Computing and Visualizing Solution Sets of Interval Linear Systems

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Reasoning Methods for Designing and Surveying Relationships Described by Sets of Functional Constraints

This work is supported by the Hungarian Scientific Research Fund (OTKA), grant T042706.

On Representations of Algebraic Polynomials by Superpositions of Plane Waves

* The author was supported by NSF Grant No. DMS 9706883.

Description Reduction for Restricted Sets of (0,1) Matrices

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function

2000 Mathematics Subject Classification: 26A33, 33C45

Characterizations of the Solution Sets of Generalized Convex Minimization Problems

2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20.

On a Summability Method Defined by Means of Hermite Polynomials

Георги С. Бойчев - В статията се разглежда метод за сумиране на редове, дефиниран чрез полиномите на Ермит. За този метод на сумиране са дадени някои Тауберови теореми.

Extremes of Bivariate Geometric Variables with Application to Bisexual Branching Processes

2000 Mathematics Subject Classification: 60J80, 60G70.

On the Remainders Obtained in Finding the Greatest Common Divisor of Two Polynomials

In 1917 Pell (1) and Gordon used sylvester2, Sylvester’s little known and hardly ever used matrix of 1853, to compute(2) the coefficients of a Sturmian remainder — obtained in applying in Q[x], Sturm’s algorithm on two polynomials f, g ∈ Z[x] of degree n — in terms of the determinants (3) of the corresponding submatrices of sylvester2. Thus, they solved a problem that had eluded both J. J. Sylvester, in 1853, and E. B. Van Vleck, in 1900. (4) In this paper we extend the work by Pell and Gordon and show how to compute (2) the coefficients of an Euclidean remainder — obtained in finding in Q[x], the greatest common divisor of f, g ∈ Z[x] of degree n — in terms of the determinants (5) of the corresponding submatrices of sylvester1, Sylvester’s widely known and used matrix of 1840. (1) See the link http://en.wikipedia.org/wiki/Anna_Johnson_Pell_Wheeler for her biography (2) Both for complete and incomplete sequences, as defined in the sequel. (3) Also known as modified subresultants. (4) Using determinants Sylvester and Van Vleck were able to compute the coefficients of Sturmian remainders only for the case of complete sequences. (5) Also known as (proper) subresultants.

Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type

MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32

Primary data sets of the hydrographic atlas of the Southern Ocean

The general knowledge of the hydrographic structure of the Southern Ocean is still rather incomplete since observations particularly in the ice covered regions are cumbersome to be carried out. But we know from the available information that thermohaline processes have large amplitudes and cover a wide range of scales in this part of the world ocean. The modification of water masses around Antarctica have indeed a worldwide impact, these processes ultimately determine the cold state of the present climate in the world ocean. We have converted efforts of the German and Russian polar research institutions to collect and validate the presently available temperature, salinity and oxygen data of the ocean south of 30°S latitude. We have carried out this work in spite of the fact that the hydrographic programme of the World Ocean Circulation Experiment (WOCE) will provide more new information in due time, but its contribution to the high latitudes of the Southern Ocean is quite sparse. The modified picture of the hydrographic structure of the Southern Ocean presented in this atlas may serve the oceanographic community in many ways and help to unravel the role of this ocean in the global climate system. This atlas could only be prepared with the altruistic assistance of many colleagues from various institutions worldwide who have provided us with their data and their advice. Their generous help is gratefully acknowledged. During two years scientists from the Arctic and Antarctic Research Institute in St. Petersburg and the Alfred Wegener Institute for Polar and Marine Research in Bremerhaven have cooperated in a fruitful way to establish the atlas and the archive of about 38749 validated hydrographic stations. We hope that both sources of information will be widely applied for future ocean studies and will serve as a reference state for global change considerations.

Of sets of offsets: Cumulative impacts and strategies for compensatory restoration

Biodiversity offsets are increasingly advocated as a flexible approach to managing the ecological costs of economic development. Arguably, however, this remains an area where policy-making has run ahead of science. A growing number of studies identify limitations of offsets in achieving ecologically sustainable outcomes, pointing to ethical and implementation issues that may undermine their effectiveness. We develop a novel system dynamic modelling framework to analyze the no net loss objective of development and biodiversity offsets. The modelling framework considers a marine-based example, where resource abundance depends on a habitat that is affected by a sequence of development projects, and biodiversity offsets are understood as habitat restoration actions. The model is used to explore the implications of four alternative offset management strategies for a regulator, which differ in how net loss is measured, and whether and how the cumulative impacts of development are considered. Our results confirm that, when it comes to offsets as a conservation tool, the devil lies in the details. Approaches to determining the magnitude of offsets required, as well as their timing and allocation among multiple developers, can result in potentially complex and undesired sets of economic incentives, with direct impacts on the ability to meet the overall objective of ecologically sustainable development. The approach and insights are of direct interest to conservation policy design in a broad range of marine and coastal contexts.

A Study on the Correlation of Bivariate And Trivariate Normal Models

Suppose two or more variables are jointly normally distributed. If there is a common relationship between these variables it would be very important to quantify this relationship by a parameter called the correlation coefficient which measures its strength, and the use of it can develop an equation for predicting, and ultimately draw testable conclusion about the parent population. This research focused on the correlation coefficient ρ for the bivariate and trivariate normal distribution when equal variances and equal covariances are considered. Particularly, we derived the maximum Likelihood Estimators (MLE) of the distribution parameters assuming all of them are unknown, and we studied the properties and asymptotic distribution of . Showing this asymptotic normality, we were able to construct confidence intervals of the correlation coefficient ρ and test hypothesis about ρ. With a series of simulations, the performance of our new estimators were studied and were compared with those estimators that already exist in the literature. The results indicated that the MLE has a better or similar performance than the others.