The current discourse delves into the effectiveness of h-index 1 as an author level metric. It further reviews and explains the algorithmic complexity of calculating h-index through algebraic method. To conduct the algebraic analysis propositional algebra, algorithm and coding techniques have been used. Some use cases have been identified with a finite data set/set of array to demonstrate the coding techniques and for further analysis. Finally, the explanation and calculative complexities to determine the index have been further simplified through geometric method of calculating the h-index using the similar use cases that was used for coding. It is concluded that determination of the h-index using Euclidean geometric method with Cartesian frame of reference provides a through and visual clarification. Finally, a set of postulates has been proposed at the end of the paper, based on the case studies.

It is proposed that when a charge current circulates in a paramagnetic metal a transverse spin imbalance will be generated, giving rise to a 'spin Hall voltage'. Similarly, that when a spin current circulates a transverse charge imbalance will be generated, hence a Hall voltage, in the absence of charge current and magnetic field. Based on these principles we propose an experiment to generate and detect a spin current in a paramagnetic metal.Consider the 'spontaneous' or 'anomalous' Hall effect [1]. In ferromagnetic metals, the Hall resistivity (transverse electric field per unit longitudinal current density) is found to be empirically fitted by the formula(in cgs units), with B the applied magnetic field and M the magnetization per unit volume. R o is the ordinary Hall coefficient and R s the 'anomalous' Hall coefficient, experimentally found to be generally substantially larger than the ordinary Hall coefficient as well as strongly temperature-dependent. Within models that assume that the electrons giving rise to magnetism in ferromagnetic metals are itinerant, a variety of mechanisms have been proposed to explain the origin of the coefficient R s . These include skew scattering by impurities and phonons, and the 'side jump' mechanism. In early work it was also proposed that the effect will arise in the absence of periodicity-breaking perturbations [2], but this is generally believed not to be correct [1]. In this paper we will not discuss the origin of the anomalous Hall effect [3]. Rather, we take the existence of the effect in ferromagnetic metals as experimental proof that electrons carrying a spin and associated magnetic moment experience a transverse force when they are moving in a longitudinal electric field, for any of the reasons listed above or others. If there is a net magnetization in the system there will be a magnetization current associated with the flow of electric current, and the transverse force will give rise to a charge imbalance in direction perpendicular to the current flow and hence to an anomalous Hall effect.Consider then the situation where no magnetization exists, that is, a paramagnetic metal or doped semiconductor, or a ferromagnetic metal above its Curie point, carrying a charge current in the x direction. The electrons still carry a spin, and the same scattering mechanism(s) that gave rise to the anomalous Hall effect in the magnetic case will scatter electrons with spin up preferentially in one direction perpendicular to the flow of current, and spin down electrons preferentially in the opposite direction. Here we have in mind a slab geometry as usually used in Hall effect experiments, and spin up and spin down directions are defined perpendicular to the plane of the slab. Because there is equal number of spin up and spin down electrons no charge imbalance will result, but we argue that a spin imbalance will: there will be an excess of up spins on one side of the sample and of down spins on the opposite side. The situation is depicted schematically in Figure 1.Although it may a...

To evaluate the validity and reliability of the Ocular Surface Disease Index (OSDI) questionnaire. Methods: Participants (109 patients with dry eye and 30 normal controls) completed the OSDI, the National Eye Institute Visual Functioning Questionnaire (NEI VFQ-25), the McMonnies Dry Eye Questionnaire, the Short Form-12 (SF-12) Health Status Questionnaire, and an ophthalmic examination including Schirmer tests, tear breakup time, and fluorescein and lissamine green staining. Results: Factor analysis identified 3 subscales of the OSDI: vision-related function, ocular symptoms, and environmental triggers. Reliability (measured by Cronbach ␣) ranged from good to excellent for the overall instrument and each subscale, and test-retest reliability was good to excellent. The OSDI was valid, effectively discriminating between normal, mild to moderate, and severe dry eye disease as defined by both physician's assessment and a composite disease severity score. The OSDI also correlated significantly with the McMonnies questionnaire, the National Eye Institute Visual Functioning Questionnaire, the physical component summary score of the Short Form-12, patient perception of symptoms, and artificial tear usage. Conclusions: The OSDI is a valid and reliable instrument for measuring the severity of dry eye disease, and it possesses the necessary psychometric properties to be used as an end point in clinical trials.

We have studied the two-dimensional Hubbard model on a square lattice with nearest-neighbor hopping. We first discuss the properties of the model within the mean-field approximation: Because of the form of the band structure, some peculiar features are found. We then discuss the simulation algorithm used and compare simulation results with exact results for 6-site chains to test the reliability of the approach. We present results for thermodynamic properties and correlation functions for lattices up to 8&&8 in spatial size. The system is found to be an antiferromagnetic insulator for all values of the coupling constant at zero temperature in the half-filled-band case, but the long-range order is much smaller than predicted by mean-field theory. We perform a finitesize-scaling analysis to determine the character of the transition at zero coupling. For non-halffilled-band cases, our results suggest that the system is always paramagnetic, in contradiction with Hartree-Fock predictions. The system does not show tendency to ferromagnetism nor triplet superconductivity in the parameter range studied. We also discuss some properties of the attractive Hubbard model in the half-filled-band case.

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Bibliometric measures of individual scientific achievement are of particular interest if they can be used to predict future achievement. Here we report results of an empirical study of the predictive power of the h index compared with other indicators. Our findings indicate that the h index is better than other indicators considered (total citation count, citations per paper, and total paper count) in predicting future scientific achievement. We discuss reasons for the superiority of the h index.citations ͉ prediction ͉ achievement T he h index of a researcher is the number of papers coauthored by the researcher with at least h citations each (1). We have recently proposed it as a representative measure of individual scientific achievement. Other commonly used bibliometric measures of individual scientific achievement are total number of papers published (N p ) and total number of citations garnered (N c ). Recently, Lehmann et al. (2,3) have argued that the mean number of citations per paper (n c ϭ N c /N p ) is a superior indicator. Here we wish to address the question: which of these four measures is best able to predict future scientific achievement?For the purposes of this article, we do not wish to dwell on the controversial question of what is the optimal definition of scientific achievement.† We are not interested in measuring the past achievement of an individual, e.g., for the purpose of awarding a prize or for election to a prestigious academy, but rather in predicting future achievement. So we could simply bypass this question by defining ''scientific achievement'' by the bibliometric measure under consideration and ask: which measure is better able to predict its future values? For example, how likely is a researcher who today has a large number of citations to gain a large number of citations in future years? To the extent that a bibliometric measure ref lects particular traits of the researcher rather than random events, it should have higher predictive power than another measure that is more dependent on random events. For example, we argued in ref. 1 that the total number of citations, N c , ''may be inf lated by a small number of 'big hits,' which may not be representative of the individual if he/she is coauthor with many others on those papers.'' For that individual, the present N c value is not likely to be a good predictor of his/her future N c values.Alternatively, among the indicators listed in the first paragraph, it may be argued that the total number of citations, N c , is the one that best reflects scientific achievement because it gives a measure of the integrated impact of a scientist's work on the work of others. Then, we would like to know: which indicator is best able to predict N c at a future time? It is certainly not obvious that the answer is N c itself.There are two slightly different questions of interest. (i) Given the value of an indicator at time t 1 , I(t 1 ), how well does it predict the value of itself or of another indicator at a future time t 2 , IЈ(t 2 )? This quest...

%e investigate the three-dimensional Hubbard model and show that paramagnon exchange near a spin-density-wave instability gives rise to a strong singlet d-wave pairing interaction. For a cubic band the singlet (d"~~and d3,a, 2) channels are enhanced while the singlet (d,~,d",d",) and triplet p-wave channels are suppressed. A unique feature of this pairing mechanism is its sensitivity to band structure and band filling.Pairing interactions for continuum fermion systems with short-range repulsive interactions have been modeled in terms of paramagnon exchange. ' 3 Here the bare singleparticle energies are described in terms of an effective mass, and the Fermi surface is spherical. As the strength

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