Elements of plane and spherical trigonometry, with its applications to the principles of navigation and nautical astronomy. With the logarithmic and trigonometrical tables.

Mode of access: Internet.

Tables of physical and chemical constants and some mathematical functions,

Mode of access: Internet.

A treatise on the integral calculus : containing the integration of explicit functions of one variable ; together with the theory of definite integrals and of elliptic functions /

Mode of access: Internet.

Research cultures and the pragmatic functions of humor in academic research presentations:A corpus-assisted analysis

Based on a corpus of English, German, and Polish spoken academic discourse, this article analyzes the distribution and function of humor in academic research presentations. The corpus is the result of a European research cooperation project consisting of 300,000 tokens of spoken academic language, focusing on the genres research presentation, student presentation, and oral examination. The article investigates difference between the German and English research cultures as expressed in the genre of specialist research presentations, and the role of humor as a pragmatic device in their respective contexts. The data is analyzed according to the paradigms of corpus-assisted discourse studies (CADS). The findings show that humor is used in research presentations as an expression of discourse reflexivity. They also reveal a considerable difference in the quantitative distribution of humor in research presentations depending on the educational, linguistic, and cultural background of the presenters, thus confirming the notion of different research cultures. Such research cultures nurture distinct attitudes to genres of academic language: whereas in one of the cultures identified researchers conform with the constraints and structures of the genre, those working in another attempt to subvert them, for example by the application of humor. © 2012 Elsevier B.V.

Representations and Positive Definite Functions on Hypergroups

Some relationships between representations of a hypergroup X, its algebras, and positive definite functions on X are studied. Also, various types of convergence of positive definite functions on X are discussed.

Abstract Subdifferential Calculus and Semi-Convex Functions

∗ The work is partially supported by NSFR Grant No MM 409/94.

Some Comments on Q-Irresolute and Quasi-Irresolute Functions

The aim of this paper is to continue the study of θ-irresolute and quasi-irresolute functions as well as to give an example of a function which is θ-irresolute but neither quasi-irresolute nor an R-map and thus give an answer to a question posed by Ganster, Noiri and Reilly. We prove that RS-compactness is preserved under open, quasi-irresolute surjections.

Practical Stability and Vector-Lyapunov Functions for Impulsive Differential Equations with "Supremum"

Stability of nonlinear impulsive differential equations with "supremum" is studied. A special type of stability, combining two different measures and a dot product on a cone, is defined. Perturbing cone-valued piecewise continuous Lyapunov functions have been applied. Method of Razumikhin as well as comparison method for scalar impulsive ordinary differential equations have been employed.

Association between mean residual life (MRL) and failure rate functions for continuous and discrete lifetime distributions

The purpose of this study was to correct some mistakes in the literature and derive a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. It was also desired to find the conditions under which the discrete failure rate function has an upside-down bathtub shape if corresponding MRL function has a bathtub shape. The study showed that if discrete MRL has a bathtub shape, then under some conditions the corresponding failure rate function has an upside-down bathtub shape. Also the study corrected some mistakes in proofs of Tang, Lu and Chew (1999) and established a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. Similarly, some mistakes in Gupta and Gupta (2000) are corrected, with the ensuing results being expanded and proved thoroughly to establish the relationship between the crossing points of the failure rate and associated MRL functions. The new results derived in this study will be useful to model various lifetime data that occur in environmental studies, medical research, electronics engineering, and in many other areas of science and technology.

CaV channels and cancer: canonical functions indicate benefits of repurposed drugs as cancer therapeutics

The importance of ion channels in the hallmarks of many cancers is increasingly recognised. This article reviews current knowledge of the expression of members of the voltage-gated calcium channel family (CaV) in cancer at the gene and protein level and discusses their potential functional roles. The ten members of the CaV channel family are classified according to expression of their pore-forming α-subunit; moreover, co-expression of accessory α2δ, β and γ confers a spectrum of biophysical characteristics including voltage dependence of activation and inactivation, current amplitude and activation/inactivation kinetics. CaV channels have traditionally been studied in excitable cells including neurones, smooth muscle, skeletal muscle and cardiac cells, and drugs targeting the channels are used in the treatment of hypertension and epilepsy. There is emerging evidence that several CaV channels are differentially expressed in cancer cells compared to their normal counterparts. Interestingly, a number of CaV channels also have non-canonical functions and are involved in transcriptional regulation of the expression of other proteins including potassium channels. Pharmacological studies show that CaV canonical function contributes to the fundamental biology of proliferation, cell-cycle progression and apoptosis. This raises the intriguing possibility that calcium channel blockers, approved for the treatment of other conditions, could be repurposed to treat particular cancers. Further research will reveal the full extent of both the canonical and non-canonical functions of CaV channels in cancer and whether calcium channel blockers are beneficial in cancer treatment.

Enhancing SPH using moving least-squares and radial basis functions

In this paper we consider two sources of enhancement for the meshfree Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving the accuracy of the particle approximation. Namely, we will consider shape functions constructed using: moving least-squares approximation (MLS); radial basis functions (RBF). Using MLS approximation is appealing because polynomial consistency of the particle approximation can be enforced. RBFs further appeal as they allow one to dispense with the smoothing-length - the parameter in the SPH method which governs the number of particles within the support of the shape function. Currently, only ad hoc methods for choosing the smoothing-length exist. We ensure that any enhancement retains the conservative and meshfree nature of SPH. In doing so, we derive a new set of variationally-consistent hydrodynamic equations. Finally, we demonstrate the performance of the new equations on the Sod shock tube problem.

On the construction of new bent functions from the max-weight and min-weight functions of old bent functions

Given a bent function f (x) of n variables, its max-weight and min-weight functions are introduced as the Boolean functions f + (x) and f − (x) whose supports are the sets {a ∈ Fn2 | w( f ⊕la) = 2n−1+2 n 2 −1} and {a ∈ Fn2 | w( f ⊕la) = 2n−1−2 n 2 −1} respectively, where w( f ⊕ la) denotes the Hamming weight of the Boolean function f (x) ⊕ la(x) and la(x) is the linear function defined by a ∈ Fn2 . f + (x) and f − (x) are proved to be bent functions. Furthermore, combining the 4 minterms of 2 variables with the max-weight or min-weight functions of a 4-tuple ( f0(x), f1(x), f2(x), f3(x)) of bent functions of n variables such that f0(x) ⊕ f1(x) ⊕ f2(x) ⊕ f3(x) = 1, a bent function of n + 2 variables is obtained. A family of 4-tuples of bent functions satisfying the above condition is introduced, and finally, the number of bent functions we can construct using the method introduced in this paper are obtained. Also, our construction is compared with other constructions of bent functions.

Harnessing the power of Drosophila model to obtain new insights on MYC and ABCC1 cellular functions: from neuroblastoma to autism spectrum disorder

MYCN amplification is a genetic hallmark of the childhood tumour neuroblastoma. MYCN-MAX dimers activate the expression of genes promoting cell proliferation. Moreover, MYCN seems to transcriptionally repress cell differentiation even in absence of MAX. We adopted the Drosophila eye as model to investigate the effect of high MYC to MAX expression ratio on cells. We found that dMyc overexpression in eye cell precursors inhibits cell differentiation and induces the ectopic expression of Antennapedia (the wing Hox gene). The further increase of MYC/MAX ratio results in an eye-to-wing homeotic transformation. Notably, dMyc overexpression phenotype is suppressed by low levels of transcriptional co-repressors and MYCN associates to the promoter of Deformed (the eye Hox gene) in proximity to repressive sites. Hence, we envisage that, in presence of high MYC/MAX ratio, the “free MYC” might inhibit Deformed expression, leading in turn to the ectopic expression of Antennapedia. This suggests that MYCN might reinforce its oncogenic role by affecting the physiological homeotic program. Furthermore, poor neuroblastoma outcome associates with a high level of the MRP1 protein, encoded by the ABCC1 gene and known to promote drug efflux in cancer cells. Intriguingly, this correlation persists regardless of chemotherapy and ABCC1 overexpression enhances neuroblastoma cell motility. We found that Drosophila dMRP contributes to the adhesion between the dorsal and ventral epithelia of the wing by inhibiting the function of integrin receptors, well known regulators of cell adhesion and migration. Besides, integrins play a crucial role during synaptogenesis and ABCC1 locus is included in a copy number variable region of the human genome (16p13.11) involved in neuropsychiatric diseases. Interestingly, we found that the altered dMRP/MRP1 level affects nervous system development in Drosophila embryos. These preliminary findings point out novel ABCC1 functions possibly defining ABCC1 contribution to neuroblastoma and to the pathogenicity of 16p13.11 deletion/duplication

Processos difusivos generalizados

We investigate several diffusion equations which extend the usual one by considering the presence of nonlinear terms or a memory effect on the diffusive term. We also considered a spatial time dependent diffusion coefficient. For these equations we have obtained a new classes of solutions and studied the connection of them with the anomalous diffusion process. We start by considering a nonlinear diffusion equation with a spatial time dependent diffusion coefficient. The solutions obtained for this case generalize the usual one and can be expressed in terms of the q-exponential and q-logarithm functions present in the generalized thermostatistics context (Tsallis formalism). After, a nonlinear external force is considered. For this case the solutions can be also expressed in terms of the q-exponential and q-logarithm functions. However, by a suitable choice of the nonlinear external force, we may have an exponential behavior, suggesting a connection with standard thermostatistics. This fact reveals that these solutions may present an anomalous relaxation process and then, reach an equilibrium state of the kind Boltzmann- Gibbs. Next, we investigate a nonmarkovian linear diffusion equation that presents a kernel leading to the anomalous diffusive process. Particularly, our first choice leads to both a the usual behavior and anomalous behavior obtained through a fractionalderivative equation. The results obtained, within this context, correspond to a change in the waiting-time distribution for jumps in the formalism of random walks. These modifications had direct influence in the solutions, that turned out to be expressed in terms of the Mittag-Leffler or H of Fox functions. In this way, the second moment associated to these distributions led to an anomalous spread of the distribution, in contrast to the usual situation where one finds a linear increase with time