The norm of the K- Th derivative of the X-symmetric power of an operator

In this paper, the exact value for the norm of directional derivatives, of all orders, for symmetric tensor powers of operators on finite dimensional vector spaces is presented. Using this result, an upper bound for the norm of all directional derivatives of immanants is obtained.

A coherent approach to non-integer order derivatives

Signal Processing, vol. 86, nº 10

Riesz potential operators and inverses via fractional centred derivatives

International Journal of Mathematics and Mathematical Sciences, Vol.2006

Analysis of diffusion process in fractured reservoirs using fractional derivative approach

The fractal geometry is used to model of a naturally fractured reservoir and the concept of fractional derivative is applied to the diffusion equation to incorporate the history of fluid flow in naturally fractured reservoirs. The resulting fractally fractional diffusion (FFD) equation is solved analytically in the Laplace space for three outer boundary conditions. The analytical solutions are used to analyze the response of a naturally fractured reservoir considering the anomalous behavior of oil production. Several synthetic examples are provided to illustrate the methodology proposed in this work and to explain the diffusion process in fractally fractured systems.

What is a fractional derivative?

This paper discusses the concepts underlying the formulation of operators capable of being interpreted as fractional derivatives or fractional integrals. Two criteria for required by a fractional operator are formulated. The Grünwald–Letnikov, Riemann–Liouville and Caputo fractional derivatives and the Riesz potential are accessed in the light of the proposed criteria. A Leibniz rule is also obtained for the Riesz potential.

Febrifugine derivative antimalarial activity: quantum mechanical predictors

Plasmodium falciparum resistant strain development has encouraged the search for new antimalarial drugs. Febrifugine is a natural substance with high activity against P. falciparum presenting strong emetic property and liver toxicity, which prevent it from being used as a clinical drug. The search for analogues that could have a better clinical performance is a current topic. We aim to investigate the theoretical electronic structure by means of febrifugine derivative family semi-empirical molecular orbital calculations, seeking the electronic indexes that could help the design of new efficient derivatives. The theoretical results show there is a clustering in well-defined ranges of several electronic indexes of the most selective molecules. The model proposed for achieving high selectivity was tested with success.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Thermal–mechanical behaviour of chitosan–cellulose derivative thermoreversible hydrogel films

CH, Chitosan; HPMC, (Hydroxypropyl)methyl cellulose; FT, Freeze-thaw; SC, Solvent casting; CH:HPMC (X:Y), pH Z, FT/SC, Chitosan and (hydroxypropyl)methyl cellulose hydrogel, at X and Y proportion (0-100), at Z pH (3.0-4.0) and prepared by freeze-thaw or solvent casting techniques; DSC, Differential scanning calorimetry; MDSC, Temperature modulated Differential scanning calorimetry; Tg, glass transition temperature; ΔH, enthalpy change; TGA, Thermogravimetric Analysis; TG, Thermogravimetry; DTG, Derivative or Differential thermogravimetry; σ, Tensile strength; ε, elongation at break; DMA, Dynamic mechanical analysis; X-Ray, X-radiation, FTIR-ATR, Attenuated total reflectance Fourier transform infrared spectroscopy; SEM, Scanning electron microscopy.

Erratum to: Thermal–mechanical behaviour of chitosan–cellulose derivative thermoreversible hydrogel films

CH, Chitosan; HPMC, (Hydroxypropyl)methyl cellulose; FT, Freeze-thaw; SC, Solvent casting; CH:HPMC (X:Y), pH Z, FT/SC, Chitosan and (hydroxypropyl)methyl cellulose hydrogel, at X and Y proportion (0-100), at Z pH (3.0-4.0) and prepared by freeze-thaw or solvent casting techniques; DSC, Differential scanning calorimetry; MDSC, Temperature modulated Differential scanning calorimetry; Tg, glass transition temperature; ΔH, enthalpy change; TGA, Thermogravimetric Analysis; TG, Thermogravimetry; DTG, Derivative or Differential thermogravimetry; σ, Tensile strength; ε, elongation at break; DMA, Dynamic mechanical analysis; X-Ray, X-radiation, FTIR-ATR, Attenuated total reflectance Fourier transform infrared spectroscopy; SEM, Scanning electron microscopy.

Influence of the elevation of the left ventricular diastolic pressure on the values of the first temporal derivative of the ventricular pressure (dP/dt)

PURPOSE: To assess the effects of the elevation of the left ventricular end-diastolic pressure (LVEDP) on the value of the 1st temporal derivative of the ventricular pressure (dP/dt). METHODS: Nineteen anesthetized dogs were studied. The dogs were mechanically ventilated and underwent thoracotomy with parasympathetic nervous system block. The LVEDP was controlled with the use of a perfusion circuit connected to the left atrium and adjusted to the height of a reservoir. The elevation of the LVEDP was achieved by a sudden increase in the height of a reservoir filled with blood. Continuous recordings of the electrocardiogram, the aortic and ventricular pressures and the dP/dt were performed. RESULTS: Elevation of the LVEDP did not result in any variation of the heart rate (167±16.0bpm, before the procedure; 167±15.5bpm, after the procedure). All the other variables assessed, including systolic blood pressure (128±18.3mmHg and 150±21.5mmHg), diastolic blood pressure (98±16.9mmHg and 115±19.8mmHg), LVEDP (5.5±2.49 and 9.3±3.60mmHg), and dP/dt (4,855 ± 1,082 mmHg/s and 5,149±1,242mmHg/s) showed significant increases following the expansion of the ventricular cavity. Although the elevation of the dP/dt was statistically significant, 6 dogs curiously showed a decrease in the values of dP/dt. CONCLUSION: Sudden elevation of the LVEDP resulted in increased values of dP/dt; however, in some dogs, this response was not uniform.

Redirection of T cells by delivering a transgenic mouse-derived MDM2 tumor antigen-specific TCR and its humanized derivative is governed by the CD8 coreceptor and affects natural human TCR expression.

Retroviral transfer of T cell antigen receptor (TCR) genes selected by circumventing tolerance to broad tumor- and leukemia-associated antigens in human leukocyte antigen (HLA)-A*0201 (A2.1) transgenic (Tg) mice allows the therapeutic reprogramming of human T lymphocytes. Using a human CD8 x A2.1/Kb mouse derived TCR specific for natural peptide-A2.1 (pA2.1) complexes comprising residues 81-88 of the human homolog of the murine double-minute 2 oncoprotein, MDM2(81-88), we found that the heterodimeric CD8 alpha beta coreceptor, but not normally expressed homodimeric CD8 alpha alpha, is required for tetramer binding and functional redirection of TCR- transduced human T cells. CD8+T cells that received a humanized derivative of the MDM2 TCR bound pA2.1 tetramers only in the presence of an anti-human-CD8 anti-body and required more peptide than wild-type (WT) MDM2 TCR+T cells to mount equivalent cytotoxicity. They were, however, sufficiently effective in recognizing malignant targets including fresh leukemia cells. Most efficient expression of transduced TCR in human T lymphocytes was governed by mouse as compared to human constant (C) alphabeta domains, as demonstrated with partially humanized and murinized TCR of primary mouse and human origin, respectively. We further observed a reciprocal relationship between the level of Tg WT mouse relative to natural human TCR expression, resulting in T cells with decreased normal human cell surface TCR. In contrast, natural human TCR display remained unaffected after delivery of the humanized MDM2 TCR. These results provide important insights into the molecular basis of TCR gene therapy of malignant disease.

Transcriptomic and functional analysis of an autolysis-deficient, teicoplanin-resistant derivative of methicillin-resistant Staphylococcus aureus.

The molecular basis of glycopeptide-intermediate S. aureus (GISA) isolates is not well defined though frequently involves phenotypes such as thickened cell walls and decreased autolysis. We have exploited an isogenic pair of teicoplanin-susceptible (strain MRGR3) and teicoplanin-resistant (strain 14-4) methicillin-resistant S. aureus strains for detailed transcriptomic profiling and analysis of altered autolytic properties. Strain 14-4 displayed markedly deficient Triton X-100-triggered autolysis compared to its teicoplanin-susceptible parent, although microarray analysis paradoxically did not reveal significant reductions in expression levels of major autolytic genes atl, lytM, and lytN, except for sle1, which showed a slight decrease. The most important paradox was a more-than-twofold increase in expression of the cidABC operon in 14-4 compared to MRGR3, which was correlated with decreased expression of autolysis negative regulators lytSR and lrgAB. In contrast, the autolysis-deficient phenotype of 14-4 was correlated with both increased expression of negative autolysis regulators (arlRS, mgrA, and sarA) and decreased expression of positive regulators (agr RNAII and RNAIII). Quantitative bacteriolytic assays and zymographic analysis of concentrated culture supernatants showed a striking reduction in Atl-derived, extracellular bacteriolytic hydrolase activities in 14-4 compared to MRGR3. This observed difference was independent of the source of cell wall substrate (MRGR3 or 14-4) used for analysis. Collectively, our results suggest that altered autolytic properties in 14-4 are apparently not driven by significant changes in the transcription of key autolytic effectors. Instead, our analysis points to alternate regulatory mechanisms that impact autolysis effectors which may include changes in posttranscriptional processing or export.

Use of the 2,3-diacyl-trehalose and the purified protein derivative in the serodiagnosis of tuberculosis in AIDS

The effect of the human immunodeficiency virus (HIV) infection on IgG production against purified protein derivative (PPD) and 2,3-diacil-trehalose (SL-IV) was investigated by an enzyme-linked immunosorbent assay (ELISA) test. Comparison between the antigens showed that immunocompetent patients produce preferentially antibodies to SL-IV than to PPD (73.3% versus 63.3%). Combination of these results showed an increase of the sensitivity to 80%, which decreased over the spectrum of immunodepression caused by HIV. In the tuberculous HIV seropositive group the sensitivities of SL-IV and PPD were 36.4% versus 40% and 0% versus 22.2% in the tuberculosis/acquired immunodeficiency syndrome (TB/AIDS) group. Combination of these results gave respectively 54.5% and 20%, showing that serological tests have limited value for diagnosis of tuberculosis in HIV infected patients. High antibody levels were observed in HIV seropositive asymptomatic group, but only two individuals were positive for both antigens. In the follow up, one of them developed tuberculous lymphadenitis, indicating that further work is needed to access the value of serological tests in predicting tuberculosis in HIV infected individuals.

Site-specific conjugation of a radioiodinated phenethylamine derivative to a monoclonal antibody results in increased radioactivity localization in tumor.

The preparation of a novel radioiodination reagent, the (aminooxy)acetyl derivative of (p-[125]-iodophenyl)ethylamine, is described. Conventional radioiodination of proteins involves the formation of iodotyrosine residues, but for in vivo applications such as thyroid or stomach immunoscintigraphy, the susceptibility of these residues to tissue dehalogenases constitutes a serious disadvantage. Using our new compound, which has a particularly nonreactive aromatic ring, we confirm and extend studies published by other workers indicating the much greater in vivo stability of iodophenyl compounds compared to the more conventional iodophenolic ones. In addition, the aminooxy group of our reagent gives a stable and specific linkage to aldehyde groups formed by periodate oxidation on the sugar moiety of antibody molecules. In vitro, favorable binding activity and high stability was obtained with a (([125I]iodoaryl)amino)oxy labeled monoclonal antibody directed against carcinoembryonic antigen. In vivo, using paired labeling experiments in nude mice bearing colon carcinoma xenografts, the (([125I]iodoaryl)amino)oxy-MAb (MAb = monoclonal antibody) was compared with the same MAb 131I-labeled by conventional chloramine-T method. Tumor 125I concentration of (arylamino)oxy MAb (measured as percent injected dose per gram) was significantly higher as compared to values obtained with a conventionally labeled 131I antibody. Additionally, thyroid uptake, an indicator of iodine release from the antibody, was up to 25 times lower after injection of 125I-MAb obtained by the new method as compared to the conventionally iodinated 131I-MAb.

A novel derivative of the chelon desferrioxamine for site-specific conjugation to antibodies.

We describe the preparation of the modified chelator aminooxyacetyl-ferrioxamine, and the replacement of its iron atom by 67Ga at high specific activity. The aminooxy function of this compound was allowed to react with the aldehyde groups generated by the periodate oxidation of the oligosaccharide of a mouse IgG1 monoclonal antibody (MAb) directed against carcino-embryonic antigen (CEA). The use of the aminooxy group allowed a stable bond to be formed between the chelon and the antibody with no need for reduction. Iron was removed from the ferrioxamine moiety and replaced by 67Ga either before or after conjugation of the chelon to the antibody. In either case the labelled antibody was injected into nude mice bearing a human colon carcinoma having the appropriate antigenicity. Unoxidized antibody, labelled with 125I by conventional methods, was co-injected as an internal control. Additional control experiments were carried out with a non-immune IgG using the same 67Ga-labelled modified chelon as above. The in vivo distribution of the modified antibodies was evaluated at various times between 24 and 96 hr after injection. The methods used were gamma-camera imaging and, more quantitatively, gamma-counting of the various organs after dissection. Interestingly, with the metal-chelon-labelled antibody, the intensity and specificity of tumor labelling was comparable and in some cases superior to the results obtained with radio-iodinated antibody. In particular, there was almost no increase in liver and spleen uptake of radioactive metal relative to radio-iodine, contrary to what has been observed with most antibodies labelled with 111In after conjugation with DTPA.