Fractional Integration and Fractional Differentiation of the M-Series

Mathematics Subject Classification: 26A33, 33C60, 44A15

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.

Fractional Integration of the Product of Bessel Functions of the First Kind

Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09

Information Matrix for Beta Distributions

2000 Mathematics Subject Classification: 33C90, 62E99.

On Some Generalizations of Classical Integral Transforms

MSC 2010: 44A15, 44A20, 33C60

A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.

Two-Point Function at Two Loops via Triangle Diagram Insertion

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

On the Riemann-Liouville Fractional q-Integral Operator Involving a Basic Analogue of Fox H-Function

2000 Mathematics Subject Classification: 33D60, 26A33, 33C60

Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values

2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15

On Generalized Weyl Fractional q-Integral Operator Involving Generalized Basic Hypergeometric Functions

Mathematics Subject Classification: 33D60, 33D90, 26A33

Relationship Between Orofacial Function, Dentofacial Morphology, And Bite Force In Young Subjects.

The aim was to evaluate the relationship between orofacial function, dentofacial morphology, and bite force in young subjects. Three hundred and sixteen subjects were divided according to dentition stage (early, intermediate, and late mixed and permanent dentition). Orofacial function was screened using the Nordic Orofacial Test-Screening (NOT-S). Orthodontic treatment need, bite force, lateral and frontal craniofacial dimensions and presence of sleep bruxism were also assessed. The results were submitted to descriptive statistics, normality and correlation tests, analysis of variance, and multiple linear regression to test the relationship between NOT-S scores and the studied independent variables. The variance of NOT-S scores between groups was not significant. The evaluation of the variables that significantly contributed to NOT-S scores variation showed that age and presence of bruxism related to higher NOT-S total scores, while the increase in overbite measurement and presence of closed lip posture related to lower scores. Bite force did not show a significant relationship with scores of orofacial dysfunction. No significant correlations between craniofacial dimensions and NOT-S scores were observed. Age and sleep bruxism were related to higher NOT-S scores, while the increase in overbite measurement and closed lip posture contributed to lower scores of orofacial dysfunction.

Impaired Compensatory Beta-cell Function And Growth In Response To High-fat Diet In Ldl Receptor Knockout Mice.

In this study, we investigated the effect of low density lipoprotein receptor (LDLr) deficiency on gap junctional connexin 36 (Cx36) islet content and on the functional and growth response of pancreatic beta-cells in C57BL/6 mice fed a high-fat (HF) diet. After 60 days on regular or HF diet, the metabolic state and morphometric islet parameters of wild-type (WT) and LDLr-/- mice were assessed. HF diet-fed WT animals became obese and hypercholesterolaemic as well as hyperglycaemic, hyperinsulinaemic, glucose intolerant and insulin resistant, characterizing them as prediabetic. Also they showed a significant decrease in beta-cell secretory response to glucose. Overall, LDLr-/- mice displayed greater susceptibility to HF diet as judged by their marked cholesterolaemia, intolerance to glucose and pronounced decrease in glucose-stimulated insulin secretion. HF diet induced similarly in WT and LDLr-/- mice, a significant decrease in Cx36 beta-cell content as revealed by immunoblotting. Prediabetic WT mice displayed marked increase in beta-cell mass mainly due to beta-cell hypertrophy/replication. Nevertheless, HF diet-fed LDLr-/- mice showed no significant changes in beta-cell mass, but lower islet-duct association (neogenesis) and higher beta-cell apoptosis index were seen as compared to controls. The higher metabolic susceptibility to HF diet of LDLr-/- mice may be explained by a deficiency in insulin secretory response to glucose associated with lack of compensatory beta-cell expansion.

Long-term Postoperative Atrophy Of Contralateral Hippocampus And Cognitive Function In Unilateral Refractory Mtle With Unilateral Hippocampal Sclerosis.

This study aimed to evaluate long-term atrophy in contralateral hippocampal volume after surgery for unilateral MTLE, as well as the cognitive outcome for patients submitted to either selective transsylvian amygdalohippocampectomy (SelAH) or anterior temporal lobe resection (ATL). We performed a longitudinal study of 47 patients with MRI signs of unilateral hippocampal sclerosis (23 patients with right-sided hippocampal sclerosis) who underwent surgical treatment for MTLE. They underwent preoperative/postoperative high-resolution MRI as well as neuropsychological assessment for memory and estimated IQ. To investigate possible changes in the contralateral hippocampus of patients, we included 28 controls who underwent two MRIs at long-term intervals. The volumetry using preoperative MRI showed significant hippocampal atrophy ipsilateral to the side of surgery when compared with controls (p<0.0001) but no differences in contralateral hippocampal volumes. The mean postoperative follow-up was 8.7 years (± 2.5 SD; median=8.0). Our patients were classified as Engel I (80%), Engel II (18.2%), and Engel III (1.8%). We observed a small but significant reduction in the contralateral hippocampus of patients but no volume changes in controls. Most of the patients presented small declines in both estimated IQ and memory, which were more pronounced in patients with left TLE and in those with persistent seizures. Different surgical approaches did not impose differences in seizure control or in cognitive outcome. We observed small declines in cognitive scores with most of these patients, which were worse in patients with left-sided resection and in those who continued to suffer from postoperative seizures. We also demonstrated that manual volumetry can reveal a reduction in volume in the contralateral hippocampus, although this change was mild and could not be detected by visual analysis. These new findings suggest that dynamic processes continue to act after the removal of the hippocampus, and further studies with larger groups may help in understanding the underlying mechanisms.

Doehlert Design-desirability Function Multi-criteria Optimal Separation Of 17 Phenolic Compounds From Extra-virgin Olive Oil By Capillary Zone Electrophoresis.

In Brazil, the consumption of extra-virgin olive oil (EVOO) is increasing annually, but there are no experimental studies concerning the phenolic compound contents of commercial EVOO. The aim of this work was to optimise the separation of 17 phenolic compounds already detected in EVOO. A Doehlert matrix experimental design was used, evaluating the effects of pH and electrolyte concentration. Resolution, runtime and migration time relative standard deviation values were evaluated. Derringer's desirability function was used to simultaneously optimise all 37 responses. The 17 peaks were separated in 19min using a fused-silica capillary (50μm internal diameter, 72cm of effective length) with an extended light path and 101.3mmolL(-1) of boric acid electrolyte (pH 9.15, 30kV). The method was validated and applied to 15 EVOO samples found in Brazilian supermarkets.