Modifying PASVART to solve singular nonlinear 2-point boundary problems

To study the buckling and post-buckling behavior of shells and various other structures, one must solve a nonlinear 2-point boundary problem. Since closed-form analytic solutions for such problems are virtually nonexistent, numerical approximations are inevitable. This makes the availability of accurate and reliable software indispensable. In a series of papers Lentini and Pereyra, expanding on the work of Keller, developed PASVART: an adaptive finite difference solver for nonlinear 2-point boundary problems. While the program does produce extremely accurate solutions with great efficiency, it is hindered by a major limitation. PASVART will only locate isolated solutions of the problem. In buckling problems, the solution set is not unique. It will contain singular or bifurcation points, where different branches of the solution set may intersect. Thus, PASVART is useless precisely when the problem becomes interesting. To resolve this deficiency we propose a modification of PASVART that will enable the user to perform a more complete bifurcation analysis. PASVART would be combined with the Thurston bifurcation solution: as adaptation of Newton's method that was motivated by the work of Koiter 3 are reinterpreted in terms of an iterative computational method by Thurston

CENTRALIZATION VERSUS DECENTRALIZATION OF DECISION MAKING AUTHORITY: EFFECTS ON INFORMATION ACQUISITION AND ECONOMIC EFFICIENCY

Agribusiness,

Schur Q-functions and degeneracy locus formulas for morphisms with symmetries

We give closed-form formulas for the fundamental classes of degeneracy loci associated with vector bundle maps given locally by (not necessary square) matrices which are symmetric (resp. skew-symmetric) w.r.t. the main diagonal. Our description uses essentially Schur Q-polynomials of a bundle, and is based on a certain push-forward formula for these polynomials in a Grassmann bundle.Comment: 22 pages, AMSTEX, misprints corrected, exposition improved. to appear in the Proceedings of Intersection Theory Conference in Bologna, "Progress in Mathematics", Birkhause

Local unitary invariants for multipartite quantum systems

A method is presented to obtain local unitary invariants for multipartite quantum systems consisting of fermions or distinguishable particles. The invariants are organized into infinite families, in particular, the generalization to higher dimensional single particle Hilbert spaces is straightforward. Many well-known invariants and their generalizations are also included.Comment: 13 page

On pointed Hopf algebras associated to unmixed conjugacy classes in S_n

Let s in S_n be a product of disjoint cycles of the same length, C the conjugacy class of s and rho an irreducible representation of the isotropy group of s. We prove that either the Nichols algebra B(C, rho) is infinite-dimensional, or the braiding of the Yetter-Drinfeld module is negative

Integral Grothendieck-Riemann-Roch theorem

We show that, in characteristic zero, the obvious integral version of the Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the Todd and Chern characters is true (without having to divide the Chow groups by their torsion subgroups). The proof introduces an alternative to Grothendieck's strategy: we use resolution of singularities and the weak factorization theorem for birational maps.Comment: 24 page

The regulation of capillary blood flow .

Thesis (Ph.D.)--Boston University

Tertullian’s Adversus Judaeos: a Tale of Two Treatises

Tertullian’s Adversus Judaeos is a controversial text of disputed origins. Until recently, it was not given much scholarly attention, because it was unclear whether or not Tertullian wrote it as an integral, finished work, intended for publication. Two aspects of the text are especially problematic. Sections of chapters 9-14 appear to be taken whole cloth from Tertullian’s Adversus Mariconem, suggesting that Adversus Judaeos, as preserved, may be a composite of two works. Also, the work is disjointed, digressive, and repetitious, unlike Tertullian’s usual standards of authorship. Nonetheless, the most recent scholarly assessment of Adversus Judaeos, based on a comprehensive rhetorical analysis, argues strongly for the work’s authenticity and integrality. My thesis, a rebuttal of this most recent position, is that Adversus Judaeos is indeed a poorly collated composite of two of Tertullian’s works: 1/ an original, rhetorically-complete, two-book Christian apology, and 2/ passages ripped (later) from Book III of Adversus Marcionem. I argue further that the original apology is grounded in issues which arose in Carthage when Septimius Severus assumed power as undisputed Emperor of Rome in 197 c.e. A comprehensive analysis of Adversus Judaeos is presented to demonstrate: 1/ that Parts I and II were written for different (although related) purposes; 2/ that the argument of Part I is not dependent upon the argument of Part II and vice versa; 3/ that a recent proposal for the rhetorical structure of Adversus Judaeos – advanced in defense of the work’s unity – omits many observable rhetorical elements; 4/ that Parts I and II have independent rhetorical structures; and 5/ that Parts of Adversus Marcionem, Book III were redacted to form a significant part of Adversus Judaeos, Part II, and not vice versa. As a whole, the results of analysis make a strong case for the composite nature of the treatise as preserved, and facilitate a proposed reconstruction of the work as originally written, most likely as part of Tertullian’s apologetic program. The original text addresses the “charge” of Christian novelty by grounding the Church securely in ancient Jewish tradition. The unfortunate redaction came later, when someone – not Tertullian – collated the original treatise with sections of Adversus Marcionem, Book III. The result adds little in the way of argument to the original treatise, and therefore the purpose of the composite, as preserved, remains a mystery

Particle-wave duality: a dichotomy between symmetry and asymmetry

Symmetry plays a central role in many areas of modern physics. Here we show that it also underpins the dual particle and wave nature of quantum systems. We begin by noting that a classical point particle breaks translational symmetry whereas a wave with uniform amplitude does not. This provides a basis for associating particle nature with asymmetry and wave nature with symmetry. We derive expressions for the maximum amount of classical information we can have about the symmetry and asymmetry of a quantum system with respect to an arbitrary group. We find that the sum of the information about the symmetry (wave nature) and the asymmetry (particle nature) is bounded by log(D) where D is the dimension of the Hilbert space. The combination of multiple systems is shown to exhibit greater symmetry and thus more wavelike character. In particular, a class of entangled systems is shown to be capable of exhibiting wave-like symmetry as a whole while exhibiting particle-like asymmetry internally. We also show that superdense coding can be viewed as being essentially an interference phenomenon involving wave-like symmetry with respect to the group of Pauli operators.Comment: 20 pages, 3 figure

On the 2D zero modes' algebra of the SU(n) WZNW model

A quantum group covariant extension of the chiral parts of the Wess-Zumino-Novikov-Witten model on a compact Lie group G gives rise to two matrix algebras with non-commutative entries. These are generated by "chiral zero modes" which combine in the 2D model into "Q-operators" which encode information about the internal symmetry and the fusion ring. We review earlier results about the SU(n) WZNW Q-algebra and its Fock representation for n=2 and display the first steps towards their generalization to higher n.Comment: 10 pages, Talk presented by L.H. at the International Workshop LT10 (17-23 June 2013, Varna, Bulgaria