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Search Results: 1 - 10 of 2088 matches for " Allan Pinkus "
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Density in Approximation Theory
Allan Pinkus
Surveys in Approximation Theory , 2005,
Abstract: Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the possibility of approximation. Is the given family of functions from which we plan to approximate dense in the set of functions we wish to approximate? In this work, we survey some of the main density results and density methods.
Density in Approximation Theory
Allan Pinkus
Mathematics , 2005,
Abstract: Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the {\it possibility of approximation}. Is the given family of functions from which we plan to approximate dense in the set of functions we wish to approximate? In this work we survey some of the main density results and density methods.
Strictly Hermitian Positive Definite Functions
Allan Pinkus
Mathematics , 2004,
Abstract: Let H be any complex inner product space with inner product <, >. We say that f : C -->C is Hermitian positive definite on H if the matrix $$(f())_{r,s=1}^n \eqno(*)$$ is Hermitian positive definite for all choice of z^1,...,z^n in H, all n. It is strictly Hermitian positive definite if the matrix (*) is also non-singular for any choice of distinct z^1,...,z^n in H. In this article we prove that if dim H >= 3, then f is Hermitian positive definite on H if and only if $$f(z) = \sum_{k,m =0}^\infty b_{k,m} z^k \oz^m \eqno(**)$$ where \oz is the conjugate of z, b_{k,m}>= 0, all k,m in Z_+, and the series converges for all z in C. We also prove that f of the form (**) is strictly Hermitian positive definite on any H if and only if the set $$J={(k, m) : b_{k,m}> 0}$$ is such that (0,0) is in J, and every arithmetic sequence in Z intersects the values {k-m : (k,m)\in J} an infinite number of times.
Strong Uniqueness
Andras Kroo,Allan Pinkus
Mathematics , 2010,
Abstract: This is a survey paper on the subject of strong uniqueness in approximation theory.
Strong Uniqueness
András Kroó,Allan Pinkus
Surveys in Approximation Theory , 2010,
Abstract: This is a survey on the subject of strong uniqueness in approximation theory.
The Life History and Habits of Spalangia Muscidarum Richardson, A Parasite of the Stable Fly
Harry Pinkus
Psyche , 1913, DOI: 10.1155/1913/56729
Abstract:
Spider Bite by Oligoctenus (Fam. Ctenid )
L. F. Pinkus
Psyche , 1934, DOI: 10.1155/1934/83582
Abstract:
Experts in Natural Resource Damages and Toxic Tort Litigation  [PDF]
Allan Kanner
Journal of Environmental Protection (JEP) , 2016, DOI: 10.4236/jep.2016.73036
Abstract:

Expert testimony plays a critical role in environmental and toxic tort litigation [1]. While most litigation settles, the work of an expert should, from the outset, be prepared with trial in mind. First and foremost, an expert, using the appropriate expertise, must be able to resolve questions that will assist the trier of fact in making determinations necessary under the law applicable to the case. In addition, an expert must demonstrate a solid scientific foundation in all of his or her opinions. Once armed with the opinions reached in the case, the forensic expert should work with the trial team to simplify proof, clarify the presentation and integrate it with other trial proof and themes [2]. This effort should include the realistic identification of any perceived or real shortcomings regarding the information available, the approach taken by or conclusions reached by the expert. Ongoing communication between the trial team and the expert throughout the discovery and pre-trial litigation is essential.

Issues Trustees Face in Natural Resource Damage Assessments, Part I  [PDF]
Allan Kanner
Journal of Environmental Protection (JEP) , 2017, DOI: 10.4236/jep.2017.84035
Abstract: The Natural Resource Damage Assessment (NRDA) process evaluates natural resource injuries arising from hazardous waste or oil spills and determines the appropriate remedies. In this article, the first of a two part series, I address the issues that Natural Resource Trustees regularly face during the NRDA process outlined in numerous environmental statutes. Large scale environmental disasters call for sound science, but also discretionary and informed decision-making specific to the particulars of the scenario faced by the trustee that will make the public whole. If the environmental statutes are read correctly, a NRDA will enable a trustee to make the best decisions regarding restoration plans and damages owed. However, constant challenges to the trustee’s authority by the responsible party during the assessment process are not only inconsistent with the trustee’s statutorily delegated authority and the purpose of the environmental statutes themselves, but add considerable delay and cost to the restoration process. This article outlines the NRDA process a trustee typically follows while addressing common misinterpretations of statutory authority that often hinder the ultimate goal of environmental restoration.
Issues Trustees Face in Natural Resource Damage Assessments, Part II  [PDF]
Allan Kanner
Journal of Environmental Protection (JEP) , 2017, DOI: 10.4236/jep.2017.84034
Abstract: The first part of this two part series laid out the process that a Natural Resource Trustee will follow to complete a sound Natural Resource Damage Assessment (NRDA) as well as the typical challenges they face from the Responsible Party. The second part will present the typical issues that the trustee will face as the NRDA is tested in a court of law. A major litigation hurdle typically concerns what counts as “sound science” under the fact specific circumstances of a particular case. Many responsible parties will attempt to challenge a trustee’s assessment under the Daubert standard, which is the test for admissibility of evidence. However, because trustees are selected for their scientific expertise and subject to applicable laws and policies, including guidance on how to conduct a NRDA, trustees are generally the best arbiters of appropriate science, and as such should not be subject to a rigorous Daubert analysis.
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