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.

Fermions: Spin, Hidden Variables, Violation of Bell’s Inequality and Quantum Entanglement

Using real fields instead of complex ones, it was recently claimed, that all fermions are made of pairs of coupled fields (strings) with an internal tension related to mutual attraction forces, related to Planck’s constant. Quantum mechanics is described with real fields and real operators. Schrodinger and Dirac equations then are solved. The solution to Dirac equation gives four, real, 2-vectors solutions ψ1=(U1D1)ψ2=(U2D2)ψ3=(U3D3)ψ4=(U4D4)where (ψ1,ψ4) are coupled via linear combinations to yield spin-up and spin-down fermions. Likewise, (ψ2,ψ3) are coupled via linear combinations to represent spin-up and spin-down anti-fermions. For an incoming entangled pair of fermions, the combined solution is Ψin=c1ψ1+c4ψ4where c1and c4are some hidden variables. By applying a magnetic field in +Z and +x the theoretical results of a triple Stern-Gerlach experiment are predicted correctly. Then, by repeating Bell’s and Mermin Gedanken experiment with three magnetic filters σθ, at three different inclination angles θ, the violation of Bell’s inequality is proven. It is shown that all fermions are in a mixed state of spins and the ratio between spin-up to spin-down depends on the hidden variables.

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.

Bell’s Theorem and Einstein’s Worry about Quantum Mechanics

With the use of a local dependency on instrument setting parameters of the probability density of local hidden variables, it is demonstrated that a Kolmogorov formulation reproduces the quantum correlation. This is the novelty of the work. In a Bell experiment, one cannot distinguish between Bell’s formula and the here presented local Kolmogorov formula. With the presented formula, no CHSH can be obtained. Therefore, the famous CHSH inequality has no excluding power concerning local extra Einstein parameter models. This result concurs with other previous research concerning difficulties with Bell’s formula.

基于S-R和分解定理的二维几何非线性问题的虚单元法求解

应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝试使用一阶虚单元求解基于S-R和分解定理的二维几何非线性问题,以克服网格畸变的影响。基于重新定义的多项式位移空间基函数,推演获得一阶虚单元分析线弹性力学问题时允许位移空间向多项式位移空间的投影表达式;按照虚单元法双线性格式的计算规则,分析处理基于更新拖带坐标法和势能率原理的增量变分方程;进而建立离散系统方程及其矩阵表达形式,并编制MATLAB求解程序;采用常规多边形网格和畸变网格,应用该文算法分析均布荷载下的悬臂梁和均匀内压下的厚壁圆筒变形。结果与已有文献和ANSYS软件的对比表明:该文算法在两种网格中均可有效执行且具备足够数值精度。总体该文算法为基于S-R和分解定理的二维几何非线性问题求解提供了一种鲁棒方法。

Fractional Noether theorem and fractional Lagrange equation of multi-scale mechano-electrophysiological coupling model of neuron membrane

Noether theorem is applied to a variable order fractional multiscale mechano-electrophysiological model of neuron membrane dynamics.The variable orders fractional Lagrange equation of a multiscale mechano-electrophysiological model of neuron membrane dynamics is given.The variable orders fractional Noether symmetry criterion and Noether conserved quantities are given.The forms of variable orders fractional Noether conserved quantities corresponding to Noether symmetry generators solutions of the model under different conditions are discussed in detail,and it is found that the expressions of variable orders fractional Noether conserved quantities are closely dependent on the external nonconservative forces and material parameters of the neuron.

面神经松解术治疗Bell麻痹后痉挛性面瘫后遗症的疗效观察

目的探讨面神经松解术治疗Bell麻痹后痉挛性面瘫后遗症的效果及可能影响其治疗效果的因素。方法回顾性分析2020年7月至2022年1月上海交通大学医学院附属新华医院神经外科32例接受面神经松解术治疗Bell麻痹后痉挛性面瘫后遗症患者的临床资料,其中术前House-Brackmann分级(简称H-B分级)Ⅱ级26例,Ⅲ级6例,病程>1年者8例,≤1年者24例。术后1年采用HB分级评估患者术后面瘫程度是否恶化,以评价手术的安全性;采用痉挛性面瘫后遗症总体缓解度自我评分方法评估总体缓解程度,并将评分<5分视为无缓解(无缓解组),≥5分视为有效缓解(有效缓解组),分析可能影响总体缓解程度的因素;采用痉挛性面瘫后遗症症状缓解度自我评分方法评估面部紧束感、面部僵硬感、联带运动、面肌抽动、睁眼困难及眼裂变小六大症状的缓解程度并计算有效缓解率。结果32例患者的手术均顺利完成。出院时HB分级Ⅱ级23例(71.9%),Ⅲ级9例(28.1%)。6例(18.8%)患者术后出现耳后区域及耳廓皮肤麻木,5例(15.6%)患者出现耳后皮肤隐痛。术后1年32例患者均获得临床随访,H-B分级Ⅱ级28例(87.5%),Ⅲ级4例(12.5%);术后存在耳部皮肤麻木或隐痛患者的症状均消失;26例(81.3%)患者的痉挛性面瘫后遗症总体得到有效缓解,6例(18.7%)无缓解,有效缓解组与无缓解组患者的性别、年龄、手术侧别、术前面瘫程度的差异均无统计学意义(均P>0.05),而病程的差异具有统计学意义(P=0.023);痉挛性面瘫后遗症六大症状的有效缓解率按上述顺序依次为93.8%(30/32)、90.6%(29/32)、81.3%(26/32)、75.0%(24/32)、50.0%(16/32)、46.9%(15/32)。结论面神经松解术可有效缓解痉挛性面瘫后遗症症状,而早期手术可能是提高手术疗效的关键。

The Bell Inequality, Inviolable by Data Used Consistently with Its Derivation, Is Satisfied by Quantum Correlations Whose Probabilities Satisfy the Wigner Inequality

It is not generally known that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of ±1’s that are writable on paper. This surprising fact is not immediately obvious from Bell’s inequality derivation based on causal random variables, but follows immediately if the same mathematical operations are applied to finite data sets. For laboratory data, the inequality is identically satisfied as a fact of pure algebra, and its satisfaction is independent of whether the processes generating the data are local, non-local, deterministic, random, or nonsensical. It follows that if predicted correlations violate the inequality, they represent no three cross-correlated data sets that can exist, or can be generated from valid probability models. Reported data that violate the inequality consist of probabilistically independent data-pairs and are thus inconsistent with inequality derivation. In the case of random variables as Bell assumed, the correlations in the inequality may be expressed in terms of the probabilities that give rise to them. A new inequality is then produced: The Wigner inequality, that must be satisfied by quantum mechanical probabilities in the case of Bell experiments. If that were not the case, predicted quantum probabilities and correlations would be inconsistent with basic algebra.

Bell’s Theorem and Instantaneous Influences at a Distance

An explicit model-example is presented to simulate Einstein-Podolsky-Rosen (EPR) experiments without invoking instantaneous influences at a distance. The model-example, together with the interpretation of past experiments by Kwiat and coworkers, uncovers logical inconsistencies in the application of Bell’s theorem to actual EPR experiments. The inconsistencies originate from topological-combinatorial assumptions that are both necessary and sufficient to derive all Bell-type inequalities including those of Wigner-d’Espagnat and Clauser-Horne-Shimony-Holt. The model-example circumvents these inconsistencies.

Recovery from Bell’s palsy after treatment using uncultured umbilical cord-derived mesenchymal stem cells:A case report

BACKGROUND Bell’s palsy is an idiopathic facial palsy with an unknown cause,and 75%of patients heal spontaneously.However,the other 25%of patients continue experiencing mild or severe disabilities,resulting in a reduced quality of life.Currently,various treatment methods have been developed to treat this disease.However,there is controversy regarding their effectiveness,and new alternative treatments are needed.CASE SUMMARY The patient suffered from left-sided facial paralysis due to Bell’s palsy for 7 years.The patient received an uncultured umbilical cord-derived mesenchymal stem cell transplant eight times for treatment.After follow-up for 32 mo,the paralysis was cured,and there was no recurrence.CONCLUSION Uncultured umbilical cord-derived mesenchymal stem cell transplantation may be a potential treatment for patients with Bell’s palsy who do not spontaneously recover.

Collapse of Bell’s Theorem

Bell’s theorem founded on Bell’s inequalities asserts that no local realistic theories can reproduce all quantum mechanical predictions for spin correlation of particle pairs. It is pointed out that the assumption of setting-independent probability makes Bell’s inequalities not impose constraint on all local realistic models and thus constitutes a theoretical loophole of Bell’s theorem. A counterexample is presented by showing that a local realistic model with appropriate probability density reproduces all quantum mechanical predictions. It becomes clear that experiments violate Bell’s inequalities because the real correlation functions are not constrained by these inequalities. It is also exposed that, rigorous logical reasoning of counter factual deduction does not permit to exclude any premises of Bell’s inequalities by a certain amount of experimental violations of these inequalities.

基于TDLAS的天然气泄漏范围重构方法

可调谐半导体激光光谱(TDLAS)技术因其灵出色的灵敏度、精度和抗干扰性的特性,现已被广泛应用于场站天然气泄漏的监测工作。为克服单台TDLAS激光遥测仪无法获得泄漏气体扩散影响范围的局限性,本文提出了一种基于多台TDLAS遥测仪协同的智能监测方法,通过在不同斜平面内对泄漏气团进行扫查,依据Brianchon定理获得不同斜平面内气体泄漏的外轮廓方程,重构天然气的三维空间泄漏影响区域,实时开展监测与预警。

Bell’s Palsy Post COVID-19 Vaccination: A Retrospective Cross-Sectional Study in a Single Tertiary Center

Introduction: Bell’s palsy is an uncommon adverse effect of the COVID-19 vaccine that has been reported in clinical trials. Even though a few studies have linked the vaccination to Bell’s palsy, the actual mechanism is uncertain. Objectives: To describe the demographic data and COVID-19 vaccines-related data with Bell’s palsy in a tertiary centre of Malaysia, Hospital Kuala Lumpur. Methods: A retrospective cross-sectional study was observed among vaccinated recipients who developed Bell’s palsy within 60 days and sought treatment in the Otorhinolaryngology Department Hospital Kuala Lumpur, Malaysia between 1st May 2021 and 30th November 2021. The demographic data, clinical history, and vaccination history were collected from clinical records. The facial paralysis was graded according to the House-Brackmann grading system. Results: A total of 26 patients with a mean age was 38.5 years;higher incidence in younger age, below 60 years old (n = 24), specifically 18 - 30 years old (n = 11). We observed an equal number in relation to gender and onset (after the first or second dose) of facial palsy. Predominantly were Malay (n = 21) and only 6 patients had comorbidities. We found there was no difference in regard to the type of vaccine among Bell’s palsy patients;Pfizer (n = 9), followed by Sinovac (n = 9) and AstraZeneca (n = 8). Conclusion: Bell’s palsy was found to be a possible adverse event of the COVID-19 vaccine. Younger groups were noted as susceptible to this rare adverse effect. However, the benefits of vaccination outweigh the risk of Bell’s palsy, which has a good prognosis. More research with larger samples is needed to determine the true relationship between vaccination and Bell’s palsy.

Einstein-Local Counter-Arguments and Counter-Examples to Bell-Type Proofs

J. S. Bell’s well-known proofs of inequalities (and related work) are shown to be invalidated by two counter-arguments (-examples) that are based on Einstein-local propositions: Bell-type inequalities of Einstein-Podolsky-Rosen experiments must include, as virtually all physical theories do, elements of physical reality and their mathematical representations that relate to continua as opposed to exclusively finite numbers. Furthermore, Bell-type inequalities must be valid for all possible experimental geometries that lead to the quantum result. Based on these propositions, violations of Bell-type inequalities are demonstrated without violating Einstein locality, without conspiracy type theories and even for the case that all known “loopholes” are closed.

Misdiagnosis of Facial Nerve Palsy: A Case Report of Sporadic Vestibular Schwannomas (Non-NFM2) Causing Facial Nerve Palsy Be Misled by Bell’s Palsy in a Child

We report a case of a rare sporadic Vestibular Schwannoma of a 9-month-old girl who had a right-sided lower motor type facial nerve palsy. The patient was initially diagnosed with Bell’s palsy and received steroid treatment accordingly, two months later the patient’s condition deteriorated, and further evaluation of CT and MRI brain was conducted that showed a mass lesion in the posterior fossa causing compression on the facial nerve. Misdiagnosis of facial nerve paralysis is common among children due to multiple related etiologies and varying rates of incidence in comparison to adults. The authors hope to address this issue in this report. Background: Facial nerve paralysis has been a matter of concern for many researchers to understand its nature, causes and presentation according to different age groups. In adults, Bell’s palsy (BP), the idiopathic form of facial nerve paralysis, is more common compared to children where most cases are due to secondary etiologies. Therefore, pediatricians are in an important position to identify these patients early in order to launch the most effective diagnostic and treatment approaches.

Products of Odd Numbers or Prime Number Can Generate the Three Members’ Families of Fermat Last Theorem and the Theorem Is Valid for Summation of Squares of More Than Two Natural Numbers

Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that An + Bn = Cn, in which n is a natural number greater than 2. We have shown that any product of two odd numbers can generate Fermat or Pythagoras triple (A, B, C) following n = 2 and also it is applicable A2 + B2 + C2 + D2 + so on =An2 where all are natural numbers.

N次幂下S-凸函数和其性质研究

以凸函数、S-凸函数、平方凸函数、平方S-凸函数的定义和性质为研究基础,根据从平方凸函数到平方S-凸函数的演变推进过程,采用了凸函数概念的代数不等式形式,给出了N次幂下S-凸函数的概念,并对其判别定理和性质进行了讨论,定义并证明了N次幂下S-凸函数的Jensen型不等式。研究表明,N次幂下S-凸函数包含了凸函数、平方凸函数、平方S-凸函数的性质,是凸函数的一种广义凸函数的推广,开辟了全新的推广途径。

Biased Random Number Generator Based on Bell's Theorem

We propose a biased random number generation protocol whose randomness is based on the violation of the Clauser Home inequality. Non-maximally entangled state is used to maximize the Bell violation. Due to the rotational asymmetry of the quantum state, the ratio of Os to ls varies with the measurement bases. The experimental partners can then use their measurement outcomes to generate the biased random bit string. The bias of their bit string can be adjusted by altering their choices of measurement bases. When this protocol is implemented in a device-independent way, we show that the bias of the bit string can still be ensured under the collective attack.

Logical Conflict between Bell’s Locality and Probability Theory

Based on “locality” considerations, John Stuart Bell and his followers have derived inequalities and theorems that, when taken together with actual experiments that have been performed by Aspect and others, appear to contradict physical reality as defined by Einstein. However, their specifically applied concept of locality is in conflict with the Fundamental Model of probability theory and the set theoretic definition of conditional probabilities. Bell-type inequalities are, therefore, not adequate to decide ponderous questions regarding physical reality.