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.

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.

Mapping social change in U.S. coastal counties: a social atlas of coastal North Carolina

This document represents a pilot effort to map social change in the coastal United States—a social atlas characterizing changing population, demographic, housing, and economic attributes. This pilot effort focuses on coastal North Carolina. The impetus for this project came from numerous discussions about the usefulness and need for a graphic representation of social change information for U.S. coastal regions. Although the information presented here will be of interest to a broad segment of the coastal community and general public, the intended target audience is coastal natural resource management professionals, Sea Grant Extension staff, urban and regional land-use planners, environmental educators, and other allied constituents interested in the social aspects of how the nation’s coasts are changing. This document has three sections. The first section provides background information about the project. The second section features descriptions of social indicators and depictions of social indicator data for 1970, 1980, 1990, and 2000, and changes from 1970 to 2000 for all North Carolina coastal counties. The third section contains three case studies describing changes in select social attributes for subsets of counties. (PDF contains 67 pages)

Fine mapping and functional analysis of the multiple sclerosis risk gene CD6

CD6 has recently been identified and validated as risk gene for multiple sclerosis (MS), based on the association of a single nucleotide polymorphism (SNP), rs17824933, located in intron 1. CD6 is a cell surface scavenger receptor involved in T-cell activation and proliferation, as well as in thymocyte differentiation. In this study, we performed a haptag SNP screen of the CD6 gene locus using a total of thirteen tagging SNPs, of which three were non-synonymous SNPs, and replicated the recently reported GWAS SNP rs650258 in a Spanish-Basque collection of 814 controls and 823 cases. Validation of the six most strongly associated SNPs was performed in an independent collection of 2265 MS patients and 2600 healthy controls. We identified association of haplotypes composed of two non-synonymous SNPs [rs11230563 (R225W) and rs2074225 (A257V)] in the 2nd SRCR domain with susceptibility to MS (Pmax(T) permutation=161024). The effect of these haplotypes on CD6 surface expression and cytokine secretion was also tested. The analysis showed significantly different CD6 expression patterns in the distinct cell subsets, i.e. – CD4+ naı¨ve cells, P = 0.0001; CD8+ naı¨ve cells, P,0.0001; CD4+ and CD8+ central memory cells, P = 0.01 and 0.05, respectively; and natural killer T (NKT) cells, P = 0.02; with the protective haplotype (RA) showing higher expression of CD6. However, no significant changes were observed in natural killer (NK) cells, effector memory and terminally differentiated effector memory T cells. Our findings reveal that this new MS-associated CD6 risk haplotype significantly modifies expression of CD6 on CD4+ and CD8+ T cells.

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

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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.

Retroviral Infections in Sheep and Goats: Small Ruminant Lentiviruses and Host Interaction

Small ruminant lentiviruses (SRLV) are members of the Retrovirus family comprising the closely related Visna/Maedi Virus (VMV) and the Caprine Arthritis-Encephalitis Virus (CAEV), which infect sheep and goats. Both infect cells of the monocyte/macrophage lineage and cause lifelong infections. Infection by VMV and CAEV can lead to Visna/Maedi (VM) and Caprine Arthritis-Encephalitis (CAE) respectively, slow progressive inflammatory diseases primarily affecting the lungs, nervous system, joints and mammary glands. VM and CAE are distributed worldwide and develop over a period of months or years, always leading to the death of the host, with the consequent economic and welfare implications. Currently, the control of VM and CAE relies on the control of transmission and culling of infected animals. However, there is evidence that host genetics play an important role in determining Susceptibility/Resistance to SRLV infection and disease progression, but little work has been performed in small ruminants. More research is necessary to understand the host-SRLV interaction.

Anatomical and developmental patterns of interleukin-2 gene expression in the mouse: analysis of IL-2 expressing cells and partial characterization of interactions involved in mediating IL-2 gene expression in vivo

Interleukin-2 (IL-2) is an important mediator in the vertebrate immune system. IL-2 is a potent growth factor that mature T lymphocytes use as a proliferation signal and the production of IL-2 is crucial for the clonal expansion of antigen-specific T cells in the primary immune response. IL-2 driven proliferation is dependent on the interaction of the lymphokine with its cognate multichain receptor. IL-2 expression is induced only upon stimulation and transcriptional activation of the IL-2 gene relies extensively on the coordinate interaction of numerous inducible and constitutive trans-acting factors. Over the past several years, thousands of papers have been published regarding molecular and cellular aspects of IL-2 gene expression and IL-2 function. The vast majority of these reports describe work that has been carried out in vitro. However, considerably less is known about control of IL-2 gene expression and IL-2 function in vivo.

To gain new insight into the regulation of IL-2 gene expression in vivo, anatomical and developmental patterns of IL-2 gene expression in the mouse were established by employing in situ hybridization and immunohistochemical staining methodologies to tissue sections generated from normal mice and mutant animals in which T -cell development was perturbed. Results from these studies revealed several interesting aspects of IL-2 gene expression, such as (1) induction of IL-2 gene expression and protein synthesis in the thymus, the primary site of T-cell development in the body, (2) cell-type specificity of IL-2 gene expression in vivo, (3) participation of IL-2 in the extrathymic expansion of mature T cells in particular tissues, independent of an acute immune response to foreign antigen, (4) involvement of IL-2 in maintaining immunologic balance in the mucosal immune system, and (5) potential function of IL-2 in early events associated with hematopoiesis.

Extensive analysis of IL-2 mRNA accumulation and protein production in the murine thymus at various stages of development established the existence of two classes of intrathymic IL-2 producing cells. One class of intrathymic IL-2 producers was found exclusively in the fetal thymus. Cells belonging to this subset were restricted to the outermost region of the thymus. IL-2 expression in the fetal thymus was highly transient; a dramatic peak ofiL-2 mRNA accumulation was identified at day 14.5 of gestation and maximal IL-2 protein production was observed 12 hours later, after which both IL-2 mRNA and protein levels rapidly decreased. Significantly, the presence of IL-2 expressing cells in the day 14-15 fetal thymus was not contingent on the generation of T-cell receptor (TcR) positive cells. The second class of IL-2 producing cells was also detectable in the fetal thymus (cells found in this class represented a minority subset of IL-2 producers in the fetal thymus) but persist in the thymus during later stages of development and after birth. Intrathymic IL-2 producers in postnatal animals were located in the subcapsular region and cortex, indicating that these cells reside in the same areas where immature T cells are consigned. The frequency of IL-2 expressing cells in the postnatal thymus was extremely low, indicating that induction of IL-2 expression and protein synthesis are indicative of a rare activation event. Unlike the fetal class of intrathymic IL-2 producers, the presence of IL-2 producing cells in the postnatal thymus was dependent on to the generation of TcR+ cells. Subsequent examination of intrathymic IL-2 production in mutant postnatal mice unable to produce either αβ or γδ T cells showed that postnatal IL-2 producers in the thymus belong to both αβ and γδ lineages. Additionally, further studies indicated that IL-2 synthesis by immature αβ -T cells depends on the expression of bonafide TcR αβ-heterodimers. Taken altogether, IL-2 production in the postnatal thymus relies on the generation of αβ or γδ-TcR^+ cells and induction of IL-2 protein synthesis can be linked to an activation event mediated via the TcR.

With regard to tissue specificity of IL-2 gene expression in vivo, analysis of whole body sections obtained from normal neonatal mouse pups by in situ hybridization demonstrated that IL-2 mRNA^+ cells were found in both lymphoid and nonlymphoid tissues with which T cells are associated, such as the thymus (as described above), dermis and gut. Tissues devoid of IL-2 mRNA^+ cells included brain, heart, lung, liver, stomach, spine, spinal cord, kidney, and bladder. Additional analysis of isolated tissues taken from older animals revealed that IL-2 expression was undetectable in bone marrow and in nonactivated spleen and lymph nodes. Thus, it appears that extrathymic IL-2 expressing cells in nonimmunologically challenged animals are relegated to particular epidermal and epithelial tissues in which characterized subsets of T cells reside and thatinduction of IL-2 gene expression associated with these tissues may be a result of T-cell activation therein.

Based on the neonatal in situ hybridization results, a detailed investigation into possible induction of IL-2 expression resulting in IL-2 protein synthesis in the skin and gut revealed that IL-2 expression is induced in the epidermis and intestine and IL-2 protein is available to drive cell proliferation of resident cells and/or participate in immune function in these tissues. Pertaining to IL-2 expression in the skin, maximal IL-2 mRNA accumulation and protein production were observed when resident Vγ_3^+ T-cell populations were expanding. At this age, both IL-2 mRNA^+ cells and IL-2 protein production were intimately associated with hair follicles. Likewise, at this age a significant number of CD3ε^+ cells were also found in association with follicles. The colocalization of IL-2 expression and CD3ε^+ cells suggests that IL-2 expression is induced when T cells are in contact with hair follicles. In contrast, neither IL-2 mRNA nor IL-2 protein were readily detected once T-cell density in the skin reached steady-state proportions. At this point, T cells were no longer found associated with hair follicles but were evenly distributed throughout the epidermis. In addition, IL-2 expression in the skin was contingent upon the presence of mature T cells therein and induction of IL-2 protein synthesis in the skin did not depend on the expression of a specific TcR on resident T cells. These newly disclosed properties of IL-2 expression in the skin indicate that IL-2 may play an additional role in controlling mature T-cell proliferation by participating in the extrathymic expansion of T cells, particularly those associated with the epidermis.

Finally, regarding IL-2 expression and protein synthesis in the gut, IL-2 producing cells were found associated with the lamina propria of neonatal animals and gut-associated IL-2 production persisted throughout life. In older animals, the frequency of IL-2 producing cells in the small intestine was not identical to that in the large intestine and this difference may reflect regional specialization of the mucosal immune system in response to enteric antigen. Similar to other instances of IL-2 gene expression in vivo, a failure to generate mature T cells also led to an abrogation of IL-2 protein production in the gut. The presence of IL-2 producing cells in the neonatal gut suggested that these cells may be generated during fetal development. Examination of the fetal gut to determine the distribution of IL-2 producing cells therein indicated that there was a tenfold increase in the number of gut-associated IL-2 producers at day 20 of gestation compared to that observed four days earlier and there was little difference between the frequency of IL-2 producing cells in prenatal versus neonatal gut. The origin of these fetally-derived IL-2 producing cells is unclear. Prior to the immigration of IL-2 inducible cells to the fetal gut and/or induction of IL-2 expression therein, IL-2 protein was observed in the fetal liver and fetal omentum, as well as the fetal thymus. Considering that induction of IL-2 protein synthesis may be an indication of future functional capability, detection of IL-2 producing cells in the fetal liver and fetal omentum raises the possibility that IL-2 producing cells in the fetal gut may be extrathymic in origin and IL-2 producing cells in these fetal tissues may not belong solely to the T lineage. Overall, these results provide increased understanding of the nature of IL-2 producing cells in the gut and how the absence of IL-2 production therein and in fetal hematopoietic tissues can result in the acute pathology observed in IL-2 deficient animals.

Teleseismic array analysis of upper mantle compressional velocity structure

Large quantities of teleseismic short-period seismograms recorded at SCARLET provide travel time, apparent velocity and waveform data for study of upper mantle compressional velocity structure. Relative array analysis of arrival times from distant (30° < Δ < 95°) earthquakes at all azimuths constrains lateral velocity variations beneath southern California. We compare dT/dΔ back azimuth and averaged arrival time estimates from the entire network for 154 events to the same parameters derived from small subsets of SCARLET. Patterns of mislocation vectors for over 100 overlapping subarrays delimit the spatial extent of an east-west striking, high-velocity anomaly beneath the Transverse Ranges. Thin lens analysis of the averaged arrival time differences, called 'net delay' data, requires the mean depth of the corresponding lens to be more than 100 km. Our results are consistent with the PKP-delay times of Hadley and Kanamori (1977), who first proposed the high-velocity feature, but we place the anomalous material at substantially greater depths than their 40-100 km estimate.

Detailed analysis of travel time, ray parameter and waveform data from 29 events occurring in the distance range 9° to 40° reveals the upper mantle structure beneath an oceanic ridge to depths of over 900 km. More than 1400 digital seismograms from earthquakes in Mexico and Central America yield 1753 travel times and 58 dT/dΔ measurements as well as high-quality, stable waveforms for investigation of the deep structure of the Gulf of California. The result of a travel time inversion with the tau method (Bessonova et al., 1976) is adjusted to fit the p(Δ) data, then further refined by incorporation of relative amplitude information through synthetic seismogram modeling. The application of a modified wave field continuation method (Clayton and McMechan, 1981) to the data with the final model confirms that GCA is consistent with the entire data set and also provides an estimate of the data resolution in velocity-depth space. We discover that the upper mantle under this spreading center has anomalously slow velocities to depths of 350 km, and place new constraints on the shape of the 660 km discontinuity.

Seismograms from 22 earthquakes along the northeast Pacific rim recorded in southern California form the data set for a comparative investigation of the upper mantle beneath the Cascade Ranges-Juan de Fuca region, an ocean-continent transit ion. These data consist of 853 seismograms (6° < Δ < 42°) which produce 1068 travel times and 40 ray parameter estimates. We use the spreading center model initially in synthetic seismogram modeling, and perturb GCA until the Cascade Ranges data are matched. Wave field continuation of both data sets with a common reference model confirms that real differences exist between the two suites of seismograms, implying lateral variation in the upper mantle. The ocean-continent transition model, CJF, features velocities from 200 and 350 km that are intermediate between GCA and T7 (Burdick and Helmberger, 1978), a model for the inland western United States. Models of continental shield regions (e.g., King and Calcagnile, 1976) have higher velocities in this depth range, but all four model types are similar below 400 km. This variation in rate of velocity increase with tectonic regime suggests an inverse relationship between velocity gradient and lithospheric age above 400 km depth.

Tunable heparan sulfate glycomimetics for modulating chemokine activity

Heparan sulfate (HS) glycosaminoglycans participate in critical biological processes by modulating the activity of a diverse set of protein binding partners. Such proteins include all known members of the chemokine superfamily, which are thought to guide the migration of distinct subsets of immune cells through their interactions with HS proteoglycans on endothelial cell surfaces. Animal-derived heparin polysaccharides have been shown to reduce inflammation levels through the inhibition of HS-chemokine interactions; however, the clinical usage of heparin as an anti-inflammatory drug is hampered by its anticoagulant activity and potential risk for side effects, such as heparin-induced thrombocytopenia (HIT).

Here, we describe an expedient, divergent synthesis to prepare defined glycomimetics of HS that recapitulate the macromolecular structure and biological activity of natural HS glycosaminoglycans. Our synthetic approach uses a core disaccharide precursor to generate a library of four differentially sulfated polymers. We show that a trisulfated glycopolymer antagonizes the chemotactic activities of pro-inflammatory chemokine RANTES with similar potency as heparin polysaccharide, without potentiating the anticoagulant activities of antithrombin III. The same glycopolymer also inhibited the homeostatic chemokine SDF-1 with significantly more efficacy than heparin. Our work offers a general strategy for modulating chemokines and dissecting the pleiotropic functions of HS/heparin through the presentation of defined sulfation motifs within multivalent polymeric scaffolds.

Molecular genetic studies on voltage-gated ion channels

Several different methods have been employed in the study of voltage-gated ion channels. Electrophysiological studies on excitable cells in vertebrates and molluscs have shown that many different voltage-gated potassium (K⁺) channels and sodium channels may coexist in the same organism. Parallel genetic studies in Drosophila have identified mutations in several genes that alter the properties of specific subsets of physiologically identified ion channels. Chapter 2 describes molecular studies that identify two Drosophila homologs of vertebrate sodium-channel genes. Mutations in one of these Drosophila sodium-channel genes are shown to be responsible for the temperature-dependent paralysis of a behavioural mutant para^ts. Evolutionary arguments, based on the partial sequences of the two Drosophila genes, suggest that subfamilies of voltage-gated sodium channels in vertebrates remain to be identified.

In Drosophila, diverse voltage-gated K⁺ channels arise from alternatively spliced mRNAs generated at the Shaker locus. Chapter 3 and the Appendices describe the isolation and characterization of several human K⁺-channel genes, similar in sequence to Shaker. Each of these human genes has a highly conserved homolog in rodents; thus, this K⁺-channel gene family probably diversified prior to the mammalian radiation. Functional K⁺ channels encoded by these genes have been expressed in Xenopus oocytes and their properties have been analyzed by electrophysiological methods. These studies demonstrate that both transient and noninactivating voltage-gated K⁺ channels may be encoded by mammalian genes closely related to Shaker. In addition, results presented in Appendix 3 clearly demonstrate that independent gene products from two K⁺-channel genes may efficiently co-assemble into heterooligomeric K⁺ channels with properties distinct from either homomultimeric channel. This finding suggests yet another molecular mechanism for the generation of K⁺-channel diversity.

Identificação de áreas sob maior risco para leishmaniose visceral na cidade de Teresina, Piauí, Brasil

O propósito desta Tese foi detectar e caracterizar áreas sob alto risco para leishmaniose visceral (LV) e descrever os padrões de ocorrência e difusão da doença, entre os anos de 1993 a 1996 e 2001 a 2006, em Teresina, Piauí, por meio de métodos estatísticos para análise de dados espaciais, sistemas de informações geográficas e imagens de sensoriamento remoto. Os resultados deste estudo são apresentados na forma de três manuscritos. O primeiro usou análise de dados espaciais para identificar as áreas com maior risco de LV na área urbana de Teresina entre 2001 e 2006. Os resultados utilizando razão de kernels demonstraram que as regiões periféricas da cidade foram mais fortemente afetadas ao longo do período analisado. A análise com indicadores locais de autocorrelação espacial mostrou que, no início do período de estudo, os agregados de alta incidência de LV localizavam-se principalmente na região sul e nordeste da cidade, mas nos anos seguintes os eles apareceram também na região norte da cidade, sugerindo que o padrão de ocorrência de LV não é estático e a doença pode se espalhar ocasionalmente para outras áreas do município. O segundo estudo teve como objetivo caracterizar e predizer territórios de alto risco para ocorrência da LV em Teresina, com base em indicadores socioeconômicos e dados ambientais, obtidos por sensoriamento remoto. Os resultados da classificação orientada a objeto apontam a expansão da área urbana para a periferia da cidade, onde antes havia maior cobertura de vegetação. O modelo desenvolvido foi capaz de discriminar 15 conjuntos de setores censitário (SC) com diferentes probabilidades de conterem SC com alto risco de ocorrência de LV. O subconjunto com maior probabilidade de conter SC com alto risco de LV (92%) englobou SC com percentual de chefes de família alfabetizados menor que a mediana (≤64,2%), com maior área coberta por vegetação densa, com percentual de até 3 moradores por domicílio acima do terceiro quartil (>31,6%). O modelo apresentou, respectivamente, na amostra de treinamento e validação, sensibilidade de 79% e 54%, especificidade de 74% e 71%, acurácia global de 75% e 67% e área sob a curva ROC de 83% e 66%. O terceiro manuscrito teve como objetivo avaliar a aplicabilidade da estratégia de classificação orientada a objeto na busca de possíveis indicadores de cobertura do solo relacionados com a ocorrência da LV em meio urbano. Os índices de acurácia foram altos em ambas as imagens (>90%). Na correlação da incidência da LV com os indicadores ambientais verificou-se correlações positivas com os indicadores Vegetação densa, Vegetação rasteira e Solo exposto e negativa com os indicadores Água, Urbana densa e Urbana verde, todos estatisticamente significantes. Os resultados desta tese revelam que a ocorrência da LV na periferia de Teresina está intensamente relacionada às condições socioeconômicas inadequadas e transformações ambientais decorrentes do processo de expansão urbana, favorecendo a ocorrência do vetor (Lutzomyia longipalpis) nestas regiões.

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.

Locally convex Riesz spaces and Archimedean quotient spaces

A Riesz space with a Hausdorff, locally convex topology determined by Riesz seminorms is called a locally convex Riesz space. A sequence {x_n} in a locally convex Riesz space L is said to converge locally to x ϵ L if for some topologically bounded set B and every real r ˃ 0 there exists N (r) and n ≥ N (r) implies x – x_n ϵ r^b. Local Cauchy sequences are defined analogously, and L is said to be locally complete if every local Cauchy sequence converges locally. Then L is locally complete if and only if every monotone local Cauchy sequence has a least upper bound. This is a somewhat more general form of the completeness criterion for Riesz – normed Riesz spaces given by Luxemburg and Zaanen. Locally complete, bound, locally convex Riesz spaces are barrelled. If the space is metrizable, local completeness and topological completeness are equivalent.

Two measures of the non-archimedean character of a non-archimedean Riesz space L are the smallest ideal A_o (L) such that quotient space is Archimedean and the ideal I (L) = { x ϵ L: for some 0 ≤ v ϵ L, n |x| ≤ v for n = 1, 2, …}. In general A_o (L) ᴝ I (L). If L is itself a quotient space, a necessary and sufficient condition that A_o (L) = I (L) is given. There is an example where A_o (L) ≠ I (L).

A necessary and sufficient condition that a Riesz space L have every quotient space Archimedean is that for every 0 ≤ u, v ϵ L there exist u₁ = sup (inf (n v, u): n = 1, 2, …), and real numbers m₁ and m₂ such that m₁ u₁ ≥ v₁ and m₂ v₁ ≥ u₁. If, in addition, L is Dedekind σ – complete, then L may be represented as the space of all functions which vanish off finite subsets of some non-empty set.

Efeito da Suplementação com L-arginina em subpopulações linfocitárias de ratos submetidos a esplenectomia total isolada ou combinada com autoimplante esplênico

A L-arginina é reconhecida como um nutriente de fundamental importância na resposta imune, apesar de seus efeitos serem, por vezes, considerados inconstantes. O autoimplante esplênico tem sido proposto como alternativa à esplenectomia total isolada, mas existem preocupações quanto à eficácia do restabelecimento da resposta imune, haja vista que o paciente pode permanecer com risco aumentado de desenvolvimento de infecção fulminante pós esplenectomia, mesmo após a regeneração morfológica do órgão. O objetivo deste estudo foi avaliar a participação da suplementação dietética com L-arginina em subpopulações linfocitárias no sangue, no baço e nos autoimplantes esplênicos de ratos submetidos a esplenectomia isolada ou combinada com autoimplante esplênico. Foram utilizados 42 ratos Sprague-Dawley machos, randomicamente distribuídos em seis grupos: 1 Controle operação simulada; 2 esplenectomia total; 3 esplenectomia total combinada com autoimplante esplênico; 4 Controle operação simulada, com suplementação de L-arginina; 5 esplenectomia total, com suplementação de L-arginina; e 6 esplenectomia total combinada com autoimplante esplênico, com suplementação de L-arginina. Os animais dos grupos 4, 5 e 6 receberam suplementação de L-arginina, uma vez ao dia, durante 15 dias anteriores a coleta sangüínea realizada imediatamente antes dos procedimentos operatórios (semanas 0 e 12). A dose utilizada foi de 1,0 g/kg/dia, administrada por via intragástrica em bolus. As avaliações foram realizadas por meio de hemograma e citometria de fluxo. A análise estatística utilizou testes paramétricos e nãoparamétricos, sendo p<0,05 considerado para a rejeição da hipótese nula. A suplementação com L-arginina acarretou elevação da contagem relativa e absoluta de neutrófilos periféricos, 12 semanas após a realização de esplenectomia total combinada com autoimplante esplênico. A esplenectomia total ocasionou diminuição da contagem relativa de linfócitos T totais, T CD4+ e T CD8β no sangue, mas a suplementação dietética com L-arginina evitou a diminuição do percentual de células T totais e T CD8β no sangue dos animais submetidos a autoimplante esplênico. Tanto a realização de autoimplante esplênico como a suplementação de L-arginina previnem a diminuição da subpopulação de linfócitos T CD4+ no sangue periférico, fato que usualmente ocorre após realização de esplenectomia total. Houve maior proliferação de células brancas / g de tecido nos autoimplante esplênico dos animais suplementados, porém a suplementação não influenciou a contagem de linfócitos T, T CD4+ e B de zona marginal de baço. A suplementação do aminoácido L-arginina após a realização de esplenectomia total combinada com autoimplante esplênico em ratos foi capaz de reverter alterações observadas em algumas das subpopulações linfocitárias, ocasionadas pela esplenectomia.