An Alternative Method for Solving a Certain Class of Fractional Kinetic Equations

An alternative method for solving the fractional kinetic equations solved earlier by Haubold and Mathai (2000) and Saxena et al. (2002, 2004a, 2004b) is recently given by Saxena and Kalla (2007). This method can also be applied in solving more general fractional kinetic equations than the ones solved by the aforesaid authors. In view of the usefulness and importance of the kinetic equation in certain physical problems governing reaction-diffusion in complex systems and anomalous diffusion, the authors present an alternative simple method for deriving the solution of the generalized forms of the fractional kinetic equations solved by the aforesaid authors and Nonnenmacher and Metzler (1995). The method depends on the use of the Riemann-Liouville fractional calculus operators. It has been shown by the application of Riemann-Liouville fractional integral operator and its interesting properties, that the solution of the given fractional kinetic equation can be obtained in a straight-forward manner. This method does not make use of the Laplace transform.Comment: 7 pages, LaTe

Towards the Formalization of Fractional Calculus in Higher-Order Logic

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to analyze a wide class of physical systems in various fields of science and engineering. In this paper, we describe an ongoing project which aims at formalizing the basic theories of fractional calculus in the HOL Light theorem prover. Mainly, we present the motivation and application of such formalization efforts, a roadmap to achieve our goals, current status of the project and future milestones.Comment: 9 page

The nature and fate of natural resins in the geosphere XIII: a probable pinaceous resin from the early Cretaceous (Barremian), Isle of Wight

Terpenoid resin is produced by all families and most genera of the order Coniferales (the conifers), and the distribution of terpenes present in most conifer resins is characteristic of the originating family. Analyses of early Cretaceous (Barremian) amber (fossil resin) from the English Wealden, Isle of Wight, southern England, by pyrolysis-gas chromatography-mass spectrometry (Py-GC-MS), indicate a terpene distribution dominated by abietane- and labdane-type terpenes. Similar distributions are observed in some species of the extant family Pinaceae. The Pinaceae are well represented within the Wealden deposits of southern England, by only one (known) species, Pityites solmsii (Seward) Seward, whereas the macro-fossil record of these deposits is dominated by the extinct conifer family Cheirolepidiaceae, for which no resin chemistry has been reported. By analogy with modern materials, it is probable that the ambers found in these deposits are derived from an extinct member of the Pinaceae, but given the absence of evidence concerning the chemotaxonomy of the Cheirolepidiaceae, this family cannot be excluded a priori as a possible paleobotanical source. These ambers may therefore be assigned to either the Pinaceae or to the Cheirolepidiaceae. These samples are the oldest ambers to date to yield useful chemotaxonomic data

Fractional dynamics pharmacokinetics–pharmacodynamic models

While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics–pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics

A numerical method to solve higher-order fractional differential equations

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order derivatives only. With this, we can rewrite FDEs in terms of a classical one and then apply any known technique. With some examples, we show the accuracy of the method

Activation of MEK1 or MEK2 isoform is sufficient to fully transform intestinal epithelial cells and induce the formation of metastatic tumors

<p>Abstract</p> <p>Background</p> <p>The Ras-dependent ERK1/2 MAP kinase signaling pathway plays a central role in cell proliferation control and is frequently activated in human colorectal cancer. Small-molecule inhibitors of MEK1/MEK2 are therefore viewed as attractive drug candidates for the targeted therapy of this malignancy. However, the exact contribution of MEK1 and MEK2 to the pathogenesis of colorectal cancer remains to be established.</p> <p>Methods</p> <p>Wild type and constitutively active forms of MEK1 and MEK2 were ectopically expressed by retroviral gene transfer in the normal intestinal epithelial cell line IEC-6. We studied the impact of MEK1 and MEK2 activation on cellular morphology, cell proliferation, survival, migration, invasiveness, and tumorigenesis in mice. RNA interference was used to test the requirement for MEK1 and MEK2 function in maintaining the proliferation of human colorectal cancer cells.</p> <p>Results</p> <p>We found that expression of activated MEK1 or MEK2 is sufficient to morphologically transform intestinal epithelial cells, dysregulate cell proliferation and induce the formation of high-grade adenocarcinomas after orthotopic transplantation in mice. A large proportion of these intestinal tumors metastasize to the liver and lung. Mechanistically, activation of MEK1 or MEK2 up-regulates the expression of matrix metalloproteinases, promotes invasiveness and protects cells from undergoing anoikis. Importantly, we show that silencing of MEK2 expression completely suppresses the proliferation of human colon carcinoma cell lines, whereas inactivation of MEK1 has a much weaker effect.</p> <p>Conclusion</p> <p>MEK1 and MEK2 isoforms have similar transforming properties and are able to induce the formation of metastatic intestinal tumors in mice. Our results suggest that MEK2 plays a more important role than MEK1 in sustaining the proliferation of human colorectal cancer cells.</p