Hoffman-Wielandt type inequality for block companion matrices of certain matrix polynomials

Matrix polynomials with unitary/doubly stochastic coefficients form the subject matter of this manuscript. We prove that if $P(\lambda)$ is a quadratic matrix polynomial whose coefficients are either unitary matrices or doubly stochastic matrices, then under certain conditions on these coefficients, the corresponding block companion matrix $C$ is diagonalizable. Consequently, if $Q(\lambda)$ is another quadratic matrix polynomial with corresponding block companion matrix $D$, then a Hoffman-Wielandt type inequality holds for the block companion matrices $C$ and $D$. Condiagonalizability of the block companion matrix of a matrix polynomial and a Hoffman-Wielandt type inequality involving coneigenvalues are also discussed.Comment: Title of the manuscript has been changed. Few more examples are added wherever necessar

The Hoffman-Wielandt (type) inequality for quaternion matrices and quaternion matrix polynomials

The purpose of this manuscript is to derive the Hoffman-Wielandt inequality and its most general form for quaternion matrices. Diagonalizabilty of the block companion matrix of certain quadratic (linear) quaternion matrix polynomials is brought out. As a consequence, we prove that if $Q(\lambda)$ is another quadratic (linear) quaternion matrix polynomial, then the Hoffman-Wielandt type inequality for their corresponding block companion matrices holds

Eigenvalue location of certain matrix polynomials

It is known that a matrix polynomial with unitary matrix coefficients has its eigenvalues in the annular region $\frac{1}{2} < |\lambda| < 2$. We prove in this short note that under certain assumptions, matrix polynomials with either doubly stochastic matrix coefficients or Schur stable matrix coefficients also have eigenvalues in similar annular regions

Computational Modeling of Business Processes

In this paper we investigate the modeling and analysis of business processes with the goal of improving their efficiency and effectiveness. The main objective of this research is to develop a computational model of business processes that takes into account relevant economic, social, organizational facets of a business process. The research develops a computational tool that will help uncover insights into the interdependencies among agents, activities, and resources in a business process

Improved time series prediction with a new method for selection of model parameters

A new method for model selection in prediction of time series is proposed. Apart from the conventional criterion of minimizing RMS error, the method also minimizes the error on the distribution of singularities, evaluated through the local Holder estimates and its probability density spectrum. Predictions of two simulated and one real time series have been done using kernel principal component regression (KPCR) and model parameters of KPCR have been selected employing the proposed as well as the conventional method. Results obtained demonstrate that the proposed method takes into account the sharp changes in a time series and improves the generalization capability of the KPCR model for better prediction of the unseen test data

A Rayleigh lidar study of the atmospheric temperature structure over Mt. Abu, India

A Nd-YAG laser based Rayleigh Lidar was set up at Guru Shikhar, Mount Abu (24.5° N, 72.7° E, altitude 1.7 km) by the Physical Research Laboratory to study the temperature structure in the altitude region of 30-75 km at tropical latitudes. Temperature profiles are derived from relative density measurements, following the method described by Hauchecorne &amp; Channin (1980). Photon counts are averaged over one hour (2 hour during the later phase) in time and 480 m in altitude. Measurements were made for about 5 nights of each month around new moon except the monsoon season (June-August). Temperature profiles obtained on 109 nights during the period November 1997 to November 2001 are used to derive average temperature profile for each month (September to May) and are compared with the CIRA-86 model. Observed temperature profiles are in good agreement with CIRA-86 below 50 km but are higher by up to 10 K above 50 km. The agreement is better during winter months. The temperature profiles are also compared with the equatorial model for the Indian region (Sasi &amp; Sengupta 1979) based on rocket and balloon measurements. Day to day variability is less than ± 5 K for altitudes below 50 km and up to ± 10 K around 70 km. The variability is the least around 40-50 km. The mean values of the stratopause level and temperature are found to be 48 km and 271 K respectively over the measurement site. Seasonal variation of the temperature below 60 km shows equinoctial and summer maxima whereas above 70 km winter maximum with equinoctial minima are seen

Origin and evolution of the zodiacal dust cloud

The astrophysical importance of the zodiacal cloud became more apparent. The most useful source of information on the structure of the zodiacal cloud is the Infrared Astronomical Satellite (IRAS) observations. A substantial fraction of the extensive IRAS data set was analyzed. Also, a numerical model was developed (SIMUL) that allows to calculate the distribution of night-sky brightness that would be produced by any particular distribution of dust particle orbits. This model includes the effects of orbital perturbations by both the planets and solar radiation, it reproduces the exact viewing geometry of the IRAS telescope, and allows for the eccentricity of the Earth's orbit. SIMUL now is used to model not just the solar system dust bands discovered by IRAS but the whole zodiacal cloud