Existence theorem for a generalized Hammerstein type equation

An existence theorem is obtained for a generalized Hammerstein type equation

A phase space approach to generalized Hamilton–Jacobi theory

Generalizations of H–J theory have been discussed before in the literature. The present approach differs from others in that it employs geometrical ideas on phase space and classical transformation theory to derive the basic equations. The relation between constants of motion and symmetries of the generalized H–J equations is then clarified. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Solution of a generalized Korteweg—de Vries equation

The solitary-wavelike solution of the generalized Korteweg-de Vries equation with mixed nonlinearity is obtained. Two asymptotic cases of the solution have been discussed and solitary wave solutions have been derived. ©1974 American Institute of Physics.

Regularized numerical integration of multibody dynamics with the generalized alpha method*

This paper discusses the consistent regularization property of the generalized α method when applied as an integrator to an initial value high index and singular differential-algebraic equation model of a multibody system. The regularization comes from within the discretization itself and the discretization remains consistent over the range of values the regularization parameter may take. The regularization involves increase of the smallest singular values of the ill-conditioned Jacobian of the discretization and is different from Baumgarte and similar techniques which tend to be inconsistent for poor choice of regularization parameter. This regularization also helps where pre-conditioning the Jacobian by scaling is of limited effect, for example, when the scleronomic constraints contain multiple closed loops or singular configuration or when high index path constraints are present. The feed-forward control in Kane's equation models is additionally considered in the numerical examples to illustrate the effect of regularization. The discretization presented in this work is adopted to the first order DAE system (unlike the original method which is intended for second order systems) for its A-stability and same order of accuracy for positions and velocities.

Solution of a generalized Korteweg-de Vries equation

The solitary-wavelike solution of the generalized Korteweg-de Vries equation with mixed nonlinearity is obtained. Two asymptotic cases of the solution have been discussed and solitary wave solutions have been derived.

Gross Family Collection 1874-1895

The collection contains the marriage contract of the merchant Lazarus Gross and Carla Hecht from 1874. Also included is a ‘Zeugnisbüchlein’ - school certificates – from Badische Volksschule for their daughter, Meta Gross (1888-1895).

On a generalized dynamic model of bi-state social interaction processes

A non-linear model, construed as a generalized version of the models put forth earlier for the study of bi-state social interaction processes, is proposed in this study. The feasibility of deriving the dynamics of such processes is demonstrated by establishing equivalence between the non-linear model and a higher order linear model.

Symmetries and constraints in generalized Hamiltonian dynamics

A general analysis of symmetries and constraints for singular Lagrangian systems is given. It is shown that symmetry transformations can be expressed as canonical transformations in phase space, even for such systems. The relation of symmetries to generators, constraints, commutators, and Dirac brackets is clarified.

Generalized aerodynamic noise equation

An exact aerodynamic noise equation is formulated for Newtonian fluids. The cause−effect problem is discussed. Finally, the importance of external additions of mass, momentum, and energy is examined. Physics of Fluids is copyrighted by The American Institute of Physics.

Rank-Augmented LU-Algorithm for Computing Generalized Matrix Inverses

A rank-augmnented LU-algorithm is suggested for computing a generalized inverse of a matrix. Initially suitable diagonal corrections are introduced in (the symmetrized form of) the given matrix to facilitate decomposition; a backward-correction scheme then yields a desired generalized inverse.

A Generalized Approach to Multiresolution Complex SAR Signal Processing

Multiresolution synthetic aperture radar (SAR) image formation has been proven to be beneficial in a variety of applications such as improved imaging and target detection as well as speckle reduction. SAR signal processing traditionally carried out in the Fourier domain has inherent limitations in the context of image formation at hierarchical scales. We present a generalized approach to the formation of multiresolution SAR images using biorthogonal shift-invariant discrete wavelet transform (SIDWT) in both range and azimuth directions. Particularly in azimuth, the inherent subband decomposition property of wavelet packet transform is introduced to produce multiscale complex matched filtering without involving any approximations. This generalized approach also includes the formulation of multilook processing within the discrete wavelet transform (DWT) paradigm. The efficiency of the algorithm in parallel form of execution to generate hierarchical scale SAR images is shown. Analytical results and sample imagery of diffuse backscatter are presented to validate the method.

Generalized self-assembly of scalable two-dimensional transition metal oxide nanosheets

Two-dimensional (2D) transition metal oxide systems present exotic electronic properties and high specific surface areas, and also demonstrate promising applications ranging from electronics to energy storage. Yet, in contrast to other types of nanostructures, the question as to whether we could assemble 2D nanomaterials with an atomic thickness from molecules in a general way, which may give them some interesting properties such as those of graphene, still remains unresolved. Herein, we report a generalized and fundamental approach to molecular self-assembly synthesis of ultrathin 2D nanosheets of transition metal oxides by rationally employing lamellar reverse micelles. It is worth emphasizing that the synthesized crystallized ultrathin transition metal oxide nanosheets possess confined thickness, high specific surface area and chemically reactive facets, so that they could have promising applications in nanostructured electronics, photonics, sensors, and energy conversion and storage devices.