Non-zero Index Research Articles

Interfacial electronic structure of magnesium deposited on Ag-covered tris(8-hydroxyquinolato) aluminum film: A synchrotron radiation photoemission study

The deposition of magnesium on tris(8-hydroxyquinolato) aluminum (Alq3) precovered with thin silver was investigated with high resolution synchrotron radiation photoemission. The noble-metal deposit first occupies the vicinity of the pyridyl ring. The appearance of a Fermi level suggests that the incorporated Ag behaves as a metallic cluster, consistent with the results of the Ag 3d cores, which show a nonzero Doniach-Sunjic singularity index of 0.061. Upon Mg adsorption on the Ag∕Alq3 surface, a MgAg mixture begins to develop such that the Ag 4d valence band becomes narrowed and its centroid shifts towards higher binding energy. A phase transformation is thus observed at the interface, from a Ag-rich phase to a Mg-rich phase. The product of the MgAg mixture prevents subsequent Mg atoms from penetrating into the Alq3 film, which grows as a metal on top of the MgAg∕Alq3 interface.

The index of the overlap Dirac operator on a discretized 2d non-commutative torus

The index, which is given in terms of the number of zero modes of the Dirac operator with definite chirality, plays a central role in various topological aspects of gauge theories. We investigate its properties in non-commutative geometry. As a simple example, we consider the U(1) gauge theory on a discretized 2d non-commutative torus, in which general classical solutions are known. For such backgrounds we calculate the index of the overlap Dirac operator satisfying the Ginsparg-Wilson relation. When the action is small, the topological charge defined by a naive discretization takes approximately integer values, and it agrees with the index as suggested by the index theorem. Under the same condition, the value of the index turns out to be a multiple of N, the size of the 2d lattice. By interpolating the classical solutions, we construct explicit configurations, for which the index is of order 1, but the action becomes of order N. Our results suggest that the probability of obtaining a non-zero index vanishes in the continuum limit, unlike the corresponding results in the commutative space.

Index Theorem in Finite Noncommutative Geometry

Noncommutative (NC) geometry is interesting since it is related to string theories and matrix models,1)–3) and it may capture some nature of quantum gravity. It is also a candidate for a new regularization of quantum field theory.4) Study about topological aspects of gauge theory on it is important since compactification of extra dimensions with nontrivial index in string theory can realize chiral gauge theory in our spacetime. Ultimately, we hope to realize such a mechanism dynamically, for instance, in IIB matrix model5) where spacetime structure has been studied intensively.6),7) Unusual properties of NC geometry may also provide a solution of strong CP problem and baryon asymmetry of the universe. Index theorem plays a key role in these studies. While it can be proved in theories with infinite degrees of freedom,8),9) it becomes a nontrivial issue in finite cases. This problem was solved in lattice gauge theory by using Ginsparg-Wilson (GW) relation,10)–13) and this idea has been successfully extended to the NC geometry. We have provided a general prescription to construct a GW Dirac operator with coupling to non-vanishing gauge field backgrounds on general finite NC geometries.14) Owing to the GW relation, an index theorem can be proved even for finite NC geometries. The index takes only integer values by construction, and it is shown to become the corresponding topological charge as the number of degrees of freedom is properly taken to infinity. While explicit construction has been provided for the fuzzy 2sphere14),15) and for the NC torus,16),17) it is possible for other cases, which will be reported in future publication. As a topologically nontrivial configuration on the fuzzy 2-sphere, we constructed ’t Hooft-Polyakov (TP) monopole configuration.18),19) We further presented a mechanism for dynamical generation of a nontrivial index, by showing that the TP monopole configurations are stabler than the topologically trivial sector in the YangMills-Chern-Simons matrix model.20) However, in order to obtain non-zero indices for these configurations, one needs to introduce a projection operator in the definition of the index. We gave an interpretation for the projection operator, and extended the index theorem to general configurations which do not necessarily satisfy the equation of motion.21) Since the U(2) gauge theory on the fuzzy sphere

The Expected Area of the Filled Planar Brownian Loop is π/5

Let B_t be a planar Brownian loop of time duration 1 (a Brownian motion conditioned so that B_0 = B_1). We consider the compact hull obtained by filling in all the holes, i.e. the complement of the unique unbounded component of R^2\B[0,1]. We show that the expected area of this hull is Pi/5. The proof uses, perhaps not surprisingly, the Schramm Loewner Evolution (SLE). Also, using the result of Yor about the law of the index of a Brownian loop, we show that the expected areas of the regions of non-zero index n equal 1/(2 Pi n^2). As a consequence, we find that the expected area of the region of index zero inside the loop is Pi/30; this value could not be obtained directly using Yor's index description.

Évaluation de la prise en charge initiale des entorses graves du genou (à propos d’une étude prospective faite aux urgences du CHU de brest)

Bundled payment programs and the Centers for Medicare and Medicaid Services removal of total knee arthroplasty (TKA) from the inpatient-only list potentially incentivize avoiding patients with extended length of stay (eLOS) and nonhome discharge (NHD). We aimed to describe which patients are most at risk of eLOS (>2 days), very eLOS (veLOS; >4 days), and NHD.Admissions for unilateral TKAs at 151 Illinois nonfederal hospitals from January 2016 to June 2018 were selected from the Illinois Hospital and Health Systems Association COMPdata administrative hospital discharge database. Records included patient age, race and ethnicity, Illinois region, insurance status, principal diagnosis, and date of procedure. Zip code level median household income, Charlson comorbidity index, and obesity status were computed. Hospitals were characterized through their bundled payment participation status, academic status, and annual knee replacement volume. Poisson regression was used to test the associations between patient and hospital characteristics and the likelihood of eLOS, veLOS, and NHD.Of the 72,359 admissions included, 25.0% had an NHD, 41.1% had eLOS, and 4.0% veLOS. Female patients, those 75 years old or more as compared to those 65-74 years old, non-Hispanic blacks, Hispanics and Asians versus non-Hispanic whites, Medicaid/uninsured patients versus those privately insured, obese patients, those with nonzero Charlson comorbidity index, and those treated at low-volume hospitals (<200 TKAs/year vs >600 TKAs/year) were more likely to have eLOS, veLOS, and/or NHD (P < .05).Arthroplasty surgeons may be incentivized to avoid the abovementioned patient groups due to bundled payment programs and recent Centers for Medicare and Medicaid Services legislation.

Quantum interferences from cross talk in J = 1/2 ↔ J = 1/2 transitions

We consider the possibility of a control field opening up multiple pathways and thereby leading to new interference and coherence effects. We illustrate the idea by considering the J=1/2↔J=1/2 transition. As a result of the additional pathways, we show the possibilities of nonzero refractive index without absorption and gain without inversion. We explain these results in terms of the coherence produced by the opening of an extra pathway.

Inverse spectral theory for symmetric operators with several gaps: scalar-type Weyl functions

Let S be the orthogonal sum of infinitely many pairwise unitarily equivalent symmetric operators with non-zero deficiency indices. Let J be an open subset of R . If there exists a self-adjoint extension S 0 of S such that J is contained in the resolvent set of S 0 and the associated Weyl function of the pair { S , S 0 } is monotone with respect to J, then for any self-adjoint operator R there exists a self-adjoint extension S ˜ such that the spectral parts S ˜ J and R J are unitarily equivalent. It is shown that for any extension S ˜ of S the absolutely continuous spectrum of S 0 is contained in that one of S ˜ . Moreover, for a wide class of extensions the absolutely continuous parts of S ˜ and S are even unitarily equivalent.

Amphiphilicity index of polar amino acids as an aid in the characterization of amino acid preference at membrane-water interfaces.

An amphiphilicity index of amino acid residues was developed for improving the method of transmembrane helix prediction. The transfer energy of a hydrocarbon stem group beyond the gamma-carbon was calculated from the accessible surface area, and used to index the amphiphilicity of the residue. Non-zero amphiphilicity index values were obtained for lysine, arginine, histidine, glutamic acid, glutamine, tyrosine and tryptophan. Those residues were found to be abundant in the end regions of transmembrane helices, indicating their preference for the membrane-water interface. The moving average of the amphiphilicity index actually showed significant peaks in the end regions of most transmembrane helices. A dispersion diagram of average amphiphilicity index versus average hydrophobicity index was devised to facilitate discrimination of transmembrane helices. The amphiphilicity index has been incorporated into a system, SOSUI, for the discrimination of membrane proteins and the prdiction of tranmembrane helical regions (http://sosui.proteome.bio.tuat.ac.jp/sosuiframe0.html).

Spin-independent transverse shift of the centre of gravity of a reflected and of a refracted light beam

The new linear and angular transverse shifts (LTS and ATS) of the centres of gravity of partially reflected and of refracted light beams are predicted. Unlike the previously known LTS and ATS, the new ones can exist at an arbitrary polarization of the incident beam. The new LTS should take place at reflection and refraction of a light beam with non-zero orbital angular momentum, particularly, of the Laguerre–Gaussian beam with non-zero azimuthal index. A parallel between the new LTS of a partially reflected light beam and the Goos–Hänchen shift is drawn.

Singular sector of the Kadomtsev–Petviashvili hierarchy, ∂̄ operators of nonzero index, and associated integrable systems

Integrable hierarchies associated with the singular sector of the Kadomtsev–Petviashvili (KP) hierarchy, or equivalently, with ∂̄ operators of nonzero index are studied. They arise as the restriction of the standard KP hierarchy to submanifolds of finite codimension in the space of independent variables. For higher ∂̄ index these hierarchies represent themselves as families of multidimensional equations with multidimensional constraints. The ∂̄-dressing method is used to construct these hierarchies. Hidden Korteweg–de Vries, Boussinesq, and hidden Gelfand–Dikii hierarchies are considered, too.

Asymptotic uniform linearity of some robust statistics under exponentially subordinated strongly dependent models

In this paper, we discuss an asymptotic distributional theory of three broad classes of robust estimators of the regression parameter namely, L-, M- and R-estimators in a linear regression model when the errors are generated by an exponentially subordinated strongly dependent process. The results are obtained as a consequence of an asymptotic uniform Taylor-type expansion of certain randomly weighted empirical processes. The limiting distributions of the estimators are nonnormal and depend on the first nonzero index of the Laguerre polynomial expansion of a class of indicator functions of the error random variables.

A fixed point index for equivariant maps

The purpose of the paper is to define a fixed point index for equivariant maps of $G$-ENR's and to state and prove some of its properties, such as the compactly fixed $G$-homotopy property, the Lefschetz property, its converse, and the retraction property. At the end, some examples are given of equivariant self-maps which have a nonzero index (hence cannot be deformed equivariantly to be fixed point free) but have a zero $G$-Nielsen invariant.

Solutions of the Ginsparg-Wilson relation

We analyze general solutions of the Ginsparg-Wilson relation for lattice Dirac operators and formulate a necessary condition for such operators to have non-zero index in the topologically nontrivial background gauge fields.

Genetic-diet interactions in the hyperkalemic periodic paralysis syndrome in quarter horses fed varying amounts of potassium: III. The relationship between plasma potassium concentration and HYPP Symptoms

Summary Six broodmares that were DNA tested to be heterozygous (H/N) and six broodmares that were tested to be homozygous negative (N/N) for Equine Hyperkalemic periodic Paralysis (HYPP), that were descendents of the same stallion, were used in a replicated 3x3 Latin square experiment to determine the genetic-diet relationships in the HYPP syndrome. 1 The mares were fed rations consisting of 65% pelleted concentrate and 35% Coastal Bermuda grass hay that provided 1.1 (diet A), 1.9 (diet B) and 2.9% (diet C) potassium in two evenly spaced meals per day. The experimental periods were 14 days long, resulting in 28 meals per period. The HYPP Symptoms Index was greater at meal 1 than meal 27 and greater when the horses were fed diet C than diet B. Plasma K + concentrations at the onset of symptoms were not different by diet or meal and averaged 3.78 mmol/L. The average time of onset of symptoms was two hours and 33 minutes after the beginning of a meal, which was not different by diet or meal. A regression analysis of 204 paired non-zero HYPP Symptoms Index values and their corresponding plasma K + concentrations at the same times, from the HYPP H/N horses, resulted in an R 2 of .449. While fed diet A, the horses' mean plasma K + values remained below 3.5 mmol/L, and no symptoms were observed. Generally, an increase in Symptoms Index followed increased plasma K + concentration when the horses were fed diets B and C at meal 1. At meal 27, the mean HYPP Symptoms Index and average plasma K + values were lower than at meal 1. However, there were increased plasma K + concentrations observed in the later post-prandial hours after meal 27, when the horses were fed diet B, that did not correspond to HYPP symptoms. In a pilot study, one horse collapsed into sternal recumbency after meal 1 when her HYPP Symptoms Index was 10 and her plasma K + concentration was 7.29 mmol/L. This horse spontaneously recovered from the episode. By meal 27, both the peak plasma K + concentration (4.6 mmol/L) and the peak HYPP Symptoms Index (1) were smaller in this horse, but they still occurred simultaneously.

Thouless energy and correlations of QCD Dirac eigenvalues

Eigenvalues and eigenfunctions of the QCD Dirac operator are studied for gauge field configurations given by a liquid of instantons. We find that for energy differences δE below an energy scale E c the eigenvalue correlations are given by random matrix theories with the chiral symmetries of the QCD partition function. For eigenvalues near zero this energy scale shows a weak volume dependence that is not consistent with E c ∼ 1 L 2 which might be expected from the pion Compton wavelength and from the behavior of the Thouless energy in mesoscopic systems. However, the numerical value of E c for our largest volumes is in rough agreement with estimates from the pion Compton wavelength. A scaling behavior consistent with E c ∼ 1/ L 2 is found in the bulk of the spectrum. For δE > E c the number variance shows a linear dependence with a slope which is larger than the non-zero multifractality index of the wave functions. Finally, the average spectral density and the scalar susceptibilities are discussed in the context of quenched chiral perturbation theory. We argue that a non-zero value of the disconnected scalar susceptibility requires a linear dependence of the number variance on δE. © 1998 Elsevier Science B.V.

Thouless Energy and Correlations of QCD Dirac Eigenvalues

Eigenvalues and eigenfunctions of the QCD Dirac operator are studied for an instanton liquid partition function. We find that for energy differences $\ensuremath{\delta}E$ below an energy scale ${E}_{c}$, identified as the Thouless energy, the eigenvalue correlations are given by random matrix theory. The value of ${E}_{c}$ shows a weak volume dependence for eigenvalues near zero and is consistent with a scaling of ${E}_{c}\ensuremath{\sim}1/{L}^{2}$ in the bulk of the spectrum in agreement with estimates from chiral perturbation theory that ${E}_{c}/\ensuremath{\Delta}\ensuremath{\approx}{F}_{\ensuremath{\pi}}^{2}{L}^{2}/\ensuremath{\pi}$ (with average level spacing $\ensuremath{\Delta}$). For $\ensuremath{\delta}E&gt;{E}_{c}$ the number variance shows a linear dependence. For the wave functions we find a small nonzero multifractality index.

An index theorem for Toeplitz operators on totally ordered groups

We show that for every totally ordered group Γ \Gamma and invertible function f ∈ C ( Γ ^ ) f\in C(\widehat \Gamma ) which does not have a logarithm, there is a representation in which the Toeplitz operator T f T_f is a Breuer-Fredholm operator with nonzero index; this representation is the GNS-representation associated to a natural unbounded trace on the Toeplitz algebra T ( Γ ) \mathcal T(\Gamma ) .

Integrable systems for ∂ operators of non-zero index

∂ operators with non-zero index are found to be associated with integrable hierarchies arising by restricting the KP hierarchy to submanifolds of finite codimension in the space of independent variables.

Effect of the Core Size on the Higher Order Modes of a Chirofiber Filled with Different Core and Cladding Chiralities

The present paper discusses the properties of higher order modes (i.e. modes corresponding to a non-zero first modal index v ≠ 0) for a chirofiber filled with different chiralities in the core and the cladding. The variation of the propagation constant s with the core radius shows a fluctuating nature for all these modes confirming and extending a previously reported result corresponding to v = 0. The presence of chirality has the general effect of increasing the number of propagating modes that can be sustained.

Periodic solutions of autonomous systems under discretization *

The existence of a sequence of periodic trajectories of a general one-step numerical scheme corresponding to a null sequence of constant time-steps is established under the assumption that the autonomous ordinary differential equation has an isolated periodic solution with non-zero topological index. The convergence of the linearly interpolated numerical curve to the original invariant curve with respect to the Hausdorff metric is also shown.