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A Classification of Lattice Rules Using the Reciprocal Lattice Generator Matrix

Description: The search for cost-effective lattice rules is a time-consuming and difficult process. After a brief overview of some of the lattice theory relevant to these rules, a new approach to this search is suggested. This -approach is based on a classification of lattice rules using "the upper triangular lattice form" of the reciprocal lattice generator matrix.
Date: June 1989
Creator: Lyness, James N.
Partner: UNT Libraries Government Documents Department

Limits of Precision in the Determination of Lattice Parameters and Stresses by the Debye-Scherrer Method

Description: Note an investigation regarding the limits of precision in the determination of lattice parameters. Experiments were performed with copper radiation on zinc samples. Even when the crystal-grain orientation is perfectly uniform, the recording of the intensity distribution will entail errors.
Date: October 1947
Creator: Ekstein, Hans & Siegel, Stanley
Partner: UNT Libraries Government Documents Department

Topologies on Complete Lattices

Description: One of the more important concepts in mathematics is the concept of order, that is, the description or comparison of two elements of a set in terms of one preceding or being smaller than or equal to the other. If the elements of a set, as pairs, exhibit certain order-type characteristics, the set is said to be a partially ordered set. The purpose of this paper is to investigate a special class of partially ordered sets, called lattices, and to investigate topologies induced on these lattices by specially defined order related properties called order-convergence and star-convergence.
Date: December 1973
Creator: Dwyer, William Karl
Partner: UNT Libraries

Consistency in Lattices

Description: Let L be a lattice. For x ∈ L, we say x is a consistent join-irreducible if x V y is a join-irreducible of the lattice [y,1] for all y in L. We say L is consistent if every join-irreducible of L is consistent. In this dissertation, we study the notion of consistent elements in semimodular lattices.
Date: May 1986
Creator: Race, David M. (David Michael)
Partner: UNT Libraries

Space Groups and Lattice Complexes

Description: From Abstract: "The lattice complex is to the space group what the site is to the point group - an assemblage of symmetry-related equivalent points. The Tables list site sets and lattice complexes in standard and alternate representation. The higher the symmetry of the crystal structures is, the more useful the lattice-complex approach should be on the road to the ultimate goal their classification."
Date: May 1973
Creator: Fisher, Werner; Burzlaff, Hans; Hellner, Erwin & Hellner, Erwin
Partner: UNT Libraries Government Documents Department

K [infinity] in Uranium - Water Lattices

Description: This report follows experiments on K[infinity], measuring the element for several red sizes, enrichments, and water-to-uranium volume ratios-(1, 2), by making use of the relation k[infinity] = 0M-[2]B-[2] (M-2 = migration area, B = buckling). The purpose of this report is to compare the experimental data for k[infinity] with values calculated from the four-factor formula k[infinity] = [eta][epsilon]pf.
Date: July 28, 1955
Creator: Auerback, T.
Partner: UNT Libraries Government Documents Department

Numerical Tests of the Improved Fermilab Action

Description: Recently, the Fermilab heavy-quark action was extended to include dimension-six and -seven operators in order to reduce the discretization errors. In this talk, we present results of the first numerical simulations with this action (the OK action), where we study the masses of the quarkonium and heavy-light systems. We calculate combinations of masses designed to test improvement and compare results obtained with the OK action to their counterparts obtained with the clover action. Our preliminary results show a clear improvement.
Date: November 1, 2010
Creator: Detar, C.; Kronfeld, A.S. & Oktay, M.B.
Partner: UNT Libraries Government Documents Department

Generalized C-sets

Description: The problem undertaken in this paper is to determine what the algebraic structure of the class of C-sets is, when the notion of sum is to be the "set sum. " While the preliminary work done by Appling took place in the space of additive and bounded real valued functions, the results here are found in the more general setting of a complete lattice ordered group. As a conseque n c e , G . Birkhof f' s book, Lattice Theory, is used as the standard reference for most of the terminology used in the paper. The direction taken is prompted by a paper by W. D. L. Appling, "A Generalization of Absolute Continuity and of an Analogue of the Lebesgue Decomposition Theorem. " Since some of the results obtained provide another approach to a problem originally studied by Nakano, and improved upon by Bernau, reference is made to their work to provide other terminology and examples of alternative approaches to the problem of lateral completion. Thus Chapter I contains a brief history of the notion of C-sets and their relationship to lattice ordered groups, along with a summary of the properties of lattice ordered groups needed for later developments. In addition, several results in the general theory of lattice ordered groups are cited to provide insight into the comparability of the assumptions that will ultimately be made about the groups. Chapter II begins with the axiomatization of the collection of nearest point functions" for the closed A-ideals of the cone of a complete lattice ordered group. The basic results in the chapter establish that the functions defined do indeed characterize the complete A-ideals, and that the maps have a 'nearest point property." The maps are then extended to the entire group and shown to correspond to the "nearest point ...
Date: August 1974
Creator: Keisler, D. Michael
Partner: UNT Libraries

Dually Semimodular Consistent Lattices

Description: A lattice L is said to be dually semimodular if for all elements a and b in L, a ∨ b covers b implies that a covers a ∧ b. L is consistent if for every join-irreducible j and every element x in L, the element x ∨ j is a join-irreducible in the upper interval [x,l]. In this paper, finite dually semimodular consistent lattices are investigated. Examples of these lattices are the lattices of subnormal subgroups of a finite group. In 1954, R. P. Dilworth proved that in a finite modular lattice, the number of elements covering exactly k elements is equal to the number of elements covered by exactly k elements. Here, it is established that if a finite dually semimodular consistent lattice has the same number of join-irreducibles as meet-irreducibles, then it is modular. Hence, a converse of Dilworth's theorem, in the case when k equals 1, is obtained for finite dually semimodular consistent lattices. Several combinatorial results are shown for finite consistent lattices similar to those already established for finite geometric lattices. The reach of an element x in a lattice L is the difference between the rank of x*, the join of x and all the elements covering x, and the rank of x; the maximum reach of all elements in L is the reach of L. Sharp lower bounds for the total number of elements and the number of elements of a given reach in a semimodular consistent lattice given the rank, the reach, and the number of join-irreducibles are found. Extremal lattices attaining these bounds are described. Similar results are then obtained for finite dually semimodular consistent lattices.
Date: May 1988
Creator: Gragg, Karen E. (Karen Elizabeth)
Partner: UNT Libraries

B ---> D* l nu with 2+1 flavors

Description: We present a calculation of the form factor for B {yields} D*l{nu} using a 2+1 improved staggered action for the light quarks (on the MILC configurations), and the Fermilab action for the heavy quarks. The form factor is computed at zero recoil using a new double ratio method which yields the form factor more directly than previous approaches.
Date: October 1, 2007
Creator: Laiho, Jack & /Fermilab /Washington U., St. Louis
Partner: UNT Libraries Government Documents Department

Lambda-bar, lambda(1) and m(b) in three-flavor (lattice) QCD

Description: The heavy-quark expansion for inclusive semi-leptonic B decays introduces {Lambda} and {lambda}1 , which are matrix elements in heavy-quark effective field theory. We review how they can be obtained from an analysis of the heavy quark mass dependence of heavy-light meson masses in lattice QCD. We present preliminary results for the bottom quark mass, mb, using {Lambda} and {lambda}1 for the Bs meson from a 2+1 sea-flavor unquenched calculation.
Date: October 1, 2006
Creator: Freeland, Elizabeth D.; Chicago, /Art Inst. of; Kronfeld, Andreas S.; Simone, James N.; Van de Water, Ruth S. & /Fermilab
Partner: UNT Libraries Government Documents Department

Update on onium masses with three flavors of dynamical quarks

Description: We update results presented at Lattice 2005 on charmonium masses. New ensembles of gauge configurations with 2+1 flavors of improved staggered quarks have been analyzed. Statistics have been increased for other ensembles. New results are also available for P-wave mesons and for bottomonium on selected ensembles.
Date: January 1, 2006
Creator: Gottlieb, Steven A.; Levkova, L.; U., /Indiana; Di Pierro, Massimo; U., /DePaul; El-Khadra, Aida Xenia et al.
Partner: UNT Libraries Government Documents Department