منابع مشابه
Efficient elliptic curve cryptosystems
Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...
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The t-expansion, a nonperturbative analytic method for calculating the ground-state expectation values of arbitrary operators of the Hamiltonian, is applied to the Mathieu equation. Connrming previous results in other systems, a t-expansion up to order t 2 is suucient to recover the behaviour of the exact solution. A very good performance is observed when a variational wave function of the form...
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In this paper, based on lectures by the authors at the May 2015 workshop Resurgence, Physics and Numbers, at the Centro di Ricerca Matematica Ennio De Giorgio of the Scuola Normale Superiore in Pisa, we explain the origin of resurgent trans-series in the Mathieu equation spectral problem, using uniform WKB and all-orders (exact) WKB. Exact quantization conditions naturally arise, and their expa...
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Recently, there has been an explosion of interest in the study of Schrijdinger operators and Jacobi matrices with almost periodic potential (see, e.g., the review [ 161). The general belief is that generically the spectrum is a Cantor set, i.e., a nowhere dense perfect, closed set. Since it is easy to prove that the spectrum is closed and perfect (see, e.g., [2]), the key is to prove that the s...
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Definition 1. Let k be a field. An algebraic variety over k is a k-scheme X such that there exists a covering by a finite number of affine open subschemes Xi which are affine varieties over k, i.e. each Xi is the affine scheme associated to a finitely generated algebra over k. A projective variety over k is a projective scheme over k, i.e. a k-scheme isomorphic to Proj k[T0, . . . , Tn]/I for a...
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ژورنال
عنوان ژورنال: Communications in Theoretical Physics
سال: 2012
ISSN: 0253-6102
DOI: 10.1088/0253-6102/58/6/08