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		<title>AI Enriched Problem Solving</title>
		<link>https://www.physicsforums.com/insights/ai-enriched-problem-solving/</link>
					<comments>https://www.physicsforums.com/insights/ai-enriched-problem-solving/#comments</comments>
		
		<dc:creator><![CDATA[Neil Parker]]></dc:creator>
		<pubDate>Sat, 28 Feb 2026 22:16:26 +0000</pubDate>
				<category><![CDATA[Mathematics Tutorials]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=50705</guid>

					<description><![CDATA[Introduction This article is written by way of a reference for my longstanding PF colleague and prolific poster of challenging Maths/geometry problems @chwala . The particular post this article will discuss is an example of one such problem which he raised on Physics Forums. https://www.physicsforums.com/threads/find-angle-adb-in-this-isoceles-triangle-given-some-extra-information.1063874/ The Problem We take the liberty of including the original...]]></description>
		
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		<title>Remote Operated Gate Control System</title>
		<link>https://www.physicsforums.com/insights/remote-operated-gate-control-system/</link>
					<comments>https://www.physicsforums.com/insights/remote-operated-gate-control-system/#respond</comments>
		
		<dc:creator><![CDATA[Neil Parker]]></dc:creator>
		<pubDate>Sat, 28 Feb 2026 22:11:58 +0000</pubDate>
				<category><![CDATA[Technology Guides]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=49988</guid>

					<description><![CDATA[Introduction This project began life in 2017 when the author had just begun experimentation with GPIO pins on a Raspberry Pi 3. At that point in time a greatly appreciated Christmas present  was an &#8220;Explorer Hat&#8221; module which provided the aspirant programmer with 5 volt tolerant input and output channels (analogue and digital) , capacitive...]]></description>
		
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		<title>Inside the Scientific Box: History and Challenges Today</title>
		<link>https://www.physicsforums.com/insights/independent-research-thinking-outside-the-box-versus-knowing-whats-in-the-box/</link>
					<comments>https://www.physicsforums.com/insights/independent-research-thinking-outside-the-box-versus-knowing-whats-in-the-box/#comments</comments>
		
		<dc:creator><![CDATA[fresh_42]]></dc:creator>
		<pubDate>Mon, 13 Oct 2025 13:54:14 +0000</pubDate>
				<category><![CDATA[Physics Articles]]></category>
		<category><![CDATA[research]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=49914</guid>

					<description><![CDATA[In Memoriam In Memory of Dr. Thomas J. LeCompte (1964-2025), Detector Designer and Champion of Education and Science. Prologue Defining &#8220;the box&#8221; Someone who shows interest in science is initially a welcome development. So are fresh ideas from unexpected quarters. In contrast, there is a scientific community that is meticulously organized down to the last...]]></description>
		
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		<title>Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality per Quantum Information Theory</title>
		<link>https://www.physicsforums.com/insights/why-entangled-photon-polarization-qubits-violate-bells-inequality-per-quantum-information-theory/</link>
					<comments>https://www.physicsforums.com/insights/why-entangled-photon-polarization-qubits-violate-bells-inequality-per-quantum-information-theory/#respond</comments>
		
		<dc:creator><![CDATA[Mark Stuckey]]></dc:creator>
		<pubDate>Mon, 29 Sep 2025 12:54:13 +0000</pubDate>
				<category><![CDATA[Physics Articles]]></category>
		<category><![CDATA[quantum physics]]></category>
		<category><![CDATA[relativity]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=49851</guid>

					<description><![CDATA[In her YouTube video Bell&#8217;s Theorem Experiments on Entangled Photons, Dr. Fugate shows how polarization-entangled photons violate Bell&#8217;s inequality. In this Insight, I will use quantum information theory to explain why such entangled photon-polarization qubits violate the version of Bell&#8217;s inequality due to John Clauser, Michael Horne, Abner Shimony, and Richard Holt known as the...]]></description>
		
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		<title>Relativator (Circular Slide-Rule) – Simulated with Desmos</title>
		<link>https://www.physicsforums.com/insights/relativator-circular-slide-rule-simulated-with-desmos/</link>
					<comments>https://www.physicsforums.com/insights/relativator-circular-slide-rule-simulated-with-desmos/#respond</comments>
		
		<dc:creator><![CDATA[robphy]]></dc:creator>
		<pubDate>Tue, 02 Sep 2025 12:55:33 +0000</pubDate>
				<category><![CDATA[Physics Articles]]></category>
		<category><![CDATA[relativity]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=49737</guid>

					<description><![CDATA[The Relativator (revisited) This is an update of my 2006 post (reconstructed in 2014) Relativator: The circular slide-rule for physicists. This is a circular slide-rule for doing relativistic calculations for elementary particle physics that I learned about from &#8211; an article by Elizabeth Wade ( &#8220;Artifact: Relativator&#8221;, Symmetry (FNAL/SLAC), 01/01/06, https://www.symmetrymagazine.org/article/december-2005january-2006/artifact-relativator  https://www.symmetrymagazine.org/sites/default/files/legacy/pdfs/200512/artifact_relativator.pdf ), which is...]]></description>
		
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		<title>What Exactly is Dirac’s Delta Function?</title>
		<link>https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/</link>
					<comments>https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/#comments</comments>
		
		<dc:creator><![CDATA[jambaugh]]></dc:creator>
		<pubDate>Fri, 29 Aug 2025 11:51:27 +0000</pubDate>
				<category><![CDATA[Mathematics Articles]]></category>
		<category><![CDATA[mathematical physics]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=26196</guid>

					<description><![CDATA[Introduction: &#8220;Convenient Notation&#8221; In Dirac&#8217;s Principles of Quantum Mechanics published in 1930 he introduced a &#8220;convenient notation&#8221; he referred  to as a &#8220;delta function&#8221; which he treated as a continuum analog to the discrete Kronecker delta.  The Kronecker delta is simply the indexed components of the identity operator in matrix algebra: [tex]\delta^j_k =\left\{\begin{array}{lcl}1&#38;\text{ if }...]]></description>
		
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		<title>Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect</title>
		<link>https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/</link>
					<comments>https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/#comments</comments>
		
		<dc:creator><![CDATA[Mark Stuckey]]></dc:creator>
		<pubDate>Wed, 27 Aug 2025 12:25:02 +0000</pubDate>
				<category><![CDATA[Physics Articles]]></category>
		<category><![CDATA[Quantum entanglement]]></category>
		<category><![CDATA[quantum physics]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=49645</guid>

					<description><![CDATA[Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated: Before we end, let&#8217;s now briefly talk about the birth of quantum information science, a pivotal shift that began in the 1990s. This is the era when researchers...]]></description>
		
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		<title>Fixing Things Which Can Go Wrong With Complex Numbers</title>
		<link>https://www.physicsforums.com/insights/fixing-things-which-can-go-wrong-with-complex-numbers/</link>
					<comments>https://www.physicsforums.com/insights/fixing-things-which-can-go-wrong-with-complex-numbers/#respond</comments>
		
		<dc:creator><![CDATA[PAllen]]></dc:creator>
		<pubDate>Sun, 20 Jul 2025 11:55:08 +0000</pubDate>
				<category><![CDATA[Mathematics Articles]]></category>
		<category><![CDATA[complex numbers]]></category>
		<category><![CDATA[mathematics self-study]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=49363</guid>

					<description><![CDATA[Abstract This article will build on the hints about treating the complex numbers as a branched surface, briefly described and pictured in section 4.2 of https://www.physicsforums.com/insights/views-on-complex-numbers/#The-Radish. Using a particular set of conventions, all the problems described in https://www.physicsforums.com/insights/things-can-go-wrong-complex-numbers/  can be removed, and the rules described there as applying only to reals generalized to complex numbers. A...]]></description>
		
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		<title>Fermat’s Last Theorem</title>
		<link>https://www.physicsforums.com/insights/fermats-last-theorem/</link>
					<comments>https://www.physicsforums.com/insights/fermats-last-theorem/#comments</comments>
		
		<dc:creator><![CDATA[fresh_42]]></dc:creator>
		<pubDate>Sun, 18 May 2025 22:50:22 +0000</pubDate>
				<category><![CDATA[Mathematics Articles]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=49230</guid>

					<description><![CDATA[Abstract Fermat&#8217;s Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n&#62;2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book...]]></description>
		
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			<slash:comments>2</slash:comments>
		
		
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		<title>Vector Spaces: Concepts, History, and Applications Guide</title>
		<link>https://www.physicsforums.com/insights/why-vector-spaces-explain-the-world-a-historical-perspective/</link>
					<comments>https://www.physicsforums.com/insights/why-vector-spaces-explain-the-world-a-historical-perspective/#comments</comments>
		
		<dc:creator><![CDATA[fresh_42]]></dc:creator>
		<pubDate>Thu, 13 Mar 2025 12:45:20 +0000</pubDate>
				<category><![CDATA[Mathematics Articles]]></category>
		<category><![CDATA[mathematics]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=49127</guid>

					<description><![CDATA[The Concept A vector space is an additively written abelian group together with a field that operates on it. Intuitive picture vs abstract definition Vector spaces are often described as a set of arrows, i.e. a line segment with a direction that can be added, stretched, or compressed. That&#8217;s where the term linear to describe...]]></description>
		
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		<title>Groups, The Path from a Simple Concept to Mysterious Results</title>
		<link>https://www.physicsforums.com/insights/groups-the-path-from-a-simple-concept-to-mysterious-results/</link>
					<comments>https://www.physicsforums.com/insights/groups-the-path-from-a-simple-concept-to-mysterious-results/#comments</comments>
		
		<dc:creator><![CDATA[fresh_42]]></dc:creator>
		<pubDate>Mon, 03 Feb 2025 01:47:02 +0000</pubDate>
				<category><![CDATA[Mathematics Tutorials]]></category>
		<category><![CDATA[mathematics self-study]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=48834</guid>

					<description><![CDATA[Introduction The concept of a group is as simple as it gets: a set with a binary operation like addition and a couple of natural laws like the requirement that the order of two consecutive operations does not matter: ##(1+2)+3=1+(2+3).## That&#8217;s it. The concept of a group is so simple that I still wonder why...]]></description>
		
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		<title>Hybrid AI Video Codecs and Modern Streaming Techniques</title>
		<link>https://www.physicsforums.com/insights/modern-video-codecs/</link>
					<comments>https://www.physicsforums.com/insights/modern-video-codecs/#respond</comments>
		
		<dc:creator><![CDATA[Bill Hobba]]></dc:creator>
		<pubDate>Sat, 25 Jan 2025 00:33:22 +0000</pubDate>
				<category><![CDATA[Technology Guides]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=47676</guid>

					<description><![CDATA[Introduction AI and Hybrid Codecs Modern Video codecs are all based on similar principles. Recently, these have been complemented by AI techniques, such as super-resolution, to form hybrid codecs. The current state of the art is one of transition to have one based only on AI eventually: https://deeprender.ai/ Codecs using only AI are several years...]]></description>
		
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		<title>Why the Tidal Bulge Doesn’t Exist – Tidal Theory Explained</title>
		<link>https://www.physicsforums.com/insights/there-is-no-tidal-bulge-2/</link>
					<comments>https://www.physicsforums.com/insights/there-is-no-tidal-bulge-2/#comments</comments>
		
		<dc:creator><![CDATA[D H]]></dc:creator>
		<pubDate>Tue, 31 Dec 2024 14:23:01 +0000</pubDate>
				<category><![CDATA[Physics Articles]]></category>
		<category><![CDATA[earth]]></category>
		<category><![CDATA[moon]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=48591</guid>

					<description><![CDATA[[CONTENT] Introduction Overview That there is no tidal bulge is the key premise of this article. Upper-level oceanography undergraduates and above know this. Yet the tidal bulge is still used to portray why the Moon is receding the Earth. If there is no tidal bulge, some other explanation is in order. That other explanation uses...]]></description>
		
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		<title>The Many Faces of Topology</title>
		<link>https://www.physicsforums.com/insights/the-many-faces-of-topology/</link>
					<comments>https://www.physicsforums.com/insights/the-many-faces-of-topology/#respond</comments>
		
		<dc:creator><![CDATA[fresh_42]]></dc:creator>
		<pubDate>Sat, 07 Dec 2024 03:26:45 +0000</pubDate>
				<category><![CDATA[Mathematics Articles]]></category>
		<category><![CDATA[mathematics self-study]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=48237</guid>

					<description><![CDATA[Abstract Topology as a branch of mathematics is a bracket that encompasses many different parts of mathematics. It is sometimes even difficult to see what all these branches have to do with each other or why they are all called topology. This article aims to shed light on this question and briefly summarize the content...]]></description>
		
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		<title>Brownian Motions and Quantifying Randomness in Physical Systems</title>
		<link>https://www.physicsforums.com/insights/brownian-motions-and-quantifying-randomness-in-physical-systems/</link>
					<comments>https://www.physicsforums.com/insights/brownian-motions-and-quantifying-randomness-in-physical-systems/#comments</comments>
		
		<dc:creator><![CDATA[ergospherical]]></dc:creator>
		<pubDate>Mon, 26 Aug 2024 12:14:45 +0000</pubDate>
				<category><![CDATA[Mathematics Articles]]></category>
		<category><![CDATA[projectile motion]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=47569</guid>

					<description><![CDATA[Stochastic calculus has come a long way since Robert Brown described the motion of pollen through a microscope in 1827. It&#8217;s now a key player in data science, quant finance, and mathematical biology. This article is drawn from notes I wrote for an undergraduate statistical physics course a few months ago. There won&#8217;t be any...]]></description>
		
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		<title>Quantum Reconstruction &amp; Bell Correlations Explained</title>
		<link>https://www.physicsforums.com/insights/pbs-video-comment-what-if-physics-is-not-describing-reality/</link>
					<comments>https://www.physicsforums.com/insights/pbs-video-comment-what-if-physics-is-not-describing-reality/#comments</comments>
		
		<dc:creator><![CDATA[Mark Stuckey]]></dc:creator>
		<pubDate>Mon, 22 Jul 2024 16:24:16 +0000</pubDate>
				<category><![CDATA[Physics Articles]]></category>
		<category><![CDATA[quantum mechanics]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=46583</guid>

					<description><![CDATA[Comment on PBS Space Time video PBS Space Time produces some very good videos on the foundations of quantum mechanics (QM), so let me comment on their video What If Physics IS NOT Describing Reality to provide (crucial) missing information. This comment pertains only to the first 9 min of the video, i.e., it has...]]></description>
		
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		<title>Aspects Behind the Concept of Dimension in Various Fields</title>
		<link>https://www.physicsforums.com/insights/aspects-behind-the-concept-of-dimension-in-various-fields/</link>
					<comments>https://www.physicsforums.com/insights/aspects-behind-the-concept-of-dimension-in-various-fields/#comments</comments>
		
		<dc:creator><![CDATA[fresh_42]]></dc:creator>
		<pubDate>Fri, 21 Jun 2024 17:42:18 +0000</pubDate>
				<category><![CDATA[Physics Articles]]></category>
		<category><![CDATA[classical physics]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=46242</guid>

					<description><![CDATA[Abstract It took until the last century for physicists and mathematicians in the Netherlands to question the Euclidean concept of dimension as length, width, and height. Luitzen Egbertus Jan Brouwer published a ground-breaking paper On the Natural Concept of Dimension (Amsterdam, [2]) in 1913 about the mathematical definition of dimension picking up a thought from...]]></description>
		
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		<title>Views On Complex Numbers</title>
		<link>https://www.physicsforums.com/insights/views-on-complex-numbers/</link>
					<comments>https://www.physicsforums.com/insights/views-on-complex-numbers/#comments</comments>
		
		<dc:creator><![CDATA[fresh_42]]></dc:creator>
		<pubDate>Fri, 07 Jun 2024 11:10:00 +0000</pubDate>
				<category><![CDATA[Mathematics Articles]]></category>
		<category><![CDATA[complex numbers]]></category>
		<category><![CDATA[mathematics]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=46007</guid>

					<description><![CDATA[Abstract Why do we need yet another article about complex numbers? This is a valid question and I have asked it myself. I could mention that I wanted to gather the many different views that can be found elsewhere &#8211; Euler&#8217;s and Gauß&#8217;s perspectives, i.e. various historical views in the light of the traditionally parallel...]]></description>
		
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			<slash:comments>70</slash:comments>
		
		
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		<title>Addition of Velocities (Velocity Composition) in Special Relativity</title>
		<link>https://www.physicsforums.com/insights/addition-of-velocities-velocity-composition-in-special-relativity/</link>
					<comments>https://www.physicsforums.com/insights/addition-of-velocities-velocity-composition-in-special-relativity/#comments</comments>
		
		<dc:creator><![CDATA[robphy]]></dc:creator>
		<pubDate>Mon, 20 May 2024 11:37:49 +0000</pubDate>
				<category><![CDATA[Physics Articles]]></category>
		<category><![CDATA[Special Relativity]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=45831</guid>

					<description><![CDATA[The &#8220;Addition of Velocities&#8221; formula (more correctly, the &#8220;Composition of Velocities&#8221; formula) in Special Relativity [tex]\frac{v_{AC}}{c}=\frac{ \frac{v_{AB}}{c}+\frac{v_{BC}}{c} }{1 + \frac{v_{AB}}{c} \frac{v_{BC}}{c}}[/tex] is a non-intuitive result that arises from a &#8220;hyperbolic-tangent of a sum&#8221;-identity in Minkowski spacetime geometry, with its use of hyperbolic trigonometry. However, I claim it is difficult to obtain this by looking at...]]></description>
		
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		<title>Schrödinger’s Cat and the Qbit</title>
		<link>https://www.physicsforums.com/insights/schrodingers-cat-and-the-qbit/</link>
					<comments>https://www.physicsforums.com/insights/schrodingers-cat-and-the-qbit/#comments</comments>
		
		<dc:creator><![CDATA[Mark Stuckey]]></dc:creator>
		<pubDate>Tue, 02 Apr 2024 13:51:19 +0000</pubDate>
				<category><![CDATA[Physics Articles]]></category>
		<category><![CDATA[quantum mechanics]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=45596</guid>

					<description><![CDATA[The concept of quantum superposition (or superposition for short) is very counterintuitive, as Schr##\ddot{\text{o}}##dinger noted in 1935 writing [1], &#8220;One can even set up quite ridiculous cases.&#8221; To make his point, he assumed a cat was closed out of sight in a box with a radioactive material that would decay with 50% probability within an...]]></description>
		
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			<slash:comments>27</slash:comments>
		
		
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		<title>The Slinky Drop Experiment Analysed</title>
		<link>https://www.physicsforums.com/insights/the-slinky-drop-experiment-analysed/</link>
					<comments>https://www.physicsforums.com/insights/the-slinky-drop-experiment-analysed/#comments</comments>
		
		<dc:creator><![CDATA[Orodruin]]></dc:creator>
		<pubDate>Thu, 28 Mar 2024 21:19:54 +0000</pubDate>
				<category><![CDATA[Physics Articles]]></category>
		<category><![CDATA[mechanics]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=45556</guid>

					<description><![CDATA[The slinky drop is a rather simple experiment. In its most basic form, it requires only a popular toy for children, a stable hand, and a keen eye. For a better view, using a modern smartphone to capture a video of the experiment also helps to capture the falling slinky. Apart from the commonly quoted...]]></description>
		
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			<slash:comments>3</slash:comments>
		
		
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		<title>Open, Flat &amp; Closed Universes: Curvature Explained</title>
		<link>https://www.physicsforums.com/insights/infinite-universe/</link>
					<comments>https://www.physicsforums.com/insights/infinite-universe/#respond</comments>
		
		<dc:creator><![CDATA[Greg Bernhardt]]></dc:creator>
		<pubDate>Sat, 16 Mar 2024 15:35:04 +0000</pubDate>
				<category><![CDATA[Physics Articles]]></category>
		<category><![CDATA[cosmology]]></category>
		<category><![CDATA[spacetime]]></category>
		<category><![CDATA[universe]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=48162</guid>

					<description><![CDATA[Standard cosmological models are classified by spatial curvature into three broad types: open, flat, and closed universes. These correspond to negative, zero, and positive spatial curvature respectively, and each case has distinct implications for the geometry and global volume of space. Open, Flat, and Closed Universes In the simplest Robertson–Walker models the three cases can...]]></description>
		
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			<slash:comments>0</slash:comments>
		
		
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		<title>Einstein Field Equations – Definition and Fast Facts</title>
		<link>https://www.physicsforums.com/insights/all-about-the-einstein-field-equations/</link>
					<comments>https://www.physicsforums.com/insights/all-about-the-einstein-field-equations/#respond</comments>
		
		<dc:creator><![CDATA[Greg Bernhardt]]></dc:creator>
		<pubDate>Mon, 26 Feb 2024 14:29:20 +0000</pubDate>
				<category><![CDATA[Physics Tutorials]]></category>
		<category><![CDATA[einstein]]></category>
		<category><![CDATA[relativity]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=48225</guid>

					<description><![CDATA[Definition/Summary The Einstein Field Equations (EFE) are a set of ten interrelated differential equations that form the core of Einstein&#8217;s general theory of relativity. These equations describe how matter and energy determine the curvature of spacetime, providing a mathematical framework to relate spacetime geometry to its energy-matter content. Mathematically, the EFE relate the Ricci curvature...]]></description>
		
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			<slash:comments>0</slash:comments>
		
		
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		<title>How to Solve a Multi-Atwood Machine Assembly</title>
		<link>https://www.physicsforums.com/insights/how-to-solve-a-multi-atwood-machine-assembly/</link>
					<comments>https://www.physicsforums.com/insights/how-to-solve-a-multi-atwood-machine-assembly/#comments</comments>
		
		<dc:creator><![CDATA[kuruman]]></dc:creator>
		<pubDate>Fri, 16 Feb 2024 16:18:12 +0000</pubDate>
				<category><![CDATA[Physics Tutorials]]></category>
		<category><![CDATA[classical physics]]></category>
		<category><![CDATA[mechanics]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=44868</guid>

					<description><![CDATA[Introduction The figure on the right shows a &#8220;double-double&#8221; Atwood machine with three ideal pulleys and four masses.  All pulleys are released from rest simultaneously.  Which of the choices below describes the angular motion of the top pulley P after some time has elapsed and why? It rotates clockwise with increasing angular speed. It rotates...]]></description>
		
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			<slash:comments>2</slash:comments>
		
		
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		<title>The Lambert W Function in Finance</title>
		<link>https://www.physicsforums.com/insights/the-lambert-w-function-in-finance/</link>
					<comments>https://www.physicsforums.com/insights/the-lambert-w-function-in-finance/#respond</comments>
		
		<dc:creator><![CDATA[Neil Parker]]></dc:creator>
		<pubDate>Fri, 09 Feb 2024 14:25:09 +0000</pubDate>
				<category><![CDATA[Mathematics Articles]]></category>
		<category><![CDATA[mathematics]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=44731</guid>

					<description><![CDATA[Preamble The classical mathematician practically by instinct views the continuous process as the &#8220;real&#8221; process, and the discrete process as an approximation to it. The mathematics of finance and certain topics in the modern theory of stochastic processes suggest that, in some cases at least, the opposite is true. Continuous processes are, generally speaking, the...]]></description>
		
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		<title>Why Division by Zero Is Impossible: 10 Mathematical Reasons</title>
		<link>https://www.physicsforums.com/insights/why-division-by-zero-is-a-bad-idea/</link>
					<comments>https://www.physicsforums.com/insights/why-division-by-zero-is-a-bad-idea/#comments</comments>
		
		<dc:creator><![CDATA[fresh_42]]></dc:creator>
		<pubDate>Thu, 11 Jan 2024 16:41:33 +0000</pubDate>
				<category><![CDATA[Mathematics Articles]]></category>
		<category><![CDATA[Mathematics FAQs]]></category>
		<category><![CDATA[mathematics]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=44769</guid>

					<description><![CDATA[A division by zero is primarily an algebraic question. The reasoning therefore follows the indirect pattern of most algebraic proofs: What if it was allowed? Then we would get a contradiction, and a contradiction is the greatest enemy of mathematical rigor. Many students tried to find a way to divide by zero once in their...]]></description>
		
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			<slash:comments>33</slash:comments>
		
		
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		<title>Sinc Function &amp; Upsampling in Digital Audio Explained</title>
		<link>https://www.physicsforums.com/insights/digital-filtering-and-exact-reconstruction-of-digital-audio/</link>
					<comments>https://www.physicsforums.com/insights/digital-filtering-and-exact-reconstruction-of-digital-audio/#respond</comments>
		
		<dc:creator><![CDATA[Bill Hobba]]></dc:creator>
		<pubDate>Thu, 14 Dec 2023 20:50:05 +0000</pubDate>
				<category><![CDATA[Technology Guides]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=44649</guid>

					<description><![CDATA[Introduction This elaborates some of the claims in my insights article on digital audio. The Sinc Function Upsampling and Zero Insertion The first link in my insights article has a section on filters, but I will detail the most critical case. The bit depth is assumed to be so large for all practical purposes that...]]></description>
		
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		<title>Modern DACs, Dither, DXD &amp; High-Res Audio Explained</title>
		<link>https://www.physicsforums.com/insights/digital-audio/</link>
					<comments>https://www.physicsforums.com/insights/digital-audio/#respond</comments>
		
		<dc:creator><![CDATA[Bill Hobba]]></dc:creator>
		<pubDate>Tue, 12 Dec 2023 01:08:57 +0000</pubDate>
				<category><![CDATA[Technology Guides]]></category>
		<category><![CDATA[audio]]></category>
		<category><![CDATA[technology]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=44584</guid>

					<description><![CDATA[Introduction First, we need some background in Digital Signals. This can be mathematically quite advanced, but since I would like this article to be accessible to as wide an audience as possible, here is a link that explains what is needed (not even Calculus is required): https://brianmcfee.net/dstbook-site/content/intro.html Shannon&#8217;s Sampling Theorem An important point not emphasized...]]></description>
		
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		<title>Series in Mathematics: From Zeno to Quantum Theory</title>
		<link>https://www.physicsforums.com/insights/series-in-mathematics-from-zeno-to-quantum-theory/</link>
					<comments>https://www.physicsforums.com/insights/series-in-mathematics-from-zeno-to-quantum-theory/#comments</comments>
		
		<dc:creator><![CDATA[fresh_42]]></dc:creator>
		<pubDate>Wed, 08 Nov 2023 02:13:49 +0000</pubDate>
				<category><![CDATA[Mathematics Articles]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=44496</guid>

					<description><![CDATA[Introduction Series play a decisive role in many branches of mathematics. They accompanied mathematical developments from Zeno of Elea (##5##-th century BC) and Archimedes of Syracuse (##3##-th century BC), to the fundamental building blocks of calculus from the ##17##-th century on, up to modern Lie theory which is crucial for our understanding of quantum theory....]]></description>
		
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			<slash:comments>3</slash:comments>
		
		
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		<title>Epsilontic – Limits and Continuity</title>
		<link>https://www.physicsforums.com/insights/epsilontic-limits-and-continuity/</link>
					<comments>https://www.physicsforums.com/insights/epsilontic-limits-and-continuity/#comments</comments>
		
		<dc:creator><![CDATA[fresh_42]]></dc:creator>
		<pubDate>Fri, 06 Oct 2023 13:41:07 +0000</pubDate>
				<category><![CDATA[Physics Articles]]></category>
		<category><![CDATA[calculus]]></category>
		<category><![CDATA[mathematics]]></category>
		<guid isPermaLink="false">https://www.physicsforums.com/insights/?p=44438</guid>

					<description><![CDATA[Abstract I remember that I had some difficulties moving from school mathematics to university mathematics. From what I read on PF through the years, I think I&#8217;m not the only one who struggled at that point. We mainly learned algorithms at school, i.e. how things are calculated. At university, I soon met a quantity called...]]></description>
		
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			<slash:comments>1</slash:comments>
		
		
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