Analysis of the ellipsometric spectra of amorphous carbon thin films for evaluation of the sp3-bonded carbon content

Using spcctroscopic ellipsometry (SE), we have measured the optical properties and optical gaps of a series of amorphous carbon (a-C) films ∼ 100-300 Å thick, prepared using a filtered beam of C+ ions from a cathodic arc. Such films exhibit a wide range of sp3-bonded carbon contents from 20 to 76 at.%, as measured by electron energy loss spectroscopy (EELS). The Taue optical gaps of the a-C films increase monotonically from 0.65 eV for 20 at.% sp3 C to 2.25 eV for 76 at.% sp3 C. Spectra in the ellipsometric angles (1.5-5 eV) have been analyzed using different effective medium theories (EMTs) applying a simplified optical model for the dielectric function of a-C, assuming a composite material with sp2 C and sp3 C components. The most widely used EMT, namely that of Bruggeman (with three-dimensionally isotropic screening), yields atomic fractions of sp3 C that correlate monotonically with those obtained from EELS. The results of the SE analysis, however, range from 10 to 25 at.% higher than those from EELS. In fact, we have found that the volume percent sp3 C from SE using the Bruggeman EMT shows good numerical agreement with the atomic percent sp3 C from EELS. The SE-EELS discrepancy has been reduced by using an optical model in which the dielectric function of the a-C is determined as a volume-fraction-weighted average of the dielectric functions of the sp2 C and sp3 C components. © 1998 Elsevier Science S.A.

Analysis of amorphous carbon thin films by spectroscopic ellipsometry

Using spectroscopic ellipsometry (SE), we have measured the optical properties of amorphous carbon (a-C) films ∼ 10-30 nm thick prepared using a filtered beam of C+ ions from a cathodic arc. Such films exhibit a wide range of sp3-bonded carbon contents from 20 to 76 at.% as measured by electron energy loss spectroscopy (EELS), and a range of optical gaps from 0.65 eV (20 at.% sp3 C) to 2.25 eV (76 at.% sp3 C) as measured by SE. SE data from 1.5 to 5 eV have been analyzed by applying the most widely used effective medium theory (EMT) namely that of Bruggeman with isotropic screening, assuming a model of the material as a composite with sp2 C and sp3 C components. Although the atomic fractions of sp3 C deduced by SE with the Bruggeman EMT correlate monotonically with those obtained by EELS, the SE results range from 10 to 25 at.% higher. The possible origins of this discrepancy are discussed within the framework of an optical composite. Improved agreement between SE and EELS is obtained by employing a simple form for the EMT, in which the effective dielectric function is determined as a volume-fraction-weighted average of the dielectric functions of the two components. © 1998 Elsevier Science B.V. All rights reserved.

Evaluación de rendimiento del grano de café (Coffea arabica L.) bajo la influencia de diferentes manejos agroforestales en Masatepe, Nicaragua

El presente trabajo de investigación se realizó en el Municipio de Masatepe, departamento de Masaya, Nicaragua se establecieron en el año 2000 dos repeticiones en el Centro de Capacitación y Servicios Regional del Café del pac í fico sur Nicaragua (Jardín Botánico) de la Unión Nicaragüense de cafetaleros (UNICAFE), y una tercera repetición en áreas del Centro Experimental de Campos Azules (CECA) del INTA, con el propósito de evaluar la Producción y el Rendimiento del grano de café bajo la influencia de diferentes manejos agroforestales. Se estu diaron 14 tratamientos distribuidos aleatoriamente en un diseño de Bloques Completos al Azar en parcelas divididas. Un Primer Factor de estudio compuesto por árboles leguminosos y no leguminosos ( Inga laurina, Simarouba glauca, Samanea saman, Tabebuia rose a ) y una parcela a pleno sol distribuidos en las parcelas grandes; un Segundo Factor de estudios compuesto por niveles de insumos (orgánico extensivo, orgánico intensivo, convencional con insumo moderados, convencional con alto insumo); distribuidos en las subparcelas. Se midieron y evaluaron las variables número de frutos en una libra, granos flotados (%), granos verdes(%), granos secos(%), granos brocados(%), granos chasparreado(%), libras uva por quintal oro, libras oro por fanega uva, fanega uva por qui ntal oro, kilogramos oro hectárea, quintales oro por hectárea. No s e encontraron diferencias significativas entre los diferentes tipos de sombra (exceptuando el ciclo 2002) favorables al tratamiento compuesto por Simaruba glauca + Tabebuia rosea con un ren dimiento de 1384.41 kg. ha - 1 grano oro; el mismo comportamiento estadístico se tuvo en los niveles de insumo siendo superior el Alto Convencional con 1334.37 kg. ha - 1 grano oro en el ciclo 2004/2005, mientras en el ciclo 2005/2006 se obtuvo diferencias sig nificativas en el factor tipo de sombra para las variables nú m er o de frutos por libras alcanzando pleno sol unos 333.66 frutos; granos flotados (4.33 % para el tratamiento S. glauca + T. rocea y Samanea saman + T. rocea con el menor porcentaje) y granos c hasparreado (2.83 % para el tratamiento de S. saman + Inga laurina ). Entre los niveles de insumo para este ciclo no mostró diferencia mínima significativa, así como en la interacción entre los factores de estudio

Experiencias de la aplicación comercial de la técnica de reproducción acelerada de semilla (TRAS) en plátano en Rivas y Nandaime

La multiplicación convencional del plátano ( Musa spp.) a través de los hijuelos del cormo, además de la baja tasa de propagación, facilita la diseminación de plagas y enfermedades. La técnica de reproducción acelerada de semillas (TRAS), una alternativa en la producción sana de semilla, fue utilizada para la multiplicación de los cultivares Plátano Enano (PE) y CENSA ¾ (C ¾) en dos viveros comerciales de Rivas y Nandaime donde se establecieron 19 canteros en cada uno. En Rivas se multiplicaron 3 933 cormos de PE y 2 307 de C ¾ a 2.5 cm entre cormos en sustratos de arena de construcción (AC) y arena de playa (AP), riego por microasperción y fertilizacion con completo (15-15-15) NPK. En Nandaime se propagaron 6 952 cormos de PE a 1.5 cm entre cormos en AC. Se regó con regadoras y mangueras y se fertilizó con Súper fértil y Súper calcio. En Rivas las plantas separadas de los cormos se sembraron en bolsas de polietileno, en mezcla de cascarilla de arroz-arena-tierra y en Nandaime en 100% tierra. Se calculó el índice de brotación (IB) de los cormos. En Rivas el IB de PE fue 4 e igualmente para C ¾. El IB de PE en Nandaime fue 3. El mejor IB de PE en Rivas resulta de la utilización inmediata de cormos frescos y yemas en mejor estado físico. El IB de PE en AC fue 5 y 3 en AP, la diferencia la explica el mayor contenido de cenizas volcánicas, minerales y capacidad de absorción de agua de AC. Se produjeron 17 039 plantas de PE y 9 052 de C ¾ en Rivas y 21 637 plantas de PE en Nandaime. Los IB obtenidos son inferiores a los de la guía técnica-UNA. No se siguieron las indicaciones de selección de semilla en el campo, distancia de siembra y momento de corte.

A short in-frame deletion in NTRK1 tyrosine kinase domain caused by a novel splice site mutation in a patient with congenital insensitivity to pain with anhidrosis

Background: Congenital insensitivity to pain with anhidrosis (CIPA) is a rare autosomal recessive genetic disease characterized by the lack of reaction to noxious stimuli and anhidrosis. It is caused by mutations in the NTRK1 gene, which encodes the high affinity tyrosine kinase receptor I for Neurotrophic Growth Factor (NGF). -- Case Presentation: We present the case of a female patient diagnosed with CIPA at the age of 8 months. The patient is currently 6 years old and her psychomotor development conforms to her age (RMN, SPECT and psychological study are in the range of normality). PCR amplification of DNA, followed by direct sequencing, was used to investigate the presence of NTRK1 gene mutations. Reverse transcriptase (RT)-PCR amplification of RNA, followed by cloning and sequencing of isolated RT-PCR products was used to characterize the effect of the mutations on NTRK1 mRNA splicing. The clinical diagnosis of CIPA was confirmed by the detection of two splice-site mutations in NTRK1, revealing that the patient was a compound heterozygote at this gene. One of these alterations, c.574+1G > A, is located at the splice donor site of intron 5. We also found a second mutation, c.2206-2 A > G, not previously reported in the literature, which is located at the splice acceptor site of intron 16. Each parent was confirmed to be a carrier for one of the mutations by DNA sequencing analysis. It has been proposed that the c.574+1G > A mutation would cause exon 5 skipping during NTRK1 mRNA splicing. We could confirm this prediction and, more importantly, we provide evidence that the novel c.2206-2A > G mutation also disrupts normal NTRK1 splicing, leading to the use of an alternative splice acceptor site within exon 17. As a consequence, this mutation would result in the production of a mutant NTRK1 protein with a seven aminoacid in-frame deletion in its tyrosine kinase domain. --Conclusions: We present the first description of a CIPA-associated NTRK1 mutation causing a short interstitial deletion in the tyrosine kinase domain of the receptor. The possible phenotypical implications of this mutation are discussed.

航天器编队飞行的动力学解析分析与阵形设计研究

随着微电子、微机械技术的进步，现代航天器逐渐向体积小、重量轻的趋势发展。结构的轻型化和小型化使得微小航天器在制造和发射上的成本大大降低，同时也使得微小航天器难以独立携带复杂的载O如何开发和利用多颗微小航天器的集群功能来完成复杂的航天任务已日趋成为各航天机构的研究热点，航天器编队飞行即是在这种背景下应运而生的。所谓航天器编队飞行，是指若干颗航天器在整个任务期间都按一定的几何形状排列和飞行，以实现资源共享、信息共享，共同完成某一特定功能。研究表明，航天器编队飞行可用于实现多种功能，如绕飞监视、天基合成孔径雷达、天基干涉仪、电子侦察及卫星导航等。诚然，若人为地施加燃料控制，航天器群可以实现所有的几何构型，然而付出的代价是巨大的。本文立足于最大限度地利用航天器的自然轨道特征，而非通过不断消耗燃料的方法实现航天器群的编队飞行。航天器编队飞行实质上对于航天器群的相对运动提出了一定的约束条件，因此充分地研究两航天器之间的相对运动是进行航天器编队设计的理论基础。然而，这一理论基础与航天器编队飞行所需结论之间仍存在很远的距离。本文在航天器相对运动的理论基础上，通过解析分析的方法研究了航天器编队飞行所需解决的一系列问题，例如：如何选择可行的编队阵形，如何在满足编队飞行约束条件下，进行航天器群的轨道设计。首先，本文在不考虑摄动力情况下，建立了两个航天器相对运动的微分方程，并得到了描述两航天器相对运动的解析解；其次，针对目前文献广泛应用的C-w方程及其解进行了理论分析，指出C-W方程解应用于编队飞行设计的局限性，即只能适用于近圆轨道近距离航天器的编队飞行设计；针对实际航天应用中常遇到的椭圆轨道航天器编队及远距离航天器编队，本文从相对运动解析解出发，经过一系列的数学推导与分析，导出了相应的编队设计公式；然后，本文考虑了环境摄动力如地球非球形摄动力、大气阻力、太阳光压力、第三引力体引力对于编队阵形的影响，以及摄动力情况下编队阵形的保持问题；最后，以卫星导航应用为例，利用本文导出的远距离编队公式设计了我国领土范围内的区域连续导航卫星系统，通过与目前的北斗卫星导航系统相比较，充分展示了航天器编队飞行的特点与应用优势。本文的创新之处体现在如下几方面：1、从理论上分析了目前广泛应用于编队飞行研究的C-W方程及其解的适用范围和局限性。2、将航天器编队飞行设计从近距离拓展至远距离，并针对名义航天器运行于圆轨道的情况，导出了名义航天器飞行方向远距离编队设计公式和大偏心率大相对倾角远距离编队设计公式。3、针对名义航天器运行于任意偏心率椭圆轨道，推导出近距离编队设计公式，并提出了5种新型编队阵形。4、首次在频域范围内研究航天器相对运动规律，突破了一般轨道参数法将航天器相对运动轨迹在近圆轨道近距离范围内进行泰勒展开的传统思路。

Quantum Efficiency And Temperature Coefficients Of Gainp/Gaas Dual-Junction Solar Cell

GaInP/GaAs dual-junction solar cell with a conversion efficiency of 25.2% has been fabricated using metalorganic chemical vapor deposition (MOCVD) technique. Quantum efficiencies of the solar cell were measured within a temperature range from 25 to 160A degrees C. The results indicate that the quantum efficiencies of the subcells increase slightly with the increasing temperature. And red-shift phenomena of absorption limit for all subcells are observed by increasing the cell's work temperature, which are consistent with the viewpoint of energy gap narrowing effect. The short-circuit current density temperature coefficients dJ (sc)/dT of GaInP subcell and GaAs subcell are determined to be 8.9 and 7.4 mu A/cm(2)/A degrees C from the quantum efficiency data, respectively. And the open-circuit cell voltage temperature coefficients dV (oc)/dT calculated based on a theoretical equation are -2.4 mV/A degrees C and -2.1 mV/A degrees C for GaInP subcell and GaAs subcell.

Synthetic, structural and mechanistic studies of interactions of carbon, nitrogen, and oxygen nucleophiles with bis-pentamethylcyclopentadienyl zirconium and hafnium derivatives

The reactivity of permethylzirconocene and permethylhafnocene complexes with various nucleophiles has been investigated. Permethylzirconocene reacts with sterically hindered ketenes and allenes to afford metallacycle products. Reaction of these cummulenes with permethylzirconocene hydride complexes affords enolate and σ-allyl species, respectively. Reactions which afford enolate products are nonstereospecific, whereas reactions which afford allyl products initially give a cis-σ-allyl complex which rearranges to its trans isomer. The mechanism of these reactions is proposed to occur either by a Lewis Acid-Lewis Base interaction (ketenes) or by formation of a π-olefin intermediate (allenes).

Permethylzirconocene haloacyl complexes react with strong bases such as lithium diisopropylamide or methylene trimethylphosphorane to afford ketene compounds. Depending on the size of the alkyl ketene substituent, the hydrogenation of these compounds affords enolate-hydride products with varying degrees of stereoselectivity. The larger the substituent, the greater is the selectivity for cis hydrogenation products.

The reaction of permethylzirconocene dihydride and permethylhafnocene dihydride with methylene trimethylphosphorane affords methyl-hydride and dimethyl derivatives. Under appropriate conditions, the metallated-ylide complex 1, (η^5-C_5(CH_3)_5)_2 Zr(H)CH_2PMe_2CH_2, is also obtained and has been structurally characterized by X-ray diffraction techniques. Reaction of 1 with CO affords (η^5-C_5(CH_3)_5)_2 Zr(C,O-η^2 -(PMe_3)HC=CO)H which exists in solution as an equilibrium mixture of isomers. In one isomer (2), the η^2-acyl oxygen atom occupies a lateral equatorial coordination position about zirconium, whereas in the other isomer (3), the η-acyl oxygen atom occupies the central equatorial position. The equilibrium kinetics of the 2→3 isomerization have been studied and the structures of both complexes confirmed by X-ray diffraction methods. These studies suggest a mechanism for CO insertion into metal-carbon bonds of the early transition metals.

Permethylhafnocene dihydride and permethylzirconocene hydride complexes react with diazoalkanes to afford η^2-N, N' -hydrazonido species in which the terminal nitrogen atom of the diazoalkane molecule has inserted into a metal-hydride or metal-carbon bond. The structure of one of these compounds, Cp*_2Zr(NMeNCTol_2)OH, has been determined by X-ray diffraction techniques. Under appropriate conditions, the hydrazonido-hydride complexes react with a second equivalent of diazoalkene to afford η' -N-hydrazonido-η^2-N, N' -hydrazonido species.

Bis(thiophenolate)pyridine pincer ligands and trivalent zirconocene complexes relevant to early transition metal polymerization catalysts

Two major topics are covered: the first chapter is focused on the development of post-metallocene complexes for propylene polymerization. The second and third chapters investigate the consequences of diisobutylaluminum hydride (HAlⁱBu₂) additives in zirconocene based polymerization systems.

The synthesis, structure, and solution behavior of early metal complexes with a new tridentate LX₂ type ligand, bis(thiophenolate)pyridine ((SNS) = (2-C₆H₄S)₂-2,6-C₅H₃N) are investigated. SNS complexes of Ti, Zr, and Ta having dialkylamido coligands were synthesized and structurally characterized. The zirconium complex, (SNS)Zr(NMe₂)₂, displays C₂ symmetry in the solid state. Solid-state structures of tantalum complexes (SNS)Ta(NMe₂)₃ and (SNS)TaCl(NEt₂)₂ also display pronounced C₂ twisting of the SNS ligand. 1D and 2D NMR experiments show that (SNS)Ta(NMe₂)₃ is fluxional with rotation about the Ta N(amide) bonds occurring on the NMR timescale. The fluxional behavior of (SNS)TaCl(NEt₂)₂ in solution was also studied by variable temperature ¹H NMR. Observation of separate signals for the diastereotopic protons of the methylene unit of the diethylamide indicates that the complex remains locked on the NMR timescale in one diastereomeric conformation at temperatures below -50 °C.

Reduction of Zr(IV) metallocenium cations with sodium amalgam (NaHg) produces EPR signals assignable to Zr(III) metallocene complexes. Thus, chloro-bridged heterobinuclear ansa-zirconocenium cation [((SBI))Zr(μ-Cl)₂AlMe₂]⁺B(C₆F₅)_4¯ (SBI = rac-dimethylsilylbis(1-indenyl)), gives rise to an EPR signal assignable to the complex (SBI)Zr^III(μ-Cl)₂AlMe₂, while (SBI)Zr^III-Me and (SBI)Zr^III(-H)2AlⁱBu₂ are formed by reduction of [(SBI)Zr(μ-Me)₂AlMe₂]⁺B(C₆F₅)_4¯ and [(SBI)Zr(μ-H)₃(AlⁱBu₂)₂]⁺B(C₆F₅)4¯, respectively. These products are also formed, along with (SBI)Zr^III-ⁱBu and [(SBI)Zr^III]⁺ AlR4¯ when (SBI)ZrMe₂ reacts with HAlⁱBu₂, eliminating isobutane en route to the Zr(III) complex. Studies concerning the interconversion reactions between these and other (SBI)Zr(III) complexes and reaction mechanisms involved in their formation are also reported.

The addition of HAlⁱBu₂ to precatalyst [(SBI)Zr(µ-H)₃(AlⁱBu₂)₂]⁺ significantly slows the polymerization of propylene and changes the kinetics of polymerization from 1st to 2nd order with respect to propylene. This is likely due to competitive inhibition by HAlⁱBu₂. When the same reaction is investigated using [(ⁿBuCp)₂Zr(μ-H)₃(AlⁱBu₂)₂]⁺, hydroalumination between propylene and HAlⁱBu₂ is observed instead of propylene polymerization.

High energy photoproduction of neutral mesons

Cross sections for the photoproduction of neutral pi, eta, rho and phi mesons on hydrogen have been measured at the Stanford Linear Accelerator Center using a missing mass spectrometer technique. The data cover photon energies between 5.0 and 17.8 GeV and four momentum transfer squared t between -.12 and -1.38 (GeV/c)².

Pion differential cross sections at lower energies show a peak at low momentum transfers, a distinctive dip and secondary maximum for t in the region -.4 to -.9 (GeV /c)², and a smooth decrease at higher momentum transfers. As photon energy increases, the dip becomes less pronounced, in contradiction to the expectations of simple Regge theories based on the exchange of omega and B trajectories only.

Eta photoproduction was measured only below 10 GeV. The cross section has about the same magnitude as the pion production cross section, but decreases exponentially with t, showing no dip.

Rho mesons appear to be diffractively produced. The differential cross section varies approximately as exp(8.5t + 2t²). It falls slowly with energy, decreasing about 35 percent from 6 GeV to 17.8 GeV. A simple quark model relation appears to describe the data well.

Phi meson cross sections are also consistent with diffraction production. The differential cross section varies approximately as exp(4t). The cross section tends to decrease slightly with photon energy.

DNA-mediated oxidation of transcription factor p53

Transcription factor p53 is the most commonly altered gene in human cancer. As a redox-active protein in direct contact with DNA, p53 can directly sense oxidative stress through DNA-mediated charge transport. Electron hole transport occurs with a shallow distance dependence over long distances through the π-stacked DNA bases, leading to the oxidation and dissociation of DNA-bound p53. The extent of p53 dissociation depends upon the redox potential of the response element DNA in direct contact with each p53 monomer. The DNA sequence dependence of p53 oxidative dissociation was examined by electrophoretic mobility shift assays using radiolabeled oligonucleotides containing both synthetic and human p53 response elements with an appended anthraquinone photooxidant. Greater p53 dissociation is observed from DNA sequences containing low redox potential purine regions, particularly guanine triplets, within the p53 response element. Using denaturing polyacrylamide gel electrophoresis of irradiated anthraquinone-modified DNA, the DNA damage sites, which correspond to locations of preferred electron hole localization, were determined. The resulting DNA damage preferentially localizes to guanine doublets and triplets within the response element. Oxidative DNA damage is inhibited in the presence of p53, however, only at DNA sites within the response element, and therefore in direct contact with p53. From these data, predictions about the sensitivity of human p53-binding sites to oxidative stress, as well as possible biological implications, have been made. On the basis of our data, the guanine pattern within the purine region of each p53-binding site determines the response of p53 to DNA-mediated oxidation, yielding for some sequences the oxidative dissociation of p53 from a distance and thereby providing another potential role for DNA charge transport chemistry within the cell.

To determine whether the change in p53 response element occupancy observed in vitro also correlates in cellulo, chromatin immunoprecipition (ChIP) and quantitative PCR (qPCR) were used to directly quantify p53 binding to certain response elements in HCT116N cells. The HCT116N cells containing a wild type p53 were treated with the photooxidant [Rh(phi)2bpy]³⁺, Nutlin-3 to upregulate p53, and subsequently irradiated to induce oxidative genomic stress. To covalently tether p53 interacting with DNA, the cells were fixed with disuccinimidyl glutarate and formaldehyde. The nuclei of the harvested cells were isolated, sonicated, and immunoprecipitated using magnetic beads conjugated with a monoclonal p53 antibody. The purified immounoprecipiated DNA was then quantified via qPCR and genomic sequencing. Overall, the ChIP results were significantly varied over ten experimental trials, but one trend is observed overall: greater variation of p53 occupancy is observed in response elements from which oxidative dissociation would be expected, while significantly less change in p53 occupancy occurs for response elements from which oxidative dissociation would not be anticipated.

The chemical oxidation of transcription factor p53 via DNA CT was also investigated with respect to the protein at the amino acid level. Transcription factor p53 plays a critical role in the cellular response to stress stimuli, which may be modulated through the redox modulation of conserved cysteine residues within the DNA-binding domain. Residues within p53 that enable oxidative dissociation are herein investigated. Of the 8 mutants studied by electrophoretic mobility shift assay (EMSA), only the C275S mutation significantly decreased the protein affinity (KD) for the Gadd45 response element. EMSA assays of p53 oxidative dissociation promoted by photoexcitation of anthraquinone-tethered Gadd45 oligonucleotides were used to determine the influence of p53 mutations on oxidative dissociation; mutation to C275S severely attenuates oxidative dissociation while C277S substantially attenuates dissociation. Differential thiol labeling was used to determine the oxidation states of cysteine residues within p53 after DNA-mediated oxidation. Reduced cysteines were iodoacetamide labeled, while oxidized cysteines participating in disulfide bonds were ¹³C₂D₂-iodoacetamide labeled. Intensities of respective iodoacetamide-modified peptide fragments were analyzed using a QTRAP 6500 LC-MS/MS system, quantified with Skyline, and directly compared. A distinct shift in peptide labeling toward ¹³C₂D₂-iodoacetamide labeled cysteines is observed in oxidized samples as compared to the respective controls. All of the observable cysteine residues trend toward the heavy label under conditions of DNA CT, indicating the formation of multiple disulfide bonds potentially among the C124, C135, C141, C182, C275, and C277. Based on these data it is proposed that disulfide formation involving C275 is critical for inducing oxidative dissociation of p53 from DNA.

A search for fractionally charged particles in cosmic rays and a theoretical interpretation of the results

An array of two spark chambers and six trays of plastic scintillation counters was used to search for unaccompanied fractionally charged particles in cosmic rays near sea level. No acceptable events were found with energy losses by ionization between 0.04 and 0.7 that of unit-charged minimum-ionizing particles. New 90%-confidence upper limits were thereby established for the fluxes of fractionally charged particles in cosmic rays, namely, (1.04 ± 0.07)x10^-10 and (2.03 ± 0.16)x10^-10 cm^-2sr^-1sec^-1 for minimum-ionizing particles with charges 1/3 and 2/3, respectively.

In order to be certain that the spark chambers could have functioned for the low levels of ionization expected from particles with small fractional charges, tests were conducted to estimate the efficiency of the chambers as they had been used in this experiment. These tests showed that the spark-chamber system with the track-selection criteria used might have been over 99% efficient for the entire range of energy losses considered.

Lower limits were then obtained for the mass of a quark by considering the above flux limits and a particular model for the production of quarks in cosmic rays. In this model, which is one involving the multi-peripheral Regge hypothesis, the production cross section and a corresponding mass limit are critically dependent on the Regge trajectory assigned to a quark. If quarks are "elementary'' with a flat trajectory, the mass of a quark can be expected to be at least 6 ± 2 BeV/c². If quarks have a trajectory with unit slope, just as the existing hadrons do, the mass of a quark might be as small as 1.3 ± 0.2 BeV/c². For a trajectory with unit slope and a mass larger than a couple of BeV/c², the production cross section may be so low that quarks might never be observed in nature.

Paranormal operator on a Hilbert space

In this thesis an extensive study is made of the set P of all paranormal operators in B(H), the set of all bounded endomorphisms on the complex Hilbert space H. T ϵ B(H) is paranormal if for each z contained in the resolvent set of T, d(z, σ(T))//(T-zI)^-1 = 1 where d(z, σ(T)) is the distance from z to σ(T), the spectrum of T. P contains the set N of normal operators and P contains the set of hyponormal operators. However, P is contained in L, the set of all T ϵ B(H) such that the convex hull of the spectrum of T is equal to the closure of the numerical range of T. Thus, N≤P≤L.

If the uniform operator (norm) topology is placed on B(H), then the relative topological properties of N, P, L can be discussed. In Section IV, it is shown that: 1) N P and L are arc-wise connected and closed, 2) N, P, and L are nowhere dense subsets of B(H) when dim H ≥ 2, 3) N = P when dimH ˂ ∞ , 4) N is a nowhere dense subset of P when dimH ˂ ∞ , 5) P is not a nowhere dense subset of L when dimH ˂ ∞ , and 6) it is not known if P is a nowhere dense subset of L when dimH ˂ ∞.

The spectral properties of paranormal operators are of current interest in the literature. Putnam [22, 23] has shown that certain points on the boundary of the spectrum of a paranormal operator are either normal eigenvalues or normal approximate eigenvalues. Stampfli [26] has shown that a hyponormal operator with countable spectrum is normal. However, in Theorem 3.3, it is shown that a paranormal operator T with countable spectrum can be written as the direct sum, N ⊕ A, of a normal operator N with σ(N) = σ(T) and of an operator A with σ(A) a subset of the derived set of σ(T). It is then shown that A need not be normal. If we restrict the countable spectrum of T ϵ P to lie on a C²-smooth rectifiable Jordan curve G_o, then T must be normal [see Theorem 3.5 and its Corollary]. If T is a scalar paranormal operator with countable spectrum, then in order to conclude that T is normal the condition of σ(T) ≤ G_o can be relaxed [see Theorem 3.6]. In Theorem 3.7 it is then shown that the above result is not true when T is not assumed to be scalar. It was then conjectured that if T ϵ P with σ(T) ≤ G_o, then T is normal. The proof of Theorem 3.5 relies heavily on the assumption that T has countable spectrum and cannot be generalized. However, the corollary to Theorem 3.9 states that if T ϵ P with σ(T) ≤ G_o, then T has a non-trivial lattice of invariant subspaces. After the completion of most of the work on this thesis, Stampfli [30, 31] published a proof that a paranormal operator T with σ(T) ≤ G_o is normal. His proof uses some rather deep results concerning numerical ranges whereas the proof of Theorem 3.5 uses relatively elementary methods.

Class two p groups as fixed point free automorphism groups

Suppose that AG is a solvable group with normal subgroup G where (|A|, |G|) = 1. Assume that A is a class two odd p group all of whose irreducible representations are isomorphic to subgroups of extra special p groups. If p^c ≠ r^d + 1 for any c = 1, 2 and any prime r where r^2d+1 divides |G| and if C_G(A) = 1 then the Fitting length of G is bounded by the power of p dividing |A|.

The theorem is proved by applying a fixed point theorem to a reduction of the Fitting series of G. The fixed point theorem is proved by reducing a minimal counter example. IF R is an extra spec r subgroup of G fixed by A₁, a subgroup of A, where A₁ centralizes D(R), then all irreducible characters of A₁R which are nontrivial on Z(R) are computed. All nonlinear characters of a class two p group are computed.

Smooth Banach spaces and approximations

If E and F are real Banach spaces let C^p,q(E, F) O ≤ q ≤ p ≤ ∞, denote those maps from E to F which have p continuous Frechet derivatives of which the first q derivatives are bounded. A Banach space E is defined to be C^p,q smooth if C^p,q(E,R) contains a nonzero function with bounded support. This generalizes the standard C^p smoothness classification.

If an L^p space, p ≥ 1, is C^q smooth then it is also C^q,q smooth so that in particular L^p for p an even integer is C^∞,∞ smooth and L^p for p an odd integer is C^p-1,p-1 smooth. In general, however, a C^p smooth B-space need not be C^p,p smooth. C_o is shown to be a non-C^2,2 smooth B-space although it is known to be C^∞ smooth. It is proved that if E is C^p,1 smooth then C_o(E) is C^p,1 smooth and if E has an equivalent C^p norm then c_o(E) has an equivalent C^p norm.

Various consequences of C^p,q smoothness are studied. If f ϵ C^p,q(E,F), if F is C^p,q smooth and if E is non-C^p,q smooth, then the image under f of the boundary of any bounded open subset U of E is dense in the image of U. If E is separable then E is C^p,q smooth if and only if E admits C^p,q partitions of unity; E is C^p,psmooth, p ˂∞, if and only if every closed subset of E is the zero set of some C^P function.

f ϵ C^q(E,F), 0 ≤ q ≤ p ≤ ∞, is said to be C_p,q approximable on a subset U of E if for any ϵ ˃ 0 there exists a g ϵ C^p(E,F) satisfying

sup/xϵU, O≤k≤q ‖ D^k f(x) - D^k g(x) ‖ ≤ ϵ.

It is shown that if E is separable and C^p,q smooth and if f ϵ C^q(E,F) is C_p,q approximable on some neighborhood of every point of E, then F is C_p,q approximable on all of E.

In general it is unknown whether an arbitrary function in C¹(l², R) is C_2,1 approximable and an example of a function in C¹(l², R) which may not be C_2,1 approximable is given. A weak form of C_∞,q, q≥1, to functions in C^q(l², R) is proved: Let {U_α} be a locally finite cover of l² and let {T_α} be a corresponding collection of Hilbert-Schmidt operators on l². Then for any f ϵ C^q(l²,F) such that for all α

sup ‖ D^k(f(x)-g(x))[T_αh]‖ ≤ 1.

xϵU_α,‖h‖≤1, 0≤k≤q