Integral Sphere Research Articles

Links and analytic invariants of superisolated singularities

Using superisolated singularities we present examples and counterexamples to some of the most important conjectures regarding invariants of normal surface singularities. More precisely, we show that the “Seiberg-Witten invariant conjecture”(of Nicolaescu and the third author), the “Universal abelian cover conjecture” (of Neumann and Wahl) and the “Geometric genus conjecture” fail (at least at that generality in which they were formulated). Moreover, we also show that for Gorenstein singularities (even with integral homology sphere links) besides the geometric genus, the embedded dimension and the multiplicity (in particular, the Hilbert-Samuel function) also fail to be topological; and in general, the Artin cycle does not coincide with the maximal (ideal) cycle.

Complex surface singularities with integral homology sphere links

Complex surface singularities with integral homology sphere links

Simultaneous EQCM and diffuse reflectance UV–visible spectroelectrochemical measurements: poly(aniline-co- o-anthranilic acid) growth and property characterization

Piezoelectric diffuse reflectance spectroelectrochemistry (PDRSEC), a new technique of diffuse reflectance spectroelectrochemistry (DRSEC) in combination with electrochemical quartz crystal microbalance (EQCM), was developed to study the electrochemical copolymerization of aniline and o-anthranilic acid in 1.0 mol l −1 HClO 4 and the properties of these copolymers. The DRSEC using an integral sphere was proven to possess a higher optical sensitivity at the unpolished piezoelectric quartz crystal electrodes used than the mirror reflectance spectroelectrochemistry mode. The copolymers grown from the copolymerization bath of different molar fractions of o-anthranilic acid ( F 1, relative to the total amount of the two monomers) showed intermediate properties between those of the homopolymers, which varied gradually with F 1. The swelling/dissolution behavior of the copolymers vs solution pH was traced via the EQCM frequency and resistance signals, and its large dependence on F 1 was found and discussed. In a HAc–NaAc buffer solution at pH 5.6, the amount of adsorbed lysozyme was found to be positively correlated with F 1, via an EQCM impedance investigation, demonstrating the feasibility of using poly(aniline-co- o-anthranilic acid) as a load-adjustable immobilization matrix for cationic proteins. The novel PDRSEC method proposed is highly recommended for surface electrochemistry studies at relatively rough electrodes.

A SURGERY DESCRIPTION OF AN INTEGRAL HOMOLOGY THREE-SPHERE RESPECTING THE CASSON INVARIANT

In 1998, C. Lescop proved that any integral homology sphere with the Casson invariant zero can be obtained from S3 by surgery on a boundary link each component of which has a trivial Alexander polynomial. In this paper, we prove that for any integral homology sphere H, there exists an integer k such that H can be obtained from S3 by surgery on a boundary link each component of which has the Alexander polynomial 1+k(t½-t-½)2.

Colorimetric Analysis in the Oral Lesion with White Light Laser

We developed the new colorimetric analysis system with the KOITO white light laser. The KOITO white light laser is a hollow cathode He-Cd laser device that simultane ously oscillates three light laser beams of three primary colors (red, green, blue) from a single laser tube. These beams are formed into a white light laser. In addition, because the oscillation wavelengths of red (635.5 nm, 636 nm), green (533.7 nm, 537.8 nm), blue (441.6 nm) color light are very near the ideal three primary colors.This system has three character. First character is non-contact type without integral sphere. Second is using pen-type probe which contain the bundle type fiber. Third is recording the rate to three colors in the standard reflex light.We examined the efficacy of this colorimetric analysis system with experimental study and clinical cases. On the other hand, we improved this system in the diagnosis of oral malignant tumor.Using this system, we could measure the color disorders in the oral cavity non-invasively, easily, immediately, exactly. Moreover we performed spectral analysis in patients with an oral squamous cell carcinoma. We found that there were bimodal peak at 650 and 690 nm at the excitation wavelength of 441.6 nm and that this result is different from the normal autofluorescenc.We consider that this coloriometric analysis system is useful to measure the color disorders in the oral cavity and has possibility to be improved in the diagnosis of oral malignant tumor.

On the kernel of the Casson invariant

We prove: Any integral homology sphere with Casson invariant zero can be obtained from S 3 by surgery on a boundary link each component of which has a trivial Alexander polynomial.

A generalized transport equation for ion implantation into infinite targets

In this paper a transport equation (TE) is derived which incorporates arbitrary distribution functions and a cut-off energy. Integral equations for the gas-like and liquid free-flight path length distribution models are both incorporated into the transport theory computer code KUBBIC using the two-parameter differential nuclear scattering cross section. Simulations for the ion As implanted into a-Si are compared with those performed using a parallel processor Monte Carlo (MC) code based on TRIM. Excellent agreement is obtained when using four versions of the liquid model, including use of the Biersack free-flight path extension formula and the time integral hard sphere approximation. In addition, the effects of varying the maximum impact parameter are investigated as is the effect of the ordering of nuclear and electronic interactions. The TE formalism and solver presented in this paper serve as a powerful tool for testing new approximations which may be incorporated into MC codes in order to improve computational efficiency.

Laser Cooling and Deceleration of Neutral Atoms by Red-Shifted Diffuse Light

We report a cooling and deceleration experiment of a thermal beam by using a nearly resonant red-shifted diffuse light in an optical integral sphere cavity. By using of this red-shifted diffuse light, the velocity of a part of thermal sodium atoms is cooled to 380 m/s and the velocity width of cooled atoms is about 18 m/s. The mechanism of this kind of laser cooling and the experimental results are discussed.

Plans' theorem for links

A finitely generated Abelian group G is a direct double if there exists H such that G = H ⊕ H. Let X̄ n be the n-sheeted cyclic covering of S 3 (or an integral homology sphere) branched over a knot. Plans' theorem states that H 1( X̄ n ; Z ) is a direct double if n is odd. This statement is wrong if the branching set is nonconnected. However: Theorem. Suppose that the branching set is a link. Then: 1. (1) If n is odd, the rank of H 1(X̄ n; Z ) is even and its p-torsion subgroup is a direct double if p  n . 2. (2) If n = 2k, let Π : X̄ 2k → X̄ 2 be the obvious map. Then Ker Π ∗ has even rank and its p-torsion subgroup is a direct double if p  k .

A. F. Losev as a Historian of Classical Culture

Over the course of A. F. Losev's many years of scholarly work, he has never paid special attention to the theory of culture as such. His research of many decades has been in the areas of literature, mythology, philosophy, logic, aesthetics, art, and language. Yet all his research is imbued with a single and carefully thought out conception of culture and the typology of cultural history. Briefly put, this conception consists in a view of culture as the historical and practical embodiment of actively pursued spiritual values at a given historical period. Anyone who has read Losev closely can think of works devoted to precisely that integral sphere of the development of the classical world where it is difficult to separate out either the material or the spiritual principles. In Losev's view this does not mean that one cannot study the history of material culture or of spiritual culture by themselves. Indeed, they can and must be given separate attention; and Losev himself has devoted many hundreds of pages ...

MEASUREMENT OF MINUTE RADIOMETRIC QUANTITIES IN THE SPECTRAL RANGE FROM VISIBLE TO NEAR INFRA-RED

This paper describes a method of calibrating the absolute spectral sensitivity of silicon photovoltaic cell. The cell was used for measuring minute radiant power, irradiance and radiant intensity of radiations, ranging from 0.4 μm to 1.1 μm. It was also used for measuring the external quantum efficiency of electroluminescent devices. The sensitivity of the system is higher than that of the conventional thermopile by three orders of magnitude. By incorporating with an integral sphere, it is very convenient to measure the radiant power, ranging from 6.3 nW to 310 mW, of any uniformly or non-uniformly distributed source.The maximum spectral efficiency Km was determined by using this system, and the accuracy of radiometrie system and photometric system was discussed. Finally, the measured optical parameters of some light-emitting diodes were examined.

Transformation groups resembling the adjoint representation

If G G is a compact, connected Lie group, the isotropy subgroups of the adjoint representation of G G are connected and the dimension of the fixed point set of a maximal torus of G G is equal to the the rank of G G . Results similar to these are given when G G acts differentiably on an integral cohomology sphere and has the adjoint representation as weak linear model. This is done by analyzing an induced action of the Weyl group of G G .

On Homogeneous Cohomology Spheres

A space is said to be a homogeneous integral cohomology k-sphere if it is a coset space G/H of a compact connected Lie group G by a closed (but not necessarily connected) subgroup Hand if HI(G/H; Z) = HI(Sk; Z) for all i. These spaces have recently come to be of some importance in the theory of transformation groups. When they arise in the study of general (nondifferentiable) transformation groups of a cohomology manifold (or of a manifold) it is usually not evident whether or not they are simply connected, let alone whether or not they are spheres. However, Borel has shown that if a homogeneous integral cohomology sphere is simply connected, then it is a sphere (see [2, 4.6], and also [3]). This fact for the even-dimensional case was also proved by H. C. Wang. On the other hand, there is a well-known example of such a space which is not simply connected. This is the quotient of SO (3) by the icosahedral subgroup I. It might be expected that there would be many more exceptional cases besides SO(3)/I, however we shall show that this is not the case. The purpose of this paper, then, is to prove that any homogeneous integral cohomology sphere G/H either is simply connected, is a circle, or is homeomorphic (naturally) to SO (3)/I. Thus, using the result of Borel, we will see that SO(3)/I is the only homogeneous integral cohomology sphere which is not a sphere. We shall use the following notation. If M and N are spaces and L is a ring then we say that M -, N if HI(M; L) HI(N; L). Z denotes the ring of integers and R denotes the field of rational numbers. If K is a compact Lie group, we denote the identity component of K by K0. We also let NG(K) be the normalizer of K in G, and Z0(K), the centralizer of K in G. We drop the subscript G when this causes no confusion. Aut (K) denotes the automorphism group of K and Int (K) denotes the group of inner automorphisms of K. If G, and G, are Lie groups then G1o G2 denotes a group of the form (G, x G2)/N, where N is a finite normal subgroup of G1 x G2, and similarly with any number of factors. That is,