Linkage of Pfister forms over C(x1,…,xn)\mathbb{C}(x_1,\ldots,x_n)

In this note, we prove the existence of a set of $n$-fold Pfister forms of cardinality $2^n$ over $\mathbb{C}(x_1,\dots,x_n)$ which do not share a common $(n-1)$-fold factor. This gives a negative answer to a question raised by Becher. The main tools are the existence of the dyadic valuation on the complex numbers and recent results on symmetric bilinear over fields of characteristic 2

Quaternion quadratic equations in characteristic 2

In this paper we present a solution for any standard quaternion quadratic equation, i.e. an equation of the form $z^2+\mu z+\nu=0$ where $\mu$ and $\nu$ belong to some quaternion division algebra $Q$ over some field $F$, assuming the characteristic of $F$ is $2$.Comment: 9 pages, 0 figure

Chain Equivalences for Symplectic Bases, Quadratic Forms and Tensor Products of Quaternion Algebras

We present a set of generators for the symplectic group which is different from the well-known set of transvections, from which the chain equivalence for quadratic forms in characteristic 2 is an immediate result. Based on the chain equivalences for quadratic forms, both in characteristic 2 and not 2, we provide chain equivalences for tensor products of quaternion algebras over fields with no nontrivial 3-fold Pfister forms. The chain equivalence for biquaternion algebras in characteristic 2 is also obtained in this process, without any assumption on the base-field.Comment: 10 page

Quality of Life Before and After Cosmetic Surgery: Should Body Dysmorphic Disorder Be Considered an Absolute or Relative Contraindication for Cosmetic Surgery?

Body Dysmorphic Disorder (BDD) has historically been regarded as a strong contraindication for cosmetic plastic surgery. New research now suggests that the contraindications to cosmetic surgery in patients with BDD may not be so absolute. This paper reviews diagnostic criteria, diagnostic challenges, and current standard of treatment of BDD. It then presents the idea of insight analysis in the BDD patient as a significant factor in determining if patients with BDD may or may not benefit from cosmetic surgery or procedures

Critical Analysis of Risk Management: A Narrative Literature Review

The objective of this study is to analyze available literature on the subject of risk management in business. Risk happens in all business functions and in every kind of activity. Risk management study commenced after World War II. The study has long been connected with the use of market insurance to guard entities and businesses from numerous losses linked with coincidences. Other methods of risk management, alternatives to market insurance, surfaced during the 1950s when market insurance was alleged as expensive and imperfect for defense contrary to clean risk. Knowing how to identify risks, attribute a value and a priority scale, design actions and mechanisms to minimize risks, and continuously monitor them, are essential to guarantee companies’ survival and create sustainable value. Risk management is the process of minimizing or mitigating the risk. It starts with the identification and evaluation of risk followed by optimal use of resources to monitor and minimize the same. Keywords: risk management, risks DOI: 10.7176/PPAR/12-5-04 Publication date:July 31st 202

The rāg that Burned down Delhi: Music and Memory between 1857 and 1947

The Urdu litterateur Shahid Ahmad Dehlvi (1906–1967) recorded a series of reflections and reminiscences about Delhi, its culture, and how that culture was brought to an end by the violence of Partition in 1947. In his essays on music, he documented the performances and personal histories of a range of singers, dancers, and instrumentalists based in Delhi in the first half of the 20th century and considered their plight after Independence. In this article, I examine three of these essays—two in Urdu and one in English—and ask two questions. Firstly, how does this author develop a sense of historical depth to the social and cultural rupture he experienced in 1947? I suggest that his Urdu essays draw upon a longer history of literary nostalgia and connect a Delhicentric understanding of Partition to the earlier crisis of 1857. Secondly, how did attending to music allow Shahid Dehlvi to explore the nuances of cultural rupture and personal loss