximum value of Uhlmann's theorem can be achieved for diagonal channels.

New Asymptotic Results on Fermat-Wiles Theorem

We analyse the Diophantine equation of Fermat xp yp = zp with p > 2 a prime, x, y, z positive nonzero integers. We consider the hypothetical solution (a, b, c) of previous equation. We use Fermat main divisors, Diophantine remainders of (a, b, c), an asymptotic approach based on Balzano Weierstrass Analysis Theorem as tools. We construct convergent infinite sequences and establish asymptotic results including the following surprising one. If z y = 1 then there exists a tight bound N such that, for all prime exponents p > N , we have xp yp zp.

SOME LIOUVILLE-TYPE THEOREMS FOR THE STATIONARY 3D MAGNETO-MICROPOLAR FLUIDS

In this paper,we prove some Liouville-type theorems for the stationary magnetomicropolar fluids under suitable conditions in three space dimensions.We first prove that the solutions are trivial under the assumption of certain growth conditions for the mean oscillations of the potentials.And then we show similar results assuming that the solutions are contained in L^(p)(R^(3))with p∈[2,9/2).Finally,we show the same result for lower values of p∈[1,9/4)with the further assumption that the solutions vanish at infinity.

Diophantine equations and Fermat's last theorem for multivariate(skew-)polynomials

Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely.The aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate(skew)-polynomials with any characteristic.

AAK Theorem and a Design of Multidimensional BIBO Stable Filters

Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with a realizable (rational) transfer function thanks to the Adamjan, Arov and Krein (AAK) theorem. It is well known that the one dimensional AAK results give the best approximation of a polynomial as a rational function in the Hankel semi norm. We suppose that the Hankel matrix associated to the transfer function has a finite rank.

Some convergence theorems of fuzzy concave integral on fuzzyσ-algebra

In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.

Duhamel原理在求解非齐次微分方程中的应用

本文围绕Duhamel原理在求解非齐次微分方程中的应用展开探讨.基于比较法,以常微分方程实例与偏微分方程实例为切入点,证明了相关Duhamel原理及推导出对应问题的解,结果的比较可使学生对求解方法更为印象深刻,并能将该原理灵活应用于求解各类非齐次的微分方程.

Small Modular Solutions to Fermat’s Last Theorem

The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infinitely many solutions if the problem is recast in terms of modular arithmetic. Over a hundred years ago Issai Schur was able to show that for any n there is always a sufficiently large prime p0such that for all primes p≥p0the congruence xn+yn≡zn(modp)has a non-trivial solution. Schur’s argument wasnon-constructive, and there is no systematic method available at present to construct specific examples for small primes. We offer a simple method for constructing all possible solutions to a large class of congruences of this type.

Whole Perfect Vectors and Fermat’s Last Theorem

A naïve discussion of Fermat’s last theorem conundrum is described. The present theorem’s proof is grounded on the well-known properties of sums of powers of the sine and cosine functions, the Minkowski norm definition, and some vector-specific structures.

Vanishing Theorems for p-Harmonic Forms on Submanifolds in Spheres

In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold andδ>1(n-1)p2/4n[p-1+(p-1)2kp],we prove a vanishing theorem for p-harmonicℓ-forms.

A Study on High School Mathematics Teaching Design Based on Teaching for Robust Understanding: Taking the Cosine Theorem as an Example

Teachers’teaching behavior plays a crucial role in students’development,and there are problems in the current teaching behavior of mathematics teachers such as ignoring students’cognitive needs,lack of equal opportunities for students’classroom performance as well as lack of formative evaluation of students.In order to solve the phenomenon,this paper analyzes and explains how to promote teaching based on the Teaching for Robust Understanding(TRU)evaluation framework with the goal of focusing on the development of all students,taking the teaching design of The Cosine Theorem as an example,and provides ideas and methods for first-line high school mathematics teachers.

The Njiki’s Fundamental Theorem-Definition on Fractions in the Mathematical Set ℚ and by Extension in ℝ and ℂ, for the Purpose of Leading to the Construction of Some Algebraic Structures as Its Theoretical Applications and for the Practical Ones

The purpose of the research in the NJIKI’s fundamental THEOREM-DEFINITION on fractions in the mathematical set ℚand by extension in ℝand ℂand in order to construct some algebraic structures is about the proved EXISTENCE and the DEFINITION by NJIKI of two INNOVATIVE, IMPORTANT and TEACHABLE operations of addition or additive operations, in ℚ, marked ⊕and +α,β, and taken as VECTORIAL, TRIANGULAR, of THREE or PROPORTIONAL operations and in order to make THEM not be different from the RATIONAL ONE, +, but to bring much more and new information on fractions, and, by extension in ℝand ℂ. And the very NJIKI’s fundamental THEOREM-DEFINITION having many APPLICATIONS in the everyday life of the HUMAN BEINGS and without talking about computer sciences, henceforth being supplied with very interesting new ALGORITHMS. And as for the work done in the research, it will be waiting for its extension to be done after publication and along with the research results concerned.

非齐次动力方程Duhamel项的精细积分

提出了不需要矩阵求逆运算的求解Duhamel积分项的精细积分方法．通过将精细积分法的关键思想——加法定理和增量存储——直接应用于Duhamel积分响应矩阵的求解,可给出当非齐次项分别为多项式、正弦／余弦以及指数函数等基本形式时Duhamel积分在计算机上的精确解．特别的,该算法不依赖于系统矩阵(或相关矩阵)的形态．当系统矩阵奇异或接近奇异时,其优越性更为显著．算例验证了该算法的有效性．

改良腹腔镜辅助Duhamel结肠次全切除术治疗长段型先天性巨结肠症

目的探讨改良腹腔镜辅助Duhamel结肠次全切除术治疗长段型先天性巨结肠症（Hirschsprung disease,HD）的并发症和疗效。方法回顾分析2010年3月~2014年1月12例长段型HD资料,男7例,女5例,中位年龄8月（5月~6岁）。其中移行区位于降结肠近端8例,横结肠2例,结肠肝曲1例,升结肠1例。7例行结肠造瘘。手术主要改良之处：经肛门齿状线上方直肠后壁切口将结肠拖出至肛门外,用Endo-GIA肛门外切断并封闭,保留直肠残端4~5 cm。然后结合Deloyer技术将升结肠拖下与原直肠后壁端侧吻合,再将Endo-GIA切缝器两肢分别放入原直肠和新直肠,切开两段肠管间隔并行侧侧吻合。观察术中术后并发症及排便功能。结果 12例均在腹腔镜辅助下完成次全结肠切除升结肠Duhamel拖出术,平均手术时间170 min（125~240 min）,未出现术中并发症,无吻合口漏。4例诉肛周疼痛,1例术后5天便血,保守治疗治愈。大便频率2周以内4~15次/天,恢复到正常排便频率（1~2次/天）时间平均3.5月（2.2~5个月）。平均随访时间32个月（3~46个月）,2例术后小肠结肠炎,1例早期有便秘症状,均保守治疗治愈。无闸门综合征和粪石发生,无大便失禁。结论改良腹腔镜辅助Duhamel结肠次全切除术治疗长段型HD安全有效,排便频率恢复正常快。肛门外处理直肠盲端简单可靠,腹壁创伤小。

改良Soave根治术与改良Duhamel根治术治疗小儿先天性巨结肠症的效果

目的对比分析改良Soave根治术与改良Duhamel根治术治疗小儿先天性巨结肠症的效果。方法将118例该院收治的小儿先天性巨结肠症患儿随机均分为对照组和观察组,各59例。对照组给予改良Duhamel根治术治疗,观察组给予改良Soave根治术治疗。观察并记录两组手术时间、手术出血量、术后禁食时间及术后住院时间等手术情况,比较两组生活质量和肛门功能评分及术后并发症发生情况。结果观察组手术时间、手术出血量、术后禁食时间及术后住院时间均低于对照组(P=0.045、0.001、0.041及0.006);观察组患儿生活质量和肛门功能评分及优良率均高于对照组(P=0.010和0.009);观察组总体术后并发症发生率低于对照组(P=0.001)。结论改良Soave根治术治疗小儿先天性巨结肠症的效果优于改良Duhamel根治术,术后并发症少,改善肛门功能,提升生活质量,值得临床推广。

Duhamel项的精细积分方法在非线性微分方程数值求解中的应用

基于Duhamel项的精细积分方法,构造了几种求解非线性微分方程的数值算法。首先将非线性微分方程在形式上划分为线性部分和非线性部分,对非线性部分进行多项式近似,利用Duhamel积分矩阵,导出了非线性方程求解的一般格式。然后结合传统的数值积分技术,例如Adams线性多步法等,构造了基于精细积分方法的相应算法。本文算法利用了精细积分方法对线性部分求解高度精确的优点,大大提高了传统算法的数值精度和稳定性,尤其是对于刚性问题。本文构造的算法不需要对线性系统矩阵求逆,可以方便的考察不同的线性系统矩阵对算法性能的影响。数值算例验证了本文算法的有效性,并表明非线性系统的线性化矩阵作为线性部分是比较合理的选择。

手助腹腔镜结肠次全切除联合改良Duhamel术治疗重度功能性便秘

目的:观察手助腹腔镜结肠次全切除联合改良Duhamel术治疗重度功能性便秘(SFC)的近期疗效及并发症,评价其安全性和可行性。方法:2005年6月至2006年12月,对9例经非手术治疗效果欠佳的SFC患者,经过对临床症状、结肠镜检查、结肠传输试验和排粪造影等检查结果的分析,显示有明确的病理解剖和功能性异常部位,施行手助腹腔镜结肠次全切除联合改良Duhamel术治疗;观察手术安全性、术后恢复情况和并发症、便秘症状指标和术后近期随访结果。结果:8例患者手术成功,1例中转剖腹手术,术后无严重并发症,平均手术时间(284.2±26.3)min,术中出血量(141.5±65.4)ml,切口长度(10.8±1.3)cm,术后镇痛(1.8±0.6)d、肛门排气(4.2±0.6)d,下床活动(3.5±0.4)d,术后住院(9.8.±2.3)d。1例患者术后10 d出现肠梗阻症状,经内科治疗缓解,并发肺部感染和切口感染各1例。患者术后便秘症状指标明显改善[(15.4±1.6)分vs(4.2±1.4)分,P=0.000)],改善度平均为(76.3±9.5)%。患者排便频率满意率和生活质量满意率等方面获得较好结果。1例术后出现轻度便秘,应用膨胀性泻剂和促动力药后症状可缓解。结论:手助腹腔镜结肠次全切除联合改良Duhamel术获得较好的改善便秘症状满意率,且具有创伤小、出血少、安全和术后恢复快等优点。

基于Duhamel积分的车桥耦合动力分析方法

为了缩短求解车桥耦合系统动力响应的计算时间,利用振型分解法对车桥耦合系统的桥梁子系统和车辆子系统解耦,假定在每一时间步长内车桥相互作用力线性变化,借助Duhamel积分解析解,通过迭代得到系统的动力响应,提出了一种新型的车桥耦合动力分析方法.以一节四轴客车匀速通过32 m简支梁为例进行了实验研究,结果表明：本文方法得到的车桥耦合系统的动力响应结果与Newmark-β方法的结果接近,各极值点相对误差均不超过1%;在保证相同的计算精度前提下,本文方法将积分步长提高至原来的5~10倍,提高了求解速度.

普通型先天性巨结肠Duhamel改良手术临床应用

目的:总结保留扩张而不伴肥厚结肠的Duhamel改良手术治疗普通型(常见、普遍型)先天性巨结肠(Hirschsprung′sdisease,HD)的疗效及经验。方法:在25例普通型HD中,7例行扩张、肥厚的乙状结肠及移行段切除,18例仅行移行段或部分扩张、肥厚的乙状结肠切除。结果:25例病灶(狭窄段)近侧壁厚0.2cm以下扩张结肠病检为正常肠壁。1例术后第10天并发急性化脓性阑尾炎、右肾结石、直肠残端瘘。行阑尾切除、横结肠肝曲双腔造口,3个月后闭瘘治愈。除1例合并愚型病儿1年后仍有稀便晚间污裤外,无与本术式相关的并发症发生。全组病人随访6个月～8年,无大便失禁,无复发,无狭窄,无闸门综合征及盲端综合征等。结论:普通型HD行Duhamel改良手术时,病灶近侧扩张但不伴肥厚或扩张伴轻度肥厚的结肠可予以保留。本术式符合HD行Duhamel的病理生理及目前所有手术设计期望达到的目地,更接近人的肠道生理。改良后的手术更简单、更安全。

腹腔镜结合肛门外离断技术Duhamel手术治疗先天性巨结肠症的疗效观察

目的 探讨腹腔镜下结肠次全切除结合肛门外离断技术Duhamel手术治疗长段型先天性巨结肠症（HD）的并发症和疗效。方法 回顾性分析2010~2015年27例长段型HD患儿,平均年龄10月,其中移行区位于降结肠8例,横结肠7例,结肠脾曲10例,升结肠2例,16例行结肠造瘘。手术主要改良是经肛门直肠后壁切口将结肠拖出至肛门外,用Endo-GIA肛门外切断并封闭,保留直肠残端4~5 cm。然后将Endo-GIA切缝器两肢分别放入原直肠和拖下肠管,行侧侧吻合。观察术中术后并发症和排便功能。结果 所有患儿均顺利完成手术,平均手术时间155分钟,无术中并发症。平均随访时间42月,无吻合口瘘和重度肛周皮肤破溃,1例患儿术后5天便血,保守治疗好转。恢复到正常排便频率时间平均为3.6月。3例患儿术后出现小肠结肠炎,1例患儿有便秘症状,均保守治疗好转。没有盲袋炎和粪石发生,17例4岁以上患儿均达到正常排便频率。结论 改良腹腔镜辅助Duhamel结肠次全切除术治疗长段型HD安全有效,操作简单,排便频率恢复快、并发症少。