#Spectral Geometry
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Is it possible to deduce the shape of a drum from the sounds it makes? This is the kind of question that Iosif Polterovich, a professor in the Department of Mathematics and Statistics at Université de Montréal, likes to ask. Polterovich uses spectral geometry, a branch of mathematics, to understand physical phenomena involving wave propagation.
Last summer, Polterovich and his international collaborators—Nikolay Filonov, Michael Levitin and David Sher—proved a special case of a famous conjecture in spectral geometry formulated in 1954 by the eminent Hungarian-American mathematician George Pólya.
The conjecture bears on the estimation of the frequencies of a round drum or, in mathematical terms, the eigenvalues of a disk.
Continue Reading.
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"Auf und ab, rauf und nieder - haste Erkenntnisgewinne immer wieder"
The title approximately translates to "Going above and below, top and down - you'll have gains of knowledge every time".
[2023/11/15] [Black ink and watercolor on paper]
[ID: At the center of the drawing is a black 3-dimensional spiral. It forms a helix trajectory around a horn torus' axis of revolution. It roughly forms a white/grey sphere. Above the spiral is a question mark. Below the spiral is an exclamation mark. The background is watercolored in rainbow colors and merely bright.]
#helix#spiral#rainbow#colorful#color#colors#spectral colors#torus#german#knottys art#knotty et al#knotty#art#artsy#math#geometry#drawing#surreal#sphere#3d spiral
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Despite the fact that Napoleon was a bloody butcher/woodcutter, Hugo still recognizes that he was a military genius. Wellington with his geometry, precision, prudence, etc., an epitome of the old school, is simply boring. He argues that Wellington didn't truly earn the title of victor at Waterloo; instead, Napoleon's defeat was a result of chance, luck, and divine will. However, Hugo does give credit to the English and Scottish soldiers for their valour.
He then provides statistics on casualties from various Napoleonic battles, revealing Waterloo as the most devastating, with 60,000 out of 145,000 combatants perishing.
In the final paragraph, Hugo reflects on his own situation as a traveller caught on the old battlefield at night. There, he encounters eerie sights, imagining the spectral remains of Napoleon, Wellington, and the soldiers who perished at Hougomount, Mont-Saint-Jean, and other places.
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Prime numbers of the ask game let's go!
This is gonna be a long old post haha /pos
2. What math classes did you do best in?:
It's joint between Analysis in Many Variables (literally just Multivariable calculus, I don't know why they gave it a fancy name) and Complex Analysis. Both of which I got 90% in :))
3. What math classes did you like the most?
Out of the ones I've completely finished: complex analysis
Including the ones I'm taking at the moment:
Topology
5. Are there areas of math that you enjoy? What are they?
Yes! They are Topology and Analysis. Analysis was my favourite for a while but topology is even better! (I still like analysis just as much though, topology is just more). I also really like group theory and linear algebra
7. What do you like about math?
The abstractness is really nice. Like I adore how abstract things can be (which is why I really like topology, especially now we're moving onto the algebraic topology stuff). What's better is when the abstract stuff behaves in a satisfying way. Like the definition of homotopy just behaves so nicely with everything (so far) for example.
11. Tell me a funny math story.
A short one but I am not the best at arithmetic at times. During secondary school we had to do these tests every so often that tested out arithmetic and other common maths skills and during one I confidently wrote 8·3=18. I guess it's not all that funny but ¯\_(ツ)_/¯
13. Do you have any stories of Mathematical failure you’d like to share?
I guess the competition I recently took part in counts as a failure? It's supposed to be a similar difficulty to the Putnam and I'm not great at competition maths anyway. I got 1/60 so pretty bad. But it was still interesting to do and I think I'll try it again next year so not wholly a failure I think
17. Are there any great female Mathematicians (living or dead) you would give a shout-out to?
Emmy Noether is an obvious one but I don't you could understate how cool she is. I won't name my lecturers cause I don't want to be doxxed but I have a few who are really cool! One of them gave a cool talk about spectral geometry the other week!
19. How did you solve it?
A bit vague? Usually I try messing around with things that might work until one of them does work
23. Will P=NP? Why or why not?
Honestly I'm not really that well versed in this problem but from what I understand I sure hope not.
29. You’re at the club and Grigori Perlman brushes his gorgeous locks of hair to the side and then proves your girl’s conjecture. WYD?
✨polyamory✨
31. Can you share a math pickup line?
Are you a subset of a vector space of the form x+V? Because you're affine plane
37. Have you ever used math in a novel or entertaining way?
Hmm not that I can think of /lh
41. Which is better named? The Chicken McNugget theorem? Or the Hairy Ball theorem?
Hairy Ball Theorem
43. Did you ever fail a math class?
Not so far
47. Just how big is a big number?
At least 3 I'd say
53. Do you collect anything that is math-related?
Textbooks! I probably have between 20 and 30 at the moment! 5 of which are about topology :3
59. Can you reccomend any online resources for math?
The bright side of mathematics is a great YouTube channel! There is a lot of variety in material and the videos aren't too long so are a great way to get exposed to new topics
61. Does 6 really *deserve* to be called a perfect number? What the h*ck did it ever do?
I think it needs to apologise to 7 for mistakingly accusing it of eating 9
67. Do you have any math tatoos?
I don't have any tattoos at all /lh
71. 👀
A monad is a monoid in the category of endofunctors
73. Can you program? What languages do you know?
I used to be decent at using Java but I've not done for years so I'm very rusty. I also know very basic python
Thanks for the ask!!
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This is the start of a Reference thread for Starseeds. Information from LL threads will be collated here. (especially from IQ.)
To begin with, here is something from the Lyran Ring Nebula M57 thread:
There is a celestial object known as the Starseed Ring Nebula (aka M57 or Messier 57) in the constellation Lyra which has special significance for all Starseeds and Cosmic Wanderers. It is located at 20 degrees Capricorn between the Lyran fixed stars Sheliak and Sulaphat.
The reason why this beautiful nebula is so special is because it is the physical remnants of a super nova explosion of the Lyran homeland which, in galactic myth, was the original location of all humanoid races before it was destroyed by the Draco's, thus triggering the diaspora to new planets such as those civilizations located in the Pleiades, Andromeda, Casseopia, Sirius amongst many others.
Thus, strong contacts with the Ring Nebula literally points to the birthplace of humanoid star origins. This is the place from which many streams of consciousness, rays of extraterrestrial starseed races, began their evolutionary journey.
If you have a strong aspect with Sun, Moon, a personal planet, Sun/Moon midpoint, an Angle or a Node with the Lyran Ring Nebula M57 as well as strong aspects to one of the Royal Stars (Regulus, Alderbaran, Formalhaut, Antares) and the Great Attractor, I believe this is proof of a humanoid starseed identity.
For example : Sun conjunct/opposite M57 :Your essence and sense of personal power is strongly identified with your star origin.
Moon conjunct/opposite M57 : instinctual understanding/ subliminal memories of your extraterrestial origins.
South Node conjunct M57 : A highly evolved starseed/ cosmic wanderer who brings to this incarnation past life memories, knowledge and understanding of star origins which underpin current life purpose and direction.
North Node conjunct M57 : Aspiring towards an understanding of star origins being prominent in shaping life purpose/direction.
Prominent alignments with the Lyran Ring Nebula can also indicate involvement with the music of the spheres - the use of natural astronomically and resonant harmonics for healing, illumination, and for greater evolutionary purpose. You might find, for example that a person with South Node conjunct M57 brings to this incarnation a natural aptitude in this area, based on past life extra-terrestrial experience. Similarly, strong contacts are often found in the charts of musicians, artists and those involved with arts and sciences where the intention is to use harmonics of light, sound, and geometry for the expansion of consciousness. In addition, these individuals may be gifted in understanding the relationship between geometry and time--all working intelligently together. Forty octaves up from our middle musical scale lies the spectrum of visible color--light-sound musical harmonics originate from the mathematical unfoldment of time in geometric proportion. M57 inspires multi-spectral creative expression--a multiplicity of opportunity for fulfillment when individuality is creatively amalgamated into a greater expression than one could achieve alone. M57 also holds the memory pattern that unifies our diversity--reminding us that all rays of color and creed ultimately comprise and fulfill the unbounded expression of One Unified Creative Intelligence.
Use tight orbs - for Nodes, angles and luminaries - less than 1.5 or maybe 2 degrees; for other personal planets less than 1 degree.
Also important in the constellation Lyra are the fixed stars Sheliak at 18 Capricorn 53 and Sulaphat at 21 Capricorn 55. These are known as the points or horns of the Tortoise Lyre, which is the structure that carries the resonant strings of the harp which is the the Ring Nebula itself. Although important alignments with these points are not in themselves starseed indicators, they do carry their own Lyran symbolism. Sheliak embodies the wisdom of light/sound harmonics. Physically, this extremely fast rotating binary star radiates a remarkable and spectacular optical show of brilliantly changing color. Sulaphat on the other hand embodies geometric resonance in form and the ancient wisdom of the Turtle.
The other important star in Lyra is the alpha fixed star Vega at 15 Capricorn 19 - this points to where the re-unifying harmonic spectra of the Elohim (the shining ones) culminate--a new home for some upon completion of their galactic missions. Vega is stargate to Mansion Universes of Light--and represents the fulfillment and radiance of starseed missions completed. If strongly aspected along with other Royal Star contacts, this could indicate a lineline in which the influence of the Elohim is strong, along with aspirations to use this to complete the mission assigned to this incarnation. With a South Node contact to Vega, the individual may even be a fully ascended and conscious Elohim starseed master on an earth mission, assuming that there there are also strong alignments with the Great Attractor, Royal Stars and the M57.
A word on the Great Attractor - this is the most powerful point in the Universe, so powerful that it makes the Galactic Centre look miniscule. It is at 14 Sagittarius. While the Galactic Centre is the "sun of our sun", the central rotating point of the Milky Way ... the Great Attractor is a supercluster of 100,000 galaxies 250 million light years from our solar system. It is the grand central sun of a much larger group of galaxies- and it is a point that we are all being pulled towards (we are literally hurling in that direction at insane speeds). In astrology the great attractor represents the key to the mystery of the Universe. it's a very intense point that has mystical and metaphysical properties.
As such, the Great Attractor should feature strongly - preferably a tightly orbed conjunction or opposition with personal planets, angles, nodes or sun/moon midpoint in all Starseed charts where there is awakening as it points to divine harmony and the fulfulment of our spiritual destiny.
(Source)
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Now and then there is a bright radio flash somewhere in the sky. It can last anywhere from a few milliseconds to a few seconds. They appear somewhat at random, and we still aren’t sure what they are. We call them fast radio bursts (FRBs). Right now the leading theory is that they are caused by highly magnetic neutron stars known as magnetars. With observatories such as CHIME we are now able to see lots of them, which could give astronomers a new way to measure the rate of cosmic expansion. The rate of cosmic expansion is described by the Hubble parameter, which we can measure to within a few percent. Unfortunately, our various methods of measure are now so precise their uncertainties don’t overlap. This contradiction in values is known as the Hubble tension. Several re-evaluations of our methods have ruled out systematic error, so astronomers look to new independent ways to measure the Hubble parameter, which is where a new study comes in. The paper looks at using FRBs as a Hubble measure. For light from an FRB to reach us, it needs to travel millions of light-years through the diffuse intergalactic and interstellar medium. This causes the frequency of the light to spread out. The amount of spectral spreading is known as the Dispersion Measure (DM), and the greater the DM the greater the distance. So we know the distance to FRBs. But to measure cosmic expansion, we also need a second distance measure, and here the paper proposes using gravitational lensing. The geometry of an FRB measurement. Credit: Tsai, et al If the FRB light path passes relatively close to a massive object such as a star, the light can be gravitationally lensed around the object. From the width of the lensing, we have an idea of its relative distance to the FRB source. When the FRB light passes from the intergalactic medium to the more dense interstellar medium of our galaxy, there is a brightening effect known as scintillation, which gives us another distance measure A bit of geometry then allows us to calculate the Hubble parameter. Based on their calculations, the authors estimate that a single lensed FRB observation would allow them to pin down the Hubble parameter to within 6% accuracy. With 30 or more events, they should be able to increase their precision to a fraction of a percent uncertainty. This would put it on par with other methods. This should be achievable given current and planned FRB telescopes. New observation methods such as this are the only way we are going to resolve the Hubble tension. Hopefully, we will solve this mystery, and perhaps it will point us to a radically new understanding of cosmic evolution. Reference: Tsai, Anna, et al. “Scintillated microlensing: measuring cosmic distances with fast radio bursts.” arXiv preprint arXiv:2308.10830 (2023). The post Measuring Distances in the Universe With Fast Radio Bursts appeared first on Universe Today.
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A wolf in sheep's clothing
Don't be fooled by the 140 mm front and 125 mm rear: the Spectral 125 is "ready to shred" with its modern, progressive geometry. Like the Spectral 29, it has a flat steering angle of 64 degrees and a long reach – for high self-confidence in steep terrain and maximum smoothness at high speeds and in rough terrain.
#canyon#bike#bicycle#sport#art#artwork#sport bike#mountainbike#mtb#mountain bike#canyon Spectral 125 CF 8
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Following the success of 1-Click PBRSkin, now your DAZ Dragon 3 can get an Iray glow-up! Official support has been included for the DAZ Dragon 3 base, Crystal Dragon, Hellborn Dragon, and Spectral Dragon plus the Legendary Wings and Fins and DAZ Dragon 3 Wing Membrane Expansion products. 1-Click PBRDragon will work on other DAZ Dragon 3 characters providing the same geometry is used (ie no additional grafts) and the same texture types (texture, bump, and specular). This invaluable collection of scripts will allow you to: Convert a DAZ Dragon 3 figure to use the PBRSkin or PBRSkin Plus* shader Control the gamma of diffuse and translucency textures Adjust the roughness and bump strength of converted surfaces Adjust the translucency color of converted surfaces Adjust the luminance strength and emission color of Hellborn PBRSkin Plus* surfaces *PBRSkin Plus shader is required for emissive PBRSkin surfaces. What's Included and Features 1-Click PBRDragon: (.DSA and .DSE) 1 - Convert to PBRSkin Scripts: 1CPBRD Convert to PBRSkin 1CPBRD Convert to PBRSkin Plus 2 - Adjust Gamma Scripts: 1CPBRD Gamma - Horns and Claws 1CPBRD Gamma - Membrane 1CPBRD Gamma - Mouth and Teeth 1CPBRD Gamma - Skin 3 - Adjust Roughness Scripts: 1CPBRD Roughness - Horns and Claws 1CPBRD Roughness - Membrane 1CPBRD Roughness - Mouth and Teeth 1CPBRD Roughness - Skin 4 - Adjust Translucency Color Scripts: 1CPBRD Translucency Color - Horns and Claws 1CPBRD Translucency Color - Membrane 1CPBRD Translucency Color - Skin 5 - Extras: 1CPBRD Measurement Distance - Default Plus 1CPBRD Measurement Distance - Default 1CPBRD Measurement Distance - Increased Plus 1CPBRD Measurement Distance - increased 1CPBRD Transmission - OFF 1CPBRD Transmission - ON Crystal Dragon: 1CPRD Crystals SSS - Eight Material Presets 1CPRD Crystals Translucent - Eight Material Presets Hellborn Dragon: 1CPBRD Emission - Horns 1CPBRD Emission - Membrane 1CPBRD Emission - Mouth 1CPBRD Emission - Pupil 1CPBRD Emission - Sclera 1CPBRD Emission - Skin Required Products: DAZ Dragon 3 Compatible Software: Daz Studio 4.22 Install Types: DazCentral, Daz Connect, DIM, Manual Install Coming soon: https://3d-stuff.net/ #daz3d #dazstudio #3drender #3dart #daz3dstudio #irayrender #3dartwork #blender #blenderrender #blenderart #noaiart #noaiwriting #noai https://3d-stuff.net/
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Discovery of aurora-like radio emission above a sunspot
In a study published in Nature Astronomy, astronomers from New Jersey Institute of Technology’s Center for Solar-Terrestrial Research (NJIT-CSTR) have detailed radio observations of an extraordinary aurora-like display — occurring 40,000 km above a relatively dark and cold patch on the Sun, known as a sunspot.
Researchers say the novel radio emission shares characteristics with the auroral radio emissions commonly seen in planetary magnetospheres such as those around Earth, Jupiter and Saturn, as well as certain low-mass stars.
The discovery offers new insights into the origin of such intense solar radio bursts and potentially opens new avenues for understanding similar phenomena in distant stars with large starspots, according to the study’s lead author and NJIT-CSTR scientist, Sijie Yu.
“We've detected a peculiar type of long-lasting polarized radio bursts emanating from a sunspot, persisting for over a week,” said Yu. “This is quite unlike the typical, transient solar radio bursts typically lasting minutes or hours. It’s an exciting discovery that has the potential to alter our comprehension of stellar magnetic processes.”
Famous auroral light shows that are visible across the sky of Earth’s polar regions, like the Aurora Borealis or Aurora Australis, occur as solar activities disturb Earth’s magnetosphere, which facilitates the precipitation of charged particles to the Earth’s polar region where the magnetic field converges, and interacts with oxygen and nitrogen atoms in the high atmosphere. Accelerating toward the north and south poles, such electrons can generate intense radio emissions at frequencies around a few hundred kHz.
Yu’s team says the newly observed solar radio emissions, detected over a vast sunspot region temporarily forming where magnetic fields on the Sun’s surface are particularly strong, differ from previously known solar radio noise storms — both spectrally and temporally.
“Our spatially, temporally and spatially resolved analysis suggests that they are due to the electron-cyclotron maser (ECM) emission, involving energetic electrons trapped within converging magnetic field geometries,” explained Yu. “The cooler and intensely magnetic areas of sunspots provide a favorable environment for the ECM emission to occur, drawing parallels with the magnetic polar caps of planets and other stars and potentially providing a local solar analog to study these phenomena.”
“However, unlike the Earth's auroras, these sunspot aurora emissions occur at frequencies ranging from hundreds of thousands of kHz to roughly 1 million kHz — a direct result of the sunspot's magnetic field being thousands of times stronger than Earth's.”
“Our observations reveal that these radio bursts are not necessarily tied to the timing of solar flares either,” added Rohit Sharma, a scientist from the University of Applied Sciences Northwestern Switzerland (FHNW) and co-author of the study. “Instead, sporadic flare activity in nearby active regions seems to pump energetic electrons into large-scale magnetic field loops anchored at the sunspot, which then power the ECM radio emission above the region.”
The “sunspot radio aurora” is thought to exhibit rotational modulation in sync with the solar rotation, producing what Yu describes as a “cosmic lighthouse effect.”
“As the sunspot traverses the solar disk, it creates a rotating beam of radio light, similar to the modulated radio aurora we observe from rotating stars,” Yu noted. “As this sunspot radio aurora represents the first detection of its kind, our next step involves retrospective analysis. We aim to determine if some of the previously recorded solar bursts could be instances of this newly identified emission.”
The solar radio emissions, albeit weaker, are likened to stellar auroral emissions observed in the past and may suggest that starspots on cooler stars, much like sunspots, could be the sources of the certain radio bursts observed in various stellar environments.
“This observation is among the clearest evidence of radio ECM emissions we have seen from the Sun. The characteristics resemble some of those observed on our planets and other distant stars, leading us to consider the possibility that this model could be potentially applicable to other stars with starspots,” said Bin Chen, NJIT-CSTR associate professor of physics and a co-author.
The team says the latest insight, linking the behavior of our Sun and the magnetic activities of other stars, could have implications for astrophysicists to rethink their current models of stellar magnetic activity.
“We're beginning to piece together the puzzle of how energetic particles and magnetic fields interact in a system with the presence of long-lasting starspots, not just on our own Sun but also on stars far beyond our solar system,” said NJIT solar researcher Surajit Mondal.
“By understanding these signals from our own Sun, we can better interpret the powerful emissions from the most common star type in the universe, M-dwarfs, which may reveal fundamental connections in astrophysical phenomena,” added Dale Gary, NJIT-CSTR distinguished professor of physics.
The research team — including collaborators Marina Battaglia from FHNW and Tim Bastian of the National Radio Astronomy Observatory — used broadband dynamic radio imaging spectroscopy observations from the Karl G. Jansky Very Large Array to achieve the discovery.
IMAGE....Scientists uncover prolonged radio emissions above a sunspot, akin to those previously seen in the polar regions of planets and certain stars, which may reshape our understanding of intense stellar radio bursts. CREDIT Sijie Yu
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Preparation
casts=cities=spaces=collectively imagined, created, inhabited
fluid=urban environments=cultural interactions=articles, films, literature, music, paintings, performance, poetry, photography, theatre...
1.cultural context → 2. the nature of the spaces → 3. spatial spectrality → 4. propose geometries=suitable bounds
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Who can give us a list of the different divisions of mathematics, eg. Statistics, Algebra, Geometry, Trigonometry, How many others are missing?
Some of the major divisions of mathematics:
1. Algebra
2. Analysis (which includes calculus, real analysis, complex analysis, functional analysis, etc.)
3. Geometry (which includes Euclidean geometry, topology, differential geometry, etc.)
4. Number theory
5. Combinatorics
6. Logic
7. Set theory
8. Statistics (which includes probability theory, inferential statistics, and descriptive statistics)
9. Numerical analysis
10. Optimization
11.Game theory
12. Graph theory
13. Cryptography
14. Information theory
15. Applied mathematics (which includes many of the above areas applied to specific fields like physics, engineering, economics, etc.)
16. Algebraic geometry
17. Differential equations
18. Dynamical systems
19. Mathematical physics
20. Mathematical logic
21. Mathematical modeling
22. Nonlinear analysis
23. Partial differential equations
24. Representation theory
25. Topology
26. Category theory
27. Probability theory
28. Stochastic processes
29. Number theory
30. Mathematical finance
31. Arithmetic geometry
32. Homological algebra
33. Lie theory
34. Algebraic topology
35. Functional analysis
36. Operator theory
37. Geometric analysis
38. Mathematical biology
39. Control theory
40. Differential topology
41. Computational mathematics
42. Information geometry
43. Symplectic geometry
44. Measure theory
45. Algebraic combinatorics
46. Mathematical education
47. History of mathematics
48. Mathematical philosophy
49. Quantum field theory
50. Representation theory
51. Noncommutative geometry
52. Topological data analysis
53. Group theory
54. Algebraic number theory
55. Discrete mathematics
56. Game theory
57. Information theory
58. Mathematical physics
59. Mathematical logic
60. Model theory
61. Commutative algebra
62. Complex dynamics
63. Differential geometry
64. Harmonic analysis
65. Mathematical optimization
66. Mathematical statistics
67. Category theory
68. Combinatorial game theory
69. Computational algebra
70. Financial mathematics
71. Quantum computing
72. Graph theory
73. Mathematical biology
74. Mathematical physics
75. Numerical linear algebra
76. Operator algebras
77. Partial differential equations
78. Probabilistic combinatorics
79. Quantum information theory
80. Random matrix theory
81. Representation theory
82. Topological quantum field theory
83. Algebraic coding theory
84. Arithmetic combinatorics
85. Convex geometry
86. Discrete geometry
87. Financial mathematics
88. Game theory
89.Mathematical logic
90. Mathematical optimization
91. Ergodic theory
92. Geometric group theory
93. Homotopy theory
94. Inverse problems
95. K-theory
96. Model categories
97. Nonlinear analysis
Number theory
98. Optimal control
99. PDEs on manifolds
100. Quantum field theory
101. Random walks
102. Statistical mechanics
103. Algebraic topology
104. Combinatorial optimization
105. Combinatorial representation theory
106. Computational group theory
107. Convex analysis
108. Cryptography
109. Dynamical systems
110. Fractional calculus
111. Geometric topology
112. Lie groups and Lie algebras
113. Measure theory and integration
114. Operator theory and functional analysis
115. Spectral theory
116. Topological dynamics
117. Topological graph theory
118. Algorithmic graph theory
119. Applied algebraic geometry
120. Arithmetic dynamics
121. Combinatorial geometry
122. Complex analysis
123. Differential topology
124. Discrete optimization
125. Elliptic curves
126. Geometric measure theory
127. Graph coloring
128. Homological stability
129. Information-based complexity
130. Mathematical physics
131. Model theory
132. Nonlinear waves
133. Number theory
134. Orthogonal polynomials
134. Quantum mechanics
135. Smooth dynamical systems
137. Topological combinatorics
138. Topological quantum computing
139. Algebraic K-theory
140. Analytic number theory
141. Combinatorial designs
142. Computational complexity theory
143. Dynamical systems and chaos
144. Geometric analysis
145. Homotopy type theory
146. Mathematical modeling
147. Model categories
148. Nonlinear functional analysis
149. Numerical analysis
150. Operator algebras and quantum groups
151. Random structures and algorithms
152. Topological methods in combinatorics
153. Algebraic geometry and topology
154. C*-algebras
155. Computational algebraic geometry
156. Ergodic theory and entropy
157. Formal proof
158. Lie theory and representation theory
159. Mathematical finance
These are just a small selection of the many different subfields of mathematics.
The subject of mathematics is incredibly vast and diverse, encompassing many different areas of study and application.
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Photoelectrochemical (PEC) water splitting to produce hydrogen fuel was first reported 50 years ago1, yet artificial photosynthesis has not become a widespread technology. Although planar Si solar cells have become a ubiquitous electrical energy source economically competitive with fossil fuels, analogous PEC devices have not been realized, and standard Si p-type/n-type (p–n) junctions cannot be used for water splitting because the bandgap precludes the generation of the needed photovoltage. An alternative paradigm, the particle suspension reactor (PSR), forgoes the rigid design in favour of individual PEC particles suspended in solution, a potentially low-cost option compared with planar systems2,3. Here we report Si-based PSRs by synthesizing high-photovoltage multijunction Si nanowires (SiNWs) that are co-functionalized to catalytically split water. By encoding a p-type–intrinsic–n-type (p–i–n) superlattice within single SiNWs, tunable photovoltages exceeding 10 V were observed under 1 sun illumination. Spatioselective photoelectrodeposition of oxygen and hydrogen evolution co-catalysts enabled water splitting at infrared wavelengths up to approximately 1,050 nm, with the efficiency and spectral dependence of hydrogen generation dictated by the photonic characteristics of the sub-wavelength-diameter SiNWs. Although initial energy conversion efficiencies are low, multijunction SiNWs bring the photonic advantages of a tunable, mesoscale geometry and the material advantages of Si—including the small bandgap and economies of scale—to the PSR design, providing a new approach for water-splitting reactors.
Water splitting with silicon p–i–n superlattices suspended in solution | Nature
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Ionization Type Smoke Detector
Ionization type smoke detectors are some of the most common devices used in homes and buildings. They are not only easy to install but also easy to maintain. These types of devices can detect both smoke and smoke-related fires. This means that these devices can be very useful in helping people to quickly locate and identify the cause of a fire. In addition, this type of device is relatively inexpensive, making it a popular choice for many homeowners.
Refractive index of the aerosol
An ionization type smoke detector is a smoke sensor that produces an audible alarm when an ionized particle of aerosol is detected. It differs from a light scattering type smoke detector in its subtler principle. A light scattering type detector detects the scattering of light by aerosol particles, while an ionization type smoke detector generates an electrical current that is proportional to the number of ions in the air.
This study compares the responses of six different smoke detectors. Two of the detectors are ionization types, while the others are light scattering detectors.
The test chamber used in this study was a cylinder plastic bell jar of 2.2 x 104 cm3. Aerosol was generated by a dilution process. One part of the stream was directed to an optical particle counter, while the other part was mixed with 800 cm3/s of clean air.
After the aerosol was diluted, it was passed through a neutralizer. The resulting concentration of a-particles was then measured using a commercial CPC.
Shape of the aerosol
The aerosol on an ionization type smoke detector is different from that on a light scattering detector. The ionization type uses ions that are produced by the interaction of air molecules with a-radiation. It produces a small electrical current on the order of picoamps.
However, it is not as sensitive as light scattering detectors. This is due to the stochastic nature of radioactive decay. In addition, the noise level is relatively high. Besides, the output of an ionization type smoke detector depends on the concentration of the diluting air.
As a result, the aerosol on an ionization type detector is more variable than that on a light scattering detector. A study compared the performance of six detectors based on three types of ionization (light scattering, photoelectric, and electrostatic) and three light scattering technologies (photoelectric, photodetector, and laser).
To determine the most important aerosol properties, a variety of aerosol instruments were used. These included an optical particle counter and an electrical aerosol analyzer. Each instrument was used to measure the particle size distribution and number concentration.
Nature and strength of the radioactive source
An ionization type smoke detector is an ionization detector with a small americium source. This is different from a light scattering type detector with a much larger source. In an ionization type detector, ions are produced when americium-241 ionizes air molecules.
The performance of an ionization type smoke detector depends on several factors including the geometry of the ionization chamber and the strength of the radioactive source. For example, the ion drift velocity is 14 cm/s for an electric field of 10 V/cm. It is also important to account for atmospheric conditions.
There are many theories on how ionization chambers work. Some involve the use of a pair of parallel plates to trap and contain ions. Others require a simple geometric design. Regardless of the theory, a detailed test would likely involve measuring the ionization current directly.
Aside from the spectral distribution of the light source, the intensity of light scattered by smoke particles is affected by several factors, including the size and shape of the particle. Alpha particles are the largest and have the highest ionizing power. Beta particles have the same ionizing power, but are smaller and can penetrate dead skin layers.
Voltage
An ionization type smoke detector is a type of fire alarm system. It typically consists of a radioactive source, such as Americium, which ionizes the ambient air. Smoke particles attach themselves to the ions and neutralize them.
The ionization type smoke detector also features an electronic circuit that detects a difference in chamber current. When this difference reaches a threshold, the alarm goes off.
In addition, an ionization smoke detector is generally cheaper to manufacture than an optical detector. It may also be less sensitive to false alarms. However, it is worth noting that these types of smoke alarms may be slower to respond to typical house fires.
If you’re not interested in building your own detector, you could consider purchasing a commercially available smoke alarm that includes all of the features you need. Such devices often come in the form of a low-cost 16-pin dual in-line plastic package.
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Usage of Medical for those who have Afflictions inside Countryside Malawi: Do you know the Boundaries?
Results: Your imply follow-up has been Twenty-eight +/- 15 months coming from muscle tissue transposition as well as Twenty-two +/- 15 several weeks coming from stomal, end. Fistula closure without recurrence could be attained in 33 people (94%). Two several YM155 order sufferers (29%) with Crohn's condition were built with a prolonged fistula. There was neither intra-operative issues or problems related to muscle tissue desinsertion surgery. Conclusions: Recto-urethral, and rectovaginal fistula closure while using perineal approach together with pedicled gracilis muscle tissue interposition is associated with nominal deaths along with a substantial accomplishmentClostridium difficile infection (CDI) will be increasingly common, which is connected with substantial morbidity, mortality, and expense stress for sufferers as well as the health-related system. Your severeness along with rates of repeated CDI as well as linked fatality will also be raising. Advantages and drawbacks an introduction to the alterations throughout CDI epidemiology which may have took place since the change of the century and also the latest opportunity in the issue. The content such as the following within this dietary supplement handle diagnosing along with treatments for initial and also persistent CDI, and also latest practice tips to the elimination along with control over CDI in the medical center placing. Journal regarding Clinic Medicine Next year;Several:S1S4. (chemical) Next year Community of Hospital MedicationFrom the collection associated with forest canopy panels attributes by using a geometric-optical design, your spectral arena reflectance of each one component needs to be called prior knowledge. Typically, these kind of reflectances ended up received by a foregone survey utilizing an analytical spectral gadget. This article purposed to be able to get the particular natrual enviroment composition details making use of gentle detection along with varying (LiDAR) information, and also utilised any linear spectrum decomposition design to determine the reflectances from the spectral scene factors, which are regarded as knowledge in the collection associated with woodland cover include and effective seed location list (PAI(at the)) employing a simplified Li-Strahler geometric-optical style according to a Satellite Fill l'Observation de la Terre 5 (SPOT-5) high-resolution geometry (HRG) graphic. Your flying LiDAR information tend to be first accustomed to get the actual natrual enviroment framework parameters and then the percentage of the Place pixel certainly not covered by the queen's or perhaps darkness K-g of each one pixel within the sample had been calculated, that was utilized to remove the reflectances of the spectral picture parts by a straight line spectrum decomposition product. Ultimately, your woodland canopy include and PAI(e) are restored through the geometric-optical style. As the received period of SPOT-5 picture and also measured information includes a discrepancy of approximately 8 weeks, the restored consequence of forest cover include needs a further validation. The particular fairly high value involving R-2 involving the obtain response to PAI(electronic) as well as the dimensions signifies the particular productivity of our methods.
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Geometry of the Crown Chakra
The crown chakra is the seventh chakra, also known as Sahasrara in Sanskrit. The crown chakra is located at the top of the head. The crown chakra is where your physical body and individual consciousness meet the universal consciousness.
The geometry of the crown chakra consists of a circle surrounded by a thousand petals lotus. Here is where the Kundalini energy merges with Shiva to achieve liberation of human bondages.
The circle represent the purification you went through with the previous six chakras. From this point, you are ready to reach transcendence and merge with the infinite.
The moon also represents the full moon and the awakening of the conscious mind.
The thousand petals lotus represent the connection with the Divine, with the Universe
Crown Chakra – Element of Light – Platonic Solids
The crown chakra is associated with our belief system. It serves as a connection to our source and the infinite nature of our soul. Spheres inspire the mind to transcend thought.
Spheres are three-dimensional circles. Our sun is a sphere, and a star, and our source of light. The electromagnetic spectrum of light makes up less than 5% of all ordinary matter. Light that is actually visible to the human eye represents less than 2.3% of this spectrum and is created by narrow wavelengths of pure spectral colors: red, orange, yellow, green, blue and violet. Infrared light (below red) and ultra violet (above violet) are made up of frequencies that are invisible to the human eye. This full spectrum of light includes UVA, radio waves, microwaves, X-rays & gamma rays.
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