The answers to the seven millennium prize problems are all depending on either the upper bound or lower bound, left limit or right limit, inside view or outside view, front door or back door approaches...
This document discusses the Katowice Problem, which asks whether two sets X and Y must have the same cardinality if the power sets modulo finite sets P(X)/fin and P(Y)/fin are isomorphic as rings. It presents two results showing that P(ω1)/fin and P(ω2)/fin are not isomorphic, leaving open the question of whether P(ω0)/fin and P(ω1)/fin could ever be isomorphic. It then shows that if P(ω0)/fin and P(ω1)/fin were isomorphic, it would imply the existence of a non-trivial automorphism of P(ω0)/fin.
Quantum Geometry: A reunion of math and physicsRafa Spoladore
Caltech's professor Anton Kapustin "describes the relationship between mathematics and physics, mathematicians and physicists, and so on. He focuses on the noncommutative character of algebras of observables in quantum mechanics." via http://motls.blogspot.com.br/2014/11/anton-kapustin-quantum-geometry-reunion.html
This dissertation thesis investigates congruence lattices of algebras in locally finite, congruence-distributive varieties that have the congruence intersection property. It provides some general results and a complete characterization for certain types of varieties. The thesis describes congruence lattices in two ways: via direct limits and via Priestley duality. It addresses long-standing open problems in lattice theory regarding representing algebraic lattices and distributive lattices as congruence lattices of algebras.
The document contains 14 problems related to classical mechanics. Problem 1 describes two ladders leaning against two walls, with their intersection point 3 m above the ground, and asks for the distance between the walls. Problem 3 involves a pendulum whose length below a board can be varied, and asks the reader to show various relationships involving the semi-vertical angle, angular speed, and pendulum length are constant. Problem 4 describes a rod initially vertical on a table that is given an angular displacement and falls over, and asks for expressions involving the rod's angular speed, center speed, lower end speed, and the table's normal reaction.
This document introduces algorithms that are polynomial time versus non-polynomial time and defines NP-complete problems. It discusses that NP-complete problems include Satisfiability (SAT), Traveling Salesman, Knapsack and Clique problems. These problems are difficult to solve in polynomial time and are mapped to each other through polynomial time reductions. While we can solve them in exponential time, finding a polynomial time algorithm would mean P=NP.
This document provides an overview of string theory and superstring theory. It discusses the following key points:
1) A Calabi-Yau manifold is a smooth space that is Ricci flat and represents a deformation that smooths out an orbifold singularity from a space-time perspective.
2) In the 1960s, particle physics was dominated by S-matrix theory, which focused on scattering matrix properties rather than fundamental fields. S-matrix theory assumed analyticity, crossing, and unitarity of scattering amplitudes.
3) Early string theory models treated particles as vibrating strings to address limitations of S-matrix theory for high spin particles. This led to the development of bosonic string theory and super
1) John Nash presents an equation that is a 4th order covariant tensor partial differential equation applicable to the metric tensor of spacetime. This equation is formally divergence free like the Einstein vacuum equation.
2) The equation can be derived from a specific Lagrangian involving terms quadratic in the scalar curvature and Ricci tensor. Previous theorists had considered such Lagrangians in attempts at quantum gravity theories but had not focused on this specific choice.
3) The equation may allow a wider variety of gravitational waves, including compressional waves not excluded in electromagnetic theory. Standard GR only allows transverse gravitational waves.
This document discusses the Katowice Problem, which asks whether two sets X and Y must have the same cardinality if the power sets modulo finite sets P(X)/fin and P(Y)/fin are isomorphic as rings. It presents two results showing that P(ω1)/fin and P(ω2)/fin are not isomorphic, leaving open the question of whether P(ω0)/fin and P(ω1)/fin could ever be isomorphic. It then shows that if P(ω0)/fin and P(ω1)/fin were isomorphic, it would imply the existence of a non-trivial automorphism of P(ω0)/fin.
Quantum Geometry: A reunion of math and physicsRafa Spoladore
Caltech's professor Anton Kapustin "describes the relationship between mathematics and physics, mathematicians and physicists, and so on. He focuses on the noncommutative character of algebras of observables in quantum mechanics." via http://motls.blogspot.com.br/2014/11/anton-kapustin-quantum-geometry-reunion.html
This dissertation thesis investigates congruence lattices of algebras in locally finite, congruence-distributive varieties that have the congruence intersection property. It provides some general results and a complete characterization for certain types of varieties. The thesis describes congruence lattices in two ways: via direct limits and via Priestley duality. It addresses long-standing open problems in lattice theory regarding representing algebraic lattices and distributive lattices as congruence lattices of algebras.
The document contains 14 problems related to classical mechanics. Problem 1 describes two ladders leaning against two walls, with their intersection point 3 m above the ground, and asks for the distance between the walls. Problem 3 involves a pendulum whose length below a board can be varied, and asks the reader to show various relationships involving the semi-vertical angle, angular speed, and pendulum length are constant. Problem 4 describes a rod initially vertical on a table that is given an angular displacement and falls over, and asks for expressions involving the rod's angular speed, center speed, lower end speed, and the table's normal reaction.
This document introduces algorithms that are polynomial time versus non-polynomial time and defines NP-complete problems. It discusses that NP-complete problems include Satisfiability (SAT), Traveling Salesman, Knapsack and Clique problems. These problems are difficult to solve in polynomial time and are mapped to each other through polynomial time reductions. While we can solve them in exponential time, finding a polynomial time algorithm would mean P=NP.
This document provides an overview of string theory and superstring theory. It discusses the following key points:
1) A Calabi-Yau manifold is a smooth space that is Ricci flat and represents a deformation that smooths out an orbifold singularity from a space-time perspective.
2) In the 1960s, particle physics was dominated by S-matrix theory, which focused on scattering matrix properties rather than fundamental fields. S-matrix theory assumed analyticity, crossing, and unitarity of scattering amplitudes.
3) Early string theory models treated particles as vibrating strings to address limitations of S-matrix theory for high spin particles. This led to the development of bosonic string theory and super
1) John Nash presents an equation that is a 4th order covariant tensor partial differential equation applicable to the metric tensor of spacetime. This equation is formally divergence free like the Einstein vacuum equation.
2) The equation can be derived from a specific Lagrangian involving terms quadratic in the scalar curvature and Ricci tensor. Previous theorists had considered such Lagrangians in attempts at quantum gravity theories but had not focused on this specific choice.
3) The equation may allow a wider variety of gravitational waves, including compressional waves not excluded in electromagnetic theory. Standard GR only allows transverse gravitational waves.
This document discusses potentials and fields in electrostatics and electrodynamics. It introduces vector and scalar potentials, gauge transformations, and Maxwell's equations in potential form. It then covers plane wave solutions to Maxwell's equations using potentials. Retarded potentials are defined using the retarded time, and it is shown that the retarded potentials satisfy Maxwell's equations in the Lorentz gauge. Finally, it discusses Lienard-Wiechert potentials for point charges and approaches to deriving length contraction and other relativistic effects from potentials and fields.
This document discusses computational modeling of the structures of biological macromolecules like proteins docking together. It focuses on using the geometry of molecular surfaces and conformal mappings between surfaces to predict docked configurations. Circle packing is proposed as a method to construct approximate conformal mappings between molecular surfaces by triangulating one surface, constructing a circle packing with the same triangulation on a sphere, and finding conformal transformations between the surfaces and standard metrics on spheres.
This document summarizes three applications of commutative algebra to string theory. The first two applications involve interpreting certain products in topological field theory as Ext computations for sheaves on a Calabi-Yau manifold or in terms of matrix factorizations, which can be analyzed using computer algebra tools. The third application relates monodromy in string theory to solutions of differential equations, showing how monodromy can be described in terms of a computed ring.
- Isaac Newton published his theory of gravity and laws of motion in 1687 in his famous book Principia, solving the problem of explaining planetary motion.
- Newton developed calculus, which was necessary for analyzing motion, though he published the calculations in Principia using older geometrical methods due to concerns calculus would not be accepted.
- Since Newton, calculus has been essential for understanding physics and its applications in engineering and science.
An Elementary Proof of Kepler's Law of Ellipses Arpan Saha
This talk, given as a part of the Annual Seminar Weekend 2010, IIT Bombay, was centered around the hodograph
proof of Kepler’s Law of Ellipses independently discovered by Maxwell, Hamilton and Feynman.
The document summarizes 18 important mathematical problems for the next century as identified by Steve Smale. Some of the key problems discussed include:
1) The Riemann Hypothesis concerning the distribution of primes.
2) The Poincaré Conjecture regarding classifying 3-dimensional spaces.
3) The famous P vs. NP problem about the difference between solving and verifying solutions to problems.
A Unifying theory for blockchain and AILonghow Lam
This document proposes a unifying theory connecting blockchain and artificial intelligence technologies. It introduces the Lam-Visser theory and how it fits within the Damhof Quadrants framework. The document provides definitions related to the main result, which states that there exists a minimal, ultra-connected, almost everywhere linear and generic solvable, semi-countable polytope if a certain condition is met. It then discusses applications of this theory to questions of associativity and the computation of analytically independent subalgebras.
This summary provides the key points from the document in 3 sentences:
The document discusses extending results on maximal isometries to characterizing properties of Beltrami vectors and applications to questions of countability. It presents definitions for tangential arrows and canonically composite factors. The main result is a theorem stating that under certain conditions, every Euclidean group is linear, semi-reducible and maximal.
We introduce plaque inverse limits of branched covering self-maps of simply-connected Riemann surfaces and study their local topology at various irregular points.
This document discusses solving problems related to quantum mechanics and waves. It provides solutions to several problems involving waves on drum membranes, classical wave equations, particles in infinite and finite boxes, and the time evolution of waves. The document solves these problems through separation of variables, normal mode expansions, computing expectation values, and discussing qualitative features like dephasing and rephasing of waves. It also briefly discusses parameters for a two-slit light experiment.
This document provides an overview of the topics that will be covered in a finite mathematics course, including residue arithmetic, elements of finite groups/rings/fields, number theory concepts like the Euclidean algorithm and Chinese Remainder Theorem, and basics of finite vector spaces and fields. The style of the course will be leisurely and discursive, focusing on mathematical thinking and discovery. While the mathematics is classical, it will be new to students. The goal is to emphasize elegance and aesthetics over utility alone.
This document provides lecture notes on analytic geometry. It begins with an introduction discussing the goals of building an algebraic geometry framework for analytic situations by replacing topological abelian groups with condensed abelian groups. Condensed sets are defined as sheaves on the pro-étale site of the point, and behave like generalized topological spaces. The notes establish that quasiseparated condensed sets correspond to ind-compact Hausdorff spaces. This provides the needed abelian category structure to build an analytic geometry in parallel to algebraic geometry over schemes.
This document provides an overview of Euclid's Elements and developments in geometry from Euclid. It discusses Euclid's geometric structure and postulates, including his parallel postulate. It also examines attempts to prove or replace the parallel postulate, such as Playfair's postulate and the works of Proclus and Saccheri. Figures were important in developing Euclid's geometry and understanding problems like the parallel postulate.
The document discusses finding the right abstractions for reasoning problems. It describes Andreas Blass' insight about a category called PV that models problems and reductions between them. PV objects are binary relations representing problems, with morphisms describing reductions. The talk discusses using this framework and Dialectica categories to model Kolmogorov's theory of problems from 1932 and Veloso's theory. It provides examples of modeling geometry and tangent plane problems as Kolmogorov problems and reductions between them.
This document provides an outline of string theory. It begins with background on reductionism in physics and the unification of forces. String theory emerged as a way to address difficulties in quantizing gravity. There are five consistent string theories in 10 dimensions: type I open superstring theory with oriented strings; type IIA closed superstring theory with two independent sets of supersymmetry; heterotic string theories that combine bosonic and supersymmetric strings. String theory led to the discovery of supersymmetry and relates fundamental forces and particles to vibrational modes of strings.
This document provides biographical details about Albert Einstein's life and career. It describes key events such as his education in Germany and Switzerland, early work at the Swiss Patent Office, "miracle year" of 1905 when he published four groundbreaking papers on light quanta, photoelectric effect, Brownian motion, and special relativity, development of his general theory of relativity between 1907-1915, and verification of his theory through observations of star positions during a solar eclipse in 1919. The document establishes Einstein as a revolutionary physicist who changed our understanding of space, time, light, and gravity through his scientific theories.
This document provides historical context on key concepts in Schwartz space and test functions. It discusses how Laurent Schwartz defined the Schwartz space in 1947-1948 to consist of infinitely differentiable functions that, along with their derivatives, decrease faster than any polynomial. Test functions, a subset of Schwartz space, have compact support. Joseph-Louis Lagrange and Norbert Wiener helped develop the method of multiplying a function by a test function and integrating, which is fundamental to distribution theory. The term "mollifier" for test functions was coined by Kurt Friedrichs in 1944, although Sergei Sobolev had previously used them. Many mathematicians, including Leray, Sobolev, Courant, Hilbert, and Weyl,
Tim Maudlin: New Foundations for Physical GeometryArun Gupta
New Foundations for Physical Geometry
Original URL: http://www.unil.ch/webdav/site/philo/shared/summer_school_2013/NYU.ppt
Tim Maudlin
NYU
Physics & Philosophy of Time
July 25, 2013
This document proposes a new Mass-Charge modeling approach to analyze statistical fluctuations in amino acid charges in SARS-CoV-2 variants like Omicron. It introduces a normalized derivation using Excel and Matlab algorithms to examine charge and mass relationships in coronavirus spike proteins. The approach provides insights into the evolving bioinformatic trends affecting infectivity and virulence. Key contributions include a new running semi-covariance notation to analyze non-linear patterns, and integrating genomic data to set up an ending time prediction framework for the pandemic by continent. Results compare SARS-CoV-2 spike protein sequences to other coronaviruses using simplified complex variances. Findings suggest mutations depend on region and that flu virus is closer genetically to rat virus than
This document discusses potentials and fields in electrostatics and electrodynamics. It introduces vector and scalar potentials, gauge transformations, and Maxwell's equations in potential form. It then covers plane wave solutions to Maxwell's equations using potentials. Retarded potentials are defined using the retarded time, and it is shown that the retarded potentials satisfy Maxwell's equations in the Lorentz gauge. Finally, it discusses Lienard-Wiechert potentials for point charges and approaches to deriving length contraction and other relativistic effects from potentials and fields.
This document discusses computational modeling of the structures of biological macromolecules like proteins docking together. It focuses on using the geometry of molecular surfaces and conformal mappings between surfaces to predict docked configurations. Circle packing is proposed as a method to construct approximate conformal mappings between molecular surfaces by triangulating one surface, constructing a circle packing with the same triangulation on a sphere, and finding conformal transformations between the surfaces and standard metrics on spheres.
This document summarizes three applications of commutative algebra to string theory. The first two applications involve interpreting certain products in topological field theory as Ext computations for sheaves on a Calabi-Yau manifold or in terms of matrix factorizations, which can be analyzed using computer algebra tools. The third application relates monodromy in string theory to solutions of differential equations, showing how monodromy can be described in terms of a computed ring.
- Isaac Newton published his theory of gravity and laws of motion in 1687 in his famous book Principia, solving the problem of explaining planetary motion.
- Newton developed calculus, which was necessary for analyzing motion, though he published the calculations in Principia using older geometrical methods due to concerns calculus would not be accepted.
- Since Newton, calculus has been essential for understanding physics and its applications in engineering and science.
An Elementary Proof of Kepler's Law of Ellipses Arpan Saha
This talk, given as a part of the Annual Seminar Weekend 2010, IIT Bombay, was centered around the hodograph
proof of Kepler’s Law of Ellipses independently discovered by Maxwell, Hamilton and Feynman.
The document summarizes 18 important mathematical problems for the next century as identified by Steve Smale. Some of the key problems discussed include:
1) The Riemann Hypothesis concerning the distribution of primes.
2) The Poincaré Conjecture regarding classifying 3-dimensional spaces.
3) The famous P vs. NP problem about the difference between solving and verifying solutions to problems.
A Unifying theory for blockchain and AILonghow Lam
This document proposes a unifying theory connecting blockchain and artificial intelligence technologies. It introduces the Lam-Visser theory and how it fits within the Damhof Quadrants framework. The document provides definitions related to the main result, which states that there exists a minimal, ultra-connected, almost everywhere linear and generic solvable, semi-countable polytope if a certain condition is met. It then discusses applications of this theory to questions of associativity and the computation of analytically independent subalgebras.
This summary provides the key points from the document in 3 sentences:
The document discusses extending results on maximal isometries to characterizing properties of Beltrami vectors and applications to questions of countability. It presents definitions for tangential arrows and canonically composite factors. The main result is a theorem stating that under certain conditions, every Euclidean group is linear, semi-reducible and maximal.
We introduce plaque inverse limits of branched covering self-maps of simply-connected Riemann surfaces and study their local topology at various irregular points.
This document discusses solving problems related to quantum mechanics and waves. It provides solutions to several problems involving waves on drum membranes, classical wave equations, particles in infinite and finite boxes, and the time evolution of waves. The document solves these problems through separation of variables, normal mode expansions, computing expectation values, and discussing qualitative features like dephasing and rephasing of waves. It also briefly discusses parameters for a two-slit light experiment.
This document provides an overview of the topics that will be covered in a finite mathematics course, including residue arithmetic, elements of finite groups/rings/fields, number theory concepts like the Euclidean algorithm and Chinese Remainder Theorem, and basics of finite vector spaces and fields. The style of the course will be leisurely and discursive, focusing on mathematical thinking and discovery. While the mathematics is classical, it will be new to students. The goal is to emphasize elegance and aesthetics over utility alone.
This document provides lecture notes on analytic geometry. It begins with an introduction discussing the goals of building an algebraic geometry framework for analytic situations by replacing topological abelian groups with condensed abelian groups. Condensed sets are defined as sheaves on the pro-étale site of the point, and behave like generalized topological spaces. The notes establish that quasiseparated condensed sets correspond to ind-compact Hausdorff spaces. This provides the needed abelian category structure to build an analytic geometry in parallel to algebraic geometry over schemes.
This document provides an overview of Euclid's Elements and developments in geometry from Euclid. It discusses Euclid's geometric structure and postulates, including his parallel postulate. It also examines attempts to prove or replace the parallel postulate, such as Playfair's postulate and the works of Proclus and Saccheri. Figures were important in developing Euclid's geometry and understanding problems like the parallel postulate.
The document discusses finding the right abstractions for reasoning problems. It describes Andreas Blass' insight about a category called PV that models problems and reductions between them. PV objects are binary relations representing problems, with morphisms describing reductions. The talk discusses using this framework and Dialectica categories to model Kolmogorov's theory of problems from 1932 and Veloso's theory. It provides examples of modeling geometry and tangent plane problems as Kolmogorov problems and reductions between them.
This document provides an outline of string theory. It begins with background on reductionism in physics and the unification of forces. String theory emerged as a way to address difficulties in quantizing gravity. There are five consistent string theories in 10 dimensions: type I open superstring theory with oriented strings; type IIA closed superstring theory with two independent sets of supersymmetry; heterotic string theories that combine bosonic and supersymmetric strings. String theory led to the discovery of supersymmetry and relates fundamental forces and particles to vibrational modes of strings.
This document provides biographical details about Albert Einstein's life and career. It describes key events such as his education in Germany and Switzerland, early work at the Swiss Patent Office, "miracle year" of 1905 when he published four groundbreaking papers on light quanta, photoelectric effect, Brownian motion, and special relativity, development of his general theory of relativity between 1907-1915, and verification of his theory through observations of star positions during a solar eclipse in 1919. The document establishes Einstein as a revolutionary physicist who changed our understanding of space, time, light, and gravity through his scientific theories.
This document provides historical context on key concepts in Schwartz space and test functions. It discusses how Laurent Schwartz defined the Schwartz space in 1947-1948 to consist of infinitely differentiable functions that, along with their derivatives, decrease faster than any polynomial. Test functions, a subset of Schwartz space, have compact support. Joseph-Louis Lagrange and Norbert Wiener helped develop the method of multiplying a function by a test function and integrating, which is fundamental to distribution theory. The term "mollifier" for test functions was coined by Kurt Friedrichs in 1944, although Sergei Sobolev had previously used them. Many mathematicians, including Leray, Sobolev, Courant, Hilbert, and Weyl,
Tim Maudlin: New Foundations for Physical GeometryArun Gupta
New Foundations for Physical Geometry
Original URL: http://www.unil.ch/webdav/site/philo/shared/summer_school_2013/NYU.ppt
Tim Maudlin
NYU
Physics & Philosophy of Time
July 25, 2013
This document proposes a new Mass-Charge modeling approach to analyze statistical fluctuations in amino acid charges in SARS-CoV-2 variants like Omicron. It introduces a normalized derivation using Excel and Matlab algorithms to examine charge and mass relationships in coronavirus spike proteins. The approach provides insights into the evolving bioinformatic trends affecting infectivity and virulence. Key contributions include a new running semi-covariance notation to analyze non-linear patterns, and integrating genomic data to set up an ending time prediction framework for the pandemic by continent. Results compare SARS-CoV-2 spike protein sequences to other coronaviruses using simplified complex variances. Findings suggest mutations depend on region and that flu virus is closer genetically to rat virus than
Forest Environment Analysis for the Pandemic HealthJun Steed Huang
The result of our analyses of the 2021 pandemic toll suggest that pesticide residual, annual precipitation, forest coverage, economy development, pet life, etc. have different impacts on toll of each country.
Semi-covariance coefficient analysis of spike proteins from SARS-CoV-2 and other coronaviruses for viral evolution and charge characteristics associated with fatality.
The document summarizes a presentation on the origination of a homogeneous cosmos from a unique genesis and its unique entanglement speed. It discusses the general existence and motion of matter in a homogeneous cosmos, reviews relevant scientific experiments, and proposes that the entanglement speed is 9931 times the speed of light based on calculations in e=2.7 dimensions. It concludes that momentum is conservatively convertible between dimensions and that the equilibrium entanglement speed occurs at e=2.7 dimensions.
This document provides a summary of a presentation on applications of complex models for analyzing variance, covariance, and their use in autonomous vehicles. Some key points:
- Complex models allow calculating fractional moments and Hurst indexes with complex values, providing more information than real values alone.
- These techniques can be applied in various industries like engineering, agriculture, finance, research, and more.
- Autonomous buses use multiple sensor systems at different distances to gradually slow down as objects are detected.
- Complex fractional models have been used to predict gas emissions and analyze vegetation indexes over time. Stock market analysis and network anomaly detection were also mentioned.
A linear prediction based on logarithmic space (theoretically non-linear) is proposed, which is essentially a geometric series. The number of deaths of coal miners decreases year by year in that proportion.
The document discusses complex models for analyzing random variables using fractional moments and complex Hurst exponents. It begins with background on variance, covariance, and Hurst exponents. It then explains how complex Hurst exponents allow calculating fractional moments and higher-order information to better analyze relationships between variables. Applications discussed include analyzing gas emissions in coal mines, vegetation changes over time using NDVI maps, stock market fluctuations, and autonomous vehicle networks. Several academic papers and theses utilizing these complex models are also summarized.
Autonomous smart traffic control is proposed to relieve traffic congestion for bus scheduling, to intelligently accomplish tasks such as on-demand dynamic passenger pickup or drop-off.
In order to provide the design guidance for a multiple stage refrigerator for hosting a quantum computing device targeting for unmanned transportation platform. We provides a modeling analysis based on a preliminary single stage test data, by using Brain Storm Optimization algorithm.
Talks about academic ancestors like Hadamard all the way to emeritus professor Langlands along the line of functional partially in Chinese for Ph.D students understanding part of ancient mathematics of China mixed with mainly Polish mathematician Banach theorems.
This is an abstract of a long book talking about the composition of our universe, the author believes the positive & negative transmutation consisted the entire universe, there are two and only two things on the planet!
Hurst value is (1+Slope_of_Gauss_Variance_Plot)/2, where Gauss moment=2 (std-variance); Complex Hurst is (1+Slope_of_Steed_Variance_Plot)/2, where either Steed moment=1.5 (sub-variance) or Steed moment=2.5 (sup-variance), various mean of sub- and sup- can be used to obtain final Complex Hurst.
This document discusses the design considerations for a sea, land, and air robot swarm called Selabot. Selabot is designed to change shape and function for rapid development of artificial intelligence. It can collect data from volcanoes, research glaciers, fight fires, manage floods, and more. The document outlines Selabot's sensor, communication, and action modules. It also compares Selabot to existing platforms and discusses simulation results showing Selabot's cooperative behavior using algorithms based on Finsler geometry. The design is aimed to reduce weight and improve integration across environments while maintaining capabilities.
The document describes the China Bus System of the Future (CBSF) initiative, which aims to develop an intelligent autonomous new energy public bus system. It provides details on:
1) The CBSF is led by Intelligent Transport System China and implemented in numerous cities with partnerships between government, universities, and companies like Haylion and bus manufacturers.
2) Haylion is the lead technology developer focusing on areas like environment cognition, positioning, and safety systems using sensors and data fusion.
3) The initiative aims to launch trials of autonomous bus systems in cities like Shenzhen to demonstrate technologies like wireless charging infrastructure, V2X communication, and multi-sensor data processing.
Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.pptHenry Hollis
The History of NZ 1870-1900.
Making of a Nation.
From the NZ Wars to Liberals,
Richard Seddon, George Grey,
Social Laboratory, New Zealand,
Confiscations, Kotahitanga, Kingitanga, Parliament, Suffrage, Repudiation, Economic Change, Agriculture, Gold Mining, Timber, Flax, Sheep, Dairying,
This presentation was provided by Racquel Jemison, Ph.D., Christina MacLaughlin, Ph.D., and Paulomi Majumder. Ph.D., all of the American Chemical Society, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
2. 宿迁 2015 年 3 月
SQC
航模提高课程
Millennium 7 Prize Problems
1. P=NP Can the dispatcher be lazy ? 1970s
2. Hodge Can high dim space be decomposed ?
1930s
3. Poincare Apple is not same as donut ! 1900s
4. Riemann Is prime distribution regular ? 1850s
5. Yang-Mills There is always a ghost !?
1950s
6. Navier-Stokes How many solutions ? 1820s
7. Birch Swinnerton-Dyer : Only oval fly!
3. 宿迁 2015 年 3 月
SQC
航模提高课程
NP up bound NP/ != P
1. P=NP? Can the dispatcher be lazy ?
If there is an algorithm (such as a Turing machine, or a LISP
or Pascal program with unlimited memory), the correct
answer can be given for a string of length n inputs in the
most n ^ k steps, where k is an independent In the input
string of constants, then we call the problem can be solved in
the polynomial time, and it is placed in class P. Most
computer scientists believe that P ≠ NP. No one can find a
polynomial time algorithm for a non-deterministic (non-
deterministic) Polynomial complete problem.
4. 宿迁 2015 年 3 月
SQC
航模提高课程
NP lower bound /NP = P
1971 by UoT
Professor
Stephen A. Cook
et al
5. 宿迁 2015 年 3 月
SQC
航模提高课程
2. Hodge Can high dim space be
decomposed ?
Whether the shape of a given object can be formed by bonding a
simple geometric building block with increasing numbers of
dimensions. In this promotion, the geometric starting point of
the program becomes blurred and must be added without any
geometric interpretation of the parts. Hodge's conjecture that
Hodge's closed-chain components are a rational combination of
geometric components called algebraic closed chains for the
particularly perfect spatial type of projective algebra clusters.
1935 by W. V. D. Hodge
Shinichi MochizukiIUT HC/ !=
Q
7. 宿迁 2015 年 3 月
SQC
航模提高课程
道生一,一生二
3. Poincare Apple is not same as
donut !
In 1904, Poincare put forward a seemingly simple
topology of the conjecture: in a three-
dimensional space, if each closed curve can
shrink to a little, then this space must be a
three-dimensional ball. But in 1905 found the
error, modified as: "Any n-dimensional
spherical with n-dimensional closed manifold
must be homologous in the n-dimensional
sphere." Later, this conjecture was extended to
more than three-dimensional space, known as
the "high-dimensional Poincare guess. "
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二生三,三生万
More than equal to the five - dimensional Poincaré conjecture proved by Stephen
Smell;
The four-dimensional Poincaré conjecture was confirmed by Michael Friedman;
Three-dimensional Poincare conjecture proved by the Russian mathematician
Perelman;
They were awarded the 1961, 1986 and 2006 Fields Award respectively.
亏格 0 1 2 3
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Our Integel Complexity
n/ > /n > log2(n)
4. Riemann Is prime distribution regular ?
!
German mathematician Riemann (1826 ~ 1866)
observes that the frequency of prime numbers is
closely related to the structure of a well-constructed
Riemannian zeta function ζ (s). The Riemann
hypothesis asserts that all meaningful solutions of
the equation ζ (s) = 0 are on a 1/2 line: Root line!
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Space is not empty where
ghost particle hide
5. Yang-Mills There is always a ghost !?
!
In 1954, Yang Zhenning and Mills proposed
Yang - Mills norms theory, put forward the
theory of gauge field. The theory will
produce particles that carry the force, with
charge but no mass! However, the difficulty
is that if the charged particles are of no mass,
then why is there no experimental evidence?
And if the particle is assumed to be of mass,
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Space is made of ghost
mass
杨振宁
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MH370 Ns/ != S
6. Navier-Stokes How many
solutions
French engineer Navier and the British mathematician
Stoke, the sticky items are also taken into account is
the Navier-Stoke equation. Since 1943 the French
mathematician Leray proved that the solution of the
whole time after the weak solution, is the solution
unique? The result is that the strong solution is
unique. So this question becomes: the whole
solutions? Is it proof that the solution will burst in a
limited time? To solve this problem contribute to the
navigation project, especially turbulence killed
MH370 (turbulence)!
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Fractal /Ns = S
Navier - Stokes is currently only about a hundred special
solution is solved. The nonlinearity is due to convection
acceleration (the acceleration associated with the point
velocity change), so any convection will involve nonlinearity
regardless of whether the turbulence or not.
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All Ellipses Key/ = 1/0
7. Birch Swinnerton-Dyer Only oval
fly ?
Refers to the rank of any elliptic curve on the rational
domain, where the L function is equal to the order
of the Abel group. When the solution is an Abelian
point, Beech and Sternon - Dell guessed that: the
rationality of the group size with a related Zeta
function z (s) at point s = 1 near the state: If z is
equal to 0, then there are infinite number of rational
points (solution), on the contrary, if z is not equal to
0, then there are only a limited number of such
points. 1960s.
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ECC /Key = p/q
Elliptic encryption
algorithm (ECC) is a
public key cryptography
system, originally
proposed by Koblitz and
Miller in 1985, whose
mathematical basis is to
use the rational points on
elliptic curves to
compute the
computational
complexity of elliptic
discrete logarithms on
Abel addition groups The
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航模 Colloquia
Thank you for watching this
presentation!
谢谢邹青,黄佳敏,姚成,孙晨旭,
韩学波,沙龙,周嘉宇的协助。
宿迁 2015 年 3 月