A note on a curious formula for Euler's constant

In this short note we will use the residue theorem to establish a formula for Euler's constant. In particular, we offer a slightly generalized version of an interesting infinite series due to Flajolet, Gourdon, and Dumas.Comment: 4 page

Psychoanalyzing Nature, Dark Ground of Spirit

The ontological paradigms of Schelling and the late Merleau-Ponty bear striking resemblances to Spinoza’s ontology. Both were developed in response to transcendental models of a Cartesian mold, resisting tendencies to exalt the human ego to the neglect or the detriment of the more-than-human world. As such, thinkers with environmental concerns have sought to derive favorable ethical prescriptions on their basis. We begin by discerning a deadlock between two such thinkers: Ted Toadvine and Sean McGrath. With ecological responsibility in mind, both actually resist Spinozist reduction of the human being to the status of a mere mode among modes. But despite having the same general aim, they end up endorsing contrary practical conclusions. Our objective is to pinpoint the reasons behind this deadlock, indicative of two strands of post-Spinozist environmental thought which stand in tension, and to begin to propose an integrative way forward. The ethical weight afforded by Toadvine to the notion of resistance in the work of the late Merleau-Ponty, namely nature’s resistance to harmonizing, unifying pretensions, invites inquiry into two Merleau-Pontean notions he does not address: the barbarian principle, and the proposal to “Do a Psychoanalysis of Nature.” We trace these to their origins in the works of Schelling’s middle period, arguing that the Schellingian location of resistance in Spirit’s dark ground—alternately conceived as primordial Dionysiac madness, bottled-up within the substratum of consciousness—lends to an understanding of the human, and human responsibility, that harbors favorable implications for environmental ethics

A study of inverse trigonometric integrals associated with three-variable Mahler measures, and some related identities

We prove several identities relating three-variable Mahler measures to integrals of inverse trigonometric functions. After deriving closed forms for most of these integrals, we obtain ten explicit formulas for three-variable Mahler measures. Several of these results generalize formulas due to Condon and Lal\'in. As a corollary, we also obtain three $q$-series expansions for the dilogarithm

Fresnel concentrating collector

An advanced point focusing solar technology demonstrated potential for near term commercialization as a renewable energy technology. The design features combine to produce a highly efficient, low cost, safe, adaptable, durable system which is simple to manufacture, install and maintain

A study on task difficulty and acceleration stress

The results of two experiments which relate to task difficulty and the effects of environmental stress on tracking performance are discussed and compared to subjective evaluations. The first experiment involved five different sum of sine tracking tasks which humans tracked both in a static condition and under a 5 Gz acceleration stress condition. The second experiment involved similar environmental stress conditions but in this case the tasks were constructed from deterministic functions with specially designed velocity and acceleration profiles. Phase Plane performance analysis was conducted to study potential measures of workload or tracking difficulty

The Battle to Define the Scope of Attorney-Client Privilege in the Context of Insurance Company Bad Faith: A Judicial War Zone

[Excerpt] The attorney-client privilege is the oldest of the privileges for confidential communications known to the common law. \u27 The privilege is [d]eeply rooted in public policy, and plays a \u27vital role\u27 in the administration of justice. As such, the privilege is traditionally deemed worthy of maximum legal protection \u27 and it remains one of the most carefully guarded privileges and is not readily to be whittled down. The privilege has come under assault in the insurance bad faith context in recent decades resulting in a whittling down of the privilege for insurance companies as a target party. Over the past couple of decades, various courts have rendered significant decisions regarding implied waiver of the privilege in the insurance bad faith context. These courts have seemingly set a minimal threshold for waiver that is the functional equivalent of a per se waiver rule, a rule which is inconsistent with the strength of the protection normally provided the attorney-client privilege in other contexts involving non-target parties. In contrast, Arizona, one of the jurisdictions which previously appeared to create such a per se rule, may be, with recent intermediate court decisions, redefining the battle for the scope of the attorney-client privilege in the insurance bad faith context. The Arizona decisions on this issue serve as a case study regarding the analytic gymnastics courts have engaged in to create implied waiver in the insurance bad faith context. However, these decisions may also set the stage for the judicial combatants. Will the battle result in a return to the more conservative protections of the privilege provided in other contexts or will it end with a broad per se implied waiver in the insurance context? In Part I of this article, the attorney-client privilege is discussed generally, as well as specifically, in the context of insurer bad faith. In Part I.A, a general overview of the attorney-client privilege is presented. In Part I.B, express and implied waiver of the attorney-client privilege are discussed. The courts have disagreed on the general contours of the test to be applied in determining whether an implied waiver of the attorney-client privilege has occurred, and what should be the precise formulation for that determination. The courts have also disagreed as to when a client may be deemed to have injected privileged attorney-client communications into a case, causing an implied waiver. There are three general approaches to determine whether a litigant has impliedly waived the attorney-client privilege. Each of these approaches is discussed. In Part I.C, the article discusses general principles regarding insurance bad faith and how the direct assertion of the advice-of counsel defense results in waiver of the attorney-client privilege in that context. The nature and scope of the advice-of-counsel defense is explored. In Part II, the battle over the changing boundaries of waiver by implication is examined by comparing the case authority supporting expansion versus the development of three published decisions from the courts of Arizona. The discussion starts in Part IIA, where the expansion of waiver by implication is discussed. Part II.B examines a decision from the Arizona Supreme Court which followed the trend of substantial expansion of the waiver-by-implication rule and then examines two subsequent decisions from the Arizona Court of Appeals which have applied the Arizona Supreme Court precedent to reach two very different and arguably contradictory results. The first of these appellate decisions arguably takes the expansion of implied waiver to the next level-a per se rule triggering automatic waiver as a result of defending a bad faith case on a subjective belief of acting in good faith. The second appellate decision, however, takes a step back from the ledge and seeks to limit the prior ruling to its facts rather than creating a per se rule in those circumstances. Part II.C seeks to synthesize and define the battle in Arizona over the scope of implied waiver, discussing the chilling effect continued expansion of implied waiver can have upon the advice that insurance companies seek from counsel and how the recent decision from Arizona may serve as a warm front to thaw the chill that has been in the air for the last two decades

Approximating cube roots of integers, after Heron's Metrica III.20

Heron, in Metrica III.20-22, is concerned with the the division of solid figures - pyramids, cones and frustra of cones - to which end there is a need to extract cube roots. We report here on some of our findings on the conjecture by Taisbak in C.M.Taisbak, Cube roots of integers. A conjecture about Heron's method in Metrika III.20. Historia Mathematica, 41 (2014), 103-104

Tributes & Remembrances

From a memorial service held in memory of Charles Price, Professor Emeritus of Art History, at Harkness Chapel, Connecticut College, April 13, 2004. With tributes written by Barbara Zabel, Christopher London, Brian Rogers, Cynthia Willauer, Maureen McCabe and John H. B. Knowlton. Illustrations by Charles Price