Solving the Multi-discrete Logarithm Problems over a Group of Elliptic Curves with Prime Order
Jun Quan LI; Mu Lan LIU; Liang Liang XIAO
2005-01-01
In this paper, we discuss the expected number of steps in solving multi-discrete logarithm problems over a group of elliptic curves with prime order by using Pollard's rho method and parallel collision search algorithm. We prove that when using these algorithms to compute discrete logarithms,the knowledge gained through computing many logarithms does not make it easier for finding other logarithms. Hence in an elliptic cryptosystem, it is safe for many users to share the same curve, with different private keys.
Kenli Li
2008-01-01
Full Text Available Elliptic curve cryptographic algorithms convert input data to unrecognizable encryption and the unrecognizable data back again into its original decrypted form. The security of this form of encryption hinges on the enormous difficulty that is required to solve the elliptic curve discrete logarithm problem (ECDLP, especially over GF(2n, n∈Z+. This paper describes an effective method to find solutions to the ECDLP by means of a molecular computer. We propose that this research accomplishment would represent a breakthrough for applied biological computation and this paper demonstrates that in principle this is possible. Three DNA-based algorithms: a parallel adder, a parallel multiplier, and a parallel inverse over GF(2n are described. The biological operation time of all of these algorithms is polynomial with respect to n. Considering this analysis, cryptography using a public key might be less secure. In this respect, a principal contribution of this paper is to provide enhanced evidence of the potential of molecular computing to tackle such ambitious computations.
The Arithmetic of Elliptic Curves
Silverman, Joseph H
2009-01-01
Treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. This book discusses the necessary algebro-geometric results, and offers an exposition of the geometry of elliptic curves, and the formal group of an elliptic curve.
Heegner modules and elliptic curves
Brown, Martin L
2004-01-01
Heegner points on both modular curves and elliptic curves over global fields of any characteristic form the topic of this research monograph. The Heegner module of an elliptic curve is an original concept introduced in this text. The computation of the cohomology of the Heegner module is the main technical result and is applied to prove the Tate conjecture for a class of elliptic surfaces over finite fields; this conjecture is equivalent to the Birch and Swinnerton-Dyer conjecture for the corresponding elliptic curves over global fields.
An algorithm for DLP on anomalous elliptic curves over Fp
祝跃飞; 裴定一
2002-01-01
This paper improves the method of discrete logarithm on anomalous elliptic curves, and establishes an isomorphism from E(Fp) to Fp which can be more easily implemented. Fruthermore, we give an optimized algorithm for discrete logarithm on anomalous elliptic curves E(Fp).
EFFICIENT MAPPING METHODS FOR ELLIPTIC CURVE CRYPTOSYSTEMS
O.SRINIVASA RAO
2010-08-01
Full Text Available The generic name for collection of tools designed to protect data and thwart hackers is Computer Security. The major change that affected security was the introduction of distributed systems and the use of networks and communication facilities for carrying data between terminal user and computer and computer and computer. Network security measures are needed to protect data transmission. Suppose that we had a way of masking the contents of messages or other information traffic so that an attacker, even if he or she captured the message, would be unable to extract the information from the message. The common technique for doing masking is encryption. The encryption is done by using Symmetric key or public key Algorithms. The most commonly used public key algorithms are 1. Rivest Shamir Adelman(RSA and 2 Elliptic Curve cryptography In this paper two different mapping methods of the alphanumeric characters on to the x-y co ordinate of the Elliptic curve defined over a finite field Zp is proposed. The methods are 1 Static (One-to-One Mapping Method and 2 Dynamic (One-to-N Mapping Method. Dynamic mapping method will increase the strength of the Elliptic Cryptosystem. The Results have been attached. The hardness of the elliptic curve discrete logarithm problem (ECDLP is crucial for the security of elliptic curve cryptographic schemes. This report describes the state-of-the-art in mapping the alphanumerical characters on to the x-y coordinates of the elliptic curve points.
Verifiable (t, n) Threshold Signature Scheme Based on Elliptic Curve
WANG Hua-qun; ZHAO Jun-xi; ZHANG Li-jun
2005-01-01
Based on the difficulty of solving the ECDLP (elliptic curve discrete logarithm problem) on the finite field,we present a (t, n) threshold signature scheme and a verifiable key agreement scheme without trusted party. Applying a modified elliptic curve signature equation, we get a more efficient signature scheme than the existing ECDSA (elliptic curve digital signature algorithm) from the computability and security view. Our scheme has a shorter key, faster computation, and better security.
Polynomial Interpolation in the Elliptic Curve Cryptosystem
Liew K. Jie
2011-01-01
Full Text Available Problem statement: In this research, we incorporate the polynomial interpolation method in the discrete logarithm problem based cryptosystem which is the elliptic curve cryptosystem. Approach: In this study, the polynomial interpolation method to be focused is the Lagrange polynomial interpolation which is the simplest polynomial interpolation method. This method will be incorporated in the encryption algorithm of the elliptic curve ElGamal cryptosystem. Results: The scheme modifies the elliptic curve ElGamal cryptosystem by adding few steps in the encryption algorithm. Two polynomials are constructed based on the encrypted points using Lagrange polynomial interpolation and encrypted for the second time using the proposed encryption method. We believe it is safe from the theoretical side as it still relies on the discrete logarithm problem of the elliptic curve. Conclusion/Recommendations: The modified scheme is expected to be more secure than the existing scheme as it offers double encryption techniques. On top of the existing encryption algorithm, we managed to encrypt one more time using the polynomial interpolation method. We also have provided detail examples based on the described algorithm.
Rational points on elliptic curves
Silverman, Joseph H
2015-01-01
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of this book. Topics covered include the geometry and ...
ELLIPTIC CURVE CRYPTOGRAPHY BASED AUTHENTICATED KEY AGREEMENT WITH PRE-SHARED PASSWORD
Sui Aifen; Lucas C.K.Hui; Yang Yixian; K.P.Chow
2005-01-01
Based on elliptic curve Diffie-Hellman algorithm, an Elliptic Curve Authenticated Key Agreement (ECAKA) protocol with pre-shared password is proposed. Its security relies on the Elliptic Curve Discrete Logarithm Problem (ECDLP). It provides identity authentication,key validation and perfect forward secrecy, and it can foil man-in-the-middle attacks.
无
2009-01-01
We prove that (i) rank(K2(E)) 1 for all elliptic curves E defined over Q with a rational torsion point of exact order N 4; (ii) rank(K2(E)) 1 for all but at most one R-isomorphism class of elliptic curves E defined over Q with a rational torsion point of exact order 3. We give some sufficient conditions for rank(K2(EZ)) 1.
JI QingZhong; QIN HouRong
2009-01-01
We prove that (i) rank(K2(E))≥1 for all elliptic curves E defined over Q with a rational torsion point of exact order N≥ 4;(ii) rank(K2(E))≥1 for all but at most one R-isomorphism class of elliptic curves E defined over Q with a rational torsion point of exact order 3.We give some sufficient conditions for rank(K2(Ez))≥1.
Flavor Symmetry and Galois Group of Elliptic Curves
Hattori, Chuichiro; Matsuoka, Takeo; Nakanishi, Kenichi
2009-01-01
A new approach to the generation structure of fermions is proposed. We consider a brane configuration in which the brane intersection yields a two-torus in the extra space. It is assumed that the two-torus is discretized and is given by the torsion points of the elliptic curve over Q . We direct our attention to the arithmetic structure of the elliptic curve with complex multiplication (CM). In our approach the flavor symmetry including the R-parity has its origin in the Galois group of elliptic curves with CM. We study the possible types of the Galois group. The Galois group is shown to be an extension of Z_2 by some abelian group. A phenomenologically viable example of the Galois group is presented, in which the characteristic texture of fermion masses and mixings is reproduced and the mixed-anomaly conditions are satisfied.
Spectral Curves of Operators with Elliptic Coefficients
J. Chris Eilbeck
2007-03-01
Full Text Available A computer-algebra aided method is carried out, for determining geometric objects associated to differential operators that satisfy the elliptic ansatz. This results in examples of Lamé curves with double reduction and in the explicit reduction of the theta function of a Halphen curve.
Conditionally bounding analytic ranks of elliptic curves
Bober, Jonathan W
2011-01-01
We describe a method for bounding the rank of an elliptic curve under the assumptions of the Birch and Swinnerton-Dyer conjecture and the generalized Riemann hypothesis. As an example, we compute, under these conjectures, exact upper bounds for curves which are known to have rank at least as large as 20, 21, 22, 23, and 24. For the known curve of rank at least 28, we get a bound of 30.
A New Digital Multilevel Proxy Signature Scheme Based on Elliptic Curve Cryptography
QIN Yanlin; WU Xiaoping
2006-01-01
Based on the analysis of elliptic curve digital signature algorithm(ECDSA),aiming at multilevel proxy signature in which the original signer delegates the digital signature authority to several proxies and its security demands, a new multilevel proxy signature scheme based on elliptic curve discrete logarithm problem(ECDLP) is presented and its security are proved.
Pseudorandom Bits From Points on Elliptic Curves
Farashahi, Reza R
2010-01-01
Let $\\E$ be an elliptic curve over a finite field $\\F_{q}$ of $q$ elements, with $\\gcd(q,6)=1$, given by an affine Weierstra\\ss\\ equation. We also use $x(P)$ to denote the $x$-component of a point $P = (x(P),y(P))\\in \\E$. We estimate character sums of the form
Elliptic Tales Curves, Counting, and Number Theory
Ash, Avner
2012-01-01
Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. The Clay Mathematics Institute is offering a prize of 1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from
Classification of Isomonodromy Problems on Elliptic Curves
Levin, A; Zotov, A
2013-01-01
We consider the isomonodromy problems for flat $G$-bundles over punctured elliptic curves $\\Sigma_\\tau$ with regular singularities of connections at marked points. The bundles are classified by their characteristic classes. These classes are elements of the second cohomology group $H^2(\\Sigma_\\tau,{\\mathcal Z}(G))$, where ${\\mathcal Z}(G)$ is the center of $G$. For any complex simple Lie group $G$ and arbitrary class we define the moduli space of flat bundles, and in this way construct the monodromy preserving equations in the Hamiltonian form and their Lax representations. In particular, they include the Painlev\\'e VI equation, its multicomponent generalizations and elliptic Schlesinger equations. The general construction is described for punctured curves of arbitrary genus. We extend the Beilinson-Drinfeld description of the moduli space of Higgs bundles to the case of flat connections. This local description allows us to establish the Symplectic Hecke Correspondence for a wide class of the monodromy preser...
The Selmer Groups of Elliptic Curves
Fu Zheng WANG
2003-01-01
Let E/K be an elliptic curve with K-rational p-torsion points. The p-Selmer group of Eis described by the image of a map λK and hence an upper bound of its order is given in terms of theclass numbers of the S-ideal class group of K and the p-division field of E.
A Review on Elliptic Curve Cryptography for Embedded Systems
Afreen, Rahat
2011-01-01
Importance of Elliptic Curves in Cryptography was independently proposed by Neal Koblitz and Victor Miller in 1985.Since then, Elliptic curve cryptography or ECC has evolved as a vast field for public key cryptography (PKC) systems. In PKC system, we use separate keys to encode and decode the data. Since one of the keys is distributed publicly in PKC systems, the strength of security depends on large key size. The mathematical problems of prime factorization and discrete logarithm are previously used in PKC systems. ECC has proved to provide same level of security with relatively small key sizes. The research in the field of ECC is mostly focused on its implementation on application specific systems. Such systems have restricted resources like storage, processing speed and domain specific CPU architecture.
Principal $G$-bundles over elliptic curves
Friedman, R; Witten, Edward; Friedman, Robert; Morgan, John W.; Witten, Edward
1997-01-01
Let $G$ be a simple and simply connected complex Lie group. We discuss the moduli space of holomorphic semistable principal $G$-bundles over an elliptic curve $E$. In particular, we give a new proof of a theorem of Looijenga and Bernshtein-Shvartsman, that the moduli space is a weighted projective space. The method of proof is to study the deformations of certain unstable bundles coming from special maximal parabolic subgroups of $G$. We also discuss the associated automorphism sheaves and universal bundles, as well as the relation between various universal bundles and spectral covers.
A blind digital signature scheme using elliptic curve digital signature algorithm
BÜTÜN, İsmail; DEMİRER, Mehmet
2013-01-01
In this study, we propose a blind digital signature (BDS) scheme based on the elliptic curve digital signature algorithm that increases the performance significantly. The security of our scheme is based on the difficulty of the elliptic curve discrete algorithm problem. Therefore, it offers much smaller key lengths for the desired security levels, along with much faster cryptographic processes, leading to fewer hardware and software requirements. According to our simulation results, ...
Encryption of Data using Elliptic Curve over Finite fields
Kumar, D Sravana; Chandrasekhar, A; 10.5121/ijdps.2012.3125
2012-01-01
Cryptography is the study of techniques for ensuring the secrecy and authentication of the information. Public-key encryption schemes are secure only if the authenticity of the public-key is assured. Elliptic curve arithmetic can be used to develop a variety of elliptic curve cryptography (ECC) schemes including key exchange, encryption and digital signature. The principal attraction of elliptic curve cryptography compared to RSA is that it offers equal security for a smaller key-size, thereby reducing the processing overhead. In the present paper we propose a new encryption algorithm using some Elliptic Curve over finite fields
Elliptic curves and positive definite ternary forms
WANG; Xueli(
2001-01-01
［1］Pei Dingyi, Rosenberger, G. , Wang Xueli, The eligible numbers of positive definite ternary forms, Math. Zeitschriften,2000, 235: 479－497.［2］Wang Xueli, Pei Dingyi, Modular forms of 3/2 weight and one conjecture of Kaplansky, preprint.［3］Jones, B., The regularity of a genus of positive ternary quadratic forms, Trans. Amer. Math. Soc., 1931, 33: 111－124.［4］Kaplansky, I., The first nontrivial genus of positive definite ternary forms, Math. Comp., 1995, 64: 341－345.［5］Antoniadis, J. A., Bungert, M., Frey, G., Properties of twists of elliptic curves, J. Reine Angew Math., 1990, 405: 1－28.
Amicable pairs and aliquot cycles for elliptic curves
Stange, Katherine E
2009-01-01
An amicable pair for an elliptic curve E/Q is a pair of primes (p,q) of good reduction for E satisfying #E(F_p) = q and #E(F_q) = p. In this paper we study elliptic amicable pairs and analogously defined longer elliptic aliquot cycles. We show that there exist elliptic curves with arbitrarily long aliqout cycles, but that CM elliptic curves (with j not 0) have no aliqout cycles of length greater than two. We give conjectural formulas for the frequency of amicable pairs. For CM curves, the derivation of precise conjectural formulas involves a detailed analysis of the values of the Grossencharacter evaluated at a prime ideal P in End(E) having the property that #E(F_P) is prime. This is especially intricate for the family of curves with j = 0.
ISOGENOUS OF THE ELLIPTIC CURVES OVER THE RATIONALS
Abderrahmane Nitaj
2002-01-01
An elliptic curve is a pair (E, O), where E is a smooth projective curve of genus 1 and O is a point of E, called the point at infinity. Every elliptic curve can be given by a Weierstrass equationE: y2 + a1xy + a3y = x3 + a2x2 + a4x + a6.Let Q be the set of rationals. E is said to be difined over Q if the coefficients ai, i =1, 2, 3, 4, 6 are rationals and O is defined over Q.Let E/Q be an elliptic curve and let E(Q)tors be the torsion group of points of E defined over Q. The theorem of Mazur asserts that E(Q)tors is one of the following 15 groupsWe say that an elliptic curve E′/Q is isogenous to the elliptic curve E if there is an isogeny,i.e. a morphism φ: E → E′ such that φ(O) = O, where O is the point at infinity.We give an explicit model of all elliptic curves for which E(Q)tors is in the form Z/mZ where m = 9, 10, 12 or Z/2Z × Z/2mZ where m = 4, according to Mazur's theorem.Morever, for every family of such elliptic curves, we give an explicit model of all their isogenous curves with cyclic kernels consisting of rational points.
Cryptanalysis and Improvement of Signcryption Schemes on Elliptic Curves
LI Xiang-xue; CHEN Ke-fei; LI Shi-qun
2005-01-01
In this paper, we analyze two signcryption schemes on elliptic curves proposed by Zheng Yu-liang and Hideki Imai. We point out a serious problem with the schemes that the elliptic curve based signcryption schemes lose confidentiality to gain non-repudiation. We also propose two improvement versions that not only overcome the security leak inherent in the schemes but also provide public verifiability or forward security. Our improvement versions require smaller computing cost than that required by signature-thenencryption methods.
Software Implementation of Elliptic Curve Encryption over Binary Field
ZHANG Xianfeng; QIN Zhiguang; ZHOU Shijie; LIU Jinde
2003-01-01
The mathematical theory for elliptic curve encryption based on optimal normal basis (ONB) over Fm2 is introduced. Then an elliptic curve cryptography(ECC) based encryption scheme is analyzed and designed. The mechanism for key exchange based on Diffie-Hellman is described in details for further applications. Based on these theoretic foundations, the software based on ECC is developed and an application is provided. The software is characterized by excellent security as well as high efficiency.
On algebraically integrable differential operators on an elliptic curve
Etingof, Pavel
2010-01-01
We discuss explicit classification of algebraically integrable (i.e., finite gap) differential operators on elliptic curves with one and several poles. After giving a new exposition of some known results (based on differential Galois theory), we describe a conjectural classification of third order algebraically integrable operators with one pole (obtained using Maple), in particular discovering new "isolated" ones, living on special elliptic curves defined over $\\Bbb Q$. We also discuss algebraically integrable operators with several poles, with and without symmetries, and connect them to elliptic Calogero-Moser systems (in the case with symmetries, to the crystallographic ones, introduced recently by Felder, Ma, Veselov, and the first author).
Digital Multi-Signature Scheme Based on the Elliptic Curve Cryptosystem
Tzer-Shyong Chen; Kuo-Hsuan Huang; Yu-Fang Chung
2004-01-01
In the study,the digital multi-signature scheme,constructed by the integration of one-way hash function and identification scheme,are proposed based on the elliptic curve cryptosystem(ECC).To the efficiency in performance,the ECC has been generally regarded as positive; and the security caused by the Elliptic Curve Discrete Logarithm Problem(ECDLP)is highly also taken highly important.The main characteristic of the proposed scheme is that the length of the multi-signature is fixed rather than changeable and it will not increase with the number of group members.
A Fair E-Cash Scheme Based on Elliptic Curve Cryptography
WANG Changji; WU Jianping; DUAN Haixin
2004-01-01
A new fair off-line electronic cash scheme on elliptic curve cryptography was presented. The new scheme is more efficient than those by extending fair off-line electronic cash scheme from finite field into elliptic curve cryptography and introducing a new elliptic curve discrete logarithm assumption. The expiry date and denomination are embedded into the blindly signed coin by integrating partially blind signature with restrictive blind signature. A bank need not use different public keys for different coin values, shops and users need not carry a list of bank's public keys to verify in their electronic wallet. At the same time, the bank just needs to keep undue electronic coins for double spending check in his database, thus bank's database can be dramatically reduced.
Implementation of Elliptic Curve Cryptography in Binary Field
Susantio, D. R.; Muchtadi-Alamsyah, I.
2016-04-01
Currently, there is a steadily increasing demand of information security, caused by a surge in information flow. There are many ways to create a secure information channel, one of which is to use cryptography. In this paper, we discuss the implementation of elliptic curves over the binary field for cryptography. We use the simplified version of the ECIES (Elliptic Curve Integrated Encryption Scheme). The ECIES encrypts a plaintext by masking the original message using specified points on the curve. The encryption process is done by separating the plaintext into blocks. Each block is then separately encrypted using the encryption scheme.
Zeta Functions for Elliptic Curves I. Counting Bundles
Weng, Lin
2012-01-01
To count bundles on curves, we study zetas of elliptic curves and their zeros. There are two types, i.e., the pure non-abelian zetas defined using moduli spaces of semi-stable bundles, and the group zetas defined for special linear groups. In lower ranks, we show that these two types of zetas coincide and satisfy the Riemann Hypothesis. For general cases, exposed is an intrinsic relation on automorphism groups of semi-stable bundles over elliptic curves, the so-called counting miracle. All this, together with Harder-Narasimhan, Desale-Ramanan and Zagier's result, gives an effective way to count semi-stable bundles on elliptic curves not only in terms of automorphism groups but more essentially in terms of their $h^0$'s. Distributions of zeros of high rank zetas are also discussed.
On some special classes of complex elliptic curves
Canepa, Bogdan
2011-01-01
In this paper we classify the complex elliptic curves $E$ for which there exist cyclic subgroups $C\\leq (E,+)$ of order $n$ such that the elliptic curves $E$ and $E/C$ are isomorphic, where $n$ is a positive integer. Important examples are provided in the last section. Moreover, we answer the following question: given a complex elliptic curve E, when can one find a cyclic subgroup $C$ of order $n$ of $(E,+)$ such that $(E,C)\\sim(\\frac{E}{C},\\frac{E[n]}{C})$, $E[n]$ being the $n$-torsion subgroup of $E$, classifying in this way the fixed points of the action of the Fricke involution on the open modular curves $Y_0(n)$
Binary Sequences from a Pair of Elliptic Curves
CHEN Zhixiong; ZHANG Ning; XIAO Guozhen
2006-01-01
A family of binary sequences were constructed by using an elliptic curve and its twisted curves over finite fields. It was shown that these sequences possess "good" cryptographic properties of 0-1 distribution, long period and large linear complexity. The results indicate that such sequences provide strong potential applications in cryptography.
Eliminating line of sight in elliptic guides using gravitational curving
Klenø, Kaspar H.; Willendrup, Peter Kjær; Bergbäck Knudsen, Erik
2011-01-01
result in a breakdown of the geometrical focusing mechanism inherent to the elliptical shape, resulting in unwanted reflections and loss of transmission. We present a new and yet untried idea by curving a guide in such a way as to follow the ballistic curve of a neutron in the gravitational field, while...
Advanced topics in the arithmetic of elliptic curves
Silverman, Joseph H
1994-01-01
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of can...
Steinitz class of elliptic curves with complex multilication
无
2000-01-01
Let E be any elliptic curve having complex multiplication by the ring CK of integers of the quadratic number field K= Q(- D). Let H be the Hilbert class field of K. The Mordell-Weil group E(H) of H-rational points is a module over the Dedekind domain CK, its structure depends on its Steinitz class. Here the Steinits class is determined when D is any prime number. This result advances the result for the specific elliptic curves when D=10.A general theorem on structure of modules over Dedekind domain is also proposed.
An Elliptic Curve-based Signcryption Scheme with Forward Secrecy
Toorani, Mohsen; 10.3923/jas.2009.1025.1035
2010-01-01
An elliptic curve-based signcryption scheme is introduced in this paper that effectively combines the functionalities of digital signature and encryption, and decreases the computational costs and communication overheads in comparison with the traditional signature-then-encryption schemes. It simultaneously provides the attributes of message confidentiality, authentication, integrity, unforgeability, non-repudiation, public verifiability, and forward secrecy of message confidentiality. Since it is based on elliptic curves and can use any fast and secure symmetric algorithm for encrypting messages, it has great advantages to be used for security establishments in store-and-forward applications and when dealing with resource-constrained devices.
A SECURE PROXY SIGNATURE SCHEME BASED ON ELLIPTIC CURVE CRYPTOSYSTEM
Hu Bin; Jin Chenhui
2006-01-01
Proxy signature is a special digital signature which enables a proxy signer to sign messages on behalf of the original signer. This paper proposes a strongly secure proxy signature scheme and a secure multi-proxy signature scheme based on elliptic curve cryptosystem. Contrast with universal proxy signature schemes, they are secure against key substitute attack even if there is not a certificate authority in the system,and also secure against the original signer's forgery attack. Furthermore, based on the elliptic curve crypto system, they are more efficient and have smaller key size than other system. They can be used in electronics transaction and mobile agent environment.
Galois Lines for Normal Elliptic Space Curves
Ma. Cristina Lumakin Duyaguit; Hisao Yoshihara
2005-01-01
Let C be a curve, and l and lO be lines in the projective three space P3.Consider a projection πl: P3... → lO with center l, where l ∩ lO = 0. Restricting πl to C,we obtain a morphism πl |C: C → lO and an extension of fields (πl|C)*: k(lO) → k(C). If this extension is Galois, then l is said to be a Galois line. We study the defining equations,automorphisms and the Galois lines for quartic curves, and give some applications to the theory ofplane quartic curves.
New digital signature protocol based on elliptic curves
Abid, Ounasser; Ettanfouhi, Jaouad; Khadir, Omar
2013-01-01
In this work, a new digital signature based on elliptic curves is presented. We established its efficiency and security. The method, derived from a variant of ElGamal signature scheme, can be seen as a secure alternative protocol if known systems are completely broken.
Computing endomorphism rings of elliptic curves under the GRH
Bisson, Gaetan
2011-01-01
We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann hypothesis. Additionally, we improve the asymptotic complexity of previously known, heuristic, subexponential methods by describing a faster isogeny-computing routine.
On Elliptic Curves Via Heron Triangles and Diophantine Triples
F. Izadi
2014-09-01
Full Text Available In this article, we construct families of elliptic curves arising from the Heron triangles and Diophantine triples with the Mordell-Weil torsion subgroup of Z/2Z × Z/2Z. These families have ranks at least 2 and 3, respectively, and contain particular examples with rank equal to 7
Singular Fibers in Barking Families of Degenerations of Elliptic Curves
Okuda, Takayuki
2012-01-01
Takamura established a theory on splitting families of degenerations of complex curves. He introduced a powerful method for constructing a splitting family, called a barking family, in which there appear not only a singular fiber over the origin but also singular fibers over other points, called subordinate fibers. In this paper, for the case of degenerations of elliptic curves, we determine the types of these subordinate fibers.
Efficient method for finding square roots for elliptic curves over OEF
Abu-Mahfouz, Adnan M
2009-01-01
Full Text Available Elliptic curve cryptosystems like others public key encryption schemes, require computing a square roots modulo a prime number. The arithmetic operations in elliptic curve schemes over Optimal Extension Fields (OEF) can be efficiently computed...
Two-Center Black Holes, Qubits and Elliptic Curves
Lévay, Péter
2011-01-01
We relate the U-duality invariants characterizing two-center extremal black hole solutions in the stu, st^2 and t^3 models of N=2, d=4 supergravity to the basic invariants used to characterize entanglement classes of four-qubit systems. For the elementary example of a D0D4-D2D6 composite in the t^3 model we illustrate how these entanglement invariants are related to some of the physical properties of the two-center solution. Next we show that it is possible to associate elliptic curves to charge configurations of two-center composites. The hyperdeterminant of the hypercube, a four-qubit polynomial invariant of order 24 with 2894276 terms, is featuring the j invariant of the elliptic curve. We present some evidence that this quantity and its straightforward generalization should play an important role in the physics of two-center solutions.
On Lehmer's Conjecture for Polynomials and for Elliptic Curves
Silverman, Joseph H
2010-01-01
A number of authors have proven explicit versions of Lehmer's conjecture for polynomials whose coefficients are all congruent to 1 modulo m. We prove a similar result for polynomials f(X) that are divisible in (Z/mZ)[X] by a polynomial of the form 1+X+...+X^n for some n > \\epsilon*deg(f). We also formulate and prove an analogous statement for elliptic curves.
A Directly Public Verifiable Signcryption Scheme based on Elliptic Curves
Toorani, Mohsen; 10.1109/ISCC.2009.5202242
2010-01-01
A directly public verifiable signcryption scheme is introduced in this paper that provides the security attributes of message confidentiality, authentication, integrity, non-repudiation, unforgeability, and forward secrecy of message confidentiality. It provides the attribute of direct public verifiability so anyone can verify the signcryption without any need for any secret information from the corresponding participants. The proposed scheme is based on elliptic curve cryptography and is so suitable for environments with resource constraints.
Isomorphism and Generation of Montgomery-Form Elliptic Curves Suitable for Cryptosystems
LIU Duo; SONG Tao; DAI Yiqi
2005-01-01
Many efficient algorithms of Montgomery-form elliptic curve cryptology have been investigated recently. At present, there are no reported studies of the isomorphic class of the Montgomery-form elliptic curve over a finite field. This paper investigates the isomorphism of Montgomery-form elliptic curves via the isomorphism of Weierstrass-form elliptic curves and gives a table of (nearly) all the forms of Montgomery-form elliptic curves suitable for cryptographic usage. Then, an algorithm for generating a secure elliptic curve with Montgomery-form is presented. The most important advantages of the new algorithm are that it avoids the transformation from an elliptic curve's Weierstrass-form to its Montgomery-form, and that it decreases the probability of collision. So, the proposed algorithem is quicker, simpler, and more efficient than the old ones.
USING MODIFIED STERN SERIES FOR DIGITAL SIGNATURE AUTHENTICATION IN ELLIPTIC CURVE CRYPTOGRAPHY
Latha Parthiban
2011-12-01
Full Text Available This paper presents the generation of digital signature along with message recovery based on Elliptic Curve Cryptography (ECC and knapsack algorithm. In digital signature along with message recovery scheme, signature alone is sent and message is recovered from the signature (r, s. ECC provides greater security with less key size, when compared to integer factorization and discrete logarithm system. As the strength of knapsack algorithm depends on the selection of the series, the proposed algorithm uses modified Stern series which not only reduces the time complexity but also provides better security.
Cryptography on elliptic curves over p-adic number fields
XU MaoZhi; ZHAO ChunLai; FENG Min; REN ZhaoRong; YE JiQing
2008-01-01
In this paper we introduce a cryptosystem based on the quotient groups of the group of rational points of an elliptic curve defined over p-adic number field. Some addi-tional parameters are taken in this system, which have an advantage in performing point multiplication while keeping the security of ECC over finite fields. We give a method to select generators of the cryptographic groups, and give a way to represent the elements of the quotient groups with finitely bounded storage by establishing a bijection between these elements and their approximate coordinates. The addition formula under this representation is also presented.
Distribution of some sequences of points on elliptic curves
Lange, Tanja; Shparlinski, Igor
2007-01-01
We estimate character sums over points on elliptic curves over a finite field of q elements. Pseudorandom sequences can be constructed by taking linear combinations with small coefficients (for example, from the set {−1, 0, 1}) of a fixed vector of points, which forms the seed of the generator. W...... consider several particular cases of this general approach which are of special practical interest and have occurred in the literature. For each of them we show that the resulting sequence has good uniformity of distribution properties....
A Secure Elliptic Curve-Based RFID Protocol
Santi Martínez; Magda Valls; Concepcó Roig; Josep M. Miret; Francesc Giné
2009-01-01
Nowadays, the use of Radio Frequency Identification (RFID) systems in industry and stores has increased.Nevertheless, some of these systems present privacy problems that may discourage potential users. Hence, high confidence and efficient privacy protocols are urgently needed. Previous studies in the literature proposed schemes that are proven to be secure, but they have scalability problems. A feasible and scalable protocol to guarantee privacy is presented in this paper.The proposed protocol uses elliptic curve cryptography combined with a zero knowledge-based authentication scheme. An analysis to prove the system secure, and even forward secure is also provided.
Monopoles and Modifications of Bundles over Elliptic Curves
Andrey M. Levin
2009-06-01
Full Text Available Modifications of bundles over complex curves is an operation that allows one to construct a new bundle from a given one. Modifications can change a topological type of bundle. We describe the topological type in terms of the characteristic classes of the bundle. Being applied to the Higgs bundles modifications establish an equivalence between different classical integrable systems. Following Kapustin and Witten we define the modifications in terms of monopole solutions of the Bogomolny equation. We find the Dirac monopole solution in the case R × (elliptic curve. This solution is a three-dimensional generalization of the Kronecker series. We give two representations for this solution and derive a functional equation for it generalizing the Kronecker results. We use it to define Abelian modifications for bundles of arbitrary rank. We also describe non-Abelian modifications in terms of theta-functions with characteristic.
Constructing elliptic curve isogenies in quantum subexponential time
Childs, Andrew M; Soukharev, Vladimir
2010-01-01
Given two elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit an isogeny between them, but finding such an isogeny is believed to be computationally difficult. The fastest known classical algorithm takes exponential time, and prior to our work no faster quantum algorithm was known. Recently, public-key cryptosystems based on the presumed hardness of this problem have been proposed as candidates for post-quantum cryptography. In this paper, we give a subexponential-time quantum algorithm for constructing isogenies, assuming the Generalized Riemann Hypothesis (but with no other assumptions). This result suggests that isogeny-based cryptosystems may be uncompetitive with more mainstream quantum-resistant cryptosystems such as lattice-based cryptosystems. As part of our algorithm, we also obtain a second result of independent interest: we provide a new subexponential-time classical algorithm for evaluating a horizontal isogeny given its kernel i...
On the average exponent of elliptic curves modulo $p$
Freiberg, Tristan
2012-01-01
Given an elliptic curve $E$ defined over $\\mathbb{Q}$ and a prime $p$ of good reduction, let $\\tilde{E}(\\mathbb{F}_p)$ denote the group of $\\mathbb{F}_p$-points of the reduction of $E$ modulo $p$, and let $e_p$ denote the exponent of said group. Assuming a certain form of the Generalized Riemann Hypothesis (GRH), we study the average of $e_p$ as $p \\le X$ ranges over primes of good reduction, and find that the average exponent essentially equals $p\\cdot c_{E}$, where the constant $c_{E} > 0$ depends on $E$. For $E$ without complex multiplication (CM), $c_{E}$ can be written as a rational number (depending on $E$) times a universal constant. Without assuming GRH, we can determine the average exponent when $E$ has CM, as well as give an upper bound on the average in the non-CM case.
A THRESHOLD BLIND SIGNATURE FROM WEIL PAIRING ON ELLIPTIC CURVES
Cheng Xiangguo; Xu Weidong; Wang Xinmei
2006-01-01
The idea behind a (t, n) threshold blind signature is that a user can ask at least t out ofn players of a group to cooperate to generate a signature for a message without revealing its content. This paper first presents a new blind signature scheme from Weil pairing on elliptic curves. Based on this scheme, a threshold blind signature scheme is proposed. It is efficient and has the security properties of robustness and unforgeability. In the proposed scheme, the group manger is introduced to take the role of distributing the group secret key to each player. However, he cannot forge the players to generate partial blind signatures (Each partial blind signature depends on not only the secret key of the player, but also a random number the player picks). Compared with a threshold signature with a trusted third party, its advantage is obvious; Compared with a threshold signature without a trusted third party, it is more simple and efficient.
String Theory on Elliptic Curve Orientifolds and KR-Theory
Doran, Charles; Méndez-Diez, Stefan; Rosenberg, Jonathan
2015-04-01
We analyze the brane content and charges in all of the orientifold string theories on space-times of the form , where E is an elliptic curve with holomorphic or anti-holomorphic involution. Many of these theories involve "twistings" coming from the B-field and/or sign choices on the orientifold planes. A description of these theories from the point of view of algebraic geometry, using the Legendre normal form, naturally divides them into three groupings. The physical theories within each grouping are related to one another via sequences of T-dualities. Our approach agrees with both previous topological calculations of twisted KR-theory and known physics arguments, and explains how the twistings originate from both a mathematical and a physical perspective.
Holomorphic Principal Bundles Over Elliptic Curves III: Singular Curves and Fibrations
2001-01-01
Let G be a simple and simply connected complex linear algebraic group. In this paper, we discuss the generalization of the parabolic construction of holomorphic principal G-bundles over a smooth elliptic curve to the case of a singular curve of arithmetic genus one and to a fibration of Weierstrass cubics over a base B. Except for G of type E_8, the method gives a family of weighted projective spaces associated to a sum of line bundles over B. Working with the universal family of Weierstrass ...
On several families of elliptic curves with arbitrary large Selmer groups
无
2010-01-01
In this paper,we calculate the ()-Selmer groups S()(E/Q) and S()(E/Q) of elliptic curves y2 = x(x + εpD)(x + εqD) via the descent method.In particular,we show that the Selmer groups of several families of such elliptic curves can be arbitrary large.
Addition Sequence Method of Scalar Multiplication of Elliptic Curve over OEF
LIU Duo; DAI Yi-qi
2005-01-01
A new elliptic curve scalar multiplication algorithm is proposed. The algorithm uses the Frobenius map on optimal extension field (OEF) and addition sequence. We introduce a new algorithm on generating addition sequence efficiently and also give some analysis about it. Based on this algorithm, a new method of computing scalar multiplication of elliptic curve over an OEF is presented. The new method is more efficient than the traditional scalar multiplication algorithms of elliptic curve over OEF. The comparisons of traditional method and the new method are also given.
TWO FAST ALGORITHMS FOR COMPUTING POINT SCALAR MULTIPLICATIONS ON ELLIPTIC CURVES
You Lin; Wen Qiaoyan; Xu Maozhi
2004-01-01
The key operation in Elliptic Curve Cryptosystems(ECC) is point scalar multiplication. Making use of Frobenius endomorphism, Miiller and Smart proposed two efficient algorithms for point scalar multiplications over even or odd finite fields respectively. This paper reduces thementation of our Algorithm 1 in Maple for a given elliptic curve shows that it is at least as twice fast as binary method. By setting up a precomputation table, Algorithm 2, an improved version of Algorithm 1, is proposed. Since the time for the precomputation table can be considered free,Algorithm 2 is about (3/2) log2 q - 1 times faster than binary method for an elliptic curve over Fq.
Sahinoglu, Hatice
2011-01-01
This paper is a complementary to the work Rosen-Silverman, which derives a criteria on the number fields for the independence of Heegner points associated to them on non-CM elliptic curves. This paper shows that the same criteria holds for CM elliptic curves. Generalisation to Heegner points associated to a fixed conductor order of the fields can also be found in this paper.
A Heuristic Method of Scalar Multiplication of Elliptic Curve over OEF
LIU Duo; LUO Ping; DAI Yi-qi
2006-01-01
Elliptic curve cryptosystem is the focus of public key cryptology nowadays, for it has many advantages RSA lacks. This paper introduced a new heuristic algorithm on computing multiple scalar multiplications of a given point. Based on this algorithm, a new method of computing scalar multiplication of elliptic curve over optimal extension field (OEF) using Frobenius map was presented. The new method is more efficient than the traditional ones. In the last part of this paper, the comparison was given in the end.
Elliptic Curve Cryptography with Security System in Wireless Sensor Networks
Huang, Xu; Sharma, Dharmendra
2010-10-01
The rapid progress of wireless communications and embedded micro-electro-system technologies has made wireless sensor networks (WSN) very popular and even become part of our daily life. WSNs design are generally application driven, namely a particular application's requirements will determine how the network behaves. However, the natures of WSN have attracted increasing attention in recent years due to its linear scalability, a small software footprint, low hardware implementation cost, low bandwidth requirement, and high device performance. It is noted that today's software applications are mainly characterized by their component-based structures which are usually heterogeneous and distributed, including the WSNs. But WSNs typically need to configure themselves automatically and support as hoc routing. Agent technology provides a method for handling increasing software complexity and supporting rapid and accurate decision making. This paper based on our previous works [1, 2], three contributions have made, namely (a) fuzzy controller for dynamic slide window size to improve the performance of running ECC (b) first presented a hidden generation point for protection from man-in-the middle attack and (c) we first investigates multi-agent applying for key exchange together. Security systems have been drawing great attentions as cryptographic algorithms have gained popularity due to the natures that make them suitable for use in constrained environment such as mobile sensor information applications, where computing resources and power availability are limited. Elliptic curve cryptography (ECC) is one of high potential candidates for WSNs, which requires less computational power, communication bandwidth, and memory in comparison with other cryptosystem. For saving pre-computing storages recently there is a trend for the sensor networks that the sensor group leaders rather than sensors communicate to the end database, which highlighted the needs to prevent from the man
Seiberg-Witten curves and double-elliptic integrable systems
Aminov, G; Mironov, A; Morozov, A; Zotov, A
2014-01-01
An old conjecture claims that commuting Hamiltonians of the double-elliptic integrable system are constructed from the theta-functions associated with Riemann surfaces from the Seiberg-Witten family, with moduli treated as dynamical variables and the Seiberg-Witten differential providing the pre-symplectic structure. We describe a number of theta-constant equations needed to prove this conjecture for the $N$-particle system. These equations provide an alternative method to derive the Seiberg-Witten prepotential and we illustrate this by calculating the perturbative contribution. We provide evidence that the solutions to the commutativity equations are exhausted by the double-elliptic system and its degenerations (Calogero and Ruijsenaars systems). Further, the theta-function identities that lie behind the Poisson commutativity of the three-particle Hamiltonians are proven.
Seiberg-Witten curves and double-elliptic integrable systems
Aminov, G.; Braden, H. W.; Mironov, A.; Morozov, A.; Zotov, A.
2015-01-01
An old conjecture claims that commuting Hamiltonians of the double-elliptic integrable system are constructed from the theta-functions associated with Riemann surfaces from the Seiberg-Witten family, with moduli treated as dynamical variables and the Seiberg-Witten differential providing the pre-symplectic structure. We describe a number of theta-constant equations needed to prove this conjecture for the N-particle system. These equations provide an alternative method to derive the Seiberg-Witten prepotential and we illustrate this by calculating the perturbative contribution. We provide evidence that the solutions to the commutativity equations are exhausted by the double-elliptic system and its degenerations (Calogero and Ruijsenaars systems). Further, the theta-function identities that lie behind the Poisson commutativity of the three-particle Hamiltonians are proven.
Collisions in Fast Generation of Ideal Classes and Points on Hyperelliptic and Elliptic Curves
Lange, Tanja; Shparlinski, Igor
2005-01-01
Koblitz curves have been proposed to quickly generate random ideal classes and points on hyperelliptic and elliptic curves. To obtain a further speed-up a different way of generating these random elements has recently been proposed. In this paper we give an upper bound on the number of collisions...
Discreteness of Curved Spacetime from GUP
Ahmad Adel Abutaleb
2013-01-01
Full Text Available Diverse theories of quantum gravity expect modifications of the Heisenberg's uncertainty principle near the Planck scale to a so-called Generalized uncertainty principle (GUP. It was shown by some authors that the GUP gives rise to corrections to the Schrodinger , Klein-Gordon, and Dirac equations. By solving the GUP corrected equations, the authors arrived at quantization not only of energy but also of box length, area, and volume. In this paper, we extend the above results to the case of curved spacetime (Schwarzschild metric. We showed that we arrived at the quantization of space by solving Dirac equation with GUP in this metric.
FPGA Based High Speed SPA Resistant Elliptic Curve Scalar Multiplier Architecture
Khalid Javeed
2016-01-01
Full Text Available The higher computational complexity of an elliptic curve scalar point multiplication operation limits its implementation on general purpose processors. Dedicated hardware architectures are essential to reduce the computational time, which results in a substantial increase in the performance of associated cryptographic protocols. This paper presents a unified architecture to compute modular addition, subtraction, and multiplication operations over a finite field of large prime characteristic GF(p. Subsequently, dual instances of the unified architecture are utilized in the design of high speed elliptic curve scalar multiplier architecture. The proposed architecture is synthesized and implemented on several different Xilinx FPGA platforms for different field sizes. The proposed design computes a 192-bit elliptic curve scalar multiplication in 2.3 ms on Virtex-4 FPGA platform. It is 34% faster and requires 40% fewer clock cycles for elliptic curve scalar multiplication and consumes considerable fewer FPGA slices as compared to the other existing designs. The proposed design is also resistant to the timing and simple power analysis (SPA attacks; therefore it is a good choice in the construction of fast and secure elliptic curve based cryptographic protocols.
An optimal variance estimate in stochastic homogenization of discrete elliptic equations
Gloria, Antoine; 10.1214/10-AOP571
2011-01-01
We consider a discrete elliptic equation on the $d$-dimensional lattice $\\mathbb{Z}^d$ with random coefficients $A$ of the simplest type: they are identically distributed and independent from edge to edge. On scales large w.r.t. the lattice spacing (i.e., unity), the solution operator is known to behave like the solution operator of a (continuous) elliptic equation with constant deterministic coefficients. This symmetric ``homogenized'' matrix $A_{\\mathrm {hom}}=a_{\\mathrm {hom}}\\operatorname {Id}$ is characterized by $\\xi\\cdot A_{\\mathrm {hom}}\\xi=\\langle(\\xi+\
The Ising model: from elliptic curves to modular forms and Calabi-Yau equations
Bostan, A [INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105 78153 Le Chesnay Cedex (France); Boukraa, S [LPTHIRM and Departement d' Aeronautique, Universite de Blida, Blida (Algeria); Hassani, S; Zenine, N [Centre de Recherche Nucleaire d' Alger, 2 Bd. Frantz Fanon, BP 399, 16000 Alger (Algeria); Van Hoeij, M [Florida State University, Department of Mathematics, 1017 Academic Way, Tallahassee, FL 32306-4510 (United States); Maillard, J-M [LPTMC, UMR 7600 CNRS, Universite de Paris, Tour 23, 5eme etage, Case 121, 4 Place Jussieu, 75252 Paris Cedex 05 (France); Weil, J-A, E-mail: alin.bostan@inria.fr, E-mail: boukraa@mail.univ-blida.dz, E-mail: hoeij@mail.math.fsu.edu, E-mail: maillard@lptmc.jussieu.fr, E-mail: jacques-arthur.weil@unilim.fr, E-mail: njzenine@yahoo.com [XLIM, Universite de Limoges, 123 Avenue Albert Thomas, 87060 Limoges Cedex (France)
2011-01-28
We show that almost all the linear differential operators factors obtained in the analysis of the n-particle contributions of the susceptibility of the Ising model for n {<=} 6 are linear differential operators associated with elliptic curves. Beyond the simplest differential operators factors which are homomorphic to symmetric powers of the second order operator associated with the complete elliptic integral E, the second and third order differential operators Z{sub 2}, F{sub 2}, F{sub 3}, L-tilde {sub 3} can actually be interpreted as modular forms of the elliptic curve of the Ising model. A last order-4 globally nilpotent linear differential operator is not reducible to this elliptic curve, modular form scheme. This operator is shown to actually correspond to a natural generalization of this elliptic curve, modular form scheme, with the emergence of a Calabi-Yau equation, corresponding to a selected {sub 4}F{sub 3} hypergeometric function. This hypergeometric function can also be seen as a Hadamard product of the complete elliptic integral K, with a remarkably simple algebraic pull-back (square root extension), the corresponding Calabi-Yau fourth order differential operator having a symplectic differential Galois group SP(4,C). The mirror maps and higher order Schwarzian ODEs, associated with this Calabi-Yau ODE, present all the nice physical and mathematical ingredients we had with elliptic curves and modular forms, in particular an exact (isogenies) representation of the generators of the renormalization group, extending the modular group SL(2,Z) to a GL(2,Z) symmetry group.
The history of the universe is an elliptic curve
Coquereaux, Robert
2014-01-01
Friedmann-Lemaitre equations with contributions coming from matter, curvature, cosmological constant, and radiation, when written in terms of conformal time u rather than in terms of cosmic time t, can be solved explicitly in terms of standard Weierstrass elliptic functions. The spatial scale factor, the temperature, the densities, the Hubble function, and almost all quantities of cosmological interest (with the exception of t itself) are elliptic functions of u, in particular they are bi-periodic with respect to a lattice of the complex plane, when one takes u complex. After recalling the basics of the theory, we use these explicit expressions, as well as the experimental constraints on the present values of density parameters (we choose for the curvature density a small value in agreement with experimental bounds) to display the evolution of the main cosmological quantities for one real period 2 omega_r of conformal time (the cosmic time t never end but it goes to infinity for a finite value u_f < 2 omeg...
Elliptic Curves of Twin-Primes Over Gauss Field and Diophantine Equations
无
2000-01-01
@@ Let p, q be twin prime numbers with q-p=2 . Consider the elliptic curves E=E : y2 = x (x+σp)(x+σq). (σ=1) (1) E=Eσ is also denoted as E+ or E- when =+1 or -1.Here the Mordell-Weil group and the rank of the elliptic curve Eover the Gaussfield K=Q(2-1) (and over the rationalfield Q) will be determined in several cases; andresults of solutions forrelated Diophantine equations and simultaneous Pellianequations will be given. The arithmetic constructsover Q of the elliptic curve E have been studiedin ［1］, the Selmer groups are determined, results on Mordell- Weil group, rank, Shafarevich-Tate group, and torsion subgroups are also obtained. Results on torsion subgroups in ［2］ will be used here to determine E(K).
The difference between the Weil height and the canonical height on elliptic curves
Silverman, Joseph H.
1990-10-01
Estimates for the difference of the Weil height and the canonical height of points on elliptic curves are used for many purposes, both theoretical and computational. In this note we give an explicit estimate for this difference in terms of the j-invariant and discriminant of the elliptic curve. The method of proof, suggested by Serge Lang, is to use the decomposition of the canonical height into a sum of local heights. We illustrate one use for our estimate by computing generators for the Mordell-Weil group in three examples.
Formula and 2-adic valuation of L(1) of elliptic curves with CM by -3
无
2002-01-01
For the rational integers λ≡1, 3, or 5 (mod 6), considering elliptic curves y2＝x3-2433Dλ over the field (-3), the formula for the value at s=1 of Hecke L-series attached to such elliptic curves, expressed as a finite sum of values of Weierstrass -functions, is obtained. Moreover, when λ≡3 (mod 6), the lower bounds of 2-adic valuations of these values are also obtained. These results are consistent with the predictions of the conjecture of Birch and Swinnerton-Dyer in a sense, and have generalized and advanced some results in recent literature.
Curve counting on elliptically fibered Calabi-Yau 3-folds
Oberdieck, Georg
2016-01-01
Let $X$ be a Calabi-Yau threefold and let $X \\to S$ be an elliptic fibration with integral fibers. We use a derived autoequivalence and wall-crossing to prove a functional equation for the generating series of Pandharipande-Thomas invariants of $X$ over reduced classes in the base. The generating series is expressed as Noether-Lefschetz terms (counting sections and conjectured to be modular forms) times universal Jacobi forms coming from the fiber geometry. Parallel results are proven for the topological Euler characteristic of the moduli spaces. We exhibit applications and compare to known results for the Schoen Calabi-Yau, the product $\\mathrm{K3} \\times E$ and for abelian threefolds. We prove that the generating series of Pandharipande-Thomas invariants for $\\mathrm{K3} \\times E$ with respect to a primitive class on the $\\mathrm{K3}$ is a quasi-Jacobi form. We also discuss the relationship to the Noether-Lefschetz theory of K3 fibered Calabi-Yau threefolds in the case of the STU-model.
Real-Time Exponential Curve Fits Using Discrete Calculus
Rowe, Geoffrey
2010-01-01
An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.
Broken bracelets, Molien series, paraffin wax and an elliptic curve of conductor 48
Amdeberhan, Tewodros; Moll, Victor H
2011-01-01
This paper introduces the concept of necklace binomial coefficients motivated by the enumeration of a special type of sequences. Several properties of these coefficients are described, including a connection between their roots and an elliptic curve. Further links are given to a physical model from quantum mechanical supersymmetry as well as properties of alkane molecules in chemistry.
Elliptic Curves of High Rank with Nontrivial Torsion Group over $\\Q$
2001-01-01
We construct elliptic curves over $\\Q$ of high Mordell--Weil rank, with a nontrivial torsion subgroup. We improve the rank records for the cases $\\Z/2\\Z \\times \\Z/2\\Z$, $\\Z/3\\Z$, $\\Z/4\\Z$, $\\Z/5\\Z$, $\\Z/6\\Z$, $\\Z/7\\Z$ and $\\Z/8\\Z$.
A key distribution scheme using elliptic curve cryptography in wireless sensor networks
Louw, J
2016-12-01
Full Text Available Conference on Industrial Informatics (INDIN), 19-21 July 2016, Futuroscope-Poitiers, France A key distribution scheme using elliptic curve cryptography in wireless sensor networks J. Louw ; G. Niezen ; T. D. Ramotsoela ; A. M. Abu-Mahfouz Abstract...
Integrated x-ray reflectivity measurements of elliptically curved pentaerythritol crystals
Haugh, M. J.; Jacoby, K. D.; Ross, P. W. [National Security Technologies, LLC, Livermore, California 94551 (United States); Regan, S. P.; Magoon, J.; Shoup, M. J. III [Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623 (United States); Barrios, M. A.; Emig, J. A.; Fournier, K. B. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States)
2012-10-15
The elliptically curved pentaerythritol (PET) crystals used in the Supersnout 2 x-ray spectrometer on the National Ignition Facility at Lawrence Livermore National Laboratory have been calibrated photometrically in the range of 5.5-16 keV. The elliptical geometry provides broad spectral coverage and minimizes the degradation of spectral resolution due to the finite source size. The reflectivity curve of the crystals was measured using a x-ray line source. The integrated reflectivity (R{sub I}) and width of its curve ({Delta}{Theta}) were the measurements of major interest. The former gives the spectrometer throughput, and the latter gives the spectrometer resolving power. Both parameters are found to vary considerably with the radius of curvature of the crystal and with spectral energy. The results are attributed to an enhanced mosaic effect due to the increase in curvature. There are also contributions from the crystal cleaving and gluing processes.
An optimal error estimate in stochastic homogenization of discrete elliptic equations
Gloria, Antoine; 10.1214/10-AAP745
2012-01-01
This paper is the companion article to [Ann. Probab. 39 (2011) 779--856]. We consider a discrete elliptic equation on the $d$-dimensional lattice $\\mathbb{Z}^d$ with random coefficients $A$ of the simplest type: They are identically distributed and independent from edge to edge. On scales large w.r.t. the lattice spacing (i.e., unity), the solution operator is known to behave like the solution operator of a (continuous) elliptic equation with constant deterministic coefficients. This symmetric "homogenized" matrix $A_{\\mathrm{hom}}=a_{\\mathrm{hom}}\\mathrm{Id}$ is characterized by $\\xi\\cdot A_{\\mathrm{hom}}\\xi=$ for any direction $\\xi\\in\\mathbb{R}^d$, where the random field $\\phi$ (the "corrector") is the unique solution of $-\
Fourier-Mukai and Nahm transforms for holomorphic triples on elliptic curves
García-Prada, Oscar; Hernández Ruipérez, Daniel; Pioli, Fabio; Tejero Prieto, Carlos
2005-12-01
We define a Fourier-Mukai transform for a triple consisting of two holomorphic vector bundles over an elliptic curve and a homomorphism between them. We prove that in some cases, the transform preserves the natural stability condition for a triple. We also define a Nahm transform for solutions to natural gauge-theoretic equations on a triple—vortices—and explore some of its basic properties. Our approach combines direct methods with dimensional reduction techniques, relating triples over a curve with vector bundles over the product of the curve with the complex projective line.
Wang, Maocai; Dai, Guangming; Choo, Kim-Kwang Raymond; Jayaraman, Prem Prakash; Ranjan, Rajiv
2016-01-01
Information confidentiality is an essential requirement for cyber security in critical infrastructure. Identity-based cryptography, an increasingly popular branch of cryptography, is widely used to protect the information confidentiality in the critical infrastructure sector due to the ability to directly compute the user's public key based on the user's identity. However, computational requirements complicate the practical application of Identity-based cryptography. In order to improve the efficiency of identity-based cryptography, this paper presents an effective method to construct pairing-friendly elliptic curves with low hamming weight 4 under embedding degree 1. Based on the analysis of the Complex Multiplication(CM) method, the soundness of our method to calculate the characteristic of the finite field is proved. And then, three relative algorithms to construct pairing-friendly elliptic curve are put forward. 10 elliptic curves with low hamming weight 4 under 160 bits are presented to demonstrate the utility of our approach. Finally, the evaluation also indicates that it is more efficient to compute Tate pairing with our curves, than that of Bertoni et al.
Dai, Guangming
2016-01-01
Information confidentiality is an essential requirement for cyber security in critical infrastructure. Identity-based cryptography, an increasingly popular branch of cryptography, is widely used to protect the information confidentiality in the critical infrastructure sector due to the ability to directly compute the user’s public key based on the user’s identity. However, computational requirements complicate the practical application of Identity-based cryptography. In order to improve the efficiency of identity-based cryptography, this paper presents an effective method to construct pairing-friendly elliptic curves with low hamming weight 4 under embedding degree 1. Based on the analysis of the Complex Multiplication(CM) method, the soundness of our method to calculate the characteristic of the finite field is proved. And then, three relative algorithms to construct pairing-friendly elliptic curve are put forward. 10 elliptic curves with low hamming weight 4 under 160 bits are presented to demonstrate the utility of our approach. Finally, the evaluation also indicates that it is more efficient to compute Tate pairing with our curves, than that of Bertoni et al. PMID:27564373
An Interoperability Consideration in Selecting Domain Parameters for Elliptic Curve Cryptography
Ivancic, Will (Technical Monitor); Eddy, Wesley M.
2005-01-01
Elliptic curve cryptography (ECC) will be an important technology for electronic privacy and authentication in the near future. There are many published specifications for elliptic curve cryptosystems, most of which contain detailed descriptions of the process for the selection of domain parameters. Selecting strong domain parameters ensures that the cryptosystem is robust to attacks. Due to a limitation in several published algorithms for doubling points on elliptic curves, some ECC implementations may produce incorrect, inconsistent, and incompatible results if domain parameters are not carefully chosen under a criterion that we describe. Few documents specify the addition or doubling of points in such a manner as to avoid this problematic situation. The safety criterion we present is not listed in any ECC specification we are aware of, although several other guidelines for domain selection are discussed in the literature. We provide a simple example of how a set of domain parameters not meeting this criterion can produce catastrophic results, and outline a simple means of testing curve parameters for interoperable safety over doubling.
Special values of L-series attached to two families of CM elliptic curves
无
2001-01-01
Consider two families of elliptic curves y2 x3 D1 x and y2＝ x3 4 3 2＝x3-D1x and y2=x3-2433D22 over fields ( --1 )and ( -3 ) respectively. Formulae expressed by Weierstrass _qfunctions are given for special values of Hecke L-se ries attached to such elliptic curves. The lower bounds of 2-adic and 3-adic valuations of these values of Hecke L-series as well as criteria for reaching these bounds are obtained. These results are consistent with the predictions of the conjec ture of Birch and Swinnerton-Dyer; and some results in recent literature for more special case and for 2-adic valuation are also developed.
On the high rank $\\pi/3$ and $2\\pi/3$-congruent number elliptic curves
Janfada, A S
2011-01-01
In this article, we try to find high rank elliptic curves in the family $E_{n,\\theta}$ defined over $\\mathbb Q$ by the equation $y^2=x^3+2snx-(r^2-s^2)n^2x$, where $0 < \\theta < \\pi$, $\\cos(\\theta) = s/r$ is rational with $0\\leq |s|
Erich Selder
2015-01-01
Full Text Available The correspondence between right triangles with rational sides, triplets of rational squares in arithmetic succession and integral solutions of certain quadratic forms is well-known. We show how this correspondence can be extended to the generalized notions of rational θ-triangles, rational squares occurring in arithmetic progressions and concordant forms. In our approach we establish one-to-one mappings to rational points on certain elliptic curves and examine in detail the role of solutions of the θ-congruent number problem and the concordant form problem associated with nontrivial torsion points on the corresponding elliptic curves. This approach allows us to combine and extend some disjoint results obtained by a number of authors, to clarify some statements in the literature and to answer some hitherto open questions.
A Novel Elliptic curve cryptography Processor using NoC design
Javashi, Hamid
2011-01-01
In this paper, we propose an elliptic curve key generation processor over GF(2m) and GF(P) with Network-on-Chip (NoC) design scheme based on binary scalar multiplication algorithm. Over the Two last decades, Elliptic Curve Cryptography (ECC) has gained increasing acceptance in the industry and the academic community. This interest is mainly caused by the same level of security with relatively small keys provided by ECC comparing to large key size in Rivest Shamir Adleman (RSA). Parallelism can be utilized in different hierarchy levels as shown in many publications. By using NoC, a new method with the reduced latency of point multiplication (with parallel field arithmetic) is introduced in this paper.
High-performance hardware architecture of elliptic curve cryptography processor over GF(2163)
Yong-ping DAN; Xue-cheng ZOU; Zheng-lin LIU; Yu HAN; Li-hua YI
2009-01-01
We propose a novel high-performance hardware architecture of processor for elliptic curve scalar multiplication based on the Lopez-Dahab algorithm over GF(2163) in polynomial basis representation. The processor can do all the operations using an efficient modular arithmetic logic unit, which includes an addition unit, a square and a carefully designed multiplication unit. In the proposed architecture, multiplication, addition, and square can be performed in parallel by the decomposition of computation. The point addition and point doubling iteration operations can be performed in six multiplications by optimization and solution of data dependency. The implementation results based on Xilinx Virtexll XC2V6000 FPGA show that the proposed design can do random elliptic curve scalar multiplication GF(2163) in 34.11 μs, occupying 2821 registers and 13 376 LUTs.
Design of highly efficient elliptic curve crypto-processor with two multiplications over GF(2163)
DAN Yong-ping; ZOU Xue-cheng; LIU Zheng-lin; HAN Yu; YI Li-hua
2009-01-01
In this article, a parallel hardware processor is presented to compute elliptic curve scalar multiplication in polynomial basis representation. The processor is applicable to the operations of scalar multiplication by using a modular arithmetic logic unit (MALU). The MALU consists of two multiplications, one addition, and one squaring. The two multiplications and the addition or squaring can be computed in parallel. The whole computations of scalar multiplication over GF(2163) can be performed in 3 064 cycles. The simulation results based on Xilinx Virtex2 XC2V6000 FPGAs show that the proposed design can compute random GF(2163) elliptic curve scalar multiplication operations in 31.17 μs, and the resource occupies 3 994 registers and 15 527 LUTs, which indicates that the crypto-processor is suitable for high-performance application.
Implementation of diffie-Hellman key exchange on wireless sensor using elliptic curve cryptography
Khajuria, Samant; Tange, Henrik
2009-01-01
This work describes a low-cost public key cryptography (PKC) based solution for security services such as authentication as required for wireless sensor networks. We have implemented a software approach using elliptic curve cryptography (ECC) over GF (2m) in order to obtain stronger cryptography....... from Crossbow. Results has shown that the point calculation can be done fairly amount of time with relatively small space consumption......This work describes a low-cost public key cryptography (PKC) based solution for security services such as authentication as required for wireless sensor networks. We have implemented a software approach using elliptic curve cryptography (ECC) over GF (2m) in order to obtain stronger cryptography...
Computation of ATR Darmon points on non-geometrically modular elliptic curves
Guitart, Xavier
2012-01-01
ATR points were introduced by Darmon as a conjectural construction of algebraic points on certain elliptic curves for which in general the Heegner point method is not available. So far the only numerical evidence, provided by Darmon--Logan and G\\"artner, concerned curves arising as quotients of Shimura curves. In those special cases the ATR points can be obtained from the already existing Heegner points, thanks to results of Zhang and Darmon--Rotger--Zhao. In this paper we compute for the first time an algebraic ATR point on a curve which is not uniformizable by any Shimura curve, thus providing the first piece of numerical evidence that Darmon's construction works beyond geometric modularity. To this purpose we improve the method proposed by Darmon and Logan by removing the requirement that the real quadratic field be norm-euclidean, and accelerating the numerical integration of Hilbert modular forms.
Monodromy of a Class of Logarithmic Connections on an Elliptic Curve
Francois-Xavier Machu
2007-08-01
Full Text Available The logarithmic connections studied in the paper are direct images of regular connections on line bundles over genus-2 double covers of the elliptic curve. We give an explicit parametrization of all such connections, determine their monodromy, differential Galois group and the underlying rank-2 vector bundle. The latter is described in terms of elementary transforms. The question of its (semi-stability is addressed.
An Elliptic Curve Cryptography-Based RFID Authentication Securing E-Health System
2015-01-01
Mobile healthcare (M-health) systems can monitor the patients’ conditions remotely and provide the patients and doctors with access to electronic medical records, and Radio Frequency Identification (RFID) technology plays an important role in M-health services. It is important to securely access RFID data in M-health systems: here, authentication, privacy, anonymity, and tracking resistance are desirable security properties. In 2014, He et al. proposed an elliptic curve cryptography- (ECC-) b...
Sums of two biquadrate and elliptic curves of rank $\\geq 4$
Izadi, F A; Nabardi, K
2012-01-01
Let $n$ be an odd number which can be written in two different ways as sums of two biquadrate. Then we show that the elliptic curves $y^2=x^3-nx$ have rank$\\geq 4$. If $n$ is even number with the same property, then the rank$\\geq 3$. Moreover, some examples of ranks equal to 4, 5, 6, 7, and 8 are given.
Design of an Elliptic Curve Cryptography Processor for RFID Tag Chips
Zilong Liu
2014-09-01
Full Text Available Radio Frequency Identification (RFID is an important technique for wireless sensor networks and the Internet of Things. Recently, considerable research has been performed in the combination of public key cryptography and RFID. In this paper, an efficient architecture of Elliptic Curve Cryptography (ECC Processor for RFID tag chip is presented. We adopt a new inversion algorithm which requires fewer registers to store variables than the traditional schemes. A new method for coordinate swapping is proposed, which can reduce the complexity of the controller and shorten the time of iterative calculation effectively. A modified circular shift register architecture is presented in this paper, which is an effective way to reduce the area of register files. Clock gating and asynchronous counter are exploited to reduce the power consumption. The simulation and synthesis results show that the time needed for one elliptic curve scalar point multiplication over GF(2163 is 176.7 K clock cycles and the gate area is 13.8 K with UMC 0.13 μm Complementary Metal Oxide Semiconductor (CMOS technology. Moreover, the low power and low cost consumption make the Elliptic Curve Cryptography Processor (ECP a prospective candidate for application in the RFID tag chip.
Efficient Implementation of Elliptic Curve Cryptography Using Low-power Digital Signal Processor
Malik, Muhammad Yasir
2011-01-01
RSA(Rivest, Shamir and Adleman)is being used as a public key exchange and key agreement tool for many years. Due to large numbers involved in RSA, there is need for more efficient methods in implementation for public key cryptosystems. Elliptic Curve Cryptography(ECC) is based on elliptic curves defined over a finite field. Elliptic curve cryptosystems(ECC) were discovered by Victor Miller and Neal Koblitz in 1985.This paper comprises of five sections. Section I is introduction to ECC and its components. Section II describes advantages of ECC schemes and its comparison with RSA. Section III is about some of the applications of ECC. Section IV gives some embedded implementations of ECC. Section V contains ECC implementation on fixed point Digital Signal Processor(TMS320VC5416). ECC was implemented using general purpose microcontrollers and Field Programmable Gate Arrays (FPGA) before this work. DSP is more powerful than microcontrollers and much economical than FPGA. So this implementation can be efficiently u...
Secure Antnet Routing Algorithm for Scalable Adhoc Networks Using Elliptic Curve Cryptography
V. Vijayalakshmi
2007-01-01
Full Text Available The secure end-to-end route discovery in the decentralized Mobile Adhoc Networks (MANETs should have to meet the requirements of prevention of DoS attacks on data traffic, should be adaptive and fault tolerant and must have high speed, low energy overhead and scalability for future development. In this research a secure routing using antnet mechanism and mutual authentication using Elliptic Curve Cryptography (ECC has been proposed to meet the above requirements. The common perception of public key cryptography is that it is not well suited for adhoc networks as they are very complex and slow. Against this popular belief, this research implements Elliptic Curve Cryptography -a public key cryptography scheme. ECC provides a similar level of security to conventional integer-based public-key algorithms, but with much shorter keys. Because of the shorter keys ECC algorithms run faster, require less space and consume less energy. These advantages make ECC a better choice of public key cryptography, especially for a resource constrained systems like MANETs. Using the antnet routing algorithm, the highly trustable route will be selected for data transfer and each Mobile Node (MN in MANET maintains the trust value of its one-hop neighbors. The mutual authentication between source and destination is done by master key exchange using Elliptic Curve Cryptography (ECC. v
Design of an Elliptic Curve Cryptography processor for RFID tag chips.
Liu, Zilong; Liu, Dongsheng; Zou, Xuecheng; Lin, Hui; Cheng, Jian
2014-09-26
Radio Frequency Identification (RFID) is an important technique for wireless sensor networks and the Internet of Things. Recently, considerable research has been performed in the combination of public key cryptography and RFID. In this paper, an efficient architecture of Elliptic Curve Cryptography (ECC) Processor for RFID tag chip is presented. We adopt a new inversion algorithm which requires fewer registers to store variables than the traditional schemes. A new method for coordinate swapping is proposed, which can reduce the complexity of the controller and shorten the time of iterative calculation effectively. A modified circular shift register architecture is presented in this paper, which is an effective way to reduce the area of register files. Clock gating and asynchronous counter are exploited to reduce the power consumption. The simulation and synthesis results show that the time needed for one elliptic curve scalar point multiplication over GF(2163) is 176.7 K clock cycles and the gate area is 13.8 K with UMC 0.13 μm Complementary Metal Oxide Semiconductor (CMOS) technology. Moreover, the low power and low cost consumption make the Elliptic Curve Cryptography Processor (ECP) a prospective candidate for application in the RFID tag chip.
On the Mordell-Weil group of elliptic curves induced by families of Diophantine triples
Mikić, Miljen
2015-01-01
The problem of the extendibility of Diophantine triples is closely connected with the Mordell-Weil group of the associated elliptic curve. In this paper, we examine Diophantine triples $\\{k-1,k+1,c_l(k)\\}$ and prove that the torsion group of the associated curves is $\\mathbb{Z}/2\\mathbb{Z} \\times \\mathbb{Z}/2\\mathbb{Z}$ for $l=3,4$ and $l\\equiv 1$ or $2 \\pmod{4}$. Additionally, we prove that the rank is greater than or equal to 2 for all $l\\ge2$. This represents an improvement of previous res...
Korneev, V. G.
2012-09-01
BPS is a well known an efficient and rather general domain decomposition Dirichlet-Dirichlet type preconditioner, suggested in the famous series of papers Bramble, Pasciak and Schatz (1986-1989). Since then, it has been serving as the origin for the whole family of domain decomposition Dirichlet-Dirichlet type preconditioners-solvers as for h so hp discretizations of elliptic problems. For its original version, designed for h discretizations, the named authors proved the bound O(1 + log2 H/ h) for the relative condition number under some restricting conditions on the domain decomposition and finite element discretization. Here H/ h is the maximal relation of the characteristic size H of a decomposition subdomain to the mesh parameter h of its discretization. It was assumed that subdomains are images of the reference unite cube by trilinear mappings. Later similar bounds related to h discretizations were proved for more general domain decompositions, defined by means of coarse tetrahedral meshes. These results, accompanied by the development of some special tools of analysis aimed at such type of decompositions, were summarized in the book of Toselli and Widlund (2005). This paper is also confined to h discretizations. We further expand the range of admissible domain decompositions for constructing BPS preconditioners, in which decomposition subdomains can be convex polyhedrons, satisfying some conditions of shape regularity. We prove the bound for the relative condition number with the same dependence on H/ h as in the bound given above. Along the way to this result, we simplify the proof of the so called abstract bound for the relative condition number of the domain decomposition preconditioner. In the part, related to the analysis of the interface sub-problem preconditioning, our technical tools are generalization of those used by Bramble, Pasciak and Schatz.
Design And Implementation of Low Area/Power Elliptic Curve Digital Signature Hardware Core
Anissa Sghaier
2017-06-01
Full Text Available The Elliptic Curve Digital Signature Algorithm(ECDSA is the analog to the Digital Signature Algorithm(DSA. Based on the elliptic curve, which uses a small key compared to the others public-key algorithms, ECDSA is the most suitable scheme for environments where processor power and storage are limited. This paper focuses on the hardware implementation of the ECDSA over elliptic curveswith the 163-bit key length recommended by the NIST (National Institute of Standards and Technology. It offers two services: signature generation and signature verification. The proposed processor integrates an ECC IP, a Secure Hash Standard 2 IP (SHA-2 Ip and Random Number Generator IP (RNG IP. Thus, all IPs will be optimized, and different types of RNG will be implemented in order to choose the most appropriate one. A co-simulation was done to verify the ECDSA processor using MATLAB Software. All modules were implemented on a Xilinx Virtex 5 ML 50 FPGA platform; they require respectively 9670 slices, 2530 slices and 18,504 slices. FPGA implementations represent generally the first step for obtaining faster ASIC implementations. Further, the proposed design was also implemented on an ASIC CMOS 45-nm technology; it requires a 0.257 mm2 area cell achieving a maximum frequency of 532 MHz and consumes 63.444 (mW. Furthermore, in this paper, we analyze the security of our proposed ECDSA processor against the no correctness check for input points and restart attacks.
Non-Simply-Connected Gauge Groups and Rational Points on Elliptic Curves
Aspinwall, Paul S; Aspinwall, Paul S.; Morrison, David R.
1998-01-01
We consider the F-theory description of non-simply-connected gauge groups appearing in the E8 x E8 heterotic string. The analysis is closely tied to the arithmetic of torsion points on an elliptic curve. The general form of the corresponding elliptic fibration is given for all finite subgroups of E8 which are applicable in this context. We also study the closely-related question of point-like instantons on a K3 surface whose holonomy is a finite group. As an example we consider the case of the heterotic string on a K3 surface having the E8 gauge symmetry broken to (E6 x SU(3))/Z3 or SU(9)/Z3 by point-like instantons with Z3 holonomy.
SPEED UP RATIONAL POINT SCALAR MULTIPLICATIONS ON ELLIPTIC CURVES BY FROBENIUS EQUATIONS
You Lin; Zhao Junzhong; Xu Maozhi
2006-01-01
Let q be a power of a prime and φ be the Frobenius endomorphism on E(Fqk), then q = tφ- φ2.Applying this equation, a new algorithm to compute rational point scalar multiplications on elliptic curves by finding a suitable small positive integer s such that qs can be represented as some very sparse φ-polynomial is proposed. If a Normal Basis (NB) or Optimal Normal Basis (ONB) is applied and the precomputations are considered free, our algorithm will cost, on average, about 55% to 80% less than binary method, and about rithm. In addition, an effective algorithm is provided for finding such integer s.
Efficient Dynamic Threshold Group Signature Scheme Based on Elliptic Curve Cryptosystem
无
2008-01-01
The short secret key characteristic of elliptic curve cryptosystem (ECC) are integrated with the (t,n ) threshold method to create a practical threshold group signature scheme characterized by simultaneous signing. The scheme not only meets the requirements of anonymity and traceability of group signature but also can withstand Tseng and Wangs conspiracy attack. It allows the group manager to add new members and delete old members according to actual application, while the system parameters have a little change. Cryptanalysis result shows that the scheme is efficient and secure.
Jin, Chunhua; Xu, Chunxiang; Zhang, Xiaojun; Zhao, Jining
2015-03-01
Radio Frequency Identification(RFID) is an automatic identification technology, which can be widely used in healthcare environments to locate and track staff, equipment and patients. However, potential security and privacy problems in RFID system remain a challenge. In this paper, we design a mutual authentication protocol for RFID based on elliptic curve cryptography(ECC). We use pre-computing method within tag's communication, so that our protocol can get better efficiency. In terms of security, our protocol can achieve confidentiality, unforgeability, mutual authentication, tag's anonymity, availability and forward security. Our protocol also can overcome the weakness in the existing protocols. Therefore, our protocol is suitable for healthcare environments.
On the non-commutative Local Main Conjecture for elliptic curves with complex multiplication
Venjakob, Otmar
2012-01-01
This paper is a natural continuation of the joint work [6] on non-commutative Main Conjectures for CM elliptic curves: now we concentrate on the local Main Conjecture or more precisely on the epsilon-isomorphism conjecture by Fukaya and Kato in [20]. Our results rely heavily on Kato's unpublished proof of (commutative) epsilon-isomorphisms for one dimensional representations of G_{Q_p} in [24]. For the convenience of the reader we give a slight modification or rather reformulation of it in the language of [20] and extend it to the (slightly non-commutative) semi-global setting.
Fast algorithms for computing isogenies between ordinary elliptic curves in small characteristic
De Feo, Luca
2010-01-01
The problem of computing an explicit isogeny between two given elliptic curves over F_q, originally motivated by point counting, has recently awaken new interest in the cryptology community thanks to the works of Teske and Rostovstev & Stolbunov. While the large characteristic case is well understood, only suboptimal algorithms are known in small characteristic; they are due to Couveignes, Lercier, Lercier & Joux and Lercier & Sirvent. In this paper we discuss the differences between them and run some comparative experiments. We also present the first complete implementation of Couveignes' second algorithm and present improvements that make it the algorithm having the best asymptotic complexity in the degree of the isogeny.
CM elliptic curves and p-adic valuations of their L-series at s=1
无
2002-01-01
For rational integers γ and λ, consider two families of (-1) and (-3) respectively. General formulae expressed by Weierstrass -functions are given for special values of Hecke L-series attached to such elliptic curves. The uniform lower bounds of 2-adic and 3-adic valuations of these values of Hecke L-series as well as global criteria for reaching these bounds are obtained. Moreover, when γ=2 and λ=2, 4, further results of 2-adic and 3-adic valuations are obtained for the corresponding curves in more general case of D1 and some restricted D2 respectively. These results are consistent with the predictions of the conjecture of Birch and Swinnerton-Dyer, and greatly develop and generalize some results in recent literature for more special cases.
An efficient hardware architecture of a scalable elliptic curve crypto-processor over GF(2n)
Tawalbeh, Lo'ai; Tenca, Alexandre; Park, Song; Koc, Cetin
2005-08-01
This paper presents a scalable Elliptic Curve Crypto-Processor (ECCP) architecture for computing the point multiplication for curves defined over the binary extension fields (GF(2n)). This processor computes modular inverse and Montgomery modular multiplication using a new effcient algorithm. The scalability feature of the proposed crypto-processor allows a fixed-area datapath to handle operands of any size. Also, the word size of the datapath can be adjusted to meet the area and performance requirements. On the other hand, the processor is reconfigurable in the sense that the user has the ability to choose the value of the field parameter (n). Experimental results show that the proposed crypto-processor is competitive with many other previous designs.
Composite Field Multiplier based on Look-Up Table for Elliptic Curve Cryptography Implementation
Marisa W. Paryasto
2013-09-01
Full Text Available Implementing a secure cryptosystem requires operations involving hundreds of bits. One of the most recommended algorithm is Elliptic Curve Cryptography (ECC. The complexity of elliptic curve algorithms and parameters with hundreds of bits requires specific design and implementation strategy. The design architecture must be customized according to security requirement, available resources and parameter choices. In this work we propose the use of composite field to implement finite field multiplication for ECC implementation. We use 299-bit keylength represented in GF((21323 instead of in GF(2299. Composite field multiplier can be implemented using different multiplier for ground-field and for extension field. In this paper, LUT is used for multiplication in the ground-field and classic multiplieris used for the extension field multiplication. A generic architecture for the multiplier is presented. Implementation is done with VHDL with the target device Altera DE2. The work in this paper uses the simplest algorithm to confirm the idea that by dividing field into composite, use different multiplier for base and extension field would give better trade-off for time and area. This work will be the beginning of our more advanced further research that implements composite-field using Mastrovito Hybrid, KOA and LUT.
Sangook Moon
2014-01-01
Full Text Available As today’s hardware architecture becomes more and more complicated, it is getting harder to modify or improve the microarchitecture of a design in register transfer level (RTL. Consequently, traditional methods we have used to develop a design are not capable of coping with complex designs. In this paper, we suggest a way of designing complex digital logic circuits with a soft and advanced type of SystemVerilog at an electronic system level. We apply the concept of design-and-reuse with a high level of abstraction to implement elliptic curve crypto-processor server farms. With the concept of the superior level of abstraction to the RTL used with the traditional HDL design, we successfully achieved the soft implementation of the crypto-processor server farms as well as robust test bench code with trivial effort in the same simulation environment. Otherwise, it could have required error-prone Verilog simulations for the hardware IPs and other time-consuming jobs such as C/SystemC verification for the software, sacrificing more time and effort. In the design of the elliptic curve cryptography processor engine, we propose a 3X faster GF(2m serial multiplication architecture.
Elliptic curves and their torsion subgroups over number fields of type (2, 2,
无
2001-01-01
Suppose that E：y2=x(x+M)(x+N) is an elliptic curve, where M
On the Surjectivity of Galois Representations Associated to Elliptic Curves over Number Fields
Larson, Eric
2012-01-01
Given an elliptic curve $E$ over a number field $K$, the $\\ell$-torsion points $E[\\ell]$ of $E$ define a Galois representation $\\gal(\\bar{K}/K) \\to \\gl_2(\\ff_\\ell)$. A famous theorem of Serre states that as long as $E$ has no Complex Multiplication (CM), the map $\\gal(\\bar{K}/K) \\to \\gl_2(\\ff_\\ell)$ is surjective for all but finitely many $\\ell$. We say that a prime number $\\ell$ is exceptional (relative to the pair $(E,K)$) if this map is not surjective. Here we give a new bound on the largest exceptional prime, as well as on the product of all exceptional primes of $E$. We show in particular that conditionally on the Generalized Riemann Hypothesis (GRH), the largest exceptional prime of an elliptic curve $E$ without CM is no larger than a constant (depending on $K$) times $\\log N_E$, where $N_E$ is the absolute value of the norm of the conductor. This answers affirmatively a question of Serre.
Nagaraja Shylashree
2014-09-01
Full Text Available We present a new hardware realization of fast elliptic curve Multi-Scalar Point Multiplication (MSPM using the sum of products expansion of the scalars. In Elliptic curve point Multiplication latency depends on the number of one’s (Hamming Weight in the binary representation of the scalar multiplier. By reducing the effective number of one’s in the multiplier, the multiplication speed is automatically increased. Therefore we describe a new method of effectively reducing the Hamming weight of the scalar multipliers thereby reduces the number of Point Adders when multi scalar multiplication is needed. The increase in speed achieved outweighs the hardware cost and complexity.
Secure and efficient elliptic curve cryptography resists side-channel attacks
Zhang Tao; Fan Mingyu; Zheng Xiaoyu
2009-01-01
An embedded cryptosystem needs higher reconfiguration capability and security. After analyzing the newly emerging side-channel attacks on elliptic curve cryptosystem (ECC), an efficient fractional width-w NAF (FWNAF) algorithm is proposed to secure ECC scalar multiplication from these attacks. This algorithm adopts the fractional window method and probabilistic SPA scheme to recondigure the pre-computed table, and it allows designers to make a dynamic configuration on pre-computed table. And then, it is enhanced to resist SPA, DPA, RPA and ZPA attacks by using the random masking method. Compared with the WBRIP and EBRIP methods, our proposals has the lowest total computation cost and reduce the shake phenomenon due to sharp fluctuation on computation performance.
A Criterion for Elliptic Curves with Second Lowest 2-Power in L(1)(Ⅱ)
Chun Lai ZHAO
2005-01-01
Let D = p1p2… pm, where pi, p2,...,pm are distinct rational primes with p1 ≡ p2 ≡3(mod 8), pi ≡1(mod 8)(3 ≤ i ≤ m), and m is any positive integer. In this paper, we give a simple combinatorial criterion for the value of the complex L-function of the congruent elliptic curve ED2 : y2 ＝ x3-D2x at s ＝ 1, divided by the period ω defined below, to be exactly divisible by 22m-2, the second lowest 2-power with respect to the number of the Gaussian prime factors of D. As a corollary, we obtain a new series of non-congruent numbers whose prime factors can be arbitrarily many. Our result is in accord with the predictions of the conjecture of Birch and Swinnerton-Dyer.
Zhang, Zezhong; Qi, Qingqing
2014-05-01
Medication errors are very dangerous even fatal since it could cause serious even fatal harm to patients. In order to reduce medication errors, automated patient medication systems using the Radio Frequency Identification (RFID) technology have been used in many hospitals. The data transmitted in those medication systems is very important and sensitive. In the past decade, many security protocols have been proposed to ensure its secure transition attracted wide attention. Due to providing mutual authentication between the medication server and the tag, the RFID authentication protocol is considered as the most important security protocols in those systems. In this paper, we propose a RFID authentication protocol to enhance patient medication safety using elliptic curve cryptography (ECC). The analysis shows the proposed protocol could overcome security weaknesses in previous protocols and has better performance. Therefore, the proposed protocol is very suitable for automated patient medication systems.
Two-Factor User Authentication with Key Agreement Scheme Based on Elliptic Curve Cryptosystem
Juan Qu
2014-01-01
Full Text Available A password authentication scheme using smart card is called two-factor authentication scheme. Two-factor authentication scheme is the most accepted and commonly used mechanism that provides the authorized users a secure and efficient method for accessing resources over insecure communication channel. Up to now, various two-factor user authentication schemes have been proposed. However, most of them are vulnerable to smart card loss attack, offline password guessing attack, impersonation attack, and so on. In this paper, we design a password remote user authentication with key agreement scheme using elliptic curve cryptosystem. Security analysis shows that the proposed scheme has high level of security. Moreover, the proposed scheme is more practical and secure in contrast to some related schemes.
On local-global divisibility by $p^n$ in elliptic curves
Paladino, Laura; Viada, Evelina
2011-01-01
Let $ p $ be a prime number and let $k$ be a number field, which does not contain the field $\\mathbb{Q} (\\zeta_p + \\bar{\\zeta_p})$. Let $\\mathcal{E}$ be an elliptic curve defined over $k$. We prove that if there are no $k$-rational torsion points of exact order $p$ on $\\mathcal{E}$, then the local-global principle holds for divisibility by $p^n$, with $n$ a natural number. As a consequence of the deep theorems of Merel, Mazur and Kamienny we deduce that, for $p$ larger than a constant $C ([k:\\mathbb{Q}])$, depending only on the degree of $k$, there are no counterexamples to the local-global divisibility principle. In particular, for the rational numbers $C(1)=7$ and for quadratic fields $C(2)=13$.
Bagger-Witten line bundles on moduli spaces of elliptic curves
Gu, W
2016-01-01
In this paper we discuss Bagger-Witten line bundles over moduli spaces of SCFTs. We review how in general they are `fractional' line bundles, not honest line bundles, twisted on triple overlaps. We discuss the special case of moduli spaces of elliptic curves in detail. There, the Bagger-Witten line bundles does not exist as an ordinary line bundle, but rather is necessarily fractional. As a fractional line bundle, it is nontrivial (though torsion) over the uncompactified moduli stack, and its restriction to the interior, excising corners with enhanced stabilizers, is also fractional. We review and compare to results of recent work arguing that well-definedness of the worldsheet metric implies that the Bagger-Witten line bundle is torsion, and give general arguments on the existence of universal structures on moduli spaces of SCFTs, in which superconformal deformation parameters are promoted to nondynamical fields ranging over the SCFT moduli space.
Mordell-Weil groups and Selmer groups of twin-prime elliptic curves
邱德荣; 张贤科
2002-01-01
Let E = Eσ : y2 = x(x + σp)(x + σq) be elliptic curves, where σ = ±1, p and q are primenumbers with p+2 = q. (i) Selmer groups S(2)(E/Q), S(φ)(E/Q), and S(φ)(E/Q) are explicitly determined,e.g. S(2)(E+1/Q)= (Z/2Z)2, (Z/2Z)3, and (Z/2Z)4 when p ≡ 5, 1 (or 3), and 7(mod 8), respectively. (ii)When p ≡ 5 (3, 5 for σ = -1) (mod 8), it is proved that the Mordell-Weil group E(Q) ≌ Z/2Z Z/2Z,symbol, the torsion subgroup E(K)tors for any number field K, etc. are also obtained.
Elliptic Curve Based Zero Knowledge Proofs and Their Applicability on Resource Constrained Devices
Chatzigiannakis, Ioannis; Spirakis, Paul G; Stamatiou, Yannis C
2011-01-01
Elliptic Curve Cryptography (ECC) is an attractive alternative to conventional public key cryptography, such as RSA. ECC is an ideal candidate for implementation on constrained devices where the major computational resources i.e. speed, memory are limited and low-power wireless communication protocols are employed. That is because it attains the same security levels with traditional cryptosystems using smaller parameter sizes. Moreover, in several application areas such as person identification and eVoting, it is frequently required of entities to prove knowledge of some fact without revealing this knowledge. Such proofs of knowledge are called Zero Knowledge Interactive Proofs (ZKIP) and involve interactions between two communicating parties, the Prover and the Verifier. In a ZKIP, the Prover demonstrates the possesion of some information (e.g. authentication information) to the Verifier without disclosing it. In this paper, we focus on the application of ZKIP protocols on resource constrained devices. We st...
A User Authentication Scheme Based on Elliptic Curves Cryptography for Wireless Ad Hoc Networks.
Chen, Huifang; Ge, Linlin; Xie, Lei
2015-07-14
The feature of non-infrastructure support in a wireless ad hoc network (WANET) makes it suffer from various attacks. Moreover, user authentication is the first safety barrier in a network. A mutual trust is achieved by a protocol which enables communicating parties to authenticate each other at the same time and to exchange session keys. For the resource-constrained WANET, an efficient and lightweight user authentication scheme is necessary. In this paper, we propose a user authentication scheme based on the self-certified public key system and elliptic curves cryptography for a WANET. Using the proposed scheme, an efficient two-way user authentication and secure session key agreement can be achieved. Security analysis shows that our proposed scheme is resilient to common known attacks. In addition, the performance analysis shows that our proposed scheme performs similar or better compared with some existing user authentication schemes.
Attack on Digital Multi-Signature Scheme Based on Elliptic Curve Cryptosystem
Duo Liu; Ping Luo; Yi-Qi Dai
2007-01-01
The concept of multisignature, in which multiple signers can cooperate to sign the same message and any verifier can verify the validity of the multi-signature, was first introduced by Itakura and Nakamura.Several multisignature schemes have been proposed since.Chen et al.proposed a new digital multi-signature scheme based on the elliptic curve cryptosystem recently.In this paper, we show that their scheme is insecure, for it is vulnerable to the so-called active attacks, such as the substitution of a "false" public key to a "true" one in a key directory or during transmission.And then the attacker can sign a legal signature which other users have signed and forge a signature himself which can be accepted by the verifier.
Hardware Activation by Means of PUFs and Elliptic Curve Cryptography in Field-Programmable Devices
Luis Parrilla
2016-01-01
Full Text Available Reusable design using IP cores requires of efficient methods for protecting the Intellectual Property of the designer and the corresponding license agreements. In this work, a new protection procedure establishing an activation protocol in a similar way to the activation process in the software world is presented. The procedure, named SEHAS (Secure Hardware Activation System allows the distribution of cores in either Blocked (not functioning or Demo (functioning with limited features modes, while ensuring the license agreements by identifying not only the IP core but also the implementation device, using Physically Unclonable Functions (PUF. Moreover, SEHAS secures the exchange of information between the core and the core vendor using an Elliptic Curve Cryptosystem (ECC. This secure channel allows the IP core vendor to send a unique Activation Code to the core in order to switch it to the Activated Mode, thus enabling all its features.
A singular property of the supersingular elliptic curve in characteristic 2
Zapponi, Leonardo
2010-01-01
Let $E$ be the supersingular elliptic curve defined over the field $k=\\bar{\\bold F}_2$, which is unique up to $k$-isomorphism. Denote by $0_E$ its identity element and let $C\\cong\\bold A^1_k$ the quotient of $E-\\{0_E\\}$ under the action of the group $\\mbox{Isom}_k(E)$ (which is non-abelian, of order $24$). The main result of this paper asserts that the set $C(k)$ naturally parametrizes $k$-isomorphism classes of Lam\\'e covers, which are tamely ramified covers $X\\to\\bold P^1$ unramified outside three points having a particular ramification datum. This fact is surprising for two reasons: first of all, it is the first non-trivial example of a family of covers of the projective line unramified outside three points which is parametrized by the geometric points of a curve. Moreover, when considered in arbitrary characteristic, the explicit construction of Lam\\'e covers is quite involved and their arithmetic properties still remain misterious. The simplicity of the problem in characteristic $2$ has many deep consequ...
An Elliptic Curve Based Schnorr Cloud Security Model in Distributed Environment.
Muthurajan, Vinothkumar; Narayanasamy, Balaji
2016-01-01
Cloud computing requires the security upgrade in data transmission approaches. In general, key-based encryption/decryption (symmetric and asymmetric) mechanisms ensure the secure data transfer between the devices. The symmetric key mechanisms (pseudorandom function) provide minimum protection level compared to asymmetric key (RSA, AES, and ECC) schemes. The presence of expired content and the irrelevant resources cause unauthorized data access adversely. This paper investigates how the integrity and secure data transfer are improved based on the Elliptic Curve based Schnorr scheme. This paper proposes a virtual machine based cloud model with Hybrid Cloud Security Algorithm (HCSA) to remove the expired content. The HCSA-based auditing improves the malicious activity prediction during the data transfer. The duplication in the cloud server degrades the performance of EC-Schnorr based encryption schemes. This paper utilizes the blooming filter concept to avoid the cloud server duplication. The combination of EC-Schnorr and blooming filter efficiently improves the security performance. The comparative analysis between proposed HCSA and the existing Distributed Hash Table (DHT) regarding execution time, computational overhead, and auditing time with auditing requests and servers confirms the effectiveness of HCSA in the cloud security model creation.
An Elliptic Curve Based Schnorr Cloud Security Model in Distributed Environment
Muthurajan, Vinothkumar; Narayanasamy, Balaji
2016-01-01
Cloud computing requires the security upgrade in data transmission approaches. In general, key-based encryption/decryption (symmetric and asymmetric) mechanisms ensure the secure data transfer between the devices. The symmetric key mechanisms (pseudorandom function) provide minimum protection level compared to asymmetric key (RSA, AES, and ECC) schemes. The presence of expired content and the irrelevant resources cause unauthorized data access adversely. This paper investigates how the integrity and secure data transfer are improved based on the Elliptic Curve based Schnorr scheme. This paper proposes a virtual machine based cloud model with Hybrid Cloud Security Algorithm (HCSA) to remove the expired content. The HCSA-based auditing improves the malicious activity prediction during the data transfer. The duplication in the cloud server degrades the performance of EC-Schnorr based encryption schemes. This paper utilizes the blooming filter concept to avoid the cloud server duplication. The combination of EC-Schnorr and blooming filter efficiently improves the security performance. The comparative analysis between proposed HCSA and the existing Distributed Hash Table (DHT) regarding execution time, computational overhead, and auditing time with auditing requests and servers confirms the effectiveness of HCSA in the cloud security model creation. PMID:26981584
Pseudorandom Bit Sequence Generator for Stream Cipher Based on Elliptic Curves
Jilna Payingat
2015-01-01
Full Text Available This paper proposes a pseudorandom sequence generator for stream ciphers based on elliptic curves (EC. A detailed analysis of various EC based random number generators available in the literature is done and a new method is proposed such that it addresses the drawbacks of these schemes. Statistical analysis of the proposed method is carried out using the NIST (National Institute of Standards and Technology test suite and it is seen that the sequence exhibits good randomness properties. The linear complexity analysis shows that the system has a linear complexity equal to the period of the sequence which is highly desirable. The statistical complexity and security against known plain text attack are also analysed. A comparison of the proposed method with other EC based schemes is done in terms of throughput, periodicity, and security, and the proposed method outperforms the methods in the literature. For resource constrained applications where a highly secure key exchange is essential, the proposed method provides a good option for encryption by time sharing the point multiplication unit for EC based key exchange. The algorithm and architecture for implementation are developed in such a way that the hardware consumed in addition to point multiplication unit is much less.
On Elliptic Curve Primality Proving%关于椭圆曲线素性证明
张李军
2008-01-01
This paper describes the Atkin's elliptic curves primality proving algorithm and discusses all implementationdetails of this algorithm. Finally it gives the implemention of this algorithm by software and exhibits an example explicitly.This algorithm is implemented with software and this software is used to test some general large integers and acquire agood testing result. For the purpose of understanding this algorithm more clearly, a typical example is provided finally.%文章给出了由Atkin提出的一种非常有效的素性测试方法即椭圆曲线素性证明算法,详细讨论了具体实施该算法的所有细节,而且通过在计算机上编程获得了其软件实现,并用该软件来测试一般的大整数的素性,取得了很好的效果.为了清晰地展示该算法的过程,文章在最后给出了一个详细的算例.
Jungeblut, T.; Puttmann, C.; Dreesen, R.; Porrmann, M.; Thies, M.; Rückert, U.; Kastens, U.
2010-12-01
The secure transmission of data plays a significant role in today's information era. Especially in the area of public-key-cryptography methods, which are based on elliptic curves (ECC), gain more and more importance. Compared to asymmetric algorithms, like RSA, ECC can be used with shorter key lengths, while achieving an equal level of security. The performance of ECC-algorithms can be increased significantly by adding application specific hardware extensions. Due to their fine grained parallelism, VLIW-processors are well suited for the execution of ECC algorithms. In this work, we extended the fourfold parallel CoreVA-VLIW-architecture by several hardware accelerators to increase the resource efficiency of the overall system. For the design-space exploration we use a dual design flow, which is based on the automatic generation of a complete C-compiler based tool chain from a central processor specification. Using the hardware accelerators the performance of the scalar multiplication on binary fields can be increased by the factor of 29. The energy consumption can be reduced by up to 90%. The extended processor hardware was mapped on a current 65 nm low-power standard-cell-technology. The chip area of the CoreVA-VLIW-architecture is 0.24 mm2 at a power consumption of 29 mW/MHz. The performance gain is analyzed in respect to the increased hardware costs, as chip area or power consumption.
A secure RFID authentication protocol for healthcare environments using elliptic curve cryptosystem.
Zhao, Zhenguo
2014-05-01
With the fast advancement of the wireless communication technology and the widespread use of medical systems, the radio frequency identification (RFID) technology has been widely used in healthcare environments. As the first important protocol for ensuring secure communication in healthcare environment, the RFID authentication protocols derive more and more attentions. Most of RFID authentication protocols are based on hash function or symmetric cryptography. To get more security properties, elliptic curve cryptosystem (ECC) has been used in the design of RFID authentication protocol. Recently, Liao and Hsiao proposed a new RFID authentication protocol using ECC and claimed their protocol could withstand various attacks. In this paper, we will show that their protocol suffers from the key compromise problem, i.e. an adversary could get the private key stored in the tag. To enhance the security, we propose a new RFID authentication protocol using ECC. Detailed analysis shows the proposed protocol not only could overcome weaknesses in Liao and Hsiao's protocol but also has the same performance. Therefore, it is more suitable for healthcare environments.
Debiao He
2017-01-01
Full Text Available Recent advances of Internet and microelectronics technologies have led to the concept of smart grid which has been a widespread concern for industry, governments, and academia. The openness of communications in the smart grid environment makes the system vulnerable to different types of attacks. The implementation of secure communication and the protection of consumers’ privacy have become challenging issues. The data aggregation scheme is an important technique for preserving consumers’ privacy because it can stop the leakage of a specific consumer’s data. To satisfy the security requirements of practical applications, a lot of data aggregation schemes were presented over the last several years. However, most of them suffer from security weaknesses or have poor performances. To reduce computation cost and achieve better security, we construct a lightweight data aggregation scheme against internal attackers in the smart grid environment using Elliptic Curve Cryptography (ECC. Security analysis of our proposed approach shows that it is provably secure and can provide confidentiality, authentication, and integrity. Performance analysis of the proposed scheme demonstrates that both computation and communication costs of the proposed scheme are much lower than the three previous schemes. As a result of these aforementioned benefits, the proposed lightweight data aggregation scheme is more practical for deployment in the smart grid environment.
Elliptic Curve Cryptography-Based Authentication with Identity Protection for Smart Grids.
Liping Zhang
Full Text Available In a smart grid, the power service provider enables the expected power generation amount to be measured according to current power consumption, thus stabilizing the power system. However, the data transmitted over smart grids are not protected, and then suffer from several types of security threats and attacks. Thus, a robust and efficient authentication protocol should be provided to strength the security of smart grid networks. As the Supervisory Control and Data Acquisition system provides the security protection between the control center and substations in most smart grid environments, we focus on how to secure the communications between the substations and smart appliances. Existing security approaches fail to address the performance-security balance. In this study, we suggest a mitigation authentication protocol based on Elliptic Curve Cryptography with privacy protection by using a tamper-resistant device at the smart appliance side to achieve a delicate balance between performance and security of smart grids. The proposed protocol provides some attractive features such as identity protection, mutual authentication and key agreement. Finally, we demonstrate the completeness of the proposed protocol using the Gong-Needham-Yahalom logic.
Elliptic Curve Cryptography-Based Authentication with Identity Protection for Smart Grids.
Zhang, Liping; Tang, Shanyu; Luo, He
2016-01-01
In a smart grid, the power service provider enables the expected power generation amount to be measured according to current power consumption, thus stabilizing the power system. However, the data transmitted over smart grids are not protected, and then suffer from several types of security threats and attacks. Thus, a robust and efficient authentication protocol should be provided to strength the security of smart grid networks. As the Supervisory Control and Data Acquisition system provides the security protection between the control center and substations in most smart grid environments, we focus on how to secure the communications between the substations and smart appliances. Existing security approaches fail to address the performance-security balance. In this study, we suggest a mitigation authentication protocol based on Elliptic Curve Cryptography with privacy protection by using a tamper-resistant device at the smart appliance side to achieve a delicate balance between performance and security of smart grids. The proposed protocol provides some attractive features such as identity protection, mutual authentication and key agreement. Finally, we demonstrate the completeness of the proposed protocol using the Gong-Needham-Yahalom logic.
Younsung Choi
2014-06-01
Full Text Available Wireless sensor networks (WSNs consist of sensors, gateways and users. Sensors are widely distributed to monitor various conditions, such as temperature, sound, speed and pressure but they have limited computational ability and energy. To reduce the resource use of sensors and enhance the security of WSNs, various user authentication protocols have been proposed. In 2011, Yeh et al. first proposed a user authentication protocol based on elliptic curve cryptography (ECC for WSNs. However, it turned out that Yeh et al.’s protocol does not provide mutual authentication, perfect forward secrecy, and key agreement between the user and sensor. Later in 2013, Shi et al. proposed a new user authentication protocol that improves both security and efficiency of Yeh et al.’s protocol. However, Shi et al.’s improvement introduces other security weaknesses. In this paper, we show that Shi et al.’s improved protocol is vulnerable to session key attack, stolen smart card attack, and sensor energy exhausting attack. In addition, we propose a new, security-enhanced user authentication protocol using ECC for WSNs.
Compression of Tate Pairings on Elliptic Curves%椭圆曲线Tate对的压缩
胡磊
2007-01-01
利用有限域包含的循环群之间的映射,给出了特征为素数p,MOV次数为3的超奇异椭圆曲线上的一类Tate对的两种有效压缩方法,它们分别将Tate对的值从6logp比特长的串压缩到3logp和2logp比特长.两种压缩方法的实现均使用原有Tate对的优化算法的代码,不需要针对压缩对编写新的实现代码,而且两种压缩对的实现均保持原有Tate对的实现速度.%In this paper, utilizing maps between cyclic groups contained in a finite field, two efficient methods for compressing a Tate pairing defined on a supersingular elliptic curve with prime characteristic p and MOV degree 3 are presented. They compress a pairing value from a string of length of 6logp bits to ones of 3logp and 2logp bits, respectively, and an implementation for both the compressed pairings makes use of the codes for the optimized algorithm of the original pairing and no new code is needed. Both the compressed pairings achieve the speed of the original implementation.
Fan, Desheng; Meng, Xiangfeng; Wang, Yurong; Yang, Xiulun; Peng, Xiang; He, Wenqi; Dong, Guoyan; Chen, Hongyi
2013-08-10
An optical identity authentication scheme based on the elliptic curve digital signature algorithm (ECDSA) and phase retrieval algorithm (PRA) is proposed. In this scheme, a user's certification image and the quick response code of the user identity's keyed-hash message authentication code (HMAC) with added noise, serving as the amplitude and phase restriction, respectively, are digitally encoded into two phase keys using a PRA in the Fresnel domain. During the authentication process, when the two phase keys are presented to the system and illuminated by a plane wave of correct wavelength, an output image is generated in the output plane. By identifying whether there is a match between the amplitude of the output image and all the certification images pre-stored in the database, the system can thus accomplish a first-level verification. After the confirmation of first-level verification, the ECDSA signature is decoded from the phase part of the output image and verified to allege whether the user's identity is legal or not. Moreover, the introduction of HMAC makes it almost impossible to forge the signature and hence the phase keys thanks to the HMAC's irreversible property. Theoretical analysis and numerical simulations both validate the feasibility of our proposed scheme.
Instanton geometry and quantum A{sub {infinity}} structure on the elliptic curve
Herbst, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Lerche, W. [European Lab. for Particle Physics (CERN), Geneva (Switzerland); Nemeschansky, D. [University of Southern California, Los Angeles, CA (United States). Dept. of Physics
2006-03-15
We first determine and then study the complete set of non-vanishing A-model correlation functions associated with the 'long-diagonal branes' on the elliptic curve. We verify that they satisfy the relevant A{sub {infinity}} consistency relations at both classical and quantum levels. In particular we find that the A{sub {infinity}} relation for the annulus provides a reconstruction of annulus instantons out of disk instantons. We note in passing that the naive application of the Cardy-constraint does not hold for our correlators, confirming expectations. Moreover, we analyze various analytical properties of the correlators, including instanton flops and the mixing of correlators with different numbers of legs under monodromy. The classical and quantum A{sub {infinity}} relations turn out to be compatible with such homotopy transformations. They lead to a non-invariance of the effective action under modular transformations, unless compensated by suitable contact terms which amount to redefinitions of the tachyon fields. (orig.)
Choi, Younsung; Lee, Donghoon; Kim, Jiye; Jung, Jaewook; Nam, Junghyun; Won, Dongho
2014-06-10
Wireless sensor networks (WSNs) consist of sensors, gateways and users. Sensors are widely distributed to monitor various conditions, such as temperature, sound, speed and pressure but they have limited computational ability and energy. To reduce the resource use of sensors and enhance the security of WSNs, various user authentication protocols have been proposed. In 2011, Yeh et al. first proposed a user authentication protocol based on elliptic curve cryptography (ECC) for WSNs. However, it turned out that Yeh et al.'s protocol does not provide mutual authentication, perfect forward secrecy, and key agreement between the user and sensor. Later in 2013, Shi et al. proposed a new user authentication protocol that improves both security and efficiency of Yeh et al.'s protocol. However, Shi et al.'s improvement introduces other security weaknesses. In this paper, we show that Shi et al.'s improved protocol is vulnerable to session key attack, stolen smart card attack, and sensor energy exhausting attack. In addition, we propose a new, security-enhanced user authentication protocol using ECC for WSNs.
Park, YoHan; Park, YoungHo
2016-12-14
Secure communication is a significant issue in wireless sensor networks. User authentication and key agreement are essential for providing a secure system, especially in user-oriented mobile services. It is also necessary to protect the identity of each individual in wireless environments to avoid personal privacy concerns. Many authentication and key agreement schemes utilize a smart card in addition to a password to support security functionalities. However, these schemes often fail to provide security along with privacy. In 2015, Chang et al. analyzed the security vulnerabilities of previous schemes and presented the two-factor authentication scheme that provided user privacy by using dynamic identities. However, when we cryptanalyzed Chang et al.'s scheme, we found that it does not provide sufficient security for wireless sensor networks and fails to provide accurate password updates. This paper proposes a security-enhanced authentication and key agreement scheme to overcome these security weaknesses using biometric information and an elliptic curve cryptosystem. We analyze the security of the proposed scheme against various attacks and check its viability in the mobile environment.
Feature Extraction from 3D Point Cloud Data Based on Discrete Curves
Yi An
2013-01-01
Full Text Available Reliable feature extraction from 3D point cloud data is an important problem in many application domains, such as reverse engineering, object recognition, industrial inspection, and autonomous navigation. In this paper, a novel method is proposed for extracting the geometric features from 3D point cloud data based on discrete curves. We extract the discrete curves from 3D point cloud data and research the behaviors of chord lengths, angle variations, and principal curvatures at the geometric features in the discrete curves. Then, the corresponding similarity indicators are defined. Based on the similarity indicators, the geometric features can be extracted from the discrete curves, which are also the geometric features of 3D point cloud data. The threshold values of the similarity indicators are taken from [0,1], which characterize the relative relationship and make the threshold setting easier and more reasonable. The experimental results demonstrate that the proposed method is efficient and reliable.
Zerbes, Sarah
2016-01-01
Celebrating one of the leading figures in contemporary number theory – John H. Coates – on the occasion of his 70th birthday, this collection of contributions covers a range of topics in number theory, concentrating on the arithmetic of elliptic curves, modular forms, and Galois representations. Several of the contributions in this volume were presented at the conference Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John Coates in Cambridge, March 25-27, 2015. The main unifying theme is Iwasawa theory, a field that John Coates himself has done much to create. This collection is indispensable reading for researchers in Iwasawa theory, and is interesting and valuable for those in many related fields. .
A. Narayan
2013-01-01
Full Text Available The oblateness and the photogravitational effects of both the primaries on the location and the stability of the triangular equilibrium points in the elliptical restricted three-body problem have been discussed. The stability of the triangular points under the photogravitational and oblateness effects of both the primaries around the binary systems Achird, Lyeten, Alpha Cen-AB, Kruger 60, and Xi-Bootis, has been studied using simulation techniques by drawing different curves of zero velocity.
The Complexity of Proving the Discrete Jordan Curve Theorem
Nguyen, Phuong
2010-01-01
The Jordan Curve Theorem (JCT) states that a simple closed curve divides the plane into exactly two connected regions. We formalize and prove the theorem in the context of grid graphs, under different input settings, in theories of bounded arithmetic that correspond to small complexity classes. The theory $V^0(2)$ (corresponding to $AC^0(2)$) proves that any set of edges that form disjoint cycles divides the grid into at least two regions. The theory $V^0$ (corresponding to $AC^0$) proves that any sequence of edges that form a simple closed curve divides the grid into exactly two regions. As a consequence, the Hex tautologies and the st-connectivity tautologies have polynomial size $AC^0(2)$-Frege-proofs, which improves results of Buss which only apply to the stronger proof system $TC^0$-Frege.
McGee, John J.
2006-01-01
Elliptic curves have a rich mathematical history dating back to Diophantus (c. 250 C.E.), who used a form of these cubic equations to find right triangles of integer area with rational sides. In more recent times the deep mathematics of elliptic curves was used by Andrew Wiles et. al., to construct a proof of Fermat's last theorem, a problem which challenged mathematicians for more than 300 years. In addition, elliptic curves over finite fields find practical application in the areas of cr...
The Complexity of Proving the Discrete Jordan Curve Theorem
Nguyen, Phuong; Cook, Stephen
2010-01-01
The Jordan Curve Theorem (JCT) states that a simple closed curve divides the plane into exactly two connected regions. We formalize and prove the theorem in the context of grid graphs, under different input settings, in theories of bounded arithmetic that correspond to small complexity classes. The theory $V^0(2)$ (corresponding to $AC^0(2)$) proves that any set of edges that form disjoint cycles divides the grid into at least two regions. The theory $V^0$ (corresponding to $AC^0$) proves tha...
Ismed Jauhar
2016-03-01
Full Text Available Along with the many environmental changes, it enables a disaster either natural or man-made objects. One of the efforts made to prevent disasters from happening is to make a system that is able to provide information about the status of the environment that is around. Many developments in the sensor system makes it possible to load a system that will supply real-time on the status of environmental conditions with a good security system. This study created a supply system status data of environmental conditions, especially on bridges by using Ubiquitous Sensor Network. Sensor used to detect vibrations are using an accelerometer. Supply of data between sensors and servers using ZigBee communication protocol wherein the data communication will be done using the Elliptic Curve Integrated security mechanisms Encryption Scheme and on the use of Elliptic Curve key aggrement Menezes-Qu-Vanstone. Test results show the limitation of distance for communication is as far as 55 meters, with the computation time for encryption and decryption with 97 and 42 seconds extra time for key exchange is done at the beginning of communication . Keywords: Ubiquitous Sensor Network, Accelerometer, ZigBee,Elliptic Curve Menezes-Qu-Vanstone
From Holonomy of the Ising Model Form Factors to n-Fold Integrals and the Theory of Elliptic Curves
Salah Boukraa
2007-10-01
Full Text Available We recall the form factors $f^(j_{N,N}$ corresponding to the $lambda$-extension $C(N,N; lambda$ of the two-point diagonal correlation function of the Ising model on the square lattice and their associated linear differential equations which exhibit both a "Russian-doll" nesting, and a decomposition of the linear differential operators as a direct sum of operators (equivalent to symmetric powers of the differential operator of the complete elliptic integral $E$. The scaling limit of these differential operators breaks the direct sum structure but not the "Russian doll" structure, the "scaled" linear differential operators being no longer Fuchsian. We then introduce some multiple integrals of the Ising class expected to have the same singularities as the singularities of the $n$-particle contributions $chi^{(n}$ to the susceptibility of the square lattice Ising model. We find the Fuchsian linear differential equations satisfied by these multiple integrals for $n = 1, 2, 3, 4$ and, only modulo a prime, for $n = 5$ and 6, thus providing a large set of (possible new singularities of the $chi^{(n}$. We get the location of these singularities by solving the Landau conditions. We discuss the mathematical, as well as physical, interpretation of these new singularities. Among the singularities found, we underline the fact that the quadratic polynomial condition $1 + 3w + 4w^2 = 0$, that occurs in the linear differential equation of $chi^{(3}$, actually corresponds to the occurrence of complex multiplication for elliptic curves. The interpretation of complex multiplication for elliptic curves as complex fixed points of generators of the exact renormalization group is sketched. The other singularities occurring in our multiple integrals are not related to complex multiplication situations, suggesting a geometric interpretation in terms of more general (motivic mathematical structures beyond the theory of elliptic curves. The scaling limit of the (lattice
Discrete Differential Geometry and Physics of Elastic Curves
McCormick, Andrew
We develop a general computational model for a elastic rod which allows for extension and shear. The model, similar in mathematical construction to Cosserat rod theory, allows a wider variety of problems to be studied than previous models. In the first section we develop the continuous mathematical model, discretize the system to allow implementation on a computer, and then verify the model's output against classical buckling tests. We then develop a novel analytic solution for the critical buckling length of a vertically oriented, shearable elastic beam subject to gravity and show that the model's treatment of shear is correct. In the experimental section we analyze a number of different phenomena with the rod model. To begin, we explain the mechanical response of helically coiling tendrils. After self-collision is introduced, we explore the formation of plectonemes and solenoids in a highly extensible elastic string. We discuss a sheet adhering to a surface in several different regimes and use the rod model to discover a self-similarity solution in the low-damping limit. Physical entanglement is investigated in an experiment where randomly tumbled strings are used to derive scaling laws for the dynamics governing entanglement. Models for active internal forces and anisotropic surface friction are introduced to explain the mechanics of a newly observed mode of snake locomotion. Finally, we extend the model from a single filament to an arbitrary number of strings and begin exploration into behavior of cloth, ponytails, and combing hair.
Hu, Shuangwei; Lundgren, Martin; Niemi, Antti J.
2011-06-01
We develop a transfer matrix formalism to visualize the framing of discrete piecewise linear curves in three-dimensional space. Our approach is based on the concept of an intrinsically discrete curve. This enables us to more effectively describe curves that in the limit where the length of line segments vanishes approach fractal structures in lieu of continuous curves. We verify that in the case of differentiable curves the continuum limit of our discrete equation reproduces the generalized Frenet equation. In particular, we draw attention to the conceptual similarity between inflection points where the curvature vanishes and topologically stable solitons. As an application we consider folded proteins, their Hausdorff dimension is known to be fractal. We explain how to employ the orientation of Cβ carbons of amino acids along a protein backbone to introduce a preferred framing along the backbone. By analyzing the experimentally resolved fold geometries in the Protein Data Bank we observe that this Cβ framing relates intimately to the discrete Frenet framing. We also explain how inflection points (a.k.a. soliton centers) can be located in the loops and clarify their distinctive rôle in determining the loop structure of folded proteins.
Magnetization curves for non-elliptic cylindrical samples in a transverse ﬁeld
Debjani Karmakar; K V Bhagwat
2001-01-01
Using recent results for the surface current density on cylindrical surfaces of arbitrary cross-section producing uniform interior magnetic ﬁeld and an assumed set of ﬂux-fronts, solutions of Bean’s critical state model for cylindrical samples with non-elliptic cross-section are presented. Magnetization hysteresis loops for two cross-sections with different aspect ratios are obtained. A comparison with some exact results shows the limitations of this approach.
Shali xiao(肖沙里); Yingjun Pan(潘英俊); Xianxin Zhong(钟先信); Xiancai Xiong(熊先才); Guohong Yang(杨国洪); Zongli Liu(刘宗礼); Yongkun Ding(丁永坤)
2004-01-01
The X-ray spectrum emitted from laser-produced plasma contains plentiful information.X-ray spectrometer is a powerful tool for plasma diagnosis and studying the information and evolution of the plasma.X-ray concave(elliptical)curved crystals analyzer was designed and manufactured to investigate the properties of laser-produced plasma.The experiment was carried out on Mianyang Xingguang-ⅡFacility and aimed at investigating the characteristics of a high density iron plasma.Experimental results using KAP,LIF,PET,and MICA curved crystal analyzers are described,and the spectra of Au,Ti laser-produced plasma are shown.The focusing crystal analyzer clearly gave an increase in sensitivity over a flat crystal.
Chkifa, Abdellah
2015-04-08
Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that in the univariate case, the least-squares method is quasi-optimal in expectation in [A. Cohen, M A. Davenport and D. Leviatan. Found. Comput. Math. 13 (2013) 819–834] and in probability in [G. Migliorati, F. Nobile, E. von Schwerin, R. Tempone, Found. Comput. Math. 14 (2014) 419–456], under suitable conditions that relate the number of samples with respect to the dimension of the polynomial space. Here “quasi-optimal” means that the accuracy of the least-squares approximation is comparable with that of the best approximation in the given polynomial space. In this paper, we discuss the quasi-optimality of the polynomial least-squares method in arbitrary dimension. Our analysis applies to any arbitrary multivariate polynomial space (including tensor product, total degree or hyperbolic crosses), under the minimal requirement that its associated index set is downward closed. The optimality criterion only involves the relation between the number of samples and the dimension of the polynomial space, independently of the anisotropic shape and of the number of variables. We extend our results to the approximation of Hilbert space-valued functions in order to apply them to the approximation of parametric and stochastic elliptic PDEs. As a particular case, we discuss “inclusion type” elliptic PDE models, and derive an exponential convergence estimate for the least-squares method. Numerical results confirm our estimate, yet pointing out a gap between the condition necessary to achieve optimality in the theory, and the condition that in practice yields the optimal convergence rate.
Elliptic curves and their torsion subgroups over number fields of type (2, 2,
QIU; Derong; ZHANG; Xianke
2001-01-01
［1］Shi Zhong-ci, On the accuracy of the quasi-conforming and generalize conforming finite elements, Chin. Ann. Math., 1990, 11B: 148.［2］Shi Zhong-ci, Chen Shao-chun, Huang Hong-ci, Plate elements with high accuracy, Collec. Geom. Anal. Math. Phys. (ed. Li Ta-Tsien), Singapore: World Scientific, 1997, 155—164.［3］Chen Shao-chun, Shi Zhong-ci, Double set parameter method for the construction of the element stiffness matrix, Mathematica Numerica Sinica (in Chinese), 1991, 13: 286.［4］Ciarlet, P., The Finite Element Method for Elliptic Problems, Amsterdam: North-Holland, 1978.
Discrete Methods Based on First Order Reversal Curves to Identify Preisach Model of Smart Materials
LI Fan; ZHAO Jian-hui
2007-01-01
Preisach model is widely used in modeling of smart materials. Although first order reversal curves (FORCs) have often found applications in the fields of physics and geology, they are able to serve to identify Preisach model. In order to clarify the relationship between the Preisach model and the first order reversal curves, this paper is directed towards: (1) giving the reason a first order reversal curve is introduced; (2) presenting, for identifying Preisach model, two discrete methods, which are analytically based on first order reversal curves. Herein also is indicated the solution's uniqueness of these two identifying methods. At last, the validity of these two methods is verified by simulating a real smart actuator both methods have been applied to.
Roshan Duraisamy
2007-02-01
Full Text Available The secure establishment of cryptographic keys for symmetric encryption via key agreement protocols enables nodes in a network of embedded systems and remote agents to communicate securely in an insecure environment. In this paper, we propose a pure hardware implementation of a key agreement protocol, which uses the elliptic curve Diffie-Hellmann and digital signature algorithms and enables two parties, a remote agent and a networked embedded system, to establish a 128-bit symmetric key for encryption of all transmitted data via the advanced encryption scheme (AES. The resulting implementation is a protocol-on-chip that supports full 128-bit equivalent security (PoC-128. The PoC-128 has been implemented in an FPGA, but it can also be used as an IP within different embedded applications. As 128-bit security is conjectured valid for the foreseeable future, the PoC-128 goes well beyond the state of art in securing networked embedded devices.
Strangio MaurizioAdriano
2007-01-01
Full Text Available The secure establishment of cryptographic keys for symmetric encryption via key agreement protocols enables nodes in a network of embedded systems and remote agents to communicate securely in an insecure environment. In this paper, we propose a pure hardware implementation of a key agreement protocol, which uses the elliptic curve Diffie-Hellmann and digital signature algorithms and enables two parties, a remote agent and a networked embedded system, to establish a 128-bit symmetric key for encryption of all transmitted data via the advanced encryption scheme (AES. The resulting implementation is a protocol-on-chip that supports full 128-bit equivalent security (PoC-128. The PoC-128 has been implemented in an FPGA, but it can also be used as an IP within different embedded applications. As 128-bit security is conjectured valid for the foreseeable future, the PoC-128 goes well beyond the state of art in securing networked embedded devices.
Joong-Hyun Rhim; Doo-Yeoun Cho; Kyu-Yeul Lee; Tae-Wan Kim
2006-01-01
We propose a method that automatically generates discrete bicubic G1 continuous B-spline surfaces that interpolate the curve network of a ship hullform. First, the curves in the network are classified into two types: boundary curves and "reference curves". The boundary curves correspond to a set of rectangular (or triangular) topological type that can be represented with tensor-product (or degenerate) B-spline surface patches. Next, in the interior of the patches,surface fitting points and cross boundary derivatives are estimated from the reference curves by constructing "virtual" isoparametric curves. Finally, a discrete G1 continuous B-spline surface is generated by a surface fitting algorithm. Several smooth ship hullform surfaces generated from curve networks corresponding to actual ship hullforms demonstrate the quality of the method.
Fayolle, G; Fayolle, Guy; Furtlehner, Cyril
2006-01-01
This report deals with continuous limits of several one-dimensional diffusive systems, obtained from stochastic distortions of discrete curves with different kinds of coding. These systems are indeed special cases of reaction-diffusion. A general functional formalism is set up, allowing to grapple with hydrodynamic limits. We also analyse the steady-state regime, not only in the reversible case, so that the invariant measure can have a non Gibbs form. A link is made between recursion properties, which originate matrix solutions, and particle cycles in the state-graph, by introducing loop currents on the analogy with electric circuits. Also, by means of the aforementioned functional approach, a bridge is established between structural constants involved in the recursions at discrete level and the constants which appear in Lotka-Volterra equations describing the fluid limits of stationary states. Finally the Lagrangian for the current fluctuations is obtained from an iterative scheme, and the related Hamilton-J...
Concus, P.; Golub, G.H.; O' Leary, D.P.
1976-01-01
A generalized conjugate gradient method is considered for solving sparse, symmetric, positive-definite systems of linear equations, principally those arising from the discretization of boundary value problems for elliptic partial differential equations. The method is based on splitting off from the original coefficient matrix a symmetric, positive-definite one which corresponds to a more easily solvable system of equations, and then accelerating the associated iteration by using conjugate gradients. Optimality and convergence properties are presented, and the relation to other methods is discussed. Several splittings for which the method seems particularly effective are also discussed; and for some, numerical examples are given. 1 figure, 1 table. (auth)
Nafeesa Begum Jeddy
2014-01-01
Full Text Available Hierarchical Access Control in group communication is an active area of research which is difficult to achieve it. Its primary objective is to allow users of a higher authority group to access information or resource held by lower group users and preventing the lower group users to access information held by higher class users. Large collection of collaborative applications in organizations inherently has hierarchical structures for functioning, where providing security by efficient group key management is a big challenging issue. While preserving centralized methods for hierarchical access control, it is difficult to achieve efficiency as a single membership change will result in lot of changes which are difficult to maintain. So, using distributed key agreement techniques is more appropriate for this scenario. This study explore on novel group key agreement approach, which combines both the symmetric polynomial scheme and Tree Based Group elliptic Curve key exchange. Also, it yields a secure protocol suite that is good in fault-tolerant and simple. The efficiency of SP-TGECDH is better than many other schemes. Using TGECDH makes the scheme suitable small Low powered devices.
S.K. Hafizul Islam
2017-07-01
Full Text Available In the literature, many three-party authenticated key exchange (3PAKE protocols are put forwarded to established a secure session key between two users with the help of trusted server. The computed session key will ensure secure message exchange between the users over any insecure communication networks. In this paper, we identified some deficiencies in Tan’s 3PAKE protocol and then devised an improved 3PAKE protocol without symmetric key en/decryption technique for mobile-commerce environments. The proposed protocol is based on the elliptic curve cryptography and one-way cryptographic hash function. In order to prove security validation of the proposed 3PAKE protocol we have used widely accepted AVISPA software whose results confirm that the proposed protocol is secure against active and passive attacks including replay and man-in-the-middle attacks. The proposed protocol is not only secure in the AVISPA software, but it also secure against relevant numerous security attacks such as man-in-the-middle attack, impersonation attack, parallel attack, key-compromise impersonation attack, etc. In addition, our protocol is designed with lower computation cost than other relevant protocols. Therefore, the proposed protocol is more efficient and suitable for practical use than other protocols in mobile-commerce environments.
Reddy, Alavalapati Goutham; Das, Ashok Kumar; Odelu, Vanga; Yoo, Kee-Young
2016-01-01
Biometric based authentication protocols for multi-server architectures have gained momentum in recent times due to advancements in wireless technologies and associated constraints. Lu et al. recently proposed a robust biometric based authentication with key agreement protocol for a multi-server environment using smart cards. They claimed that their protocol is efficient and resistant to prominent security attacks. The careful investigation of this paper proves that Lu et al.'s protocol does not provide user anonymity, perfect forward secrecy and is susceptible to server and user impersonation attacks, man-in-middle attacks and clock synchronization problems. In addition, this paper proposes an enhanced biometric based authentication with key-agreement protocol for multi-server architecture based on elliptic curve cryptography using smartcards. We proved that the proposed protocol achieves mutual authentication using Burrows-Abadi-Needham (BAN) logic. The formal security of the proposed protocol is verified using the AVISPA (Automated Validation of Internet Security Protocols and Applications) tool to show that our protocol can withstand active and passive attacks. The formal and informal security analyses and performance analysis demonstrates that the proposed protocol is robust and efficient compared to Lu et al.'s protocol and existing similar protocols.
Alavalapati Goutham Reddy
Full Text Available Biometric based authentication protocols for multi-server architectures have gained momentum in recent times due to advancements in wireless technologies and associated constraints. Lu et al. recently proposed a robust biometric based authentication with key agreement protocol for a multi-server environment using smart cards. They claimed that their protocol is efficient and resistant to prominent security attacks. The careful investigation of this paper proves that Lu et al.'s protocol does not provide user anonymity, perfect forward secrecy and is susceptible to server and user impersonation attacks, man-in-middle attacks and clock synchronization problems. In addition, this paper proposes an enhanced biometric based authentication with key-agreement protocol for multi-server architecture based on elliptic curve cryptography using smartcards. We proved that the proposed protocol achieves mutual authentication using Burrows-Abadi-Needham (BAN logic. The formal security of the proposed protocol is verified using the AVISPA (Automated Validation of Internet Security Protocols and Applications tool to show that our protocol can withstand active and passive attacks. The formal and informal security analyses and performance analysis demonstrates that the proposed protocol is robust and efficient compared to Lu et al.'s protocol and existing similar protocols.
Zhidkov, E.P.; Mazurkevich, G.E.; Khoromsky, B.N.
1989-01-01
A method of domain decomposition with cross-points (box decomposition) is used for the solution of finite-difference elliptic boundary value problems in rectangle and in parallelepiped. Capacitance matrix and preconditioners for iterative solution of arising algebraic problem are constructed by means of Poincare-Steklov operators. The convergence properties of iterative algorithms depend on local characteristics of subdomains on the number N'' of unknowns in one direction in subdomains, and are independent of the number of subdomains and of jumps of elliptic operator coefficients as long as these jumps only occur across the subdomain boundaries. The dependence of convergence on discretization of the problem is defined by ln N'' for two-dimensional problems, by {radical}N ln N'' for three-dimensional problems. The results of numerical experiments illustrating convergence properties are presented. 18 refs., 3 figs., 4 tabs.
Vector Bundles over Elliptic Fibrations
Friedman, R; Witten, Edward; Friedman, Robert; Morgan, John W.; Witten, Edward
1997-01-01
This paper gives various methods for constructing vector bundles over elliptic curves and more generally over families of elliptic curves. We construct universal families over generalized elliptic curves via spectral cover methods and also by extensions, and then give a relative version of the construction in families. We give various examples and make Chern class computations.
Vankamamidi S Naresh; Nistala V E S Murthy
2015-10-01
In this paper a new two-round authenticated contributory group key agreement based on Elliptic Curve Diffie–Hellman protocol with Privacy Preserving Public Key Infrastructure (PP-PKI) is introduced and is extended to a dynamic authenticated contributory group key agreement with join and leave protocols for dynamic groups. The proposed protocol provides such security attributes as forward secrecy, backward secrecy, and defense against man in the middle (MITM) and Unknown keyshare security attacks and also authentication along with privacy preserving attributes like anonymity, traceability and unlinkability. In the end, they are compared with other popular Diffie–Hellman and Elliptic Curve Diffie–Hellman based group key agreement protocols and the results are found to be satisfactory.
Levin, A. M.; Olshanetsky, M. A.; Zotov, A. V.
2016-08-01
We construct twisted Calogero-Moser systems with spins as Hitchin systems derived from the Higgs bundles over elliptic curves, where the transition operators are defined by arbitrary finite-order automorphisms of the underlying Lie algebras. We thus obtain a spin generalization of the twisted D'Hoker-Phong and Bordner-Corrigan-Sasaki-Takasaki systems. In addition, we construct the corresponding twisted classical dynamical r-matrices and the Knizhnik-Zamolodchikov-Bernard equations related to the automorphisms of Lie algebras.
Abdellah Touhafi
2013-07-01
Full Text Available Typically, commercial sensor nodes are equipped with MCUsclocked at a low-frequency (i.e., within the 4–12 MHz range. Consequently, executing cryptographic algorithms in those MCUs generally requires a huge amount of time. In this respect, the required energy consumption can be higher than using a separate accelerator based on a Field-programmable Gate Array (FPGA that is switched on when needed. In this manuscript, we present the design of a cryptographic accelerator suitable for an FPGA-based sensor node and compliant with the IEEE802.15.4 standard. All the embedded resources of the target platform (Xilinx Artix-7 have been maximized in order to provide a cost-effective solution. Moreover, we have added key negotiation capabilities to the IEEE 802.15.4 security suite based on Elliptic Curve Cryptography (ECC. Our results suggest that tailored accelerators based on FPGA can behave better in terms of energy than contemporary software solutions for motes, such as the TinyECC and NanoECC libraries. In this regard, a point multiplication (PM can be performed between 8.58- and 15.4-times faster, 3.40- to 23.59-times faster (Elliptic Curve Diffie-Hellman, ECDH and between 5.45- and 34.26-times faster (Elliptic Curve Integrated Encryption Scheme, ECIES. Moreover, the energy consumption was also improved with a factor of 8.96 (PM.
de la Piedra, Antonio; Braeken, An; Touhafi, Abdellah
2013-07-29
Typically, commercial sensor nodes are equipped with MCUsclocked at a low-frequency (i.e., within the 4-12 MHz range). Consequently, executing cryptographic algorithms in those MCUs generally requires a huge amount of time. In this respect, the required energy consumption can be higher than using a separate accelerator based on a Field-programmable Gate Array (FPGA) that is switched on when needed. In this manuscript, we present the design of a cryptographic accelerator suitable for an FPGA-based sensor node and compliant with the IEEE802.15.4 standard. All the embedded resources of the target platform (Xilinx Artix-7) have been maximized in order to provide a cost-effective solution. Moreover, we have added key negotiation capabilities to the IEEE 802.15.4 security suite based on Elliptic Curve Cryptography (ECC). Our results suggest that tailored accelerators based on FPGA can behave better in terms of energy than contemporary software solutions for motes, such as the TinyECC and NanoECC libraries. In this regard, a point multiplication (PM) can be performed between 8.58- and 15.4-times faster, 3.40- to 23.59-times faster (Elliptic Curve Diffie-Hellman, ECDH) and between 5.45- and 34.26-times faster (Elliptic Curve Integrated Encryption Scheme, ECIES). Moreover, the energy consumption was also improved with a factor of 8.96 (PM).
基于FPGA的椭圆曲线密码(ECC)算法硬件设计%Hardware Design of Elliptic Curve Cryptography(ECC) Based on FPGA
赵曼; 徐和根
2013-01-01
Elliptic curve cryptosystem ( ECC) is a public key encryption system with the most secure unit key security at present, the application of FPGA and hardware design to implement the ECC cryptography have become a concern in the field of information security. The further study of the elliptic curve encryption and decryption is based on the theory, using the verilog hardware description language and schematic design method to achieve the ECC encryption algorithm, with high-speed and low-power characteristics.%椭圆曲线密码体制(elliptic curve cryptosystem,ECC)是目前已知的单位密钥安全性最高的一种公钥加密体制,使用FPGA等硬件设计方法来实现ECC密码系统已成为信息安全领域引人关注的研究.该文在深入研究椭圆曲线加解密理论基础上,使用Verilog硬件描述语言和原理图输入法共同实现了ECC加密算法,具有高速、低功耗的特点.
Hu, Shuangwei; Niemi, Antti J
2012-01-01
The theory of string-like continuous curves and discrete chains have numerous important physical applications. Here we develop a general geometrical approach, to systematically derive Hamiltonian energy functions for these objects. In the case of continuous curves, we demand that the energy function must be invariant under local frame rotations, and it should also transform covariantly under reparametrizations of the curve. This leads us to consider energy functions that are constructed from the conserved quantities in the hierarchy of the integrable nonlinear Schr\\"odinger equation (NLSE). We point out the existence of a Weyl transformation that we utilize to introduce a dual hierarchy to the standard NLSE hierarchy. We propose that the dual hierarchy is also integrable, and we confirm this to the first non-trivial order. In the discrete case the requirement of reparametrization invariance is void. But the demand of invariance under local frame rotations prevails, and we utilize it to introduce a discrete va...
Fraggedakis, D.; Papaioannou, J.; Dimakopoulos, Y.; Tsamopoulos, J.
2017-09-01
A new boundary-fitted technique to describe free surface and moving boundary problems is presented. We have extended the 2D elliptic grid generator developed by Dimakopoulos and Tsamopoulos (2003) [19] and further advanced by Chatzidai et al. (2009) [18] to 3D geometries. The set of equations arises from the fulfillment of the variational principles established by Brackbill and Saltzman (1982) [21], and refined by Christodoulou and Scriven (1992) [22]. These account for both smoothness and orthogonality of the grid lines of tessellated physical domains. The elliptic-grid equations are accompanied by new boundary constraints and conditions which are based either on the equidistribution of the nodes on boundary surfaces or on the existing 2D quasi-elliptic grid methodologies. The capabilities of the proposed algorithm are first demonstrated in tests with analytically described complex surfaces. The sequence in which these tests are presented is chosen to help the reader build up experience on the best choice of the elliptic grid parameters. Subsequently, the mesh equations are coupled with the Navier-Stokes equations, in order to reveal the full potential of the proposed methodology in free surface flows. More specifically, the problem of gas assisted injection in ducts of circular and square cross-sections is examined, where the fluid domain experiences extreme deformations. Finally, the flow-mesh solver is used to calculate the equilibrium shapes of static menisci in capillary tubes.
Bell-Curve Genetic Algorithm for Mixed Continuous and Discrete Optimization Problems
Kincaid, Rex K.; Griffith, Michelle; Sykes, Ruth; Sobieszczanski-Sobieski, Jaroslaw
2002-01-01
In this manuscript we have examined an extension of BCB that encompasses a mix of continuous and quasi-discrete, as well as truly-discrete applications. FVe began by testing two refinements to the discrete version of BCB. The testing of midpoint versus fitness (Tables 1 and 2) proved inconclusive. The testing of discrete normal tails versus standard mutation showed was conclusive and demonstrated that the discrete normal tails are better. Next, we implemented these refinements in a combined continuous and discrete BCB and compared the performance of two discrete distance on the hub problem. Here we found when "order does matter" it pays to take it into account.
Elliptic Carmichael Numbers and Elliptic Korselt Criteria
Silverman, Joseph H
2011-01-01
Let E/Q be an elliptic curve, let L(E,s)=\\sum a_n/n^s be the L-series of E/Q, and let P be a point in E(Q). An integer n > 2 having at least two distinct prime factors will be be called an elliptic pseudoprime for (E,P) if E has good reduction at all primes dividing n and (n+1-a_n)P = 0 (mod n). Then n is an elliptic Carmichael number for E if n is an elliptic pseudoprime for every P in E(Z/nZ). In this note we describe two elliptic analogues of Korselt's criterion for Carmichael numbers, and we analyze elliptic Carmichael numbers of the form pq.
Tala-Tebue, E.; Tsobgni-Fozap, D. C.; Kenfack-Jiotsa, A.; Kofane, T. C.
2014-06-01
Using the Jacobi elliptic functions and the alternative ( G'/ G-expansion method including the generalized Riccati equation, we derive exact soliton solutions for a discrete nonlinear electrical transmission line in (2+1) dimension. More precisely, these methods are general as they lead us to diverse solutions that have not been previously obtained for the nonlinear electrical transmission lines. This study seeks to show that it is not often necessary to transform the equation of the network into a well-known differential equation before finding its solutions. The solutions obtained by the current methods are generalized periodic solutions of nonlinear equations. The shape of solutions can be well controlled by adjusting the parameters of the network. These exact solutions may have significant applications in telecommunication systems where solitons are used to codify or for the transmission of data.
Odesskii, A V [L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow (Russian Federation)
2002-12-31
This survey is devoted to associative Z{sub {>=}}{sub 0}-graded algebras presented by n generators and n(n-1)/2 quadratic relations and satisfying the so-called Poincare-Birkhoff-Witt condition (PBW-algebras). Examples are considered of such algebras, depending on two continuous parameters (namely, on an elliptic curve and a point on it), that are flat deformations of the polynomial ring in n variables. Diverse properties of these algebras are described, together with their relations to integrable systems, deformation quantization, moduli spaces, and other directions of modern investigations.
Moshirfar, Majid; Calvo, Charles M; Kinard, Krista I; Williams, Lloyd B; Sikder, Shameema; Neuffer, Marcus C
2011-01-01
This study analyzes the characteristics of donor and recipient tissue preparation between the Hessburg-Barron and Hanna punch and trephine systems by using elliptical curve fitting models, light microscopy, and anterior segment optical coherence tomography (AS-OCT). Eight millimeter Hessburg-Barron and Hanna vacuum trephines and punches were used on six cadaver globes and six corneal-scleral rims, respectively. Eccentricity data were generated using measurements from photographs of the corneal buttons and were used to generate an elliptical curve fit to calculate properties of the corneal button. The trephination angle and punch angle were measured by digital protractor software from light microscopy and AS-OCT images to evaluate the consistency with which each device cuts the cornea. The Hanna trephine showed a trend towards producing a more circular recipient button than the Barron trephine (ratio of major axis to minor axis), ie, 1.059 ± 0.041 versus 1.110 ± 0.027 (P = 0.147) and the Hanna punch showed a trend towards producing a more circular donor cut than the Barron punch, ie, 1.021 ± 0.022 versus 1.046 ± 0.039 (P = 0.445). The Hanna trephine was demonstrated to have a more consistent trephination angle than the Barron trephine when assessing light microscopy images, ie, ±14.39° (95% confidence interval [CI] 111.9-157.7) versus ±19.38° (95% CI 101.9-150.2, P = 0.492) and OCT images, ie, ±8.08° (95% CI 106.2-123.3) versus ±11.16° (95% CI 109.3-132.6, P = 0.306). The angle created by the Hanna punch had less variability than the Barron punch from both the light microscopy, ie, ±4.81° (95% CI 101.6-113.9) versus ±11.28° (95% CI 84.5-120.6, P = 0.295) and AS-OCT imaging, ie, ±9.96° (95% CI 95.7-116.4) versus ±14.02° (95% CI 91.8-123.7, P = 0.825). Statistical significance was not achieved. The Hanna trephine and punch may be more accurate and consistent in cutting corneal buttons than the Hessburg-Barron trephine and punch when evaluated using
Moshirfar, Majid; Calvo, Charles M; Kinard, Krista I; Williams, Lloyd B; Sikder, Shameema; Neuffer, Marcus C
2011-01-01
Background: This study analyzes the characteristics of donor and recipient tissue preparation between the Hessburg-Barron and Hanna punch and trephine systems by using elliptical curve fitting models, light microscopy, and anterior segment optical coherence tomography (AS-OCT). Methods: Eight millimeter Hessburg-Barron and Hanna vacuum trephines and punches were used on six cadaver globes and six corneal-scleral rims, respectively. Eccentricity data were generated using measurements from photographs of the corneal buttons and were used to generate an elliptical curve fit to calculate properties of the corneal button. The trephination angle and punch angle were measured by digital protractor software from light microscopy and AS-OCT images to evaluate the consistency with which each device cuts the cornea. Results: The Hanna trephine showed a trend towards producing a more circular recipient button than the Barron trephine (ratio of major axis to minor axis), ie, 1.059 ± 0.041 versus 1.110 ± 0.027 (P = 0.147) and the Hanna punch showed a trend towards producing a more circular donor cut than the Barron punch, ie, 1.021 ± 0.022 versus 1.046 ± 0.039 (P = 0.445). The Hanna trephine was demonstrated to have a more consistent trephination angle than the Barron trephine when assessing light microscopy images, ie, ±14.39° (95% confidence interval [CI] 111.9–157.7) versus ±19.38° (95% CI 101.9–150.2, P = 0.492) and OCT images, ie, ±8.08° (95% CI 106.2–123.3) versus ±11.16° (95% CI 109.3–132.6, P = 0.306). The angle created by the Hanna punch had less variability than the Barron punch from both the light microscopy, ie, ±4.81° (95% CI 101.6–113.9) versus ±11.28° (95% CI 84.5–120.6, P = 0.295) and AS-OCT imaging, ie, ±9.96° (95% CI 95.7–116.4) versus ±14.02° (95% CI 91.8–123.7, P = 0.825). Statistical significance was not achieved. Conclusion: The Hanna trephine and punch may be more accurate and consistent in cutting corneal buttons than
张福伟; 刘进生
2012-01-01
By using the variational method and critical point theory, especially critical group and Morse theory, combined with the matrix theory and space dimension, taking into account the critical points of both positive and negative energy functional, the multiplicity of solutions of 1-dimensional nonlinear discrete elliptic resonant problem was investigated. Under some assumptions, two kinds of new sufficient conditions were obtained under which there exist at least two nonzero solutions. An example was given to verify the obtained results. The results showed that, under the same assumptions, the number of known solutions of 1-dimensional resonant problem is more than that of multidimensional resonant problem.%利用变分方法与临界点理论,特别是临界群与Morse理论,结合矩阵理论与空间维数,同时考虑正、负能量泛函的临界点,研究了一维非线性离散椭圆共振问题解的多重性.在一定的假设条件下,得到了此类问题至少存在两个非零解的两类新的充分条件,并给出了具体应用的实例.结果表明:在相同的假设条件下,一维共振问题比多维共振问题得到的解更多.
Zhu, Ling; van de Ven, Glenn; Long, R J; Watkins, Laura L; Pota, Vincenzo; Napolitano, Nicola R; Forbes, Duncan A; Brodie, Jean; Foster, Caroline
2016-01-01
We construct a suite of discrete chemo-dynamical models of the giant elliptical galaxy NGC 5846. These models are a powerful tool to constrain both the mass distribution and internal dynamics of multiple tracer populations. We use Jeans models to simultaneously fit stellar kinematics within the effective radius $R_{\\rm e}$, planetary nebula (PN) radial velocities out to $3\\, R_{\\rm e}$, and globular cluster (GC) radial velocities and colours out to $6\\,R_{\\rm e}$. The best-fitting model is a cored DM halo which contributes $\\sim 10\\%$ of the total mass within $1\\,R_{\\rm e}$, and $67\\% \\pm 10\\%$ within $6\\,R_{\\rm e}$, although a cusped DM halo is also acceptable. The red GCs exhibit mild rotation with $v_{\\rm max}/\\sigma_0 \\sim 0.3$ in the region $R > \\,R_{\\rm e}$, aligned with but counter-rotating to the stars in the inner parts, while the blue GCs and PNe kinematics are consistent with no rotation. The red GCs are tangentially anisotropic, the blue GCs are mildly radially anisotropic, and the PNe vary from r...
Zhu, Ling; Romanowsky, Aaron J.; van de Ven, Glenn; Long, R. J.; Watkins, Laura L.; Pota, Vincenzo; Napolitano, Nicola R.; Forbes, Duncan A.; Brodie, Jean; Foster, Caroline
2016-11-01
We construct a suite of discrete chemo-dynamical models of the giant elliptical galaxy NGC 5846. These models are a powerful tool to constrain both the mass distribution and internal dynamics of multiple tracer populations. We use Jeans models to simultaneously fit stellar kinematics within the effective radius Re, planetary nebula (PN) radial velocities out to 3 Re, and globular cluster (GC) radial velocities and colours out to 6 Re. The best-fitting model is a cored dark matter halo which contributes ˜10 per cent of the total mass within 1 Re, and 67 per cent ± 10 per cent within 6 Re, although a cusped dark matter halo is also acceptable. The red GCs exhibit mild rotation with vmax/σ0 ˜ 0.3 in the region R > Re, aligned with but counter-rotating to the stars in the inner parts, while the blue GCs and PNe kinematics are consistent with no rotation. The red GCs are tangentially anisotropic, the blue GCs are mildly radially anisotropic, and the PNe vary from radially to tangentially anisotropic from the inner to the outer region. This is confirmed by general made-to-measure models. The tangential anisotropy of the red GCs in the inner regions could stem from the preferential destruction of red GCs on more radial orbits, while their outer tangential anisotropy - similar to the PNe in this region - has no good explanation. The mild radial anisotropy of the blue GCs is consistent with an accretion scenario.
Zampini, Stefano
2016-06-02
Balancing Domain Decomposition by Constraints (BDDC) methods have proven to be powerful preconditioners for large and sparse linear systems arising from the finite element discretization of elliptic PDEs. Condition number bounds can be theoretically established that are independent of the number of subdomains of the decomposition. The core of the methods resides in the design of a larger and partially discontinuous finite element space that allows for fast application of the preconditioner, where Cholesky factorizations of the subdomain finite element problems are additively combined with a coarse, global solver. Multilevel and highly-scalable algorithms can be obtained by replacing the coarse Cholesky solver with a coarse BDDC preconditioner. BDDC methods have the remarkable ability to control the condition number, since the coarse space of the preconditioner can be adaptively enriched at the cost of solving local eigenproblems. The proper identification of these eigenproblems extends the robustness of the methods to any heterogeneity in the distribution of the coefficients of the PDEs, not only when the coefficients jumps align with the subdomain boundaries or when the high contrast regions are confined to lie in the interior of the subdomains. The specific adaptive technique considered in this paper does not depend upon any interaction of discretization and partition; it relies purely on algebraic operations. Coarse space adaptation in BDDC methods has attractive algorithmic properties, since the technique enhances the concurrency and the arithmetic intensity of the preconditioning step of the sparse implicit solver with the aim of controlling the number of iterations of the Krylov method in a black-box fashion, thus reducing the number of global synchronization steps and matrix vector multiplications needed by the iterative solver; data movement and memory bound kernels in the solve phase can be thus limited at the expense of extra local ops during the setup of
Application of Elliptic Curve Cryptography in CA Mobile Payment%椭圆曲线密码在移动支付CA中的应用
王艳红; 袁春花
2014-01-01
The mobile payment based on mobile phone or some other mobile terminals brings people convenience, but its security is-sues are also increasingly prominent. By exploring the structure of mobile payment system and the elliptic curve cryptography system, in view of the security problems of the mobile payment system, this paper designs a CA trust model in the mobile payment system, after analyzing the model, the ellipse curve algorithm is applied to it, ensuring the security of the mobile payment system.%基于手机等移动终端的移动支付在带给大家快捷方便的同时，移动支付的安全性问题也日益突出。通过探讨移动支付系统结构以及椭圆曲线密码系统，针对移动支付系统存在的安全问题，设计了移动支付系统中一种CA的信任模型，对该模型分析之后，将椭圆曲线算法应用到其中，保证了移动支付系统的安全。
NURBS curve discrete algorithm based on equal arc-length principle%等弧长原则的NURBS曲线离散算法
贾春阳; 杨岳; 陈峰
2014-01-01
NURBS曲线广泛应用于工业产品复杂曲线曲面设计中，但在实际应用中常遇到曲线离散的几何处理问题。针对NURBS曲线离散问题，提出了一种按等弧长原则对NURBS曲线进行离散的方法。该方法引入步长函数控制离散曲线段的弧长，采用积分法和迭代法调整步长函数以控制曲线的离散精度，通过误差检验方法校验曲线离散的逼近精度。通过实际算例，验证了NURBS曲线等弧长离散算法的合理性和有效性。%NURBS curves are widely used in complex curves and curved surfaces of industrial product design, but geometry processing problems of curve discrete are found in practical applications. According to the NURBS curve discrete problems, a method of curve discrete based on equal arc-length principle is put forward. Step function is introduced to control the length of the discrete curve, and the precision of curve discrete can be controlled by adjusting step function through integration and itera-tive methods. The approximation accuracy of curve division is checked by error checking algorithm. The rationality and validity of the NURBS curve discrete based on equal arc-length principle are verified by practical calculation example.
Barth, TIm
2002-01-01
This viewgraph presentation provides information on optimizing the travel distance between two points on a curved surface. The presentation addresses the single source shortest path problem, fast algorithms for estimating the eikonal equation, fast schemes and barrier theorems, and the discontinuous Galerkin method, including hyperbolic causality, finite element method, scalars, and marching the discontinuous Galerkin Eikonal approximation.
Moshirfar M
2011-08-01
Full Text Available Majid Moshirfar1, Charles M Calvo2, Krista I Kinard1, Lloyd B Williams1, Shameema Sikder3, Marcus C Neuffer11University of Utah, Department of Ophthalmology and Visual Sciences, Salt Lake City, UT, USA; 2University of Nevada, School of Medicine, Las Vegas, NV, USA; 3Wilmer Eye Institute, Johns Hopkins University, Baltimore, MD, USABackground: This study analyzes the characteristics of donor and recipient tissue preparation between the Hessburg-Barron and Hanna punch and trephine systems by using elliptical curve fitting models, light microscopy, and anterior segment optical coherence tomography (AS-OCT.Methods: Eight millimeter Hessburg-Barron and Hanna vacuum trephines and punches were used on six cadaver globes and six corneal-scleral rims, respectively. Eccentricity data were generated using measurements from photographs of the corneal buttons and were used to generate an elliptical curve fit to calculate properties of the corneal button. The trephination angle and punch angle were measured by digital protractor software from light microscopy and AS-OCT images to evaluate the consistency with which each device cuts the cornea.Results: The Hanna trephine showed a trend towards producing a more circular recipient button than the Barron trephine (ratio of major axis to minor axis, ie, 1.059 ± 0.041 versus 1.110 ± 0.027 (P = 0.147 and the Hanna punch showed a trend towards producing a more circular donor cut than the Barron punch, ie, 1.021 ± 0.022 versus 1.046 ± 0.039 (P = 0.445. The Hanna trephine was demonstrated to have a more consistent trephination angle than the Barron trephine when assessing light microscopy images, ie, ±14.39° (95% confidence interval [CI] 111.9–157.7 versus ±19.38° (95% CI 101.9–150.2, P = 0.492 and OCT images, ie, ± 8.08° (95% CI 106.2–123.3 versus ± 11.16° (95% CI 109.3–132.6, P = 0.306. The angle created by the Hanna punch had less variability than the Barron punch from both the light microscopy
Provably Secure Signcryption Scheme Based on Elliptic Curve%基于椭圆曲线的可证明安全的签密方案
任艳丽; 陆梅宁
2011-01-01
A signcryption scheme can realize signature and encryption simultaneously, and its cost is smaller than the sum of signature and encryption. However, most signcryption schemes do not have strict security proof. This paper proposes a signcryption scheme based on difficult problems of elliptic curve group. The scheme is efficient and only needs one pair operation. It proves that the scheme is semantic secure and unforgeable in the standard model. Moreover, the scheme has non-repudiation, forward security and public verification.%签密方案可以同时实现保密和认证,且实现代价小于加密和签名之和,但大多数签密方案都没有严格的安全证明.为此,基于椭圆曲线群上的困难问题提出一个可证明安全的签密方案.方案仅需要一次双线性对运算,实现快速.在标准模型下,证明该方案既具有密文不可区分性与签名不可伪造性,也具有不可否认性、前向安全性和公开可验证性.
An algorithm based on elliptic interpolation for generating random curves%一种基于椭圆插值的随机曲线生成算法
李玲; 魏玮
2012-01-01
在计算机图形学中,建立复杂的结构或形状的模型是一个核心问题.随机曲线的生成在计算机游戏,电影,建筑模型,城市规划和虚拟现实等领域中,也扮演着十分重要的角色.本文主要研究二值图像中随机产生曲线的算法,算法首先采用随机的方法产生初始点和终结点,再利用椭圆内随机插值的方法产生插值点,以新产生的点和其相邻点做为初始点与终结点,再利用椭圆内随机插值的方法产生新的插值点,依此类推最后得到由诸多插值点组成的整条曲线.该过程中为了保证曲线收敛,假设先产生的插值点对曲线的形成趋势影响大,后产生的随机点对曲线的形成趋势影响小.并且,在插值过程中,只对相邻插值点进行下一步插值.结合椭圆内产生的随机曲线的过程,使用Visual C++软件来实现随机曲线的生成算法并进行结果的详细分析,同时做相应的说明和结论来改善用户交互系统.%The building of geometric models with complex shapes and structures is one of the key issues in computer graphics. Random curves also play important roles in many domains such as computer games, movies, architectural models, urban planning, virtual reality etc. In this paper, we present a novel synthesis algorithm for procedurally generating random curves in binary image. The first step is to generate the starting point and ending point randomly; The second step is to generate the interpolative point by using the elliptic interpolation method; The third step is to generate the next new interpolative point by starting with the new point and ending with its adjacent point. These new points though quite few, finally constitute the whole curve. To ensure the convergence of the curve, we firstly assume that the earlier interpolative points have more impact on the trend of the curve, while the latter points has less impact. The second assumption is to generate new points only between the
Elliptic Curve Cryptography with Java
Klima, Richard E.; Sigmon, Neil P.
2005-01-01
The use of the computer, and specifically the mathematics software package Maple, has played a central role in the authors' abstract algebra course because it provides their students with a way to see realistic examples of the topics they discuss without having to struggle with extensive computations. However, Maple does not provide the computer…
Elliptic hypergeometric functions
Spiridonov, V P
2016-01-01
This is author's Habilitation Thesis (Dr. Sci. dissertation) submitted at the beginning of September 2004. It is written in Russian and is posted due to the continuing requests for the manuscript. The content: 1. Introduction, 2. Nonlinear chains with the discrete time and their self-similar solutions, 3. General theory of theta hypergeometric series, 4. Theta hypergeometric integrals, 5. Biorthogonal functions, 6. Elliptic hypergeometric functions with |q|=1, 7. Conclusion, 8. References. It contains an outline of a general heuristic scheme for building univariate special functions through self-similar reductions of spectral transformation chains, which allowed construction of the differential-difference q-Painleve equations, as well as of the most general known set of elliptic biorthogonal functions comprising all classical orthogonal polynomials and biorthogonal rational functions. One of the key results of the thesis consists in the discovery of genuinely transcendental elliptic hypergeometric functions d...
Degenerating the elliptic Schlesinger system
Aminov, G. A.; Artamonov, S. B.
2013-01-01
We study various ways of degenerating the Schlesinger system on the elliptic curve with R marked points. We construct a limit procedure based on an infinite shift of the elliptic curve parameter and on shifts of the marked points. We show that using this procedure allows obtaining a nonautonomous Hamiltonian system describing the Toda chain with additional spin sl(N, ℂ) degrees of freedom.
2011-01-01
We construct elliptic curves over the field $\\mathbf{Q}(\\sqrt{-3})$ with torsion group $\\mathbf{Z}/3\\mathbf{Z} \\times \\mathbf{Z}/3\\mathbf{Z}$ and ranks equal to 7 and an elliptic curve over the same field with torsion group $\\mathbf{Z}/3\\mathbf{Z} \\times \\mathbf{Z}/6\\mathbf{Z}$ and rank equal to 6.
The Closest Point Method and Multigrid Solvers for Elliptic Equations on Surfaces
Chen, Yujia
2015-01-01
© 2015 Society for Industrial and Applied Mathematics. Elliptic partial differential equations are important from both application and analysis points of view. In this paper we apply the closest point method to solve elliptic equations on general curved surfaces. Based on the closest point representation of the underlying surface, we formulate an embedding equation for the surface elliptic problem, then discretize it using standard finite differences and interpolation schemes on banded but uniform Cartesian grids. We prove the convergence of the difference scheme for the Poisson\\'s equation on a smooth closed curve. In order to solve the resulting large sparse linear systems, we propose a specific geometric multigrid method in the setting of the closest point method. Convergence studies in both the accuracy of the difference scheme and the speed of the multigrid algorithm show that our approaches are effective.
Cardona, Carlos [Physics Division, National Center for Theoretical Sciences, National Tsing-Hua University,Hsinchu, Taiwan 30013 (China); Gomez, Humberto [Instituto de Fisica - Universidade de São Paulo,Caixa Postal 66318, 05315-970 São Paulo, SP (Brazil); Facultad de Ciencias Basicas, Universidad Santiago de Cali,Calle 5 62-00 Barrio Pampalinda, Cali, Valle (Colombia)
2016-06-16
Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a ℂP{sup 2} space. We show that for the simplest integrand, namely the n−gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ−algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.
Dynamical Masses of Elliptical Galaxies
Gerhard, O E
2002-01-01
Recent progress in the dynamical analysis of elliptical galaxy kinematics is reviewed. Results reported briefly include (i) the surprisingly uniform anisotropy structure of luminous ellipticals, (ii) their nearly flat (to $\\sim 2R_e$) circular velocity curves, (iii) the Tully-Fisher and $M/L - L$ relations and the connection to the Fundamental Plane, and (iv) the large halo mass densities implied by the dynamical models.
椭圆曲线 y2= px（x2-2）的整数点%The Integral Points on the Elliptic Curve y2 =px(x2-2)
赵晶晶
2016-01-01
Let p be a positive prime such that p is square free.We proved that if every prime divisor q of p satis fies q≡3(mod8),then the elliptic curve in title has no positive integer points;if every prime divi-sor q of p satisfies q≡5(mod 8),then the elliptic curve in title has at most two positive integer points.%设 p 是大于1的无平方因子的正奇数。证明了如果 p 的素因素 q 都满足 q≡3（mod 8），则椭圆曲线 y2= px（x2-2）无正整数点；如果 p 的素因素 p 都满足 q≡5（mod 8），则椭圆曲线 y2=px（x2-2）至多有2组正整数点。
Spatial curved beam model and mechanical analysis of elliptical spiral stairs%椭圆旋转楼梯的空间曲梁模型与内力分析
周平槐; 张群力; 杨学林
2012-01-01
建筑中经常出现曲线型旋转楼梯,其内力分析较为复杂,国内少见这种楼梯的计算理论。结合实际工程,利用微分几何等数学方法,建立了椭圆旋转楼梯中心线为椭圆螺旋线、楼梯内外边线则为中心线主法矢上的等距线的数学模型的空间曲梁模型。基于楼梯的曲梁简化计算模型,同时选用了接近于实际作用的荷载等效作用曲线,推导出在单位力和均布荷载作用下梯梁上任一点的内力计算公式,并与有限元分析结果作了比较。分析表明,空间曲梁模型能较好地描述椭圆旋转楼梯的几何性质,公式推导和有限元分析所得的内力十分接近。其他旋转形式的楼梯,也可参考上述方法建立与其形状一致的数学模型以及内力分析,为设计提供依据。%There are many curve spiral stairs which inner forces are hard to analyze in buildings, and theories and methods of these stairs are rare domestically. Under the background of the project, the spatial curve beam differential model is established by mathematical method such as differential geometry and so on, which the center curve as elliptical helix, and the inside and outside edges as offset curves on the main normal vector of the center curve. The curve beam is modeled simply. After the equal load-curve is adopted, calculation formulas of inner forces under unit load and under vertical uniform load are obtained. Compared with the results of finite element methods （ FEM ） , it shows that mathematical modeling is in agreement with elliptical spiral stairs, the inner forces from formulations and FEM are similar. It can be reference for spiral stairs to establish the mathematical model and then analyze inner forces for design these stairs.
Linear Diophantine Equation Discrete Log Problem and the AA{\\beta}-Cryptosystem
Ariffin, M R K; Abu, N A; Mandangan, A; Atan, K A M
2011-01-01
The Linear Diophantine Equation Discrete Log Problem (LDEDLP) is a discrete log problem on the linear Diophantine equation U=Vx+y. A proper implementation of LDEDLP would render an attacker to search for two private parameters amongst the exponentially many solutions. The search would involve a key space of size at least 2^k, where k is the length of the private key. LDEDLP follows a simple mathematical structure. Its low computational requirement would enable communication devices with low computing power to deploy secure communication procedures efficiently. Similar to the cryptographic schemes based on the Elliptic Curve Discrete Log Problem (ECDLP), cryptographic schemes based upon the LDEDLP are also able to produce secure key exchange schemes and asymmetric cryptographic schemes. The AA{\\beta}-cryptosystem is one such cryptographic scheme. The AA{\\beta}-cryptosystem transmits a two-parameter ciphertext analogous to the El-Gamal and elliptic curve cryptosystems. The AA{\\beta}-cryptosystem consists of bas...
基于椭圆曲线的云存储数据完整性的验证研究%Validation of cloud storage data integrity based on elliptic curve
陈志忠
2016-01-01
Since the commonly⁃used cloud storage data integrity verification scheme can′t meet the requirement of data vali⁃dation,the cloud storage data integrity verification scheme ECPDP based on elliptic curve is put forward. The elliptic curve schemes of cloud storage data integrity verification with two⁃party participation,three⁃party participation and dynamic verifica⁃tion were designed respectively. And then the performance comparison experiments for the traditional PDP and ECPDP cloud storage data integrity verification schemes were performed based on OpenSSL code library. The experimental results show that the ECPDP scheme is better than the traditional PDP scheme in the aspects of protocol pretreatment performance,verification performance and challenge performance,and has high protocol safety.%针对当前常用的云存储数据完整性验证方案已无法适应数据验证需要的问题，提出了基于椭圆曲线的云存储数据完整性验证方案ECPDP，分别设计了二方参与、三方参与和动态验证的云存储数据验证的椭圆曲线方案。然后基于OpenSSL密码库对传统PDP和ECPDP云存储数据完整性验证方案进行了性能对比实验，实验结果表明，ECPDP方案在协议的预处理性能、验证性能及挑战性能方面均较传统的PDP协议有所提高，且不降低协议的安全性。
A Discretization of the Nonholonomic Chaplygin Sphere Problem
Yuri N. Fedorov
2007-03-01
Full Text Available The celebrated problem of a non-homogeneous sphere rolling over a horizontal plane was proved to be integrable and was reduced to quadratures by Chaplygin. Applying the formalism of variational integrators (discrete Lagrangian systems with nonholonomic constraints and introducing suitable discrete constraints, we construct a discretization of the n-dimensional generalization of the Chaplygin sphere problem, which preserves the same first integrals as the continuous model, except the energy. We then study the discretization of the classical 3-dimensional problem for a class of special initial conditions, when an analog of the energy integral does exist and the corresponding map is given by an addition law on elliptic curves. The existence of the invariant measure in this case is also discussed.
Homaeinezhad, M R; Atyabi, S A; Daneshvar, E; Ghaffari, A; Tahmasebi, M
2010-12-01
The aim of this study is to describe a robust unified framework for segmentation of the phonocardiogram (PCG) signal sounds based on the false-alarm probability (FAP) bounded segmentation of a properly calculated detection measure. To this end, first the original PCG signal is appropriately pre-processed and then, a fixed sample size sliding window is moved on the pre-processed signal. In each slid, the area under the excerpted segment is multiplied by its curve-length to generate the Area Curve Length (ACL) metric to be used as the segmentation decision statistic (DS). Afterwards, histogram parameters of the nonlinearly enhanced DS metric are used for regulation of the α-level Neyman-Pearson classifier for FAP-bounded delineation of the PCG events. The proposed method was applied to all 85 records of Nursing Student Heart Sounds database (NSHSDB) including stenosis, insufficiency, regurgitation, gallop, septal defect, split sound, rumble, murmur, clicks, friction rub and snap disorders with different sampling frequencies. Also, the method was applied to the records obtained from an electronic stethoscope board designed for fulfillment of this study in the presence of high-level power-line noise and external disturbing sounds and as the results, no false positive (FP) or false negative (FN) errors were detected. High noise robustness, acceptable detection-segmentation accuracy of PCG events in various cardiac system conditions, and having no parameters dependency to the acquisition sampling frequency can be mentioned as the principal virtues and abilities of the proposed ACL-based PCG events detection-segmentation algorithm.
Elliptic and magneto-elliptic instabilities
Lyra Wladimir
2013-04-01
Full Text Available Vortices are the fundamental units of turbulent flow. Understanding their stability properties therefore provides fundamental insights on the nature of turbulence itself. In this contribution I briely review the phenomenological aspects of the instability of elliptic streamlines, in the hydro (elliptic instability and hydromagnetic (magneto-elliptic instability regimes. Vortex survival in disks is a balance between vortex destruction by these mechanisms, and vortex production by others, namely, the Rossby wave instability and the baroclinic instability.
On Fibonacci Numbers Which Are Elliptic Carmichael
2014-12-27
On Fibonacci numbers which are elliptic Carmichael Florian Luca School of Mathematics University of the Witwatersrand P. O. Box Wits 2050, South...CM elliptic curve with CM field different from Q( √ −1), then the set of n for which the nth Fibonacci number Fn is elliptic Carmichael for E is of...number. 1. REPORT DATE 27 DEC 2014 2. REPORT TYPE 3. DATES COVERED 00-00-2014 to 00-00-2014 4. TITLE AND SUBTITLE On Fibonacci Numbers Which Are
Chaotic properties of the elliptical stadium
Markarian, R K; De Pinto-Carvalho, S; Markarian, Roberto; Kamphorst, Sylvie Oliffson; de Carvalho, Sonia Pinto
1995-01-01
The elliptical stadium is a curve constructed by joining two half-ellipses, with half axes a>1 and b=1, by two straight segments of equal length 2h. In this work we find bounds on h, for a close to 1, to assure the positiveness of a Lyapunov exponent. We conclude that, for these values of a and h, the elliptical stadium billiard mapping is ergodic and has the K-property.
A Study of Hyperelliptic Curves in Cryptography
Reza Alimoradi
2016-08-01
Full Text Available Elliptic curves are some specific type of curves known as hyper elliptic curves. Compared to the integer factorization problem(IFP based systems, using elliptic curve based cryptography will significantly decrease key size of the encryption. Therefore, application of this type of cryptography in systems that need high security and smaller key size has found great attention. Hyperelliptic curves help to make key length shorter. Many investigations are done with regard to improving computations, hardware and software implementation of these curves, their security and resistance against attacks. This paper studies and analyzes researches done about security and efficiency of hyperelliptic curves.
Yang, Xiaoli; Hofmann, Ralf; Dapp, Robin; van de Kamp, Thomas; Rolo, Tomy dos Santos; Xiao, Xianghui; Moosmann, Julian; Kashef, Jubin; Stotzka, Rainer
2015-01-01
High-resolution, three-dimensional (3D) imaging of soft tissues requires the solution of two inverse problems: phase retrieval and the reconstruction of the 3D image from a tomographic stack of two-dimensional (2D) projections. The number of projections per stack should be small to accommodate fast tomography of rapid processes and to constrain X-ray radiation dose to optimal levels to either increase the duration of in vivo time-lapse series at a given goal for spatial resolution and/or the conservation of structure under X-ray irradiation. In pursuing the 3D reconstruction problem in the sense of compressive sampling theory, we propose to reduce the number of projections by applying an advanced algebraic technique subject to the minimisation of the total variation (TV) in the reconstructed slice. This problem is formulated in a Lagrangian multiplier fashion with the parameter value determined by appealing to a discrete L-curve in conjunction with a conjugate gradient method. The usefulness of this reconstruction modality is demonstrated for simulated and in vivo data, the latter acquired in parallel-beam imaging experiments using synchrotron radiation. (C) 2015 Optical Society of America
基于有向性椭圆曲线的改进数字签密算法研究%Improved Digital Signcryption Algorithm Based on Cryptographic Elliptic Curve
陈画
2013-01-01
This article expounds basic information related to digital signature and digital signcryption. Based on the integrated analysis on various existing digital signature programs and signcryption programs, and utilizing the difficulty of oval curve discrete logarithmic problem, this paper proposes the improved digital signcryption algorithm on the basis of aeoplotropism ellipitc curve so as to meet the optimized target of reducing seeking inverse operation in the process of signcryption proof procedure. Aeoplotropism means only the specipient can make the signcryption. Experiments show that this improved algorithm has a significant effect of accelerating operation.%论文首先介绍了数字签名及数字签密的相关基础知识,在综合分析现存各类数字签名方案和签密方案的基础上,以减少签名验证过程中的求逆运算为优化目标,利用椭圆曲线离散对数问题的难解性,该文提出了一类基于有向性椭圆曲线的改进数字签密算法,有向性即只有指定的接收者才能解签密,通过实验证明,该改进算法能够加快运算速度,具有显著的优化效果.
Random Matrix Theory and Elliptic Curves
2014-11-24
the Riemann zeta-function higher up than ever previously reached – so the support led to a new world-record for the verification of the Riemann...frequency of vanishing of quadratic twists of modular L-functions, In Number Theory for the Millennium I: Proceedings of the Millennial Conference on
Elliptic Curve Blind Digital Signature Schemes
YOULin; YANGYixian; WENQiaoyan
2003-01-01
Blind signature schemes are important cryptographic protocols in guaranteeing the privacy or anonymity of the users.Three new blind signature schemes and their corresponding generalizations are pro-posed. Moreover, their securities are simply analyzed.
Measuring Shapes of Cosmological Images I Ellipticity and Orientation
Rahman, N A; Rahman, Nurur; Shandarin, Sergei F.
2003-01-01
We suggest a set of morphological measures that we believe can help in quantifying the shapes of two-dimensional cosmological images such as galaxies, clusters, and superclusters of galaxies. The method employs non-parametric morphological descriptors known as the Minkowski functionals in combination with geometric moments widely used in the image analysis. For the purpose of visualization of the morphological properties of contour lines we introduce three auxiliary ellipses representing the vector and tensor Minkowski functionals. We study the discreteness, seeing, and noise effects on elliptic contours as well as their morphological characteristics such as the ellipticity and orientation. In order to reduce the effect of noise we employ a technique of contour smoothing. We test the method by studying simulated elliptic profiles with various ellipticities ranging from E0 to E7 and illustrate the usefulness by measuring ellipticities and orientations of $K_s$ images of eight elliptics, three spirals and one p...
Dmitri Talalaev
2009-12-01
Full Text Available In this paper we construct the quantum spectral curve for the quantum dynamical elliptic gl_n Gaudin model. We realize it considering a commutative family corresponding to the Felder's elliptic quantum group E_{τ,h}(gl_n and taking the appropriate limit. The approach of Manin matrices here suits well to the problem of constructing the generation function of commuting elements which plays an important role in SoV and Langlands concept.
Rubtsov, V; Talalaev, D
2009-01-01
In this paper we construct the quantum spectral curve for the quantum dynamical elliptic gl(n) Gaudin model. We realize it considering a commutative family corresponding to the Felder's elliptic quantum group and taking the appropriate limit. The approach of Manin matrices here suits well to the problem of constructing the generation function of commuting elements which plays an important role in SoV and Langlands concept.
Bernstein, Daniel J.; Birkner, Peter; Lange, Tanja;
2013-01-01
This paper introduces EECM-MPFQ, a fast implementation of the elliptic-curve method of factoring integers. EECM-MPFQ uses fewer modular multiplications than the well-known GMP-ECM software, takes less time than GMP-ECM, and finds more primes than GMP-ECM. The main improvements above the modular......-arithmetic level are as follows: (1) use Edwards curves instead of Montgomery curves; (2) use extended Edwards coordinates; (3) use signed-sliding-window addition-subtraction chains; (4) batch primes to increase the window size; (5) choose curves with small parameters and base points; (6) choose curves with large...
On Fibonacci Numbers Which Are Elliptic Korselt Numbers
2014-11-17
On Fibonacci numbers which are elliptic Korselt numbers Florian Luca School of Mathematics University of the Witwatersrand P. O. Box Wits 2050, South...is a CM elliptic curve with CM field Q( √ −d), then the set of n for which the nth Fibonacci number Fn satisfies an elliptic Korselt criterion for Q...SUBTITLE On Fibonacci Numbers Which Are Elliptic Korselt Numbers 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d
Local identities involving Jacobi elliptic functions
Avinash Khare; Arul Lakshminarayan; Uday Sukhatme
2004-06-01
We derive a number of local identities involving Jacobi elliptic functions and use them to obtain several new results. First, we present an alternative, simpler derivation of the cyclic identities discovered by us recently, along with an extension to several new cyclic identities. Second, we obtain a generalization to cyclic identities in which successive terms have a multiplicative phase factor exp$(2i=s)$, where $s$ is any integer. Third, we systematize the local identities by deriving four local `master identities' analogous to the master identities for the cyclic sums discussed by us previously. Fourth, we point out that many of the local identities can be thought of as exact discretizations of standard non-linear differential equations satisfied by the Jacobi elliptic functions. Finally, we obtain explicit answers for a number of definite integrals and simpler forms for several indefinite integrals involving Jacobi elliptic functions.
Mutations of the cluster algebra of type {A}_{1}^{(1)} and the periodic discrete Toda lattice
Nobe, Atsushi
2016-07-01
A direct connection between two sequences of points, one of which is generated by seed mutations of the cluster algebra of type {A}1(1) and the other by time evolutions of the periodic discrete Toda lattice, is explicitly given. In this construction, each of them is realized as an orbit of a QRT map, and specialization of the parameters in the maps and appropriate choices of the initial points relate them. The connection with the periodic discrete Toda lattice enables us a geometric interpretation of the seed mutations of the cluster algebra of type {A}1(1) as an addition of points on an elliptic curve.
Mineev, Mark [Los Alamos National Laboratory
2008-01-01
The planar elliptic extension of the Laplacian growth is, after a proper parametrization, given in a form of a solution to the equation for areapreserving diffeomorphisms. The infinite set of conservation laws associated with such elliptic growth is interpreted in terms of potential theory, and the relations between two major forms of the elliptic growth are analyzed. The constants of integration for closed form solutions are identified as the singularities of the Schwarz function, which are located both inside and outside the moving contour. Well-posedness of the recovery of the elliptic operator governing the process from the continuum of interfaces parametrized by time is addressed and two examples of exact solutions of elliptic growth are presented.
Multilevel quadrature of elliptic PDEs with log-normal diffusion
Harbrecht, Helmut
2015-01-07
We apply multilevel quadrature methods for the moment computation of the solution of elliptic PDEs with lognormally distributed diffusion coefficients. The computation of the moments is a difficult task since they appear as high dimensional Bochner integrals over an unbounded domain. Each function evaluation corresponds to a deterministic elliptic boundary value problem which can be solved by finite elements on an appropriate level of refinement. The complexity is thus given by the number of quadrature points times the complexity for a single elliptic PDE solve. The multilevel idea is to reduce this complexity by combining quadrature methods with different accuracies with several spatial discretization levels in a sparse grid like fashion.
无
2010-01-01
This is the note for a series of lectures that the author gave at the Centre de Recerca Matemtica (CRM), Bellaterra, Barcelona, Spain on October 19–24, 2009. The aim is to give a comprehensive description of some recent work of the author and his students on generalisations of the Gross-Zagier formula, Euler systems on Shimura curves, and rational points on elliptic curves.
Quantitative analysis of spirality in elliptical galaxies
Dojcsak, Levente
2013-01-01
We use an automated galaxy morphology analysis method to quantitatively measure the spirality of galaxies classified manually as elliptical. The data set used for the analysis consists of 60,518 galaxy images with redshift obtained by the Sloan Digital Sky Survey (SDSS) and classified manually by Galaxy Zoo, as well as the RC3 and NA10 catalogues. We measure the spirality of the galaxies by using the Ganalyzer method, which transforms the galaxy image to its radial intensity plot to detect galaxy spirality that is in many cases difficult to notice by manual observation of the raw galaxy image. Experimental results using manually classified elliptical and S0 galaxies with redshift <0.3 suggest that galaxies classified manually as elliptical and S0 exhibit a nonzero signal for the spirality. These results suggest that the human eye observing the raw galaxy image might not always be the most effective way of detecting spirality and curves in the arms of galaxies.
Projected Elliptical Distributions
Winfried Stute; Uwe Werner
2005-01-01
We introduce a new parametrization of elliptically contoured densities and study the associated family of projected (circular) distributions. In particular we investigate the trigonometric moments and some convolution properties.
李学斌
2014-01-01
在模具和航空等制造业，常会遇到复杂曲线曲面的数控加工。为满足提高加工NURBS曲线曲面精度和高速加工的要求，提出了将NURBS曲面采用等参数线法离散成一族NURBS曲线的直接插补算法。其优点是可将一阶、二阶导矢和控制弓高误差而自动调整进给速度的计算放在插补前的预处理中集中进行。%In the mould and aviation manufacturing industries, it is often faced with the numerical control machining of the complex curves and surfaces. In order to satisfy the requirements of improving the precision of machining NURBS curves and surfaces and the requirements of high-speed machining, the direct interpolation algorithm that can discrete the NURBS surfaces into the gens of NURBS curves by using the isoparametric curve method is presented. The advantage of this method is that the guide vectors of the first order and the second order and the calculation of automatically adjusting the feeding speed for control of the bow height error can be pretreated before interpolation.
Effects of Surface Emitting and Cumulative Collisions on Elliptic Flow
LIU Jian-Li; WU Feng-Juan; ZHANG Jing-Bo; TANG Gui-Xin; HUO Lei
2008-01-01
@@ The integral and differential elliptic flow of partons is calculated using the multiphase transport model for Au+Au collisions at centre-of-mass energy √SNN=200 GeV.It is shown that elliptic flow of partons freezing out at early time,which is affected mainly by surface emittance,decreases with time and elliptic flow of partons freezing out at late time,which is dominated by cumulative collisions,increases with time.The elliptic flow of partons freezing out early has a large contribution to the flatting of curve of final differential elliptic flow at large transverse momentum.It is argued that the effect of surface emittance is not neglectable.
$\\mathcal{D}$-elliptic sheaves and odd Jacobians
Papikian, Mihran
2011-01-01
We examine the existence of rational divisors on modular curves of $\\mathcal{D}$-elliptic sheaves and on Atkin-Lehner quotients of these curves over local fields. Using a criterion of Poonen and Stoll, we show that in infinitely many cases the Tate-Shafarevich groups of the Jacobians of these Atkin-Lehner quotients have non-square orders.
On the index of noncommutative elliptic operators over C*-algebras
Savin, Anton Yu; Sternin, Boris Yu
2010-05-01
We consider noncommutative elliptic operators over C*-algebras, associated with a discrete group of isometries of a manifold. The main result of the paper is a formula expressing the Chern characters of the index (Connes invariants) in topological terms. As a corollary to this formula a simple proof of higher index formulae for noncommutative elliptic operators is obtained. Bibliography: 36 titles.
Elliptic grid generation based on Laplace equations and algebraic transformations
Spekreuse, S.P. [National Aerospace Lab., Amsterdam (Netherlands)
1995-04-01
An elliptic grid generation method is presented to generate boundary conforming grids in domains in 2D and 3D physical space and on minimal surfaces and parametrized surfaces in 3D physical space. The elliptic grid generation method is based on the use of a composite mapping. This composite mapping consists of a nonlinear transfinite algebraic transformation and an elliptic transformation. The elliptic transformation is based on the Laplace equations for domains, or on the Laplace-Beltrami equations for surfaces. The algebraic transformation maps the computational space one to-one onto a parameter space. The elliptic transformation maps the parameter space one-to-one onto the domains or surfaces. The composition of these two mapping is a differentiable one-to-one mapping from computational space onto the domains or surfaces and has a nonvanishing Jacobian. This composite mapping defines the grid point distribution in the interior of the domains or surfaces. For domains and minimal surfaces, the composite mapping obeys a nonlinear elliptic Poisson system with control functions completely defined by the algebraic transformation. The solution of the Poisson systems is obtained by Picard iteration and black-box multigrid solvers. For parametrized curved surfaces, it is not necessary to define and solve a nonlinear elliptic Poisson system. Instead a linear elliptic system and an inversion problem is solved to generate the grid in the interior of the surface.
Reconfigurable Optical Spectra from Perturbations on Elliptical Whispering Gallery Resonances
Mohageg, Makan; Maleki, Lute
2008-01-01
Elastic strain, electrical bias, and localized geometric deformations were applied to elliptical whispering-gallery-mode resonators fabricated with lithium niobate. The resultant perturbation of the mode spectrum is highly dependant on the modal indices, resulting in a discretely reconfigurable optical spectrum. Breaking of the spatial degeneracy of the whispering-gallery modes due to perturbation is also observed.
MONOTONE ITERATION FOR ELLIPTIC PDEs WITH DISCONTINUOUS NONLINEAR TERMS
Zou Qingsong
2005-01-01
In this paper, we use monotone iterative techniques to show the existence of maximal or minimal solutions of some elliptic PDEs with nonlinear discontinuous terms. As the numerical analysis of this PDEs is concerned, we prove the convergence of discrete extremal solutions.
Rarefied elliptic hypergeometric functions
Spiridonov, V P
2016-01-01
We prove exact evaluation formulae for two multiple rarefied elliptic beta integrals related to the simplest lens space. These integrals generalize the multiple type I and II van Diejen-Spiridonov integrals attached to the root system $C_n$. Symmetries of the rarefied elliptic analogue of the Euler-Gauss hypergeometric function are described and the corresponding generalization of the hypergeometric equation is constructed. An extension of the latter function to the root system $C_n$ and applications to some eigenvalue problems are briefly discussed.
佘东明
2013-01-01
作者给出了一类椭圆曲线 Ed2：y2＝ x3- d2 x的Artin Root Number的精确表达式，这里d＝π1⋯πrω1⋯ωs q1⋯qt是一些互不相同的“标准”的高斯素数的乘积。这是在赵春来的相关结果的推广。%We give an explicit formula of the Artin root number of the class of elliptic curves Ed2 :y2 = x3- d2 x ,w here d = π1 ...πrω1 ...ωsq1 ...qt is a product of distinct ‘canonical’ Gaussian prime numbers .It is a slight generalization of the relative result from Zhao Chunlai .
Introducing elliptic, an R Package for Elliptic and Modular Functions
Robin K. S. Hankin
2006-01-01
Full Text Available This paper introduces the elliptic package of R routines, for numerical calculation of elliptic and related functions. Elliptic functions furnish interesting and instructive examples of many ideas of complex analysis, and the package illustrates these numerically and visually. A statistical application in fluid mechanics is presented.
Smith, Stuart T.; Badami, Vivek G.; Dale, Jami S.; Xu, Ying
1997-03-01
This paper presents closed form equations based on a modification of those originally derived by Paros and Weisbord in 1965, for the mechanical compliance of a simple monolithic flexure hinge of elliptic cross section, the geometry of which is determined by the ratio ɛ of the major and minor axes. It is shown that these equations converge at ɛ=1 to the Paros and Weisbord equations for a hinge of circular section and at ɛ ⇒∞ to the equations predicted from simple beam bending theory for the compliance of a cantilever beam. These equations are then assessed by comparison with results from finite element analysis over a range of geometries typical of many hinge designs. Based on the finite element analysis, stress concentration factors for the elliptical hinge are also presented. As a further verification of these equations, a number of elliptical hinges were manufactured on a CNC milling machine. Experimental data were produced by applying a bending moment using dead weight loading and measuring subsequent angular deflections with a laser interferometer. In general, it was found that predictions for the compliance of elliptical hinges are likely to be within 12% for a range of geometries with the ratio βx(=t/2ax) between 0.06 and 0.2 and for values of ɛ between 1 and 10.
Waalkens, Holger; Wiersig, Jan; Dullin, Holger R.
1997-01-01
The exact and semiclassical quantum mechanics of the elliptic billiard is investigated. The classical system is integrable and exhibits a separatrix, dividing the phase space into regions of oscillatory and rotational motion. The classical separability carries over to quantum mechanics, and the Schr
Elliptic Schlesinger system and Painleve VI
Chernyakov, Yu [Institute of Theoretical and Experimental Physics, Moscow (Russian Federation); Levin, A M [Institute of Oceanology, Moscow (Russian Federation); Olshanetsky, M [Institute of Theoretical and Experimental Physics, Moscow (Russian Federation); Zotov, A [Institute of Theoretical and Experimental Physics, Moscow (Russian Federation)
2006-09-29
We consider an elliptic generalization of the Schlesinger system (ESS) with positions of marked points on an elliptic curve and its modular parameter as independent variables (the parameters in the moduli space of the complex structure). This system was originally discovered by Takasaki (hep-th/9711095) in the quasi-classical limit of the SL(N) vertex model. Our derivation is purely classical. ESS is defined as a symplectic quotient of the space of connections of bundles of degree 1 over the elliptic curves with marked points. The ESS is a non-autonomous Hamiltonian system with pairwise commuting Hamiltonians. The system is bi-Hamiltonian with respect to the linear and introduced here quadratic Poisson brackets. The latter are the multi-colour form of the Sklyanin-Feigin-Odesski classical algebras. The ESS is the monodromy independence condition on the complex structure for the linear systems related to the flat bundle. The case of four points for a special initial data is reduced to the Painleve VI equation in the form of the Zhukovsky-Volterra gyrostat, proposed in our previous paper.
Elliptic Genera and 3d Gravity
Benjamin, Nathan; /Stanford U., ITP /SLAC; Cheng, Miranda C.N.; /Amsterdam U., Inst. Math.; Kachru, Shamit; /Stanford U., ITP /SLAC; Moore, Gregory W.; /Rutgers U., Piscataway; Paquette, Natalie M.; /Stanford U., ITP /SLAC
2016-03-30
We describe general constraints on the elliptic genus of a 2d supersymmetric conformal field theory which has a gravity dual with large radius in Planck units. We give examples of theories which do and do not satisfy the bounds we derive, by describing the elliptic genera of symmetric product orbifolds of K3, product manifolds, certain simple families of Calabi–Yau hypersurfaces, and symmetric products of the “Monster CFT”. We discuss the distinction between theories with supergravity duals and those whose duals have strings at the scale set by the AdS curvature. Under natural assumptions, we attempt to quantify the fraction of (2,2) supersymmetric conformal theories which admit a weakly curved gravity description, at large central charge.
Threshold Signature Scheme Based on Discrete Logarithm and Quadratic Residue
FEI Ru-chun; WANG Li-na
2004-01-01
Digital signature scheme is a very important research field in computer security and modern cryptography.A(k,n) threshold digital signature scheme is proposed by integrating digital signature scheme with Shamir secret sharing scheme.It can realize group-oriented digital signature, and its security is based on the difficulty in computing discrete logarithm and quadratic residue on some special conditions.In this scheme, effective digital signature can not be generated by any k-1 or fewer legal users, or only by signature executive.In addition, this scheme can identify any legal user who presents incorrect partial digital signature to disrupt correct signature, or any illegal user who forges digital signature.A method of extending this scheme to an Abelian group such as elliptical curve group is also discussed.The extended scheme can provide rapider computing speed and stronger security in the case of using shorter key.
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
Khaled A. Gepreel
2012-01-01
Full Text Available We modified the rational Jacobi elliptic functions method to construct some new exact solutions for nonlinear differential difference equations in mathematical physics via the lattice equation, the discrete nonlinear Schrodinger equation with a saturable nonlinearity, the discrete nonlinear Klein-Gordon equation, and the quintic discrete nonlinear Schrodinger equation. Some new types of the Jacobi elliptic solutions are obtained for some nonlinear differential difference equations in mathematical physics. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.
A New Cryptosystem Based on Factoring and Discrete Logarithm Problems
E. S. Ismail
2011-01-01
Full Text Available Problem statement: A cryptosystem allows a sender to send any confidential or private message using a receivers public key and later the receiver confirms the integrity of the received message using his secret key. Currently the existing cryptosystems were developed based on a single hard problem like factoring, discrete logarithm, residuosity, knapsack or elliptic curve discrete logarithm. Although these schemes appear secure, one day in a near future they may be broken if one finds a solution of a single hard problem. Approach: To solve this problem, we developed a new cryptosystem based on two hard problems; factoring and discrete logarithm. We integrated the two problems in our encrypting and decrypting equations so that the former depends on two public keys whereas the latter depends on two corresponding secret keys. Results: The new cryptosystem is shown secure against the most three considering attacks. The efficiency performance of our scheme only requires 3Texp +Tmul + Thash time complexity for encryption and 2Texp + Tmul time complexity for decryption and this magnitude of complexity is considered minimal for multiple hard problems-like cryptosystems. Conclusion: The new cryptosystem based on multiple hard problems provides longer and higher security level than that schemes based on a single hard problem. The adversary has to solve the two problems simultaneously in order to recover a corresponding plaintext (message from the received ciphertext (encrypted message.
Retrieval of Rayleigh Wave Ellipticity from Ambient Vibration Recordings
Maranò, Stefano; Hobiger, Manuel; Fäh, Donat
2017-01-01
The analysis of ambient vibrations is a useful tool in microzonation and geotechnical investigations. Ambient vibrations are composed to a large part of surface waves, both Love and Rayleigh waves. One reason to analyse surface waves is that they carry information about the subsurface. The dispersion curve of Rayleigh waves and Love waves can be retrieved using array processing techniques. The Rayleigh wave ellipticity, including the sense of rotation of the particle motion, can also be retrieved using array techniques. These quantities are used in an inversion procedure aimed at obtaining a structural model of the subsurface. The focus of this work is the retrieval of Rayleigh wave ellipticity. We show applications of the (ML) method presented in Maranó et al. (2012) to a number of sites in Switzerland. The sites examined are chosen to reflect a wide range of soil conditions that are of interest in microzonation studies. Using a synthetic wavefield with known structural model, we compare our results with theoretical ellipticity curves and we show the accuracy of the considered algorithm. The sense of rotation of the particle motion (prograde vs. retrograde) is also estimated. In addition, we show that by modelling the presence of both Love and Rayleigh waves it is possible to mitigate the disruptive influence of Love waves on the estimation of Rayleigh wave ellipticity. Using recordings from several real sites, we show that it is possible to retrieve the ellipticity curve over a broad range of frequencies. Fundamental modes and higher modes are retrieved. Singularities of the ellipticity, corresponding to a change of the sense of rotation from prograde to retrograde (or vice versa), are detected with great accuracy. Knowledge of Rayleigh wave ellipticity, including the sense of rotation, is useful in several ways. The ellipticity angle allows us to pinpoint accurately the frequency of singularities (i.e., peaks and zeros of the H/V representation of the
Ellipticity induced in vacuum birefringence
Torgrimsson, Greger
2014-01-01
We consider signals of photon-photon scattering in laser-based, low energy experiments. In particular, we consider the ellipticity induced on a probe beam by a strong background field, and compare it with a recent worldline expression for the photon polarisation flip amplitude. When the probe and the background are plane waves, the ellipticity is equal to the flip amplitude. Here we investigate the ellipticity-amplitude relation for more physical fields.
Sørensen, John Aasted
2011-01-01
The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...
DJAIRO G. DEFIGUEIREDO
2000-12-01
Full Text Available In this paper we treat the question of the existence of solutions of boundary value problems for systems of nonlinear elliptic equations of the form - deltau = f (x, u, v,Ñu,Ñv, - deltav = g(x, u, v, Ñu, Ñv, in omega, We discuss several classes of such systems using both variational and topological methods. The notion of criticality takes into consideration the coupling, which plays important roles in both a priori estimates for the solutions and Palais-Smale conditions for the associated functional in the variational case.
Degenerate elliptic resonances
Gentile, G
2004-01-01
Quasi-periodic motions on invariant tori of an integrable system of dimension smaller than half the phase space dimension may continue to exists after small perturbations. The parametric equations of the invariant tori can often be computed as formal power series in the perturbation parameter and can be given a meaning via resummations. Here we prove that, for a class of elliptic tori, a resummation algorithm can be devised and proved to be convergent, thus extending to such lower-dimensional invariant tori the methods employed to prove convergence of the Lindstedt series either for the maximal (i.e. KAM) tori or for the hyperbolic lower-dimensional invariant tori
Image Ellipticity from Atmospheric Aberrations
De Vries, W H; Asztalos, S J; Rosenberg, L J; Baker, K L
2007-01-01
We investigate the ellipticity of the point-spread function (PSF) produced by imaging an unresolved source with a telescope, subject to the effects of atmospheric turbulence. It is important to quantify these effects in order to understand the errors in shape measurements of astronomical objects, such as those used to study weak gravitational lensing of field galaxies. The PSF modeling involves either a Fourier transform of the phase information in the pupil plane or a ray-tracing approach, which has the advantage of requiring fewer computations than the Fourier transform. Using a standard method, involving the Gaussian weighted second moments of intensity, we then calculate the ellipticity of the PSF patterns. We find significant ellipticity for the instantaneous patterns (up to more than 10%). Longer exposures, which we approximate by combining multiple (N) images from uncorrelated atmospheric realizations, yield progressively lower ellipticity (as 1 / sqrt(N)). We also verify that the measured ellipticity ...
DAI Chao-Qing; MENG Jian-Ping; ZHANG Jie-Fang
2005-01-01
The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schrodinger equation. When the modulous m → 1or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.
Elliptic flow in small systems due to elliptic gluon distributions?
Hagiwara, Yoshikazu; Hatta, Yoshitaka; Xiao, Bo-Wen; Yuan, Feng
2017-08-01
We investigate the contributions from the so-called elliptic gluon Wigner distributions to the rapidity and azimuthal correlations of particles produced in high energy pp and pA collisions by applying the double parton scattering mechanism. We compute the 'elliptic flow' parameter v2 as a function of the transverse momentum and rapidity, and find qualitative agreement with experimental observations. This shall encourage further developments with more rigorous studies of the elliptic gluon distributions and their applications in hard scattering processes in pp and pA collisions.
Flach, S
1998-01-01
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattic...
Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics
Khaled A. Gepreel
2012-01-01
Full Text Available We put a direct new method to construct the rational Jacobi elliptic solutions for nonlinear differential difference equations which may be called the rational Jacobi elliptic functions method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential difference equations in mathematical physics via the lattice equation and the discrete nonlinear Schrodinger equation with a saturable nonlinearity. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.
Perturbation of sectorial projections of elliptic pseudo-differential operators
Booss-Bavnbek, Bernhelm; Chen, Guoyuan; Lesch, Matthias;
2012-01-01
Over a closed manifold, we consider the sectorial projection of an elliptic pseudo-differential operator A of positive order with two rays of minimal growth. We showthat it depends continuously on A when the space of pseudo-differential operators is equipped with a certain topology whichwe...... explicitly describe. Our main application deals with a continuous curve of arbitrary first order linear elliptic differential operators over a compact manifold with boundary. Under the additional assumption of the weak inner unique continuation property, we derive the continuity of a related curve...... of Calderón projections and hence of the Cauchy data spaces of the original operator curve. In the Appendix, we describe a topological obstruction against a verbatim use of R. Seeley’s original argument for the complex powers, which was seemingly overlooked in previous studies of the sectorial projection....
Discrete doubly periodic and solitary wave solutions for the semi-discrete coupled mKdV equations
Wu Xiao-Fei; Zhu Jia-Min; Ma Zheng-Yi
2007-01-01
In this paper, the improved Jacobian elliptic function expansion approach is extended and applied to constructing discrete solutions of the semi-discrete coupled modified Korteweg de Vries (mKdV) equations with the aid of the symbolic computation system Maple. Some new discrete Jacobian doubly periodic solutions are obtained. When the modulus M → 1, these doubly periodic solutions degenerate into the corresponding solitary wave solutions, including kink-type, bell-type and other types of excitations.
Some new addition formulae for Weierstrass elliptic functions.
Eilbeck, J Chris; England, Matthew; Onishi, Yoshihiro
2014-11-08
We present new addition formulae for the Weierstrass functions associated with a general elliptic curve. We prove the structure of the formulae in n-variables and give the explicit addition formulae for the 2- and 3-variable cases. These new results were inspired by new addition formulae found in the case of an equianharmonic curve, which we can now observe as a specialization of the results here. The new formulae, and the techniques used to find them, also follow the recent work for the generalization of Weierstrass functions to curves of higher genus.
Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries
Braun, Volker; Cvetič, Mirjam; Donagi, Ron; Poretschkin, Maximilian
2017-07-01
We provide the first explicit example of Type IIB string theory compactification on a globally defined Calabi-Yau threefold with torsion which results in a four-dimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of Z_2× Z_2 . Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of second cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the cfour-dimensional theory.
Discrete Stein characterizations and discrete information distances
Ley, Christophe
2012-01-01
We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals.
Domain decomposition based iterative methods for nonlinear elliptic finite element problems
Cai, X.C. [Univ. of Colorado, Boulder, CO (United States)
1994-12-31
The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...
The two-loop sunrise integral and elliptic polylogarithms
Adams, Luise; Weinzierl, Stefan [Institut fuer Physik, Johannes Gutenberg-Universitaet Mainz (Germany); Bogner, Christian [Institut fuer Physik, Humboldt-Universitaet zu Berlin (Germany)
2016-07-01
In this talk, we present a solution for the two-loop sunrise integral with arbitrary masses around two and four space-time dimensions in terms of a generalised elliptic version of the multiple polylogarithms. Furthermore we investigate the elliptic polylogarithms appearing in higher orders in the dimensional regularisation ε of the two-dimensional equal mass solution. Around two space-time dimensions the solution consists of a sum of three elliptic dilogarithms where the arguments have a nice geometric interpretation as intersection points of the integration region and an elliptic curve associated to the sunrise integral. Around four space-time dimensions the sunrise integral can be expressed with the ε{sup 0}- and ε{sup 1}-solution around two dimensions, mass derivatives thereof and simpler terms. Considering higher orders of the two-dimensional equal mass solution we find certain generalisations of the elliptic polylogarithms appearing in the ε{sup 0}- and ε{sup 1}-solutions around two and four space-time dimensions. We show that these higher order-solutions can be found by iterative integration within this class of functions.
Discrete Torsion and Symmetric Products
Dijkgraaf, R
1999-01-01
In this note we point out that a symmetric product orbifold CFT can be twisted by a unique nontrivial two-cocycle of the permutation group. This discrete torsion changes the spins and statistics of corresponding second-quantized string theory making it essentially ``supersymmetric.'' The long strings of even length become fermionic (or ghosts), those of odd length bosonic. The partition function and elliptic genus can be described by a sum over stringy spin structures. The usual cubic interaction vertex is odd and nilpotent, so this construction gives rise to a DLCQ string theory with a leading quartic interaction.
A Secured Authentication Protocol for SIP Using Elliptic Curves Cryptography
Chen, Tien-Ho; Yeh, Hsiu-Lien; Liu, Pin-Chuan; Hsiang, Han-Chen; Shih, Wei-Kuan
Session initiation protocol (SIP) is a technology regularly performed in Internet Telephony, and Hyper Text Transport Protocol (HTTP) as digest authentication is one of the major methods for SIP authentication mechanism. In 2005, Yang et al. pointed out that HTTP could not resist server spoofing attack and off-line guessing attack and proposed a secret authentication with Diffie-Hellman concept. In 2009, Tsai proposed a nonce based authentication protocol for SIP. In this paper, we demonstrate that their protocol could not resist the password guessing attack and insider attack. Furthermore, we propose an ECC-based authentication mechanism to solve their issues and present security analysis of our protocol to show that ours is suitable for applications with higher security requirement.
On Primitive Elements in Finite Fields and on Elliptic Curves
Shparlinskiĭ, I. E.
1992-02-01
An asymptotic formula for the number of primitive polynomials of the form f (x) + a, a = 1, ..., h, where f (x)inFp[x], is obtained, "on the average" over all polynomials f of fixed degree, and an estimate for the number of "sparse" factorable polynomials is also obtained.
Elliptic Curve Cryptography on Smart Cards Without Coprocessors
2000-09-20
Lecture Notes in Computer Science , 1998...implementation for arithmetic operations in GF (2n). In Asiacrypt ’96. Springer-Verlag Lecture Notes in Computer Science , 1996. [9] E. De Win, S. Mister, B...pages 252–266, Berlin, 1998. Springer-Verlag Lecture Notes in Computer Science . [10] P. Gaudry, F. Hess, and N. P. Smart. Constructive and
Cryptanalysis of an Elliptic Curve-based Signcryption Scheme
Toorani, Mohsen
2010-01-01
The signcryption is a relatively new cryptographic technique that is supposed to fulfill the functionalities of encryption and digital signature in a single logical step. Although several signcryption schemes are proposed over the years, some of them are proved to have security problems. In this paper, the security of Han et al.'s signcryption scheme is analyzed, and it is proved that it has many security flaws and shortcomings. Several devastating attacks are also introduced to the mentioned scheme whereby it fails all the desired and essential security attributes of a signcryption scheme.
Secure Authentication of WLAN Based on Elliptic Curve Cryptosystem
无
2007-01-01
The security of wireless local area network (WLAN) becomes a bottleneck for its further applications.At present, many standard organizations and manufacturers of WLAN try to solve this problem. However, owing to the serious secure leak in IEEE802.11 standards, it is impossible to utterly solve the problem by simply adding some remedies. Based on the analysis on the security mechanism of WLAN and the latest techniques of WLAN security, a solution to WLAN security was presented. The solution makes preparation for the further combination of WLAN and Internet.
The Performance Impact of Elliptic Curve Cryptography on DNSSEC Validation
Rijswijk-Deij, van Roland; Hageman, Kasper; Sperotto, Anna; Pras, Aiko
2017-01-01
The Domain Name System is a core Internet infrastructure that translates names to machine-readable information, such as IP addresses. Security flaws in DNS led to a major overhaul, with the introduction of the DNS Security Extensions. DNSSEC adds integrity and authenticity to the DNS using digital s
Making the case for elliptic curves in DNSSEC
Rijswijk-Deij, van Roland; Sperotto, Anna; Pras, Aiko
2015-01-01
The Domain Name System Security Extensions (DNSSEC) add authenticity and integrity to the DNS, improving its security. Unfortunately, DNSSEC is not without problems. DNSSEC adds digital signatures to the DNS, significantly increasing the size of DNS responses. This means DNSSEC is more susceptible t
Cubic Curves, Finite Geometry and Cryptography
Bruen, A A; Wehlau, D L
2011-01-01
Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational points are also surveyed. A possible strengthening of the security of elliptic curve cryptography is proposed using a `shared secret' related to the group law. Cubic curves are also used in a new way to construct sets of points having various combinatorial and geometric properties that are of particular interest in finite Desarguesian planes.
Elliptical X-Ray Spot Measurement
Richardson, R A; Weir, J T; Richardson, Roger A.; Sampayan, Stephen; Weir, John T.
2000-01-01
The so-called roll bar measurement uses a heavy metal material, optically thick to x-rays, to form a shadow of the x-ray origination spot. This spot is where an energetic electron beam interacts with a high Z target. The material (the "roll bar") is slightly curved to avoid alignment problems. The roll bar is constructed and positioned so that the x-rays are shadowed in the horizontal and vertical directions, so information is obtained in two dimensions. If a beam profile is assumed (or measured by other means), the equivalent x-ray spot size can be calculated from the x-ray shadow cast by the roll bar. Thus the ellipticity of the beam can be calculated, assuming the ellipse of the x-ray spot is aligned with the roll bar. The data is recorded using a scintillator and gated camera. Data will be presented from measurements using the ETA II induction LINAC. The accuracy of the measurement is checked using small elliptical targets.
A parallel fast multipole method for elliptic difference equations
Liska, Sebastian
2014-01-01
A new fast multipole formulation for solving elliptic PDEs on unbounded domains and its parallel implementation are presented. This method formally discretizes the PDE on an infinite Cartesian grid, and then solves the corresponding difference equations. In the analog to solving continuous inhomogeneous differential equations using Green's functions, the proposed method uses the fundamental solution of the discrete operator on an infinite grid, or lattice Green's function. Fast solutions O(N) are achieved by using a kernel-independent interpolation-based fast multipole method. Unlike other fast multipole algorithms, our approach exploits the regularity of the underlying Cartesian grid and the efficiency of FFTs to reduce the computation time. Our parallel implementation allows communications and computations to be overlapped and requires minimal global synchronization. The accuracy, efficiency, and parallel performance of the method are demonstrated through numerical experiments on the discrete 3D Poisson equ...
Mariela Olguín
2015-01-01
Full Text Available The objective of this work is to make the numerical analysis, through the finite element method with Lagrange’s triangles of type 1, of a continuous optimal control problem governed by an elliptic variational inequality where the control variable is the internal energy g. The existence and uniqueness of this continuous optimal control problem and its associated state system were proved previously. In this paper, we discretize the elliptic variational inequality which defines the state system and the corresponding cost functional, and we prove that there exist a discrete optimal control and its associated discrete state system for each positive h (the parameter of the finite element method approximation. Finally, we show that the discrete optimal control and its associated state system converge to the continuous optimal control and its associated state system when the parameter h goes to zero.
李修美
2013-01-01
设p,q为奇素数且q-p=2.本文将在类数为1的虚二次域上考虑椭圆曲线y2=x(x±p)(x±q)及其对偶曲线,并在某些具体条件下给出它们的赛莫群和沙法列维奇-泰特群的(ψ)-(2-)部分的信息.%Let p and q be odd prime numbers with q-p =2.The (ψ)-Selmer groups,Shafarevich-Tate groups((ψ)-and 2-paxt) and their dual ones as well the Mordell-Weil groups of elliptic curves y2 =x(x ± p)(x ± q) over imaginary quadratic number fields of class number one are determined explicitly in many cases.
Waelbroeck, H
1999-01-01
We propose a theory of deterministic chaos for discrete systems, based on their representations in symbolic history spaces Ømega. These are spaces of semi-infinite sequences, as the one-sided shift spaces, but endowed with a more general topology which we call a semicausal topology. We show that define metrical properties, including the correlation dimension of the attractor. Examples are considered: Asymmetric neural networks and random cellular automata are not chaotic. A neural network model with memory, on the other hand, does appear to be an example of discrete chaos.
Caltagirone, Jean-Paul
2014-01-01
This book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling. The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the H
Augusto Hernández Vidal
2011-12-01
Full Text Available In order to strengthen the concept of municipal autonomy, this essay proposes an extensive interpretation of administrative discretion. Discretion is the exercise of free judgment given by law to authorities for performing official acts. This legislative technique seems to be suitable whenever the legislative is intended to legislate over the essential core of municipal autonomy. This way, an eventual abuse of that autonomy could be avoided, for the disproportional restriction of the local faculty to oversee the local issues. This alternative is presented as a tool to provide with dynamism the performing of administrative activities as well, aiming to assimilate public administration new practices.
A Lower Bound for Chaos on the Elliptical Stadium
Canale, E; Oliffson-Kamphorst, S; De Pinto-Carvalho, S; Canale, Eduardo; Markarian, Roberto; Kamphorst, Sylvie Oliffson; Carvalho, Sonia Pinto de
1997-01-01
The elliptical stadium is a plane region bounded by a curve constructed by joining two half-ellipses by two parallel segments of equal length. The billiard inside it, as a map, generates a two parameters family of dynamical systems. It is known that the system is ergodic for a certain region of the parameter space. In this work we study the stability of a particular family of periodic orbits obtaining good bounds for the chaotic zone.
Design of elliptic cylindrical thermal cloak with layered structure
Yuan, Xuebo; Lin, Guochang; Wang, Youshan
2017-01-01
Thermal cloak has potential applications in thermal protection and sensing. Based on the theories of spatial transformation and effective medium, layered structure of elliptic cylindrical thermal cloak was designed. According to theoretical analysis and numerical simulation, the layered structure has typical characteristics of perfect thermal cloak. The external temperature field remains unchanged, while the internal temperature gradient decreases obviously. Meanwhile, the cloaking effect is stable in any direction. The cloaking effect can be improved by increasing the number of discretization layers or reducing the cloak thickness. The elliptic cylindrical cloak can be considered as cylindrical cloak when the focal distance is close to zero. This study has provided an effective way for realizing thermal cloak with more complex shapes.
Hong-ying Man; Zhong-ci Shi
2006-01-01
In this paper, we discuss the finite volume element method of P1-nonconforming quadrilateral element for elliptic problems and obtain optimal error estimates for general quadrilateral partition. An optimal cascadic multigrid algorithm is proposed to solve the nonsymmetric large-scale system resulting from such discretization. Numerical experiments are reported to support our theoretical results.
Energy and the Elliptical Orbit
Nettles, Bill
2009-03-01
In the January 2007 issue of The Physics Teacher, Prentis, Fulton, Hesse, and Mazzino describe a laboratory exercise in which students use a geometrical analysis inspired by Newton to show that an elliptical orbit and an inverse-square law force go hand in hand. The historical, geometrical, and teamwork aspects of the exercise are useful and important. This paper presents an exercise which uses an energy/angular momentum conservation model for elliptical orbits. This exercise can be done easily by an individual student and on regular notebook-sized paper.
Lessons on Black Holes from the Elliptic Genus
Giveon, Amit; Troost, Jan
2014-01-01
We further study the elliptic genus of the cigar SL(2,R)/U(1) coset superconformal field theory. We find that, even in the small curvature, infinite level limit, there are holomorphic and non-holomorphic parts that are due to the discrete states and a mismatch in the spectral densities of the continuum, respectively. The mismatch in the continuum is universal, in the sense that it is fully determined by the asymptotic cylindrical topology of the cigar's throat. Since modularity of the elliptic genus requires both the holomorphic and non-holomorphic parts, the holomorphic term is universal as well. The contribution of the discrete states is thus present even for perturbative strings propagating in the background of large Schwarzschild black holes. We argue that the discrete states live at a stringy distance from the tip of the cigar both from the conformal field theory wave-function analysis and from a holonomy space perspective. Thus, the way string theory takes care of its self-consistency seems to have impo...
Dyka, Zoya
2012-04-13
During recent years elliptic curve cryptography (ECC) has gained significant attention especially for devices with scarce resources such as wireless sensor nodes. Hardware implementations are considered to be the key enabler for using ECC on this class of devices. Out of the operations needed to execute ECC the polynomial multiplication is the one which is investigated most since it is one of the most complex field operations and executed very often. The majority of research papers focuses on reducing the number of partial- multiplications while neglecting the increased effort for additions of the partial products. This thesis investigates how the latter can be optimized. A reduction of additions can be achieved by using pre-defined processing sequences for summing up partial products. In this work a method to find the optimized processing sequence is presented. It is applied to 10 multiplication methods of polynomials over GF(2{sup n}). For example when applied to the generalized Karatsuba multiplication [18] the optimized processing sequence saves up to 39 per cent of XOR-gates in average for polynomials with a length up to 600 bits. In addition it is known that combining different multiplication methods reduced the total complexity of the multiplier. For example using the classical MM for calculation of small partial products in combination with other MMs can improve chip-parameters of the resulting multipliers. An optimal combination of several multiplication approaches for which the optimized processing sequence of XOR-operations is used reduces the area and energy consumption of the resulting multiplier significantly. This work presents an algorithm to determine the optimal combination of multiplication methods with pre-defined processing sequences for hardware implementation of an highly efficient polynomial multiplier in GF(2{sup n}). The combinations determined by this algorithm save in average 12 % of the chip-area for polynomials with a length up to 600
Sørensen, John Aasted
2011-01-01
examples on regular languages. Apply these concepts to new problems. Finite state machines: Define a finite state machine as a 6-tuble; describe simple finite state machines by tables and graphs; pattern recognition by finite state machines; minimizing the number of states in a finite state machine......The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... of natural numbers. Apply these concepts to new problems. Division and factorizing: Define a prime number and apply Euclid´s algorithm for factorizing an integer. Regular languages: Define a language from the elements of a set; define a regular language; form strings from a regular language; construct...
Elliptic Flow Measurement at ALICE
Simili, E.L.
2008-01-01
In view of the upcoming ALICE experiment, a dedicated detector to study ultra-relativistic heavy ion collisions at the Large Hadron Collider (LHC) at CERN, the present thesis has been devoted to the study of Elliptic Flow, i.e. the azimuthal anisotropy in the momenta distribution of the final state
Energy and the Elliptical Orbit
Nettles, Bill
2009-01-01
In the January 2007 issue of "The Physics Teacher," Prentis, Fulton, Hesse, and Mazzino describe a laboratory exercise in which students use a geometrical analysis inspired by Newton to show that an elliptical orbit and an inverse-square law force go hand in hand. The historical, geometrical, and teamwork aspects of the exercise are useful and…
Fourier Series and Elliptic Functions
Fay, Temple H.
2003-01-01
Non-linear second-order differential equations whose solutions are the elliptic functions "sn"("t, k"), "cn"("t, k") and "dn"("t, k") are investigated. Using "Mathematica", high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these non-elementary functions that are…
The ESS elliptical cavity cryomodules
Darve, Christine; Bosland, Pierre; Devanz, Guillaume; Olivier, Gilles; Renard, Bertrand; Thermeau, Jean-Pierre
2014-01-01
The European Spallation Source (ESS) is a multi-disciplinary research centre under design and construction in Lund, Sweden. This new facility is funded by a collaboration of 17 European countries and is expected to be up to 30 times brighter than today's leading facilities and neutron sources. The ESS will enable new opportunities for researchers in the fields of life sciences, energy, environmental technology, cultural heritage and fundamental physics. A 5 MW long pulse proton accelerator is used to reach this goal. The pulsed length is 2.86 ms, the repetition frequency is 14 Hz (4 % duty cycle), and the beam current is 62.5 mA. The superconducting section of the Linac accelerates the beam from 80 MeV to 2.0 GeV. It is composed of one string of spoke cavity cryomodule and two strings of elliptical cavity cryomodules. These cryomodules contain four elliptical Niobium cavities operating at 2 K and at a frequency of 704.42 MHz. This paper introduces the thermo-mechanical design, the prototyping and the expected operation of the ESS elliptical cavity cryomodules. An Elliptical Cavity Cryomodule Technology Demonstrator (ECCTD) will be built and tested in order to validate the ESS series production.
TWO PROBLEMS OF HERMITE ELLIPTIC EQUATIONS
Huaug Feirain
2009-01-01
In this article, the author investigates some Hermite elliptic equations in a modified Sobolev space introduced by X. Ding [2]. First, the author shows the existence of a ground state solution of semilinear Hermite elliptic equation. Second, the author studies the eigenvalue problem of linear Hermite elliptic equation in a bounded or unbounded domain.
The Satake sextic in elliptic fibrations on K3
Malmendier, Andreas
2016-01-01
We describe explicit formulas relevant to the F-theory/heterotic string duality that reconstruct from a specific Jacobian elliptic fibration on the Shioda-Inose surface covering a generic Kummer surface the corresponding genus-two curve using the level-two Satake coordinate functions. We derive explicitly the rational map on the moduli space of genus-two curves realizing the algebraic correspondence between a sextic curve and its Satake sextic. We will prove that it is not the original sextic defining the genus-two curve, but its corresponding Satake sextic which is manifest in the F-theory model, dual to the $\\mathfrak{so}(32)$ heterotic string with an unbroken $\\mathfrak{so}(28)\\oplus \\mathfrak{su}(2)$ gauge algebra.
Preconditioning for Mixed Finite Element Formulations of Elliptic Problems
Wildey, Tim
2013-01-01
In this paper, we discuss a preconditioning technique for mixed finite element discretizations of elliptic equations. The technique is based on a block-diagonal approximation of the mass matrix which maintains the sparsity and positive definiteness of the corresponding Schur complement. This preconditioner arises from the multipoint flux mixed finite element method and is robust with respect to mesh size and is better conditioned for full permeability tensors than a preconditioner based on a diagonal approximation of the mass matrix. © Springer-Verlag Berlin Heidelberg 2013.
Discrete geodesics and cellular automata
Arrighi, Pablo
2015-01-01
This paper proposes a dynamical notion of discrete geodesics, understood as straightest trajectories in discretized curved spacetime. The notion is generic, as it is formulated in terms of a general deviation function, but readily specializes to metric spaces such as discretized pseudo-riemannian manifolds. It is effective: an algorithm for computing these geodesics naturally follows, which allows numerical validation---as shown by computing the perihelion shift of a Mercury-like planet. It is consistent, in the continuum limit, with the standard notion of timelike geodesics in a pseudo-riemannian manifold. Whether the algorithm fits within the framework of cellular automata is discussed at length. KEYWORDS: Discrete connection, parallel transport, general relativity, Regge calculus.
A New Digital Signature Scheme Based on Factoring and Discrete Logarithms
E. S. Ismail
2008-01-01
Full Text Available Problem statement: A digital signature scheme allows one to sign an electronic message and later the produced signature can be validated by the owner of the message or by any verifier. Most of the existing digital signature schemes were developed based on a single hard problem like factoring, discrete logarithm, residuosity or elliptic curve discrete logarithm problems. Although these schemes appear secure, one day in a near future they may be exploded if one finds a solution of the single hard problem. Approach: To overcome this problem, in this study, we proposed a new signature scheme based on multiple hard problems namely factoring and discrete logarithms. We combined the two problems into both signing and verifying equations such that the former depends on two secret keys whereas the latter depends on two corresponding public keys. Results: The new scheme was shown to be secure against the most five considering attacks for signature schemes. The efficiency performance of our scheme only requires 1203Tmul+Th time complexity for signature generation and 1202Tmul+Th time complexity for verification generation and this magnitude of complexity is considered minimal for multiple hard problems-like signature schemes. Conclusions: The new signature scheme based on multiple hard problems provides longer and higher security level than that scheme based on one problem. This is because no enemy can solve multiple hard problems simultaneously.
Parker, R Gary
1988-01-01
This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms.Several appendixes are included which review the fundamental ideas o
Elliptic Diophantine equations a concrete approach via the elliptic logarithm
Tzanakis, Nikos
2013-01-01
This book presents in a unified way the beautiful and deep mathematics, both theoretical and computational, on which the explicit solution of an elliptic Diophantine equation is based. It collects numerous results and methods that are scattered in literature. Some results are even hidden behind a number of routines in software packages, like Magma. This book is suitable for students in mathematics, as well as professional mathematicians.
The mimetic finite difference method for elliptic problems
Veiga, Lourenço Beirão; Manzini, Gianmarco
2014-01-01
This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for those scientists and engineers that are interested in the computational properties of the mimetic finite difference method such as the accuracy, stability, robustness, and efficiency. Many examples are provided to help the reader to understand and implement this method. This monograph also provides the essential background material and describes basic mathematical tools required to develop further the mimetic discretization technology and to extend it to various applications.
Discrete structures in F-theory compactifications
Till, Oskar
2016-05-04
In this thesis we study global properties of F-theory compactifications on elliptically and genus-one fibered Calabi-Yau varieties. This is motivated by phenomenological considerations as well as by the need for a deeper understanding of the set of consistent F-theory vacua. The global geometric features arise from discrete and arithmetic structures in the torus fiber and can be studied in detail for fibrations over generic bases. In the case of elliptic fibrations we study the role of the torsion subgroup of the Mordell-Weil group of sections in four dimensional compactifications. We show how the existence of a torsional section restricts the admissible matter representations in the theory. This is shown to be equivalent to inducing a non-trivial fundamental group of the gauge group. Compactifying F-theory on genus-one fibrations with multisections gives rise to discrete selection rules. In field theory the discrete symmetry is a broken U(1) symmetry. In the geometry the higgsing corresponds to a conifold transition. We explain in detail the origin of the discrete symmetry from two different M-theory phases and put the result into the context of torsion homology. Finally we systematically construct consistent gauge fluxes on genus-one fibrations and show that these induce an anomaly free chiral spectrum.
Convective heat transfer from a heated elliptic cylinder at uniform wall temperature
Kaprawi, S.; Santoso, Dyos [Mechanical Department of Sriwijaya University, Jl. Raya Palembang-Prabumulih Km. 32 Inderalaya 50062 Ogan Ilir (Indonesia)
2013-07-01
This study is carried out to analyse the convective heat transfer from a circular and an elliptic cylinders to air. Both circular and elliptic cylinders have the same cross section. The aspect ratio of cylinders range 0-1 are studied. The implicit scheme of the finite difference is applied to obtain the discretized equations of hydrodynamic and thermal problem. The Choleski method is used to solve the discretized hydrodynamic equation and the iteration method is applied to solve the discretized thermal equation. The circular cylinder has the aspect ratio equal to unity while the elliptical cylinder has the aspect ratio less than unity by reducing the minor axis and increasing the major axis to obtain the same cross section as circular cylinder. The results of the calculations show that the skin friction change significantly, but in contrast with the elliptical cylinders have greater convection heat transfer than that of circular cylinder. Some results of calculations are compared to the analytical solutions given by the previous authors.
An improved elliptic guide concept for a homogeneous neutron beam without direct line of sight
Zendler, C; Lieutenant, K
2014-01-01
Ballistic neutron guides are efficient for neutron transport over long distances, and in particular elliptically shaped guides have received much attention lately. However, elliptic neutron guides generally deliver an inhomogeneous divergence distribution when used with a small source, and do not allow kinks or curvature to avoid a direct view from source to sample. In this article, a kinked double-elliptic solution is found for neutron transport to a small sample from a small (virtual) source, as given e.g. for instruments using a pinhole beam extraction with a focusing feeder. A guide consisting of two elliptical parts connected by a linear kinked section is shown by VITESS simulations to deliver a high brilliance transfer as well as a homogeneous divergence distribution while avoiding direct line of sight to the source. It performs better than a recently proposed ellipse-parabola hybrid when used in a ballistic context with a kinked or curved central part. Another recently proposed solution, an analyticall...
Transmission eigenvalues for elliptic operators
Hitrik, Michael; Ola, Petri; Päivärinta, Lassi
2010-01-01
A reduction of the transmission eigenvalue problem for multiplicative sign-definite perturbations of elliptic operators with constant coefficients to an eigenvalue problem for a non-selfadjoint compact operator is given. Sufficient conditions for the existence of transmission eigenvalues and completeness of generalized eigenstates for the transmission eigenvalue problem are derived. In the trace class case, the generic existence of transmission eigenvalues is established.
Firth, Jean M
1992-01-01
The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree cour...
ERROR REDUCTION IN ADAPTIVE FINITE ELEMENT APPROXIMATIONS OF ELLIPTIC OBSTACLE PROBLEMS
Dietrich Braess; Carsten Carstensen; Ronald H.W. Hoppe
2009-01-01
We consider an adaptive finite element method (AFEM) for obstacle problems associated with linear second order elliptic boundary value problems and prove a reduction in the energy norm of the discretization error which leads to R-linear convergence. This result is shown to hold up to a consistency error due to the extension of the discrete multipliers (point functionals) to H-1 and a possible mismatch between the continuous and discrete coincidence and noncoincidence sets. The AFEM is based on a residual-type error estimator consisting of element and edge residuals. The a posteriori error analysis reveals that the significant difference to the unconstrained case lies in the fact that these residuals only have to be taken into account within the discrete noncoincidence set. The proof of the error reduction property uses the reliability and the discrete local efficiency of the estimator as well as a perturbed Galerkin orthogonality. Numerical results are given illustrating the performance of the AFEM.
Poiseuille flow in curved spaces
Debus, J -D; Succi, S; Herrmann, H J
2015-01-01
We investigate Poiseuille channel flow through intrinsically curved (campylotic) media, equipped with localized metric perturbations (campylons). To this end, we study the flux of a fluid driven through the curved channel in dependence of the spatial deformation, characterized by the campylon parameters (amplitude, range and density). We find that the flux depends only on a specific combination of campylon parameters, which we identify as the average campylon strength, and derive a universal flux law for the Poiseuille flow. For the purpose of this study, we have improved and validated our recently developed lattice Boltzmann model in curved space by considerably reducing discrete lattice effects.
A curvature theory for discrete surfaces based on mesh parallelity
Bobenko, Alexander Ivanovich
2009-12-18
We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces\\' areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discrete isothermic minimal surfaces and surfaces of constant mean curvature. We discuss various types of natural Gauss images, the existence of principal curvatures, constant curvature surfaces, Christoffel duality, Koenigs nets, contact element nets, s-isothermic nets, and interesting special cases such as discrete Delaunay surfaces derived from elliptic billiards. © 2009 Springer-Verlag.
Elliptically distributed lozenge tilings of a hexagon
Betea, Dan
2011-01-01
We present a detailed study of a 4 parameter family of elliptic weights on tilings of a hexagon introduced by Borodin, Gorin and Rains, and generalize some of their results. In the process, we connect the combinatorics of the model with the theory of elliptic special functions. We first analyze some properties of the measure and introduce canonical coordinates that are useful for combinatorially interpreting results. We then show how the computed $n$-point function (called the elliptic Selberg density) and transitional probabilities connect to the theory of $BC_n$-symmetric multivariate elliptic special functions and difference operators discovered by Rains. In particular, the difference operators intrinsically capture the combinatorial model under study, while the elliptic Selberg density is a generalization (deformation) of probability distributions pervasive in the theory of random matrices and interacting particle systems. Based on quasi-commutation relations between elliptic difference operators, we cons...
Parameter likelihood of intrinsic ellipticity correlations
Capranico, Federica; Schaefer, Bjoern Malte
2012-01-01
Subject of this paper are the statistical properties of ellipticity alignments between galaxies evoked by their coupled angular momenta. Starting from physical angular momentum models, we bridge the gap towards ellipticity correlations, ellipticity spectra and derived quantities such as aperture moments, comparing the intrinsic signals with those generated by gravitational lensing, with the projected galaxy sample of EUCLID in mind. We investigate the dependence of intrinsic ellipticity correlations on cosmological parameters and show that intrinsic ellipticity correlations give rise to non-Gaussian likelihoods as a result of nonlinear functional dependencies. Comparing intrinsic ellipticity spectra to weak lensing spectra we quantify the magnitude of their contaminating effect on the estimation of cosmological parameters and find that biases on dark energy parameters are very small in an angular-momentum based model in contrast to the linear alignment model commonly used. Finally, we quantify whether intrins...
SL(2;R)/U(1) supercoset and elliptic genera of Non-compact Calabi-Yau Manifolds
Eguchi, T
2004-01-01
We first discuss the relationship between the SL(2;)/U(1) supercoset and = 2 Liouville theory and make a precise correspondence between their representations. We shall show that the discrete unitary representations of SL(2;)/U(1) theory correspond exactly to those massless representations of = 2 Liouville theory which are closed under modular transformations and studied in our previous work [18]. It is known that toroidal partition functions of SL(2;)/U(1) theory (2D Black Hole) contain two parts, continuous and discrete representations. The contribution of continuous representations is proportional to the space-time volume and is divergent in the infinite-volume limit while the part of discrete representations is volume-independent. In order to see clearly the contribution of discrete representations we consider elliptic genus which projects out the contributions of continuous representations: making use of the SL(2;)/U(1), we compute elliptic genera for various non-compact space-times such as the conifold, ...
Non-paraxial Elliptical Gaussian Beam
WANG Zhaoying; LIN Qiang; NI Jie
2001-01-01
By using the methods of Hertz vector and angular spectrum transormation, the exact solution of non-paraxial elliptical Gaussion beam with general astigmatism based on Maxwell′s equations is obtained. We discussed its propagation characteristics. The results show that the orientation of the elliptical beam spot changes continuously as the beam propagates through isotropic media. Splitting or coupling of beam spots may occur for different initial spot size. This is very different from that of paraxial elliptical Gaussian beam.
Multiple elliptic gamma functions associated to cones
Winding, Jacob
2016-01-01
We define generalizations of the multiple elliptic gamma functions and the multiple sine functions, associated to good rational cones. We explain how good cones are related to collections of $SL_r(\\mathbb{Z})$-elements and prove that the generalized multiple sine and multiple elliptic gamma functions enjoy infinite product representations and modular properties determined by the cone. This generalizes the modular properties of the elliptic gamma function studied by Felder and Varchenko, and the results about the usual multiple sine and elliptic gamma functions found by Narukawa.
Nonparaxial Propagation of Vectorial Elliptical Gaussian Beams
Wang Xun
2016-01-01
Full Text Available Based on the vectorial Rayleigh-Sommerfeld diffraction integral formulae, analytical expressions for a vectorial elliptical Gaussian beam’s nonparaxial propagating in free space are derived and used to investigate target beam’s propagation properties. As a special case of nonparaxial propagation, the target beam’s paraxial propagation has also been examined. The relationship of vectorial elliptical Gaussian beam’s intensity distribution and nonparaxial effect with elliptic coefficient α and waist width related parameter fω has been analyzed. Results show that no matter what value of elliptic coefficient α is, when parameter fω is large, nonparaxial conclusions of elliptical Gaussian beam should be adopted; while parameter fω is small, the paraxial approximation of elliptical Gaussian beam is effective. In addition, the peak intensity value of elliptical Gaussian beam decreases with increasing the propagation distance whether parameter fω is large or small, and the larger the elliptic coefficient α is, the faster the peak intensity value decreases. These characteristics of vectorial elliptical Gaussian beam might find applications in modern optics.
Solitons on Noncommutative Torus as Elliptic Algebras and Elliptic Models
Hou, B Y; Shi, K J; Yue, R H; Hou, Bo-Yu; Peng, Dan-tao; Shi, Kang-Jie; Yue, Rui-Hong
2001-01-01
For the noncommutative torus ${\\cal T}$, in case of the N.C. parameter $\\theta = \\frac{Z}{n}$ and the area of ${\\cal T}$ is an integer, we construct the basis of Hilbert space ${\\cal H}_n$ in terms of $\\theta$ functions of the positions of $n$ solitons. The Wilson loop wrapping the solitons around the torus generates the algebra ${\\cal A}_n$. We find that ${\\cal A}_n$ is isomorphic to the $Z_n \\times Z_n$ Heisenberg group on $\\theta$ functions. We find the explicit form for the solitons local translation operators, show that it is the generators $g$ of an elliptic $su(n)$, which transform covariantly by the global gauge transformation of the Wilson loop in ${\\cal A}_n$. Then by acting on ${\\cal H}_n$ we establish the isomorphism of ${\\cal A}_n$ and $g$. Then it is easy to give the projection operators corresponding to the solitons and the ABS construction for generating solitons. We embed this $g$ into elliptic Gaudin and C.M. models to give the dynamics. For $\\theta$ generic case, we introduce the crossing p...
Nonlinear elliptic-parabolic problems
Kim, Inwon C
2012-01-01
We introduce a notion of viscosity solutions for a general class of elliptic-parabolic phase transition problems. These include the Richards equation, which is a classical model in filtration theory. Existence and uniqueness results are proved via the comparison principle. In particular, we show existence and stability properties of maximal and minimal viscosity solutions for a general class of initial data. These results are new even in the linear case, where we also show that viscosity solutions coincide with the regular weak solutions introduced in [Alt&Luckhaus 1983].
Chopper z-scan technique for elliptic Gaussian beams.
Dávila-Pintle, J A; Reynoso-Lara, E; Bravo-García, Y E
2016-09-05
This paper reports an improvement to the chopper z-scan technique for elliptic Gaussian beams. This improvement results in a higher sensitivity by measuring the ratio of eclipsing time to rotating period (duty cycle) of a chopper that eclipses the beam along the main axis. It is shown that the z-scan curve of the major axis is compressed along the z-axis. This compression factor is equal to the ratio between the minor and major axes. It was found that the normalized peak-valley difference with respect to the linear value does not depend on the axis along which eclipsing occurs.
Automorphic forms for elliptic function fields
Lorscheid, Oliver
2010-01-01
Let $F$ be the function field of an elliptic curve $X$ over $\\F_q$. In this paper, we calculate explicit formulas for unramified Hecke operators acting on automorphic forms over $F$. We determine these formulas in the language of the graph of an Hecke operator, for which we use its interpretation in terms of $\\P^1$-bundles on $X$. This allows a purely geometric approach, which involves, amongst others, a classification of the $\\P^1$-bundles on $X$. We apply the computed formulas to calculate the dimension of the space of unramified cusp forms and the support of a cusp form. We show that a cuspidal Hecke eigenform does not vanish in the trivial $\\P^1$-bundle. Further, we determine the space of unramified $F'$-toroidal automorphic forms where $F'$ is the quadratic constant field extension of $F$. It does not contain non-trivial cusp forms. An investigation of zeros of certain Hecke $L$-series leads to the conclusion that the space of unramified toroidal automorphic forms is spanned by the Eisenstein series $E(\\...
Felder's elliptic quantum group and elliptic hypergeometric series on the root system A_n
Rosengren, Hjalmar
2010-01-01
We introduce a generalization of elliptic 6j-symbols, which can be interpreted as matrix elements for intertwiners between corepresentations of Felder's elliptic quantum group. For special parameter values, they can be expressed in terms of multivariable elliptic hypergeometric series related to the root system A_n. As a consequence, we obtain new biorthogonality relations for such series.
Elliptical Fourier analysis: fundamentals, applications, and value for forensic anthropology.
Caple, Jodi; Byrd, John; Stephan, Carl N
2017-02-17
The numerical description of skeletal morphology enables forensic anthropologists to conduct objective, reproducible, and structured tests, with the added capability of verifying morphoscopic-based analyses. One technique that permits comprehensive quantification of outline shape is elliptical Fourier analysis. This curve fitting technique allows a form's outline to be approximated via the sum of multiple sine and cosine waves, permitting the profile perimeter of an object to be described in a dense (continuous) manner at a user-defined level of precision. A large amount of shape information (the entire perimeter) can thereby be collected in contrast to other methods relying on sparsely located landmarks where information falling in between the landmarks fails to be acquired. First published in 1982, elliptical Fourier analysis employment in forensic anthropology from 2000 onwards reflects a slow uptake despite large computing power that makes its calculations easy to conduct. Without hurdles arising from calculation speed or quantity, the slow uptake may partly reside with the underlying mathematics that on first glance is extensive and potentially intimidating. In this paper, we aim to bridge this gap by pictorially illustrating how elliptical Fourier harmonics work in a simple step-by-step visual fashion to facilitate universal understanding and as geared towards increased use in forensic anthropology. We additionally provide a short review of the method's utility for osteology, a summary of past uses in forensic anthropology, and software options for calculations that largely save the user the trouble of coding customized routines.
Matrix factorizations and elliptic fibrations
Omer, Harun
2016-09-01
I use matrix factorizations to describe branes at simple singularities of elliptic fibrations. Each node of the corresponding Dynkin diagrams of the ADE-type singularities is associated with one indecomposable matrix factorization which can be deformed into one or more factorizations of lower rank. Branes with internal fluxes arise naturally as bound states of the indecomposable factorizations. Describing branes in such a way avoids the need to resolve singularities. This paper looks at gauge group breaking from E8 fibers down to SU (5) fibers due to the relevance of such fibrations for local F-theory GUT models. A purpose of this paper is to understand how the deformations of the singularity are understood in terms of its matrix factorizations. By systematically factorizing the elliptic fiber equation, this paper discusses geometries which are relevant for building semi-realistic local models. In the process it becomes evident that breaking patterns which are identical at the level of the Kodaira type of the fibers can be inequivalent at the level of matrix factorizations. Therefore the matrix factorization picture supplements information which the conventional less detailed descriptions lack.
Matrix factorizations and elliptic fibrations
Harun Omer
2016-09-01
Full Text Available I use matrix factorizations to describe branes at simple singularities of elliptic fibrations. Each node of the corresponding Dynkin diagrams of the ADE-type singularities is associated with one indecomposable matrix factorization which can be deformed into one or more factorizations of lower rank. Branes with internal fluxes arise naturally as bound states of the indecomposable factorizations. Describing branes in such a way avoids the need to resolve singularities. This paper looks at gauge group breaking from E8 fibers down to SU(5 fibers due to the relevance of such fibrations for local F-theory GUT models. A purpose of this paper is to understand how the deformations of the singularity are understood in terms of its matrix factorizations. By systematically factorizing the elliptic fiber equation, this paper discusses geometries which are relevant for building semi-realistic local models. In the process it becomes evident that breaking patterns which are identical at the level of the Kodaira type of the fibers can be inequivalent at the level of matrix factorizations. Therefore the matrix factorization picture supplements information which the conventional less detailed descriptions lack.
Weak homology of elliptical galaxies
Bertin, G; Principe, M D
2002-01-01
We start by studying a small set of objects characterized by photometric profiles that have been pointed out to deviate significantly from the standard R^{1/4} law. For these objects we confirm that a generic R^{1/n} law, with n a free parameter, can provide superior fits (the best-fit value of n can be lower than 2.5 or higher than 10), better than those that can be obtained by a pure R^{1/4} law, by an R^{1/4}+exponential model, and by other dynamically justified self--consistent models. Therefore, strictly speaking, elliptical galaxies should not be considered homologous dynamical systems. Still, a case for "weak homology", useful for the interpretation of the Fundamental Plane of elliptical galaxies, could be made if the best-fit parameter n, as often reported, correlates with galaxy luminosity L, provided the underlying dynamical structure also follows a systematic trend with luminosity. We demonstrate that this statement may be true even in the presence of significant scatter in the correlation n(L). Pr...
Discretization of topological spaces
Amini, Massoud; Golestani, Nasser
2014-01-01
There are several compactification procedures in topology, but there is only one standard discretization, namely, replacing the original topology with the discrete topology. We give a notion of discretization which is dual (in categorical sense) to compactification and give examples of discretizations. Especially, a discretization functor from the category of $\\alpha$-scattered Stonean spaces to the category of discrete spaces is constructed which is the converse of the Stone-\\v{C}ech compact...
Curve Matching with Applications in Medical Imaging
Bauer, Martin; Bruveris, Martins; Harms, Philipp
2015-01-01
In the recent years, Riemannian shape analysis of curves and surfaces has found several applications in medical image analysis. In this paper we present a numerical discretization of second order Sobolev metrics on the space of regular curves in Euclidean space. This class of metrics has several...
Principal Curves on Riemannian Manifolds
Hauberg, Søren
2015-01-01
Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only...... in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimize a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend...... from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls...
Isolated elliptical galaxies in the local Universe
Lacerna, I; Avila-Reese, V; Abonza-Sane, J; del Olmo, A
2015-01-01
We have studied a sample of 89 very isolated elliptical galaxies at z < 0.08 and compared their properties with elliptical galaxies located in a high-density environment such as the Coma supercluster. Our aim is to probe the role of environment on the morphological transformation and quenching of elliptical galaxies as a function of mass. In addition, we elucidate about the nature of a particular set of blue and star-forming isolated ellipticals identified here. We study physical properties of ellipticals such as color, specific star formation rate, galaxy size and stellar age as a function of stellar mass and environment based on SDSS data. We analyze in more detail the blue star-forming isolated ellipticals through photometric characterization using GALFIT and infer their star formation history using STARLIGHT. Among the isolated ellipticals ~ 20% are blue, 8% are star-forming and ~ 10% are recently quenched, while among the Coma ellipticals ~ 8% are blue and just <= 1% are star-forming or recently qu...
Spatial scan statistics using elliptic windows
Christiansen, Lasse Engbo; Andersen, Jens Strodl; Wegener, Henrik Caspar
of confocal elliptic windows and propose a new way to present the information when a spatial point process is considered. This method gives smooth changes for smooth expansions of the set of clusters. A simulation study is used to show how the elliptic windows outperforms the usual circular windows...
Discrete Curvatures and Discrete Minimal Surfaces
Sun, Xiang
2012-06-01
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.
CHEBYSHEV WEIGHTED NORM LEAST-SQUARES SPECTRAL METHODS FOR THE ELLIPTIC PROBLEM
Sang Dong Kim; Byeong Chun Shin
2006-01-01
We develop and analyze a first-order system least-squares spectral method for the second-order elliptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the L2w-and H-1w,- norm of the residual equations and then we replace the negative norm by the discrete negative norm and analyze the discrete Chebyshev weighted least-squares method. The spectral convergence is derived for the proposed method. We also present various numerical experiments. The Legendre weighted least-squares method can be easily developed by following this paper.
Biala, T A; Jator, S N
2015-01-01
In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.
Elliptic annular Josephson tunnel junctions in an external magnetic field: the statics
Monaco, Roberto; Granata, Carmine; Vettoliere, Antonio
2015-01-01
symmetric electrodes a transverse magnetic field is equivalent to an in-plane field applied in the direction of the current flow. Varying the ellipse eccentricity we reproduce all known results for linear and ring-shaped JTJs. Experimental data on high-quality Nb/Al-AlOx/Nb elliptic annular junctions...... or in the perpendicular direction. We report a detailed study of both short and long elliptic annular junctions having different eccentricities. For junctions having a normalized perimeter less than one the threshold curves are derived and computed even in the case with one trapped Josephson vortex. For longer junctions...
Elliptically fibered Calabi–Yau manifolds and the ring of Jacobi forms
Huang, Min-xin, E-mail: minxin@ustc.edu.cn [Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Hefei, Anhui 230026 (China); Katz, Sheldon, E-mail: katz@math.uiuc.edu [Department of Mathematics, University of Illinois at Urbana–Champaign, 1409 W. Green St., Urbana, IL 61801 (United States); Klemm, Albrecht, E-mail: aklemm@th.physik.uni-bonn.de [Bethe Center for Theoretical Physics (BCTP), Physikalisches Institut, Universität Bonn, 53115 Bonn (Germany)
2015-09-15
We give evidence that the all genus amplitudes of topological string theory on compact elliptically fibered Calabi–Yau manifolds can be written in terms of meromorphic Jacobi forms whose weight grows linearly and whose index grows quadratically with the base degree. The denominators of these forms have a simple universal form with the property that the poles of the meromorphic form lie only at torsion points. The modular parameter corresponds to the fibre class while the role of the string coupling is played by the elliptic parameter. This leads to very strong all genus results on these geometries, which are checked against results from curve counting.
International Workshop on Elliptic and Parabolic Equations
Schrohe, Elmar; Seiler, Jörg; Walker, Christoph
2015-01-01
This volume covers the latest research on elliptic and parabolic equations and originates from the international Workshop on Elliptic and Parabolic Equations, held September 10-12, 2013 at the Leibniz Universität Hannover. It represents a collection of refereed research papers and survey articles written by eminent scientist on advances in different fields of elliptic and parabolic partial differential equations, including singular Riemannian manifolds, spectral analysis on manifolds, nonlinear dispersive equations, Brownian motion and kernel estimates, Euler equations, porous medium type equations, pseudodifferential calculus, free boundary problems, and bifurcation analysis.
PARTITION PROPERTY OF DOMAIN DECOMPOSITION WITHOUT ELLIPTICITY
Mo Mu; Yun-qing Huang
2001-01-01
Partition property plays a central role in domain decomposition methods. Existing theory essentially assumes certain ellipticity. We prove the partition property for problems without ellipticity which are of practical importance. Example applications include implicit schemes applied to degenerate parabolic partial differential equations arising from superconductors, superfluids and liquid crystals. With this partition property, Schwarz algorithms can be applied to general non-elliptic problems with an h-independent optimal convergence rate. Application to the time-dependent Ginzburg-Landau model of superconductivity is illustrated and numerical results are presented.
Microwave gas breakdown in elliptical waveguides
Koufogiannis, I. D.; Sorolla, E., E-mail: eden.sorolla@epfl.ch; Mattes, M. [École Polytechnique Fédérale de Lausanne, Laboratoire d’Électromagnétisme et d' Acoustique (LEMA), Station 11, CH-1015 Lausanne (Switzerland)
2014-01-15
This paper analyzes the microwave gas discharge within elliptical waveguides excited by the fundamental mode. The Rayleigh-Ritz method has been applied to solve the continuity equation. The eigenvalue problem defined by the breakdown condition has been solved and the effective diffusion length of the elliptical waveguide has been calculated, what is used to find the corona threshold. This paper extends the microwave breakdown model developed for circular waveguides and shows the better corona withstanding capabilities of elliptical waveguides. The corona breakdown electric field threshold obtained with the variational method has been compared with the one calculated with the Finite Elements Method, showing excellent agreement.
Elliptic Functions with Disconnected Julia Sets
Koss, Lorelei
2016-06-01
In this paper, we investigate elliptic functions of the form fΛ = 1/(1 + (℘Λ)2), where ℘Λ is the Weierstrass elliptic function on a real rhombic lattice. We show that a typical function in this family has a superattracting fixed point at the origin and five other equivalence classes of critical points. We investigate conditions on the lattice which guarantee that fΛ has a double toral band, and we show that this family contains the first known examples of elliptic functions for which the Julia set is disconnected but not Cantor.
Principal Curves on Riemannian Manifolds.
Hauberg, Soren
2016-09-01
Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimizes a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend to imply that the methods only work well when the manifold is mostly flat within the support of the generating distribution. We argue that instead of generalizing linear Euclidean models, it is more fruitful to generalize non-linear Euclidean models. Specifically, we extend the classic Principal Curves from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls of traditional geodesic approaches. We empirically demonstrate the effectiveness of the Riemannian principal curves on several manifolds and datasets.
New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
Aminov, G. [ITEP, Moscow (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny (Russian Federation); Mironov, A. [ITEP, Moscow (Russian Federation); Lebedev Physics Institute, Moscow (Russian Federation); National Research Nuclear University MEPhI, Moscow (Russian Federation); Institute for Information Transmission Problems, Moscow (Russian Federation); Morozov, A. [ITEP, Moscow (Russian Federation); National Research Nuclear University MEPhI, Moscow (Russian Federation); Institute for Information Transmission Problems, Moscow (Russian Federation)
2016-08-15
Integrable N-particle systems have an important property that the associated Seiberg-Witten prepotentials satisfy the WDVV equations. However, this does not apply to the most interesting class of elliptic and double-elliptic systems. Studying the commutativity conjecture for theta functions on the families of associated spectral curves, we derive some other non-linear equations for the perturbative Seiberg-Witten prepotential, which turn out to have exactly the double-elliptic system as their generic solution. In contrast with the WDVV equations, the new equations acquire non-perturbative corrections which are straightforwardly deducible from the commutativity conditions. We obtain such corrections in the first non-trivial case of N = 3 and describe the structure of non-perturbative solutions as expansions in powers of the flat moduli with coefficients that are (quasi)modular forms of the elliptic parameter. (orig.)
New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
Aminov, G; Morozov, A
2016-01-01
Integrable N-particle systems have an important property that the associated Seiberg-Witten prepotentials satisfy the WDVV equations. However, this does not apply to the most interesting class of elliptic and double-elliptic systems. Studying the commutativity conjecture for theta-functions on the families of associated spectral curves, we derive some other non-linear equations for the perturbative Seiberg-Witten prepotential, which turn out to have exactly the double-elliptic system as their generic solution. In contrast with the WDVV equations, the new equations acquire non-perturbative corrections which are straightforwardly deducible from the commutativity conditions. We obtain such corrections in the first non-trivial case of N=3 and describe the structure of non-perturbative solutions as expansions in powers of the flat moduli with coefficients that are (quasi)modular forms of the elliptic parameter.
The origin of discrete symmetries in F-theory models
2015-01-01
While non-abelian groups are undoubtedly the cornerstone of Grand Unified Theories (GUTs), phenomenology shows that the role of abelian and discrete symmetries is equally important in model building. The latter are the appropriate tool to suppress undesired proton decay operators and various flavour violating interactions, to generate a hierarchical fermion mass spectrum, etc. In F-theory, GUT symmetries are linked to the singularities of the elliptically fibred K3 manifolds; they are of ADE ...
Elliptical instability in terrestrial planets and moons
Cébron, David; Moutou, Claire; Gal, Patrice Le; 10.1051/0004-6361/201117741
2012-01-01
The presence of celestial companions means that any planet may be subject to three kinds of harmonic mechanical forcing: tides, precession/nutation, and libration. These forcings can generate flows in internal fluid layers, such as fluid cores and subsurface oceans, whose dynamics then significantly differ from solid body rotation. In particular, tides in non-synchronized bodies and libration in synchronized ones are known to be capable of exciting the so-called elliptical instability, i.e. a generic instability corresponding to the destabilization of two-dimensional flows with elliptical streamlines, leading to three-dimensional turbulence. We aim here at confirming the relevance of such an elliptical instability in terrestrial bodies by determining its growth rate, as well as its consequences on energy dissipation, on magnetic field induction, and on heat flux fluctuations on planetary scales. Previous studies and theoretical results for the elliptical instability are re-evaluated and extended to cope with ...
Theory of the quadrature elliptic birdcage coil.
Leifer, M C
1997-11-01
This paper presents the theory of the quadrature birdcage coil wound on an elliptic cylindrical former. A conformal transformation of the ellipse to a circular geometry is used to derive the optimal sampling of the continuous surface current distribution to produce uniform magnetic fields within an elliptic cylinder. The analysis is rigorous for ellipses of any aspect ratio and shows how to produce quadrature operation of the elliptic birdcage with a conventional hybrid combiner. Insight gained from the transformation is also used to analyze field homogeneity, find the optimal RF shield shape, and specify component values to produce the correct current distribution in practice. Measurements and images from a 16-leg elliptic birdcage coil at both low and high frequencies show good quadrature performance, homogeneity, and sensitivity.
AC Dielectrophoresis Using Elliptic Electrode Geometry
S. M. Rezaul Hasan
2011-01-01
Full Text Available This paper presents negative AC dielectrophoretic investigations using elliptic electrode geometry. Simulations of the electric field gradient variation using various ratios of the semimajor and the semiminor axis were carried out to determine the optimum elliptic geometry for the dielectrophoretic electrokinetics of specimen in an assay with laminar (low Reynolds number fluid flow. Experimental setup of the elliptic electrode assembly using PCB fabrication and electrokinetic accumulation of specimen in a dielectrophoretic cage is also being reported. Using an actuating signal between 1 kHz and 1 MHz, successful trapping of 45 μm polystyrene beads suspended in distilled water was demonstrated due to negative dielectrophoresis near 100 kHz using the novel elliptic electrode.
Elliptic Polylogarithms and Basic Hypergeometric Functions
Passarino, Giampiero
2016-01-01
Multiple elliptic polylogarithms can be written as (multiple) integrals of products of basic hypergeometric functions. The latter are computable, to arbitrary precision, using a q-difference equation and q-contiguous relations.
The formation history of elliptical galaxies
De Lucia, G; White, S D M; Croton, D; Kauffmann, G; Lucia, Gabriella De; Springel, Volker; White, Simon D. M.; Croton, Darren; Kauffmann, Guinevere
2006-01-01
We take advantage of the largest high-resolution simulation of cosmic structure growth ever carried out -- the Millennium Simulation of the concordance LambdaCDM cosmogony -- to study how the star formation histories, ages and metallicities of elliptical galaxies depend on environment and on stellar mass. We concentrate on a galaxy formation model which is tuned to fit the joint luminosity/colour/morphology/clustering distribution of low redshift galaxies. Massive ellipticals in this model have higher metal abundances, older luminosity-weighted ages, shorter star formation timescales, but lower assembly redshifts than less massive systems. Within clusters the typical masses, ages and metal abundances of ellipticals are predicted to decrease, on average, with increasing distance from the cluster centre. We also quantify the effective number of progenitors of ellipticals as a function of present stellar mass, finding typical numbers below 2 for M* < 10^{11} Msun, rising to about 5 for the most massive system...
Groupoids, Discrete Mechanics, and Discrete Variation
GUO Jia-Feng; JIA Xiao-Yu; WU Ke; ZHAO Wei-Zhong
2008-01-01
After introducing some of the basic definitions and results from the theory of groupoid and Lie algebroid,we investigate the discrete Lagrangian mechanics from the viewpoint of groupoid theory and give the connection between groupoids variation and the methods of the first and second discrete variational principles.
Zhou, Jianqin
2011-01-01
The discrete cosine transform (DCT), introduced by Ahmed, Natarajan and Rao, has been used in many applications of digital signal processing, data compression and information hiding. There are four types of the discrete cosine transform. In simulating the discrete cosine transform, we propose a generalized discrete cosine transform with three parameters, and prove its orthogonality for some new cases. A new type of discrete cosine transform is proposed and its orthogonality is proved. Finally, we propose a generalized discrete W transform with three parameters, and prove its orthogonality for some new cases.
Mimetic discretization methods
Castillo, Jose E
2013-01-01
To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and
Dynamical family properties and dark halo scaling relations of giant elliptical galaxies
Gerhard, O E; Saglia, R P; Bender, R; Gerhard, Ortwin; Kronawitter, Andi; Bender, Ralf
2001-01-01
Based on a uniform dynamical analysis of line-profile shapes for 21 luminous round elliptical galaxies, we have investigated the dynamical family relations of ellipticals: (i) The circular velocity curves (CVCs) of elliptical galaxies are flat to within ~10% for R>~0.2R_e. (ii) Most ellipticals are moderately radially anisotropic; their dynamical structure is surprisingly uniform. (iii) Elliptical galaxies follow a Tully-Fisher (TF) relation, with v_c^max=300 km/s for an L_B^* galaxy. At given v_c^max, they are ~1 mag fainter in B and appear to have slightly lower baryonic mass than spirals even for maximum M/L_B. (iv) The luminosity dependence of M/L_B is confirmed. The tilt of the Fundamental Plane is not caused by dynamical non-homology, nor only by an increasing dark matter fraction with L. It is, however, consistent with stellar population models based on published metallicities and ages. The main driver is therefore probably metallicity, and a secondary population effect is needed to explain the K-band ...
Heavy Flavour Electron Elliptic Flow
Gutierrez Ortiz, Nicolas Gilberto
Due to the large mass of the Charm and Beauty quarks, they are c reated in the very first moments of the ultra-high energy nucleus-nucleus collisions taking place at the CERN LHC, therefore, they should be unaware of the geome try of the colli- sion system and carry no azimuthal anisotropies. Similarly , the energy loss via gluon radiation for these massive quarks should be suppressed, th e so-called dead cone ef- fect. Although the observation of elliptic flow in the electro ns produced through the semileptonic decay of these heavy mesons is an indirect meas urement, throughout this thesis it will be shown that a strong correlation exists between the momentum anisotropy of the mother and daughter particles. In the low t ransverse momentum region such measurement would establish whether or not the s ystem reaches local thermal equilibrium. While at large transverse momentum, t he observation of collec- tivity for the heavy flavours can be understood only if the col lisional and radiative in-medium interaction...
Dust processing in elliptical galaxies
Hirashita, Hiroyuki; Villaume, Alexa; Srinivasan, Sundar
2015-01-01
We reconsider the origin and processing of dust in elliptical galaxies. We theoretically formulate the evolution of grain size distribution, taking into account dust supply from asymptotic giant branch (AGB) stars and dust destruction by sputtering in the hot interstellar medium (ISM), whose temperature evolution is treated by including two cooling paths: gas emission and dust emission (i.e. gas cooling and dust cooling). With our new full treatment of grain size distribution, we confirm that dust destruction by sputtering is too efficient to explain the observed dust abundance even if AGB stars continue to supply dust grains, and that, except for the case where the initial dust-to-gas ratio in the hot gas is as high as $\\sim 0.01$, dust cooling is negligible compared with gas cooling. However, we show that, contrary to previous expectations, cooling does not help to protect the dust; rather, the sputtering efficiency is raised by the gas compression as a result of cooling. We additionally consider grain grow...
Approximate Schur complement preconditioning of the lowest order nodal discretizations
Moulton, J.D.; Ascher, U.M. [Univ. of British Columbia, Vancouver, British Columbia (Canada); Morel, J.E. [Los Alamos National Lab., NM (United States)
1996-12-31
Particular classes of nodal methods and mixed hybrid finite element methods lead to equivalent, robust and accurate discretizations of 2nd order elliptic PDEs. However, widespread popularity of these discretizations has been hindered by the awkward linear systems which result. The present work exploits this awkwardness, which provides a natural partitioning of the linear system, by defining two optimal preconditioners based on approximate Schur complements. Central to the optimal performance of these preconditioners is their sparsity structure which is compatible with Dendy`s black box multigrid code.
Integral Models of Extremal Rational Elliptic Surfaces
Jarvis, Tyler J; Ricks, Jeremy R
2009-01-01
Miranda and Persson classified all extremal rational elliptic surfaces in characteristic zero. We show that each surface in Miranda and Persson's classification has an integral model with good reduction everywhere (except for those of type X_{11}(j), which is an exceptional case), and that every extremal rational elliptic surface over an algebraically closed field of characteristic p > 0 can be obtained by reducing one of these integral models mod p.
An elliptic quantum algebra for sl$_{2}$
Foda, O E; Jimbo, M; Kedem, R; Miwa, T; Yan, H
1994-01-01
An elliptic deformation of \\widehat{sl}_2 is proposed. Our presentation of the algebra is based on the relation RLL=LLR^*, where R and R^* are eight-vertex R-matrices with the elliptic moduli chosen differently. In the trigonometric limit, this algebra reduces to a quotient of that proposed by Reshetikhin and Semenov-Tian-Shansky. Conjectures concerning highest weight modules and vertex operators are formulated, and the physical interpretation of R^* is discussed.
Discrete mathematics, discrete physics and numerical methods
Felice Iavernaro
2007-12-01
Full Text Available Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difﬁculty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences of Fichera about discrete and continuous world, we shall present some considerations about discrete phenomena which arise when designing numerical methods or discrete models for some classical physical problems.
Formation, Evolution and Properties of Isolated Field Elliptical Galaxies
Niemi, Sami-Matias; Nurmi, Pasi; Saar, Enn
2010-01-01
[Abridged] We study the properties, evolution and formation mechanisms of isolated field elliptical galaxies. We create a mock catalogue of isolated field elliptical galaxies from the Millennium Simulation Galaxy Catalogue, and trace their merging histories. The formation, identity and assembly redshifts of simulated isolated and non-isolated elliptical galaxies are studied and compared. Observational and numerical data are used to compare age, mass, and the colour-magnitude relation. Our results, based on simulation data, show that almost seven per cent of all elliptical galaxies brighter than -19mag in B-band can be classified as isolated field elliptical galaxies. Isolated field elliptical galaxies show bluer colours than non-isolated elliptical galaxies and they appear younger, in a statistical sense, according to their mass weighted age. Isolated field elliptical galaxies also form and assemble at lower redshifts compared to non-isolated elliptical galaxies. About 46 per cent of isolated field elliptical...
Discrete Wigner function dynamics
Klimov, A B; Munoz, C [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44410, Guadalajara, Jalisco (Mexico)
2005-12-01
We study the evolution of the discrete Wigner function for prime and the power of prime dimensions using the discrete version of the star-product operation. Exact and semiclassical dynamics in the limit of large dimensions are considered.
The “loxodromic”curve and the herringbone
Roberto Corazzi
2012-06-01
Full Text Available In hemisphere domes the development of the spirals of the herringbone creates a “loxodromic” curve. The curve of the herringbone comes closer and closer to the poles of the sphere. A structure with an octagonal base, presents greater difficulties in the application of this technique; its structure does not have the same continuity as the round dome; as observed previously, each "vela" is a portion of an elliptical cylinder, and not a sphere.
Seidl, Gerhart
2014-01-01
We present a simple generalization of Noether's theorem for discrete symmetries in relativistic continuum field theories. We calculate explicitly the conserved current for several discrete spacetime and internal symmetries. In addition, we formulate an analogue of the Ward-Takahashi identity for the Noether current associated with a discrete symmetry.
Fabrication of elliptical SRF cavities
Singer, W.
2017-03-01
The technological and metallurgical requirements of material for high-gradient superconducting cavities are described. High-purity niobium, as the preferred metal for the fabrication of superconducting accelerating cavities, should meet exact specifications. The content of interstitial impurities such as oxygen, nitrogen, and carbon must be below 10 μg g-1. The hydrogen content should be kept below 2 μg g-1 to prevent degradation of the quality factor (Q-value) under certain cool-down conditions. The material should be free of flaws (foreign material inclusions or cracks and laminations) that can initiate a thermal breakdown. Traditional and alternative cavity mechanical fabrication methods are reviewed. Conventionally, niobium cavities are fabricated from sheet niobium by the formation of half-cells by deep drawing, followed by trim machining and electron beam welding. The welding of half-cells is a delicate procedure, requiring intermediate cleaning steps and a careful choice of weld parameters to achieve full penetration of the joints. A challenge for a welded construction is the tight mechanical and electrical tolerances. These can be maintained by a combination of mechanical and radio-frequency measurements on half-cells and by careful tracking of weld shrinkage. The main aspects of quality assurance and quality management are mentioned. The experiences of 800 cavities produced for the European XFEL are presented. Another cavity fabrication approach is slicing discs from the ingot and producing cavities by deep drawing and electron beam welding. Accelerating gradients at the level of 35-45 MV m-1 can be achieved by applying electrochemical polishing treatment. The single-crystal option (grain boundary free) is discussed. It seems that in this case, high performance can be achieved by a simplified treatment procedure. Fabrication of the elliptical resonators from a seamless pipe as an alternative is briefly described. This technology has yielded good
Vinet, Luc [Universite de Montreal, PO Box 6128, Station Centre-ville, Montreal QC H3C 3J7 (Canada); Zhedanov, Alexei [Donetsk Institute for Physics and Technology, Donetsk 83114 (Ukraine)
2009-10-30
We construct new families of elliptic solutions of the restricted Toda chain. The main tool is a special (so-called Stieltjes) ansatz for the moments of corresponding orthogonal polynomials. We show that the moments thus obtained are related to three types of Lame polynomials. The corresponding orthogonal polynomials can be considered as a generalization of the Stieltjes-Carlitz elliptic polynomials.
Exposition on affine and elliptic root systems and elliptic Lie algebras
Azam, Saeid; Yousofzadeh, Malihe
2009-01-01
This is an exposition in order to give an explicit way to understand (1) a non-topological proof for an existence of a base of an affine root system, (2) a Serre-type definition of an elliptic Lie algebra with rank =>2, and (3) the isotropic root multiplicities of those elliptic Lie algebras.
Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients
Bonito, Andrea
2013-01-01
Elliptic PDEs with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electromagnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could even be unknown beforehand. One of the obstacles to treating such discontinuity problems is that the usual perturbation theory for elliptic PDEs assumes bounds for the distortion of the coefficients in the L∞ norm and this in turn requires that the discontinuities are matched exactly when the coefficients are approximated. We present a new approach based on distortion of the coefficients in an Lq norm with q < ∞ which therefore does not require the exact matching of the discontinuities. We then use this new distortion theory to formulate new adaptive finite element methods (AFEMs) for such discontinuity problems. We show that such AFEMs are optimal in the sense of distortion versus number of computations, and report insightful numerical results supporting our analysis. © 2013 Societ y for Industrial and Applied Mathematics.
The Structure of Galaxies: III. Two Structural Families of Ellipticals
Schombert, James M
2015-01-01
Using isophotal radius correlations for a sample of 2MASS ellipticals, we have constructed a series of template surface brightness profiles to describe the profile shapes of ellipticals as a function of luminosity. The templates are a smooth function of luminosity, yet are not adequately matched to any fitting function supporting the view that ellipticals are weakly non-homologous with respect to structure. Through comparison to the templates, it is discovered that ellipticals are divided into two families; those well matched to the templates and a second class of ellipticals with distinctly shallower profile slopes. We refer to these second type of ellipticals as D class, an old morphological designation acknowledging diffuse appearance on photographic material. D ellipticals cover the same range of luminosity, size and kinematics as normal ellipticals, but maintain a signature of recent equal mass dry mergers. We propose that normal ellipticals grow after an initial dissipation formation era by accretion of...
Generalized Rayleigh quotient and finite element two-grid discretization schemes
2009-01-01
This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of finite element approximate eigenvalue. 3) Based on the work of Xu Jinchao and Zhou Aihui, finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and non-conforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.
Generalized Rayleigh quotient and finite element two-grid discretization schemes
YANG YiDu; FAN XinYue
2009-01-01
This study discusses generalized Rayleigh quotient and high efficiency finite element dis-cretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of finite element approximate eigenvalue. 3) Based on the work of Xu Jinchao and Zhou Aihui, finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and non-conforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.
Discrete fields, general relativity, other possible implications and experimental evidences
De Souza, M M
2001-01-01
The physical meaning, the properties and the consequences of a discrete scalar field are discussed; limits for the validity of a mathematical description of fundamental physics in terms of continuous fields are a natural outcome of discrete fields with discrete interactions. The discrete scalar field is ultimately the gravitational field of general relativity, necessarily, and there is no place for any other fundamental scalar field, in this context. Part of the paper comprehends a more generic discussion about the nature, if continuous or discrete, of fundamental interactions. There is a critical point defined by the equivalence between the two descriptions. Discrepancies between them can be observed far away from this point as a continuous-interaction is always stronger below it and weaker above it than a discrete one. It is possible that some discrete-field manifestations have already been observed in the flat rotation curves of galaxies and in the apparent anomalous acceleration of the Pioneer spacecrafts...
Maliassov, S.Y. [Texas A& M Univ., College Station, TX (United States)
1996-12-31
An approach to the construction of an iterative method for solving systems of linear algebraic equations arising from nonconforming finite element discretizations with nonmatching grids for second order elliptic boundary value problems with anisotropic coefficients is considered. The technique suggested is based on decomposition of the original domain into nonoverlapping subdomains. The elliptic problem is presented in the macro-hybrid form with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence axe independent of values of coefficients and mesh step size.
Fast Bilinear Maps from the Tate-Lichtenbaum Pairing on Hyperelliptic Curves
Frey, Gerhard; Lange, Tanja
2006-01-01
Pairings on elliptic curves recently obtained a lot of attention not only as a means to attack curve based cryptography but also as a building block for cryptosystems with special properties like short signatures or identity based encryption. In this paper we consider the Tate pairing on hyperell...
AGN feedback in elliptical galaxies: numerical simulations
Ciotti, L
2011-01-01
The importance of feedback (radiative and mechanical) from massive black holes at the centers of elliptical galaxies is not in doubt, given the well established relation among black hole mass and galaxy optical luminosity. Here, with the aid of high-resolution hydrodynamical simulations, we discuss how this feedback affects the hot ISM of isolated elliptical galaxies of different mass. The cooling and heating functions include photoionization plus Compton heating, the radiative transport equations are solved, and the mechanical feedback due to the nuclear wind is also described on a physical basis; star formation is considered. In the medium-high mass galaxies the resulting evolution is highly unsteady. At early times major accretion episodes caused by cooling flows in the recycled gas produced by stellar evolution trigger AGN flaring: relaxation instabilities occur so that duty cycles are small enough to account for the very small fraction of massive ellipticals observed to be in the QSO-phase, when the accr...
Nonlinear elliptic equations of the second order
Han, Qing
2016-01-01
Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and "elementary" proofs for results in important special cases. This book will serve as a valuable resource for graduate stu...
Discrete Film Cooling in a Rocket with Curved Walls
2009-12-01
fully developed flow in a porous-wall pipe, Nu comparisons were made between a numerical simulation and experimental Poiseuille flow for transpiration...determine the blowing parameter. By solving the Couette -simplified momentum equation and using the Reynolds analogy a result similar to, but simpler
AN INTERPOLATING CURVE SUBDIVISION SCHEME BASED ON DISCRETE FIRST DERIVATIVE
ALBEIRO ESPINOSA BEDOYA
2013-01-01
tortuosidad. Un análisis de las distribuciones de frecuencia obtenidas para esta propiedad, empleando la prueba de KruskalWallis, revela que el esquema DFDS posee los menores valores de tortuosidad en un rango más estrecho.
The elliptic model for social fluxes
Herrera-Yagüe, C; Smoreda, Z; Couronné, T; Zufiria, PJ; González, MC
2013-01-01
We analyze the anonymous communications patterns of 25 million users from 3 different countries. Grouping costumer by their location (most used phone tower or billing zip code) we build social networks at three levels: tower, city and region for each of the three countries. We propose an elliptic model, which considers the number of relationships between two locations is reversely proportional to the population in the ellipse whose focuses are in such locations. We compare the performance of this model to recent transportation models and find elliptic model overcomes their performance in all scenarios, showing human relationships are at least as influenced by geographical factors as human mobility is.
Electromagnetic Invisibility of Elliptic Cylinder Cloaks
YAO Kan; LI Chao; LI Fang
2008-01-01
Structures with unique electromagnetic properties are designed based on the approach of spatial coordinate transformations of Maxwell's equations.This approach is applied to scheme out invisible elliptic cylinder cloaks,which provide more feasibility for cloaking arbitrarily shaped objects.The transformation expressions for the anisotropic material parameters and the field distribution are derived.The cloaking performances of ideal and lossy elliptic cylinder cloaks are investigated by finite element simulations. It is found that the cloaking performance will degrade in the forward direction with increasing loss.
Hintermüller, M.
2008-06-01
An output-least-squares formulation for a class of parameter identification problems for elliptic variational inequalities is considered. Based on the concept of C-stationarity an active set type solver with feasibility restoration is introduced. It is shown that the new method relates to the so-called implicit programming techniques in the context of mathematical programs with equilibrium constraints. In the discrete setting, in order to overcome the ill-posedness of the problem, the parameter of interest is discretized on a coarser mesh than the state of the system. In addition, if the parameter corresponds to the coefficient in the bilinear form of the underlying differential operator, an interior-point treatment is employed to maintain the coercivity of the elliptic operator. Moreover, the computational domain for the coefficient depends on the measurement data. The paper ends with a report on numerical tests including an application to a simplified lubrication problem in a rolling element device.
Ayuso Dios, Blanca
2013-10-30
We introduce and analyze two-level and multilevel preconditioners for a family of Interior Penalty (IP) discontinuous Galerkin (DG) discretizations of second order elliptic problems with large jumps in the diffusion coefficient. Our approach to IPDG-type methods is based on a splitting of the DG space into two components that are orthogonal in the energy inner product naturally induced by the methods. As a result, the methods and their analysis depend in a crucial way on the diffusion coefficient of the problem. The analysis of the proposed preconditioners is presented for both symmetric and non-symmetric IP schemes; dealing simultaneously with the jump in the diffusion coefficient and the non-nested character of the relevant discrete spaces presents additional difficulties in the analysis, which precludes a simple extension of existing results. However, we are able to establish robustness (with respect to the diffusion coefficient) and near-optimality (up to a logarithmic term depending on the mesh size) for both two-level and BPX-type preconditioners, by using a more refined Conjugate Gradient theory. Useful by-products of the analysis are the supporting results on the construction and analysis of simple, efficient and robust two-level and multilevel preconditioners for non-conforming Crouzeix-Raviart discretizations of elliptic problems with jump coefficients. Following the analysis, we present a sequence of detailed numerical results which verify the theory and illustrate the performance of the methods. © 2013 American Mathematical Society.
Vidal-Codina, F.; Nguyen, N. C.; Giles, M. B.; Peraire, J.
2015-09-01
We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basis approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.
Vidal-Codina, F., E-mail: fvidal@mit.edu [Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Nguyen, N.C., E-mail: cuongng@mit.edu [Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Giles, M.B., E-mail: mike.giles@maths.ox.ac.uk [Mathematical Institute, University of Oxford, Oxford (United Kingdom); Peraire, J., E-mail: peraire@mit.edu [Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)
2015-09-15
We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basis approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.
Ariwahjoedi, Seramika; Kosasih, Jusak Sali; Rovelli, Carlo; Zen, Freddy Permana
2016-01-01
Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background independence. To maintain these assumptions, restrictions are given to the theory by introducing cut-offs, both in ultraviolet and infrared regime. Having a well-defined statistical picture of discrete Regge geometry, we take the infinite degrees of freedom (large n) limit. We argue that the correct limit consistent with the restrictions and the background independence concept is not the continuum limit of statistical mechanics, but the thermodynamical limit.
Digital and discrete geometry theory and algorithms
Chen, Li
2014-01-01
This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences. It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData.The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms. The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and a
Buckling of elliptical rings under uniform external pressure
Tang, Y.
1991-04-03
A thin, elastic elliptical ring is subjected to uniform external pressure. The lowest critical pressure is computed and presented for various ratio of the major axis to the minor axis of the elliptical ring. It is found that the critical pressure for an elliptical ring is higher than that for the circular ring whose diameter is equal to the major axis of the elliptical ring. It can be shown that under the same external pressure, the axial force developed in the elliptical ring is less than that developed in the corresponding circular ring. Thus, a higher pressure is required to buckle the elliptical rings. Therefore, by changing the shape of the ring from circular to elliptical, the capability of the ring to sustain the external pressure can be increased substantially. The results of this study can be useful in the design of elliptical reinforcing rings and thin-walled tubes subjected to external pressure.
Adjoint Based A Posteriori Analysis of Multiscale Mortar Discretizations with Multinumerics
Tavener, Simon
2013-01-01
In this paper we derive a posteriori error estimates for linear functionals of the solution to an elliptic problem discretized using a multiscale nonoverlapping domain decomposition method. The error estimates are based on the solution of an appropriately defined adjoint problem. We present a general framework that allows us to consider both primal and mixed formulations of the forward and adjoint problems within each subdomain. The primal subdomains are discretized using either an interior penalty discontinuous Galerkin method or a continuous Galerkin method with weakly imposed Dirichlet conditions. The mixed subdomains are discretized using Raviart- Thomas mixed finite elements. The a posteriori error estimate also accounts for the errors due to adjoint-inconsistent subdomain discretizations. The coupling between the subdomain discretizations is achieved via a mortar space. We show that the numerical discretization error can be broken down into subdomain and mortar components which may be used to drive adaptive refinement.Copyright © by SIAM.
Discrete mathematics, discrete physics and numerical methods
Felice Iavernaro; Donato Trigiante
2007-01-01
Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difﬁculty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences o...
Slow Wave Characteristics of Helix Structure with Elliptical Cross Section
XIE Jian-Xiang; WEI Yan-Yu; GONG Yu-Bin; Fu Cheng-Fang; YUE Ling-Na; WANG Wen-Xiang
2007-01-01
We present a novel helix slow wave structure with an elliptical cross section shielded by an elliptical waveguide.The rf characteristics including dispersion properties,interaction impedance of zero mode in this structure have been studied in detail.The theoretical results reveal that weaker dispersion even abnormal dispersion characteristics is obtained with the increasing eccentricity of the elliptical waveguide,while the interaction impedance is enhanced by enlarging the eccentricity of elliptical helix.
The arithmetic of elliptic fibrations in gauge theories on a circle
Grimm, Thomas W.; Kapfer, Andreas; Klevers, Denis
2016-06-01
The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.
The arithmetic of elliptic fibrations in gauge theories on a circle
Grimm, Thomas W. [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 Munich (Germany); Institute for Theoretical Physics,Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Center for Extreme Matter and Emergent Phenomena,Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Kapfer, Andreas [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 Munich (Germany); Klevers, Denis [Theory Group, Physics Department, CERN,CH-1211, Geneva 23 (Switzerland)
2016-06-20
The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.
Cvetic, Mirjam; Piragua, Hernan
2013-01-01
We study F-theory compactifications with U(1)xU(1) gauge symmetry on elliptically fibered Calabi-Yau manifolds with a rank two Mordell-Weil group. We find that the natural presentation of an elliptic curve E with two rational points and a zero point is the generic Calabi-Yau onefold in dP_2. We determine the birational map to its Tate and Weierstrass form and the coordinates of the two rational points in Weierstrass form. We discuss its resolved elliptic fibrations over a general base B and classify them in the case of B=P^2. A thorough analysis of the generic codimension two singularities of these elliptic Calabi-Yau manifolds is presented. This determines the general U(1)xU(1)-charges of matter in corresponding F-theory compactifications. The matter multiplicities for the fibration over P^2 are determined explicitly and shown to be consistent with anomaly cancellation. Explicit toric examples are constructed, both with U(1)xU(1) and SU(5)xU(1)xU(1) gauge symmetry. As a by-product, we prove the birational eq...
The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle
Grimm, Thomas W; Klevers, Denis
2016-01-01
The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional ...
Denoising of magnetotelluric signals by polarization analysis in the discrete wavelet domain
Carbonari, R.; D'Auria, L.; Di Maio, R.; Petrillo, Z.
2017-03-01
Magnetotellurics (MT) is one of the prominent geophysical methods for underground deep exploration and, thus, appropriate for applications to petroleum and geothermal research. However, it is not completely reliable when applied in areas characterized by intense urbanization, as the presence of cultural noise may significantly affect the MT impedance tensor estimates and, consequently, the apparent resistivity values that describe the electrical behaviour of the investigated buried structures. The development of denoising techniques of MT data is thus one of the main objectives to make magnetotellurics reliably even in urban or industrialized environments. In this work we propose an algorithm for filtering of MT data affected by temporally localized noise. It exploits the discrete wavelet transform (DWT) that, thanks to the possibility to operates in both time and frequency domain, allows to detect transient components of the MT signal, likely due to disturbances of anthropic nature. The implemented filter relies on the estimate of the ellipticity of the polarized MT wave. The application of the filter to synthetic and field MT data has proven its ability in detecting and removing cultural noise, thus providing apparent resistivity curves more smoothed than those obtained by using raw signals.
Global analysis of a buck regulator. [for voltage using discrete control law
Edwards, D. B.; Caughey, T. K.
1978-01-01
Sufficient conditions for global stability of a buck regulator using a discrete control law are found. The method of paired systems and Liapunov functions are used to establish global stability and to study the convergence of the regulator. A heuristic argument is given that the optimal switching curves associated with the paired continuous systems approximate the optimal switching curves of the discrete systems.
Elliptical instability in hot Jupiter systems
Cébron, David; Gal, Patrice Le; Moutou, Claire; Leconte, J; Sauret, Alban
2013-01-01
Several studies have already considered the influence of tides on the evolution of systems composed of a star and a close-in companion to tentatively explain different observations such as the spin-up of some stars with hot Jupiters, the radius anomaly of short orbital period planets and the synchronization or quasi-synchronization of the stellar spin in some extreme cases. However, the nature of the mechanism responsible for the tidal dissipation in such systems remains uncertain. In this paper, we claim that the so-called elliptical instability may play a major role in these systems, explaining some systematic features present in the observations. This hydrodynamic instability, arising in rotating flows with elliptical streamlines, is suspected to be present in both planet and star of such systems, which are elliptically deformed by tides. The presence and the influence of the elliptical instability in gaseous bodies, such as stars or hot Jupiters, are most of the time neglected. In this paper, using numeri...
The sunrise integral and elliptic polylogarithms
Adams, Luise; Weinzierl, Stefan
2016-01-01
We summarize recent computations with a class of elliptic generalizations of polylogarithms, arising from the massive sunrise integral. For the case of arbitrary masses we obtain results in two and four space-time dimensions. The iterated integral structure of our functions allows us to furthermore compute the equal mass case to arbitrary order.
Nonlinear quasimodes near elliptic periodic geodesics
Albin, Pierre; Marzuola, Jeremy L; Thomann, Laurent
2011-01-01
We consider the nonlinear Schr\\"odinger equation on a compact manifold near an elliptic periodic geodesic. Using a geometric optics construction, we construct quasimodes to a nonlinear stationary problem which are highly localized near the periodic geodesic. We show the nonlinear Schr\\"odinger evolution of such a quasimode remains localized near the geodesic, at least for short times.
Nonlinear second order elliptic equations involving measures
Marcus, Moshe
2013-01-01
This book presents a comprehensive study of boundary value problems for linear and semilinear second order elliptic equations with measure data,especially semilinear equations with absorption. The interactions between the diffusion operator and the absorption term give rise to a large class of nonlinear phenomena in the study of which singularities and boundary trace play a central role.
Nomenclature of polarized light - Elliptical polarization
Clarke, D.
1974-01-01
Alternative handedness and sign conventions for relating the orientation of elliptical polarization are discussed. The discussion proceeds under two headings: (1) snapshot picture, where the emphasis for the convention is contained in the concept of handedness; and (2) angular momentum consideration, where the emphasis for the convention is strongly associated with mathematical convention and the sign of the fourth Stokes parameter.
Regression Model With Elliptically Contoured Errors
Arashi, M; Tabatabaey, S M M
2012-01-01
For the regression model where the errors follow the elliptically contoured distribution (ECD), we consider the least squares (LS), restricted LS (RLS), preliminary test (PT), Stein-type shrinkage (S) and positive-rule shrinkage (PRS) estimators for the regression parameters. We compare the quadratic risks of the estimators to determine the relative dominance properties of the five estimators.
Circular and Elliptic Submerged Impinging Water Jets
Claudey, Eric; Benedicto, Olivier; Ravier, Emmanuel; Gutmark, Ephraim
1999-11-01
Experiments and CFD have been performed to study circular and elliptic jets in a submerged water jet facility. The tests included discharge coefficient measurement to evaluate pressure losses encountered in noncircular nozzles compared to circular ones. Three-dimensional pressure mappings on the impingement surface and PIV measurement of the jet mean and turbulent velocity have been performed at different compound impingement angles relative to the impingement surface and at different stand-off distances. The objective was to investigate the effect of the non-circular geometry on the flow field and on the impact region. The tests were performed in a close loop system in which the water was pumped through the nozzles into a clear Plexiglas tank. The Reynolds numbers were typically in the range of 250000. Discharge coefficients of the elliptic nozzle was somewhat lower than that of the circular jet but spreading rate and turbulence level were higher. Pressure mapping showed that the nozzle exit geometry had an effect on the pressure distribution in the impact region and that high-pressure zones were generated at specific impact points. PIV measurements showed that for a same total exit area, the elliptic jets affected a surface area that is 8the equivalent circular. The turbulence level in the elliptic jet tripled due to the nozzle design. Results of the CFD model were in good agreement with the experimental data.
Spatial scan statistics using elliptic windows
Christiansen, Lasse Engbo; Andersen, Jens Strodl; Wegener, Henrik Caspar
2006-01-01
The spatial scan statistic is widely used to search for clusters. This article shows that the usually applied elimination of secondary clusters as implemented in SatScan is sensitive to smooth changes in the shape of the clusters. We present an algorithm for generation of a set of confocal elliptic...
Fluxon Dynamics in Elliptic Annular Josephson Junctions
Monaco, Roberto; Mygind, Jesper
2016-01-01
We analyze the dynamics of a magnetic flux quantum (current vortex) trapped in a current-biased long planar elliptic annular Josephson tunnel junction. The system is modeled by a perturbed sine-Gordon equation that determines the spatial and temporal behavior of the phase difference across the tu...
Solving Nonlinear Wave Equations by Elliptic Equation
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
Spatial scan statistics using elliptic windows
Christiansen, Lasse Engbo; Andersen, Jens Strodl; Wegener, Henrik Caspar
2006-01-01
windows and propose a new way to present the information when a spatial point process is considered. This method gives smooth changes for smooth expansions of the set of clusters. A simulation study is used to show how the elliptic windows outperforms the usual circular windows. The proposed method...
On an asymptotically linear elliptic Dirichlet problem
Zhitao Zhang
2002-01-01
Full Text Available Under very simple conditions, we prove the existence of one positive and one negative solution of an asymptotically linear elliptic boundary value problem. Even for the resonant case at infinity, we do not need to assume any more conditions to ensure the boundness of the (PS sequence of the corresponding functional. Moreover, the proof is very simple.
Decay of eigenfunctions of elliptic PDE's
Herbst, Ira; Skibsted, Erik
We study exponential decay of eigenfunctions of self-adjoint higher order elliptic operators on Rd. We show that the possible critical decay rates are determined algebraically. In addition we show absence of super-exponentially decaying eigenfunctions and a refined exponential upper bound....
无
2007-01-01
The hatches for inspecting are usually designed with elliptical holes in airplane structures, so computation of the stress intensity factor of three dimensional crack at elliptical holes is pivotal for damage tolerance analysis of these structures. In this paper, weight function is derived for a two dimensional through cracks at elliptical holes by applying a compounding method. Stress intensity factor formulas for an internal surface semi-elliptical crack in elliptical holes are obtained using the three dimensional weight function method. Stress intensity factors for an internal surface semi-elliptical crack in elliptical holes under remote tension are computed. At the same time, research on how radius of curvature for elliptical holes affect stress intensity factors was conducted. Stress intensity factors decrease when radius of curvature increases. Some results and conclusions which are of practical value are given.
Djidel, S.; Bouamar, M.; Khedrouche, D.
2016-04-01
This paper presents a performances study of UWB monopole antenna using half-elliptic radiator conformed on elliptical surface. The proposed antenna, simulated using microwave studio computer CST and High frequency simulator structure HFSS, is designed to operate in frequency interval over 3.1 to 40 GHz. Good return loss and radiation pattern characteristics are obtained in the frequency band of interest. The proposed antenna structure is suitable for ultra-wideband applications, which is, required for many wearable electronics applications.
Preconditioning cubic spline collocation method by FEM and FDM for elliptic equations
Kim, Sang Dong [KyungPook National Univ., Taegu (Korea, Republic of)
1996-12-31
In this talk we discuss the finite element and finite difference technique for the cubic spline collocation method. For this purpose, we consider the uniformly elliptic operator A defined by Au := -{Delta}u + a{sub 1}u{sub x} + a{sub 2}u{sub y} + a{sub 0}u in {Omega} (the unit square) with Dirichlet or Neumann boundary conditions and its discretization based on Hermite cubic spline spaces and collocation at the Gauss points. Using an interpolatory basis with support on the Gauss points one obtains the matrix A{sub N} (h = 1/N).
Finite Discrete Gabor Analysis
Søndergaard, Peter Lempel
2007-01-01
on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...
Discrete Mathematics Re "Tooled."
Grassl, Richard M.; Mingus, Tabitha T. Y.
1999-01-01
Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)
Chang, Lay Nam; Minic, Djordje; Takeuchi, Tatsu
2012-01-01
We construct a discrete quantum mechanics using a vector space over the Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discrete quantum mechanics cannot be reproduced with any hidden variable theory.
Lee, Taeyoung; McClamroch, N Harris
2007-01-01
Discrete control systems, as considered here, refer to the control theory of discrete-time Lagrangian or Hamiltonian systems. These discrete-time models are based on a discrete variational principle, and are part of the broader field of geometric integration. Geometric integrators are numerical integration methods that preserve geometric properties of continuous systems, such as conservation of the symplectic form, momentum, and energy. They also guarantee that the discrete flow remains on the manifold on which the continuous system evolves, an important property in the case of rigid-body dynamics. In nonlinear control, one typically relies on differential geometric and dynamical systems techniques to prove properties such as stability, controllability, and optimality. More generally, the geometric structure of such systems plays a critical role in the nonlinear analysis of the corresponding control problems. Despite the critical role of geometry and mechanics in the analysis of nonlinear control systems, non...
Morris, J; Johnson, S
2007-12-03
The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.
Okuyama, Yoshifumi
2014-01-01
Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...
Burgin, Mark
2010-01-01
Continuous models used in physics and other areas of mathematics applications become discrete when they are computerized, e.g., utilized for computations. Besides, computers are controlling processes in discrete spaces, such as films and television programs. At the same time, continuous models that are in the background of discrete representations use mathematical technology developed for continuous media. The most important example of such a technology is calculus, which is so useful in physics and other sciences. The main goal of this paper is to synthesize continuous features and powerful technology of the classical calculus with the discrete approach of numerical mathematics and computational physics. To do this, we further develop the theory of fuzzy continuous functions and apply this theory to functions defined on discrete sets. The main interest is the classical Intermediate Value theorem. Although the result of this theorem is completely based on continuity, utilization of a relaxed version of contin...
Le Botlan D.
2006-12-01
Full Text Available Dans un champ magnétique hétérogène, le signal RMN de précession libre (FID suit une évolution gaussienne. Le traitement du signal par une méthode discrète peut donner des composantes qui ne correspondent pas à un état physique réel. Par contre l'utilisation d'une méthode de déconvolution continue nous a donné des résultats quantitatifs tout à fait satisfaisants permettant de déterminer les distributions de temps de relaxation correspondant à des états intermédiaires entre les phases solides et liquides. La RMN du domaine du temps peut ainsi être considérée comme une méthode analytique complémentaire des techniques habituellement utilisées pour l'étude de composés complexes hétérogènes ATD, ACD, isothermes de sorption, etc. In a heterogeneous magnetic field, the freely precessing NMR signal (FID describes a Gaussian curve. Processing the signal using a discrete method can give rise to components that do not correspond to a real physical state. However, with a continuous deconvolution method, which gives quite satisfactory quantitative results, it is possible to determine the distributions of relaxation times that correspond to intermediate states between solid and liquid phases. Time-dependent NMR can thus be used to supplement the usual analytical methods, such as DTA, DCA and sorption isotherms, for studying complex heterogeneous compounds.
Jacobi-Bessel Analysis Of Antennas With Elliptical Apertures.
Rahmat-Samii, Y.
1989-01-01
Coordinate transformation improves convergence pattern analysis of elliptical-aperture antennas. Modified version of Jacobi-Bessel expansion for vector diffraction analysis of reflector antennas uses coordinate transformation to improve convergence with elliptical apertures. Expansion converges rapidly for antennas with circular apertures, but less rapidly for elliptical apertures. Difference in convergence behavior between circular and elliptical Jacobi-Bessel algorithms indicated by highest values of indices m, n, and p required to achieve same accuracy in computed radiation pattern of offset paraboloidal antenna with elliptical aperture.
Analysis of the Dynamic Characteristics of Elliptical Gears
Liu, Xing; Nagamura, Kazuteru; Ikejo, Kiyotaka
To date, elliptical gear has been commonly used in automobile, automatic machinery, pumps, flow meters and printing presses for its particular non-uniform rotation. However, the dynamic characteristics of elliptical gears have not been clarified yet. In this study, The calculation as well as the experiment of two elliptical gears, which are a single elliptical gear and a double elliptical gear, is carried out to analyze the dynamic characteristics of elliptical gears. General factors including the torque, the rotation speed and the tooth root stress of the test gears are investigated. According to the analysis conducted in this study, the dynamic input torque variation of elliptical gear becomes larger along with the increase of operating gear rotation speed and the experimental one increases much faster than the calculated one over the Critical Rotation Speed of Tooth Separation (CRSTS) of elliptical gear. The experimental input rotation speed varies according to the variation of input torque, leading to the difference between the experimental output rotation speed and the desired one. The calculation results of the CRSTS of elliptical gears are almost equal to the experimental ones. The dynamic load variation ratios of elliptical gear at different angular position as well as their changing trends with operating gear rotation speed are quite different from each other. And the experimental dynamic load variation ratios of elliptical gear show difference from the calculated ones because of tooth separation and tooth impact. The agreement of the calculation and experimental results proves the validity of this study.
Mining the Suzaku Archive for Elliptical Galaxies
Loewenstein, Michael
Despite significant progress, our understanding of the formation and evolution of giant elliptical galaxies is incomplete. Many unresolved details about the star formation and assembly history, dissipation and feedback processes, and how these are connected in space and time relate to complex gasdynamical processes that are not directly observable, but that leave clues in the form of the level and pattern of heavy element enrichment in the hot ISM. The low background and relatively sharp spectral resolution of the Suzaku X-ray Observatory XIS CCD detectors enable one to derive a particularly extensive abundance pattern in the hot ISM out to large galactic radii for bright elliptical galaxies. These encode important clues to the chemical and dynamical history of elliptical galaxies. The Suzaku archive now includes data on many of the most suitable galaxies for these purposes. To date, these have been analyzed in a very heterogeneous manner -- some at an early stage in the mission using instrument calibration and analysis tools that have greatly evolved in the interim. Given the level of maturity of the data archive, analysis software, and calibration, the time is right to undertake a uniform analysis of this sample and interpret the results in the context of a coherent theoretical framework for the first time. We propose to (1) carefully and thoroughly analyze the available X-ray luminous elliptical galaxies in the Suzaku database, employing the techniques we have established in our previous work to measure hot ISM abundance patterns. Their interpretation requires careful deconstruction within the context of physical gasdynamical and chemical evolutionary models. Since we have developed models for elliptical galaxy chemical evolution specifically constructed to place constraints on the history and development of these systems based on hot ISM abundances, we are uniquely positioned to interpret -- as well as to analyze -- X-ray spectra of these objects. (2) We will
Online Learning in Discrete Hidden Markov Models
Alamino, Roberto C.; Caticha, Nestor
2007-01-01
We present and analyse three online algorithms for learning in discrete Hidden Markov Models (HMMs) and compare them with the Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalisation error we draw learning curves in simplified situations. The performance for learning drifting concepts of one of the presented algorithms is analysed and compared with the Baldi-Chauvin algorithm in the same situations. A brief discussion about learning and symmetry breaking b...
A technique for measuring the quality of an elliptically bent pentaerythritol [PET(002)] crystal.
Haugh, M J; Jacoby, K D; Barrios, M A; Thorn, D; Emig, J A; Schneider, M B
2016-11-01
We present a technique for determining the X-ray spectral quality from each region of an elliptically curved PET(002) crystal. The investigative technique utilizes the shape of the crystal rocking curve which changes significantly as the radius of curvature changes. This unique quality information enables the spectroscopist to verify where in the spectral range that the spectrometer performance is satisfactory and where there are regions that would show spectral distortion. A collection of rocking curve measurements for elliptically curved PET(002) has been built up in our X-ray laboratory. The multi-lamellar model from the XOP software has been used as a guide and corrections were applied to the model based upon measurements. But, the measurement of RI at small radius of curvature shows an anomalous behavior; the multi-lamellar model fails to show this behavior. The effect of this anomalous RI behavior on an X-ray spectrometer calibration is calculated. It is compared to the multi-lamellar model calculation which is completely inadequate for predicting RI for this range of curvature and spectral energies.
A technique for measuring the quality of an elliptically bent pentaerythritol [PET(002)] crystal
Haugh, M. J.; Jacoby, K. D.; Barrios, M. A.; Thorn, D.; Emig, J. A.; Schneider, M. B.
2016-11-01
We present a technique for determining the X-ray spectral quality from each region of an elliptically curved PET(002) crystal. The investigative technique utilizes the shape of the crystal rocking curve which changes significantly as the radius of curvature changes. This unique quality information enables the spectroscopist to verify where in the spectral range that the spectrometer performance is satisfactory and where there are regions that would show spectral distortion. A collection of rocking curve measurements for elliptically curved PET(002) has been built up in our X-ray laboratory. The multi-lamellar model from the XOP software has been used as a guide and corrections were applied to the model based upon measurements. But, the measurement of RI at small radius of curvature shows an anomalous behavior; the multi-lamellar model fails to show this behavior. The effect of this anomalous RI behavior on an X-ray spectrometer calibration is calculated. It is compared to the multi-lamellar model calculation which is completely inadequate for predicting RI for this range of curvature and spectral energies.
Fast finite difference solvers for singular solutions of the elliptic Monge-Amp\\'ere equation
Froese, Brittany D
2010-01-01
The elliptic Monge-Amp\\`ere equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in dynamic meteorology, elasticity, geometric optics, image processing and image registration. Solutions can be singular, in which case standard numerical approaches fail. In this article we build a finite difference solver for the Monge-Amp\\'ere equation, which converges even for singular solutions. Regularity results are used to select a priori between a stable, provably convergent monotone discretization and an accurate finite difference discretization in different regions of the computational domain. This allows singular solutions to be computed using a stable method, and regular solutions to be computed more accurately. The resulting nonlinear equations are then solved by Newton's method. Computational results in two and three dimensions validate the claims of accuracy and solution speed. A computational example is presented which demonstrates the nece...
Collier, Nathaniel Oren
2014-09-17
SUMMARY: We compare the computational efficiency of isogeometric Galerkin and collocation methods for partial differential equations in the asymptotic regime. We define a metric to identify when numerical experiments have reached this regime. We then apply these ideas to analyze the performance of different isogeometric discretizations, which encompass C0 finite element spaces and higher-continuous spaces. We derive convergence and cost estimates in terms of the total number of degrees of freedom and then perform an asymptotic numerical comparison of the efficiency of these methods applied to an elliptic problem. These estimates are derived assuming that the underlying solution is smooth, the full Gauss quadrature is used in each non-zero knot span and the numerical solution of the discrete system is found using a direct multi-frontal solver. We conclude that under the assumptions detailed in this paper, higher-continuous basis functions provide marginal benefits.
ESTIMATING TORSION OF DIGITAL CURVES USING 3D IMAGE ANALYSIS
Christoph Blankenburg
2016-04-01
Full Text Available Curvature and torsion of three-dimensional curves are important quantities in fields like material science or biomedical engineering. Torsion has an exact definition in the continuous domain. However, in the discrete case most of the existing torsion evaluation methods lead to inaccurate values, especially for low resolution data. In this contribution we use the discrete points of space curves to determine the Fourier series coefficients which allow for representing the underlying continuous curve with Cesàro’s mean. This representation of the curve suits for the estimation of curvature and torsion values with their classical continuous definition. In comparison with the literature, one major advantage of this approach is that no a priori knowledge about the shape of the cyclic curve parts approximating the discrete curves is required. Synthetic data, i.e. curves with known curvature and torsion, are used to quantify the inherent algorithm accuracy for torsion and curvature estimation. The algorithm is also tested on tomographic data of fiber structures and open foams, where discrete curves are extracted from the pore spaces.
Distance of Sample Measurement Points to Prototype Catalog Curve
Hjorth, Poul G.; Karamehmedovic, Mirza; Perram, John;
2006-01-01
We discuss strategies for comparing discrete data points to a catalog (reference) curve by means of the Euclidean distance from each point to the curve in a pump's head H vs. flow Qdiagram. In particular we find that a method currently in use is inaccurate. We propose several alternatives...
Formulae for Arithmetic on Genus 2 Hyperelliptic Curves
Lange, Tanja
2005-01-01
The ideal class group of hyperelliptic curves can be used in cryptosystems based on the discrete logarithm problem. In this article we present explicit formulae to perform the group operations for genus 2 curves. The formulae are completely general but to achieve the lowest number of operations w...
Torus Bifurcation Under Discretization
邹永魁; 黄明游
2002-01-01
Parameterized dynamical systems with a simple zero eigenvalue and a couple of purely imaginary eigenvalues are considered. It is proved that this type of eigen-structure leads to torns bifurcation under certain nondegenerate conditions. We show that the discrete systems, obtained by discretizing the ODEs using symmetric, eigen-structure preserving schemes, inherit the similar torus bifurcation properties. Fredholm theory in Banach spaces is applied to obtain the global torns bifurcation. Our results complement those on the study of discretization effects of global bifurcation.
Aydin, Alhun; Sisman, Altug
2016-03-01
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic.
The Hodge-elliptic genus, spinning BPS states, and black holes
Kachru, Shamit
2016-01-01
We perform a refined count of BPS states in the compactification of M-theory on $K3 \\times T^2$, keeping track of the information provided by both the $SU(2)_L$ and $SU(2)_R$ angular momenta in the $SO(4)$ little group. Mathematically, this four variable counting function may be expressed via the motivic Donaldson-Thomas counts of $K3 \\times T^2$, simultaneously refining Katz, Klemm, and Pandharipande's motivic Donaldson-Thomas counts on $K3$ and Oberdieck-Pandharipande's Gromov-Witten counts on $K3 \\times T^2$. This provides the first full answer for motivic curve counts of a compact Calabi-Yau threefold. Along the way, we develop a Hodge-elliptic genus for Calabi-Yau manifolds -- a new counting function for BPS states that interpolates between the Hodge polynomial and the elliptic genus of a Calabi-Yau.
The generalized Euler-Poinsot rigid body equations: explicit elliptic solutions
Fedorov, Yuri N.; Maciejewski, Andrzej J.; Przybylska, Maria
2013-10-01
The classical Euler-Poinsot case of the rigid body dynamics admits a class of simple but non-trivial integrable generalizations, which modify the Poisson equations describing the motion of the body in space. These generalizations possess first integrals which are polynomial in the angular momenta. We consider the modified Poisson equations as a system of linear equations with elliptic coefficients and show that all the solutions of it are single-valued. By using the vector generalization of the Picard theorem, we derive the solutions explicitly in terms of sigma-functions of the corresponding elliptic curve. The solutions are accompanied by a numerical example. We also compare the generalized Poisson equations with the classical third order Halphen equation.
Collisionless evaporation from cluster elliptical galaxies
Muccione, V
2003-01-01
We describe a particular aspect of the effects of the parent cluster tidal field (CTF) on stellar orbits inside cluster Elliptical galaxies. In particular we discuss, with the aid of a simple numerical model, the possibility that collisionless stellar evaporation from elliptical galaxies is an effective mechanism for the production of the recently discovered intracluster stellar populations. A preliminary investigation, based on very idealized galaxy density profiles (Ferrers density distributions), showed that over an Hubble time, the amount of stars lost by a representative galaxy may sum up to the 10% of the initial galaxy mass, a fraction in interesting agreement with observational data. The effectiveness of this mechanism is due to the fact that the galaxy oscillation periods near equilibrium configurations in the CTF are comparable to stellar orbital times in the external galaxy regions. Here we extend our previous study to more realistic galaxy density profiles, in particular by adopting a triaxial Her...
Elliptic differential equations theory and numerical treatment
Hackbusch, Wolfgang
2017-01-01
This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.
Performance of an elliptically tapered neutron guide
Mühlbauer, Sebastian; Stadlbauer, Martin; Böni, Peter; Schanzer, Christan; Stahn, Jochen; Filges, Uwe
2006-11-01
Supermirror coated neutron guides are used at all modern neutron sources for transporting neutrons over large distances. In order to reduce the transmission losses due to multiple internal reflection of neutrons, ballistic neutron guides with linear tapering have been proposed and realized. However, these systems suffer from an inhomogeneous illumination of the sample. Moreover, the flux decreases significantly with increasing distance from the exit of the neutron guide. We propose using elliptically tapered guides that provide a more homogeneous phase space at the sample position as well as a focusing at the sample. Moreover, the design of the guide system is simplified because ellipses are simply defined by their long and short axes. In order to prove the concept we have manufactured a doubly focusing guide and investigated its properties with neutrons. The experiments show that the predicted gains using the program package McStas are realized. We discuss several applications of elliptic guides in various fields of neutron physics.
Performance of an elliptically tapered neutron guide
Muehlbauer, Sebastian [Physik-Department E21, Technische Universitaet Muenchen, D-85747 Garching (Germany)]. E-mail: sebastian.muehlbauer@frm2.tum.de; Stadlbauer, Martin [Physik-Department E21, Technische Universitaet Muenchen, D-85747 Garching (Germany); Boeni, Peter [Physik-Department E21, Technische Universitaet Muenchen, D-85747 Garching (Germany); Schanzer, Christan [Labor fuer Neutronenstreuung, Paul Scherrer Institut, CH-5232 Villingen PSI (Switzerland); Stahn, Jochen [Labor fuer Neutronenstreuung, Paul Scherrer Institut, CH-5232 Villingen PSI (Switzerland); Filges, Uwe [Labor fuer Neutronenstreuung, Paul Scherrer Institut, CH-5232 Villingen PSI (Switzerland)
2006-11-15
Supermirror coated neutron guides are used at all modern neutron sources for transporting neutrons over large distances. In order to reduce the transmission losses due to multiple internal reflection of neutrons, ballistic neutron guides with linear tapering have been proposed and realized. However, these systems suffer from an inhomogeneous illumination of the sample. Moreover, the flux decreases significantly with increasing distance from the exit of the neutron guide. We propose using elliptically tapered guides that provide a more homogeneous phase space at the sample position as well as a focusing at the sample. Moreover, the design of the guide system is simplified because ellipses are simply defined by their long and short axes. In order to prove the concept we have manufactured a doubly focusing guide and investigated its properties with neutrons. The experiments show that the predicted gains using the program package McStas are realized. We discuss several applications of elliptic guides in various fields of neutron physics.
Modelling elliptically polarised Free Electron Lasers
Henderson, J R; Freund, H P; McNeil, B W J
2016-01-01
A model of a Free Electron Laser operating with an elliptically polarised undulator is presented. The equations describing the FEL interaction, including resonant harmonic radiation fields, are averaged over an undulator period and generate a generalised Bessel function scaling factor, similar to that of planar undulator FEL theory. Comparison between simulations of the averaged model with those of an unaveraged model show very good agreement in the linear regime. Two unexpected results were found. Firstly, an increased coupling to harmonics for elliptical rather than planar polarisarised undulators. Secondly, and thought to be unrelated to the undulator polarisation, a signficantly different evolution between the averaged and unaveraged simulations of the harmonic radiation evolution approaching FEL saturation.
The invertible double of elliptic operators
Booss-Bavnbek, Bernhelm; Lesch, Matthias; Zhu, Chaofeng
We construct a canonical invertible double for general first order elliptic differential operators over smooth compact manifolds with boundary and derive a natural formula for the Calderon projector which yields a generalization of the famous Cobordism Theorem. Assuming symmetric principal symbol...... of the tangential operator and unique continuation property (UCP) from the boundary, we obtain the continuous dependence of the Calderon projection on the data. The details of our results are available on arxiv arXiv:0803.4160 .......We construct a canonical invertible double for general first order elliptic differential operators over smooth compact manifolds with boundary and derive a natural formula for the Calderon projector which yields a generalization of the famous Cobordism Theorem. Assuming symmetric principal symbol...
Electron capture from coherent elliptic Rydberg states
Day, J.C.; DePaola, B.D.; Ehrenreich, T.; Hansen, S.B.; Horsdal-Pedersen, E.; Leontiev, Y.; Mogensen, K.S. [Institute of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C (Denmark)
1997-12-01
Experimental relative cross sections for electron capture by singly charged ions (Na{sup +}) from coherent elliptic states of principal quantum number n=25 are presented. An interval of reduced impact velocities from about 1{endash}2 is covered. Absolute reaction cross sections could not be determined precisely, but the eccentricity of the coherent elliptic states and their orientation relative to the ion-impact velocity were varied to expose the dependence of the electron-capture process on the initial motion of the electron. The dependencies on eccentricity and orientation are generally strong and they vary sharply with impact velocity. Qualitatively, the observations agree fairly well with classical trajectory Monte Carlo (CTMC) calculations, as expected for the large quantum numbers involved, but significant deviations of a systematic nature do remain, showing that some aspects of the capture reactions studied are described poorly by classical physics as represented by the CTMC model. {copyright} {ital 1997} {ital The American Physical Society}
The Shapes and Ages of Elliptical Galaxies
De Jong, R S; Jong, Roelof S. de; Davies, Roger L.
1996-01-01
In this paper we investigate the relation between the detailed isophotal shape of elliptical galaxies and the strength of the H beta absorption in their spectra. We find that disky galaxies have higher H beta indices. Stellar population synthesis models show that the H beta line is a good age indicator, hence disky galaxies tend to have younger mean ages than boxy galaxies. We show that the observed trend can be brought about by a contaminating young population, which we associate with the disky component. This population need only account for a small fraction of the total mass, for example if a contaminating population of age of 2 Gyrs is superimposed on an old (12 Gyr) elliptical galaxy, then the observed trend can be explained if it contributes only 10% to the total mass. The size of this effect is consistent with the estimates of disk-to-total light ratios from surface photometry.
Fast adaptive elliptical filtering using box splines
Chaudhury, Kunal Narayan; Unser, Michael
2009-01-01
We demonstrate that it is possible to filter an image with an elliptic window of varying size, elongation and orientation with a fixed computational cost per pixel. Our method involves the application of a suitable global pre-integrator followed by a pointwise-adaptive localization mesh. We present the basic theory for the 1D case using a B-spline formalism and then appropriately extend it to 2D using radially-uniform box splines. The size and ellipticity of these radially-uniform box splines is adaptively controlled. Moreover, they converge to Gaussians as the order increases. Finally, we present a fast and practical directional filtering algorithm that has the capability of adapting to the local image features.
MIB Galerkin method for elliptic interface problems
Xia, Kelin; Zhan, Meng; Wei, Guo-Wei
2014-01-01
Summary Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex interfaces, geometric singularities and low solution regularities. The Cartesian grid based triangular elements are employed to avoid the time consuming mesh generation procedure. Consequently, the interface cuts through elements. To ensure the continuity of classic basis functions across the interface, two sets of overlapping elements, called MIB elements, are defined near the interface. As a result, differentiation can be computed near the interface as if there is no interface. Interpolation functions are constructed on MIB element spaces to smoothly extend function values across the interface. A set of lowest order interface jump conditions is enforced on the interface, which in turn, determines the interpolation functions. The performance of the proposed MIB Galerkin finite element method is validated by numerical experiments with a wide range of interface geometries, geometric singularities, low regularity solutions and grid resolutions. Extensive numerical studies confirm
Elliptic stars in a chaotic night
Jaeger, T
2010-01-01
We study homeomorphisms of the two-torus, homotopic to the identity, whose rotation set has non-empty interior. For such maps, we give a purely topological characterisation of elliptic islands in a chaotic sea in terms of local rotation subsets. We further show that the chaotic regime defined in this way cannot contain any Lyapunov stable points. In order to demonstrate our results, we introduce a parameter family inspired by an example of Misiurewicz and Ziemian.
On a fourth order superlinear elliptic problem
M. Ramos
2001-01-01
Full Text Available We prove the existence of a nonzero solution for the fourth order elliptic equation $$Delta^2u= mu u +a(xg(u$$ with boundary conditions $u=Delta u=0$. Here, $mu$ is a real parameter, $g$ is superlinear both at zero and infinity and $a(x$ changes sign in $Omega$. The proof uses a variational argument based on the argument by Bahri-Lions cite{BL}.
Photoacoustic cell using elliptical acoustic focusing
Heritier, J.-M.; Fouquet, J. E.; Siegman, A. E.
1982-01-01
A photoacoustic cell has been developed in the form of an elliptical cylinder in which essentially all the acoustic energy generated by a laser beam passing down one axis is focused onto a cylindrical acoustic tranducer located along the other axis. Preliminary measurements on a liquid-filled cell of this design show high sensitivity and a notably clean impulse response. A similar design may be useful for photoacoustic measurements in vapors as well.
Evaluation of Fifth Degree Elliptic Singular Moduli
Bagis, Nikos
2012-01-01
Our main result in this article is a formula for the extraction of the solution of the fifth degree modular polynomial equation i.e. the value of $k_{25^nr_0}$, when we know only two consecutive values $k_{r_0}$ and $k_{r_0/25}$. By this way we reduce the problem of solving the depressed equation if we known two consecutive values of the Elliptic singular moduli $k_r$.
Deformed Virasoro Algebras from Elliptic Quantum Algebras
Avan, J.; Frappat, L.; Ragoucy, E.
2017-09-01
We revisit the construction of deformed Virasoro algebras from elliptic quantum algebras of vertex type, generalizing the bilinear trace procedure proposed in the 1990s. It allows us to make contact with the vertex operator techniques that were introduced separately at the same period. As a by-product, the method pinpoints two critical values of the central charge for which the center of the algebra is extended, as well as (in the gl(2) case) a Liouville formula.
MIB Galerkin method for elliptic interface problems.
Xia, Kelin; Zhan, Meng; Wei, Guo-Wei
2014-12-15
Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex interfaces, geometric singularities and low solution regularities. The Cartesian grid based triangular elements are employed to avoid the time consuming mesh generation procedure. Consequently, the interface cuts through elements. To ensure the continuity of classic basis functions across the interface, two sets of overlapping elements, called MIB elements, are defined near the interface. As a result, differentiation can be computed near the interface as if there is no interface. Interpolation functions are constructed on MIB element spaces to smoothly extend function values across the interface. A set of lowest order interface jump conditions is enforced on the interface, which in turn, determines the interpolation functions. The performance of the proposed MIB Galerkin finite element method is validated by numerical experiments with a wide range of interface geometries, geometric singularities, low regularity solutions and grid resolutions. Extensive numerical studies confirm the
A Jacobian elliptic single-field inflation
Villanueva, J.R. [Universidad de Valparaiso, Instituto de Fisica y Astronomia, Valparaiso (Chile); Centro de Astrofisica de Valparaiso, Valparaiso (Chile); Gallo, Emanuel [FaMAF, Universidad Nacional de Cordoba, Cordoba (Argentina); Instituto de Fisica Enrique Gaviola (IFEG), CONICET, Cordoba (Argentina)
2015-06-15
In the scenario of single-field inflation, this field is described in terms of Jacobian elliptic functions. This approach provides, when constrained to particular cases, analytic solutions already known in the past, generalizing them to a bigger family of analytical solutions. The emergent cosmology is analyzed using the Hamilton-Jacobi approach and then the main results are contrasted with the recent measurements obtained from the Planck 2015 data. (orig.)
A Jacobian elliptic single-field inflation
Villanueva, J R
2015-01-01
In the scenario of single-field inflation, this field is done in terms of Jacobian elliptic functions. This approach provides, when constrained to particular cases, analytic solutions already known in the past, generalizing them to a bigger family of analytical solutions. The emergent cosmology is analysed using the Hamilton-Jacobi approach and then, the main results are contrasted with the recent measurements obtained from the Planck 2015 data.
Radio Mode Outbursts in Giant Elliptical Galaxies
Nulsen, Paul; Forman, William; Churazov, Eugene; McNamara, Brian; David, Laurence; Murray, Stephen
2009-01-01
Outbursts from active galactic nuclei (AGN) affect the hot atmospheres of isolated giant elliptical galaxies (gE's), as well as those in groups and clusters of galaxies. Chandra observations of a sample of nearby gE's show that the average power of AGN outbursts is sufficient to stop their hot atmospheres from cooling and forming stars, consistent with radio mode feedback models. The outbursts are intermittent, with duty cycles that increases with size.
Limits of Functions and Elliptic Operators
Siddhartha Gadgil
2004-05-01
We show that a subspace of the space of real analytical functions on a manifold that satisfies certain regularity properties is contained in the set of solutions of a linear elliptic differential equation. The regularity properties are that is closed in $L^2(M)$ and that if a sequence of functions $f_n$ in converges in $L^2(M)$, then so do the partial derivatives of the functions $f_n$.
Pearls of Discrete Mathematics
Erickson, Martin
2009-01-01
Presents methods for solving counting problems and other types of problems that involve discrete structures. This work illustrates the relationship of these structures to algebra, geometry, number theory and combinatorics. It addresses topics such as information and game theories
Goodrich, Christopher
2015-01-01
This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...
LAMINAR FLUID FLOW IN HELICAL ELLIPTICAL PIPE
无
2000-01-01
In this paper, using an orthogonal curvilinear coordinate system and solving the complete N-S equations, we analyzed the flow in a helical elliptical duct by the perturbation method. The first-order solutions of the stream function Ψ, axial velocity w and the velocity of secondary flow (u, v) were obtained. The effects of torsion, curvature and the axial pressure gradient on the secondary flow were discussed in detail. The study indicates that the torsion has first-order effect on the secondary flow in a helical elliptical pipe, the secondary flow is dominated by torsion when the axial pressure gradient is small and for increasing gradient the secondary flow is eventually dominated by the effect due to curvature. The fact that the torsion has no effect on fluid flow in a helical pipe with a circular cross section was also confirmed. The most important conclusion is that the flow in a helical elliptical pipe to the first-order can be obtained as a combination of the flow in a toroidal pipe and the flow in a twisted pipe.
The Stellar Halos of Massive Elliptical Galaxies
Greene, Jenny E; Comerford, Julia M; Gebhardt, Karl; Adams, Joshua J
2012-01-01
We use the Mitchell Spectrograph (formerly VIRUS-P) on the McDonald Observatory 2.7m Harlan J. Smith Telescope to search for the chemical signatures of massive elliptical galaxy assembly. The Mitchell Spectrograph is an integral-field spectrograph with a uniquely wide field of view (107x107 sq arcsec), allowing us to achieve remarkably high signal-to-noise ratios of ~20-70 per pixel in radial bins of 2-2.5 times the effective radii of the eight galaxies in our sample. Focusing on a sample of massive elliptical galaxies with stellar velocity dispersions sigma* > 150 km/s, we study the radial dependence in the equivalent widths (EWs) of key metal absorption lines. By twice the effective radius, the Mgb EWs have dropped by ~50%, and only a weak correlation between sigma* and Mgb EW remains. The Mgb EWs at large radii are comparable to those seen in the centers of elliptical galaxies that are approximately an order of magnitude less massive. We find that the well-known metallicity gradients often observed within ...
Elliptic Solvers for Adaptive Mesh Refinement Grids
Quinlan, D.J.; Dendy, J.E., Jr.; Shapira, Y.
1999-06-03
We are developing multigrid methods that will efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final product will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of other Laboratory groups. The focus of this work is research on serial and parallel elliptic algorithms and the inclusion of our black-box multigrid techniques into this new setting. The approach applies the Los Alamos object-oriented class libraries that greatly simplify the development of serial and parallel adaptive mesh refinement applications. In the final year of this LDRD, we focused on putting the software together; in particular we completed the final AMR++ library, we wrote tutorials and manuals, and we built example applications. We implemented the Fast Adaptive Composite Grid method as the principal elliptic solver. We presented results at the Overset Grid Conference and other more AMR specific conferences. We worked on optimization of serial and parallel performance and published several papers on the details of this work. Performance remains an important issue and is the subject of continuing research work.
The Discrete Wavelet Transform
1991-06-01
focuses on bringing together two separately motivated implementations of the wavelet transform , the algorithm a trous and Mallat’s multiresolution...decomposition. These algorithms are special cases of a single filter bank structure, the discrete wavelet transform , the behavior of which is governed by...nonorthogonal multiresolution algorithm for which the discrete wavelet transform is exact. Moreover, we show that the commonly used Lagrange a trous
Discrete computational structures
Korfhage, Robert R
1974-01-01
Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasize
Coco, Armando; Russo, Giovanni
2013-05-01
In this paper we present a numerical method for solving elliptic equations in an arbitrary domain (described by a level-set function) with general boundary conditions (Dirichlet, Neumann, Robin, etc.) on Cartesian grids, using finite difference discretization and non-eliminated ghost values. A system of Ni+Ng equations in Ni+Ng unknowns is obtained by finite difference discretization on the Ni internal grid points, and second order interpolation to define the conditions for the Ng ghost values. The resulting large sparse linear system is then solved by a multigrid technique. The novelty of the papers can be summarized as follows: general strategy to discretize the boundary condition to second order both in the solution and its gradient; a relaxation of inner equations and boundary conditions by a fictitious time method, inspired by the stability conditions related to the associated time dependent problem (with a convergence proof for the first order scheme); an effective geometric multigrid, which maintains the structure of the discrete system at all grid levels. It is shown that by increasing the relaxation step of the equations associated to the boundary conditions, a convergence factor close to the optimal one is obtained. Several numerical tests, including variable coefficients, anisotropic elliptic equations, and domains with kinks, show the robustness, efficiency and accuracy of the approach.
Feng, Wenqiang, E-mail: wfeng1@vols.utk.edu [Department of Mathematics, The University of Tennessee, Knoxville, TN 37996 (United States); Salgado, Abner J., E-mail: asalgad1@utk.edu [Department of Mathematics, The University of Tennessee, Knoxville, TN 37996 (United States); Wang, Cheng, E-mail: cwang1@umassd.edu [Department of Mathematics, The University of Massachusetts, North Dartmouth, MA 02747 (United States); Wise, Steven M., E-mail: swise1@utk.edu [Department of Mathematics, The University of Tennessee, Knoxville, TN 37996 (United States)
2017-04-01
We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a general framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems – including thin film epitaxy with slope selection and the square phase field crystal model – are carried out to verify the efficiency of the scheme.
Feng, Wenqiang; Salgado, Abner J.; Wang, Cheng; Wise, Steven M.
2017-04-01
We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a general framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems - including thin film epitaxy with slope selection and the square phase field crystal model - are carried out to verify the efficiency of the scheme.
Multiphasic growth curve analysis.
Koops, W.J.
1986-01-01
Application of a multiphasic growth curve is demonstrated with 4 data sets, adopted from literature. The growth curve used is a summation of n logistic growth functions. Human height growth curves of this type are known as "double logistic" (n = 2) and "triple logistic" (n = 3) growth curves (Bock
Discrete geometric structures for architecture
Pottmann, Helmut
2010-06-13
The emergence of freeform structures in contemporary architecture raises numerous challenging research problems, most of which are related to the actual fabrication and are a rich source of research topics in geometry and geometric computing. The talk will provide an overview of recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels and on the physical realization of supporting beams and nodes. A study of quadrilateral meshes with planar faces reveals beautiful relations to discrete differential geometry. In particular, we discuss meshes which discretize the network of principal curvature lines. Conical meshes are among these meshes; they possess conical offset meshes at a constant face/face distance, which in turn leads to a supporting beam layout with so-called torsion free nodes. This work can be generalized to a variety of multilayer structures and laid the ground for an adapted curvature theory for these meshes. There are also efforts on segmenting surfaces into planar hexagonal panels. Though these are less constrained than planar quadrilateral panels, this problem is still waiting for an elegant solution. Inspired by freeform designs in architecture which involve circles and spheres, we present a new kind of triangle mesh whose faces\\' in-circles form a packing, i.e., the in-circles of two triangles with a common edge have the same contact point on that edge. These "circle packing (CP) meshes" exhibit an aesthetic balance of shape and size of their faces. They are closely tied to sphere packings on surfaces and to various remarkable structures and patterns which are of interest in art, architecture, and design. CP meshes constitute a new link between architectural freeform design and computational conformal geometry. Recently, certain timber structures motivated us to study discrete patterns of geodesics on surfaces. This
Elliptical Galaxies: Rotationally Distorted, After All
Caimmi, R.
2009-12-01
Full Text Available On the basis of earlier investigations onhomeoidally striated Mac Laurin spheroids and Jacobi ellipsoids (Caimmi and Marmo2005, Caimmi 2006a, 2007, different sequences of configurations are defined and represented in the ellipticity-rotation plane, $({sf O}hat{e}chi_v^2$. The rotation parameter, $chi_v^2$, is defined as the ratio, $E_mathrm{rot}/E_mathrm{res}$, of kinetic energy related to the mean tangential equatorial velocity component, $M(overline{v_phi}^2/2$, to kineticenergy related to tangential equatorial component velocity dispersion, $Msigma_{phiphi}^2/2$, andresidual motions, $M(sigma_{ww}^2+sigma_{33}^2/2$.Without loss of generality (above a thresholdin ellipticity values, the analysis is restricted to systems with isotropic stress tensor, whichmay be considered as adjoint configurationsto any assigned homeoidally striated density profile with anisotropic stress tensor, different angular momentum, and equal remaining parameters.The description of configurations in the$({sf O}hat{e}chi_v^2$ plane is extendedin two respects, namely (a from equilibriumto nonequilibrium figures, where the virialequations hold with additional kinetic energy,and (b from real to imaginary rotation, wherethe effect is elongating instead of flattening,with respect to the rotation axis.An application is made toa subsample $(N=16$ of elliptical galaxies extracted from richer samples $(N=25,~N=48$of early type galaxies investigated within theSAURON project (Cappellari et al. 2006, 2007.Sample objects are idealized as homeoidallystriated MacLaurinspheroids and Jacobi ellipsoids, and theirposition in the $({sf O}hat{e}chi_v^2$plane is inferred from observations followinga procedure outlined in an earlier paper(Caimmi 2009b. The position of related adjoint configurations with isotropic stresstensor is also determined. With a singleexception (NGC 3379, slow rotators arecharacterized by low ellipticities $(0lehat{e}<0.2$, low anisotropy parameters$(0ledelta<0
蒋纯志; 谢超; 刘又文
2011-01-01
The electro-elastic interaction between a piezoelectric screw dislocation and an elliptical piezoelectric inhomogeneity, which contains an electrically conductive confocal elliptical rigid core under remote anti-plane shear stresses and in-plane electrical load is dealt with. The anaJytical solutions to the elastic field and the electric field, the interracial stress fields of inhomogeneity and matrix under longitudinal shear and the image force acting on the dislocation are derived by means of complex method. The effect of material properties and geometric configurations of the rigid core on interracial stresses generated by a remote uniform load, rigid core and material electroelastic properties on the image force is discussed.
Fast Multipole-Based Elliptic PDE Solver and Preconditioner
Ibeid, Huda
2016-12-07
Exascale systems are predicted to have approximately one billion cores, assuming Gigahertz cores. Limitations on affordable network topologies for distributed memory systems of such massive scale bring new challenges to the currently dominant parallel programing model. Currently, there are many efforts to evaluate the hardware and software bottlenecks of exascale designs. It is therefore of interest to model application performance and to understand what changes need to be made to ensure extrapolated scalability. Fast multipole methods (FMM) were originally developed for accelerating N-body problems for particle-based methods in astrophysics and molecular dynamics. FMM is more than an N-body solver, however. Recent efforts to view the FMM as an elliptic PDE solver have opened the possibility to use it as a preconditioner for even a broader range of applications. In this thesis, we (i) discuss the challenges for FMM on current parallel computers and future exascale architectures, with a focus on inter-node communication, and develop a performance model that considers the communication patterns of the FMM for spatially quasi-uniform distributions, (ii) employ this performance model to guide performance and scaling improvement of FMM for all-atom molecular dynamics simulations of uniformly distributed particles, and (iii) demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, FMM is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity
Caloric curve of star clusters.
Casetti, Lapo; Nardini, Cesare
2012-06-01
Self-gravitating systems, such as globular clusters or elliptical galaxies, are the prototypes of many-body systems with long-range interactions, and should be the natural arena in which to test theoretical predictions on the statistical behavior of long-range-interacting systems. Systems of classical self-gravitating particles can be studied with the standard tools of equilibrium statistical mechanics, provided the potential is regularized at small length scales and the system is confined in a box. The confinement condition looks rather unphysical in general, so that it is natural to ask whether what we learn with these studies is relevant to real self-gravitating systems. In order to provide an answer to this question, we consider a basic, simple, yet effective model of globular clusters: the King model. This model describes a self-consistently confined system, without the need of any external box, but the stationary state is a nonthermal one. In particular, we consider the King model with a short-distance cutoff on the interactions, and we discuss how such a cutoff affects the caloric curve, i.e., the relation between temperature and energy. We find that the cutoff stabilizes a low-energy phase, which is absent in the King model without cutoff; the caloric curve of the model with cutoff turns out to be very similar to that of previously studied confined and regularized models, but for the absence of a high-energy gaslike phase. We briefly discuss the possible phenomenological as well as theoretical implications of these results.
Modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies
James Q. Feng; C. F. Gallo
2011-01-01
We present an efficient,robust computational method for modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies.With appropriate mathematical treatments,the apparent numerical difficulties associated with singularities in computing elliptic integrals are completely removed.Using a boundary element discretization procedure,the governing equations are transformed into a linear algebra matrix equation that can be solved by straightforward Gauss elimination in one step without further iterations.The numerical code implemented according to our algorithm can accurately determine the surface mass density distribution in a disk galaxy from a measured rotation curve (or vice versa).For a disk galaxy with a typical fiat rotation curve,our modeling results show that the surface mass density monotonically decreases from the galactic center toward the periphery,according to Newtonian dynamics.In a large portion of the galaxy,the surface mass density follows an approximately exponential law of decay with respect to the galactic radial coordinate.Yet the radial scale length for the surface mass density seems to be generally larger than that of the measured brightness distribution,suggesting an increasing mass-to- light ratio with the radial distance in a disk galaxy.In a nondimensionalized form,our mathematical system contains a dimensionless parameter which we call the “galactic rotation number” that represents the gross ratio of centrifugal force and gravitational force.The value of this galactic rotation number is determined as part of the numerical solution.Through a systematic computational analysis,we have illustrated that the galactic rotation number remains within ±10％ of 1.70 for a wide variety of rotation curves.This implies that the total mass in a disk galaxy is proportional to V(0)2 Rg,with V(0) denoting the characteristic rotation velocity (such as the “fiat” value in a typical rotation curve) and Rg the radius of the galactic
Inverse Coefficient Problems for Nonlinear Elliptic Variational Inequalities
Run-sheng Yang; Yun-hua Ou
2011-01-01
This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic variational inequalities. The unknown coefficient of elliptic variational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic variational inequalities is unique solvable for the given class of coefficients. The existence of quasisolutions of the inverse problems is obtained.
The Evolution of Elliptic Flow Under First Order Phase Transition
冯启春; 王清尚; 刘剑利; 任延宇; 张景波; 霍雷
2012-01-01
Elliptic flow for non-central Au＋Au collisions at √SNN=200 GeV is investigated with a 2＋1 dimensional hydrodynamic model. We analyze the softening effect by the velocity along the axis. The contribution of the elliptic flow from the QGP phase, mixed phase and hadron gas phase is studied. The relation between the sound horizon and evolution of the elliptic flow is discussed.
Quadrature Uncertainty and Information Entropy of Quantum Elliptical Vortex States
Banerji, Anindya; Panigrahi, Prasanta. K.; Singh, Ravindra Pratap; Chowdhury, Saurav; Bandyopadhyay, Abir
2012-01-01
We study the quadrature uncertainty of the quantum elliptical vortex state using the associated Wigner function. Deviations from the minimum uncertainty states were observed due to the absence of the Gaussian nature. In our study of the entropy, we noticed that with increasing vorticity, entropy increases for both the modes. We further observed that, there exists an optimum value of ellipticity which gives rise to maximum entanglement of the two modes of the quantum elliptical vortex states. ...
Multiple sine, multiple elliptic gamma functions and rational cones
Tizzano, Luigi
2015-01-01
We define generalizations of the multiple elliptic gamma functions and the multiple sine functions, labelled by rational cones in $\\mathbb{R}^r$. For $r=2,3$ we prove that the generalized multiple elliptic gamma functions enjoy a modular property determined by the cone. This generalizes the modular properties of the elliptic gamma function studied by Felder and Varchenko. The generalized multiple sine enjoy a related infinite product representation, generalizing the results of Narukawa for the ordinary multiple sine functions.
Prateek Sharma
2015-04-01
Full Text Available Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of events in time. So this paper aims at introducing about Discrete-Event Simulation and analyzing how it is beneficial to the real world systems.
Kondakci, H Esat; Saleh, Bahaa E A
2016-01-01
When a disordered array of coupled waveguides is illuminated with an extended coherent optical field, discrete speckle develops: partially coherent light with a granular intensity distribution on the lattice sites. The same paradigm applies to a variety of other settings in photonics, such as imperfectly coupled resonators or fibers with randomly coupled cores. Through numerical simulations and analytical modeling, we uncover a set of surprising features that characterize discrete speckle in one- and two-dimensional lattices known to exhibit transverse Anderson localization. Firstly, the fingerprint of localization is embedded in the fluctuations of the discrete speckle and is revealed in the narrowing of the spatial coherence function. Secondly, the transverse coherence length (or speckle grain size) is frozen during propagation. Thirdly, the axial coherence depth is independent of the axial position, thereby resulting in a coherence voxel of fixed volume independently of position. We take these unique featu...
Discrete systems and integrability
Hietarinta, J; Nijhoff, F W
2016-01-01
This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thoroug...
Discrete Classical Electromagnetic Fields
De Souza, M M
1997-01-01
The classical electromagnetic field of a spinless point electron is described in a formalism with extended causality by discrete finite transverse point-vector fields with discrete and localized point interactions. These fields are taken as a classical representation of photons, ``classical photons". They are all transversal photons; there are no scalar nor longitudinal photons as these are definitely eliminated by the gauge condition. The angular distribution of emitted photons coincides with the directions of maximum emission in the standard formalism. The Maxwell formalism and its standard field are retrieved by the replacement of these discrete fields by their space-time averages, and in this process scalar and longitudinal photons are necessarily created and added. Divergences and singularities are by-products of this averaging process. This formalism enlighten the meaning and the origin of the non-physical photons, the ones that violate the Lorentz condition in manifestly covariant quantization methods.
THE MIXED PROBLEM FOR DEGENERATE ELLIPTIC EQUATIONS OF SECOND ORDER
Guochun Wen
2005-01-01
The present paper deals with the mixed boundary value problem for elliptic equations with degenerate rank 0. We first give the formulation of the problem and estimates of solutions of the problem, and then prove the existence of solutions of the above problem for elliptic equations by the above estimates and the method of parameter extension. We use the complex method, namely first discuss the corresponding problem for degenerate elliptic complex equations of first order, afterwards discuss the above problem for degenerate elliptic equations of second order.
Heterodyne detector for measuring the characteristic of elliptically polarized microwaves
Leipold, Frank; Nielsen, Stefan Kragh; Michelsen, Susanne
2008-01-01
In the present paper, a device is introduced, which is capable of determining the three characteristic parameters of elliptically polarized light (ellipticity, angle of ellipticity, and direction of rotation) for microwave radiation at a frequency of 110 GHz. The device consists of two...... be calculated. Results from measured and calculated wave characteristics of an elliptically polarized 110 GHz microwave beam for plasma heating launched into the TEXTOR-tokamak experiment are presented. Measurement and calculation are in good agreement. ©2008 American Institute of Physics...
SOLVABILITY FOR NONLINEAR ELLIPTIC EQUATION WITH BOUNDARY PERTURBATION
无
2007-01-01
The solvability of nonlinear elliptic equation with boundary perturbation is considered. The perturbed solution of original problem is obtained and the uniformly valid expansion of solution is proved.
Partial differential equations IX elliptic boundary value problems
Egorov, Yu; Shubin, M
1997-01-01
This EMS volume gives an overview of the modern theory of elliptic boundary value problems. The contribution by M.S. Agranovich is devoted to differential elliptic boundary problems, mainly in smooth bounded domains, and their spectral properties. This article continues his contribution to EMS 63. The contribution by A. Brenner and E. Shargorodsky concerns the theory of boundary value problems for elliptic pseudodifferential operators. Problems both with and without the transmission property, as well as parameter-dependent problems are considered. The article by B. Plamenevskij deals with general differential elliptic boundary value problems in domains with singularities.
Note on twisted elliptic genus of K3 surface
Eguchi, Tohru, E-mail: eguchi@yukawa.kyoto-u.ac.j [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Hikami, Kazuhiro, E-mail: KHikami@gmail.co [Department of Mathematics, Naruto University of Education, Tokushima 772-8502 (Japan)
2011-01-03
We discuss the possibility of Mathieu group M{sub 24} acting as symmetry group on the K3 elliptic genus as proposed recently by Ooguri, Tachikawa and one of the present authors. One way of testing this proposal is to derive the twisted elliptic genera for all conjugacy classes of M{sub 24} so that we can determine the unique decomposition of expansion coefficients of K3 elliptic genus into irreducible representations of M{sub 24}. In this Letter we obtain all the hitherto unknown twisted elliptic genera and find a strong evidence of Mathieu moonshine.
Generalized duality in curved string backgrounds
Giveon, Amit; Roček, Martin
1992-08-01
The elements of O(d, d, Z) are shown to be discrete symmetries of the space of curved string backgrounds that are independent of d coordinates. The explicit action of the symmetries on the backgrounds is described. Particular attention is paid to the dilaton transformation. Such symmetries identify different cosmological solutions and other (possibly) singular backgrounds; for example, it is shown that a compact black string is dual to a charged black hole. The extension to the heterotic string is discussed.
Generalized Duality in Curved String-Backgrounds
Giveon, Amit; Giveon, Amit; Rocek, Martin
1992-01-01
The elements of $O(d,d,\\Z)$ are shown to be discrete symmetries of the space of curved string backgrounds that are independent of $d$ coordinates. The explicit action of the symmetries on the backgrounds is described. Particular attention is paid to the dilaton transformation. Such symmetries identify different cosmological solutions and other (possibly) singular backgrounds; for example, it is shown that a compact black string is dual to a charged black hole. The extension to the heterotic string is discussed.
Colors of Ellipticals from GALEX to Spitzer
Schombert, James M.
2016-12-01
Multi-color photometry is presented for a large sample of local ellipticals selected by morphology and isolation. The sample uses data from the Galaxy Evolution Explorer (GALEX), Sloan Digital Sky Survey (SDSS), Two Micron All-Sky Survey (2MASS), and Spitzer to cover the filters NUV, ugri, JHK and 3.6 μm. Various two-color diagrams, using the half-light aperture defined in the 2MASS J filter, are very coherent from color to color, meaning that galaxies defined to be red in one color are always red in other colors. Comparison to globular cluster colors demonstrates that ellipticals are not composed of a single age, single metallicity (e.g., [Fe/H]) stellar population, but require a multi-metallicity model using a chemical enrichment scenario. Such a model is sufficient to explain two-color diagrams and the color-magnitude relations for all colors using only metallicity as a variable on a solely 12 Gyr stellar population with no evidence of stars younger than 10 Gyr. The [Fe/H] values that match galaxy colors range from -0.5 to +0.4, much higher (and older) than population characteristics deduced from Lick/IDS line-strength system studies, indicating an inconsistency between galaxy colors and line indices values for reasons unknown. The NUV colors have unusual behavior, signaling the rise and fall of the UV upturn with elliptical luminosity. Models with blue horizontal branch tracks can reproduce this behavior, indicating the UV upturn is strictly a metallicity effect.
Velocity dispersion around ellipticals in MOND
Tiret, O; Angus, G W; Famaey, B; Zhao, H S
2007-01-01
We investigate how different models that have been proposed for solving the dark matter problem can fit the velocity dispersion observed around elliptical galaxies, on either a small scale (~ 20kpc) with stellar tracers, such as planetary nebulae, or large scale (~ 200kpc) with satellite galaxies as tracers. Predictions of Newtonian gravity, either containing pure baryonic matter, or embedded in massive cold dark matter (CDM) haloes, are compared with predictions of the modified gravity of MOND. The standard CDM model has problems on a small scale, and the Newtonian pure baryonic model has difficulties on a large scale, while a fit with MOND is possible on both scales.
Three Dimensional Interface Problems for Elliptic Equations
无
2007-01-01
The author studies the structure of solutions to the interface problems for second order linear elliptic partial differential equations in three space dimension. The set of singular points consists of some singular lines and some isolated singular points. It is proved that near a singular line or a singular point, each weak solution can be decomposed into two parts, a singular part and a regular part. The singular parts are some finite sum of particular solutions to some simpler equations, and the regular parts are bounded in some norms, which are slightly weaker than that in the Sobolev space H2.
Young circumnuclear disks in elliptical galaxies
Sil'Chenko, Olga K.
2009-04-01
By means of integral-field spectroscopy with the Multi-Pupil Field/Fiber Spectrograph of the Russian 6-m telescope we have studied the central parts of NGC 759 and NGC 83— regular (non-interacting, without strong nuclear activity) round red luminous ( M B =-20.8--21.6) elliptical galaxies which are however known to possess molecular gas. In both galaxies we have found central stellar disks with the extension of 1-2 kpc along the radius which are evidently being formed just now.
Energy loss as the origin of an universal scaling law of the elliptic flow
Andrés, Carlota; Pajares, Carlos
2016-01-01
It is shown that the excellent scaling of the elliptic flow found for all centralities, species and energies from RHIC to the LHC for $p_{T}$ less than the saturation momentum is a consequence of the energy lost by a parton interacting with the color field produced in a nucleus-nucleus collision. In particular, the deduced shape of the scaling curve describes correctly all the data. We discuss the possible extensions to higher $p_{T}$, proton-nucleus and proton-proton collisions as well as higher harmonics.
Application of multiquadric method for numerical solution of elliptic partial differential equations
Sharan, M. [Indian Inst. of Tech., New Delhi (India); Kansa, E.J. [Lawrence Livermore National Lab., CA (United States); Gupta, S. [Govt. Girls Sr. Sec. School I, Madangir, New Delhi (India)
1994-01-01
We have used the multiquadric (MQ) approximation scheme for the solution of elliptic partial differential equations with Dirichlet and/or Neumann boundary conditions. The scheme has the advantage to use the data points in arbitrary locations with an arbitrary ordering. Two dimensional Laplace, Poisson and Biharmonic equations describing the various physical processes, have been taken as the test examples. The agreement is found to be very good between the computed and exact solutions. The method also provides an excellent approximation with curve boundary.
Energy loss as the origin of a universal scaling law of the elliptic flow
Andres, Carlota; Pajares, Carlos [Universidade de Santiago de Compostela, Instituto Galego de Fisica de Altas Enerxias IGFAE, Santiago de Compostela, Galicia (Spain); Braun, Mikhail [Saint Petersburg State University, Department of High-Energy Physics, Saint Petersburg (Russian Federation)
2017-03-15
It is shown that the excellent scaling of the elliptic flow found for all centralities, species and energies from RHIC to the LHC for p{sub T} less than the saturation momentum is a consequence of the energy lost by a parton interacting with the color field produced in a nucleus-nucleus collision. In particular, the deduced shape of the scaling curve describes correctly all the data. We discuss the possible extensions to higher p{sub T}, proton-nucleus and proton-proton collisions as well as higher harmonics. (orig.)
Introductory discrete mathematics
Balakrishnan, V K
2010-01-01
This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0-3 cover fundamental operations involv
Discrete breathers in crystals
Dmitriev, S. V.; Korznikova, E. A.; Baimova, Yu A.; Velarde, M. G.
2016-05-01
It is well known that periodic discrete defect-containing systems, in addition to traveling waves, support vibrational defect-localized modes. It turned out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Since the nodes of the system are all on equal footing, it is only through the special choice of initial conditions that a group of nodes can be found on which such a mode, called a discrete breather (DB), will be excited. The DB frequency must be outside the frequency range of the small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically conserve its vibrational energy forever provided no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery in them of DBs was only a matter of time. It is well known that periodic discrete defect-containing systems support both traveling waves and vibrational defect-localized modes. It turns out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Because the nodes of the system are all on equal footing, only a special choice of the initial conditions allows selecting a group of nodes on which such a mode, called a discrete breather (DB), can be excited. The DB frequency must be outside the frequency range of small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically preserve its vibrational energy forever if no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery of DBs in them was only a matter of time. Experimental studies of DBs encounter major technical difficulties, leaving atomistic computer simulations as the primary investigation tool. Despite
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well a
Arzano, Michele; Kowalski-Glikman, Jerzy
2016-09-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.
Weak Elliptical Distortion of the Milky Way Potential traced by Open Clusters
Zi Zhu
2008-01-01
From photometric observations and star counts, the existence of a bar in the cen-tral few kpc of the Galaxy is suggested. It is generally thought that our Galaxy is surrounded by a massive invisible halo. The gravitational potential of the Galaxy is therefore made non-axisymmetric generated by the central tfiaxial bar, by the outer triaxial halo, and/or by the spiral structures. Selecting nearly 300 open clusters with complete spatial velocity measure-ments and ages, we were able to construct the rotation curve of the Milky Way within a range of 3 kpc of the Sun. Using a dynamic model for an assumed elliptical disk, a clear weak el-liptical potential of the disk with ellipticity of ε(R0) = 0.060 ± 0.012 is detected, the Sun is found to be near the minor axis, displaced by 30°± 3°. The motion of the clusters is suggested to be on an oval orbit rather than on a circular one.
A Non-Zero Hadronic Elliptic Flow with a Vanished Partonic Elliptic Flow in a Coalescence Scenario
LIU Jian-Li; SHAN Lian-Qiang; FENG Qi-Chun; WU Feng-Juan; ZHANG Jing-Bo; TANG Gui-Xin; HUO Lei
2009-01-01
The elliptic flow of a hadron is calculated using a quark coalescence model based on the quark phase space distribution produced by a free streaming locally thermalized quark in a two-dimensional transverse plane at initial time. Without assuming the quark's elliptic flow, it is shown that the hadron obtains a non-zero elliptic flow in this model. The elliptic flow of the hadron is shown to be sensitive to both space momentum correlation and the hadron's internal structure. Quark number scaling is obtained only for some special cases.
Froese, Brittany D
2012-01-01
The theory of viscosity solutions has been effective for representing and approximating weak solutions to fully nonlinear Partial Differential Equations (PDEs) such as the elliptic Monge-Amp\\`ere equation. The approximation theory of Barles-Souganidis [Barles and Souganidis, Asymptotic Anal., 4 (1999) 271-283] requires that numerical schemes be monotone (or elliptic in the sense of [Oberman, SIAM J. Numer. Anal, 44 (2006) 879-895]. But such schemes have limited accuracy. In this article, we establish a convergence result for nearly monotone schemes. This allows us to construct finite difference discretizations of arbitrarily high-order. We demonstrate that the higher accuracy is achieved when solutions are sufficiently smooth. In addition, the filtered scheme provides a natural detection principle for singularities. We employ this framework to construct a formally second-order scheme for the Monge-Amp\\`ere equation and present computational results on smooth and singular solutions.
Numerical computation of space-charge fields of electron bunches in a beam pipe of elliptical shape
Markovik, A.
2005-09-28
This work deals in particularly with 3D numerical simulations of space-charge fields from electron bunches in a beam pipe with elliptical cross-section. To obtain the space-charge fields it is necessary to calculate the Poisson equation with given boundary condition and space charge distribution. The discretization of the Poisson equation by the method of finite differences on a Cartesian grid, as well as setting up the coefficient matrix A for the elliptical domain are explained in the section 2. In the section 3 the properties of the coefficient matrix and possible numerical algorithms suitable for solving non-symmetrical linear systems of equations are introduced. In the following section 4, the applied solver algorithms are investigated by numerical tests with right hand side function for which the analytical solution is known. (orig.)
There are four natural curves in the spinal column. The cervical, thoracic, lumbar, and sacral curvature. The curves, along with the intervertebral disks, help to absorb and distribute stresses that occur from everyday activities such as walking or from ...