Fixed and Best Proximity Points of Cyclic Jointly Accretive and Contractive Self-Mappings

p(>= 2)-cyclic and contractive self-mappings on a set of subsets of a metric space which are simultaneously accretive on the whole metric space are investigated. The joint fulfilment of the p-cyclic contractiveness and accretive properties is formulated as well as potential relationships with cyclic self-mappings in order to be Kannan self-mappings. The existence and uniqueness of best proximity points and fixed points is also investigated as well as some related properties of composed self-mappings from the union of any two adjacent subsets, belonging to the initial set of subsets, to themselves.

On Best Proximity Point Theorems and Fixed Point Theorems for p-Cyclic Hybrid Self-Mappings in Banach Spaces

This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent (K-Lambda)hybrid p-cyclic self-mappings relative to a Bregman distance Df, associated with a Gâteaux differentiable proper strictly convex function f in a smooth Banach space, where the real functions Lambda and K quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping.Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings.

Some Results on Fixed and Best Proximity Points of Multivalued

This paper is devoted to investigate the fixed points and best proximity points of multivalued cyclic self-mappings on a set of subsets of complete metric spaces endowed with a partial order under a generalized contractive condition involving a Hausdorff distance. The existence and uniqueness of fixed points of both the cyclic self-mapping and its associate composite self-mappings on each of the subsets are investigated, if the subsets in the cyclic disposal are nonempty, bounded and of nonempty convex intersection. The obtained results are extended to the existence of unique best proximity points in uniformly convex Banach spaces.

Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings

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Colonization and development of Oribatida mite communities (Acari: Oribatida) in the forest reclaimed limestone mine dumps

In order to study the colonization and development of moss mites (Oribatida) communities in a Scots pine forest of a reclaimed limestone mine dump in Northern Poland, 3 plots from the dump were chosen. The selected plots differed in age, 5 years old, 35 and 50 years old. From a total of 30 samples 499 mites (Acari) were extracted in Tullgren funnel from which 262 were Oribatida. Abundance (N) was analyzed in all mites and after determining the species of both, juvenile and adult stages of oribatids, the following indices were analyzed: Abundance (N), Dominance (D), Species diversity (S), Species richness (s) and Shannon’s diversity index (H). Regarding to the results obtained; oribatid mites were dominant with the highest abundance in all assemblages (Plot 1: 139 Oribatida /299 Acari. Plot 2: 40/55 and Plot 3: 83/145). Tectocepheus velatus showed a very high dominance (45,99%) in plot 1; the highest value for Shannon’s diversity index belonged to plot 3. On the other hand, juvenile’s percentage was significantly higher than adult’s percentage, especially at plot 2 (95,02%). These results made us to conclude that the high abundance of oribatids in the youngest forest is due to T. velatus’s high abundance and that plot 3 is the best habitat for mites. Finally, the high occurrence of juvenile stages requires keeping on studying the area.

Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

Part I. A study of the velocity structure of the earth by the use of core phases. Part II. The 1971 San Fernando earthquake series focal mechanisms and tectonics

The initial objective of Part I was to determine the nature of upper mantle discontinuities, the average velocities through the mantle, and differences between mantle structure under continents and oceans by the use of P'dP', the seismic core phase P'P' (PKPPKP) that reflects at depth d in the mantle. In order to accomplish this, it was found necessary to also investigate core phases themselves and their inferences on core structure. P'dP' at both single stations and at the LASA array in Montana indicates that the following zones are candidates for discontinuities with varying degrees of confidence: 800-950 km, weak; 630-670 km, strongest; 500-600 km, strong but interpretation in doubt; 350-415 km, fair; 280-300 km, strong, varying in depth; 100-200 km, strong, varying in depth, may be the bottom of the low-velocity zone. It is estimated that a single station cannot easily discriminate between asymmetric P'P' and P'dP' for lead times of about 30 sec from the main P'P' phase, but the LASA array reduces this uncertainty range to less than 10 sec. The problems of scatter of P'P' main-phase times, mainly due to asymmetric P'P', incorrect identification of the branch, and lack of the proper velocity structure at the velocity point, are avoided and the analysis shows that one-way travel of P waves through oceanic mantle is delayed by 0.65 to 0.95 sec relative to United States mid-continental mantle.

A new P-wave velocity core model is constructed from observed times, dt/dΔ's, and relative amplitudes of P'; the observed times of SKS, SKKS, and PKiKP; and a new mantle-velocity determination by Jordan and Anderson. The new core model is smooth except for a discontinuity at the inner-core boundary determined to be at a radius of 1215 km. Short-period amplitude data do not require the inner core Q to be significantly lower than that of the outer core. Several lines of evidence show that most, if not all, of the arrivals preceding the DF branch of P' at distances shorter than 143° are due to scattering as proposed by Haddon and not due to spherically symmetric discontinuities just above the inner core as previously believed. Calculation of the travel-time distribution of scattered phases and comparison with published data show that the strongest scattering takes place at or near the core-mantle boundary close to the seismic station.

In Part II, the largest events in the San Fernando earthquake series, initiated by the main shock at 14 00 41.8 GMT on February 9, 1971, were chosen for analysis from the first three months of activity, 87 events in all. The initial rupture location coincides with the lower, northernmost edge of the main north-dipping thrust fault and the aftershock distribution. The best focal mechanism fit to the main shock P-wave first motions constrains the fault plane parameters to: strike, N 67° (± 6°) W; dip, 52° (± 3°) NE; rake, 72° (67°-95°) left lateral. Focal mechanisms of the aftershocks clearly outline a downstep of the western edge of the main thrust fault surface along a northeast-trending flexure. Faulting on this downstep is left-lateral strike-slip and dominates the strain release of the aftershock series, which indicates that the downstep limited the main event rupture on the west. The main thrust fault surface dips at about 35° to the northeast at shallow depths and probably steepens to 50° below a depth of 8 km. This steep dip at depth is a characteristic of other thrust faults in the Transverse Ranges and indicates the presence at depth of laterally-varying vertical forces that are probably due to buckling or overriding that causes some upward redirection of a dominant north-south horizontal compression. Two sets of events exhibit normal dip-slip motion with shallow hypocenters and correlate with areas of ground subsidence deduced from gravity data. Several lines of evidence indicate that a horizontal compressional stress in a north or north-northwest direction was added to the stresses in the aftershock area 12 days after the main shock. After this change, events were contained in bursts along the downstep and sequencing within the bursts provides evidence for an earthquake-triggering phenomenon that propagates with speeds of 5 to 15 km/day. Seismicity before the San Fernando series and the mapped structure of the area suggest that the downstep of the main fault surface is not a localized discontinuity but is part of a zone of weakness extending from Point Dume, near Malibu, to Palmdale on the San Andreas fault. This zone is interpreted as a decoupling boundary between crustal blocks that permits them to deform separately in the prevalent crustal-shortening mode of the Transverse Ranges region.

I. Electron spin relaxation studies of manganese(II) complexes in acetonitrile. II. Nuclear spin relaxation studies of bromine in tetrabromomanganese(II) in acetonitrile

Magnetic resonance techniques have given us a powerful means for investigating dynamical processes in gases, liquids and solids. Dynamical effects manifest themselves in both resonance line shifts and linewidths, and, accordingly, require detailed analyses to extract desired information. The success of a magnetic resonance experiment depends critically on relaxation mechanisms to maintain thermal equilibrium between spin states. Consequently, there must be an interaction between the excited spin states and their immediate molecular environment which promote changes in spin orientation while excess magnetic energy is coupled into other degrees of freedom by non-radiative processes. This is well known as spin-lattice relaxation. Certain dynamical processes cause fluctuations in the spin state energy levels leading to spin-spin relaxation and, here again, the environment at the molecular level plays a significant role in the magnitude of interaction. Relatively few electron spin relaxation studies of solutions have been conducted and the present work is addressed toward the extension of our knowledge in this area and the retrieval of dynamical information from line shape analyses on a time scale comparable to diffusion controlled phenomena.

Specifically, the electron spin relaxation of three Mn⁺²3d⁵ complexes, Mn(CH₃CN)₆⁺², MnCl₄^-2 in acetonitrile has been studied in considerable detail. The effective spin Hamiltonian constants were carefully evaluated under a wide range of experimental conditions. Resonance widths of these Mn⁺² complexes were studied in the presence of various excess ligand ions and as a function of concentration, viscosity, temperature and frequency (X-band, ~9.5 Ԍ Hz and K-band, ~35 Ԍ Hz).

A number of interesting conclusions were drawn from these studies. For the Et₄NCl-₄^-2 system several relaxation mechanisms leading to resonance broadening were observed. One source appears to arise through spin-orbit interactions caused by modulation of the ligand field resulting from transient distortions of the complex imparted by solvent fluctuations in the immediate surroundings of the paramagnetic ion. An additional spin relaxation was assigned to the formation of ion pairs [Et₄N⁺…MnCl₄^-2] and it was possible to estimate the dissociation constant for this specie in acetonitrile.

The Bu₄NBr-MnBr₄^-2 study was considerably more interesting. As in the former case, solvent fluctuations and ion-pairing of the paramagnetic complex [Bu₄N⁺…MnBr₄^-2] provide significant relaxation for the electronic spin system. Most interesting, without doubt, is the onset of a new relaxation mechanism leading to resonance broadening which is best interpreted as chemical exchange. Thus, assuming that resonance widths were simply governed by electron spin state lifetimes, we were able to extract dynamical information from an interaction in which the initial and final states are the same

MnBr₄^-2 + Br^- = MnBr₄^-2 + Br^-.

The bimolecular rate constants were obtained at six different temperatures and their magnitudes suggested that the exchange is probably diffusion controlled with essentially a zero energy of activation. The most important source of spin relaxation in this system stems directly from dipolar interactions between the manganese 3d⁵ electrons. Moreover, the dipolar broadening is strongly frequency dependent indicating a deviation between the transverse and longitudinal relaxation times. We are led to the conclusion that the 3d⁵ spin states of ion-paired MnBr₄^-2 are significantly correlated so that dynamical processes are also entering the picture. It was possible to estimate the correlation time, ^Td, characterizing this dynamical process.

In Part II we study nuclear magnetic relaxation of bromine ions in the MnBr4-2-Bu4NBr-acetonitrile system. Essentially we monitor the 79Br and 81Br linewidths in response to the [MnBr4-2]/[Br-] ratio with the express purpose of supporting our contention that exchange is occurring between "free" bromine ions in the solvent and bromine in the first coordination sphere of the paramagnetic anion. The complexity of the system elicited a two-part study: (1) the linewidth behavior of Bu4NBr in anhydrous CH3CN in the absence of MnBr4-2 and (2) in the presence of MnBr4-2. It was concluded in study (1) that dynamical association, Bu4NBr k1= Bu4N+ + Br-, was modulating field-gradient interactions at frequencies high enough to provide an estimation of the unimolecular rate constant, k1. A comparison of the two isotopic bromine linewidth-mole fraction results led to the conclusion that quadrupole interactions provided the dominant relaxation mechanism. In study (2) the "residual" bromine linewidths for both 79Br and 81Br are clearly controlled by quadrupole interactions which appear to be modulated by very rapid dynamical processes other than molecular reorientation. We conclude that the "residual" linewidth has its origin in chemical exchange and that bromine nuclei exchange rapidly between a "free" solvated ion and the paramagnetic complex, MnBr4-2.

Global and local challenges for best practices in assessment. The 9th Conference on the International Test Commission. Book of abstracts

The 9th International Test Commission Conference (ITC) took place at the Miramar Palace in San Sebastian, Spain, between the 2nd and 5th of July, 2014. The Conference was titled, “Global and Local Challenges for Best Practices in Assessment.” The International Test Commission, ITC (www.intestcom.org), is an association of national psychological associations, test commissions, publishers, and other organizations, as well as individuals who are committed to the promotion of effective testing and assessment policies and to the proper development, evaluation, and uses of educational and psychological instruments. The ITC facilitates the exchange of information among members and stimulates their cooperation on problems related to the construction, distribution, and uses of psychological and educational tests and other psychodiagnostic tools. This volume contains the abstracts of the contributions presented at the 9th International Test Commission Conference. The four themes of the Conference were closely linked to the goals of the ITC: - Challenges and Opportunities in International Assessment. - Application of New Technoloogies and New Psychometric Models in Testing. - Standards and Guidelines for Best Testing Practices. - Testing in Multilingual and Multicultural Contexts.

Os indicadores de desempenho instituídos pelo TCU para as Instituições Federais de Ensino Superior: análise empírica do período de 2008 a 2010,

A Gestão Pública tem incorporado boas práticas de administração mediante foco no resultado eficiente e na transparência. A utilização de indicadores de desempenho exerce um papel fundamental para espelhar a real situação do órgão e suas possibilidades de melhoria. No caso específico das universidades federais, o Tribunal de Contas da União (TCU) estabeleceu um conjunto de nove indicadores a serem medidos por essas unidades e divulgados através de seus relatórios de gestão. A dificuldade interpretativa advinda de visualizar, simultaneamente, esses critérios avaliativos contidos nesse conjunto e suas interdependências, fomentou a elaboração desta pesquisa. O estudo objetiva analisar e sintetizar o conjunto de indicadores de desempenho, atinentes a 53 universidades federais, referentes aos anos de 2008 a 2010, a fim de identificar um modelo de simplificação para auxiliar os controles interno e externo. A metodologia utilizada é a da Análise Fatorial, uma técnica estatística multivariada de interdependência, e pouco explorada em pesquisas anteriores nessa temática, além de testes de regressão linear e da Análise Envoltória de Dados (DEA), esta já amplamente utilizada na literatura, a fim de possibilitar ratificar as associações e interpretações dos resultados. Os testes mostraram uma aderência satisfatória da técnica aos dados coletados, permitindo identificar dois fatores que pudessem explicar 61,8% do conjunto informacional original. Com ratificação da DEA, esses fatores foram associados ao desempenho e ao custo, e a relação entre os dois foi interpretada como um índice de eficiência. O fator atrelado ao desempenho foi intitulado o indicador sumarizado de todo o conjunto estabelecido pelo TCU, tendo sido encontrado correlação alta e significativa com o Ranking Universitário Folha, mostrando que eles possuem semelhantes poderes discriminantes, mesmo tendo sido oriundos de bases de cálculo distintas. Ademais, destacam-se os seguintes resultados complementares: 1) Embora o custo influencie para o desempenho das universidades federais, ele não é preponderante, mas os indicadores de envolvimento com a pós-graduação e qualificação do corpo docente são os mais relevantes; 2) Os indicadores de resultado não sofrem muita influência do custo, sobretudo o de recursos humanos (funcionários), mostrando que de uma maneira geral há ineficiência na gestão de pessoal das universidades; 3) A utilização da DEA mostrou que a escolha das variáveis realmente pode redundar em resultados distintos e não correlatos significativamente, apresentando uma limitação quanto à certificação dos escores de eficiência obtidos.

Diversidade e padrões estruturais da vegetação halófila-psamófila das restingas do Rio de Janeiro

As restingas do Estado do Rio de Janeiro são áreas de sedimentação predominantemente quaternária, descontínuas geograficamente, formadas em função das mudanças paleoclimáticas, flutuações do nível do mar e transporte longitudinal de sedimentos. A diversidade e a estrutura da vegetação halófila-psamófila presente nestas restingas são os principais focos deste estudo, onde foram analisadas a similaridade florística, as formas de vida e síndrome de dispersão, o padrão de riqueza e diversidade, a distribuição das espécies e os parâmetros de cobertura vegetal, serrapilheira, solo desnudo e salinidade da água do mar. Foram amostradas nove áreas de restinga, a saber, Praia do Sul, Marambaia, Grumari, Marapendi, Maricá, Massambaba, Barra de São João, Jurubatiba e São João da Barra. Foram encontradas 90 espécies, distribuídas em 33 famílias, 69 gêneros, sendo as famílias de maior riqueza específica: Asteraceae (10), Poaceae (9 espécies), Fabaceae (9) e Rubiaceae (6). Foi registrada uma baixa riqueza de espécies nas áreas avaliadas, variando de 25 a 48. Somente 11 espécies ocorreram em todas as áreas (Alternanthera maritima, Blutaparon portulacoides, Canavalia rosea, Cereus fernambucensis, Euphorbia hyssopifolia, Ipomoea imperati, Ipomoea pes-caprae, Panicum racemosum, Remirea maritima, Sporobolus virginicus, Stenotaphrum secundatum), e 12 são dominantes, em uma ou mais áreas (Allagoptera arenaria, Alternanthera maritima, Blutaparon portulacoides, Canavalia rosea, Ipomoea imperati, Ipomoea pes-caprae, Mollugo verticillata, Panicum racemosum, Remirea maritima, Spermacoce capitata, Sporobolus virginicus, Stenotaphrum secundatum), existindo um grande número de espécies raras. O índice de diversidade de Shannon variou de 1,49 a 2,40, e a equabilidade de Pielou de 0,82 a 0,60. O agrupamento formou dois grandes grupos, sendo o primeiro constituído por Barra de São João, Praia do Sul, Marambaia, Grumari e Marapendi, e o segundo por Jurubatiba, São João da Barra, Maricá e Massambaba. As áreas mais similares floristicamente foram Maricá e Massambaba (58%), Grumari e Marapendi (56%), e Barra de São João e Praia do Sul (50%). A vegetação apresenta uma flora característica, com diferença na composição entre as áreas, e similaridade entre áreas geograficamente mais próximas. Um terço das espécies identificadas são caméfitos (34,56%), seguida por fanerófitos (20,98%), geófitos (16,04%), hemicriptófitos (12,34%), terófitos (13,58%) e duas lianas. Na dispersão predomina a autocoria (41,97%), anemocoria (33,33%) e zoocoria (24,69%). O tamanho das áreas perpendicularmente ao mar não está relacionado com aumento da riqueza, nem apresenta o padrão de aumento com o distanciamento do mar. Existem diferenças da riqueza e da diversidade entre as áreas, não havendo uma homogeneidade ao longo do litoral. Há uma zonação, com espécies distribuídas próximas ao mar (Allagoptera arenaria, Alternanthera maritima, Blutaparon portulacoides, Canavalia rosea, Cassytha filiformis, Cereus fernambucensis, Hydrocotyle bonariensis, Ipomoea pes-caprae, Schinus terebinthifolia, Sophora tomentosa, Stenotaphrum secundatum, Cyrtocymura scorpioides), e ao longo do gradiente perpendicular ao mar (Chamaecrista flexuosa, Euphorbia hyssopifolia, Ipomoea imperati, Mollugo verticillata, Panicum racemosum, Paspalum maritimum, Remirea maritima, Sporobolus virginicus). O modelo de série logarítmica é o que melhor representa a vegetação, independente da diversidade ou riqueza. A cobertura vegetal variou entre as áreas. A serrapilheira e o solo desnudo estão estreitamente relacionados com a cobertura vegetal, havendo variação entre as áreas.

Approximate Best Proximity Points of Cyclic Self-maps in Metric Spaces and Cyclic Asymptotic Regularity

3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) Madrid, AUG 28-31, 2014 / editado por Vagenas, EC; Vlachos, DS; Bastos, C; Hofer, T; Kominis, Y; Kosmas, O; LeLay, G; DePadova, P; Rode, B; Suraud, E; Varga, K

On contractive cyclic fuzzy maps in metric spaces and some related results on fuzzy best proximity points and fuzzy fixed points

This paper investigates some properties of cyclic fuzzy maps in metric spaces. The convergence of distances as well as that of sequences being generated as iterates defined by a class of contractive cyclic fuzzy mapping to fuzzy best proximity points of (non-necessarily intersecting adjacent subsets) of the cyclic disposal is studied. An extension is given for the case when the images of the points of a class of contractive cyclic fuzzy mappings restricted to a particular subset of the cyclic disposal are allowed to lie either in the same subset or in its next adjacent one.

Salmon stocking by the Lancashire River Authority: investigations into the requirements and methods best suited to the area

All species of fish are able to propagate and maintain their numbers provided that no adverse influence occurs to change the compatible environment, the salmon is no exception. Propagation of fish by artificial means has long been a subject of discussion amongst fishery workers and views have been expressed (both favourable and unfavourable) on the merits of the various methods employed. In an attempt to discover whether artificial propagation was necessary and also to find the best methods of propagation to adopt in the various rivers, a phased programme of investigation into natural spawning efficiency and the results obtained by various methods of artificial propagation was started in the Lancashire River Board area during 1957. The object being to seek information on: (1) The survival of ova from natural spawnings to the eyed and alevin stages. (2) The population density of feeding fry (from natural spawnings) at various intervals of development. (3) The viability of green ova and eyed ova- when planted artificially. (4a) The survival to 0+ parr from implants of eyed ova unfed fry and fed fry. (4b) Populations per unit area of 0+ parr from various planting densities of eyed ova, unfed fry and fed fry. Sampling stations were selected on the Rivers Ribble, Lune and Wyre watersheds for the purpose of marking and examination of natural salmon redds.