Applications of local methods to diophantine equations

This paper describes an authentication scheme that uses Diophantine equations based generation of the secret locations to embed the authentication and recovery watermark in the DWT sub-bands. The security lies in the difficulty of finding a solution to the Diophantine equation. The scheme uses the content invariant features of the image as a self-authenticating watermark and a quantized down sampled approximation of the original image as a recovery watermark for visual authentication, both embedded securely using secret locations generated from solution of the Diophantine equations formed from the PQ sequences. The scheme is mildly robust to Jpeg compression and highly robust to Jpeg2000 compression. The scheme also ensures highly imperceptible watermarked images as the spatio –frequency properties of DWT are utilized to embed the dual watermarks.

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Comparative analysis and verification of engineering methods of shallow cracks effect for fracture toughness prediction for reactor pressure vessels

Voprosy Materialovedeniya ◽

10.22349/1994-6716-2019-100-4-140-165 ◽

2020 ◽

pp. 140-165

Author(s):

V. I. Kostylev ◽

B. Z. Margolin

Keyword(s):

Experimental Data ◽

Fracture Toughness ◽

Comparative Analysis ◽

Nuclear Reactor ◽

Probabilistic Approach ◽

Pressure Vessels ◽

Local Methods ◽

European Method ◽

Shallow Crack ◽

Reactor Pressure

The main features of shallow cracks fracture are considered, and a brief analysis of methods allowing to predict the temperature dependence of the fracture toughness KJC (T) for specimens with shallow cracks is given. These methods include DA-method, (JQ)-method, (J-T)-method, “local methods” with its multiparameter probabilistic approach, GP method uses power approach, and also two engineering methods – RMSC (Russian Method for Shallow Crack) and EMSC (European Method for Shallow Crack). On the basis of 13 sets of experimental data for national and foreign steels, a detailed verification and comparative analysis of these two engineering methods were carried out on the materials of the VVER and PWR nuclear reactor vessels considering the effect of shallow cracks.

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Development of the mathematic model of disymmetric bigram cryptosystem based on a parametric solution family of multi-degree system of Diophantine equations✱

13th International Conference on Security of Information and Networks ◽

10.1145/3433174.3433596 ◽

2020 ◽

Author(s):

Valeriy Osipyan ◽

Kirill Litvinov

Keyword(s):

Diophantine Equations ◽

Mathematic Model ◽

Parametric Solution

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The resolution property via Azumaya algebras

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crelle-2021-0002 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Siddharth Mathur

Keyword(s):

Azumaya Algebras ◽

Algebraic Space ◽

Local Methods ◽

Artin Stacks ◽

Resolution Property

Abstract Using formal-local methods, we prove that a separated and normal tame Artin surface has the resolution property. By proving that normal tame Artin stacks can be rigidified, we ultimately reduce our analysis to establishing the existence of Azumaya algebras. Our construction passes through the case of tame Artin gerbes, tame Artin curves, and algebraic space surfaces, each of which we establish independently.

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