Representation Theory Arising From Groups In Physics

A representation is a group homomorphism whose image is a group of invertible matrices. Representations and their associated matrices are analyzed through well-established techniques from linear algebra. We characterize representations by a unique decomposition into irreducible representations just as we characterize the decomposition of matrices into their eigenspaces. Through the study of these representations, we uncover mathematical relationships that underlie groups with physical applications. Due to physical symmetries, we study how the irreducible representations of groups that embody the actions of even the most basic rotations are utilized in the computation of irreducible representations groups that reflect more complicated mechanics, like the Poincar\\u27e Group. Further, we utilize the representations of the abstract braid group to gain key insights into understanding the behavior of anyonic systems in quantum mechanics. Finally, we explore the behavior of Fibonacci anyons for ways to understand to illustrate the underlying braid relations

Tom’s European Fantasies: Commodifying Authenticity in The Talented Mr. Ripley

Patricia Highsmith’s The Talented Mr. Ripley (1955) allegorizes the American project of restructuring postwar Europe into its mirror image. In this study, Tom Ripley, Highsmith’s famed sociopathic impersonator, is read as a personified simulacrum of American hegemony that erases the original referent of humanity and history. It will investigate the way Tom’s self-effacement through his high-stake performance reflects the waning historicity of his cultural surroundings. Through his incorporation of Dickie Greenleaf’s intimate “moods” and Europe’s authentic “atmospheres” into a synthetic personality, Tom also transforms his European dwellings such as his Venetian palazzo into a spatial simulacrum without historical depth or continuity. This paper will shed light on how the globalization of American culture during the Cold War fabricated a new consumerist subjectivity that devours and incorporates other cultures

“Alexander the Great: A Lesson Taught by Roman Historians”

The image of Alexander the Great, “according to the many legends he was a king, a hero, a god, a conqueror, a philosopher, a scientist, a prophet, a statesman, and a visionary.” This is the story of Alexander the Great that is taught. The deeds of valor are truly awe-inspiring to those who take them at face value. Alexander is seen as a man who broke the mold. Libraries have been devoted to the study of Alexander. However, over the past sixty years scholars have become divided about their understanding of such a figure. There is one school of thought that still sees him as an inspirational leader. There is however a new story that is being explored, one that tells of a bloodthirsty man, always in search of the next battle, constantly putting himself and others in danger

An Effective Nonprofit Board-Executive Relationship Starts With Defined Roles

Nonprofit executive directors have three, seven, and sometimes over 15 bosses. Their relationship with the board is complex to navigate, but it is crucial to organizational success

Pine-ing for a Voice: Vegetal agencies, New Materialism and State Control through the Wollemi Pine

Attending to Wollemia nobilis (Wollemi Pine), we read this plant as ensconced and mobilised by political and politicised forces, towards distinct colonial and imperial ends. Seeking to work beyond a language of flowers, we attune to the appropriation and weaponisation of plants; a language beyond the merely decorative or affective, towards understandings of plants performing agency and political power.  Our reading of the Wollemi pine emerges from the scorched summer of 2019/2020, in which much of Australia caught alight, and during which the Wollemi was placed in danger of disappearing for a second, and perhaps final, time. A prehistoric tree, long thought extinct, before its rediscovery in 1994, the Wollemi holds special significance, but further, value within an Australian cultural context. In light of this significance, the Wollemi is apprehended and manipulated towards political ends. Within the frame of this text, we consider not only the contemporary diplomacy and governance within which the Wollemi is ensnared, but too, the legacies of Invasion and colonisation which support the mobilisation of the Wollemi in this manner.  Framing our approach within the broader context of contemporary ecological theory and in a manner attentive to frames of New Materialism, we engage with the entanglements of plant language, agency and being — as a means through which we can attune to our shared mattering and ongoing struggles for sovereignty amidst a rapidly changing natural world. 

George Eliot established her own philosophy for living

In the Hall of Fame of the nineteenth-century English novelists there has been for the last forty or fifty years one conspicuously empty place. Dickens, Scott, Jane Austin, the Brontes, George Meredith, Thomas Hardy, these have remained unchallenged in their greatness

An Exploration Into the Design of a Portable Music Player for People With Alzheimer’s and Dementia

An exploration into the design of a portable music player for people with Alzheimer\u27s and dementia