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.

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.

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.

Trigonometric Regularization and Continuation Method Based Time-Optimal Control of Hypersonic Vehicles

Aiming at the time-optimal control problem of hypersonic vehicles(HSV)in ascending stage,a trigonometric regularization method(TRM)is introduced based on the indirect method of optimal control.This method avoids analyzing the switching function and distinguishing between singular control and bang-bang control,where the singular control problem is more complicated.While in bang-bang control,the costate variables are unsmooth due to the control jumping,resulting in difficulty in solving the two-point boundary value problem(TPBVP)induced by the indirect method.Aiming at the easy divergence when solving the TPBVP,the continuation method is introduced.This method uses the solution of the simplified problem as the initial value of the iteration.Then through solving a series of TPBVP,it approximates to the solution of the original complex problem.The calculation results show that through the above two methods,the time-optimal control problem of HSV in ascending stage under the complex model can be solved conveniently.

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.

Application Analysis of Doctor-Nurse Cooperation Follow-up Model Based on the Internet Platform in Continuation Care of Patients after Urooncology Surgery

Objective:To explore the application effect of a doctor-nurse cooperation follow-up model based on an Internet platform in the continuation of care for patients after uro-oncology surgery.Methods:A convenient sampling method was used to select patients with urinary system tumors who underwent surgery in the Department of Urology in Grade III A general hospital in Shanghai from May to August 2022.Patients who underwent surgery from May to June 2022 were assigned to the control group,and those who underwent surgery from July to August 2022 were assigned to the experimental group.The control group received routine post-discharge nursing health education and telephone follow-up.On the basis of routine discharge guidance,the experimental group implemented the intervention method based on the Internet platform in continuation care.The levels of self-management efficacy,satisfaction,and incidence of unplanned readmission were compared one month after discharge between the two groups.Results:One month after discharge,the self-management efficacy of the experimental group(90.15±7.92)was significantly higher than that of the control group(79.10±7.84),and the patient satisfaction score(97.83±2.32)was significantly higher than that of the control group(90.23±2.58),with statistical significance(P<0.05).Additionally,the incidence of unplanned readmissions within one month after discharge in the experimental group(1.59%)was slightly lower than that in the control group(4.84%).Conclusion:The doctor-nurse cooperation follow-up model based on the Internet platform in continuation care can significantly improve the self-management efficiency of patients after discharge and enhance patient satisfaction,providing a new approach for discharge follow-up of urological tumor patients after surgery.

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.

Web 2.0-Comet-Continuations模式在局部放电实时监测中的应用

针对传统Web模式的实时系统具有的用户体验不理想、数据延迟高和响应速度慢等缺点,通过对Ajax技术和Web工作模式深入分析研究,采用Web 2.0、Comet、Continuations相结合的方式,结合电缆终端局部放电实时监测系统例证,将三维谱图网格化并结合div技术模拟桌面应用程序局部刷新。该模式下系统具有无闪烁、实时性高的特点,并且即使在连接大量客户端时,服务器也只需消耗较少的CPU和内存资源。

An inverse Q-filter algorithm based on stable wavefield continuation

Stability is the key to inverse Q-filtering. In this paper we present a stable approach to inverse Q-filtering, based on the theory of wavefield downward continuation. It is implemented in a layered manner, assuming a layered-earth Q model. For each individual constant Q layer, the seismic wavefield recorded at the surface is first extrapolated down to the top of the current layer and a constant Q inverse filter is then applied to the current layer. When extrapolating within the overburden, a stable wavefield continuation algorithm in combination with a stabilization factor is applied. This avoids accumulating inverse Q-filter errors within the overburden. Within the current constant Q layer, we use Gabor spectral analysis on the signals to pick time-variant gain-constrained frequencies and then deduce the corresponding gain-constrained amplitudes to stabilize the inverse Q-filtering algorithm. The algorithm is tested and verified application to field data.

不同强度运动抑制糖尿病大鼠肾脏PI3K/AKT/mTOR信号通路改善自噬的比较

背景:2型糖尿病损害肾功能。研究表明运动干预可以保护肾脏;鸢尾素可以通过抑制磷脂酰肌醇3-激酶/蛋白激酶B/雷帕霉素靶蛋白信号通路恢复自噬,保护糖尿病肾病患者的肾功能。目的:探讨运动能否通过抑制肾脏磷脂酰肌醇3-激酶/蛋白激酶B/雷帕霉素靶蛋白信号通路过度激活来恢复自噬,改善肾损伤,以及分析不同方式运动产生影响的差异。方法:将6周龄的SD大鼠随机分为空白对照组(正常大鼠)和糖尿病组,其中糖尿病组大鼠经过高脂高糖喂养加腹腔注射低剂量1%链脲佐菌素(30 mg/kg)建立2型糖尿病模型。造模成功后再将糖尿病组大鼠随机分成糖尿病模型组、中强度持续运动组和高强度间歇运动组。两个运动组大鼠分别进行8周不同强度运动干预。取材后采用葡萄糖氧化酶法检测大鼠空腹血糖,使用试剂盒检测糖化血红蛋白水平,Elisa法检测血清胰岛素浓度,计算胰岛素抵抗指数,RT-PCR检测肾组织磷脂酰肌醇3-激酶、蛋白激酶B、雷帕霉素靶蛋白、Beclin-1、podocin、nephrin的基因表达量,Western Blot检测肾组织雷帕霉素靶蛋白及自噬标记蛋白LC3-1、LC3-2、Beclin-1的蛋白表达量。结果与结论:①2型糖尿病大鼠空腹血糖和糖化血红蛋白水平极显著性升高,胰岛素抵抗水平显著上升,胰岛素水平显著下降;两种运动均能使2型糖尿病大鼠空腹血糖和糖化血红蛋白水平极显著下降,胰岛素抵抗水平显著下降,胰岛素水平显著上升;与中强度持续运动组相比,高强度间歇运动组胰岛素水平显著上升。②2型糖尿病大鼠podocin、nephrin基因表达量显著降低;两种不同形式运动均能显著提高其表达;与高强度间歇运动组相比,中等强度持续性运动组足细胞相关蛋白基因表达有进一步上升趋势,但无显著性差异。③2型糖尿病大鼠肾组织磷脂酰肌醇3-激酶、蛋白激酶B、mTORC1的mRNA及蛋白的表达量显著增加,自噬标志蛋白Beclin-1、LC3-2表达量以及LC3-2/LC3-1显著降低;两种不同形式运动均能使肾组织磷脂酰肌醇3-激酶、蛋白激酶B、mTORC1的mRNA及雷帕霉素靶蛋白蛋白的表达量显著降低,自噬标志蛋白Beclin-1、LC3-2以及LC3-2/LC3-1显著升高;与中等强度持续性运动组相比,高强度间歇运动的磷脂酰肌醇3-激酶、蛋白激酶B、mTORC1的mRNA及雷帕霉素靶蛋白的蛋白表达量有进一步下降的趋势,Beclin-1、LC3-2以及LC3-2/LC3-1有进一步升高的趋势,但仅Beclin-1有显著性差异。④结果说明2型糖尿病肾脏足细胞损伤,自噬受到抑制,与磷脂酰肌醇3-激酶/蛋白激酶B/mTORC1信号通路被异常激活密切相关。高强度间歇运动和中等强度持续性运动可以保护糖尿病肾脏,减少足细胞损伤,促进自噬恢复,这可能与运动抑制磷脂酰肌醇3-激酶/蛋白激酶B/雷帕霉素靶蛋白信号通路过度激活有关。与中等强度持续性运动相比,高强度间歇运动恢复自噬的效果呈更优趋势,但足细胞蛋白表达稍有下降。

THEOREMS OF INTERVAL FUZZY SET AND ITS OPERATION RULES

Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuzzy set are studied firstly, and then the cut set of interval fuzzy set is proposed. Moreover, the decomposition theo- rem, the representation theorem and the extension theorem of interval fuzzy set are presented. Finally, examples are given to demonstrate that the classical fuzzy set is a special case of interval fuzzy set and interval fuzzy set is an effective expansion of the classical fuzzy set.

The Growth Theorem for Convex Maps on the Banach Space

In this paper,the growth theorem for convex maps on the Banach space is given, this is: ‖f(x)‖≤‖x‖/(1-‖x‖),x∈B the estimate is best possible for Hilbert space.

Joint PP and PS AVO inversion based on Bayes theorem

Based on the Aki-Richards approximate equations for reflection coefficients and Bayes theorem, we developed an inversion method to estimate P- and S-wave velocity contrasts and density contrast from combined PP and PS data. This method assumes that the parameters satisfy a normal distribution and introduces the covariance matrix to describe the degree of correlation between the parameters and thus to improve the inversion stability. Then, we suppose that the parameter sequence is subject to the Cauchy distribution and employs another matrix Q to describe the parameter sequence sparseness to improve the inversion result resolution. Tests on both synthetic and real multi-component data prove that this method is valid, efficient, more stable, and more accurate compared to methods using PP data only.

Several Fundamental Theorems and Conservative Integrals in Quasicrystal Elasticity Theory

Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.

On Some Fundamental Theorems in Stability Theory

This paper gives several fundamental theorems for the stability, uniform stability, asymptotic stability and uniform asymptotic stability. Those theorems allow the derivative of Lyapunov functions to be positive on certain sets,relax the restriction about the rate of change of state variable in a system to be bounded in Marachkov's theorem and extend the related results in [4—7].