Direct and Converse Theorems for Generalized Bernstein-Type Operators

2000 Mathematics Subject Classification: 41A25, 41A27, 41A36.

Unified min-max and interlacing theorems for linear operators

There exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant-Fischer type formulae. Carlson and Sa [D. Carlson and E.M. Sa, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77-103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case.

Reduction theorems for operators on the cones of monotone functions

For a quasilinear operator on the semiaxis a reduction theorem is proved on the cones of monotone functions in Lp - Lq setting for 0 < q < ∞, 1<= p < ∞. The case 0 < p < 1 is also studied for operators with additional properties. In particular, we obtain critera for three-weight inequalities for the Hardy-type operators with Oinarov' kernel on monotone functions in the case 0 < q < p <= 1.

New higher-derivative R-4 theorems for graviton scattering

The nonminimal pure spinor formalism for the superstring is used to prove two new multiloop theorems which are related to recent higher-derivative R-4 conjectures of Green, Russo, and Vanhove. The first theorem states that when 0 < n < 12, partial derivative R-n(4) terms in the Type II effective action do not receive perturbative contributions above n/2 loops. The second theorem states that when n <= 8, perturbative contributions to partial derivative R-n(4) terms in the IIA and IIB effective actions coincide. As shown by Green, Russo, and Vanhove, these results suggest that d=4 N=8 supergravity is ultraviolet finite up to eight loops.

Ghost poles in the nucleon propagator in the linear sigma model approach and its role in pi N low-energy theorems

Complex mass poles, or ghost poles, are present in the Hartree-Fock solution of the Schwinger-Dyson equation for the nucleon propagator in renormalizable models with Yukawa-type meson-nucleon couplings, as shown many years ago by Brown, Puff and Wilets (BPW), These ghosts violate basic theorems of quantum field theory and their origin is related to the ultraviolet behavior of the model interactions, Recently, Krein et.al, proved that the ghosts disappear when vertex corrections are included in a self-consistent way, softening the interaction sufficiently in the ultraviolet region. In previous studies of pi N scattering using ''dressed'' nucleon propagator and bare vertices, did by Nutt and Wilets in the 70's (NW), it was found that if these poles are explicitly included, the value of the isospin-even amplitude A((+)) is satisfied within 20% at threshold. The absence of a theoretical explanation for the ghosts and the lack of chiral symmetry in these previous studies led us to re-investigate the subject using the approach of the linear sigma-model and study the interplay of low-energy theorems for pi N scattering and ghost poles. For bare interaction vertices we find that ghosts are present in this model as well and that the A((+)) value is badly described, As a first approach to remove these complex poles, we dress the vertices with phenomenological form factors and a reasonable agreement with experiment is achieved, In order to fix the two cutoff parameters, we use the A((+)) value for the chiral limit (m(pi) --> 0) and the experimental value of the isoscalar scattering length, Finally, we test our model by calculating the phase shifts for the S waves and we find a good agreement at threshold. (C) 1997 Elsevier B.V. B.V.

Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring

A ten-dimensional super-Poincaré covariant formalism for the superstring was recently developed which involves a BRST operator constructed from superspace matter variables and a pure spinor ghost variable. A super-Poincaré covariant prescription was defined for computing tree amplitudes and was shown to coincide with the standard RNS prescription. In this paper, picture-changing operators are used to define functional integration over the pure spinor ghosts and and to construct a suitable b ghost. A super-Poincaré covariant prescription is then given for the computation of N-point multiloop amplitudes. One can easily prove that massless N-point multiloop amplitudes vanish for N < 4, confirming the perturbative finiteness of superstring theory. One can also prove the Type IIB S-duality conjecture that R4 terms in the effective action receive no perturbative contributions above one loop. © SISSA/ISAS 2004.

Weighted Theorems on Fractional Integrals in the Generalized Hölder Spaces via Indices mω and Mω

Mathematics Subject Classification: 26A16, 26A33, 46E15.

Nonlinear Normalization in Limit Theorems for Extremes

2000 Mathematics Subject Classification: 60G70, 60F05.

Approximation Properties of Schurer-Stancu Type Polynomials

MSC 2010: 41A25, 41A35

Mucopolysaccharidosis Type Ii: Identification Of 30 Novel Mutations Among Latin American Patients.

In this study, 103 unrelated South-American patients with mucopolysaccharidosis type II (MPS II) were investigated aiming at the identification of iduronate-2-sulfatase (IDS) disease causing mutations and the possibility of some insights on the genotype-phenotype correlation The strategy used for genotyping involved the identification of the previously reported inversion/disruption of the IDS gene by PCR and screening for other mutations by PCR/SSCP. The exons with altered mobility on SSCP were sequenced, as well as all the exons of patients with no SSCP alteration. By using this strategy, we were able to find the pathogenic mutation in all patients. Alterations such as inversion/disruption and partial/total deletions of the IDS gene were found in 20/103 (19%) patients. Small insertions/deletions/indels (<22 bp) and point mutations were identified in 83/103 (88%) patients, including 30 novel mutations; except for a higher frequency of small duplications in relation to small deletions, the frequencies of major and minor alterations found in our sample are in accordance with those described in the literature.

Pyrimidine-5'-nucleotidase Campinas, A New Mutation (p.r56g) In The Nt5c3 Gene Associated With Pyrimidine-5'-nucleotidase Type I Deficiency And Influence Of Gilbert's Syndrome On Clinical Expression.

Pyrimidine-5'-nucleotidase type I (P5'NI) deficiency is an autosomal recessive condition that causes nonspherocytic hemolytic anemia, characterized by marked basophilic stippling and pyrimidine nucleotide accumulation in erythrocytes. We herein present two African descendant patients, father and daughter, with P5'N deficiency, both born from first cousins. Investigation of the promoter polymorphism of the uridine diphospho glucuronosyl transferase 1A (UGT1A) gene revealed that the father was homozygous for the allele (TA7) and the daughter heterozygous (TA6/TA7). P5'NI gene (NT5C3) gene sequencing revealed a further change in homozygosity at amino acid position 56 (p.R56G), located in a highly conserved region. Both patients developed gallstones; however the father, who had undergone surgery for the removal of stones, had extremely severe intrahepatic cholestasis and, liver biopsy revealed fibrosis and siderosis grade III, leading us to believe that the homozygosity of the UGT1A polymorphism was responsible for the more severe clinical features in the father. Moreover, our results show how the clinical expression of hemolytic anemia is influenced by epistatic factors and we describe a new mutation in the P5'N gene associated with enzyme deficiency, iron overload, and severe gallstone formation. To our knowledge, this is the first description of P5'N deficiency in South Americans.

Elevated Micronucleus Frequency In Patients With Type 2 Diabetes, Dyslipidemia And Periodontitis.

The over-production of reactive oxygen species (ROS) can cause oxidative damage to a large number of molecules, including DNA, and has been associated with the pathogenesis of several disorders, such as diabetes mellitus (DM), dyslipidemia and periodontitis (PD). We hypothesise that the presence of these diseases could proportionally increase the DNA damage. The aim of this study was to assess the micronucleus frequency (MNF), as a biomarker for DNA damage, in individuals with type 2 DM, dyslipidemia and PD. One hundred and fifty patients were divided into five groups based upon diabetic, dyslipidemic and periodontal status (Group 1 - poor controlled DM with dyslipidemia and PD; Group 2 - well-controlled DM with dyslipidemia and PD; Group 3 - without DM with dyslipidemia and PD; Group 4 - without DM, without dyslipidemia and with PD; and Group 5 - without DM, dyslipidemia and PD). Blood analyses were carried out for fasting plasma glucose, HbA1c and lipid profile. Periodontal examinations were performed, and venous blood was collected and processed for micronucleus (MN) assay. The frequency of micronuclei was evaluated by cell culture cytokinesis-block MN assay. The general characteristics of each group were described by the mean and standard deviation and the data were submitted to the Mann-Whitney, Kruskal-Wallis, Multiple Logistic Regression and Spearman tests. The Groups 1, 2 and 3 were similarly dyslipidemic presenting increased levels of total cholesterol, low density lipoprotein cholesterol and triglycerides. Periodontal tissue destruction and local inflammation were significantly more severe in diabetics, particularly in Group 1. Frequency of bi-nucleated cells with MN and MNF, as well as nucleoplasmic bridges, were significantly higher for poor controlled diabetics with dyslipidemia and PD in comparison with those systemically healthy, even after adjusting for age, and considering Bonferroni's correction. Elevated frequency of micronuclei was found in patients affected by type 2 diabetes, dyslipidemia and PD. This result suggests that these three pathologies occurring simultaneously promote an additional role to produce DNA impairment. In addition, the micronuclei assay was useful as a biomarker for DNA damage in individuals with chronic degenerative diseases.

Antioxidant And Anti-diabetic Potential Of Passiflora Alata Curtis Aqueous Leaves Extract In Type 1 Diabetes Mellitus (nod-mice).

Leaves of Passiflora alata Curtis were characterized for their antioxidant capacity. Antioxidant analyses of DPPH, FRAP, ABTS, ORAC and phenolic compounds were made in three different extracts: aqueous, methanol/acetone and ethanol. Aqueous extract was found to be the best solvent for recovery of phenolic compounds and antioxidant activity, when compared with methanol/acetone and ethanol. To study the anti-inflammatory properties of this extract in experimental type 1 diabetes, NOD mice were divided into two groups: the P. alata group, treated with aqueous extract of P. alata Curtis, and a non-treated control group, followed by diabetes expression analysis. The consumption of aqueous extract and water ad libitum lasted 28 weeks. The treated-group presented a decrease in diabetes incidence, a low quantity of infiltrative cells in pancreatic islets and increased glutathione in the kidney and liver (p<0.05), when compared with the diabetic and non-diabetic control-groups. In conclusion, our results suggest that the consumption of aqueous extract of P. alata may be considered a good source of natural antioxidants and compounds found in its composition can act as anti-inflammatory agents, helping in the control of diabetes.

Undulatory Physical Resistance Training Program Increases Maximal Strength In Elderly Type 2 Diabetics.

To investigate the effects of a specific protocol of undulatory physical resistance training on maximal strength gains in elderly type 2 diabetics. The study included 48 subjects, aged between 60 and 85 years, of both genders. They were divided into two groups: Untrained Diabetic Elderly (n=19) with those who were not subjected to physical training and Trained Diabetic Elderly (n=29), with those who were subjected to undulatory physical resistance training. The participants were evaluated with several types of resistance training's equipment before and after training protocol, by test of one maximal repetition. The subjects were trained on undulatory resistance three times per week for a period of 16 weeks. The overload used in undulatory resistance training was equivalent to 50% of one maximal repetition and 70% of one maximal repetition, alternating weekly. Statistical analysis revealed significant differences (p<0.05) between pre-test and post-test over a period of 16 weeks. The average gains in strength were 43.20% (knee extension), 65.00% (knee flexion), 27.80% (supine sitting machine), 31.00% (rowing sitting), 43.90% (biceps pulley), and 21.10% (triceps pulley). Undulatory resistance training used with weekly different overloads was effective to provide significant gains in maximum strength in elderly type 2 diabetic individuals.

Brooke-spiegler Syndrome Clinically Misdiagnosed As Neurofibromatosis Type 1.

26