Title
Generalized Curvature and Torsion in Nonstandard Analysis: Nonstandard Technical Treatment for Some Differential Geometry Concep,Used
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The two notions of curvature and torsion have a great role in differential geometry and they have more applications in different scientific areas like: computer vision image improvement, dielectric surfaces, chemical interatomic surfaces, biological membranes, and double bubbles). There are several classical studies of curvature and some nonstandard studies about differential geometry, but none of them treated the problem of curvature at or near singular points. Black holes are one of a real examples about singularity which has highly energy at its singular point that make hastily change of the value of the curvature of any curve pass throughout it. Our investigation throughout this book is to use nonstandard tools for treating such problems, the study of this subject leads to introduce a more general definition about curvature and torsion which enable us to find the curvature and torsion values of points includes in an infinitesimal neighborhood of singularities rather than, finding the value of it at ordinary points.
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Shipping & Returns
Shipping
We ship your order within 2–3 business days for USA deliveries and 5–8 business days for international shipments. Once your package has been dispatched from our warehouse, you'll receive an email confirmation with a tracking number, allowing you to track the status of your delivery.
Returns
To facilitate a smooth return process, a Return Authorization (RA) Number is required for all returns. Returns without a valid RA number will be declined and may incur additional fees. You can request an RA number within 15 days of the original delivery date. For more details, please refer to our Return & Refund Policy page.
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Warranty
We provide a 2-year limited warranty, from the date of purchase for all our products.
If you believe you have received a defective product, or are experiencing any problems with your product, please contact us.
This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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Your payment information is processed securely. We do not store credit card details nor have access to your credit card information.
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