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# Topic: Gaussian

###### In the News (Sat 16 Feb 19)

 Gaussian in hpcpower Gaussian 98 is currently installed on the hkuhpcc system. Gaussian 03 is currently installed on the hpcpower system. Gaussian can be run using 2 CPUs in the same node for speed up. www.hku.hk /cc/ccsystem/hpcpower/gaussian.html   (0 words)

 PlanetMath: Gaussian integer   (Site not responding. Last check: ) of all Gaussian integers is a subring of This is version 6 of Gaussian integer, born on 2001-10-15, modified 2003-10-08. For instance, they are a subring of the complex numbers, their graph on the complex plane forms a lattice of "squares", and they are a Euclidean domain. planetmath.org /encyclopedia/GaussianIntegers.html   (153 words)

 NationMaster - Encyclopedia: Gaussian integer   (Site not responding. Last check: ) The norm of a Gaussian integer is the natural number defined as In linear algebra, functional analysis and related areas of mathematics, a norm is a function which assigns a positive length or size to all vectors in a vector space, other than the zero vector. The ring of Gaussian integers is the integral closure of Z in the field of Gaussian rationals Q(i) consisting of the complex numbers whose real and imaginary part are both rational. The ring of Gaussian integers was introduced by Carl Friedrich Gauss in 1829 - 1831 (see [1]) while studying reciprocity laws which are generalisations of the theorem of quadratic reciprocity which he had first succeeded in proving in 1796. www.nationmaster.com /encyclopedia/Gaussian-integer   (1376 words)

 Gaussian curvature Summary Gaussian curvature is a numerical quantity associated with an area of a surface that describes the intrinsic geometric property of that area. The Gaussian curvature of a sphere is not equal to that of a flat sheet of paper and therefore one cannot shape a piece of paper into a sphere. A corollary of this theorem is that the Gaussian curvature is invariant under isometric deformations of the surface. www.bookrags.com /Gaussian_curvature   (1037 words)

 Spatial Filters - Gaussian Smoothing The idea of Gaussian smoothing is to use this 2-D distribution as a `point-spread' function, and this is achieved by convolution. The effect of Gaussian smoothing is to blur an image, in a similar fashion to the mean filter. One of the principle justifications for using the Gaussian as a smoothing filter is due to its homepages.inf.ed.ac.uk /rbf/HIPR2/gsmooth.htm   (1121 words)

 Gaussian Gaussian 03 is the latest in the Gaussian series of electronic structure programs. Gaussian 03 is used by chemists, chemical engineers, biochemists, physicists and others for research in established and emerging areas of chemical interest. Gaussian 03 expands the range of chemical systems that it can model to periodic systems such as polymers and crystals via its periodic boundary conditions (PBC) methods. www.additive-net.de /software/gaussian/index.shtml   (1223 words)

 Gaussian on the Chem Cluster Gaussian is available to any student or faculty who have an account on the Chemistry Cluster. Organizing your work in Gaussian is important to preserving not only the information you produce, but also to preserving your sanity when you're trying to find a particular calculation. Outside of GaussView, you must use a special command to run Gaussian calculations because it allows the computer to give each calculation an equal share of the processor: no one calculation which is running on the computer can grab more than its share of CPU power. www.udel.edu /chem/computing/gaussian.html   (0 words)

 The Gaussian Processes Web Site Gaussian processes are in my view the simplest and most obvious way of defining flexible Bayesian regression and classification models, but despite some past usage, they appear to have been rather neglected as a general-purpose technique. The Gaussian processes can highlight areas of the input space where prediction quality is poor, due to the lack of data or its complexity, by indicating the higher variance around the predicted mean. We derive novel analytic expressions for the predictive mean and variance for Gaussian kernel shapes under the assumption of a Gaussian input distribution in the static case, and of a recursive Gaussian predictive density in iterative forecasting. www.gaussianprocess.org   (0 words)

 ACM Sigplan Notices 28, 11 (Nov 1993), 22-27. Once the basic concepts are in hand, we should revel in the polymorphism of Gaussian integers as pairs of integers, as well as atomic elements of the Gaussian ring, much as we revel in the dual role of C "ints" as both integers and bit strings. We know that for a Gaussian integer divisor m+ni, we need m^2+n^2 distinct remainders, so the most elegant choice of representative remainders is a square of area m^2+n^2 which is tilted at an angle of atan(n/m);[5] equivalently, we consider the remainder fraction r/d to reside in an upright square of area 1. Interestingly, Gaussian halftones[25] can be done only if l has no prime factors p=4k+3 which have odd exponents; this makes it difficult to provide a number of grey levels which is exactly a power of two. home.pipeline.com /~hbaker1/Gaussian.html   (6038 words)

 Gaussian 98: Business Solution | NEC   (Site not responding. Last check: ) Gaussian 98 can predict energies, molecular structures, vibrational frequencies and numerous molecular properties for systems in the gas phase and in solution, and it can model both their ground state and excited state. Gaussian 98 allows systems to be studied in the gas phase as well as in solution via its Self-Consistent Reaction Field (SCRF) capabilities. Gaussian 98 can predict the electronic spectra and excited state properties for any system which it is capable of studying in the ground state. www.nec.co.jp /hpc/mediator/sxm_e/software/50.html   (280 words)

 Gaussian 03: electronic structure program, distributed by NET Engineering Gaussian 03 is used by chemists, chemical engineers, biochemists, physicists and others for research in established and emerging areas of chemical interest. Using Gaussian 03 enables you to choose the appropriate approach for the system you are studying, rather than being forced to frame the problem to fit the capabilities and limitations of a particular model. In Gaussian 03, improvements to these algorithms [57] means that their performance gains can be realized for systems of more modest size as well (~100 atoms for pure DFT calculations and ~150 atoms with hybrid functionals). www.net-eng.it /eng/products/gaussian/gaussian-ing.html   (3196 words)

 Welcome to HPCVL -- Gaussian FAQ Gaussian input files have to be set up according to a scheme that is explained in the "User's Reference". This means that if you use Gaussian, you will be doing so on a specific subset of processors to maximize the performance of the program, and minimize the interference with other applications. HPCVL requires users of Gaussian to sign a statement in which they state that they are informed about the terms of the license. www.hpcvl.org /faqs/gaussian/gaussian-faq.html   (1675 words)

 NSC: Chemistry: Gaussian The Gaussian quantum chemistry program is available to users at NSC under the condition that published work include citation of the program (further details). To run Gaussian one has to provide it with one input file called xxxx.com where xxxx is an arbitrarily chosen string. To run Gaussian on Mozart with use of 4 processors with use of 10GB memory for 1 hour (memory allocation is given in xxxx.com), submit the shell script below to the queue (the submit command is: qsub scriptname). www.nsc.liu.se /software/chemistry/gaussian   (1361 words)

 GAUSSIAN(1L) manual page Gaussian 98 is a computational chemistry program that uses methods of electronic structure theory. The subg98 command may be used to submit a Gaussian 98 job to a batch queue and rung98 may be used to invoke Gaussian 98 interactively. Gaussian 98 may also be run interactively using the command rung98 or by specifying the option -int on the subg98 command line, but it is recommended that you do this for small test jobs only. www-rcd.cc.purdue.edu /Cluster/gaussian1.html   (2025 words)

 Gaussian on Biowulf Gaussian can predict energies, molecular structures, vibrational frequencies-along with the numerous molecular properties that are dervied from these three basic computation types-for systems in the gas phase and in solution, and it can model them in both their ground state and excited states. When the L0 command '%chk=' is given in a Gaussian command script, and the stated checkpoint file already exists, Gaussian attempts to import the checkpoint file and begin running with data from the file. Gaussian jobs must be submitted to the altix in a unique fashion, where the machine type (altix), number of processors (ncpus), and memory (4GB) must be explicitly defined: biowulf.nih.gov /apps/gaussian   (1907 words)

 Experiments with a Gaussian Merging-Splitting Algorithm for HMM Training for Speech Recognition Thus, the PTM Gaussians may not be appropriate for initializing the Gaussians in the individual state clusters, and may result in inefficient use of the parameters. We then split the Gaussian for each Genone into two by slightly perturbing the mean of the Gaussian along the direction of the standard deviation vector, and reestimate the model by further EM training. This guarantees that at all stages of the algorithm, the Gaussians are robustly estimated for all Genones. www.nist.gov /speech/publications/darpa98/html/am10/am10.htm   (3967 words)

 Math Forum - Ask Dr. Math The reason behind this is that -1 has a multiplicative inverse in the integers (we say it's a "unit") : (-1)(-1) = 1, and multiplying by -1 does not change the divisibility properties (the divisors and multiples) of a number. With that in mind, we say that two Gaussian integers are relatively prime if their gcd is 1, -1, i, or -i, which is the same as saying that their gcd divides 1. In the Gaussian integers, the condition r >= 0 is meaningless. www.mathforum.org /library/drmath/view/62690.html   (914 words)

 Gaussian.Com Gaussian and GaussView Help Available in Japanese: HIT Corp. Ltd. Gaussian 03 and GaussView 3.0 are available now for a variety of Unix, Windows and Mac OS X systems. The truth about the "statements" on the "Banned by Gaussian" website. www.gaussian.com   (73 words)

 Gaussian Blur Effect A Gaussian Blur is a general purpose blur filter. A Gaussian Blur is distinct from other blurs in that it has a well defined effect on different levels of detail within an image. As well as having this well defined and consistent frequency response, certain characteristics of the Gaussian function mean that large blurs can be applied much faster than other similar kinds of filters. www.websupergoo.com /helpie/source/2-effects/gaussianblur.htm   (156 words)

 Gaussian Gaussian is a connected system of programs for performing semiempirical and ab initio molecular orbital calculations. Gaussian uses several scratch files in the course of its computation. Also, Gaussian will use up to 4 processors during the run; this should be specified on the command line via the -n flag so that the batch system allocates the correct number of processors. helix.nih.gov /apps/structbio/gaussian   (984 words)

 Tsirelson : Gaussian measures The modern theory of Gaussian measures lies at the intersection of the theory of random processes, functional analysis, and mathematical physics and is closely connected with diverse applications in quantum field theory, statistical physics, financial mathematics, and other areas of sciences. The study of Gaussian measures combines ideas and methods from probability theory, nonlinear analysis, geometry, linear operators, and topological vector spaces in a beautiful and nontrivial way. The Gaussian isoperimetry implies highly general theorems about the probability distribution of the norm of a Gaussian random vector, as well as the maximum of a Gaussian random process. www.tau.ac.il /~tsirel/Research/Gaussian/main.html   (748 words)

 Image - Gaussian Blur A Gaussian probability curve is the classic bell-shaped curve with a higher probability in the center of the curve and lower probabilities to either side. A Gaussian blur effect takes each pixel in an RGB or RGBa image and mixes it with adjacent pixels with Gaussian probability so that the pixel has great effect near its original location and less effect (in a bell curve shaped way) farther away from its original location. Gaussian blurs are most often used to create "drop shadow" effects. exchange.manifold.net /manifold/manuals/5_userman/mfd50Image__Gaussian_Blur.htm   (847 words)

 Gaussian — CSC   (Site not responding. Last check: ) Gaussian 03, Revision C.02 is available on Corona. Gaussian 03, Revision B.02 is available on IBMSC. To be able to use Gaussian on Corona your user-id has to be added to Corona's Gaussian users group. www.csc.fi /english/research/software/gaussian   (375 words)

 Gaussian, Error and Complementary Error function   (Site not responding. Last check: ) The gaussian function goes to zero at plus and minus infinity while all the derivatives of any order evaluated at x = 0 are zero. The gaussian function, error function and complementary error function are frequently used in probability theory since the normalized gaussian curve represents the probability distribution with standard deviation Gaussian (upper) and the complementary error function on a semi-logarithmic scale. ece-www.colorado.edu /~bart/book/gaussian.htm   (299 words)

 Gaussian-Type Functions For example, the 3-21G basis set has one contracted Gaussian function that is a linear combination of three primitive Gaussian functions for each inner-shell atomic orbital and two basis functions, one contracted Gaussian function that is a linear combination of two primitive Gaussians and one primitive Gaussian function, for each valence orbital. The 6-31G* basis set represents each inner-shell orbital with one contracted Gaussian function that is a linear combination of six primitive Gaussian functions and each valence orbital with two basis functions, one contracted Gaussian function that is a linear combination of three primitive Gaussians and one primitive Gaussian function. In addition, six d-type Gaussian functions for each nonhydrogen atom in the second or third period are included in the basis set. www.chm.davidson.edu /ronutt/che401/Gaussian/Gaussian.htm   (599 words)

 Research Computing Technologies Gaussian 98 can serve as a powerful tool for exploring areas of chemical interest like substituent effects, reaction mechanisms, potential energy surfaces, and excitation energies. Gaussian 98 can be executed in serial mode on a single node or in parallel mode on multiple cluster nodes for improved throughput. To print the output from a Gaussian 98 job, use the sftp or scp command to transfer the output file to a machine which does have printing capabilities, such as your personal workstation, and print the output from that machine. www.ats.ucla.edu /rct/software/chemistry/gaussian98.htm   (1041 words)

 PlanetMath: Gaussian prime   (Site not responding. Last check: ) The real and the imaginary parts must be of different parity. Sometimes Gaussian primes are simply called “complex primes,” which is an incorrect term found in some of the older literature. This is version 4 of Gaussian prime, born on 2007-04-07, modified 2007-04-19. planetmath.org /encyclopedia/GaussianPrime.html   (189 words)

 Gaussian Distribution   (Site not responding. Last check: ) The Gaussian distribution is a continuous function which approximates the exact binomial distribution of events. The nature of the gaussian gives a probability of 0.683 of being within one standard deviation of the mean. The Gaussian distribution is also commonly called the "normal distribution" and is often described as a "bell-shaped curve". hyperphysics.phy-astr.gsu.edu /hbase/math/gaufcn.html   (178 words)

 Gaussian Elimination Gaussian Elimination is considered the workhorse of computational science for the solution of a system of linear equations. Gaussian Elimination is a systematic application of elementary row operations to a system of linear equations in order to convert the system to upper triangular form. As we go through the steps of Gaussian Elimination with our 3 x 3 example system, keep in mind that although the numbers in the augmented matrix may change significantly after each elementary row operation, our solution set has not changed. ceee.rice.edu /Books/CS/chapter2/linear43.html   (621 words)

 Gaussian   (Site not responding. Last check: ) Gaussian 98 is part of the gaussian module. Gaussian jobs may be submitted to the PBS batch system in the ND HPCC using a script like this. Gaussian is available from Notre Dame AFS space in the gaussian module. www.nd.edu /~sgi/software/packages/gaussian.html   (303 words)

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