The Periodic Table of Primes

Over millennia, nobody has been able to predict where prime numbers sprout or how they spread. This study establishes the Periodic Table of Primes (PTP) using four prime numbers 2, 3, 5, and 7. We identify 48 integers out of a period 2×3×5×7=210 to be the roots of all primes as well as composites without factors of 2, 3, 5, and 7. Each prime, twin primes, or composite without factors of 2, 3, 5, and 7 is an offspring of the 48 integers uniquely allocated on the PTP. Three major establishments made in the article are the Formula of Primes, the Periodic Table of Primes, and the Counting Functions of Primes and Twin Primes.

An Interdisciplinary Perspective from the Earth Scientist's Periodic Table:Similarity and Connection between Geochemistry and Metallurgy

In 2003,Railsback proposed the Earth Scientist's Periodic Table,which displays a great deal of elemental geology information in accordance with the natural environment of the earth.As an applied science,metallurgy is based on mineral composition and element behavior,that is similar to geochemistry.In this paper,connections and similarities between geology and metallurgy are identified,based on geochemical laws and numerous metallurgical cases.An obvious connection is that simple cations w让h high and low ionic potential are commonly extracted by hydrometallurgy,while those with intermediate ionic potential are extracted by pyrometallurgy.In addition,element affinity in geology is associated with element migration in metallurgic phases.To be specific,in pyrometallurgy,lithophile elements tend to gather in slags,chalcophile elements prefer the matte phase,siderophile elements are easily absorbed into metal melt,and atmophile elements readily enter the gas phase.Furthermore,in hydrometallurgy,the principles of hard/soft acids and bases(HSABs)offer an explanation of how precipitation and dissolution occur in different solutions,especially for fluoride and chloride.This article provides many metallurgical examples based on the principles of geochemistry to verify these similarities and connections.

A Specific Periodic Table for Chemistry of Organic, Semi-Organic and Inorganic Elements: Compatibility with the Even-Odd Rule,the Number of Electrons and the Isoelectronicity Rule

Following the introduction of the new even-odd and isoelectronic rules and definitions affecting the understanding of electronic structure and bonds, the author has thought necessary to summarize understandings in the form of a table. The classical periodic table, a simple tool used by generations of physicists, is here extended to become a useful tool aimed specifically at chemists. In chemistry, position and number of covalent bonds of each atom are needed, as well as the exact location of charges. The table gives the number of possible bonds for each element and reveals how it is affected by charges. Additionally, the specific table indicates for each atom its isoelectronic elements and highlights the distinction between organic and inorganic elements. Discussion is led on the first two rows of the table by successfully comparing its statement with more than 50 well-known liquid and gaseous compounds.

Covalent Bonds Creation between Gas and Liquid Phase Change: Compatibility with Covalent and Even-Odd Rules Based on a “Specific Periodic Table for Liquids”

A decrease in temperature will eventually turn a gas into liquid and then into a solid. Each of these phase change shows a higher degree in cohesion of molecules. While it is usually admitted that molecules in solids form additional connections, the cohesion of molecules in liquids is usually explained by changes in kinetics of molecules. Given that the density of a solid is nearly the same than that of a liquid, the present paper assumes a different stand and considers that connections between molecules must be similar in liquids and in solids. The difference between gas, in which molecules are entirely loose, and liquid, is therefore the presence of an additional connection between gaseous molecules. This paper describes how and where these connections are built with the help of a few rules and a “specific periodic table for liquids”. The coherence of this approach is reinforced by its capacity to explain phase change of forty well-known molecules containing inorganic and organic elements.

Basic Steps in Chemical Dissociation of Gaseous Molecules Using an Even-Odd Rule, a Specifically Adapted Periodic Table and a Covalent Bonding Rule

When writing equations of chemical dissociation, students and scholars are taught two fundamental rules to balance the equation. On both sides of the equation, the types of elements and their quantity are conserved, as well as the global electrical charge. This paper introduces additional methods during dissociation of gaseous compounds, to precisely describe how electrical charges locally move and how bonding structures are modified. Specific rules revolving around electrons pairs displacements are developed and applied to about 150 dissociations of small gaseous molecules using atoms from the three first rows of the periodic table. Results obtained tend to demonstrate the relevance of these tools for chemists.

Interesting Features of Ionization Potentials for Elements(Z≤119)along the Periodic Table

The ionization potential （IP） is a basic property of an atom, which has many applications such as in element analysis. With the Dirac-Slater methods （i.e., mean field theory）, IPs of all occupied orbitals for elements with atomic number （Z ≤ 119） are calculated conveniently and systematically. Compared with available experimental measurements, the theoretical accuracies of IPs for various occupied orbitals are ascertained. The map of the inner orbital IPs with Mood accuracies should be useful to select x-ray energies for element analysis. Based on systematic variations of the first IPs for the outermost orbitals in good agreement with experimental values as well as other IPs, mechanisms of electronic configurations of all atomic elements （Z ≤ 119） along the periodic table are elucidated. It is interesting to note that there exist some deficiencies of the intermediate orbital IPs, which are due to electron correlations and should be treated beyond the mean field theory.

Interpretation of Dark Matter and Quark-Gluon Plasma: The Generation of the Periodic Table Elements and Its Phase Diagram: A Novel Millennium Power Plant

This paper presents a novel physical interpretation of the state of matter of the quark-gluon as the most fundamental building blocks in nature. Such a model is derived based on the assumption that dark matter and dark energy behave as a perfect ideal fluid at extremely high temperature. By the virtue of Boltzmann constant of the ideal gas law and NASA’s Cosmic Microwave Background Explorer (CMB) which estimate that the space has an average temperature close to 2.7251 Kelvin, then the equivalent mass-energy of the fundamental particle of the dark matter/dark energy is determined. Moreover, assuming a uniform space dark energy/dark matter density, then the critical temperature at which the dark matter has a unity entity per volume is identified as 64 × 1012 K. The calculated critical temperature of the quark-gluon plasma is found to be proportional to the temperature generated by colliding heavy ions at the Relativistic Heavy Ion Collider (RHIC) and European Organization for Nuclear Research (CERN). Moreover, the individual critical temperatures of the quark-gluon plasma matter at which the elements of the Periodic Table are generated are explicitly determined. The generation temperature trend of the elements of the Periodic Table groups and Periods is then demonstrated. Accordingly, the phase diagram of the quark-gluon state matter is proposed. Finally, a new model of quark-gluon power generation plant is proposed and aims to serve humanity with new energy sources in the new millennium.

The Nuclear Chemistry Odd-Even Periodic Table of the Elements

Odd-Even Periodic Table of Chemical Elements designed by the authors settles the position of Hydrogen and Helium, Additionally, it yields no exceptional arrangements for neither the Lanthanides, Actinide and Super Actinides nor the six empty spots and the controversy on the positions of hydrogen and helium has been settled. It plays an important role in comparing the stability of nucleons and predicting the ordinal of the terminal element.

IUPAC Periodic Table Quantum Mechanics Consistent

Most periodic tables of the chemical elements are between 96% and 100% in accord with quantum mechanics. Three elements only do not fit correctly into the official tables, in disagreement with the spherical harmonics and the Pauli exclusion principle. Helium, belonging to the s-block, should be placed beside hydrogen in the s-block instead of the p-block. Lutetium and lawrencium belonging to the d-block of the transition metals should not be in the f-block of the lanthanides or the actinoids. With these slight modifications, the IUPAC table becomes quantum mechanics consistent.

The Knees-Ankles-Toe in Cosmic Rays and the Periodic Table of Elementary Particles

This paper posits the discovery of the new elementary particles from the energy spectrum for the knees-ankles-toe of cosmic rays. The energy spectrum from 109 eV to 1020 eV appears to follow a single power law except few breaks at the knees-ankles-toe. The power index increases at the first knee and the second knee, and decreases at the ankle. Above 4 × 1019 eV, the power index increases as the “toe”. The fine structure of the cosmic ray spectrum shows that an ankle with decrease in power index is in between the first knee and the second knee, resulting in two knees, two ankles, and one toe. This paper posits that the knees-ankles-toe are explained by the very high-energy fermions and bosons in the periodic table of elementary particles that places all known leptons, quarks, gauge bosons, and the Higgs boson in the table with the calculated masses in good agreement with observed values. In the periodic table, some high-energy dimensional fermions (Fd where d= dimensional orbital number from 5 to 11) and bosons (Bd) are involved in the knees-ankles-toe. At the knees and the toe, some parts of the energies from the energy sources of cosmic rays are spent to generate Fd and Bd, resulting in the increase of power index. The ankles are the the middle points (midpoints) between the adjacent dimensional fermions and bosons. At a midpoint, the energy is too high to keep the thermally unstable high-energy dimensional particle,resulting in the decay and the decrease of power index. The calculated masses of B8, the midpoint, F9, the midpoint, and B9, are 1.7 × 1015, 2 × 1016, 2.4 × 1017, 2.8 × 1018, and 3.2 × 1019 eV, respectively, which are in good agreement with observed 3 × 1015, 2 × 1016, 3 × 1017, 3 × 1018, and 4 × 1019 eV for the first knee, the first ankle, the second knee, the second ankle, and the toe, respectively. The mass of F10 is 4.4 × 1021 eV beyond the GZK limit, so F10 and above are not observed.

The Periodic Table of Elementary Particles Based on String Theory

In this paper, all elementary particles (leptons, quarks, gauge bosons, and the Higgs boson) can be placed in the periodic table of elementary particles based on string theory with oscillating spacetime dimension number, instead of conventional string theory with fixed space-time dimension number. Dimension number oscillates between 11D and 10D and between 10D and 4D reversibly. The oscillation of space-time dimension number (D) is accompanied by mass dimension number (d) to represent mass. Space-time dimension number decreases with increasing mass dimension number, decreasing speed of light and increasing rest mass. 4D particle originally is 4D10d particle, and has the lowest speed of light and the highest rest mass. With the same energy, the relation between adjacent mass dimensions is Md-1=Mdαd2, where M is rest mass, d is mass dimension number, and α is the fine structure constant. According to the proposed cosmology, the non-gravitational 4D10d particles were sliced into 4D4d core particles surrounded by 6 separated mass dimensions as the 6 dimensional orbitals constituting the non-gravitational forces (electromagnetism, strong, and weak). The combination of the 6 dimensional orbitals and the gravitational 4D10d particle resulted in the 7 dimensional orbitals. As the periodic table of elements based on the atomic orbitals, the periodic table of elementary particles is based on the combination of the two asymmetrical sets of the 7 dimensional orbitals. One set as the principal dimensional orbitals is mainly for leptons and gauge bosons, and another set as the auxiliary orbitals is mainly for individual quarks. The calculated constituent masses of leptons, quarks, gauge bosons, and the Higgs boson are in good agreement with the observed values. For examples, the calculated mass of top quark is 176.5 GeV in good agreement with the observed 173.34 GeV, and the calculated average mass of the Higgs boson is 128.8 GeV in good agreements with the observed 125 or 126 GeV.

Atom’s Nuclear Structure and the Periodic Table of the Chemical Elements

A new method for the identification of the chemical Elements isotopes takes advantage of the isotope Neutron Excess (NE) number. The repre-sentation of the natural isotopes in the Z-NE plane reveals a surprising correspondence between atom’s nuclear and electronic structures. Nuclear directs the atom electronic structure in spite of the alternative set of numbers ruling the two main atom’s compartments. These compartments appear better integrated than actually considered. The Mendeleev periodic table is rooted in the atom’s nuclear structure. Two recent studies arrive to identical conclusions.

Study on the methods to calculate the numbers of elements in every period in the periodic table

The previous methods of figuring the numbers of chemical elements is summed up in this paper. Based on that, another two creative calculative methods are introduced as well.

Pseudoscalar Top-Bottom Quark-Antiquark Composite as the Resonance with 28 GeV at the LHC: Hadron Masses and Higgs Boson Masses Based on the Periodic Table of Elementary Particles

This paper posits that the observed resonance with 28 GeV at the LHC is the pseudoscalar top-bottom quark-antiquark composite which has the calculated mass of 27.9 GeV derived from the periodic table of elementary particles. The calculated mass is for the mass of?. In the periodic table of elementary particles, t quark (13.2 GeV) in the pseudoscalar top-bottom quark-antiquark composite is only a part of full t quark (175.4 GeV), so pseudoscalar?(26.4 GeV) cannot exist independently, and can exist only in the top-bottom quark-antiquark composite. As shown in the observation at the LHC, the resonance with 28 GeV weakens significantly at the higher energy collision (13 TeV), because at the higher collision energy, low-mass pseudoscalar? in the composite likely becomes independent full high-mass vector? moving out of the composite. The periodic table of elementary particles is based on the seven mass dimensional orbitals derived from the seven extra dimensions of 11 spacetime dimensional membrane. The calculated masses of hadrons are in excellent agreement with the observed masses of hadrons by using only five known constants. For examples, the calculated masses of proton, neutron, pion (π±), and pion (±0) are 938.261, 939.425, 139.540, and 134.982 MeV in excellent agreement with the observed 938.272, 939.565, 139.570, and 134.977MeV, respectively with 0.0006%, 0.01%, 0.02%, and 0.004%, respectively for the difference between the calculated and observed mass. The calculated masses of the Higgs bosons as the intermediate vector boson composites are in excellent agreements with the observed masses. In conclusion, the calculated masses of the top-bottom quark-antiquark composite (27.9 GeV), hadrons, and the Higgs bosons by the periodic table of elementary particles are in excellent agreement with the observed masses of resonance with 28 GeV at the LHC, hadrons, and the Higgs bosons, respectively.

Stability in Liquid Phases of Molecular Compounds Composed of Saturated Atoms: Application with the Even-Odd Rule and a Specific Periodic Table for Liquids

Building on the idea that molecules in liquid phase associate into multi-molecular complexes through covalent bonds, the present article focuses on the possible structures of these complexes. Saturation at atomic level is a key concept to understand where connections occur and how far molecules aggregate. A periodic table for liquids with saturation levels is proposed, in agreement with the even-odd rule, for both organic and inorganic elements. With the aim at reaching the most stable complexes, meaning no other chemical reactions can occur in the liquid phase, the structure of complexes resulting from liquefaction of about 30 molecules is devised. The article concludes that complexes in liquids generally assume rounded shapes of an intermediate size between gas and solid structures. It shows that saturation and covalent bonds alone can explain the specific properties of liquids. While it is generally acknowledged that molecular energy in gases and solids are respectively linear kinetic and vibratory, we suggest that rotatory energy dominates in liquids.

The Periodic Table of Elementary Particles for Baryonic Matter and Dark Matter: Upward-Going ANITA Events

This paper posits that the upward-going ANITA events are derived from the cosmic ray of the baryonic-dark matter (BDM) Higgs boson. In the extended standard model (ESM) for baryonic matter and dark matter, the spontaneous symmetry breaking through the Higgs mechanism for the symmetrical massless baryonic matter left-handed neutrinos and massless dark matter right-handed neutrinos produced massless baryonic matter left-handed neutrinos, sterile massive dark matter neutrinos, and the BDM Higgs boson. The BDM Higgs boson is the composite of the high-mass tau neutrino and the high-mass dark matter neutrino. During the passage through the high-density part of the Earth, the BDM Higgs boson is transformed into the oscillating BDM Higgs boson between the composite of the high-mass tau neutrino and the high-mass dark matter neutrino and the composite of the high-mass tau neutrino and the low-mass dark matter neutrino. The oscillating BDM Higgs boson decays into the high-mass tau neutrino with the extra energy and the low-mass dark matter neutrino (27 eV) in the low-density water-ice layer of the Earth. The high-mass tau neutrino is converted into ultra-high-energy tau neutrino which decays into tau lepton through the charged-current interactions, and tau lepton emerges from the surface of ice. Based on the periodic table of elementary particles, the calculated value for the high-mass tau neutrino with the extra energy is 0.47 EeV in good agreement with the observed 0.56 and 0.6 EeV. The periodic table of elementary particles for baryonic matter, dark matter, and gravity is based on the seven principal mass dimensional orbitals for stable baryonic matter leptons (electron and left-handed neutrinos), gauge bosons, gravity, and dark matter and the seven auxiliary mass dimensional orbitals for unstable leptons (muon and tau) and quarks, and calculates accurately the masses of all elementary particles and the cosmic rays by using only five known constants.

Uses of the Buys-Ballot Table in Time Series Analysis

Uses of the Buys-Ballot table for choice of appropriate transformation (using the Bartlett technique), assessment of trend and seasonal components and choice of model for time series decomposition are discussed in this paper. Uses discussed are illustrated with numerical examples when trend curve is linear, quadratic and exponential.

A Table That Produces Elements

How do elements originate, how atoms are formed, and what are the laws? According to the unified logic of “Tong Yi Lun Thought”, combined with the elements’ attributes and the atomic composition that have been discovered now, after determining that the mechanism of increasing yang in the atomic system is the increase of proton number, the Bian Zheng relationship among proton, neutron and electron determines that there are only 128 kinds of elements in the atomic system. At the same time, element atoms have corresponding logical relations when they are generated.

The Gastropod Shell Structure as a Blueprint for a Periodic System: A New Theory for Element Configurations

The purpose of this article is to propose a new design for the periodic table of elements. The new design is based on a three-dimensional (3D) model of the gastropod shell structure and presents a mechanism of the formation of elements that reflects the laws of nature that guide the formation of the gastropod shell, electron orbitals, and element structure. The author also identifies challenges associated with the current standard periodic table, such as the positions of hydrogen, helium, lanthanides, and actinides. The author’s research is a response to the IUPAC’s request, dating back to 2016, to settle unresolved disputes surrounding the current standard periodic table. Hence, the author proposes the “Gastropod Shell Model”, which presents the periodic system in 2D and 3D snail shells based on a hypothesized unifying principle guiding the formation of elements: the universal unified theory that considers the spiral and vortex forms as the bridge between energy and matter. The author was able to position hydrogen, helium, lanthanides, and actinides uniquely in their proposed periodic system to solve problems associated with their positions in the standard periodic table. Readers will be interested in uncovering the “hypothesized unifying principle guiding the formation of elements”.

秦汉畤祭遗址出土玉人功用研究

目前发现秦汉畤祭遗址的祭祀坑内,多是男女玉人一对与玉琮组合,应是畤祭礼仪最主要的祭祀形式。文章认为玉琮象征天圆地方,是祭天礼地的祭器。周秦汉时期奉行“以天为父,以地为母”之信仰,男女玉人与琮组合用于祭祀,正符合天为阳,地为阴,以天为父,以地为母的认知。并由此推断,男女玉人应分别是受祭的天神和地神之神主,用驷马车载之前往雍地进行畤祭之礼。西汉畤祭仍然继续沿用秦故礼仪,此正是由春秋至西汉数百年间,畤祭所用男女玉人造型及功用基本相同的缘由所在。