Resolution of Grandi’s Paradox as Extended to Complex Valued Functions

Grandi’s paradox, which was posed for a real function of the form 1/(1+ x), has been resolved and extended to complex valued functions. Resolution of this approximately three-hundred-year-old paradox is accomplished by the use of a consistent truncation approach that can be applied to all the series expansions of Grandi-type functions. Furthermore, a new technique for improving the convergence characteristics of power series with alternating signs is introduced. The technique works by successively averaging a series at different orders of truncation. A sound theoretical justification of the successive averaging method is demonstrated by two different series expansions of the function 1/(1+ ex ) . Grandi-type complex valued functions such as 1/(i + x) are expressed as consistently-truncated and convergence-improved forms and Fagnano’s formula is established from the series expansions of these functions. A Grandi-type general complex valued function is introduced and expanded to a consistently truncated and successively averaged series. Finally, an unorthodox application of the successive averaging method to polynomials is presented.

COVID-19 mortality paradox(United States vs Africa):Mass vaccination vs early treatment

The coronavirus disease 2019(COVID-19)mortality rate in 55 African countries is almost 4.5 times lower than in the coronavirus disease 2019(COVID-19)despite Africa having over 4.2 times more people.This mortality paradox is also evident when comparing Nigeria,a heavily populated,poorly vaccinated and weakly mandated country to Israel,a small,highly vaccinated and strictly mandated country.Nigeria has almost 4 times lower COVID mortality than Israel.In this Field of Vision perspective,I explain how this paradox has evolved drawing upon my academic,clinical and social experience.Since April 2020,I’ve developed and been using the Egyptian immune-modulatory Kelleni’s protocol to manage COVID-19 patients including pediatric,geriatric,pregnant,immune-compromised and other individuals suffering from multiple comorbidities.It’s unfortunate that severe acute respiratory syndrome coronavirus 2 is still evolving accompanied by more deaths.However in Africa,we’ve been able to live without anxiety or mandates throughout the pandemic because we trust science and adopted early treatment using safe,and effective repurposed drugs that have saved the majority of COVID-19 patients.This article represents an African and Egyptian tale of honor.

Solving the Olbers’s Paradox, Explaining the “Red-Shift”, and Challenging the Relativities by “Sun Matters Theory” and “Sun Model of Universe”, an Evolution of the Einstein’s Static Universe Model

Olbers’s paradox, known as the dark night paradox, is an argument in astrophysics that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. Big-Bang theory was used to partially explain this paradox, while introducing new problems. Hereby, we propose a better theory, named Sun Matters Theory, to explain this paradox. Moreover, this unique theory supports and extended the Einstein’s static universe model proposed by Albert Einstein in 1917. Further, we proposed our new universe model, “Sun Model of Universe”. Based on the new model and novel theory, we generated innovative field equation by upgrading Einstein’s Field Equation through adding back the cosmological constant, introducing a new variable and modifying the gravitationally-related concepts. According to the Sun Model of Universe, the dark matter and dark energy comprise the so-called “Sun Matters”. The observed phenomenon like the red shift is explained as due to the interaction of ordinary light with Sun Matters leading to its energy and frequency decrease. In Sun Model, our big universe consists of many universes with ordinary matter at the core mixed and surrounded with the Sun Matters. In those universes, the laws of physics may be completely or partially different from that of our ordinary universe with parallel civilizations. The darkness of night can be easily explained as resulting from the interaction of light with the Sun Matters leading to the sharp decrease in the light intensity. Sun Matters also scatter the light from a star, which makes it shining as observed by Hubble. Further, there is a kind of Sun Matters named “Sun Waters”, surrounding every starts. When lights pass by the sun, the Sun Waters deflect the lights to bend the light path. According to the Sun Model, it is the light bent not the space bent that was proposed in the theory of relativities.

柚子(Citrus grandis Osbeck)S-like核酸酶基因CgSL1的分离与特征分析

从柚子 (Citrus grandis Osbeck) 2个自交不亲和品种溪蜜柚和度尾蜜柚的花柱中克隆出一个类似 S核酸酶基因 Cg SL1(C.grandis S- like RNase) ,它的 c DNA序列全长 10 74 bp,编码 2 97个氨基酸。通过与其它植物S- like核酸酶和 S核酸酶氨基酸序列进行比较 ,发现 Cg SL1类似于 S- like核酸酶 ,与拟南芥中的 RNS2一致性为6 2 .5 %。对 Cg SL1的表达分析表明该基因在花柱、花药、叶片不同器官以及花柱的不同发育阶段均有表达 ,且在花柱中的表达随衰老增强 ,由此推测它可能与衰老有关。

The seeming paradox of adenosine receptors as targets for the treatment of Alzheimer's disease: agonists or antagonists?

Alzheimer＇s disease （AD） is the most common neurodegenerative disorder, and its incidence is relatively high among elderly people, affecting about 1-2% of the population between 60-65 years old and rising dramatically （about 30%） in people aged 80 years or older （Selkoe, 2002）. Nowadays, considering the increasing mean lifespan of populations in developed countries, the disease is becoming more and more a health concern, and the search for an effective cure has turned into＂a real need＂.

Parrondo's paradox for chaos control and anticontrol of fractional-order systems

We present the generalized forms of Parrondo＇s paradox existing in fractional-order nonlinear systems. The gener- alization is implemented by applying a parameter switching （PS） algorithm to the corresponding initial value problems associated with the fractional-order nonlinear systems. The PS algorithm switches a system parameter within a specific set of N 〉 2 values when solving the system with some numerical integration method. It is proven that any attractor of the concerned system can be approximated numerically. By replacing the words ＂winning＂ and ＂loosing＂ in the classical Parrondo＇s paradox with ＂order＂ and ＂chaos＂, respectively, the PS algorithm leads to the generalized Parrondo＇s paradox： chaos1 ＋ chaos2 ＋..- ＋ chaosN = order and order1 ＋ order2 ＋.-. ＋ orderN = chaos. Finally, the concept is well demon- strated with the results based on the fractional-order Chen system.

Large eustachian valve fostering paradoxical thromboembolism:passive bystander or serial partner in crime?

Catheter-based closure of patent foramen ovale(PFO)is more effective than medical therapy in the prevention of recurrent stroke[1].It is likely that a proportion of patients evaluated for potential transcatheter PFO closure has actually different anatomical variants particularly common in the right atrium such as eustachian valve,Chiari network,Thebesian valve and Crista Terminalis.Notably,the eustachian valve may represent an increased risk factor for left circulation thromboembolism beyond that associated with PFO size and shunting.Such patients may benefit the most from percutaneous closure procedure.

A Resolution of the Black Hole Information Paradox via Transfinite Set Theory

A black hole is essentially a relativistic as well as a quantum object. Therefore the information paradox of black holes is a consequence of the clash between these two most fundamental theories of modern physics. It is logical to conclude that a resolution of the problem requires some form of a quantum gravity theory. The present work proposes such a resolution using set theory and pointless spacetime geometry.

Radial Electric Field in Tokamak Plasmas as a Physical Consequence of Ehrenfest’s Paradox

A simplified form and some possible theoretical resolutions of the so-called Ehrenfest’s Paradox are described. A relation between physical consequences of this relativistic paradox and charge density ρ of tokamak plasma is shown. Plasma experiments which could resolve the Ehrenfest’s Paradox are presented.

Resolution of Hardy’s Paradox within Spacetime Physics and the Ithaca Interpretation of Quantum Mechanics

By religiously adhering to physics in spacetime and taking the final verdict of N.D. Mermin’s Ithaca interpretation of quantum mechanics seriously, Hardy’s paradox is completely resolved. It is then concluded that logical and mathematically consistent physical theories must be put in spacetime related formalism such as noncommutative geometry and E-infinity theory to avoid quantum paradoxes. At a minimum, we should employ the philosophy behind consistent quantum interpretation such as that of the famous Ithaca interpretation of D. Mermin.

Coral reef ecological pump for gathering and retaining nutrients and exporting carbon:a review and perspectives

How coral reefs with high productivity and biodiversity can flourish in oligotrophic tropical oceans has inspired substantial research on coral reef ecosystems.Increasing evidence shows that similar to water in an oasis in the desert,there are stable nutrient supplies to coral reefs in oligotrophic oceans.Here,with emphasis on the fluxes of organic matter,we summarize at the ecosystem level(1)the multiple input pathways of external nutrients,(2)the storage of nutrients in reef organisms,(3)the efficient retaining and recycling of dissolved and particulate organic matter within coral reef ecosystems,(4)the distinctly high phytoplankton productivity and biomass inside and near oceanic coral reefs,and(5)the export of reef-related organic carbon to adjacent open oceans.These properties enable coral reefs to function as ecological“pumps”for gathering nutrients across ecosystems and space,retaining and recycling nutrients within the ecosystem,supporting high phytoplankton productivity,and exporting organic carbon to adjacent open oceans.Particularly,the high phytoplankton productivity and biomass make waters around coral reefs potential hotspots of carbon export to ocean depths via the biological pump.We demonstrate that organic carbon influx is vital for coral reef ecosystems’carbon budget and carbon export.The concept of the coral reef ecological pump provides a framework to improve the understanding of the functioning of the coral reef ecosystem and its responses to disturbance.Prospects of the coral reef ecological pump in coral reef studies are discussed in changing oceans driven by human activities and global change in the Anthropocene.

Hilbert’s First Problem and the New Progress of Infinity Theory

In the 19th century, Cantor created the infinite cardinal number theory based on the “1-1 correspondence” principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it the first problem in his famous speech on mathematical problems, which shows the importance of this question. We know that the infinitesimal problem triggered the second mathematical crisis in the 17-18th centuries. The Infinity problem is no less important than the infinitesimal problem. In the 21st century, Sergeyev introduced the Grossone method from the principle of “whole is greater than part”, and created another ruler for measuring infinite sets. The discussion in this paper shows that, compared with the cardinal number method, the Grossone method enables infinity calculation to achieve a leap from qualitative calculation to quantitative calculation. According to Grossone theory, there is neither the largest infinity and infinitesimal, nor the smallest infinity and infinitesimal. Hilbert’s first problem was caused by the immaturity of the infinity theory.

A Combined Heterotic String and Kähler Manifold Elucidation of Ordinary Energy,Dark Matter,Olbers’s Paradox and Pure Dark Energy Density of the Cosmos

We utilize the topological-geometrical structure imposed by the Heterotic superstring theory on spacetime in conjunction with the K3 Kähler manifold to explain the mysterious nature of dark matter and its coupling to the pure dark energy density of the cosmos. The analogous situations in the case of a Kerr black hole as well as the redundant components of the Riemannian tensor are pointed out and the final result was found to be in complete agreement with all previous theoretical ones as well as all recent accurate measurements and cosmic observations. We conclude by commenting briefly on the Cantorian model of Zitterbewegung and the connection between Olbers’s paradox and dark energy.

沙田柚自交花柱S_1-RNase的免疫胶体金定位

采用免疫胶体金标记抗体技术成功地检测了沙田柚自交花柱中存在的S1 RNase 结果表明 :沙田柚自花授粉后 1,2 ,3d 1/ 2处花柱段的S1 RNase分别定位于内质网、高尔基区、纤维内壁和纤维外壁 ;同时分析了自花授粉后 1～ 3d的S1 RNase的动态变化 ,及其参与沙田柚自交不亲和反应的可能机理 。

沙田柚S-RNase基因的克隆及序列分析

利用高通量测序技术对沙田柚自交和异交花柱进行转录组测序。通过差异分析得到沙田柚S-RNase基因序列。该基因全长为1 238bp(GenBank登录号为KP172529),开放阅读框(ORF)全长为834bp,共编码278个氨基酸,编码的蛋白质的相对分子质量为31.402kDa,理论等电点为5.30。S-RNase蛋白为亲水性蛋白,共有17个可能的磷酸化位点。氨基酸序列分析表明,其编码的氨基酸与柚Citrus maxima、沙糖桔Citrus reticulata和甜橙Citrus sinensis的同源性分别为99%、98%和96%。系统进化树显示沙田柚S-RNase基因与柚、沙糖桔和甜橙亲缘关系很近,属于同一进化分支。

沙田柚花柱S-糖蛋白的纯化和N-端序列测定

以人工自花授粉 3 d后的沙田柚 (Citrusgrandisvar.Shatinyu Hort.)花柱为材料 ,切取 1 /2部位处花柱组织 ,匀浆后 ,进行抽提和硫酸铵盐析 ,得到 3 5%级分的蛋白质粗提液 ,此液经聚丙烯酰胺凝胶电泳检测 ,显示出 9条蛋白质带 ;经 Con A-Sepharose 4 B亲和柱层析 ,特异峰 (S#)仅显示 1条蛋白质带 ,恰好是 3 5%级分中近正极端的 2种蛋白质中的一种最优势蛋白质 ;部分生化性质测定结果表明 ,该蛋白质为碱性糖蛋白 ,糖含量为 9.2 % ,由 2个亚基组成 ,相对分子质量分别为 3 8.0 ku,3 2 .0 ku,等电点分别约为 7.5,7.2 ;生物活性测定结果表明 ,该蛋白质能抑制离体 (in vitro)萌发自花花粉花粉管的生长 ;氨基酸序列分析表明 ,3 2 .0 ku组分 N-端 1 5个氨基酸序列与矮牵牛 ,花烟草等的

Braess模型与城市网络的空间复杂化探讨

B raess交通网络模型是经典的图论模型,但该模型同时具有很强的地理学色彩。B raess借助一个简单的网络揭示了出人意料的地理现象:增加交通路线有时反而降低运输效率。从理论地理学的角度对B raess网络进行了数学抽象,然后利用规划理论、图论和微分方程解析等方法揭示出区域-城市地理系统的空间复杂化两个重要动因:空间相互作用和宏观对称破坏。

Earth: Review Article

Every year on 22 April, we have celebrated Earth Day and the beautiful planet we call home. Earth Day, established in 1970, has been used to highlight our planet’s environmental challenges and raise awareness of the importance of protecting our world for future generations [1]. To provide the protection of our planet, we should explain Earth’s environmental challenges to the best of our knowledge in frames of contemporary Geophysics. This paper gives a short overview of the developed Hypersphere World-Universe Model (WUM) and pay particular attention to the principal role of Dark Matter (DM) in the Earth’s life. In this manuscript, we discuss different aspects of the Earth: a condition of Young Earth before the Beginning of life on It;Internal Structure;“The 660-km Boundary” that we named Geomagma;Random Variations of Earth’s Rotational Speed on a daily basis;Origin of Moon;Expanding Earth;Internal Heating;Faint Young Sun paradox;Geocorona and Planetary Coronas;High-Energy Atmospheric Physics. WUM proposed principally different ways to solve the problems of Internal Heating, Origin of the Moon, and Faint Young Sun paradox based on DM core of the Earth. The Model revealed the fact that the Sun Activity causes the Geomagma Activity and, as a consequence, Random Variations of Earth’s Rotational Speed by the varying Sun’s magnetic field.

美与伟大的依存悖论——T.S.艾略特与新批评派的文论异趣

艾略特的早期文论一度是新批评派重要的灵感源泉,但新批评派对艾略特的思想并非全盘接收,而是从“文本中心”的立场对之进行了修正。因此,当后期艾略特皈依了宗教、走向更加宽广的宗教文化视野时,双方的龃龉也就越来越突出。艾略特提出的“感受力的统一”、“客观对应物”以及文学与神学的双重标准,与新批评派“意图谬误”、“感受谬误”及对纯文学标准的坚持,形成了鲜明的分野。从对立于新批评派的角度来看,后期艾略特突破极端文本中心的困境,来到一个更宽广深入的文化境遇,恰恰对于新批评派突破自身瓶颈具有最直接的借鉴作用。在思考艾略特和新批评派歧异的过程中,我们清晰觉察到了文学“美”与“伟大”相互依存之中的悖论。

Calculation of the parameters of georesistivi－ty anisotropy and case history of earthquake precursors

This paper has discussed the effective resistivity ellipse and the paradoxical phenomenon of anisotropy. Two cases have been discussed, namely: there are three measuring lines at arbitrary angles with one another and there are two mutually perpendicular measuring lines and an additional measurement of the transversal effective resistivity. For these cases, the paper has given the methods for quantitatively calculating the parameters of georesistivity anisotropy. The formulae given include those for calculating the azimuth (of the principal axis of minimum resistivity ρ 1, the average resistivity ( ρ 1ρ 3) 1/2 , (ρ 2ρ 3) 1/2 , and the anisotropy coefficient λ=(ρ 2/ρ 1 ) 1/2 . As a case history, the data observed by the Datong geoelectricity station have been processed with reference to the results of in situ resistivity measurement in media subjected to shear. The results of analysis have led to the following understandings. Before and after the Datong M S6.1 earthquake on October 19, 1989, the abnormal rise of NE trending georesistivity and abnormal fall of NW trending georesistivity observed at the Datong and Yangyuan stations were caused by the pure shear acting on the medium. The major principal compression was in NE direction, which made an acute angle with the strike of the seismic fault plane, and thus there was a greater shear stress but very small normal stress so that the fault was likely to slide but the earthquake was only of moderate magnitude. The states of stress in medium were the same before and after earthquake and therefore the georesistivity precursor was of the same sign as that of co seismic variations.