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Distribution Theory & Applications (V9)This book is an introductory course to the very important theory of distributions, as well as its applications in the resolution of partial differential equations (PDEs). It begins with a chapter of general interest, on the fundamental spaces (or test function spaces). The book advances and concludes with a chapter on Sobolev spaces, which are known to be very important in the resolution of PDEs. The very basic properties of distributions are examined
This book is an introductory course to the very important theory of distributions, as well as its applications in the resolution of partial differential equations (PDEs). It begins with a chapter of general interest, on the fundamental spaces (or test function spaces). The book advances and concludes with a chapter on Sobolev spaces, which are known to be very important in the resolution of PDEs.The very basic properties of distributions are examined in detail. Several formal methods have been first used, without rigorous justifications (Dirac function, principal value of Cauchy, finite parts of Hadamard). They find their natural frame in distribution theory. It is the same for Laplace transformation which is a fundamental tool in symbolic calculations.A detailed treatment is given to the convolution product for it is a central theme in distribution theory. Another very important instrument, covered in several chapters, is the Fourier transformation which is among the most fundamental tools in different mathematical disciplines, and also in physics. Convolution algebras, which are sufficient for the treatment of classical PDEs, are used in various applications.The general frame for the resolution of PDEs is the theory of kernels -- the first elements of which are sufficient to show the practicality of distribution theory in applications.Comments are provided to clarify the settings and sustain calculations. This book may be used by mathematicians, physicists, engineers and graduate students.Shipping Notes
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★★★★★ 4
Slippery when wet!!!
Color: Pink & Beige, Size: Medium/Large(fits size 8 to 11)
“These moisturizing slippers are actually really comfortable and feel great on the feet. They’re soft, cozy, and do help moisturize while you wear them. I also think they’re a good value for the money. The only downside is that once your feet get moisturized, they can get slippery inside the slippers, so I wouldn’t recommend walking around too much in them. Better for relaxing and letting your feet soak up the moisture than for being up and moving around.”
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Reviewed in the United States on May 26, 2026
★★★★★ 5
Love them
Color: Pink & Beige, Size: Medium/Large(fits size 8 to 11)
I wear a size 11.5 in ladies shoe and these just barely fit. Butttt after I put lotion on my feet and slipped these on and left them on for about 30 mins. It left my feet really soft! They work great as intended. Would buy again
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Reviewed in the United States on January 31, 2026
★★★★★ 3
Effective but may be uncomfortable
Color: Pink & Beige, Size: Medium/Large(fits size 8 to 11)
I have eczema on my feet and use a prescription cream that I leave on overnight. I often have a problem sleeping in socks but the silicone feels cool on my feet. The only drawback I have is the opening of the socks feel very tight around my ankles making them uncomfortable on me. I wish the opening was a bit more flexible.
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Reviewed in the United States on September 20, 2025
★★★★★ 1
Burned my already sensitive feet, too big
Color: Pink & Beige, Size: Medium/Large(fits size 8 to 11)
Feels icky, and the heat gets trapped and literally felt like my feet were being burned by these. The bottoms of these feel prickly and they are way too big. You have to sit still and cannot walk in them.
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Reviewed in the United States on April 22, 2026
★★★★★ 5
Just as good as paraffin wax
Color: Pink & Beige, Size: Medium/Large(fits size 8 to 11)
I might prefer these socks over paraffin wax. They are comfy and very moisturizing. I use these socks once a week to keep the heels and soles of my feet moisturized between pedicures. I rinse with warm, soapy water then hang to dry. They are hard to walk in, but there's a saying printed in the socks that's says something to the effect of "take a break, stay off your feet" lol I love that as a reminder to put my feet up and relax
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Reviewed in the United States on April 9, 2026
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