Steffensen Methods for Solving Generalized Equations

2000 Mathematics Subject Classification: 65G99, 65K10, 47H04.

Generalized D-Symmetric Operators I

2000 Mathematics Subject Classification: Primary: 47B47, 47B10; secondary 47A30.

On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)

MSC 2010: 46F30, 46F10

Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term

2000 Mathematics Subject Classification: 34C10, 34C15.

Inverse Problems Involving Generalized Axial-Symmetric Helmholtz Equation

MSC 2010: 35J05, 33C10, 45D05

Number Sequences in an Integral Form with a Generalized Convolution Property and Somos-4 Hankel Determinants

MSC 2010: 11B83, 05A19, 33C45

Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

MSC2010: 30C45, 33C45

Bayesian and Frequentist Two-Sample Predictions of the Inverse Weibull Model Based on Generalized Order Statistics

2000 Mathematics Subject Classification: 62E16,62F15, 62H12, 62M20.

Generalized Derivations and Norm Equality in Normed Ideals

2000 Mathematics Subject Classification: 47A10, 47A12, 47A30, 47B10, 47B20, 47B37, 47B47, 47D50.

On the generalized Kato spectrum

2010 Mathematics Subject Classification: 47A10.

Contesting gender stereotypes stimulates generalized fairness in the selection of leaders

Exposure to counter-stereotypic gender role models (e.g., a woman engineer) has been shown to successfully reduce the application of biased gender stereotypes. We tested the hypothesis that such efforts may more generally lessen the application of stereotypic knowledge in other (non-gendered) domains. Specifically, based on the notion that counter-stereotypes can stimulate a lesser reliance on heuristic thinking, we predicted that contesting gender stereotypes would eliminate a more general group prototypicality bias in the selection of leaders. Three studies supported this hypothesis. After exposing participants to a counter-stereotypic gender role model, group prototypicality no longer predicted leadership evaluation and selection. We discuss the implications of these findings for groups and organizations seeking to capitalize on the benefits of an increasingly diverse workforce.

Strongly localized moving discrete dissipative breather-solitons in Kerr nonlinear media supported by intrinsic gain

We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau-type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in the absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations and slower, large-oscillation modes. The velocities and the oscillation periods are typically related by lattice commensurability and exhibit period-doubling bifurcations to chaotically "walking" modes under parameter variations. If the model is augmented by intersite Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime for moving solitons increases considerably, and a richer scenario appears including Hopf bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in the presence of weak disorder. © 2014 American Physical Society.

Generalized KPCA by adaptive rules in feature space

Principal component analysis (PCA) is well recognized in dimensionality reduction, and kernel PCA (KPCA) has also been proposed in statistical data analysis. However, KPCA fails to detect the nonlinear structure of data well when outliers exist. To reduce this problem, this paper presents a novel algorithm, named iterative robust KPCA (IRKPCA). IRKPCA works well in dealing with outliers, and can be carried out in an iterative manner, which makes it suitable to process incremental input data. As in the traditional robust PCA (RPCA), a binary field is employed for characterizing the outlier process, and the optimization problem is formulated as maximizing marginal distribution of a Gibbs distribution. In this paper, this optimization problem is solved by stochastic gradient descent techniques. In IRKPCA, the outlier process is in a high-dimensional feature space, and therefore kernel trick is used. IRKPCA can be regarded as a kernelized version of RPCA and a robust form of kernel Hebbian algorithm. Experimental results on synthetic data demonstrate the effectiveness of IRKPCA. © 2010 Taylor & Francis.

Medical conditions and depressive, anxiety, and somatic symptoms in older adults with and without generalized anxiety disorder

OBJECTIVE: The objective of this study was to examine medical illness and anxiety, depressive, and somatic symptoms in older medical patients with generalized anxiety disorder (GAD). METHOD: A case-control study was designed and conducted in the University of California, San Diego (UCSD) Geriatrics Clinics. A total of fifty-four older medical patients with GAD and 54 matched controls participated. MEASUREMENTS: The measurements used for this study include: Brief Symptom Inventory-18, Mini International Neuropsychiatric Interview, and the Anxiety Disorders Interview Schedule. RESULTS: Older medical patients with GAD reported higher levels of somatic symptoms, anxiety, and depression than other older adults, as well as higher rates of diabetes and gastrointestinal conditions. In a multivariate model that included somatic symptoms, medical conditions, and depressive and anxiety symptoms, anxiety symptoms were the only significant predictors of GAD. CONCLUSION: These results suggest first, that older medical patients with GAD do not primarily express distress as somatic symptoms; second, that anxiety symptoms in geriatric patients should not be discounted as a byproduct of medical illness or depression; and third, that older adults with diabetes and gastrointestinal conditions may benefit from screening for anxiety.

Generalized correlated equilibrium for two-person games in extensive form with perfect information

A correlation scheme (leading to a special equilibrium called “soft” correlated equilibrium) is applied for two-person finite games in extensive form with perfect information. Randomization by an umpire takes place over the leaves of the game tree. At every decision point players have the choice either to follow the recommendation of the umpire blindly or freely choose any other action except the one suggested. This scheme can lead to Pareto-improved outcomes of other correlated equilibria. Computational issues of maximizing a linear function over the set of soft correlated equilibria are considered and a linear-time algorithm in terms of the number of edges in the game tree is given for a special procedure called “subgame perfect optimization”.