The period function of the generalized Lotka-Volterra centers

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Embedding theorems of function classes, I

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The third order Melnikov function of a quadratic center under quadratic perturbation

We study quadratic perturbations of the integrable system (1+x)dH; where H =(x²+y²)=2: We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles.

On the homotopy theory of spectral categories

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A new look at the Heston characteristic function

A new expression for the characteristic function of log-spot in Heston model is presented. This expression more clearly exhibits its properties as an analytic characteristic function and allows us to compute the exact domain of the moment generating function. This result is then applied to the volatility smile at extreme strikes and to the control of the moments of spot. We also give a factorization of the moment generating function as product of Bessel type factors, and an approximating sequence to the law of log-spot is deduced.

Semigroup analysis of structured populations with distributed states-at-birth arising in mathematical aquaculture

Motivated by the modelling of structured parasite populations in aquaculture we consider a class of physiologically structured population models, where individuals may be recruited into the population at different sizes in general. That is, we consider a size-structured population model with distributed states-at-birth. The mathematical model which describes the evolution of such a population is a first order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In case of a separable fertility function we deduce a characteristic equation and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.

Aspects of Iwasawa theory over function fields

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Spectral analysis of random sparse matrices

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Cirp function and characterisation in RNA and microRNAs

In order to search for novel genes involved in cell proliferation, the hypothesis was that by infecting primary cells with a cDNA library of immortal cells would render immortalizing genes. Consequently it has been discovered CIRP (Cold inducible RNA-binding protein). Mammalian cells exposed to mild hypothermia show a general inhibition of protein synthesis and a concomitant increase in the expression of a small number of cold-shock mRNAs and proteins. Rbm3, another RNA binding protein belonging to the same family, has been postulated to facilitate protein synthesis at mild cold shock. To investigate if the same occurs for CIRP, CIRP was overexpressed in primary cells and protein sintesis was measured. Interestingly, CIRP increased protein synthesis, however, such increase did not involve an increase in the polysome fraction or affected the ribosome profile. In addition, the effect caused by CIRP inhibition or knockdown was also analyzed. Different siRNAs against CIRP were tested. Once checked their efficiency by decreasing CIRP at mRNA and protein levels, proliferation was tested by BrdU, cell number (DAPI) and proliferation curves were performed. Interestingly, CIRP provoke a decreased proliferation in primary cells: MEFs, HMEC; and cancer cells: TERA2 and HeLa. In conclusion, we describe for the first time that CIRP bypasses replicative senescence when over-expressed at physiological temperature (37ºC) by increasing a general protein synthesis. This effect is achieved through ERK1/2 activation in MEFs.The decrease in growth rate found in mammalian cells treated with mild cold stress is not entirely attributable to arrested metabolism. This decrease may also involve an active process in which CIRP and other stress-responsive proteins play a fundamental role in stimulating proliferation. Although most cell proteins are down-regulated or inhibited with cold stress, CIRP is activated to maintain cells in an active proliferative status and its overexpression at 37°C might be potentially oncogenic.

On spectral properties of the modified convolution operator

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Krein's strings whose spectral functions are of polynomial growth

In case Krein's strings with spectral functions of polynomial growth a necessary and su fficient condition for the Krein's correspondence to be continuous is given.

Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps

Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence