Powers of Cosine and Sine

This paper presents expressions for sums of powers of sine and cosine in terms of the basis for the field extension obtained by adjoining the sine or cosine to the field of rational numbers.Comment: AMS-LaTex, 36 page

Notes On An Approach To Apery's Constant

The Basel problem, solved by Leonhard Euler in 1734, asks to resolve $\zeta(2)$, the sum of the reciprocals of the squares of the natural numbers, i.e. the sum of the infinite series: \begin{equation} \sum_{i=1}^{\infty}\frac{1}{n^2}=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\ldots\notag \end{equation} The same question is posed regarding the summation of the reciprocals of the cubes of the natural numbers, $\zeta(3)$. The resulting constant is known as Apery's constant. A YouTube channel, 3BlueBrown, produced a video entitled, "Why is pi here? And why is it squared? A geometric answer to the Basel problem". The video presents the work of John W\"astlund. The equations can be extended to $\zeta(n)$, but the geometric argument is lost. We try to explore these equations for $\zeta(n)$.Comment: AMS-LaTeX, 67 page

Treatment Acceptability by Label and Role

This study examined differences in ratings of treatment acceptability among groups of individuals who are often involved in the recommendation, selection, implementation, and evaluation of behavioral interventions in the educational setting; teachers, school psychologists, and school social workers. An analogue-type study was conducted, utilizing a written case description of a 3rd grader exhibiting a problem behavior, a written case description of an intervention applied to that problem behavior, and a 15-item instrument utilized in rating treatment acceptability (IRP-15) . Also varied in the study was a label (LD, BD, ADD) placed on the student in the vignette, and intervention type (positive or negative-based). There was a significant effect of professional group membership on ratings of treatment acceptability. There was an effect of intervention type on treatment acceptability, however, no label bias was noted. A group by intervention-type interaction was also noted. Implications of the present study, and future research directions are discussed

Hybrid LTA vehicle controllability as affected by buoyancy ratio

The zero and low speed controllability of heavy lift airships under various wind conditions as affected by the buoyancy ratio are investigated. A series of three hybrid LTA vehicls were examined, each having a dynamic thrust system comprised of four H-34 helicopters, but with buoyant envelopes of different volumes (and hence buoyancies), and with varying percentage of helium inflation and varying useful loads (hence gross weights). Buoyancy ratio, B, was thus examined varying from approximately 0.44 to 1.39. For values of B greater than 1.0, the dynamic thrusters must supply negative thrust (i.e. downward)

The opioid receptor: emergence through millennia of pharmaceutical sciences

Throughout history humanity has searched for an optimal approach to the use of opioids that maximizes analgesia while minimizing side effects. This review reflects upon the conceptualization of the opioid receptor and the critical role that the pharmaceutical sciences played in its revelation. Opium-containing formulations have been delivered by various routes of administration for analgesia and other therapeutic indications for millennia. The concept of a distinct site of opium action evolved as practitioners developed innovative delivery methods, such as intravenous administration, to improve therapeutic outcomes. The introduction of morphine and synthetic opioids engendered the prevalent assumption of a common opioid receptor. Through consideration of structure-activity relationships, spatial geometry, and pharmacological differences of known ligands, the idea of multiple opioid receptors emerged. By accessing the high-affinity property of naloxone, the opioid receptor was identified in central and peripheral nervous system tissue. The endogenous opioid neuropeptides were subsequently discovered. Application of mu-, delta-, and kappa- opioid receptor-selective ligands facilitated the pharmacological characterization and distinctions between the three receptors, which were later cloned and sequenced. Opioid receptor signal transduction pathways were described and attributed to specific physiological outcomes. The crystal structures of mu, delta, kappa, and nociceptin/orphanin FQ receptors bound to receptor-selective ligands have been elucidated. Comparison of these structures reveal locations of ligand binding and engagement of signal transduction pathways. Expanding knowledge regarding the structure and actions of the opioid receptor fuels contemporary strategies for driving the activity of opioid receptors toward maximizing therapeutic and minimizing adverse outcomes

Effects of Wing and Nacelle Modifications on Drag and Wake Characteristics of a Bomber-Type Airplane Model

An investigation of a model of a large four-engine bomber was conducted in the Langley 19-f'oot pressure tunnel to determine the effects of several wing and nacelle modifications on drag characteristics and air flow characteristics at the tail. Leading-edge gloves, trailing-edge extensions, and modified nacelle afterbodies were tested individual ly and in combination. The effects of the various modifications were determined by force tests, tuft observations, and turbulence s1ITveys in the region of the tail. Tests were made with fixed and natural transition on the wing and with propellers operating and propellers off. Most of the tests were con- ducted at a Reynolds number of approximately 2.6 x 106. The results indicated that application of certain of the modifications provided worth-while improvements in the characteristics or the model. The flow over the wing and flaps was improved, the drag was reduced, and the turbulence in the region of the tail was reduced. Trailing-edge extensions were the most effective individual modification in improving the flow over the wing with wing flaps neutral, cowl and intercooler flaps clos ed. Modified nacelle afterbodies were the most effectiv8 individual edification in reducing drag with either fixed or natural transition on the wing; however, trailin6-edge extensions were slightly more effective with fixed transition. Combinations of either leading or trailing-edge extensions and modified afterbodies were more effective than either modification alone. With cowl and intercooler flaps open, trailing-edge extensions with modified afterbodies provided substantial improvement in flow and drag characteristics. With wing flaps deflected, enclosing the flap behind the inboard nacelle within an extended afterbody or cutting the flaps at the nacelle appeared. to be the most promising methods of improving the f low over the flaps and the tail. Although the results of hot-wire-anenometer surveys were not conclusive in regard to buffeting characteristics, the modifications did educe the turbulence at the tail with wing flaps both neutral and deflected. The modifications, as a rule, were favorable to maximum lift. Appreciable reductions in longitudinal stability of the model were caused by addition of leading -edge gloves and tr ailing -edge extensions

Investigations on the Peach 4 Debrite, a Late Pleistocene Mass Movement on the Northwest British Continental Margin

The Peach 4 debrite is the most recent in a series of large scale Pleistocene MTDs within the Barra fan on the northwest British continental margin. Geophysical data indicate that Peach 4 was formed through a combination of blocky and muddy debris flows and affects an area of ~ 700 km2. BGS core sample 56 -10 36, located directly over the Peach 4 debrite, provides a minimum age of 14.68 ka cal BP for the last major failure. An upwards fining turbidite sequence in BGS core sample 56 -10 239 is associ-ated with increased As and S concentrations, indicators of diagenetic pyrite which forms under anoxic conditions. It is proposed that As and S concentrations may pro-vide a method of distinguishing between contourite and turbidite sedimentation, though further research is required

Lincoln, the Friendly Neighbor

The sculpture depicts a full-length Abraham Lincoln dressed in a suit. He stands with two children - male and female - and a dog. This particular sculpture is number one in a limited release of thirty.https://scholarsjunction.msstate.edu/fvw-statuettes-and-figurines/1031/thumbnail.jp