A Caputo fractional derivative of a function with respect to another function

In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor’s Theorem, Fermat’s Theorem, etc., are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided.

Fractional differential equations with dependence on the Caputo-Katugampola derivative

In this paper we present a new type of fractional operator, the Caputo–Katugampola derivative. The Caputo and the Caputo–Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy type problem, with dependence on the Caputo–Katugampola derivative, is proven. A decomposition formula for the Caputo–Katugampola derivative is obtained. This formula allows us to provide a simple numerical procedure to solve the fractional differential equation.

Sensitivity Analysis in Convex Optimization through the Circatangent Derivative

The main goal of this paper is to analyse the sensitivity of a vector convex optimization problem according to variations in the right-hand side. We measure the quantitative behavior of a certain set of Pareto optimal points characterized to become minimum when the objective function is composed with a positive function. Its behavior is analysed quantitatively using the circatangent derivative for set-valued maps. Particularly, it is shown that the sensitivity is closely related to a Lagrange multiplier solution of a dual program.

Preliminary structure-activity relationship studies on some novel s-substituted aliphatic analogues of 5-{1-[(4- chlorophenyl) sulfonyl]-3-piperidinyl}-1, 3, 4-oxadiazol-2-yl sulfide

Purpose: To study the structure-activity relationships of synthetic multifunctional sulfides through evaluation of lipoxygenase and anti-bacterial activities. Methods: S-substituted derivatives of the parent compound 5-(1-(4-chlorophenylsulfonyl) piperidin-3- yl)-1, 3, 4-oxadiazole-2-thiol were synthesized through reaction with different saturated and unsaturated alkyl halides in DMF medium, with NaH catalyst. Spectral characterization of each derivative was carried out with respect to IR, 1H - NMR, 13C - NMR and EI - MS. The lipoxygenase inhibitory and antibacterial activities of the derivatives were determined using standard procedures. Results: Compound 5e exhibited higher lipoxygenase inhibitory potential than the standard (Baicalein®), with % inhibition of 94.71 ± 0.45 and IC50 of 20.72 ± 0.34 μmoles/L. Compound 5b showed significant antibacterial potential against all the bacterial strains with % inhibition ranging from 62.04 ± 2.78, 69.49 ± 0.41, 63.38 ± 1.97 and 59.70 ± 3.70 to 78.32 ± 0.41, while MIC ranged from 8.18 ± 2.00, 10.60 ± 1.83, 10.84 ± 3.00, 9.81 ± 1.86 and 11.73 ± 5.00 μmoles/L for S. typhi, E. coli, P. aeruginosa, B. subtilis and S. aureus, respectively. Compounds 5d, 5e and 5g showed good antibacterial activity against S. typhi and B. subtilis bacterial strains. Conclusion: The results suggest that compound 5e bearing n-pentyl group is a potent lipoxygenase inhibitor, while compound 5b with n-propyl substitution is a strong antibacterial agent. In addition, compounds 5d, 5e and 5g bearing n-butyl, n-pentyl and n-octyl groups, respectively, are good antibacterial agents against S. typhi and B. subtilis.

S-Alkylated/aralkylated 2-(1H-indol-3-yl-methyl)-1,3,4- oxadiazole-5-thiol derivatives. 1. Synthesis and characterization

Purpose: To synthesize and characterize S-alkylated/aralkylated 2-(1H-indol-3-ylmethyl)-1,3,4- oxadiazole-5-thiol derivatives. Methods: 2-(1H-indol-3-yl)acetic acid (1) was reacted with absolute ethanol and catalytic amount of sulfuric acid to form ethyl 2-(1H-indol-3-yl)acetate (2) which was transformed to 2-(1H-indol-3- yl)acetohydrazide (3) by refluxing with hydrazine hydrate in methanol. Ring closure reaction of 3 with carbon disulfide and ethanolic potassium hydroxide yielded 2-(1H-indol-3-ylmethyl)-1,3,4-oxadiazole-5- thiol (4) which was finally treated with alkyl/aralkyl halides (5a-u) in DMF and NaH to yield Salkylated/ aralkylated 2-(1H-indol-3-ylmethyl)-1,3,4-oxadiazole-5-thiols (6a-u). Structural elucidation was done by IR, 1H-NMR and EI-MS techniques Results: 2-(1H-indol-3-ylmethyl)-1,3,4-oxadiazole-5-thiol (4) was synthesized as the parent molecule and was characterized by IR and the spectrum showed peaks resonating at (cm-1) 2925 (Ar-H), 2250 (S-H ), 1593 (C=N ) and 1527 (Ar C=C ); 1H-NMR spectrum showed signals at δ 11.00 (s, 1H, NH-1ʹ), 7.49 ( br.d, J = 7.6 Hz, 1H, H-4\'), 7.37 (br.d, J = 8.0 Hz, 1H, H-7\'), 7.34 (br.s, 1H, H-2\'), 7.09 (t, J = 7.6 Hz, 1H, H-5\'), 7.00 (t, J = 7.6 Hz, 1H, H-6\') and 4.20 (s, 2H, CH2-10ʹ). EI-MS presented different fragments peaks at m/z 233 (C11H9N3OS)˙+ [M+2]+, 231 (C11H9N3OS)˙+ [M]+, 158 (C10H8NO)+, 156 (C10H8N2)˙+, 130 (C9H8N)+. The derivatives (6a-6u) were prepared and characterized accordingly. Conclusion: S-alkylated/aralkylated 2-(1H-indol-3-ylmethyl)-1,3,4-oxadiazole-5-thiols (6a-u) were successfully synthesized.

S-Alkylated/aralkylated 2-(1H-indol-3-yl-methyl)-1,3,4- oxadiazole-5-thiol derivatives. 2. Anti-bacterial, enzymeinhibitory and hemolytic activities

Purpose: To evaluate the antibacterial, enzyme-inhibitory and hemolytic activities of Salkylated/ aralkylated 2-(1H-indol-3-ylmethyl)-1,3,4-oxadiazole-5-thiol derivatives. Methods: Antibacterial activities of the compounds were evaluated using broth dilution method in 96 well plates. Enzyme inhibitory activities assays were investigated against α-glucosidase, butyrylcholinesterase (BchE) and lipoxygenase (LOX) using acarbose, eserine and baicalien as reference standards, respectively. A mixture of enzyme, test compound and the substrate was incubated and variation in absorbance noted before and after incubation. In tests for hemolytic activities, the compounds were incubated with red blood cells and variations in absorbance were used as indices their hemolytic activities. Results: The compounds were potent antibacterial agents. Five of them exhibited very good antibacterial potential similar to ciprofloxacin, and had minimum inhibitory concentrations (MIC) of at least 9.00 ± 4.12 μM against S. aureus, E.coli, and B. subtilis. One of the compounds had strong enzyme inhibitory potential against α-glucosidase, with IC50 of 17.11 ± 0.02 μg/mL which was better than that of standard acarbose (IC50 38.25 ± 0.12 μg/mL). Another compound had 1.5 % hemolytic activity. Conclusion: S-Alkylated/aralkylated 2-(1H-indol-3-ylmethyl)-1,3,4-oxadiazole-5-thiol deviratives with valuable antibacterial, anti-enzymatic and hemolytic activities have been successfully synthesized. These compounds may be useful in the development of pharmaceutical products.

Fiber scaffolds of poly (glycerol-dodecanedioate) and its derivative via electrospinning for neural tissue engineering

Peripheral nerves have demonstrated the ability to bridge gaps of up to 6 mm. Peripheral Nerve System injury sites beyond this range need autograft or allograft surgery. Central Nerve System cells do not allow spontaneous regeneration due to the intrinsic environmental inhibition. Although stem cell therapy seems to be a promising approach towards nerve repair, it is essential to use the distinct three-dimensional architecture of a cell scaffold with proper biomolecule embedding in order to ensure that the local environment can be controlled well enough for growth and survival. Many approaches have been developed for the fabrication of 3D scaffolds, and more recently, fiber-based scaffolds produced via the electrospinning have been garnering increasing interest, as it offers the opportunity for control over fiber composition, as well as fiber mesh porosity using a relatively simple experimental setup. All these attributes make electrospun fibers a new class of promising scaffolds for neural tissue engineering. Therefore, the purpose of this doctoral study is to investigate the use of the novel material PGD and its derivative PGDF for obtaining fiber scaffolds using the electrospinning. The performance of these scaffolds, combined with neural lineage cells derived from ESCs, was evaluated by the dissolvability test, Raman spectroscopy, cell viability assay, real time PCR, Immunocytochemistry, extracellular electrophysiology, etc. The newly designed collector makes it possible to easily obtain fibers with adequate length and integrity. The utilization of a solvent like ethanol and water for electrospinning of fibrous scaffolds provides a potentially less toxic and more biocompatible fabrication method. Cell viability testing demonstrated that the addition of gelatin leads to significant improvement of cell proliferation on the scaffolds. Both real time PCR and Immunocytochemistry analysis indicated that motor neuron differentiation was achieved through the high motor neuron gene expression using the metabolites approach. The addition of Fumaric acid into fiber scaffolds further promoted the differentiation. Based on the results, this newly fabricated electrospun fiber scaffold, combined with neural lineage cells, provides a potential alternate strategy for nerve injury repair.^

A bioengineered nisin derivative, M21A, in combination with food grade additives eradicates biofilms of Listeria monocytogenes

The burden of foodborne disease has large economic and social consequences worldwide. Despite strict regulations, a number of pathogens persist within the food environment, which is greatly contributed to by a build-up of resistance mechanisms and also through the formation of biofilms. Biofilms have been shown to be highly resistant to a number of antimicrobials and can be extremely difficult to remove once they are established. In parallel, the growing concern of consumers regarding the use of chemically derived antimicrobials within food has led to a drive toward more natural products. As a consequence, the use of naturally derived antimicrobials has become of particular interest. In this study we investigated the efficacy of nisin A and its bioengineered derivative M21A in combination with food grade additives to treat biofilms of a representative foodborne disease isolate of Listeria monocytogenes. Investigations revealed the enhanced antimicrobial effects, in liquid culture, of M21A in combination with citric acid or cinnamaldehyde over its wild type nisin A counterpart. Subsequently, an investigation was conducted into the effects of these combinations on an established biofilm of the same strain. Nisin M21A (0.1 μg/ml) alone or in combination with cinnamaldehyde (35 μg/ml) or citric acid (175 μg/ml) performed significantly better than combinations involving nisin A. All combinations of M21A with either citric acid or cinnamaldehyde eradicated the L. monocytogenes biofilm (in relation to a non-biofilm control). We conclude that M21A in combination with available food additives could further enhance the antimicrobial treatment of biofilms within the food industry, simply by substituting nisin A with M21A in current commercial products such as Nisaplin® (Danisco, DuPont).

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

Characterization of commercial double-walled carbon nanotube material : composition, structure, and heat capacity

A purified commercial double-walled carbon nanotube (DWCNT) sample was investigated by transmission electron microscopy (TEM), thermogravimetry (TG), and Raman spectroscopy. Moreover, the heat capacity of the DWCNT sample was determined by temperature-modulated differential scanning calorimetry in the range of temperature between -50 and 290 °C. The main thermo-oxidation characterized by TG occurred at 474 °C with the loss of 90 wt% of the sample. Thermo-oxidation of the sample was also investigated by high-resolution TG, which indicated that a fraction rich in carbon nanotube represents more than 80 wt% of the material. Other carbonaceous fractions rich in amorphous coating and graphitic particles were identified by the deconvolution procedure applied to the derivative of TG curve. Complementary structural data were provided by TEM and Raman studies. The information obtained allows the optimization of composites based on this nanomaterial with reliable characteristics.

Business Service Management

Business Service Management describes the emerging discipline dedicated to the IT-enabled management of services as corporate assets. Business Service Management deals with the service orientation of the organisation and the provisioning and use of business services. The term business service describes an autonomous transformational capability that is offered to and consumed by external or internal customers for their benefit. The prefix ‘business’ stresses that such a service has a market value, requires the ability to be managed internally as a corporate asset and that its implementation is technology-agnostic. While business services (or so called capabilities) have attracted the attention of many vendors and organisations, a lack of understanding of the activities required for the successful management of such business services remains a critical issue. In order to fill this gap, a framework consisting of Service Lifecycle Management, Service Value Management, Service Relationship Management and Service Enablement is proposed. This Framework has the potential to provide organisations with the much needed guidance in their attempts to convert current IT-driven service initiatives into successful service-centric business models.

Unusual hydrate stabilization in the two-dimensional layered structure of quinacrinium bis(2-carboxy-4,5-dichlorobenzoate) tetrahydrate, a proton-transfer compound of the drug quinacrine

The crystal structure of the hydrated proton-transfer compound of the drug quinacrine [rac-N'-(6-chloro-2-methoxyacridin-9-yl)-N,N-diethylpentane-1,4-diamine] with 4,5-dichlorophthalic acid, C23H32ClN3O2+ . 2(C8H3Cl2O4-).4H2O (I), has been determined at 200 K. The four labile water molecules of solvation form discrete ...O--H...O--H... hydrogen-bonded chains parallel to the quinacrine side chain, the two N--H groups of which act as hydrogen-bond donors for two of the water acceptor molecules. The other water molecules, as well as the acridinium H atom, also form hydrogen bonds with the two anion species and extend the structure into two-dimensional sheets. Between these sheets there are also weak cation--anion and anion--anion pi-pi aromatic ring interactions. This structure represents only the third example of a simple quinacrine derivative for which structural data are available but differs from the other two in that it is unstable in the X-ray beam due to efflorescence, probably associated with the destruction of the unusual four-membered water chain structures.