On Discrete Hopf Fibrations, Grand Unification Groups, the Barnes-Wall, Leech Lattices, and Quasicrystals

A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) how a subsequent 2-1 mapping (projection) of P16 onto a 8D-hyperplane might furnish the 2160 vertices of the uniform 241 polytope in 8-dimensions, and such that one can capture the chain sequence of polytopes 241,231,221,211in D=8,7,6,5dimensions, leading, respectively, to the sequence of Coxeter groups E8,E7,E6,SO(10)which are putative GUT group candidates. An embedding of the E8⊕E8and E8⊕E8⊕E8lattice into the Barnes-Wall Λ16 and Leech Λ24 lattices, respectively, is explicitly shown. From the 16D lattice E8⊕E8one can generate two separate families of Elser-Sloane 4D quasicrystals (QC’s) with H4 (icosahedral) symmetry via the “cut-and-project” method from 8D to 4D in each separate E8 lattice. Therefore, one obtains in this fashion the Cartesian product of two Elser-Sloane QC’s Q×Qspanning an 8D space. Similarly, from the 24D lattice E8⊕E8⊕E8one can generate the Cartesian product of three Elser-Sloane 4D quasicrystals (QC’s) Q×Q×Qwith H4 symmetry and spanning a 12D space.

Purchasing policy model based on components/parts unification

This paper presents a mathematical model for components/parts unification (CPU) policy. This model considers two components/parts that are functionally interchangeable but purchased from suppliers with different prices and quality characteristics. Because of the buyer's quality preference and suppliers' discount rates for bulky purchases, the model assists the procurement manager to determine how best to purchase the components/parts to meet its demand while minimizing the total acquisition costs.

Coordinate unification method of high-precision composite measurement in two dimensions

Multi-sensor coordinate unification in dimensional metrology is used in order to get holistic, more accurate and reliable information about a workpiece based on several or multiple measurement values from one or more sensors. Because of the problem that standard ball is deficient as a standard artifact in the coordinate unification of high-precision composite measurement in two dimensions （2D） , a new method is proposed in this paper which uses angle gauge blocks as standard artifacts to achieve coordinate unification between the image sensor and the tactile probe. By comparing the standard ball with the angle gauge block as a standard artifact, theoretical analysis and experimental results are given to prove that it is more precise and more convenient to use angle gauge blocks as standard artifacts to achieve coordinate unification of high-precision composite measurement in two dimensions.

Unification and Harmonization in True Color Image City Map

True color image city map is a sort of new-style map which combines the high resolution image and map symbols and shows both advantages in visualization. At the same time, the map unification and harmonization should be taken into account dur-ing the design process, since some visual conflicts appear when map symbols overlaid on the true color image. The objective of this research is to explore the rules in the process of true color image city map design based on chromatic and aesthetic knowledge. At the end, taking the Image Atlas of Guangzhou as an example, image color adjustment, road network presentation, and symbol de-signing issues will be discussed in the application.

Unification of Gravitational and Electromagnetic Fields Using Gauge Symmetry

A new method for the unification of gravitational and electromagnetic forces is proposed. Previously, Kaluza-Klein theory dealt with the unification, but it has not yet been established as a complete theory. The main reason for this is that Kaluza-Klein theory has various contradictions due to the use of a 5-dimensional metric tensor. In this paper, unlike the conventional method, various equations related to gravitational and electromagnetic force are derived without any contradiction by processing equations having gauge symmetry within a 4-dimensional range. In this process, we propose that Maxwell’s equations for the electromagnetic force are expressed more simply and implicitly than the existing tensor form. Using the gauge symmetry, it shows that electromagnetic force can exist in single metric tensor along with gravity. In addition, since geodesic equations can be derived in the form of coordinate transformation, it has been shown that they are consistent with the existing equations. As a result, it has shown that they are consistent with the existing physical equations without contradiction.

Unification of Gravitational and Electromagnetic Fields in Curved Space-Time Using Gauge Symmetry of Bianchi Identities

This paper deals with the generalization of the linear theory of the unification of gravitational and electromagnetic fields using 4-dimensional gauge symmetry in order to solve the contradictions from the Kaluza-Klein theory’s unification of the gravitational and electromagnetic fields. The unification of gravitational and electromagnetic fields in curved space-time starts from the Bianchi identity, which is well known as a mathematical generalization of the gravitational equation, and by using the existing gauge symmetry condition, equations for the gravitational and electromagnetic fields can be obtained. In particular, the homogeneous Maxwell’s equation can be obtained from the first Bianchi identity, and the inhomogeneous Maxwell’s equation can be obtained from the second Bianchi identity by using Killing’s equation condition of the curved space-time. This paper demonstrates that gravitational and electromagnetic fields can be derived from one equation without contradiction even in curved space-time, thus proving that the 4-dimensional metric tensor using the gauge used for this unification is more complete. In addition, geodesic equations can also be derived in the form of coordinate transformation, showing that they are consistent with the existing equations, and as a result, they are consistent with the existing physical equations.

G-CPT Symmetry of Quantum Emergence and Submergence—An Information Conservational Multiagent Cellular Automata Unification of CPT Symmetry and CP Violation for Equilibrium-Based Many-World Causal Analysis of Quantum Coherence and Decoherence

An equilibrium-based YinYang bipolar dynamic Generalization of CPT (G-CPT) symmetry is introduced based on energy/information conservational quantum emergence-submergence. As a bottleneck of quantum computing, quantum decoherence or collapse has been plaguing quantum mechanics for decades. It is suggested that the crux of the problem can trace its origin back to the incompleteness of CPT symmetry due to the lack of holistic representation for equilibrium-based bipolar coexistence. In this work, the notion of quantum emergence-submergence is coined as two opposite processes with bipolar energy/information conservation. The new notion leads to G-CPT symmetry supported by a Bipolar Quantum Cellular Automata (BQCA) interpretation of quantum mechanics. It is shown that the new interpretation further leads to the unification of electromagnetic particle-antiparticle bipolarity and gravitational action-reaction bipolarity as well as CPT symmetry and CP violation into a philosophically, geometrically and logically different quantum gravity theory. On one hand, G-CPT symmetry enables a Bipolar Quantum Agent (BQA) to emerge as a bipolar quantum superposition or entanglement coupled to a globally coherent BQCA;on the other hand, G-CP violation supports a causal theory of BQA submergence or decoupling from the global coherence. In turn, BQAs can submerge from one world but emerge in another within YinYang bipolar quantum geometry. It is suggested that all logical, physical, social, biological and mental worlds are bipolar quantum entangled under G-CPT symmetry. It is contended that G-CPT symmetry constitutes an analytical paradigm of quantum mechanics and quantum gravity—a fundamental departure from “what goes around comes around”. The new paradigm leads to a number of predictions and challenges.

The Coupling Constants for.an Electroweak Model with an SU（4）PS ×SU（4）EW Unification Symmetry

We introduce the sequence of spontaneous symmetry breaking of a coupling between Pati-Salam and electroweak symmetries SU（ 4 ）PS × SU（ 4 ）EW in order to establish a mathematically consistent relation among the coupling constants at grand unification energy scale. With the values of baryon minus lepton quantum numbers of known quarks and leptons, by including right-handed neutrinos, we can lind the mixing angle relations at different energy levels up to the electromagnetic U（1）EM scale.

"universe collapse model"and its roles in the unification of four fundamental forces and the origin and the evolution of the universe

To unify the four known fundamental forces and provide an explanation for the origin and the evolution of the universe are two long-term goals of theoretical physics. Here a “universe collapse model” has been proposed. The universe consists of Matter and No-matter. No-matter is the universal energy that constructs a consistent universe field, presenting a spiral wave motion at the speed of light at the small scale. The partial collapse of the universal energy forms the particles of the universal energy in a variety of sizes, which are called as the elementary particles. These elementary particles form atom and matter, which construct the galaxies. The collapse of the universe field induces the formation of the universe collapse potential (UCP) and universe collapse force (UCF), and the later is represented by four different aspects of the fundamental forces at the large or small scales. The mathematical equation and the derivation of UCP and UCF are described, and possible experimental tests are also suggested. Therefore, this new model may give a novel explanation for the unification of four fundamental forces and the origin and the evolution of the universe.

Axiomatic Affine Unification with Large Gravitational Vector Field Yields Vector-Metric Theory of Gravitation, Electromagnetism and Field Description of Mass-Particles

Under assumption of existence of extremely large gravitational vector field, this paper proposes a road map for building an Axiomatic Eddington Affine Unification theory yielding both Maxwell’s electromagnetism and Vector-metric theory of gravitation, in which inverse of the square-magnitude of the vector serves as Newton’s gravitational constant. The dependence of the vector’s magnitude with distance may offer an explanation of both Pioneer anomaly and “star rotation abnormality” in some Galaxies. In addition, the theory provides formalism for a classical description of atomic particles (such as protons and electrons) with highly non-linear equations and highly localized solutions. The existence of large Gravitational vector field can, for some variables (sub-fields), lead to elliptical type?differential equations (unlike in Maxwell’s electromagnetism, which is hyperbolic ), that by its nature forbids the existence independent waves and their propagation. Proposed Unified field description might provide the avenue for smooth transition to the world Quantum physics.

China's Compulsory Product Certification System (Four Unification)

On December 17, 2001, the State General Administration for Quality Supervision and Inspection and Quarantine and the Certification and Accreditation Administration co-held the news release conference in the Great Hall of the People for publicizing the laws of the National Compulsory Product Certification System ("Four Unification"). This is a

Plank Scale with Siva’s Constant “K”—A New Road to Grand Unification

Based on Vd = K equation and the consideration that maximum velocity is “velocity of light”, diameter of a space time for a particular fundamental force has been calculated. With Siva’s classical equation for space time, the quantity of fundamental force has been calculated in terms of relative energy with photon. This has been converted into relative force and the relative forces interpreted in terms of coupling constants of fundamental forces. All the fundamental forces are manifestation of space time material only. Space time will be different for different fundamental forces and their elementary force carrying particles. Specially, it has elaborated the difference between mass and energy for gravity space time. A generalized equation of space time and coupling constants has been derived. This equation can be used to calculate the space time parameters of other fundamental forces by knowing the coupling constant and vice versa. Space time parameters will be different for fundamental forces. In order to keep the parameters such as c,G,h,lp,tp and mp applicable to all other fundamental forces, a new parameter Siva’s constant “K” has been introduced. Thus all the observations are based on “K” and transformation is possible by a new additional parameter “K” such that c=h=G=K=1 instead of c=h=G=1. Ultimately, this paper may be a ground work to discuss lot of issues such as “consciousness” and “decoding of quantum information” in future.

Coordination mechanism of developing unification of urban agglomeration: A case study of south Sichuan urban agglomerations

With the expansion of the urbanization, the urban agglomeration is forming in the region and showing a unification trend. The development of urban agglomeration and its unification depends on the coordination of the division of labor. It is significant to the further development of urban agglomeration that the coordination mechanism was constructed. Taking the south Sichuan urban agglomerations(SSUA) as an example, the research analyzes the current situation and problems of cities' unification, studies the industrial distribution layout and designs the framework of the regionally coordinated development. Then the author constructs the coordination mechanism of urban agglomeration development and presents strategies for the coordinated development of urban agglomeration and its unification.

Social Equity： View from Pension System Unification

With the aging process, people been looked after properly in the old age has already become an important index to the national happiness index. Nowadays, government has a increasingly clear roadmap in promoting the development of pension system. Pension system unification refers to the same pension system for workers in public institutions and enterprises. It is a relative concept to the dual pension system. It has positive effect on social equity. But it also has many problems. In this article, author explained the relation between pension system unification and social equity on the basic of analyzing viewpoints of several scholars. And make comments by extending it and analyzing it.

What can Remove the Obstacles from the Process of Asian Unification

Presently, the regional economic cooperation in Asia is developing fast and well with the ASEAN as an axis and with the proactive participation of major Asian nations such as China, 3apan, Korea and India. While envisaging the bright prospect, the unification process, however, is destined to encounter some obstacles and difficulties. By analyzing the hindrance, as well the reasons why Asia lags far behind Europe in unification, the author believes that Asian nations should draw on the lessons and experiences of European countries and learn their principle of subsidiary （bottom-up approaches）, which may serve as the key solution for Asia to overcome the impending obstructions.

Towards the Unification of All Interactions (The First Part: The Spinor Wave)

For the unification of gravitation with electromagnetism, weak and strong interactions, we use a unique and very simple framework, the Clifford algebra of space . We enlarge our previous wave equation to the general case, including all leptons, quarks and antiparticles of the first generation. The wave equation is a generalization of the Dirac equation with a compulsory non-linear mass term. This equation is form invariant under the group of the invertible elements in the space algebra. The form invariance is fully compatible with the gauge invariance of the standard model. The wave equations of the different particles come by Lagrange equations from a Lagrangian density and this Lagrangian density is the sum of the real parts of the wave equations. Both form invariance and gauge invariance are exact symmetries, not only partial or broken symmetries. Inertia is already present in the part of the gauge group and the inertial chiral potential vector simplifies weak interactions. Relativistic quantum physics is then a naturally yet unified theory, including all interactions.

Reference unification and reference linking:Concept,functionalities and inhibiting elements.A case study of Chinese Science Citation Database

In comparing reference unification to reference linking,the authors found that reference linking yield similar result as that of reference unification.An investigative study was conducted by these authors at Chinese Science Citation Database(CSCD)of National Science Library(NSL)of the ChineseAcademy of Sciences(CAS),it was found that there were three inhibiting elements in invoking a reference unification solution and the same is true for a reference linking solution.Firstly,it was difficult to define a minimum set of data elements for matching.Secondly,it had a problem of data inaccuracy and/or data incompleteness.Thirdly,it was hard to determine an appropriate linking result that produced the desired document for the user.Thus these authors suggest that getting Digital Object Identifier(DOI)for each journal article is a good way to bring about reference unification and also to improve metadata quality simultaneously at the same time.Therefore,DOI has a pivotal role to play in terms of bringing about reference unification and/or a reference linking.

Unification Might Be Achievable by a Hypothesis of Instantaneous Time-Jumps during Photon and Graviton Interactions (A Brief Note)

Quantum theory according to the Copenhagen interpretation holds that, when a quantum interaction is observed (i.e., “measured”), the observer’s measuring devices temporarily become a part of the quantum system. Relativity theory holds that the event clock of the absorbed or emitted photon or graviton is frozen in time relative to all clocks outside the observed system. If we harmonize both theories, this would appear to imply that time continuity must be interrupted at each instant of observed photon or graviton interaction with matter. It is as if a segment of space-time is clipped out during each such observed interaction. If so, we must dispense with the notion of an absolutely smooth and continuous space-time and replace it with an observation-dependent, discontinuous, relativistic/quantum space-time. Mathematical physicists should be able to model this hypothesis (call it a “time-jump hypothesis”) and its inherent discontinuous space-time in their further efforts at unification.

Harmonization and Unification: Ecological View of Nature in Wordworth's Poem——Taking “Nutting” for Example

William Wordsworth,as the representative poet of the romanticism,plays an important role in the history of the EnglishLiterature and is considered an ecological poet.He pursues the harmonious and unified relationship with man and nature,and con-tributes to the development process of the social.Taking the poem"Nutting"for example,Wordsworth’s ecological view of natureand its reasons,and the realistic significance of his view on nature to the modern world,especially under the background of the ad-vocacy of the community of destiny of human beings,will be explicated and analyzed.