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A 'string function' for describing the propagation of large-scale potential energy anomalies in a rotating fluid

GEOPHYSICAL AND ASTROPHYSICAL FLUID DYNAMICS 2000年第1-2期92卷 31-64页

作者： Tyler, RH Käse, R Inst Meereskunde Abt Theoret Ozeanog D-24105 Kiel Germany

Just as a stream function gives both a qualitative and quantitative description of the flow, a 'string function' can be constructed to describe the propagation in a rotating fluid of large-scale energy anomalies such as eddies and Rossby waves. To simply introduce the string function in this paper, we consider only a homogenous 1-layer fluid. In this case, the string function is inversely proportional to large-scare potential vorticity and the contours of both are aligned. The string function contains more information, however, because the propagation speeds are described by the contour spacing. We introduce the string function and use it to derive and reinterpret governing equations for linear and nonlinear shallow-water dynamics. The string function allows for simple evolution equations incorporating both beta and topographic effects.

关键词： potential vorticity geostrophic contours string function eddy propagation Rossby wave

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A numerical study of the string function using a primitive equation ocean model

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GEOPHYSICAL AND ASTROPHYSICAL FLUID DYNAMICS 2000年第1-2期92卷 65-83页

作者： Tyler, RH Käse, R Inst Meereskunde Abt Theoret Ozeanog D-24105 Kiel Germany

We use results from a primitive-equation ocean numerical model (SCRUM) to test a theoretical 'string function' formulation put forward by Tyler and Kase in another article in this issue. The string function acts as a stream function for the large-scale potential energy flow under the combined beta and topographic effects. The model results verify that large-scale anomalies propagate along the string function contours with a speed correctly given by the cross-string gradient. For anomalies having a scale similar to the Rossby radius, material rates of change in the layer mass following the string velocity are balanced by material rates of change in relative vorticity following the flow velocity. It is shown that large-amplitude anomalies can be generated when wind stress is resonant with the string function configuration.

关键词： potential vorticity geostrophic contours string function eddy propagation Rossby wave numerical model

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Computability of string functions over algebraic structures

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MATHEMATICAL LOGIC QUARTERLY 1998年第1期44卷 1-44页

作者： Hemmerling, A Ernst Moritz Arndt Univ Greifswald Inst Math & Comp Sci D-17487 Greifswald Germany

We present a model of computation for string functions over single-sorted, total algebraic structures and study some basic features of a general theory of computability within this framework. Our concept generalizes the Blum-Shub-Smale setting of computability over the reals and other rings. By dealing with strings of arbitrary length instead of tuples of fixed length, some suppositions of deeper results within former approaches to generalized recursion theory become superfluous. Moreover, this gives the basis for introducing computational complexity in a BSS-like manner. Relationships both to classical computability and to Friedman's concept of eds computability are established. Two kinds of nondeterminism as well as several variants of recognizability are investigated with respect to interdependencies on each other and on properties of the underlying structures. For structures of finite signatures, there are universal programs with the usual characteristics. :For the general case of not necessarily finite signature, this subject will be studied in a separate, forthcoming paper.

关键词： computability over structures general recursion theory string function nondeterminism recognizability

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Crystal bases of the Fock space representations and string functions

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JOURNAL OF ALGEBRA 2004年第1期280卷 313-349页

作者： Kang, SJ Kwon, JH Seoul Natl Univ Dept Math Seoul 130743 South Korea Korea Inst Adv Study Sch Math Seoul 130012 South Korea

Let U-q (g) be the quantum affine algebra of type A(n)((1)), A(2n-1)((2)), A(2n)((2)), B-n((1)), D-n((1)) and D-n+1((2)), and let F(Lambda) be the Fock space representation for a level 1 dominant integral weight A. Using the crystal basis of F(Lambda) and its characterization in terms of abacus, we construct an explicit bijection between the set of weight vectors in F(Lambda)(lambda-mdelta) (m greater than or equal to 0) for a maximal weight lambda and the set of certain ordered sequences of partitions. As a corollary, we obtain the string function of the basic representation V(Lambda). (C) 2004 Elsevier Inc. All rights reserved.

关键词： quantum affine algebra Fock space representation crystal basis string function

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Associative string functions

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ASIAN-EUROPEAN JOURNAL OF MATHEMATICS 2014年第4期7卷 1450059-1-1450059-18页

作者： Lehtonen, Erkko Marichal, Jean-Luc Teheux, Bruno Univ Lisbon Ctr Algebra Ave Prof Gama Pinto 2 P-1649003 Lisbon Portugal Univ Lisbon Fac Ciencias Dept Matemat P-1749016 Lisbon Portugal Univ Luxembourg 6 Math Res Unit FSTC L-1359 Luxembourg Luxembourg

We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. We discuss this new property and describe certain classes of associative string functions. We also characterize the recently introduced preassociative functions as compositions of associative string functions with injective unary maps. Finally, we provide descriptions of the classes of associative and preassociative functions which depend only on the length of the input.

关键词： Associativity preassociativity string function functional equation axiomatization

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Relaxations of associativity and preassociativity for variadic functions

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FUZZY SETS AND SYSTEMS 2016年 299卷 89-97页

作者： Couceiro, Miguel Marichal, Jean-Luc Teheux, Bruno Univ Lorraine Inria Nancy Grand Est CNRS LORIA BP239 F-54506 Vandoeuvre Les Nancy France Univ Luxembourg FSTC Math Res Unit 6 Rue Coudenhove Kalergi L-1359 Luxembourg Luxembourg

In this paper we consider two properties of variadic functions, namely associativity and preassociativity, that are pertaining to several data and language processing tasks. We propose parameterized relaxations of these properties and provide their descriptions in terms of factorization results. We also give an example where these parameterized notions give rise to natural hierarchies of functions and indicate their potential use in measuring the degrees of associativeness and preassociativeness. We illustrate these results by several examples and constructions and discuss some open problems that lead to further directions of research. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Associativity Preassociativity Variadic function string function functional equation Axiomatization

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Affine crystal graphs and two-colored partitions

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LETTERS IN MATHEMATICAL PHYSICS 2006年第2期75卷 171-186页

作者： Kwon, JH Univ Seoul Dept Math Seoul 130743 South Korea

We define the cores and the quotients of the elements in the crystal graph of the basic representation ofA(2n-2)((2)) ,or D-n((1)) and then obtain new combinatorial interpretations of the character and the string func... 详细信息

关键词： Quantum group affine crystal graph partition string function

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Repetition Pattern Attack on Multi-word-containing Securestring 2.0 Objects 11

Repetition Pattern Attack on Multi-word-containing SecureStr...

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11th International Conference on Distributed Computing and Internet Technology (ICDCIT)

作者： Fahrnberger, Guenter Univ Hagen North Rhine Westphalia Germany

ISBN: (纸本)9783319149769;9783319149776

Cloud computing appeals to private individuals and particularly enterprises at a progressive rate, but a noticeable percentage of them refuse it due to mistrust or missing commitment to security. The cryptosystem Securestring 2.0 was designed to outweigh these deficits through the support of blind computations on character strings. Repetition pattern attacks count among the most hazardous enemies of Securestring 2.0 objects because reoccurring ciphergrams within them may reveal linguistic identifying features of the correspondent plaintext. This paper analyzes and compares the success probability of repetition pattern attacks on the following three sorts of Securestring 2.0 objects: singleword- containing ones, multi-word-containing ones with a known number of words plus unknown delimiter positions, and multi-word-containing ones with an unknown number of words plus unknown boundary locations. The latter type is expected to provide the highest privacy.

关键词： Blind computing Character string Character string function Character string operation Cloud Cloud computing Dictionary Attack Repetition Pattern Repetition Pattern Attack Secure computing string string function string operation

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A Second View on Securestring 2.0

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10th International Conference on Distributed Computing and Internet Technology (ICDCIT)

作者： Fahrnberger, Guenter Univ Hagen Univ Str 1 D-58097 Hagen Germany

ISBN: (纸本)9783319044835;9783319044828

Many companies have thought about using external hosting solutions. Cloud computing as such a solution attracts prospective users who want to avoid initial costs and standing expenses with the underlying pay-as-you-use model. The outsourcing of sensitive information implies security risks, like eavesdropping and sabotage, for them as soon as they pass any unconfident area. If an outhouse hosting solution serves as data storage only, then an end-to-end cryptosystem without the necessity of having homomorphic properties comes up with the answer. Moreover, secure computations on the encrypted data need the use of more complex cryptosystems. Securestring 1.0 [3] and Securestring 2.0 [4] were proposed as such complex cryptosystems that focus on computing on encrypted character strings in untrustworthy environments (like clouds). While Securestring 1.0 offered a too inflexible approach, Securestring 2.0 as its improvement was introduced textually at a high level only so far. This paper contributes to foster the understanding of Securestring 2.0 by providing performance analysis for its supported operations plus formal definitions, theorems and proofs.

关键词： blind computing character string character string function character string operation cloud cloud computing secure computing string function string operation

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Securestring 3.0 A Cryptosystem for Blind Computing on Encrypted Character strings 11

SecureString 3.0 A Cryptosystem for Blind Computing on Encry...

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11th International Conference on Distributed Computing and Internet Technology (ICDCIT)

作者： Fahrnberger, Guenter Heneis, Kathrin Univ Hagen North Rhine Westphalia Germany Univ Vienna A-1010 Vienna Austria

ISBN: (纸本)9783319149769;9783319149776

If (electronic) computations need to be undertaken, then mostly performance or commercial aspects lead to the selection for an optimal executing computer. In case the beneficiary of the computation upshots does not wholly confide in any computers except his ones, trust becomes his major decision criterion instead. Blind computing can do the trick to (re) win the beneficiary's confidence. This paper ameliorates the well-known cryptosystem Securestring 2.0 concerning privacy through pangram ciphertexts and referring integrity through secret sharing. The emerging cryptosystem of this amelioration is called Securestring 3.0 that facilities blind computing on encrypted character strings through an untrusted host.

关键词： Blind computing Character string Character string function Character string operation Cloud Cloud computing Secret Sharing Secure computing string string function string operation

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