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	Symmetric Pseudoprimes (Site not responding. Last check: 2007-11-07)
		A symmetric pseudoprime relative to f is any composite integer c such that f(z^c)=0 (mod c) for every root z of f.
		Symmetric pseudoprimes tend to be more rare relative to polynomials with larger Galois groups.
		The smallest symmetric pseudoprime relative to this polynomial that is the product of two splitting primes is N = 2258745004684033 = (27439297)(82317889) I suspect that this is the smallest symmetric pseudoprime of any composition relative to the quintic, but I have not made an exhaustive search.
	www.meta-religion.com /Mathematics/Articles/symmetric_pseudoprimes.htm (610 words)

	A Survey of Venn Diagrams: Symmetric Diagrams (Site not responding. Last check: 2007-11-07)
		A necessary condition for the existence of a symmetric n-Venn diagram is that n be a prime number.
		Many symmetric diagrams are known for n = 2,3,5,7, and a few beautifully complex examples for n=11 (the large figure that appears twice in the title section of these pages, Victoria, is a simple polar symmetric 7-Venn diagram).
		Another way of viewing it is that the diagram is composed of 2 copies of the ''pie-slice'' forming the top 1/2 of the diagram, with the curves labelled in the second copy by a permutation by a permutation of the colours in the first pie-slice.
	www.combinatorics.org /Surveys/ds5/VennSymmEJC.html (1903 words)

	The Venn Diagram Page -- Symmetric Diagrams (Site not responding. Last check: 2007-11-07)
		Although symmetric diagrams are known for n = 2,3,5,7, none is known for n = 11 or any larger prime.
		One of Grünbaum's examples is a remarkable non-monotone symmetric Venn diagram.
		There are no known symmetric non-monotone Venn diagrams with polar symmetry, but there are 33 known that do not have polar symmetry.
	www.theory.csc.uvic.ca /~cos/oldvenn/VennSymmEJC.html (2178 words)

	Symmetric Function Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-11-07)
		In mathematics, a symmetric function of multiple variables is one that is invariant under permutation of its variables.
		The theory of symmetric polynomials is part of the theory of polynomial equations, and also a substantial chapter of combinatorics.
		A basic theorem states that any symmetric polynomial function S of n variables can be expressed as a polynomial in the elementary symmetric functions.
	search.localcolorart.com /search/encyclopedia/Symmetric_function (682 words)

	RFC 2440 (rfc2440) - OpenPGP Message Format
		With public-key encryption, the object is encrypted using a symmetric encryption algorithm.
		With symmetric-key encryption, an object may be encrypted with a symmetric key derived from a passphrase (or other shared secret), or a two-stage mechanism similar to the public-key method described above in which a session key is itself encrypted with a symmetric algorithm keyed from a shared secret.
		The symmetric cipher used may be specified in an Public-Key or Symmetric-Key Encrypted Session Key packet that precedes the Symmetrically Encrypted Data Packet.
	www.faqs.org /rfcs/rfc2440.html (15932 words)

	Symmetric Key Encryption
		Symmetric key encryption is used for authentication and exchange of secret data on the world wide web.
		The information is authentic because the information with one symmetric key can only be decrypted with the same key.
		The sender and receiver know that they are talking to each other if the symmetric key has not been exposed.
	faculty.quinnipiac.edu /business/accounting/webquest/kirschner/symmetric_key_encryption.asp (679 words)

	Loeks Symmetric Spaces Page
		In order to study p-adic symmetric spaces and their representation theory it is important to have a classification of the k-involutions together with their fine structure of restricted root systems with multiplicities and Weyl groups.
		Motivation: That a study of p-adic symmetric spaces is a natural extension of the study of real semisimple symmetric spaces and also of p-adic groups is not easily seen.
		Recall that the Riemannian symmetric spaces can be defined as those Riemannian manifolds M such that any point x in M has a normal neighborhood on which the geodesic symmetry with respect to x is an isometry.
	www4.ncsu.edu /~loek/research/symm.html (1231 words)

	RFC 1421 (rfc1421) - Privacy Enhancement for Internet Electronic Mail: Par
		When symmetric cryptography is used for DEK encryption, an IK is a single symmetric key shared between an originator and a recipient.
		Appropriate symmetric encryption algorithms, modes and identifiers, MIC computation algorithms and identifiers, and encrypted DEK and MIC formats are defined in RFC 1423.
		For the symmetric case, IK components are identified in PEM headers through use of mailbox specifiers in traditional Internet-wide form ("user@domain-qualified-host").
	www.faqs.org /rfcs/rfc1421.html (10909 words)

	The GNU Privacy Handbook
		The key used to drive the symmetric cipher is derived from a passphrase supplied when the document is encrypted, and for good security, it should not be the same passphrase that you use to protect your private key.
		Symmetric encryption is useful for securing documents when the passphrase does not need to be communicated to others.
		A symmetric cipher is a cipher that uses the same key for both encryption and decryption.
	www.gnupg.org /gph/en/manual.html (13839 words)

	Symmetric Pseudoprimes
		A better generalization is to impose the appropriate congruence condition on all symmetric functions of the roots.
		In other words, given a monic polynomial f with integer coefficients, a symmetric pseudoprime relative to f is defined as a composite integer N such that every elementary symmetric function of the Nth powers of the roots of f is congruent (mod N) to the same function of the first powers.
		In the articles listed below, basic propositions and computational techniques associated with symmetric pseudoprimes are presented, along with specific examples relative to selected polynomials of degrees 1 to 5, and the final article describes complete congruence conditions on the terms of arbitrary linear recurring sequences.
	mathpages.com /home/kmath003/kmath003.htm (590 words)

	Symmetric Eigenvalue Decomposition Classes
		Encapsulates the eigenvalues and eigenvectors of a symmetric matrix, a Hermitian in the complex case.
		Symmetric eigenvalue server classes, which allow the computation of only the eigenvalues in a given range and (optionally) their corresponding eigenvectors.
		Symmetric eigenvalue server classes and the Hermitian eigenvalue server class, respectively, allow the computation of a subset of the eigenvalues and (optionally) their corresponding eigenvectors.
	www.roguewave.com /support/docs/sourcepro/lapackref/2-5.html (210 words)

	Manipulation of Triangular and Symmetric Matrices
		At CERN, matrices are often stored row-wise (TC-convention); furthermore, symmetric matrices are stored packed as the lower left triangular part only, i.e., the Ith diagonal element is found in position I(I+1)/2.
		symmetric matrix is taken to be stored in the packed form with M(M+1)/2 elements.
		These are also stored in the packed form with all the zeros dropped; therefore, care has to be taken in the interpretation of a packed matrix as to whether it represents a symmetric or lower triangular array.
	wwwasdoc.web.cern.ch /wwwasdoc/shortwrupsdir/f112/top.html (230 words)

	What are symmetric and asymmetric ciphers? (Site not responding. Last check: 2007-11-07)
		Symmetric systems are also known as shared secret systems or private key systems.
		Symmetric ciphers are significantly faster than asymmetric ciphers, but the requirements for key exchange make them difficult to use.
		DES and AES / Rijndael are symmetric ciphers.
	www.tech-faq.com /symmetric-asymmetric.shtml (271 words)

	perl.com: Symmetric Cryptography in Perl
		Algorithms that use the same key for both encryption and decryption are called symmetric ciphers.
		The decision cannot be made without research, but IDEA is often considered the best practical choice for a general purpose cipher.
		Symmetric ciphers usually use randomly generated keys (typically between 64 and 256 bits in length), and computers are notoriously bad at truly random number generation.
	www.perl.com /pub/a/2001/07/10/crypto.html (960 words)

	Symmetric Broadband
		Symmetric Broadband is a wholesale VoIP carrier that provides high performance Internet Protocol connectivity to gateways across North America.
		Symmetric Broadband gateways are located in its fully redundant data centers in San Jose, Seattle, New York, Montreal, Toronto and Vancouver.
		Symmetric Broadband, a Peer 1 Network company, was founded to provide a high performance VoIP network utilizing Peer 1's facilities and fully redundant dedicated IP network.
	www.symmetricbroadband.com (343 words)

	Business Wire: STB Systems acquires Symmetric, Inc.; Deal strengthens Symmetric's position in 3D graphics boards market ... (Site not responding. Last check: 2007-11-07)
		Symmetric will continue to market its 3D graphics products to original equipment manufacturers and value-added resellers worldwide, while STB will aggressively promote and sell Symmetric's technology to first-tier OEM customers.
		"Symmetric is one of 3Dlabs' closest partners and we are delighted to see them as part of STB -- one of the true pioneers in the graphics board industry," said Neil Trevett, vice president of marketing for 3Dlabs, Inc.
		Symmetric sells boards through resellers and OEMs as well as direct channels and currently supports Intel and Alpha platforms, with others to follow shortly.
	www.findarticles.com /p/articles/mi_m0EIN/is_1997_March_24/ai_19239644 (767 words)

	Distributed Capabilities with Symmetric keys (Site not responding. Last check: 2007-11-07)
		We now look at the earlier practice of symmetric key crypto and note that many of the same problems may be solved with symmetric keys as well.
		Symmetric keys cost less to use but the protocols may be more complex.
		In short, with symmetric connections, Y may be, and must be aware of each of its correspondentsâ”those who may send it messages.
	www.cap-lore.com /CapTheory/Dist/SymDist.html (829 words)

	Schultz & Schumacher: The Use and Misuse of Conditional Symmetric Instability (Site not responding. Last check: 2007-11-07)
		Dry symmetric instability is a generalization of both inertial instability and dry gravitational instability.
		In observational studies that assess symmetric instability from limited observations such as single soundings, the geostrophic wind is often approximated by the total wind and stated explicitly as such (e.g, Emanuel 1983b, 1988; Byrd 1989; Reuter and Aktary 1995).
		As discussed in section 4, the results of Emanuel (1985) and Thorpe and Emanuel (1985) indicate that weak positive symmetric stability in the warm air in the presence of frontogenesis leads to a single band of ascent that narrows as the symmetric stability approaches neutrality.
	www.nssl.noaa.gov /csi/csimwr.html (15894 words)

	A^1-local symmetric spectra, by J.F. Jardine (Site not responding. Last check: 2007-11-07)
		The weak equivalences for this structure are stable equivalences, defined by analogy with the definitions given by Hovey, Shipley and Smith for ordinary symmetric spectra and by Jardine for presheaves of symmetric spectra, except that one suspends by the Morel-Voevodsky object T, and the underlying unstable category is the A^1-local category of simplicial presheaves.
		The homotopy category obtained from the category of presheaves of symmetric T-spectra is equivalent to the Morel-Voevodsky stable category.
		The details of the basic construction of the original proper closed simplicial model structure underlying the Morel-Voevodsky stable category are required to handle the symmetric case, and are written out in the first three sections of this paper.
	www.math.uiuc.edu /K-theory/0350 (246 words)

	Foundry Networks : Services : FAQs : Symmetric SLB (Site not responding. Last check: 2007-11-07)
		In Symmetric SLB, all the ServerIrons are active, whereas in a Hot Standby configuration, one ServerIron is active while the other is in standby mode.
		In Symmetric SLB, one of the ServerIrons is the default active ServerIron for a given VIP, while the other ServerIrons are standbys for that VIP.
		To assign Symmetric SLB priority, use the sym-priority command.
	www.foundrynet.com /services/faqs/symmetricSLB.html (278 words)

	Symmetric Coupling for Eddy Current Problems
		In this paper a novel symmetric finite element method-boundary element method-coupling for the $\mathbf{E}$-based eddy current model is derived in a rigorous fashion.
		It yields a variational problem with symmetric bilinear form that is coercive in the natural function spaces.
		Unknowns are the electric field inside the conductor and the equivalent surface current related to the magnetic field.
	epubs.siam.org /sam-bin/dbq/article/38046 (192 words)

	Description of symmetric
		Symmetric matrices are similar to banded matrices in that there is only access to a particular band of the matrix.
		The difference is that in an MTL symmetric matrix,
		The following is an example of a symmetric matrix:
	www.osl.iu.edu /research/mtl/reference/html/symmetric.html (78 words)

	Timing the Symmetric and Generalized Symmetric Eigenproblem
		Four different matrix types are provided for timing the symmetric eigenvalue routines.
		For the symmetric eigenvalue problem, the path names for the four data types are
		The (optional) characters after the path name indicate the computations to be timed, as in the input file for the nonsymmetric eigenvalue problem.
	www.netlib.org /lapack/lawn41/node104.html (656 words)

	Snake Oil Warning Signs:Encryption Software to Avoid
		Symmetric ciphers require both the sender and the recipient to have the same key.
		1], compares symmetric keys against one type of asymmetric key: those based on the ``factoring problem'' or the ``discrete log problem.'' (Algorithms based on the ``elliptical curve discrete log problem'' are more resistant to brute-force attacks and can use much smaller keys.
		Typically, in public key cryptosystems, the message to be sent is encrypted with a symmetric key that was specifically generated for that message.
	www.interhack.net /people/cmcurtin/snake-oil-faq.html (4062 words)

	Trader's Roundtable :: View topic - Non-Symmetric trading systems
		A Symmetric trading system is one that uses the same rules and the same parameter values and the same position sizing, for every single trade in every single market.
		Lovers of Symmetric systems may be surprised when they run tests Long Only, then Short Only, then Long and Short.
		And Run 11 is the Symmetric operation, with Shorts at the same position size (1.0%) as Longs.
	www.tradingblox.com /forum/viewtopic.php?t=1668 (1090 words)

	Symmetric Bipartite Tables for Accurate Function Approximation (Site not responding. Last check: 2007-11-07)
		Our method for designing bipartite tables, called the Symmetric Bipartite Table Method, utilizes symmetry in the table entries to reduce the overall memory requirements.
		It has several advantages over previous bipartite table methods in that it (1) provides a closed form solution for the table entries, (2) has tight bounds on the maximum absolute error, (3) requires smaller table lookups to achieve a given accuracy, and (4) can be applied to a wide range of functions.
		Compared to conventional table lookups, the symmetric bipartite tables presented in this paper are 15.0 to 41.7 times smaller when the operand size is 16 bits and 99.1 to 273.9 times smaller when the operand size is 24 bits.
	csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/proceedings/&toc=comp/proceedings/arith/1997/7846/00/7846toc.xml&DOI=10.1109/ARITH.1997.614893 (259 words)

	PlanetMath: symmetric (Site not responding. Last check: 2007-11-07)
		, then the number of possible symmetric relations on
		This is version 10 of symmetric, born on 2002-02-02, modified 2004-05-29.
		Object id is 1647, canonical name is Symmetric.
	planetmath.org /encyclopedia/Symmetric.html (40 words)

	Symmetric Indefinite Lanczos Method Z. Bai, T. Ericsson, and T. Kowalski
		Such eigenvalue problems come from various applications, such as the linearization of a certain quadratic eigenvalue problem, which often arises in the modeling of damped structural systems; see §9.2.
		The algorithm is referred to as a symmetric indefinite Lanczos method.
		The main trouble with this method is that the basis vectors are orthogonal with respect to an indefinite inner product, so there is no assurance that they will be linearly independent.
	www.cs.utk.edu /~dongarra/etemplates/node296.html (151 words)

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