Obstruction Theory Research Articles

조수기용 증기분사 열교환기에 대한 모델링

Steam injection heater is the most widely used method for fresh water generator throughout industry. This method is often chosen because of its simplicity. The steam bubbles condense and give up their heat to the surrounding liquid. Experimental study on steam injection heater has been performed in order to find the effect of major parameter. And conservation equation and Bernoulli obstruction theory are used for numerical simulation model of vapor flow-rate. Qualitative comparisons between simulations and measurements show a good agreement and the simulation models are thereby verified.

Computational topology of equivariant maps from spheres to complements of arrangements

The problem of the existence of an equivariant map is a classical topological problem ubiquitous in topology and its applications. Many problems in discrete geometry and combinatorics have been reduced to such a question and many of them resolved by the use of equivariant obstruction theory. A variety of concrete techniques for evaluating equivariant obstruction classes are introduced, discussed and illustrated by explicit calculations. The emphasis is on D 2 n D_{2n} -equivariant maps from spheres to complements of arrangements, motivated by the problem of finding a 4 4 -fan partition of 2 2 -spherical measures, where D 2 n D_{2n} is the dihedral group. One of the technical highlights is the determination of the D 2 n D_{2n} -module structure of the homology of the complement of the appropriate subspace arrangement, based on the geometric interpretation for the generators of the homology groups of arrangements.

Obstruction theory on 8-manifolds

This paper gives a uniform, self-contained, and fairly direct approach to a variety of obstruction-theoretic problems on 8-manifolds. We give necessary and sufficient cohomological criteria for the existence of complex and quaternionic structures on eight-dimensional vector bundles and for the reduction of the structure group of such bundles to U(3) by the homomorphism U(3) → O(8) given by the Lie algebra representation of PU(3).

Totally Greedy Coin Sets and Greedy Obstructions

A coin set is a strictly increasing list of positive integers that always begins with 1. A coin set is called greedy when the simple greedy change-making algorithm always produces the fewest number of coins in change. Here, the greedy change-making algorithm repeatedly selects the largest denomination coin less than the remaining amount until it has assembled the correct change. Pearson has provided an efficient algorithm for determining whether a coin set is greedy. We study a stricter property on coin sets, called total greediness, which requires that all initial subsequences of the coin set also be greedy, and a simple property makes it easy to test if a coin set is totally greedy. We begin to explore the theory of greedy obstructions– those coin sets that cannot be extended to greedy coin sets by the addition of coins in larger denominations.

Local-to-global spectral sequences for the cohomology of diagrams

We construct local-to-global spectral sequences for the cohomology of a diagram, which compute the cohomology of the full diagram in terms of smaller pieces. These are motivated by the obstruction theory of D. Blanc et al. [D. Blanc, M.W. Johnson, J.M. Turner, On realizing diagrams of Π -algebras, Algebraic Geom. Topol. 6 (2006) 763–807] for realizing a diagram of Π -algebras, but are valid in quite general algebraic settings.

Electron microscopy study of peripheral nerves in the uvulae of snorers and obstructive sleep apnoea patients

The pathophysiology of snoring and obstructive sleep apnoea is still unclear. Two theories are proposed. The first is the obstructive theory, which postulates palatopharyngeal muscle hypertrophy leading to airway narrowing; there is no neural role. The second is the neurogenic theory, which postulates neural degeneration due to vibratory stretch trauma, leading to muscle atrophy and collapse. As identification of nerve fibres in the uvula and palate is difficult and time-consuming, all previous studies aiming to differentiate between these two theories have been based on indirect observation of the muscles, rather than direct study of the nerves. We conducted a prospective study to directly observe and study nerve fibres in uvular specimens from 10 cases of obstructive sleep apnoea, compared with specimens from 10 cases of simple snoring, using transmission electron microscopy. Five autopsy cases served as controls. Obstructive sleep apnoea was associated with definite degenerative changes in myelinated and unmyelinated nerve endings. These degenerative changes were present to a lesser degree and in a smaller proportion of cases of simple snoring. The events postulated by the neurogenic theory of obstructive sleep apnoea appear to play an important role in the pathophysiology of snoring and obstructive sleep apnoea.

Symmetric obstruction theories and Hilbert schemes of points on threefolds

Recall that in an earlier paper by one of the authors DonaldsonThomas type invariants were expressed as certain weighted Euler characteristics of the moduli space. The Euler characteristic is weighted by a certain canonical Z-valued constructible function on the moduli space. This constructible function associates to any point of the moduli space a certain invariant of the singularity of the space at the point. In the present paper, we evaluate this invariant for the case of a singularity which is an isolated point of a C ∗ -action and which admits a symmetric obstruction theory compatible with the C ∗ -action. The answer is (−1) d , where d is the dimension of the Zariski tangent space. We use this result to prove that for any threefold, proper or not, the weighted Euler characteristic of the Hilbert scheme of n points on the threefold is, up to sign, equal to the usual Euler characteristic. For the case of a projective Calabi-Yau threefold, we deduce that the DonaldsonThomas invariant of the Hilbert scheme of n points is, up to sign, equal to the Euler characteristic. This proves a conjecture of Maulik-NekrasovOkounkov-Pandharipande.

First description of polycystic kidney disease in a Portuguese journal

The first description of polycystic kidney disease (PKD) in a Portuguese medical journal occurred in 1918 when Dr Custodio Cabeca published a manuscript in Medicina Contemporânea, a medical journal founded in 1883 by Dr Miguel Bombarda (1851–1910) and Dr Sousa Martins (1843–1897), two important teachers at the Medical School in Lisbon [1]. A reprint of the manuscript dedicated to his colleague, Professor Daniel de Mattos (1845–1921), who was the teacher of Surgery in Medical Faculty of the University of Coimbra, was found by manual searching in the files of the library of this institution (Figure 1). In this manuscript Dr Cabeca reported his experience in treating eight patients with PKD (two of whom he nephrectomised) and reviewed the current knowledge on the pathophysiology of PKD. In his paper, Dr Cabeca started reviewing the pathophysiology of the disease and gave preference to the theory of ‘fetal papilitis’, or obstructive theory, that was proposed by Virchow (1821–1902), as opposed by the theories of neoplastic degeneration and the theory of congenital origin of the disease.

Realizing modules over the homology of a DGA

Let A be a DGA over a field and X a module over H ∗ ( A ) . Fix an A ∞ -structure on H ∗ ( A ) making it quasi-isomorphic to A . We construct an equivalence of categories between A n + 1 -module structures on X and length n Postnikov systems in the derived category of A -modules based on the bar resolution of X . This implies that quasi-isomorphism classes of A n -structures on X are in bijective correspondence with weak equivalence classes of rigidifications of the first n terms of the bar resolution of X to a complex of A -modules. The above equivalences of categories are compatible for different values of n . This implies that two obstruction theories for realizing X as the homology of an A -module coincide.

Obstruction theory for normal Aleksandrov-Čech cohomologies and Hopf generalized classification theorems

Obstruction theory for normal Aleksandrov-Čech cohomologies and Hopf generalized classification theorems

Comparing homotopy categories

AbstractGiven a suitable functorT:→between model categories, we define a long exact sequence relating the homotopy groups of anyXεwith those ofTX, and use this to describe an obstruction theory for lifting an objectGεto. Examples include finding spaces with given homology or homotopy groups.

Quantitative analysis of uvular muscles in cases of simple snoring and obstructive sleep apnea: an image analysis study

Studies on the histopathological changes of the palatine muscles in cases of obstructive sleep apnea (OSA) and simple snoring are controversial, while some authors confirm the presence of muscle hypertrophy and increase in total muscle bulk (obstructive theory), others deny this confirming the presence of muscle atrophy and decrease in the muscle bulk (neurogenic theory), but all these studies depended on subjective observer dependent methods to calculate the muscle bulk. We are carrying a unique study to calculate the muscle bulk in uvular specimens in ten cases of OSA comparing it to ten cases with simple snoring and controls using digital computer dependent software (image analysis). Cases of OSA are associated with definite increase in the total muscle bulk of the palatine muscles when compared to cases of simple snoring and controls. Uvular muscular hypertrophy and the obstructive theory seem to explain the pathophysiology of OSA.

The homotopy category of pseudofunctors and translation cohomology

We develop the obstruction theory of the 2-category of abelian track categories, pseudofunctors and pseudonatural transformations by using the cohomology of categories. The obstructions are defined in Baues–Wirsching cohomology groups. We introduce translation cohomology to classify endomorphisms in the 2-category of abelian track categories. In a sequel to this paper we will show, under certain conditions which are satisfied by all homotopy categories, that a translation cohomology class determines the exact triangles of a triangulated category.

Jacobi identities in low-dimensional topology

The Jacobi identity is the key relation in the definition of a Lie algebra. In the last decade, it has also appeared at the heart of the theory of finite type invariants of knots, links and 3-manifolds (and is there called the IHX relation). In addition, this relation was recently found to arise naturally in a theory of embedding obstructions for 2-spheres in 4-manifolds in terms of Whitney towers. This paper contains the first proof of the four-dimensional version of the Jacobi identity. We also expose the underlying topological unity between the three- and four-dimensional IHX relations, deriving from a beautiful picture of the Borromean rings embedded on the boundary of an unknotted genus 3 handlebody in 3-space. This picture is most naturally related to knot and 3-manifold invariants via the theory of grope cobordisms.

Using equivariant obstruction theory in combinatorial geometry

A significant group of problems coming from the realm of combinatorial geometry can be approached fruitfully through the use of Algebraic Topology. From the first such application to Kneser's problem in 1978 by Lovász [L. Lovász, Knester's conjecture, chromatic number of distance graphs on the sphere, Acta. Sci. Math (Szeged) 45 (1983) 317–323] through the solution of the Lovász conjecture [E. Babson, D. Kozlov, Proof of Lovasz conjecture, Annals of Mathematics (2) (2004), submitted for publication; C. Schultz, A short proof of w 1 n ( Hom ( C 2 r + 1 , K n + 2 ) ) = 0 for all n and a graph colouring theorem by Babson and Kozlov, 2005, arXiv: math.AT/0507346v2], many methods from Algebraic Topology have been developed. Specifically, it appears that the understanding of equivariant theories is of the most importance. The solution of many problems depends on the existence of an elegantly constructed equivariant map. A variety of results from algebraic topology were applied in solving these problems. The methods used ranged from well known theorems like Borsuk–Ulam and Dold theorem to the integer/ideal-valued index theories. Recently equivariant obstruction theory has provided answers where the previous methods failed. For example, in papers [R.T. Živaljević, Equipartitions of measures in R 4 , arXiv: math.0412483, Trans. Amer. Math. Soc., submitted for publication] and [P. Blagojević, A. Dimitrijević Blagojević, Topology of partition of measures by fans and the second obstruction, arXiv: math.CO/0402400, 2004] obstruction theory was used to prove the existence of different mass partitions. In this paper we extract the essence of the equivariant obstruction theory in order to obtain an effective general position map scheme for analyzing the problem of existence of equivariant maps. The fact that this scheme is useful is demonstrated in this paper with three applications: (A) a “half-page” proof of the Lovász conjecture due to Babson and Kozlov [E. Babson, D. Kozlov, Proof of Lovasz conjecture, Annals of Mathematics (2) (2004), submitted for publication] (one of two key ingredients is Schultz' map [C. Schultz, A short proof of w 1 n ( Hom ( C 2 r + 1 , K n + 2 ) ) = 0 for all n and a graph colouring theorem by Babson and Kozlov, 2005, arXiv: math.AT/0507346v2]), (B) a generalization of the result of V. Makeev [V.V. Makeev, Equipartitions of continuous mass distributions on the sphere an in the space, Zap. Nauchn. Sem. S.-Petersburg (POMI) 252 (1998) 187–196 (in Russian)] about the sphere S 2 measure partition by 3-planes (Section 3), and (C) the new ( a , b , a ) , class of 3-fan 2-measures partitions (Section 3). These three results, sorted by complexity, share the spirit of analyzing equivariant maps from spheres to complements of arrangements of subspaces.

Computational differential topology

Some of the more differential aspects of the nascent field of computational topology are introduced and treated in considerable depth. Relevant categories based upon stratified geometric objects are proposed, and fundamental problems are identified and discussed in the context of both differential topology and computer science. New results on the triangulation of objects in the computational differential categories are proven, and evaluated from the perspective of effective computability (algorithmic solvability). In addition, the elements of innovative, effectively computable approaches for analyzing and obtaining computer generated representations of geometric objects based upon singularity/stratification theory and obstruction theory are formulated. New methods for characterizing complicated intersection sets are proven using differential analysis and homology theory. Also included are brief descriptions of several implementation aspects of some of the approaches described, as well as applications of the results in such areas as virtual sculpting, virtual surgery, modeling of heterogeneous biomaterials, and high speed visualizations.

Poincaré invariants

We construct an obstruction theory for relative Hilbert schemes in the sense of [K. Behrend, B. Fantechi, The intrinsic normal cone, Invent. Math. 128 (1) (1997) 45–88] and compute it explicitly for relative Hilbert schemes of divisors on smooth projective varieties. In the special case of curves on a surface V , our obstruction theory determines a virtual fundamental class [ [ Hilb V m ] ] ∈ A m ( m − k ) 2 ( Hilb V m ) , which we use to define Poincaré invariants ( P V + , P V − ) : H 2 ( V , Z ) ⟶ Λ ∗ H 1 ( V , Z ) × Λ ∗ H 1 ( V , Z ) . These maps are invariant under deformations, satisfy a blow-up formula, and a wall crossing formula for surfaces with p g ( V ) = 0 . For the case q ( V ) ≥ 1 , we calculate the wall crossing formula explicitly in terms of fundamental classes of certain Brill–Noether loci for curves. We determine the invariants completely for ruled surfaces, and rederive from this classical results of Nagata and Lange. The invariant ( P V + , P V − ) of an elliptic fibration is computed in terms of its multiple fibers. When the fibered product Hilb V m × Pic V m Hilb V k − m is empty, there exists a more geometric obstruction theory, which gives rise to a second virtual fundamental class { Hilb V m } ∈ A m ( m − k ) 2 + p g ( V ) ( Hilb V m ) . We show that { Hilb V m } = [ [ Hilb V m ] ] when p g ( V ) = 0 , and use the second obstruction theory to prove that [ [ Hilb V m ] ] = 0 when p g ( V ) > 0 and Hilb V m × Pic V m Hilb V k − m = 0̸ . We conjecture that our Poincaré invariants coincide with the full Seiberg–Witten invariants of [Ch. Okonek, A. Teleman, Seiberg–Witten invariants for manifolds with b + = 1 , and the universal wall crossing formula, Internat. J. Math. 7 (6) (1996) 811–832] computed with respect to the canonical orientation data. The main evidence for this conjecture is based on the existence of an Kobayashi–Hitchin isomorphism which identifies the moduli spaces of monopoles with the corresponding Hilbert schemes. We expect this isomorphism to identify also the corresponding virtual fundamental classes. This more conceptual conjecture is true in the smooth case. Using the blow-up formula, the wall crossing formula, and a case by case analysis for surfaces of Kodaira dimension less than 2, we are able to reduce our conjecture to the following assertion: deg [ [ Hilb V m ] ] = ( − 1 ) χ ( O V ) for minimal surfaces V of general type with p g ( V ) > 0 and q ( V ) > 0 .

Instantaneous orifice discharge coefficient of a physical, driven model of the human larynx

The quasisteady approximation is often made in the study of phonatory aerodynamics to facilitate the modeling of time-varying air flows through the self-oscillating vocal folds. The unsteady, pulsating flow is approximated by a sequence of steady flows through representative configurations of the vocal folds at rest. Previous studies have discussed the accuracy of this approximation for a range of orifice geometries, and flow conditions. The purpose of the present study was to further evaluate the quasisteady approximation experimentally using an improved procedure, from a direct comparison between the discharge coefficients of steady jets through fixed orifices and unsteady jets through modulated orifices of identical shape, area, and transglottal pressures at a given time. Life-scale convergent and divergent glottis-shaped rubber orifices were used in a rigid-walled tube and a low Mach number flow representative of human phonation. It was found that the quasisteady approximation is valid during 70% of the duty cycle, when the Reynolds number was above 3000, for a frequency of oscillations of 100 Hz. The steady form of Bernoulli's equation along a streamline, and Bernoulli's flow obstruction theory were found to be reasonably accurate for the unsteady flows. These models break down at low Reynolds numbers, near the beginning and the end of the duty cycle, due to viscous effects and to the influence of flow displaced by the motion of the walls.

The influence of the acoustic feedback on the fluid-structure interaction within single-reed mouthpieces: A numerical investigation

The aim of this article is to complement a previous numerical study conducted to investigate the flow behavior in single‐reed woodwind instruments during dynamic regimes with a moving reed [J. Acoust. Soc. Am. 120, 3362 (2006)]. The code uses a fully‐coupled scheme based on the lattice Boltzmann method and on a finite‐difference scheme to represent the interaction between the reed and the fluid field. The previous study had suggested that, during a dynamic regime and in the absence of acoustic feedback, the flow behavior diverges significantly from what is predicted by the current quasi‐stationary models based on the Bernoulli obstruction theory. The present work provides a further investigation on the same topic by taking into account the influence of the acoustic feedback from the bores open end and its interaction with the mean flow within the mouthpiece‐reed system. This is achieved by coupling the previous mouthpiece‐reed model to a digital waveguide whose reflection function is described by a low‐order digital filter to represent the open‐end boundary condition. [The first author would like to thank CAPES for supporting his doctoral research.]

Realizability of algebraic Galois extensions by strictly commutative ring spectra

We discuss some of the basic ideas of Galois theory for commutative S-algebras originally formulated by John Rognes. We restrict our attention to the case of finite Galois groups and to global Galois extensions. We describe parts of the general framework developed by Rognes. Central roles are played by the notion of strong duality and a trace mapping constructed by Greenlees and May in the context of generalized Tate cohomology. We give some examples where algebraic data on coefficient rings ensures strong topological consequences. We consider the issue of passage from algebraic Galois extensions to topological ones by applying obstruction theories of Robinson and Goerss-Hopkins to produce topological models for algebraic Galois extensions and the necessary morphisms of commutative S-algebras. Examples such as the complex $ K-theory spectrum as a KO-algebra indicate that more exotic phenomena occur in the topological setting. We show how in certain cases topological abelian Galois extensions are classified by the same Harrison groups as algebraic ones, and this leads to computable Harrison groups for such spectra. We end by proving an analogue of Hilbert's theorem 90 for the units associated with a Galois extension.