An Expansion Formula for Fractional Derivatives and its Application

An expansion formula for fractional derivatives given as in form of a series involving function and moments of its k-th derivative is derived. The convergence of the series is proved and an estimate of the reminder is given. The form of the fractional derivative given here is especially suitable in deriving restrictions, in a form of internal variable theory, following from the second law of thermodynamics, when applied to linear viscoelasticity of fractional derivative type

On a initial value problem arising in mechanics

We study initial value problem for a system consisting of an integer order and distributed-order fractional differential equation describing forced oscillations of a body attached to a free end of a light viscoelastic rod. Explicit form of a solution for a class of linear viscoelastic solids is given in terms of a convolution integral. Restrictions on storage and loss moduli following from the Second Law of Thermodynamics play the crucial role in establishing the form of the solution. Some previous results are shown to be special cases of the present analysis

Distributional framework for solving fractional differential equations

We analyze solvability of a special form of distributed order fractional differential equations within the space of tempered distributions supported by the positive half-line

The Role of Regulatory T Cells and TH17 Cells in Multiple Myeloma

The development of multiple myeloma (MM) involves a series of genetic alterations and changes in the bone marrow microenvironment, favoring the growth of the tumor and failure of local immune control. Quantitative and functional alterations in CD4+ and CD8+ T cells have been described in MM. The balance between T regulatory cells (Treg) and T helper (Th) 17 cells represents one essential prerequisite for maintaining anti-tumor immunity in MM. Tregs play an important role in the preservation of self-tolerance and modulation of overall immune responses against infections and tumor cells. In MM patients, Tregs seem to contribute to myeloma-related immune dysfunction and targeting them could, therefore, help to restore and enhance vital immune responses. Th17 cells protect against fungal and parasitic infections and participate in inflammatory reactions and autoimmunity. The interplay of TGF-β and IL-6, expressed at high levels in the bone marrow of myeloma patients, may affect generation of Th17 cells both directly or via other pro-inflammatory cytokines and thereby modulate antitumor immune responses. A detailed analysis of the balance between Tregs and Th17 cells seems necessary in order to design more effective and less toxic modes of immunotherapy myeloma which still is an uncurable malignancy

Growth, processing, and optical properties of epitaxial Er_2O_3 on silicon

Erbium-doped materials have been investigated for generating and amplifying light in low-power chip-scale optical networks on silicon, but several effects limit their performance in dense microphotonic applications. Stoichiometric ionic crystals are a potential alternative that achieve an Er^(3+) density 100× greater. We report the growth, processing, material characterization, and optical properties of single-crystal Er_2O_3 epitaxially grown on silicon. A peak Er^(3+) resonant absorption of 364 dB/cm at 1535nm with minimal background loss places a high limit on potential gain. Using high-quality microdisk resonators, we conduct thorough C/L-band radiative efficiency and lifetime measurements and observe strong upconverted luminescence near 550 and 670 nm

Bifurcation analysis of rotating axially compressed imperfect nano-rod

Static stability problem for axially compressed rotating nano-rod clamped at one and free at the other end is analyzed by the use of bifurcation theory. It is obtained that the pitchfork bifurcation may be either super- or sub-critical. Considering the imperfections in rod's shape and loading, it is proved that they constitute the two-parameter universal unfolding of the problem. Numerical analysis also revealed that for non-locality parameters having higher value than the critical one interaction curves have two branches, so that for a single critical value of angular velocity there exist two critical values of horizontal force

Intraperitoneal bevacizumab for control of malignant ascites due to advanced-stage gastrointestinal cancers: A multicentre double-blind, placebo-controlled phase II study - AIO SUP-0108

PURPOSE: Malignant ascites is debilitating for patients with advanced cancer. As shown previously, tumour cell production of vascular endothelial growth factor might be a major cause of the formation of malignant ascites. Intraperitoneal bevacizumab could therefore be an option for symptom control in refractory ascites. PATIENTS AND METHODS: Patients with advanced gastrointestinal cancer and malignant ascites who had undergone paracentesis at least twice within the past 4 weeks were randomly assigned in a 2:1 ratio to intraperitoneal bevacizumab (400 mg absolute) or placebo after paracentesis. During the 8-week treatment period, a minimum interval of 14 d was kept between the applications of the study drug. Primary end-point was paracentesis-free survival (ParFS). RESULTS: Fifty-three patients (median age 63 years) were randomised. Forty-nine patients received at least one study drug application and qualified for the main analysis. The proportion of patients with at least one common toxicity criteria grade III-V event was similar with 20/33 (61%) on bevacizumab and 11/16 (69%) on placebo. Median ParFS was 14 d (95% confidence interval [CI]: 11-17) in the bevacizumab arm and 10.5 d (95% CI: 7-21) on placebo (hazard ratio 0.74, 95% CI: 0.40-1.37; P = 0.16). The longest paracentesis-free period was 19 d on bevacizumab (range 6-66 d) and 17.5 d in the placebo arm (range 4-42) (P = 0.85). Median overall survival was 64 d (95% CI: 45-103) on bevacizumab compared to 31.5 d (95% CI: 20-117) on placebo (P = 0.31). CONCLUSION: Intraperitoneal bevacizumab was well tolerated. Overall, treatment did not result in a significantly better symptom control of malignant ascites. However, patients defined by specific immune characteristics may benefit

Fractional variational calculus of variable order

We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.Comment: Submitted 26-Sept-2011; accepted 18-Oct-2011; withdrawn by the authors 21-Dec-2011; resubmitted 27-Dec-2011; revised 20-March-2012; accepted 13-April-2012; to 'Advances in Harmonic Analysis and Operator Theory', The Stefan Samko Anniversary Volume (Eds: A. Almeida, L. Castro, F.-O. Speck), Operator Theory: Advances and Applications, Birkh\"auser Verlag (http://www.springer.com/series/4850

Targeting MAGE-C1/CT7 Expression Increases Cell Sensitivity to the Proteasome Inhibitor Bortezomib in Multiple Myeloma Cell Lines

The MAGE-C1/CT7 encodes a cancer/testis antigen (CTA), is located on the chromosomal region Xq26-27 and is highly polymorphic in humans. MAGE-C1/CT7 is frequently expressed in multiple myeloma (MM) that may be a potential target for immunotherapy in this still incurable disease. MAGEC1/CT7 expression is restricted to malignant plasma cells and it has been suggested that MAGE-C1/CT7 might play a pathogenic role in MM; however, the exact function this protein in the pathophysiology of MM is not yet understood. Our objectives were (1) to clarify the role of MAGE-C1/CT7 in the control of cellular proliferation and cell cycle in myeloma and (2) to evaluate the impact of silencing MAGE-C1/CT7 on myeloma cells treated with bortezomib. Myeloma cell line SKO-007 was transduced for stable expression of shRNA-MAGE-C1/CT7. Downregulation of MAGE-C1/CT7 was confirmed by real time quantitative PCR and western blot. Functional assays included cell proliferation, cell invasion, cell cycle analysis and apoptosis. Western blot showed a 70-80% decrease in MAGE-C1/CT7 protein expression in inhibited cells (shRNA-MAGE-C1/CT7) when compared with controls. Functional assays did not indicate a difference in cell proliferation and DNA synthesis when inhibited cells were compared with controls. However, we found a decreased percentage of cells in the G2/M phase of the cell cycle among inhibited cells, but not in the controls (p < 0.05). When myeloma cells were treated with bortezomib, we observed a 48% reduction of cells in the G2/M phase among inhibited cells while controls showed 13% (empty vector) and 9% (ineffective shRNA) reduction, respectively (p < 0.01). Furthermore, inhibited cells treated with bortezomib showed an increased percentage of apoptotic cells (Annexin V+/PI-) in comparison with bortezomib-treated controls (p < 0.001). We found that MAGE-C1/CT7 protects SKO-007 cells against bortezomib-induced apoptosis. Therefore, we could speculate that MAGE-C1/CT7 gene therapy could be a strategy for future therapies in MM, in particular in combination with proteasome inhibitors.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Laboratory of Molecular Biology and Genomics, Ludwig Institute for Cancer Research, São Paulo Branch, BrazilUniversidade Federal de São Paulo, Disciplina Hematol & Hemoterapia, São Paulo, BrazilLudwig Inst Canc Res, Lab Mol Biol & Genom, São Paulo, BrazilRecepta Biopharma, Ludwig Inst Canc Res, São Paulo, BrazilInCor, Fac Med, Setor Vetores Virais, Lab Genet & Cardiol Mol, São Paulo, BrazilJohns Hopkins Univ, Sch Med, Dept Neurosurg, Ludwig Collaborat Grp, Baltimore, MD 21205 USAUniv Med Ctr Hamburg Eppendorf, Dept Med 2, Hamburg, GermanyUniversidade Federal de São Paulo, Disciplina Hematol & Hemoterapia, São Paulo, BrazilWeb of Scienc