## Lithiation of 1 -cyanomethylbenzotriazole (4) with LDA and subsequent reactions with alkyl halides or car-bony1 compounds afforded the cowesponding 1 -(a- cyanoalky1)-and 1-(a-cyanoalkeny1)-benzotriazoles. Bromination of 4 with NBS formed 1 -(brornocyanomethyl) benzotriazole. 1 -Cyanoalkylbenz
On 1-1 Bivariate Transformations
β Scribed by J.M. Fitzpatrick; L.L. Schumaker
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 450 KB
- Volume
- 72
- Category
- Article
- ISSN
- 0021-9045
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β¦ Synopsis
We study a class of one-to-one tensor mappings defined on a rectangular region of the plane. Such mappings are of interest in image processing, computer vision, biological morphology, cartography, and medical imaging. The mappings are constructed as tensor-products of univariate functions, and the main result is a set of constraints on the parameters of the mapping which assure that it is one-to-one. We illustrate the method by showing how to construct one-to-one mappings using tensor-product polynomials and tensor-product splines. (\quad: 1993) Academic Press, Inc
π SIMILAR VOLUMES
## Abstract In this paper the index ~2~__F__~1~βtransform is defined on a space of generalized functions by using the method of adjoints. We prove that smooth functions having suitable asymptotic behaviors around zero and infinite are ~2~__F__~1~βtransforms of generalized functions.