Особенности попередельного способа калькуляции себестоимости продукции в перерабатывающем производстве

We are interested in the asymptotic stability of equilibria of structured populations modelled in terms of systems of Volterra functional equations coupled with delay differential equations. The standard approach based on studying the characteristic equation of the linearized system is often involved or even unattainable. Therefore, we propose and investigate a numerical method to compute the eigenvalues of the associated infinitesimal generator. The latter is discretized by using a pseudospectral approach, and the eigenvalues of the resulting matrix are the sought approximations. An algorithm is presented to explicitly construct the matrix from the model coefficients and parameters. The method is tested first on academic examples, showing its suitability also for a class of mathematical models much larger than that mentioned above, including neutral- and mixed-type equations. Applications to cannibalism and consumer\u2013resource models are then provided in order to illustrate the efficacy of the proposed technique, especially for studying bifurcations

Collocation of Next-Generation Operators for Computing the Basic Reproduction Number of Structured Populations

We contribute a full analysis of theoretical and numerical aspects of the collocation approach recently proposed by some of the authors to compute the basic reproduction number of structured population dynamics as spectral radius of certain infinite-dimensional operators. On the one hand, we prove under mild regularity assumptions on the models coefficients that the concerned operators are compact, so that the problem can be properly recast as an eigenvalue problem thus allowing for numerical discretization. On the other hand, we prove through detailed and rigorous error and convergence analyses that the method performs the expected spectral accuracy. Several numerical tests validate the proposed analysis by highlighting diverse peculiarities of the investigated approach

Immunofluorescence evaluation of Myf5 and MyoD in masseter muscle of unilateral posterior crossbite patients

A unilateral posterior crossbite is a malocclusion where the low activity of the affected masseter muscle is compensated by the contralateral muscle hypertrophy. It is still unknown if, in the same condition, myogenesis with new fibre formation takes place. Aim: the aim of the present study was to evaluate the expression of myogenesis markers, such as Myf5 and MyoD, in masseter muscles of unilateral posterior crossbite patients. Materials and methods: biopsies from fifteen surgical patients with unilateral posterior crossbites have been analysed by immunofluorescence reactions. The results show the expression of Myf5 and MyoD in the contralateral muscle but not in the ipsilateral one. Moreover, statistical analysis shows the higher number of satellite cells in the contralateral side if compared to the ipsilateral one. Conclusions: these results suggest that in contralateral muscle, hyperplastic events take place, as well as hypertrophy

Microsatellite instability in thyroid tumours and tumour-like lesions

Fifty-one thyroid tumours and tumour-like lesions were analysed for instability at ten dinucleotide microsatellite loci and at two coding mononucleotide repeats within the transforming growth factor β (TGF-β) type II receptor (TβRII) and insulin-like growth factor II (IGF-II) receptor (IGFIIR) genes respectively. Microsatellite instability (MI) was detected in 11 out of 51 cases (21.5%), including six (11.7%) with MI at one or two loci and five (9.8%) with Ml at three or more loci (RER+ phenotype). No mutations in the TβRII and IGFIIR repeats were observed. The overall frequency of MI did not significantly vary in relation to age, gender, benign versus malignant status and tumour size. However, widespread MI was significantly more frequent in follicular adenomas and carcinomas than in papillary and Hürthle cell tumours: three out of nine tumours of follicular type (33.3%) resulted in replication error positive (RER+), versus 1 out of 29 papillary carcinomas (3.4%, P = 0.01), and zero out of eight Hürthle cell neoplasms. Regional lymph node metastases were present in five MI-negative primary cancers and resulted in MI-positive in two cases. © 1999 Cancer Research Campaig

Multistep high-order interpolants of Runge-Kutta methods

AbstractWe consider a p-order Runge-Kutta method K(n)i = ƒ(xn + cih, yn + hΣνj=1aijK(n)j), i = 1,…,ν, yn+1=yn + hΣνi=1biK(n)i, for solving an initial-value problem for ordinary differential equations. The aim of this paper is to construct p-order interpolants by using the values furnished by the method on N successive intervals of integration. By using Lagrange interpolation one can obtain a p-order interpolant over p intervals, but we are interested in finding the minimum number of intervals needed to obtain this. We provide the conditions to be satisfied and we obtain an estimation of the number N. Some examples are given

On the computation of the joint spectral radius: numerical experiments

In this paper we deal with the computation of the spectral radius of a family of matrices. We summarize some of the numerical experiments contained in the master thesis of L. Menazzi. In particular, we present the the results obtained by using a suitable norm in Gripenberg's algorithm

On the stability of Runge-Kutta methods for delay intergral equations

We present a class of Runge-Kutta methods for the numerical solution of a class of delay integral equations (DIEs) described by two different kernels and with a fixed delay \u3c4. The stability properties of these methods are investigated with respect to a test equation with linear kernels depending on complex parameters. The results are then applied to collocation methods. In particular we obtain that any collocation method for DIEs, resulting from an A-stable collocation method for ODEs, with a stepsize which is submultiple of the delay \u3c4, preserves the asymptotic stability properties of the analytic solution

A one-step subregion method for delay differential equations

We study a one-step method for delay differential equations, which is equivalent to an implicit Runge-Kutta method. It approximates the solution in the whole interval with a piecewise polynomial of fixed degree n. For an appropiate choice of the mesh points, it provides uniform convergence 0(hn+1) and the superconvergence 0(h2n) at the nodes