The Infinity Tree: Representing Infinities of Real Numbers with Countably Infinite Tree Structures

This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers is not countably infinite. Likewise, countably infinite tree structures could represent all real numbers, and all points in any number of dimensions in multi-dimensional spaces. The objective of this paper is not to overturn previous research based on Cantor’s argument, but to suggest that this situation may be treated as a definitional or axiomatic choice. This paper proposes a “non-Cantorian” branch of cardinality theory, representing all these infinities with countably infinite tree structures. This approach would be consistent with the Continuum Hypothesis.

How Prime Numbers Are Interconnected and Built with Two Equations: Addition and Subtraction Rules the Function (6µ)

Are all prime numbers linked by four simple functions? Can we predict when a prime will appear in a sequence of primes? If we classify primes into two groups, Group 1 for all primes that appear before ζ (such that , for instance 5, ), an even number divisible by 3 and 2, and Group 2 for all primes that are after ζ (such that , for instance 7), then we find a simple function: for each prime in each group, , where n is any natural number. If we start a sequence of primes with 5 for Group 1 and 7 for Group 2, we can attribute a μ value for each prime. The μ value can be attributed to every prime greater than 7. Thus for Group 1, and . Using this formula, all the primes appear for , where μ is any natural number.

The Quantum Microverse: A Prime Number Framework for Understanding the Universe

This study aims to demonstrate a proof of concept for a novel theory of the universe based on the Fine Structure Constant (α), derived from n-dimensional prime number property sets, specifically α = 137 and α = 139. The FSC Model introduces a new perspective on the fundamental nature of our universe, showing that α = 137.036 can be calculated from these prime property sets. The Fine Structure Constant, a cornerstone in Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD), implies an underlying structure. This study identifies this mathematical framework and demonstrates how the FSC model theory aligns with our current understanding of physics and cosmology. The results unveil a hierarchy of α values for twin prime pairs U{3/2} through U{199/197}. These values, represented by their fraction parts α♊ (e.g., 0.036), define the relative electromagnetic forces driving quantum energy systems. The lower twin prime pairs, such as U{3/2}, exhibit higher EM forces that decrease as the twin pairs increase, turning dark when they drop below the α♊ for light. The results provide classical definitions for Baryonic Matter/Energy, Dark Matter, Dark Energy, and Antimatter but mostly illustrate how the combined α♊ values for three adjacent twin primes, U{7/5/3/2} mirrors the strong nuclear force of gluons holding quarks together.

Integration of pore structure modulation and B,N co-doping for enhanced capacitance deionization of biomass-derived carbon

Biomass-derived carbon has demonstrated great potentials as advanced electrode for capacitive deionization(CDI),owing to good electroconductivity,easy availability,intrinsic pores/channels.However,conventional simple pyrolysis of biomass always generates inadequate porosity with limited surface area.Moreover,biomass-derived carbon also suffers from poor wettability and single physical adsorption of ions,resulting in limited desalination performance.Herein,pore structure optimization and element co-doping are integrated on banana peels(BP)-derived carbon to construct hierarchically porous and B,N co-doped carbon with large ions-accessible surface area.A unique expansionactivation(EA)strategy is proposed to modulate the porosity and specific surface area of carbon.Furthermore,B,N co-doping could increase the ions-accessible sites with improved hydrophilicity,and promote ions adsorption.Benefitting from the synergistic effect of hierarchical porosity and B,N co-doping,the resultant electrode manifest enhanced CDI performance for NaCl with large desalination capacity(29.5 mg g^(-1)),high salt adsorption rate(6.2 mg g^(-1)min^(-1)),and versatile adsorption ability for other salts.Density functional theory reveals the enhanced deionization mechanism by pore and B,N co-doping.This work proposes a facile EA strategy for pore structure modulation of biomass-derived carbon,and demonstrates great potentials of integrating pore and heteroatoms-doping on constructing high-performance CDI electrode.

Probing the effects of lithium doping on structures, properties, and stabilities of magnesium cluster anions

Bimetallic clusters have aroused tremendous interest because the property changes like structure,size,and composition have occurred.Herein,a structural search of the global minimum for anionic LiMg_(n)^(-)(n=2-11) clusters is performed using an efficient crystal structure analysis by particle swarm optimization(CALYPSO) structural searching program with subsequent density functional theory(DFT) calculations.A great variety of low energetic isomers are converged,and the most stable ones are confirmed by comparing their total energy of each size.It is found that the LiMg_(n)^(-)clusters are structurally consistent with corresponding Mg clusters anions except for LiMg_(5)^(-)and LiMg_(7)^(-).In all the doped clusters,the Li atom prefers to occupy the convex position.Simulated photoelectron spectra(PES),Infrared(IR),and Raman spectra of LiMg_(n)^(-)could be used as an essential evidence for identifying cluster structures experimentally in the future.Stability study reveals that a tower-like structure of LiMg_(9)^(-)has prominent stability and can be identified as a magic number cluster.The reason might be that there are both closed-shell 1S^(2)1P^(6)1D^(10)2S^(2) electronic configurations and stronger Li-Mg bonds caused by sp hybridization in the LiMg_(9)^(-)cluster.

A Conceptual Model of Our Universe Derived from the Fine Structure Constant (α)

The Fine Structure Constant (α) is a dimensionless value that guides much of quantum physics but with no scientific insight into why this specific number. The number defines the coupling constant for the strength of the electromagnetic force and is precisely tuned to make our universe functional. This study introduces a novel approach to understanding a conceptual model for how this critical number is part of a larger design rather than a random accident of nature. The Fine Structure Constant (FSC) model employs a Python program to calculate n-dimensional property sets for prime number universes where α equals the whole number values 137 and 139, representing twin prime universes without a fractional constant. Each property is defined by theoretical prime number sets that represent focal points of matter and wave energy in their respective universes. This work aims to determine if these prime number sets can reproduce the observed α value, giving it a definable structure. The result of the FSC model produces a α value equal to 137.036, an almost exact match. Furthermore, the model indicates that other twin prime pairs also have a role in our functional universe, providing a hierarchy for atomic orbital energy levels and alignment with the principal and azimuthal quantum numbers. In addition, it construes stable matter as property sets with the highest ratio of twin prime elements. These results provide a new perspective on a mathematical structure that shapes our universe and, if valid, has the structural complexity to guide future research.

Vibration Source Number Estimation of A Shell Structure

It has been challenging to correctly separate the mixed signals into source components when the source number is not known a priori.To reveal the complexity of the measured vibration signals,and provide the priori information for the blind source separation,in this paper,we propose a novel source number estimation based on independent component analysis(ICA)and clustering evaluation analysis,and then carry out experiment studies with typical mechanical vibration signals from a shell structure.The results demonstrate that the proposed ICA based source number estimation performs stably and robustly for the shell structure.

Structured condition numbers and statistical condition estimation for the LDU factorization

In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setting the specific norms and weight parameters, we present the expressions of the structured normwise, mixed, componentwise condition numbers and the corresponding results for unstructured ones. In addition, we investigate the statistical estimation of condition numbers of LDU factorization using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, and devise three algorithms. Finally, we compare the structured condition numbers with the corresponding unstructured ones in numerical experiments.

Occurrence of Fibonacci numbers in development and structure of animal forms: Phylogenetic observations and epigenetic significance

A survey of zoological literature affirmed the wide occurrence of Fibonacci numbers in the organization of acellular and prokaryotic life forms as well as in some eukaryotic protistans and in the embryonic development and adult forms of many living and fossil remains of metazoan animals. A detailed comparative analysis of the axial skeleton of a fossil fish and humans revealed a new rule of the “nested triad” of bones organized along the proximal to distal axis of limb appendages. This growth pattern and its ubiquity among living vertebrates appear to underlie a profound rule of pattern formation that is dictated in part by the genetics and epigenetic mechanisms of stem cell clonal development.

Improvement of the Algorithm for Computing Adjusted Structure Number for Determination of Backlog Maintenance

The pavement strength is very important for the evaluation of backlog maintenance. The current trend in many developing countries used pavement conditions index-PCI in estimating maintenance costs. The PCI can only justify periodic and routine recurrent maintenance. The condition strength is rarely determined in a flexible pavement creating an opportunity for back long maintenance. This paper reports the study conducted to develop and improve the algorithm for estimating the adjusted structure number to estimate the remaining thickness of the flexible pavement. The analysis of eight ways of computing structure numbers from FWD data ware analyzed and found that the improvement of the HDM 3 - 4 models can influence the usefulness of data collected from road asset management in Tanzania. The algorithm for estimating structural numbers from CBR was improved to compute adjusted structural numbers finally used to estimate the remaining life of the flexible pavement. The analysis of the network of about 6900 km including ST and AM was found that 64.72% were very good, 12% were Good, 10% were fair and 7.84% were poor and 5.4% were very poor.

氮含量对Ti-B-C-N薄膜微观结构和性能的影响

采用反应磁控溅射法在高速钢基体上制备氮原子分数分别为10.8%,15.6%,28.1%,36.4%的Ti-B-C-N薄膜,研究了氮含量对薄膜微观结构、硬度和摩擦磨损性能的影响。结果表明:Ti-B-C-N薄膜均由α-Fe和Ti(C,N)纳米晶组成,具有Ti(C,N)纳米晶镶嵌在非晶基体相中的纳米复合结构;随着氮含量增加,非晶相含量增加,Ti(C,N)纳米晶的含量和晶粒尺寸减小;随着氮含量增加,Ti-B-C-N薄膜的显微硬度增大,摩擦因数和磨损率均减小,表面磨痕变浅,磨损机制由剥落和微观犁削转变为微观抛光。

从“数量名+NP”话题句看话题和述题的复杂依存关系

汉语“数量名+NP”在特定语境中可作话题,被赋予定指理解,但同时也凸显数量特征,是有标记话题。该结构要求述题须表达数量特征,但受句子体特征和语用因素影响其内部也有细微差别。“数量名”话题自身的特征与“话题—述题”的陈述关系决定结构对述题的要求,而述题的构造和语义也有助于话题指称类型的理解,二者相互依存。

Structure, Stability and Vibrational Spectra of LaC_5~n(n=-1,0,+1) Clusters

用密度泛含方法研究了ＬａＣ５ｎ（ｎ＝－１，０，＋１）分子簇的结构和稳定性及振动光谱，对这个六原子体系提出了三种可能构型，点群结构为Ｃ２ｖ对称性．第一个构型为Ｌａ接在弯曲的Ｃ５链上，第二个是Ｌａ通过二个键与Ｃ５环相连第三个是Ｌａ通过一个键与Ｃ５环相连；结果表明，第一个构型即当Ｌａ接在弯曲的Ｃ５链上时能量最低．振动光谱分析指出，当ｎ＝－１时，第二个构型为局域极小值；当ｎ＝＋１时，第一个和第二个构型为局域极小值；对ｎ＝０，局域极小值没有找到．

人恶性胸膜间皮瘤DNA从头测序及基因突变分析

通过DNA从头测序分析人胸膜间皮瘤发生的高关联度突变基因。提取恶性胸膜间皮瘤(MPM)组织和正常胸膜组织DNA,构建基因文库,用Illumina HiSeqX Ten PE 150平台测序,将测序结果与人类基因组数据库的参考序列进行比对、注释,并对测序结果进行过滤、错误率分布检查、GC含量分布检查分析。MPM组织DNA平均过滤37829946 bp,错误率小于0.12%,GC含量占41.17%,而正常胸膜组织DNA平均过滤39089681 bp,错误率小于0.1%,GC含量占41.7%,两者测序质量均在Q 30(≥80%)以上,MPM为87.43%,正常胸膜为88.36%。以上高质量测序数据通过BWA比对到参考基因组(GRCh 37/hg 19),得到最初比对序列,利用重复标记后的比对序列进行覆盖度、深度等统计,覆盖深度达到10 X以上该突变位点可信。结果显示,实验病例XL14覆盖深度达到10 X的占98.59%,覆盖率达到99.83%;对照病例Z5占98.50%,覆盖率达到99.79%。对该序列进行基因注释分析,发现一系列单核苷酸多态性、基因插入缺失、基因结构变异、基因拷贝数变异,筛选出总变异位点数29277个,可能致病的变异位点数22个,致病性的变异位点数5个,不确定变异有害性的位点数为3353个,其余变异位点均为良性。进一步对突变基因进行富集、关联性分析,预测出突变基因TXNDC2与人胸膜间皮瘤的发生高度相关,相关系数达到0.8以上;突变基因PIEN、ABCC1、UGT1A7、UGT1A3、UGT1A4、UGT1A9、ALDH3B1、UGT1A5等与人胸膜间皮瘤有一定关联性,关联度在0~0.2之间。基因TXNDC2、PIEN、ABCC1、UGT1A7、UGT1A3、UGT1A4、UGT1A9、ALDH3B1、UGT1A5的变异可能与人胸膜间皮瘤的发生发展有关。本实验为人胸膜间皮瘤分子诊断提供了参考。

Effect of nutrient level on phytoplankton community structure in different water bodies

Increasing levels of pollution within water bodies can cause eutrophication and an associated rapid growth in and reproduction of phytoplankton. Although most frequently occurring in bodies of water such as lakes and dams, in recent years an increasing number of river systems in China have suffered serious algal blooms. The community structure of phytoplankton may differ, however, dependent on the hydrodynamic conditions and nutrient levels within the water body. The field investigation results obtained from a stagnant river in Suzhou City and Taihu Lake, China, showed that in water with higher concentrations of nitrogen and phosphorus, Chlorophyta became the predominant species and in water with lower concentrations of nitrogen and phosphorus, Cyanobacteria became the predominant species. Growth experiments with competitive species, Microcystis aeruginosa Kutz and Scenedesmus quadricauda （Turp.）, were conducted at three different nutrient levels. The biomass of algae in pure and mixed cultures was measured under conditions of different N/P ratios at oligotrophic, eutrophic and hypertrophic nutrient levels. The results indicated that the most suitable state for the growth and reproduction of M. aeruginosa and S. quadricauda were eutrophic conditions in both pure and mixed cultures. Under competition, however, the lower medium nutrient levels favoured M. aeruginosa, while the higher medium nutrient levels better suited S. quadricauda. Under similar hydrodynamic conditions, the community structure of phytoplankton in the water body was determined by the dominant species in competition for nutrients.

Microstructure and shear strength of the brazed joint of Ti(C,N)-based cermet to steel

Firm joins were obtained between Ti（C,N）-based cermet and steel with Ag-Cu-Zn-Ni filler metal by vacuum brazing. The effects of technological parameters such as brazing temperature, holding time, and filler thickness on the shear strength of the joints were investigated. The microstructure of welded area and the reaction products of the filler metal were examined by scanning electron microscopy （SEM）, metallographic microscope （OM）, energy-dispersive X-ray analysis （EDS）, and X-ray diffraction （XRD）. The brazing temperature of 870℃, holding time of 15 min, and filler thickness of 0.4 mm are a set of optimum technological parameters, under which the maximum shear strength of the joints, 176.5 MPa, is achieved. The results of microstructure show that the wettability of the filler metal on Ti（C,N）-based cermet and steel is well. A mutual solution layer and a diffusion layer exist between the welding base materials and the filler metal.

Seismological study on the crustal structure of Tengchong volcanic-geothermal area

Based upon the deep seismic sounding profile conducted in the Tengchong volcanic-geothermal area, a two-dimensional crustal P velocity structure is obtained by use of the finite-difference inversion and the forward travel-time fitting method. The crustal model shows that there is a low velocity zone in upper crust in the Tengchong area, which may be related to the volcanic-geothermal activities, and two intracrustal faults (the LonglingRuili fault and Tengchong fault) exist on the profile, where the Tengchong fault may extend to the Moho discontinuity. Meanwhile, based on teleseismic data recorded by a temporary seismic network, we obtained the S-wave velocity structures beneath the RehaiRetian region in the Tengchong area, which show the low S-wave velocity anomaly in upper crust. The authors discuss the causes of Tengchong volcanic eruption based on the deep crustal structure. The crustal structure in the Tengchong volcanic-geothermal area is characterized by low P-wave and S-wave velocity, low resistivity, high heat-flow value and low Q value. The P-wave velocity in the upper mantle is also low. For this information, it can be induced that the magma in the crust is derived from the upper mantle, and the low velocity anomaly in upper crust in the Tengchong area may be related to the differentiation of magma. The Tengchong volcanoes are close to an active plate boundary and belong to plate boundary volcanoes.

Magnetic properties and structure of (001)-oriented [CoPt/C]_n /Ag nanocomposite films on the glass substrates

The highly （1301） oriented triple system of [CoPt/C]n/Ag films was deposited on glass substrates by DC and RF magnetron sputtering. After annealing at 600℃ for 30 min, thin films become magnetically hard with coercivities in the range of 160-875 kA/m because of high anisotropy associated with the L10 ordered phase. C doping plays an important role in improving （001） texture and reducing the intergrain interactions. The oriented growth of CoPt films was influenced strongly by the number of repetitions （n） of CoPt/C. By controlling the C content and the number of repetitions （n） of CoPt/C, nearly perfect （001） orientation can be obtained in the [CoPt3nm/C3nm]5/Ag50 nm.

Crystal and Molecular Structure of Bis-N,N’(dithiodi-2,1-phennylene)benzamide

The crystal structure of the title compound ((C 6H 5CONC 6H 4S) 2, M r =229) has been determined by X ray diffraction analysis. The crystal belongs to triclinic space group P 1 with cell parameters: a=7.957(4), b=11.570(7), c=12 335(6), α=76.68(4), β=81.48(4), γ=87.26(4)°, V=1092.9 3, Z=2, D c =1 39g/cm 3, F(000)=476, μ (Mo Kα )=2.7mm -1 . The final R factor is 0.0373 for 3764 observed reflections. The result of X ray diffraction analysis indicates that all of these single bond lengths are obviously shorter than that of standard single bond. Those atoms might take part in a conjugate system. The electrons for sp 3 hybridized S(1) and S(2) move toward two sides and the densities of electronic cloud among them are reduced and can be easily broken. The obtained results can explain the reaction mechanism of the title compound.