Theorems in functional analysis | Banach spaces | Partial differential equations | Normed spaces

Fichera's existence principle

In mathematics, and particularly in functional analysis, Fichera's existence principle is an existence and uniqueness theorem for solution of functional equations, proved by Gaetano Fichera in 1954. More precisely, given a general vector space V and two linear maps from it onto two Banach spaces, the principle states necessary and sufficient conditions for a linear transformation between the two dual Banach spaces to be invertible for every vector in V. (Wikipedia).

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Seyyed Hossein Nasr - Arguing God from Being?

This ontological and much-debated argument for God's existence claims that a 'Perfect Being' must exist because 'existence' is a perfection. The newer 'Modal Ontological Argument' claims that if a 'Necessary Being' could conceivably exist - in any possible world - a Necessary Being (being

From playlist Big Questions About God - Closer To Truth - Core Topic

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Alister McGrath - Arguing God from Pure Existence?

That there is 'something' and not 'nothing', and that science cannot explain why, is truly fascinating. Does this mean that there is a God? Some argue that if a 'Perfect Being' could exist, a Perfect Being must exist, because a Perfect Being is necessary. There must be something wrong with

From playlist Big Questions About God - Closer To Truth - Core Topic

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Teach Astronomy - The Anthropic Principle

http://www.teachastronomy.com/ The anthropic principle is an extraordinary idea that is somewhat controversial even amongst scientists. It's possible that the existence of life in the universe is not an accident, that the role of life in the universe is more central than we might imagine.

From playlist 29. Prospects of Nonhuman Intelligences

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The Truth is Terrible - Nietzsche's Idea of an Aesthetic Justification for Existence

Brian Leiter discusses the thought of Nietzsche at Davidson College a few years back. The truth is terrible, Nietzsche tells us. There is no God, the universe lacks any ultimate meaning or purpose, and is filled with gratuitous pointless suffering. Our only relief comes with nonexistence u

From playlist Social & Political Philosophy

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What would Einstein have thought about anthropic reasoning?

Einstein envisioned understanding all the features of our single, unique universe. But as Brian Greene explains, should the speculative possibility that we’re part of a multiverse prove true, this goal would radically change. Subscribe to our YouTube Channel for all the latest from World

From playlist Science Unplugged: Anthropic Principle

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(ML 19.2) Existence of Gaussian processes

Statement of the theorem on existence of Gaussian processes, and an explanation of what it is saying.

From playlist Machine Learning

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Video3-4: Existence and Uniqueness Them; Definition of Wronskian. Elementary Differential Equations

Elementary Differential Equations Video3-4: Existence and Uniqueness Theorem; the Definition and applications of Wronskian on linear dependence Course playlist: https://www.youtube.com/playlist?list=PLbxFfU5GKZz0GbSSFMjZQyZtCq-0ol_jD

From playlist Elementary Differential Equations

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Hubert Dreyfus - The Mystery of Existence

If all that exists—everything imaginable, physical and nonphysical—is 'something'. Why is there 'something' rather than 'nothing'? Wouldn't 'nothing' be simpler than any sort of 'something'? It's a haunting wonderment. Click here to watch more interviews with Hubert Dreyfus http://bit.ly/

From playlist Closer To Truth - Hubert Dreyfus Interviews

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Teach Astronomy - Observing the Universe

http://www.teachastronomy.com/ The strong version of the anthropic principle in essence states that the observed values of physical and cosmological quantities are not accidents but are connected somehow with our existence as observers of the universe. The universe was built for us. This

From playlist 29. Prospects of Nonhuman Intelligences

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Is the Anthropic Principle Significant? | Episode 1904 | Closer To Truth

Is the Anthropic Principle significant? Here’s the claim: conditions of the universe relate to the presence of observers. Does the Anthropic Principle convey deep insights? Or thwart science? For sure, it’s often misunderstood and controversial. Featuring interviews with Bernard Carr, Pedr

From playlist Closer To Truth | Season 19

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Is the Anthropic Principle scientific?

In this video, I explain why the anthropic principle is a good, scientific principle. First I explain the difference between the strong and the weak anthropic principle. Then I name some examples of the use of the weak anthropic principle and explain its relation to the multiverse. Finally

From playlist Philosophy of Science

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CTNT 2020 - Elliptic curves and the local-global principle for quadratic forms - Asher Auel

The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2020 - Conference Videos

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Total Functions in the Polynomial Hierarchy - Robert Kleinberg

Computer Science/Discrete Mathematics Seminar I Topic: Total Functions in the Polynomial Hierarchy Speaker: Robert Kleinberg Affiliation: Cornell University Date: February 08, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

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Well-ordering Principle and Division Algorithm || Polynomial Prerequisites || Intermediate Algebra

Here I have already diverted from the standard Principle as the Well-ordering Principle usually goes with the Natural Numbers (ℕ) and the Division Algorithm over the Integers (ℤ). Here's some more nice content. Well-ordering Principle: 1. https://en.wikipedia.org/wiki/Well-ordering_princi

From playlist Summer of Math Exposition 2 videos

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Why a Fine-Tuned Universe? | Episode 107 | Closer To Truth

How can so many numbers of nature, the constants and relationships of physics, be so spot-on perfect for humans to exist? Beware: there is more than one answer lurking here. Featuring interviews with John Leslie, Steven Weinberg, David Gross, John Polkinghorne, Robin Collins, and Paul Davi

From playlist Closer To Truth | Season 1

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Do General Principles Govern All Science? | Episode 1004 | Closer To Truth

Are there "general principles" that encompass all sciences, that explain even beyond the sciences? What would that mean about our world and about us? Featuring interviews with Geoffrey West, Martin Rees, Stuart Kauffman, Holmes Rolston III, and David Deutsch. Season 10, Episode 4 - #Close

From playlist Closer To Truth | Season 10

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Arguing God from First Cause | Episode 112 | Closer To Truth

Does everything need a cause? Everything in the universe surely does. But what about the universe as a whole? And what about God - assuming God exists - does God need a cause? Featuring interviews with William Craig, Quentin Smith, Alister McGrath, David Shatz, Charles Harper, and Peter va

From playlist Closer To Truth | Season 1

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Is Life and Mind Inevitable in the Cosmos? | Episode 902 | Closer To Truth

Our universe must be "just so" in order for life and mind-for us-to exist. "Just so" is called "fine-tuning," and it cries out for explanation. Featuring interviews with J. Gott, Frank Wilczek, Robert Laughlin, Raymond Kurzweil, Robert Russell, and Peter van Inwagen. Season 9, Episode 2 -

From playlist Closer To Truth | Season 9

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A Defense of Classical Theology (Part 6): The Argument from Change

In part 6, I will present an argument for the unactualized actualizer starting from the reality of change, building off of what we covered in the previous part concerning the act-potency distinction. We will then prove the divine attributes from the unactualized actualizer and then conclud

From playlist Theology

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Does the Past Still Exist?

To try out our new course (and many others on math and science), go to https://brilliant.org/sabine. You can get started for free, and the first 200 will get 20% off the annual premium subscription. Albert Einstein taught us that space and time belong together to a common entity: space-ti

From playlist Philosophy of Science

Related pages

Differential operator | Functional (mathematics) | Linear map | Gaetano Fichera | Banach space | Functional analysis | Vector space | Dual space | Surjective function | Lax–Milgram theorem | Boundary value problem