The Physics Inside Topological Quantum Field Theories

We show that the equations of motion defined over a specific field space are realizable as operator conditions in the physical sector of a generalized Floer theory defined over that field space. The ghosts associated with such a construction are found not to be dynamical. This construction is applied to gravity on a four dimensional manifold, $M$; whereupon, we obtain Einstein's equations via surgery, along $M$, in a five-dimensional topological quantum field theory.Comment: LaTeX, 7 page

Lattice-Ordered Algebras That are Subdirect Products of Valuation Domains

An f-ring (i.e., a lattice-ordered ring that is a subdirect product of totally ordered rings) A is called an SV-ring if A/P is a valuation domain for every prime ideal P of A. If M is a maximal ℓ-ideal of A , then the rank of A at M is the number of minimal prime ideals of A contained in M, rank of A is the sup of the ranks of A at each of its maximal ℓ-ideals. If the latter is a positive integer, then A is said to have finite rank, and if A = C(X) is the ring of all real-valued continuous functions on a Tychonoff space, the rank of X is defined to be the rank of the f-ring C(X), and X is called an SV-space if C(X) is an SV-ring. X has finite rank k iff k is the maximal number of pairwise disjoint cozero sets with a point common to all of their closures. In general f-rings these two concepts are unrelated, but if A is uniformly complete (in particular, if A = C(X)) then if A is an SV-ring then it has finite rank. Showing that ihis latter holds makes use of the theory of finite-valued lattice-ordered (abelian) groups. These two kinds of rings are investigated with an emphasis on the uniformly complete case. Fairly powerful machinery seems to have to be used, and even then, we do not know if there is a compact space X of finite rank that fails to be an SV-space

Quasi F-Covers of Tychonoff Spaces

A Tychonoff topological space is called a quasi F-space if each dense cozero-set of X is C*-embedded in X. In Canad. J. Math. 32 (1980), 657-685 Dashiell, Hager, and Henriksen construct the minimal quasi F-cover QF(X) of a compact space X as an inverse limit space, and identify the ring C(QF(X)) as the order-Cauchy completion of the ring C*(X). In On perfect irreducible preimages, Topology Proc. 9 (1984), 173-189, Vermeer constructed the minimal quasi F-cover of an arbitrary Tychonoff space. In this paper the minimal quasi F-cover of a compact space X is constructed as the space of ultrafilters on a certain sublattice of the Boolean algebra of regular closed subsets of X. The relationship between QF(X) and QF(βX) is studied in detail, and broad conditions under which β(QF(X)) = QF(βX) are obtained, together with examples of spaces for which the relationship fails. (Here βX denotes the Stone-Cech compactification of X.) The role of QF(X) as a projective object in certain topological categories is investigated

Spaces X in Which All Prime z-Ideals of C(X) Are Minimal or Maximal

Quasi P-spaces are defined to be those Tychonoff spaces X such that each prime z-ideal of C(X) is either minimal or maximal. This article is devoted to a systematic study of these spaces, which are an obvious generalization of P-spaces. The compact quasi P-spaces are characterized as the compact spaces which are scattered and of Cantor-Bendixson index no greater than 2. A thorough account of locally compact quasi P-spaces is given. If X is a cozero-complemented space and every nowhere dense zeroset is a z-embedded P-space, then X is a quasi P-space. Conversely, if X is a quasi P-space and F is a nowhere dense z-embedded zeroset, then F is a P-space. On the other hand, there are examples of countable quasi P-spaces with no P-points at all. If a product X times Y is normal and quasi P, then one of the factors must be a P-space. Conversely, if one of the factors is a compact quasi P-space and the other a P-space then the product is quasi P. If X is normal and X and Y are cozero-complemented spaces and f: X → Y is a closed continuous surjection which has the property that f-1(Z) is nowhere dense for each nowhere dense zeroset Z, then if X is quasi P, so is Y. The converse fails even with more stringent assumptions on the map f. The paper then closes with a number of open questions, amongst which the most glaring is whether the free union of quasi P-spaces is always quasi P

Ultrastructure study of the transgenic REN2 rat aorta – part 2: media, external elastic lamina, and adventitia

BackgroundThe renin-angiotensin-aldosterone system (RAAS) plays an important role in the development and progression of vascular stiffness, hypertension and accelerated atherosclerosis, which are associated with the metabolic syndrome (MetS) and type 2 diabetes mellitus. In addition to the intima, RAAS plays an important role in vascular media and adventitial remodeling. Methods Descending thoracic aortas of young male transgenic heterozygous (mRen2) 27 (Ren2) rats were utilized for ultrastructural study. This lean model of hypertension, insulin resistance, and oxidative stress harbors the mouse renin gene and is known to have increased aortic tissue levels of angiotensin II, angiotensin type 1 receptors, and elevated plasma aldosterone levels. ResultsUltrastructural observations substantiate known and novel findings in the tunica media, internal and external elastic lamina, and tunica adventitia, which includes: increased media collagen - proteoglycan matrix expansion, increased secretory and proliferative activity and migration of vascular smooth muscle cells (VSMCs) into a newly developing subendothelial neointima, increased VSMC caveolae, mitochondria degeneration, apoptosis; and lipid retention at the elastin lamellar interface. Openings in the external elastic lamina allow pericyte-to-VSMC contacts. The tunica adventitia exhibits stromal pericyte hyperplasia with actively synthetic phenotype and pericyte-pericyte connections. ConclusionWhile these studies only represent a single snapshot in time, they provide an evaluation of early abnormal ultrastructural vascular remodeling in Ren-2 models of the conduit-elastic thoracic aorta

A Minimal Regular Ring Extension of C(X)

Let G(X) denote the smallest (von Neumann) regular ring of real-valued functions with domain X that contains C(X), the ring of continuous real-valued functions on a Tikhonov topological space (X,Τ). We investigate when G(X) coincides with the ring C(X,Τδ) of continuous real-valued functions on the space (X,Τδ), where Τδ is the smallest Tikhonov topology on X for which tau subset of or equal to tau(delta) and C(X,Τδ) is von Neumann regular. The compact and metric spaces for which G(X) = C(X,Τδ) are characterized. Necessary, and different sufficient, conditions for the equality to hold more generally are found

Radiationless Travelling Waves In Saturable Nonlinear Schr\"odinger Lattices

The longstanding problem of moving discrete solitary waves in nonlinear Schr{\"o}dinger lattices is revisited. The context is photorefractive crystal lattices with saturable nonlinearity whose grand-canonical energy barrier vanishes for isolated coupling strength values. {\em Genuinely localised travelling waves} are computed as a function of the system parameters {\it for the first time}. The relevant solutions exist only for finite velocities.Comment: 5 pages, 4 figure

Soil erosion and some means for its control

The control of soil erosion on the many farms where it is still a problem would not be difficult if it required only an understanding of the critical physical relationships between climate, topography, plant cover, water and soil as well as an ability to prescribe the proper engineering and agronomic measures for each situation. Soil losses, when greatly in excess of those produced by natural geological processes, result from the use of particular farming practices and cropping systems. While an understanding of the physical conditions which produce this erosion is essential, so is an understanding of the reasons that farmers choose the methods of farming which expose their soil to the hazard of heavy erosion losses.https://lib.dr.iastate.edu/specialreports/1027/thumbnail.jp

Topologies and Cotopologies Generated by Sets of Functions

Let L be either [0, 1] or {0, 1} with the usual order. We study topologies on a set X for which the cozero-sets of certain subfamilies H of Lx form a base, and the properties imposed on such topologies by hypothesizing various order-theoretic conditions on H. We thereby obtain useful generalizations of extremely disconnected spaces, basically disconnected spaces, and F-spaces. In particular we use these tools to study the space of minimal prime ideals of certain commutative rings

Combination Therapy with Monoamine Oxidase Inhibitors and Other Antidepressants or Stimulants: Strategies for the Management of Treatment‐Resistant Depression

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/111275/1/phar1576.pd