Distributional versions of Littlewood's Tauberian theorem

We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We apply these Tauberian results to deduce a number of Tauberian theorems for power series where Ces\`{a}ro summability follows from Abel summability. We also use our general results to give a new simple proof of the classical Littlewood one-sided Tauberian theorem for power series.Comment: 15 page

Catecholaminergic signalling through thymic nerve fibres, thymocytes and stromal cells is dependent on both circulating and locally synthesized glucocorticoids

Glucocorticoids have been shown to modulate the expression of noradrenaline metabolizing enzymes and beta(2)- and alpha(1B)-adrenoceptors in a tissue- and cell- specific manner. In the thymus, apart from extensive sympathetic innervation, a regulatory network has been identified that encompasses catecholamine-containing non-lymphoid and lymphoid cells. We examined a putative role of adrenal- and thymus-derived glucocorticoids in modulation of rat thymic noradrenaline levels and adrenoceptor expression. Seven days postadrenalectomy, the thymic levels of mRNAs encoding tyrosine hydroxylase, dopamine beta-hydroxylase, monoamine oxidase-A and, consequently, noradrenaline were decreased. Catecholamine content was diminished in autofluorescent nerve fibres (judging by the intensity of fluorescence) and thymocytes (considering HPLC measurements of noradrenaline and the frequency of tyrosine hydroxylase-positive cells), while it remained unaltered in non-lymphoid autofluorescent cells. In addition, adrenalectomy diminished the thymocyte expression of beta(2)- and alpha(1B)-adrenoceptors at both mRNA and protein levels. Administration of ketoconazole (an inhibitor of glucocorticoid synthesis/action; 25 mg kg(-1) day(-1), s.c.) to glucocorticoid-deprived rats increased the thymic levels of tyrosine hydroxylase, dopamine beta-hydroxylase and, consequently, noradrenaline. The increased intensity of the autofluorescent cell fluorescence in ketoconazole-treated rats indicated an increase in their catecholamine content, and suggested differential glucocorticoid-mediated regulation of catecholamines in thymic lymphoid and non-lymphoid cells. In addition, ketoconazole increased the thymocyte expression of alpha(1B)-adrenoceptors. Thus, this study indicates that in the thymus, as in some other tissues, glucocorticoids not only act in concert with cateholamines, but they may modulate catecholamine action by tuning thymic catecholamine metabolism and adrenoceptor expression in a cell-specific manner. Additionally, the study indicates a role of thymus-derived glucocorticoids in this modulation

Variational Problems with Fractional Derivatives: Euler-Lagrange Equations

We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these two bounds coincide, we derive a new form of Euler-Lagrange equations. We use approximations for fractional derivatives in the Lagrangian and obtain the Euler-Lagrange equations which approximate the initial Euler-Lagrange equations in a weak sense

Glucocorticoids, master modulators of the thymic catecholaminergic system?

There is evidence that the major mediators of stress, i.e., catecholamines and glucocorticoids, play an important role in modulating thymopoiesis and consequently immune responses. Furthermore, there are data suggesting that glucocorticoids influence catecholamine action. Therefore, to assess the putative relevance of glucocorticoid-catecholamine interplay in the modulation of thymopoiesis we analyzed thymocyte differentiation/maturation in non-adrenalectomized and andrenalectomized rats subjected to treatment with propranolol (0.4 mg.100 g body weight(-1).day(-1)) for 4 days. The effects of beta-adrenoceptor blockade on thymopoiesis in non-adrenalectomized rats differed not only quantitatively but also qualitatively from those in adrenalectomized rats. In adrenalectomized rats, besides a more efficient thymopoiesis [judged by a more pronounced increase in the relative proportion of the most mature single-positive TCR alpha beta(high) thymocytes as revealed by two-way ANOVA; for CD4(+)CD8(-)F (1,20) = 10.92, P lt 0.01; for CD4(-)CD8(+)F (1,20) = 7.47, P lt 0.05], a skewed thymocyte maturation towards the CD4(-)CD8(+) phenotype, and consequently a diminished CD4(+)CD8(-)/CD4(-)CD8(+) mature TCR alpha beta(high) thymocyte ratio (3.41 +/- 0.21 in non-adrenalectomized rats vs 2.90 +/- 0.31 in adrenalectomized rats, P lt 0.05) were found. Therefore, we assumed that catecholaminergic modulation of thymopoiesis exhibits a substantial degree of glucocorticoid-dependent plasticity. Given that glucocorticoids, apart from catecholamine synthesis, influence adrenoceptor expression, we also hypothesized that the lack of adrenal glucocorticoids affected not only beta-adrenoceptor- but also alpha-adrenoceptor-mediated modulation of thymopoiesis

Generalized Hamilton's Principle with Fractional Derivatives

We generalize Hamilton's principle with fractional derivatives in Lagrangian L(t,y(t),{}_0D_t^\al y(t),\alpha) so that the function $y$ and the order of fractional derivative $\alpha$ are varied in the minimization procedure. We derive stationarity conditions and discuss them through several examples

Aging diminishes the resistance of AO rats to EAE: putative role of enhanced generation of GM-CSF Expressing CD4+T cells in aged rats

Background: Aging influences immune response and susceptibility to EAE in a strain specific manner. The study was designed to examine influence of aging on EAE induction in Albino Oxford (AO) rats. Results: Differently from 3-month-old (young) rats, which were resistant to EAE induction, the majority of aged (24-26-month-old) rats developed mild chronic form of EAE. On 16th day post-immunization, when in aged rats the neurological deficit reached plateau, more mononuclear cells, including CD4+ T lymphocytes was retrieved from spinal cord of aged than young rats. The frequencies of IL-17+ and GM-CSF+ cells within spinal cord infiltrating CD4+ lymphocytes were greater in aged rats. To their increased frequency contributed the expansion of GM-CSF + IL-17 + IFN-gamma+ cells, which are highly pathogenic in mice. The expression of the cytokines (IL-1 beta and IL-23/p19) driving GM-CSF + IL-17 + IFN-gamma + cell differentiation in mice was also augmented in aged rat spinal cord mononuclear cells. Additionally, in aged rat spinal cord the expansion of GM-CSF + IL-17-IFN-gamma- CD4+ T lymphocytes was found. Consistently, the expression of mRNAs for IL-3, the cytokine exhibiting the same expression pattern as GM-CSF, and IL-7, the cytokine driving differentiation of GM-CSF + IL-17-IFN-gamma- CD4 + lymphocytes in mice, was upregulated in aged rat spinal cord mononuclear cells, and the tissue, respectively. This was in accordance with the enhanced generation of the brain antigen-specific GM-CSF+ CD4+ lymphocytes in aged rat draining lymph nodes, as suggested by (i) the higher frequency of GM-CSF+ cells (reflecting the expansion of IL-17-IFN-gamma- cells) within their CD4+ lymphocytes and (ii) the upregulated GM-CSF and IL-3 mRNA expression in fresh CD4+ lymphocytes and MBP-stimulated draining lymph node cells and IL-7 mRNA in lymph node tissue from aged rats. In agreement with the upregulated GM-CSF expression in aged rats, strikingly more CD11b + CD45(int) (activated microglia) and CD45(hi) (mainly proinflammatory dendritic cells and macrophages) cells was retrieved from aged than young rat spinal cord. Besides, expression of mRNA for SOCS1, a negative regulator of proinflammatory cytokine expression in innate immunity cells, was downregulated in aged rat spinal cord mononuclear cells. Conclusions: The study revealed that aging may overcome genetic resistance to EAE, and indicated the cellular and molecular mechanisms contributing to this phenomenon in AO rats

Sex Bias in Pathogenesis of Autoimmune Neuroinflammation: Relevance for Dimethyl Fumarate Immunomodulatory/Anti-oxidant Action

In the present study, upon showing sexual dimorphism in dimethyl fumarate (DMF) efficacy to moderate the clinical severity of experimental autoimmune encephalomyelitis (EAE) in Dark Agouti rats, cellular and molecular substrate of this dimorphism was explored. In rats of both sexes, DMF administration from the day of immunization attenuated EAE severity, but this effect was more prominent in males leading to loss of the sexual dimorphism observed in vehicle-administered controls. Consistently, in male rats, DMF was more efficient in diminishing the number of CD4+ T lymphocytes infiltrating spinal cord (SC) and their reactivation, the number of IL-17+ T lymphocytes and particularly cellularity of their highly pathogenic IFN-gamma+GM-CSF+IL-17+ subset. This was linked with changes in SC CD11b+CD45+TCR alpha beta- microglia/proinflammatory monocyte progeny, substantiated in a more prominent increase in the frequency of anti-inflammatory phygocyting CD163+ cells and the cells expressing high surface levels of immunoregulatory CD83 molecule (associated with apoptotic cells phagocytosis and implicated in downregulation of CD4+ T lymphocyte reactivation) among CD11b+CD45+TCR alpha beta- cells in male rat SC. These changes were associated with greater increase in the nuclear factor (erythroid-derived 2)-like 2 expression in male rats administered with DMF. In accordance with the previous findings, DMF diminished reactive nitrogen and oxygen species generation and consistently, SC level of advanced oxidation protein products, to the greater extent in male rats. Overall, our study indicates sex-specificity in the sensitivity of DMF cellular and molecular targets and encourages sex-based clinical research to define significance of sex for action of therapeutic agents moderating autoimmune neuroinflammation-/oxidative stress-related nervous tissue damage