Weil's converse theorem with poles

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Test vectors for Rankin-Selberg LL-functions

We study the local zeta integrals attached to a pair of generic representations $(\pi,\tau)$ of $GL_n\times GL_m$, $n>m$, over a $p$-adic field. Through a process of unipotent averaging we produce a pair of corresponding Whittaker functions whose zeta integral is non-zero, and we express this integral in terms of the Langlands parameters of $\pi$ and $\tau$. In many cases, these Whittaker functions also serve as a test vector for the associated Rankin-Selberg (local) $L$-function.Comment: arXiv admin note: text overlap with arXiv:1804.0772

Value Chains of Botanical and Herbal Medicinal Products: A European Perspective

In recent years, the quality of botanicals has come under increased scrutiny. Despite the availability of numerous high-quality products from reputable companies, health care professionals, patients, and consumers are understandably concerned about questionable botanical ingredients in various consumer products. In Europe, this includes products that are generally unlicensed and unregistered supplements (also referred to as “botanicals”), which are often poorly regulated, or even totally unregulated, depending on the country of jurisdiction

Medicinal plant analysis: A historical and regional discussion of Chinese publication trends and emergent complex techniques

The analysis of medicinal plants has had a long history, and especially with regard to assessing a plant’s quality. The first techniques were organoleptic using the physical senses of taste, smell, and appearance. Then gradually these led on to more advanced instrumental techniques. Though different countries have their own traditional medicines China currently leads the way in terms of the number of publications focused on medicinal plant analysis and number of inclusions in their Pharmacopoeia. The monographs contained within these publications give directions on the type of analysis that should be performed, and for manufacturers, this typically means that they need access to more and more advanced instrumentation. We have seen developments in many areas of analytical analysis and particularly the development of chromatographic and spectroscopic methods and the hyphenation of these techniques. The ability to process data using multivariate analysis software has opened the door to metabolomics giving us greater capacity to understand the many variations of chemical compounds occurring within medicinal plants, allowing us to have greater certainty of not only the quality of the plants and medicines but also of their suitability for clinical research. Refinements in technology have resulted in the ability to analyze and categorize plants effectively and be able to detect contaminants and adulterants occurring at very low levels. However, advances in technology cannot provide us with all the answers we need in order to deliver high-quality herbal medicines and the more traditional techniques of assessing quality remain as important today