Some spectral equivalences between Schrodinger operators

Spectral equivalences of the quasi-exactly solvable sectors of two classes of Schrodinger operators are established, using Gaudin-type Bethe ansatz equations. In some instances the results can be extended leading to full isospectrality. In this manner we obtain equivalences between PT-symmetric problems and Hermitian problems. We also find equivalences between some classes of Hermitian operators.Comment: 14 page

Development of an advanced composite aileron for the L-1011 transport aircraft

Significant improvements in structural efficiency can be achieved by the utilization of advanced composites for construction of aircraft secondary structures. Careful evaluation of alternate designs and materials for the L-1011 advanced composite inboard aileron has led to the selection of several unique material combinations and easily manufactured structural configurations. The advanced composite aileron is a direct replacement for the metal aileron with a weight savings of 23 percent. Due to the configurational simplicity of the components within the composite aileron, and because it contains 50 percent fewer parts and fasteners than the metal aileron, it is predicted that the composite aileron will be cost competitive with the metal aileron in a production environment. Structural analysis of the composite aileron, in conjunction with the design data, concept verification, and ground tests, indicates that the composite aileron design meets or exceeds structural requirements

Logika narodu: Nacjonalizm, logika formalna i międzywojenna Polska

Between the World Wars, a robust research community emerged in the nascent discipline of mathematical logic in Warsaw. Logic in Warsaw grew out of overlapping imperial legacies, launched mainly by Polish-speaking scholars who had trained in Habsburg universities and had come during the First World War to the University of Warsaw, an institution controlled until recently by Russia and reconstructed as Polish under the auspices of German occupation. The intellectuals who formed the Warsaw School of Logic embraced a patriotic Polish identity. Competitive nationalist attitudes were common among interwar scientists – a stance historians have called “Olympic internationalism,” in which nationalism and internationalism interacted as complementary rather than conflicting impulses.One of the School’s leaders, Jan Łukasiewicz, developed a system of notation that he promoted as a universal tool for logical research and communication. A number of his compatriots embraced it, but few logicians outside Poland did; Łukasiewicz’s notation thus inadvertently served as a distinctively national vehicle for his and his colleagues’ output. What he had intended as his most universally applicable invention became instead a respected but provincialized way of writing. Łukasiewicz’s system later spread in an unanticipated form, when postwar computer scientists found aspects of its design practical for working under the specific constraints of machinery; they developed a modified version for programming called “Reverse Polish Notation” (RPN). RPN attained a measure of international currency that Polish notation in logic never had, enjoying a global career in a different discipline outside its namesake country. The ways in which versions of the notation spread, and remained or did not remain “Polish” as they traveled, depended on how readers (whether in mathematical logic or computer science) chose to read it; the production of a nationalized science was inseparable from its international reception.W okresie międzywojennym w rodzącej się dyscyplinie logiki matematycznej w Warszawie wyłoniła się silna społeczność badawcza. Logika w Warszawie wyrosła w wyniku nakładających się na siebie imperialnych spuścizn, dzięki działaniom głównie polskojęzycznych uczonych, którzy kształcili się na uniwersytetach habsburskich i przybyli w czasie I wojny światowej na Uniwersytet Warszawski, instytucję kontrolowaną do niedawna przez Rosję i zrekonstruowaną jako polską pod auspicjami niemieckiego okupanta. Intelektualiści, którzy tworzyli Warszawską Szkołę Logiki, przyjęli patriotyczną polską tożsamość. Konkurencyjne postawy nacjonalistyczne były powszechne wśród naukowców międzywojennych – stanowisko, które historycy nazwali „internacjonalizmem olimpijskim”, w którym nacjonalizm i internacjonalizm oddziaływały jako impulsy raczej wzajemnie się uzupełniające niż sprzeczne.Jeden z liderów Szkoły, Jan Łukasiewicz, opracował system notacji, który promował jako uniwersalne narzędzie do badań i komunikacji w logice. Wielu jego rodaków przyjęło ten system notacji, ale niewielu logików poza Polską. W ten sposób notacja Łukasiewicza nieumyślnie posłużyła jemu i jego współpracownikom jako narzędzie specyficznie polskie. Wynalazek, który w zamyśle miał być najbardziej uniwersalną formą zapisu, stał się szanowanym, lecz zrozumiałym tylko w kraju narzędziem. System notacji Łukasiewicza później rozprzestrzenił się w nieprzewidzianej formie, gdy powojenni informatycy zdali sobie sprawę z praktycznej użyteczności jego aspektów do pracy w specyficznych uwarunkowaniach maszynowych i opracowali zmodyfikowaną wersję tej notacji do programowania o nazwie „Reverse Polish Notation” (RPN). RPN osiągnął miarę waluty międzynarodowej, której nigdy nie miała polska notacja w logice, ciesząc się globalną karierą w innej dyscyplinie poza krajem jej imiennika. Drogi, w jakich wersje tej notacji rozprzestrzeniły się i pozostały lub nie pozostały „polskie” podczas tej podróży, zależały od tego, jak czytelnicy (zajmujący się logiką matematyczną albo informatyką) postanowili czytać tę notację; tworzenie znacjonalizowanej nauki było nierozerwalnie związane z jej międzynarodową recepcją

Advanced composite aileron for L-1011 transport aircraft: Design and analysis

Detail design of the composite aileron has been completed. The aileron design is a multi-rib configuration with single piece upper and lower covers mechanically fastened to the substructure. Covers, front, spar and ribs are fabricated with graphite/epoxy tape or fabric composite material. The design has a weight savings of 23 percent compared to the aluminum aileron. The composite aileron has 50 percent fewer fasteners and parts than the metal aileron and is predicted to be cost competitive. Structural integrity of the composite aileron was verified by structural analysis and an extensive test program. Static, failsafe, and vibration analyses have been conducted on the composite aileron using finite element models and specialized computer programs for composite material laminates. The fundamental behavior of the composite materials used in the aileron was determined by coupon tests for a variety of environmental conditions. Critical details of the design were interrogated by static and fatigue tests on full-scale subcomponents and subassemblies of the aileron

Advanced composite aileron for L-1011 transport aircraft: Aileron manufacture

The fabrication activities of the Advanced Composite Aileron (ACA) program are discussed. These activities included detail fabrication, manufacturing development, assembly, repair and quality assurance. Five ship sets of ailerons were manufactured. The detail fabrication effort of ribs, spar and covers was accomplished on male tools to a common cure cycle. Graphite epoxy tape and fabric and syntactic epoxy materials were utilized in the fabrication. The ribs and spar were net cured and required no post cure trim. Material inconsistencies resulted in manufacturing development of the front spar during the production effort. The assembly effort was accomplished in subassembly and assembly fixtures. The manual drilling system utilized a dagger type drill in a hydraulic feed control hand drill. Coupon testing for each detail was done

Distribution of E/N and N sub e in a cross-flow electric discharge laser

The spatial distribution of the ratio of electric field to neutral gas density on a flowing gas, multiple pin-to-plane discharge was measured in a high-power, closed loop laser. The laser was operated at a pressure of 140 torr (1:7:20, CO2, N2, He) with typically a 100 meter/second velocity in the 5 x 8 x 135 centimeter discharge volume. E/N ratios ranged from 2.7 x 10 to the minus 16th power to 1.4 x 10 to the minus 16th power volts/cu cm along the discharge while the electron density ranged from 2.8 x 10 to the 10th power to 1.2 x 10 to the 10th power cm/3

Small-signal gain diagnostic measurements in a flowing CO2 pin discharge laser

Small-signal gain diagnostic measurements were conducted on closed loop, high power, carbon dioxide laser to assess the coupling between gas flow velocity and resonator saturation. Parameters investigated included optical cavity and discharge power. Results of gain measurements within and downstream of the excitation volume are presented for a laser gas composition He:N2:CO2 of 10:7:1 at 90 torr. The gain at constant discharge power was observed to be dependent upon discharge power level and time. An important result of this study is that the effects of gain swept downstream of the discharge region must be considered in the resonator design if efficient extraction of stored optical energy is desired

A wide bandwidth free-electron laser with mode locking using current modulation

A new scheme for mode locking a free-electron laser (FEL) amplifier is proposed based on electron beam current modulation. It is found that certain properties of the original concept (Thompson and McNeil 2008 Phys. Rev. Lett. 100 203901), based on the energy modulation of electrons, are improved, including the spectral brightness of the source and the purity of the series of short pulses. Numerical comparisons are made between the new and old schemes and between a mode-locked FEL and a self-amplified spontaneous emission FEL. Illustrative examples using a hypothetical mode-locked FEL amplifier are provided. The ability to generate intense coherent radiation with a large bandwidth is demonstrated

Advanced composite aileron for L-1011 transport aircraft, task 1

Structural design and maintainability criteria were established and used as a guideline for evaluating a variety of configurations and materials for each of the major subcomponents. From this array of subcomponent designs, several aileron assemblies were formulated and analyzed. The selected design is a multirib configuration with sheet skin covers mechanically fastened to channel section ribs and spars. Qualitative analysis of currently available composite material systems led to the selection of three candidate materials on which comparative structural tests were conducted to measure the effects of environment and impact damage on mechanical property retention. In addition, each system was evaluated for producibility characteristics. From these tests, Thornel 300/5208 unidirectional tape was selected for the front spar and covers, and Thornel 300 fabric/5208 was chosen for the ribs