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Ph.D. Recipients and their Thesis Abstracts. Quasisymmetric Functions and Flag Enumeration in Eulerian Posets. Abstract: We study the tqm research paper, algebraic and enumerative combinatorial aspects of Eulerian posets and their quasisymmetric generating functions. These generating functions span the so-called peak algebra Pi, which originated with Stembridge's theory of research paper note enriched P -partitions. Remarkably, many constructs in the peak algebra that are natural in tqm research the context of enriched P -partitions are also important from the viewpoint of flag enumeration. For example, we show that the fundamental basis of peak functions arising from enriched P -partitions of chains is precisely the basis that is needed to properly encode the cd -index, a common invariant in the study of convex polytopes and note taking, Eulerian posets. Paper? As another example, the descents-to-peaks map, which relates the ordinary and enriched theories of P -partitions, turns out to be important for computing the flag-enumerative information of an oriented matroid based on that of the underlying matroid.

We introduce a family of advantages in education Eulerian posets, called posets of signed order ideals. Each of these posets is defined by appropriately signing a distributive lattice. We establish that the paper, flag-enumerative relationship between a poset of signed order ideals and its underlying distributive lattice is completely analogous to that between an oriented matroid and making process essay, its underlying matroid. Furthermore, we show that these posets are EL-shellable, they have non-negative cd -indices, and their quasisymmetric generating functions enumerate the enriched P -partitions of certain labeled posets. We analyze the (external) Hopf algebra structure on Pi, showing it to be dual to the concatenation Hopf algebra on letters of tqm research paper odd degree. Consequently, Pi is freely generated as a commutative algebra. Upon closer inspection of the generators, we find that Pi is tqm research paper free as a module over the ring of Schur Q -functions. Much of our analysis builds on basic properties of a monomial-like basis for the peak algebra, as well as a recursively defined basis of eigenvectors for the descents-to-peaks map. We give a simple criterion, in tqm research terms of advantages this monomial basis, for determining when an element of Pi is paper symmetric.

Homological Results in Commutative Algebra. Abstract: We discuss a bound on the multiplicity of ideals in the first chapter. Herzog and Srinivasan have conjectured that for any homogeneous k -algebra of thinking in education codimension d , the multiplicity is tqm research bounded by. where $M_i$ is the maximal degree of an i th syzygy. Using the minimal free resolutions as constructed by Peeva and Sturmfels, we show that this bound holds for codimension 2 lattice ideals. The topic of chapter two is ideals having three generators. It is known due to thesis code generator, work by Burch and by Kohn that any projective dimension may be realized by a 3-generated ideal. Buchsbaum and Eisenbud conjectured that the tail of any resolution may be realized by paper, a 3-generated ideal.

This result and a generalization was shown by tqm research, Bruns. We introduce a family of ideals and prove that for each n the tqm research, resolution of the ideal in n variables from the family has the same tail as the Koszul resolution on those n variables. In chapter three we attempt to extend the result of chapter two to wireless networking thesis, ideals generated by binomials. We display binomial examples in 4, 5 and 6 variables. A binomial example having the same tail as the Koszul complex for n = 7 is not found, but we do display 3-generated binomial examples having projective dimensions seven and eight. Shuffles and paper, Shellings via Projection Maps. Abstract: Projection maps which appear in the theory of buildings and oriented matroids are closely related to the notion of shellability. This was first observed by Bjorner. In the first chapter, we give an axiomatic treatment of advantages of critical in education either concept and show their equivalence. We also axiomatize duality in this setting. As applications of tqm research these ideas, we prove a duality theorem on world literature essay ib requirements buildings and give a geometric interpretation of the tqm research paper, flag h vector.

The former may be regarded as a q -analogue of the Dehn-Sommerville equations. We also briefly discuss the connection with the advantages of critical in education, random walks introduced by Bidigare, Hanlon and Rockmore. The random-to-top and the riffle shuffle are two well-studied methods for shuffling a deck of cards. These correspond to paper, the symmetric group S_n , i.e., the advantages thinking, Coxeter group of type A_ . In the second chapter, we give analogous shuffles for the Coxeter groups of type B_n and D_n . Paper? These can be interpreted as shuffles on a signed'' deck of cards. With these examples as motivation, we abstract the notion of a shuffle algebra which captures the connection between the algebraic structure of the shuffles and the geometry of the Coxeter groups. Making Essay? We also give new joker shuffles of type A_ and briefly discuss the generalization to buildings which leads to q -analogues. Subspace Subcodes and Generalized Coset Codes. Abstract: This dissertation considers codes that are formed using certain subsets of algebraic error-control codes and signal space codes. We first consider subspace subcodes of Reed-Solomon (SSRS) codes. We prove a conjecture of Hattori concerning how to identify subspaces that give an SSRS code whose dimension exceeds a certain lower bound.

We next consider generalized coset codes, which are built using partitions of signal space codes. We extend the concepts of paper generalized coset codes in Euclidean space by defining generalized coset codes in Lee space. Essay? We prove that all linear codes over tqm research Z _ m are realizable as these new Lee-generalized coset codes. This implies that linear codes over Z _ m have desirable symmetry properties. We also discuss some relationships among integer lattices, linear codes over Z _4, and generalized coset codes. Enumeration in Geometric Lattices and advantages thinking in education, the.

Abstract: This work primarily deals with questions relating to the enumeration of chains in tqm research paper geometric lattices. The study of geometric lattices arose in the process of characterizing the lattices of subspaces formed by world ib requirements, a finite set of paper points in projective or affine space, and ordered by inclusion. More generally geometric lattices encode the structure of matroids (or combinatorial geometries), which take an axiomatic approach to paper, the concept of dependence. The flag Whitney numbers of a geometric lattice count the number of chains of the lattice with elements having specified ranks. We are interested in the linear inequalities satisfied by the flag Whitney numbers. We present a lower bond on the flag Whitney numbers of a lattice in terms of its rank and number of atoms. We also show that all flag Whitney numbers are simultaneously minimized by tqm research paper, the lattice corresponding to the near pencil arrangement of points in R ^ n . Thinking In Education? Next we focus on rank 3 geometric lattices and give a collection of inequalities which imply all the linear inequalities satisfied by the flag Whitney numbers of rank 3 geometric lattices. We further describe the smallest closed convex set containing the paper, flag Whitney numbers of rank 3 lattices corresponding to oriented matroids. The ab -index is a polynomial associated to a lattice which contains all of the information regarding the flag Whitney numbers. We give a recurrence relation for the ab -index of families of lattices satisfying a particular set of wireless networking thesis conditions.

We also give a collection of tqm research paper inequalities for the ab -index of geometric lattices. Finally, we turn our attention to the group algebra of the symmetric group. The peak set of thinking in education a permutation $sigma$ is the set $ $. We prove the existence of tqm research a subalgebra of Solomon's descent algebra in which elements are sums of permutations that share a common peak set. Linear Inequalities for Flag f-Vectors of Polytopes. Abstract: Here we study the combinatorics of polytopes. A polytope P is the convex hull of a finite set of points in networking thesis R ^ d , and its boundary is paper a collection of lower-dimensional polytopes known as the faces of P . The flag f -vector of P counts the faces of paper note taking each dimension and their incidences with one another. We would like to paper, know what linear inequalities the entries of the flag f -vector satisfy. First we present some of the history of this problem, along with the thesis code, necessary mathematical background. We discuss several special classes of polytopes, including simplicials, simples, cubicals and zonotopes, whose flag f -vectors satisfy inequalities not satisfied by all polytopes.

Then we define Stanley's toric g -vector, which can be used to generate many linear inequalities for flag f -vectors. We prove Meisinger's conjecture that some of these inequalities are implied by others. In addition, we consider the cd -index, another source of many inequalities. We show that not all of these are consequences of the non-negativity of the toric g -vector. We then use linear inequalities satisfied by lower-dimensional polytopes to generate linear relations satisfied by simplicial, simple, k -simplicial and paper, k -simple polytopes, and cubical zonotopes. We also examine a g -vector for cubical polytopes proposed by Adin and give evidence that supports the conjecture g _2 = 0. In particular, we show this to hold for the class of almost simple cubical polytopes, where one might expect it is thesis most likely to tqm research, fail.

Next we improve upon previously known linear inequalities satisfied by zonotopes. Finally, we construct examples of another special class of polytopes, the self-dual polytopes. Derived Categories of Twisted Sheaves on Calabi-Yau Manifolds. Abstract: This dissertation is research note primarily concerned with the study of derived categories of twisted sheaves on Calabi-Yau manifolds. Twisted sheaves occur naturally in a variety of problems, but the most important situation where they are relevant is in the study of moduli problems of semistable sheaves on varieties. Although universal sheaves may not exist as such, in many cases one can construct them as twisted universal sheaves. Tqm Research? In fact, the twisting is an intrinsic property of the moduli problem under consideration. A fundamental construction due to Mukai associates to a universal sheaf is a transform between the derived category of the original space and the derived category of the wireless thesis, moduli space, which often turns out to be an equivalence. Paper? In the present work we study what happens when the universal sheaf is replaced by a twisted one.

Under these circumstances we obtain a transform between the derived category of sheaves on the original space and the derived category of twisted sheaves on the moduli space. The dissertation is divided into two parts. Thesis Generator? The first part presents the main technical tools: the Brauer group, twisted sheaves and their derived category, as well as a criterion for checking whether an tqm research integral transform is an equivalence (a so-called Fourier-Mukai transform). When this is the case we also obtain results regarding the cohomological transforms associated to process nursing, the ones on the level of derived categories. In the second part we apply the theoretical results of the first part to a large set of relevant examples. We study smooth elliptic fibrations and the relationship between the theory of tqm research paper twisted sheaves and in education, Ogg-Shafarevich theory, K _3 surfaces, and elliptic Calabi-Yau threefolds. In particular, the study of elliptic Calabi-Yau threefolds leads us to an example which is likely to provide a counterexample to the generalization of the Torelli theorem from K _3 surfaces to threefolds. A similarity between the examples we study and certain examples considered by Vafa-Witten and Aspinwall-Morrison shows up, although we can only guess the relationship between these two situations at the moment. Representations and Characters of an Extension of tqm research SL(3,R) by an Outer Automorphism.

Abstract: Not available. Centralizers of Finite Subgroups of Automorphisms and Outer Automorphisms of Free Groups. Abstract: In this work we consider centralizers of finite subgroups of automorphisms and outer automorphisms of a finitely generated free group. The work of S. Krstic reveals that the centralizer of a finite subgroup of outer automorphisms (resp. Essay Ib Requirements? automorphisms) of a free group is generated by isomorphisms and Nielsen transformations of reduced G -graphs (resp. Tqm Research Paper? pointed G -graphs). Here this characterization is exploited to find necessary and networking, sufficient conditions for the centralizer of a finite subgroup of outer automorphisms (resp. automorphisms) to be finite. Cohomology of Aut(F_n) Abstract: For odd primes p , we examine the Farrell cohomology H ^*(Aut( F _ p –1)); Z _ p )) of the group of automorphisms of a free group F _ p –1) on 2( p –1) generators, with coefficients in the integers localized at tqm research, the prime ( p )subset Z . This extends results in [12] by Glover and Mislin, whose calculations yield H ^*(Aut( F_n ); Z _ p )) for n in p –1, p and is concurrent with work by Chen in [9] where he calculates H ^*(Aut( F_n ); Z _ p )) for n in p +1, p +2. The main tools used are Ken Brown's Normalizer spectral sequence from [7], a modification of Krstic and Vogtmann's proof of the contractibility of fixed point sets for outer space in [19], and a modification of the Degree Theorem of Hatcher and Vogtmann in [15]. Other cohomological calculations in the paper yield that H ^5( Q_m ; Z ) never stabilizes as m toinfty, where Q_m is the quotient of the spine X_m of auter space introduced in [15] by Hatcher and Vogtmann. This contrasts with the thesis, theorems in [15] where various stability results are shown for tqm research, H^n (Aut( F_m ); Z ), H^n (Aut( F_m ); Q ), and H^n ( Q_m ; Q ).

Actions of Artin Groups and Automorphism Groups on R -Trees. Abstract: This dissertation determines the ways in thesis code which two classes of groups act by paper, isometries on R -trees. The first groups studied are the advantages of critical, two-generator Artin groups A _ n +1, where 2 n +1 is half the length of the relator. In the case where 2 n +1 is tqm research prime, all abelian and non-abelian A _ n +1-actions are found, thus determining by Bass-Serre theory all of the graph of groups decompositions of A _ n +1. The same techniques are applied to a three-generator Artin group, the braid group on four strands, enabling a description of wireless networking thesis all of tqm research its actions on R -trees. The second groups studied are the pure symmetric automorphism groups P Sigma_ n of a free group on n generators; these groups consist of the automorphisms mapping every generator to a conjugate of itself.

All exceptional abelian P Sigma_ n -actions on R -trees are found in tqm research the sense that their length functions are given. This information determines the Bieri-Neumann-Strebel invariant of paper P Sigma_ n using Brown's characterization. The invariant tells which normal subgroups of P Sigma_ n with abelian quotient are finitely generated. Internal Categories and Quantum Groups. Abstract: Let be a monoidal category with equalizes that are preserved by the tensor product. The notion of categories internal to , and extending the usual notion of internal categories, which is obtained when is a category with products and equalizers. The basic theory of internal categories is developed and several applications to quantum groups are found. Generator? Delta categories are defined; these are algebraic objects that generalize groups or bialgebras, in the sense that attached to paper, them there is a monoidal category of representations. Quantum groups are constructed from delta categories.

In particular a construction of quantum groups generalizing that of Drinfeld and Jimbo is presented. An invariant of finite dimensional quasitriangular Hopf algebras is constructed. Homological Methods in note the Theory of Splines. Abstract: This thesis is tqm research paper devoted to the study of splines, which are piecewise polynomial functions of paper a prescribed order of smoothness on a triangulated (or otherwise polyhedrally subdivided) region Delta of R ^ d. Tqm Research? The set of splines of degree at advantages thinking, most k (i.e. each individual polynomial is of degree at most k ) forms a vector space C^r_k (Delta). It turns out that a good way to study C^r_k (Delta) is to paper, embed Delta in R ^ d +1, and tqm research paper, form the cone hatDelta of Delta with the origin. Then the set of tqm research paper splines (of all degrees) on hatDelta is a graded module C^r (hatDelta) over the polynomial ring R in d +1 variables, and the dimension of thinking C^r_k (Delta) is the dimension of tqm research C^r (hatDelta) in degree exactly k. The thesis follows the work of Billera and Rose, who defined a chain complex such that C^r_k (Delta) appears as the top homology module, and approaches the problem from the viewpoint of homological algebra (but using a different chain complex (Cal R/Cal J)). First, we analyze the lower homology modules in the planar case, and prove that the decision, module C^r (hatDelta) is tqm research free if and only if the module H_ 1(Cal R/Cal J) vanishes. We prove that this latter module has finite length, and is nonzero whenever Delta has positive genus. For a fixed configuration Delta, we prove a criterion which gives sufficient conditions for thesis code, C^r (hatDelta) to tqm research, be nonfree, i.e. for advantages of critical thinking, H_ 1(Cal R/Cal J) to be nonzero. Next, we relate the local geometry of paper Delta (the arrangement of world literature essay ib requirements lines at each vertex) to ideals generated by powers of homogeneous linear forms in paper R [ x , y ], and completely describe the resolutions possible for such ideals.

This result, together with results on the homology modules, allows us to determine the Hilbert polynomial for C^r (hatDelta). In the final chapter, we consider the situation for an arbitrary d -dimensional simplicial complex Delta. Generalizing the planar results, we obtain bounds on wireless the dimension of the tqm research, homology modules H_i (Cal R/Cal J) for all i d . Specializing to the case where Delta is a topological d -ball, we use a spectral sequence argument to relate the lower homology modules to C^r (hatDelta). For example, we prove that C^r (hatDelta) is free iff H_i (Cal R/Cal J) is tqm research zero for all i d . Paper? As a corollary, we find if C^r (hatDelta) is free, then C^r (hatDelta) is determined entirely by local data. Solving Sparse Polynomial Systems. Abstract: The computation of thinking in education all solutions of a system of polynomial equations is a basic and in general hard problem.

The main techniques for accomplishing this task in an algorithmic manner, Grobner bases, multivariate resultants and tqm research, continuation methods have received a great deal of attention recently. This thesis describes continuation methods for advantages thinking, numerically determining all complex solutions of a system of polynomial equations. The emphasis is on the set up of continuation problems which require as few paths as possible, rather than on the numerical process of path following. The key to efficient continuation methods is to realize the system to tqm research paper, be solved as a generic element in a one dimensional parameterized family. Polynomial systems which arise from practical problems usually have associated physical parameters, and are thus already presented as members of a parameterized family. In the first chapter we discuss the advantages of critical in education, total space of such a parameterized family and its implications for continuation methods.

The main body of the thesis deals with the application of tqm research toric deformations, and polyhedral subdivisions to produce continuation methods which are optimal for systems with a given collection of support sets = _1. _ n . We identify monomials x ^ q = x _1^ q _1. x_n ^ q_n with lattice points q =( q _1. q _ n )in Z ^ n and allow polynomials of the form. where i =1. n and the coefficients c _ i , q are complex. A famous result of Bernstein sates that, for generic choices of coefficients, the mixed volume of the Newton polytopes _ i = conv( _ i ) is equal to the number of isolated solutions in making process essay ( C *)^ n . In Chapter 2, the concepts of Minkowski addition, mixed volume, and fine mixed subdivisions are presented. The use of fine mixed subdivisions of the Minkowski sum _ i +. + _ n in computing mixed volumes generalizes the use of triangulations in volume computation. Paper? Computational techniques for computing mixed subdivisions via deformation are also described. In Chapter 3, these techniques are adapted to provide a constructive proof of Bernstein's theorem, as well as a generalization of advantages thinking Bernstein's theorem to counting roots in C ^ n . The algorithms described here have been implemented in a program called Pelican . Chapter 4 describes Pelican and provides a tutorial and paper, reference manual. Algebraic K-Theory and Assembly for Complexes of taking Groups. Abstract: I define the algebraic K -theory K_i(RG(X)) for a complex of groups G(X) and a ring R , incorporating the combinatorial structure of X as well as group-theoretic data. If G is the fundamental group of G(X) , I construct a comparison map K_i(RG(X)) to K_i(RG) and show that it is an isomorphism under certain geometric conditions on G(X) . In addition I define an assembly map H_i(G(X);K(R)) to K_i(RG(X)) relating the homology of tqm research paper G(X) to its K -theory. There is a natural transformation from the decision making essay, assembly map for G(X) to the ordinary assembly map for the group G, which is an equivalence when the above geometric hypothesis holds.

Normsets and Rings of tqm research Algebraic Integers. Abstract: Let F be a finite field extension of K which is, in making nursing turn, a finite field extension of Q , the rational numbers with rings of integers R and T respectively. We will also make the assumption that T is a unique factorization domain. Tqm Research? It is well-known that the norm function N_K^F from F to K maps R into a multiplicative submonoid S of T which we will call the thesis code generator, normset of tqm research paper R (with respect to T ). Intuitively, the richer and more intricate multiplicative structure of the ring R could be lost in the translation to the normset. Much information, however, is world essay ib requirements retained in the structure of the multiplicative monoid S . It is the aim of this dissertation to investigate certain properties of the tqm research paper, monoid S and deduce what those properties tell us about R . We will also ask what certain properties of R tell us about S . In the first chapter, we investigate unique factorization properties. There is world literature essay a natural way to define the concept of unique factorization in the normset S . The most important result of the first chapter is the fact that if K is Galois over tqm research F , then R has unique factorization if and only if S has unique factorization. We also define a more general class of fields where the unique factorization of S implies the networking thesis, unique factorization of R . In the second chapter, we look at tqm research paper, the relationship between the class group of R and the structure of the normset will be investigated. Decision Essay? It will be shown that a property of a normset called saturation will measure how the Galois group acts on the class group, and from this some consequences about the structure of the class group of R can be deduced. In the tqm research paper, third chapter it is shown that in world ib requirements the Galois case, the normset determines the tqm research paper, field extension. We also give an example of two non-Galois extensions such that the prime decomposition laws are identical, but the decision process nursing essay, normsets are not.

In the final chapter, we use the techniques of this thesis to prove some factorization results about orders in quadratic number fields. Geometry and tqm research, Combinatorics of Chow Forms. Abstract: The Chow form of a variety is similar to a resultant. Given d +1 linear forms on a d -dimensional projective variety, the Chow form is a polynomial in the coefficients of the linear forms (unique up to multiplication by a nonzero constant) which is zero if and thesis code, only if the linear forms have a common zero on the variety. We can also express the Chow form in terms of the ( d +1) x ( d +1) minors of the matrix of coefficients. This doctoral dissertation describes some of the combinatorial and geometric properties of the Chow form of a variety. In chapter 1, we give an introduction to Chow forms and describe how to perform some basic geometric operations on tqm research paper varieties by manipulating their Chow forms. In chapter 2, we study the combinatorics of Chow forms of thinking point sets in projective spaces and compare and contrast this theory with the theory of binary forms (which are Chow forms of point sets in P ^1).

We also consider the tqm research paper, inhomogeneous version of this theory, the thesis code, theory of multisymmetric functions . We give proofs for tqm research paper, many of the assertions made in this paper, and also a counterexample to one of them. In chapter 3, we consider the Chow polytope as a combinatorial invariant of the Chow form. We show that the Chow polytope of the ruled join of two varieties (a construction used in intersection theory) is the Cartesian product of the Chow polytopes after a change of scale. We also investigate the stratification of the Chow variety of plane conics (whose points are the research note, coefficient vectors of their Chow forms) induced by paper, the different Chow polytopes. In chapter 4, we present a geometric algorithm for computing the Chow form of a ruled join in stages, and give examples of thesis its use. Tqm Research? Chapter 5 is somewhat disconnected from the remainder of the advantages of critical in education, thesis; it proves that all connected complexes of coordinate lines in P ^3 are initial complexes of space curves. This is paper a partial converse to note taking, the cited result of Kalkbrener and Sturmfels that all initial complexes of irreducible varieties are connected. Appendix A describes some MAPLE code written by the author to implement the algorithms of Section 2.1.3 and to make it easier to execute the algorithm of Section 4.2. Algebraic and Combinatorial Methods for Face Enumeration in tqm research Polytopes.

Abstract: Let P be a d -dimensional polytope and S a subset of d –1. We denote by literature ib requirements, f_S(P) the number of chains of faces whose dimensions make up S . The flag f -vector is the vector made up of all such flag numbers. This thesis studies linear and non-linear conditions on the flag f -vectors of several classes of tqm research polytopes. We define a noncommutative algebra whose elements can be viewed as linear forms of flag numbers of decision making essay polytopes. Tqm Research? By studying this algebra, we derive new proofs of the linear relations on flag f -vectors.

We also obtain results about the CD-index and symmetric linear forms having same value on any polytope and of critical thinking, its dual. We study linear equalities and inequalities on flag f -vectors of zonotopes. The method is to tqm research paper, construct a class of zonotopes to establish a lower bound for the span of flag f -vectors. We also find a class of inequalities on flag numbers of zonotopes; some of the inequalities from this class do not hold for decision process, general polytopes. In the case of the cube, we prove the g -conjecture in paper a stronger form, i.e., the generalized g -vector of cubes satisfy Kruskal-Katona inequality, which is stronger than the Macaulay inequality. On Semi-Linear Representations Over Local Fields.

Abstract: In the theory of Galois representations, as the name implies, Galois groups are studied via their matrix representations. In case the ground field is a p -adic field, the set of (continuous) representations of its absolute Galois group by integral p -adic matrices has the natural structure of a metric space. One of the main results of wireless this thesis is that this metric space is bounded. Some related computations are given, describing the tqm research, metric in advantages detail for some special representations. Also discussed are some natural invariants of the representations, and the extent to which they determine the representations. The Semistability at Infinity for Multiple Extension Groups. Abstract: Semistability at infinity is tqm research a geometric invariant used to study the ends of world a locally finite, connected CW complex. Paper? One can use this definition to define the notion of the semistability at infinity for a finitely presented group. Much work has been done (especially by M. Mihalik) to show many classes of finitely presented groups are semistable. He has also given a definition of semistability for research, finitely generated groups that generalizes the original definition. He has used it successfully to show semistability for certain classes of finitely presented groups that are built up from tqm research, finitely generated semistable subgroups.

It is unknown at this time whether or not all finitely presented groups with a finite number of ends are semistable at infinity. The purpose of this dissertation is to use this alternative notion of semistability for finitely generated groups and prove the class of finitely generated groups containing an infinite, finitely generated subnormal subgroup of finite index are semistable at infinity. This would generalize two earlier results of Mihalik. As a consequence, I will show the finitely presented analog of the main result. A Combinatorial Geometry of the Whitehead Torsion of Finite Abelian Groups. Abstract: Given an odd prime p and an arbitrary finite abelian p -group G , except for the exponent, not much is known about the invariants of the wireless networking thesis, Whitehead torsion SK _1( Z [ G ]). Roger C. Alperin, R. Keith Dennis, Robert Oliver and tqm research paper, Michael R. Stein have succeeded in using class field theory to give a simplified combinatorial description using norm residue symbols and the integral logarithm of L. Taylor and R. Tqm Research Paper? Oliver. In this thesis, inspired by tqm research paper, the delicate explicit calculations of specific groups by Oliver, we attempt to develop a combinatorial geometry that may facilitate a better understanding of the ib requirements, complications involved in these computations. Chapter 1 introduces cocyclic homogeneous functions, and explains how they relate to the existing theory. Chapter 2 builds the combinatorial machinery that is relevant to the calculations in this essay.

The resulting geometry seems to borrow the notion of paper a tree from graph theory, and amalgamate it with the idea of a characteristic function from analysis! Chapter 3 should convince the reader that this geometry is fruitful; for even with rather crude tools, one can exploit the wireless networking thesis, transfer homomorphism to deduce useful conclusions for a large class of SK _1. In Chapter 4, we bring this geometry to focus on G simeq ( Z _ p^e )^2 and calculate explicitly the top rank in addition to other results. The main difference between the approach of Alperin-Dennis-Stein and ours is that instead of using the full flexibility in paper the choice of representatives of the orbits in the character group of G , we specialize to one particular choice. We close the essay by wireless networking thesis, debunking a hitherto hope that monomorphisms of tqm research finite abelian p -groups should induce monomorphisms on the SK _1's. Explicit Weight Two Motivic Cohomology Complexes and Algebraic K-Theory. Abstract: Beilinson et al.'s Motivic Cohomology Complex is advantages of critical in education related to paper, a motivic complex (considered earlier by essay, Lichtenbaum) formed using groups related to the scissors congruence groups. This involves an algebraic study of configurations of lines in projective space.

One thereby obtains a more precise relationship between the cohomology of Beilinson's complex and tqm research, lower dimensional K -groups. Most of the proofs omitted in Beilinson et al. Tqm Research Paper? are supplied here. There is tqm research also a list of certain torsional elements of the third K -group for fields between the rationales and the real cyclotomics. The relevant key words are: Aomoto, polylogarithm, torsion in K _3, scissors congruence group, configurations of tqm research paper lines in projective space, motivic cohomology. Combinatorial Structure on the Hilbert Scheme. Abstract: In this thesis, the component structure of the tqm research paper, Hilbert scheme is investigated.

The techniques used to carry out this investigation include Grobner bases, state polytopes, Hartshorne's fans, normal bundles, Borel-fixed ideals, and methods from deformation theory. Signed Sequences and Rolle's Restrictions: Why Not All Real Differentiable Functions and Polynomials Satisfying Rolle's Theorem Are Constructible. Abstract: We investigate which sign sequences can be generated by a single univariate polynomial, and show that there are restrictions other than Rolle's theorem on polynomials. We then prove a fifth order Rolle's theorem, showing that an arrangement of research paper roots satisfying the classical Rolle's theorem is not constructable by a real differentiable function. Rewriting Systems for Coxeter Groups. Abstract: A finite complete rewriting system for a group is a finite presentation which gives a solution to the word problem and tqm research, a regular language of normal forms for the group. In this thesis it is shown that the fundamental group of an orientable closed surface of genus g has a finite complete rewriting system, using the usual generators a _1. a_g , b _1. b_g along with generators representing their inverses. Constructions of finite complete rewriting systems are also given for research note, any Coxeter group G satisfying one of the following hypotheses. 1) G has three or fewer generators. 2) G does not contain a special subgroup of the form s_i, s_j, s_k | s ^2_ i = s ^2_ j = s ^2_ k = ( s_i s_j )^2 = ( s_i s_k )^ m = ( s_j s_k )^ n =1 with m and n both finite and not both equal to two. Endomorphisms of Negatively Curved Polygonal Groups.

Abstract: The theory of automorphisms of free products with amalgamation is well-understood. We examine the dimension 2 analogue of a free product with amalgamation, a polygonal amalgam, and show that in general the automorphisms of polygonal amalgams are similarly well-behaved. Special Values of L-Functions of Curves Over Finite Fields. Abstract: The central theme is to establish an tqm research equality L = chi, relating the wireless networking, value of L -function to an appropriate Euler characteristic. The first chapter studies various cohomologies, giving the definitions of the Euler characteristics and proving necessary properties. The second chapter uses lambda-adic cohomology to compute values of L -functions and proves the main theorem. Groups of Piecewise Linear Homeomorphisms. Abstract: Given a compact subinterval of the real line, the order preserving piecewise linear homeomorphisms of the tqm research paper, interval form a group under composition. In this thesis we study subgroups of such groups obtained by restricting the slopes and singularities occurring in the homeomorphisms. We also consider analogous groups of homeomorphisms and bijections of the circle. This class of groups contains examples which have furnished the first examples of finitely presented infinite simple groups.

We extend this by exhibiting simple subgroups in all of these groups, and showing them to be finitely presented in some cases. We then consider subgroups obtained by restricting slopes to a finitely generated subgroup of the nursing, rationals generated by tqm research paper, integers, say n _1, n _2. n_k , and insisting that the singularities lie in generator Z [1 / ( n _1 n _2. n_k )]. We construct contractible CW complexes on which these groups act with finite stabilizers, yielding classifying spaces as the quotients. We obtain combinatorial information about the groups by studying these classifying spaces. We compute homology and obtain finite presentations.

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And each resume format has strengths and note weaknesses. The three types of resume formats are: How do you know which one is tqm research, best for you? The reverse-chronological resume format is for advantages of critical thinking in education, everyone. Your mom, your little sister, and your uncle can all use a reverse-chronological resume format. The combination resume format is for people who want to show off their skills a little bit before jumping into their experience because they are either a career changer or a high-level professional. The functional resume format , aka the skills-based resume format, is tqm research paper, controversial and should be avoided by everyone.

More on that later. Bonus: Download FREE ultimate checklist of 54 things you need to do before you send your resume. “Resume 101 Checklist.” Speaking of skills, find out thesis code generator what skills are the tqm research paper, most desirable and how to thinking in education, put them on a resume. Tqm Research! The guide has a great infographic too: What Skills to wireless thesis, Put on a Resume? [Examples+ 6 Tips] The Usual Choice - The Reverse-chronological Resume. The reverse-chronological resume format is the most common format and can be used by virtually anyone applying for paper, a job. It is the bread and butter of resume formats. Benefits of the decision making essay, Reverse-chronological Format. 1. It’s standard. Paper! Recruiters are used to scanning this easy-to-read resume format. They will automatically know where your information is, and that you’ve sent a complete resume.

2. Applicant Tracking Systems (ATS) can read it too . It is easy for the robots to find the different sections of your resume when you use the reverse-chronological format. 3. The reverse-chronological resume format puts an emphasis on work history and experience . If you are an average job seeker, your work history is research paper, where most of your relevant skills will be located. Weaknesses of the Reverse-chronological Resume Format. Tqm Research! 1. It’s standard. Choosing this standard resume format is safe, but it will look like all of the tqm research paper, other resumes in tqm research paper, the pile. So you will need to make an extra effort to catch a recruiter’s eye and essay showcase your skills and achievements. 2. The reverse-chronological format puts an emphasis on work history and experience.

If you have large gaps in your work history or no experience then it may not be the best format for showing off your skills. The reverse-chronological resume format places an emphasis on your job history by putting it at the top of the resume under the contact information. You start by listing your most recent work and follow with past jobs in a reverse chronological order - thus the paper, name of the format. Think of it like eating dessert before you get your main course followed by an appetizer. Wireless! And it’s great because starting with dessert at the top of your resume is a good way to paper, catch the attention of the recruiter.

Here is what a reverse-chronological resume format sample looks like. We created it in thesis generator, our resume builder (you can make your resume here): As you can see in the resume format sample, the experience section comes first followed by the education section and other additional sections. Are you struggling with how to tqm research paper, write a resume? Read our complete guide: So how do you dress up this standard resume format so that it works best for you and attracts attention? How To Improve Your Resume By Adding These 3 Sections. Here are three ways that you can dress up a boring, old reverse-chronological resume format: Add a resume summary or resume objective. World Ib Requirements! Add achievements to your experience section. Add a Hobbies and Interests Section. I recommend starting with a carefully constructed resume objective or a resume summary. Choose the resume objective if you are an entry-level applicant, changing your career, or have very little experience. All other professionals should opt for tqm research, the resume summary.

Resume objectives and summaries are confusing, and they are hard to paper, write. So, we’ve written complete guides about writing resume summaries and objectives so that you don’t have to struggle anymore. We’ve also made examples for almost any profession so you can see a sample from your own field of paper, expertise. The Only Way to Use Resume Objectives [20+ Examples] (read now) 7 Resume Summary Tips That Will Get You the world, Job [INFOGRAPHIC] (read now) Adding your achievements within the experience section as bullet points is a way to get your top accomplishments at the top of your resume. Pro Tip: Use the PAR (Problem Action Result) approach to writing about your achievements: In situation P (Problem) I did A (Action) which led to R (Result) . So to paper, pick a completely random and made up example: My previous employer wanted to increase revenue (P) so I created a new marketing campaign on Facebook (A) which led to a 15% increase in sales and advantages of critical thinking in education a 10% increase in revenue (R) . Finally, adding a hobbies and interests section will give recruiters a fuller image of tqm research paper, you as a person. While it may seem unprofessional to include such an informal section in the format of a resume, a lot of businesses are beginning to advantages, look for candidates who will fit in with their office culture. Paper! Your personal interests can make you more attractive and memorable to a recruiter, and signal that you would be a good fit for the company. If you want to tqm research paper, find out more about the benefits of a hobbies and interests section and how to add one to your resume, you can read the tqm research, article below.

The Only Way To Put Hobbies Interests on a Resume [5 Tips] (read now) How to Use a Combination Resume Format to Boost Skills. A combination resume format is the only real alternative to the reverse-chronological resume format. As the nursing, name implies, the combination resume format combines aspects of the other two resume formats, focusing on skills without throwing out the tqm research paper, experience section. The experience section is still important and near the top of essay, your resume just like in paper, a reverse-chronological resume format. You start a combination resume format with a resume summary (aka Qualifications Summary). Making Nursing Essay! Your resume summary can be formatted as a paragraph or as a list of tqm research paper, bullet points, and is a short, snappy introduction that highlights your career progress and skill set. Your experience section comes next. Here is where the reverse-chronological and combination resume formats differ.

With the combination resume format , you can emphasize your skills by grouping the bullet points under specific, skill-based subheadings. As you list your roles and responsibilities under each job, you can organize the bullet points like this: Cinderella Bootcamp (2009-01 - present) Her Royal Highness, Princess Event Organizer. Spearhead team building activities for groups of up to 10 housekeeping princesses. Head up and manage a team of 15 mice responsible for kitchen and housekeeping duties. Project management involving the motivation of a team of 20+ bluebirds responsible for thesis, camp laundry, with a 10% increase in productivity after two months. Conduct webinars on how to wash dishes in tqm research paper, glass heels. Orchestrate the decision process, creation of internal communications between different departments. Responsible for organizing, writing, and communicating the daily schedules and activities of both staff and bootcamp participants. Pro Tip: Grouping your bullet points under such subheadings is also good for providing ATS with keywords . The emphasis that the tqm research, combination resume format places on skills is what makes it a good choice for talented professionals, who have a lot of skills and experience, and career changers.

Career changers are able to focus on skills that will translate from their old role or profession to their new one. After the advantages, skills-based experience section, the combination format continues in the same way as the tqm research, reverse-chronological format: education and advantages of critical additional sections. Why the tqm research, Functional Resume Format is Dysfunctional. A functional resume format takes the pressure off of your job history and refocuses on your skills and abilities. Sounds great right? In fact, the format of code, a functional resume just throws job history out of the window. On a functional resume, an tqm research, experience section is research paper note taking, reduced to a list of old, dusty employers at the bottom of the resume. You can eliminate dates and your roles and responsibilities. Tqm Research! The bulk of the resume becomes a place for showcasing your skills in any order you see fit. Decision! If you aren’t careful, it can look like a jumble of random skills listed under vague headlines like “customer service skills” or “leadership skills.” You do not have to link these skills with job experience or explain how you got them. So your leadership skills could come from being the paper, oldest sibling in decision making process, your family.

And your awesome customer service skills could go all the way back to that time when you were five years old with a lemonade stand in paper, your front yard. The fact that there is no specific information or proof that you learned your skills in any sort of job setting is the real weakness of the functional resume format. The lack of proof alone makes you look suspicious and could result in a recruiter simply throwing out your resume. There are experts that will tell you that it is a good format for students , people who have gaps in their work history, or people who are changing their careers. But it just makes you look sneaky - like you’re hiding something. It is also not good for ATS because the tqm research, robots can't scan your resume for tqm research paper, dates or specific sections. I would recommend not using the functional resume format if you can avoid it. Here's How to Choose a File Format - PDF Resume Vs. Word Resume. Should you save you create a PDF resume or a Word resume? The benefit of creating a PDF resume is that your resume formatting will not get messed up when it is wireless networking thesis, opened by a recruiter.

It also gives you more creative freedom as you'd use platforms such as Photoshop or InDesign to tqm research paper, create a PDF resume. At the same time, your resume may need to pass through Applicant Tracking System (ATS) software. And some ATS software may have trouble reading a PDF resume. ATS does not like graphs or tables and requires plain text. Advantages Thinking In Education! In that case, a Word resume is probably a better choice. Tqm Research! In any situation, having both formats on hand is best practice. Bonus: Download FREE ultimate checklist of 54 things you need to do before you send your resume. Making Essay! “Resume 101 Checklist.” While there are not many resume formats to choose from, the choice is important. The format of a resume really comes down to whether or not you want to tqm research, focus on your skills or your career progression.

Either way, you have to find ways to overcome the thesis, cookie cutter nature of resume formats without coloring too far out tqm research of the lines. You also have to make sure that a recruiter doesn’t take one look at the format of paper, your resume and decide that you are trying to hide something. The best way to enhance a standard resume format is to improve each section and to place your most important skills and tqm research achievements near the top third of your resume. If you can open with a great resume summary, followed by strong skills, experience, and achievements sections, then you can make any old resume format work for nursing essay, you. Do you have any questions about choosing the right resume format for your position? Is there anything else that should be included in the article?

Leave a comment. Natalie is a writer at Uptowork. She loves writing about tqm research resumes and of critical eating tacos more than life itself. She spends her free time reading complicated novels and binge watching TV series.

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Anxiety , Family , Father 861 Words | 3 Pages. chance to go back another time. I have more than a handful of relatives in paper the Middle East. Some of my family members live throughout the many small cities . in wireless networking thesis Israel, with the tqm research paper majority living in the city of paper, Jerusalem, also known as “The Holy City”. Aside from that, I have a couple of my grandfather’s family living in Beirut, Lebanon, a fairly small country that stretches across the Mediterranean Sea and tqm research lies directly North of Israel. Along with my family being a strong reason for my return, the cuisine. Arabic language , Dead Sea , Family 1615 Words | 4 Pages.

?Fred Cotten Descriptive Essay September 27, 2014 English 1010 - 85 A Mini Vacation to Atlanta, Georgia Traveling is one . of my family’s favorite things to do. The family has visited numerous places throughout the United States, however, none are as memorable as Atlanta, Georgia. In Atlanta, there are many places to go and thesis generator sights to see such as: Cola-cola factory, Cabbage Patch Kids Factory, Under Ground Mall, the tqm research paper Zoo, Atlanta Braves Stadium, Six Flags Over Georgia, Stone Mountain Park, and. 1996 Summer Olympics , Atlanta , Atlanta metropolitan area 788 Words | 3 Pages. My first Car Enc1101 March 11, 2012 Descriptive essay My first car was my first most prized possession.

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1996 albums , 2005 singles , Akira Kurosawa 1256 Words | 4 Pages. Descriptive essay example If you are having problems with writing of a descriptive essay you . should certainly look for a descriptive essay example (or even maybe several examples). Descriptive essays have their distinctive features and compulsory elements. A writer has to develop chosen topic in such a way, so that reader have no further questions on the issue. What are these issues? These may be people, events, facts etc. Descriptive essay examples will certainly help aspiring writers compose. Emotion , Essay , Essays 738 Words | 3 Pages. ?Name Professor Course Name and Number Date Descriptive Essay One of tha problems with growing older is losing tha wonder and . fascination of tha world that children see. Paper Note Taking? With tha everyday drudgery of paper, life, it gets harder and harder to see tha world with tha child like perspective that we all once did. This is tha reason that having children has been so exciting because I can once again regain tha opportunity to see tha world through thair innocent, creative eyes.

Thare are few places where tha. Disney Vacation Club , Epcot , Magic Kingdom 1533 Words | 6 Pages. the absolutely best part of any school day. Research Taking? I was put in between a rock and a hard place. As everyone else started fileling out of the . room , a silence began to pervade the place.

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Family , Metaphor , Nicholas 1304 Words | 4 Pages. had to pass the front porch and turn around the tqm research paper back. We wanted to make as little noise as possible so we pitched our shoes. Tqm Research? We slowly followed the porch’s . rails, keeping both eyes on the front door and windows. Paper? We froze when a shadow passed the living room window. Generator? When there was no further movement we continued along the porch until we reached the farthest corner of the house and paper turned around back. When we finally reached the pile of gravel, we instantly grabbed handfuls and shoved them into the. 971 Words | 3 Pages. ? Descriptive Essays vs. Narrative Essays Many people have different preferences on what type of writing style . Ib Requirements? they think is more superior to another, I believe descriptive writing to paper be more excellent writing style then narrative. I can tell you that there are a few similarities and a few differences between the two.

I prefer Descriptive essays , rather than narrative essays . In my belief, it's that the descriptive essays are more effective when an author is trying to convey a story or get a. Essay , Fiction , Narrative 1153 Words | 4 Pages. College Writing 2 October 2012 Descriptive Essay A compact two-door car might not mean a lot to someone, but to me, working . and improving my car is my favorite thing to essay ib requirements do. When I am not inside my house or hanging out with my friends, you’ll be sure to find me working or cleaning my car. Paper? For most people, leaving their car stock is passable for their needs, but to me it’s not. My car is modified which makes it one of a kind. My car consists of its exterior, interior, and performance level.

Automobile , Color , Headlamp 2139 Words | 5 Pages. Descriptive paper Mercedez 1 How It Feels To Be in a Live Poker Tournament About five years ago I used to date this guy, whose mother . loved to go to the casino. Wireless Thesis? When I first heard about her going, I just couldn’t understand why she would get so excited about going there. Tqm Research Paper? She would come home and say how she had the best time and how she got so lucky. She claimed that her son would give her luck and other small things that she would do, to claim she received luck that night.

I would just look. Card game , Game , Luck 1678 Words | 4 Pages. ?My name Professor name English 115 date Essay 1 Do You Want to Build a Snowman? Is incredible all that a piece of paper can reflect . about someone life, these pieces of paper illustrated by characters or passages can be meaningful for us, all the decision making process nursing essay memories this brought to people minds, those wonderful papers are called pictures. When we thought of paper, pictures we just take those for granted. The images shown in pictures tell us more than one thing at once, it depends on thinking in education everyone perceptions about. 2008 albums , Debut albums , English-language films 935 Words | 3 Pages. eye and I would be good, but it’s that time and tqm research I sit up. Eyes still shut sitting in paper my bed, I think about seeing my family and I get a burst of paper, energy. It’s . been two long years since the last time I’ve seen them. I’m going home!

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much of the descriptive elements in paper your essay . World? * 5 Determine what you want the reader to feel about what you are writing. Paper? . What kind of words or images can convey this feeling? * Use a lot of adjectives. They're the describing words. Thesis Code Generator? * * 6 Make sure there is tqm research enough detail in your essay to create a mental image for the reader. * Visualize the note occasion or memory in your mind and describe. More than many other types of paper, essays , descriptive essays strive to create. Emotion , Essay , Feeling 910 Words | 4 Pages. while checking the radios inside the boat and making sure the crew on land can hear you. Code? Climbing into a fire proof suit and a full life jacket, when zipped . all up you fit just snug in the cockpit of the tqm research paper boat as to advantages in education make sure you still have enough room to snap the paper steering wheel into place.

When that shiny wood finished bottom of the boat leaves the trailer and world literature essay ib requirements touches gently down into the water the game is on. Tqm Research? Having the research paper taking little boys that like playing in the water all day offer to take you out. American films , Boat racing , Debut albums 1069 Words | 3 Pages. wedding took place making the sky have a pinkish-purple color. The wind was soft when it touched my cheek.

The beach, sunset, and tqm research paper the small gathering made . her wedding memorable and magical. People watched as they were walking by note or even from their hotel rooms above us. Tqm Research Paper? Strangers cheered when my aunt and uncle shared their first kiss as a married couple. It was only close family and friends who went to her wedding. World Essay? The people who went were only the people who could afford to go. It was very small and beautiful.

English-language films , Haleakala , Hawaii 1110 Words | 3 Pages.