Analysis of one model of the immune system

The article deals with development of a tumor in the cylindrical space. A model with two parameters - lymphocytes and tumor cells - described in [1] is taken as a base of the research. Some generalization of the model is done. The research, results of which are described in [2, 3], was continued. The relationship between the surface and volumetric tumor cells of classical forms is obtained. It turns out, that even in general case the trivial stationary point is of a saddle type. [...]

Kai kurie kombinatorikos ir statistikos mokymo ypatumai

The paper deals with some definitions of combinatorial and statistical terms. Trying to find out why some certain knowledge of combinatory, probability theory ant statistics is difficult to acquire for pupils, some schoolbooks of mathematics are examined. The definitions of terms like Combinations, Arrangements, Sample are analyzed. Some shortcomings of the definitions are highlighted together with proposals for their improvement.  Straipsnyje nagrinėjamos kai kurių kombinatorikos ir statistikos terminų apibrėžtys. Siekiant išsiaiškinti, kodėl mokiniai taip sunkiai įsisavina tam tikras kombinatorikos, tikimybių teorijos ir statistikos srities žinias, analizuojama mokomoji literatūra – nagrinėjamos derinių, gretinių ir imties sąvokos bei jų apibrėžtys. Parodomi mokykliniuose vadovėliuose pasitaikantys suformuluotų apibrėžčių trūkumai ir pasiūloma, kaip jų išvengti. &nbsp

Matematinių objektų ypatumai. Funkcija

The article deals with some possibledefinitionsof function. Shortagesof function definitionused at schools are discussed. Some concrete examples of improper use of definitions like function and expression, function and its graph are analyzed. Furthermore, some features of recording dimensional and not dimensional variables and their functions are discussed.Straipsnyje yra analizuojama funkcijos sąvoka. Išskiriami matematiniai objektai, kurie dažnai be pagrindo tapatinami su funkcija. Aptarti matinių dydžių funkcijų ypatumai. Pateikti pavyzdžiai, iliustruojantys netinkamą sąvokų  „formulė“, „išraiška“, „grafikas“ vartojimą. &nbsp

Matematinių objektų ypatumai. Matiniai dydžiai

The article deals with formulating of dimensional problems. It is shown what kind of difficulties arises when in one formula dimensional figures are used together with figures without any dimension. The problem of invariability of a formula in respect to change of dimension is introduced. Solutions of the problem are proposed

Mathematical modelling of the development of a cylindrical tumour

The article deals with interaction of tumour cells and leucocytes in the cylindrical cavities. This type of interaction is typical in the cases of development of a tumour in the intestine, blood vessel or in a bone cavity. Two cases are separated: the case of soft and hard tumour. In the case of a solid tumour, leucocytes can interact only with the surface cells of the tumour. This type of interaction is described by the system of two nonlinear first degree differential equations. The expressions of stationary points are obtained and analysis of their stability is performed. In the case of a soft tumour the system of two partial differential equations with first order derivatives and initial and boundary conditions is proposed. An algorithm for computing the numeric solution of the mathematical model is applied. In this case the diffusion of leucocytes and their ability to reach the tumour cells in the whole volume of the tumour is included. The algorithm is constructed and the system is solved numerically. Bifurcation curve is obtained. It separates two qualitatively different areas on the two parameter plane. Under the same initial parameters in the first area development of the tumour cells cannot be stopped, whereas in the second area leukocytes defeat the tumour cells.DOI: http://dx.doi.org/10.15181/csat.v2i1.18

Protecting or destructing? Local perceptions of environmental consideration in Lithuanian forestry

Environmental consideration is an important facet of modern forestry. However, its perceptions by those who own and manage the forest are seldom investigated. After reviewing the evolution of pertinent legislative requirements, this study scrutinizes the attitudes towards environmental consideration, based on qualitative interviews of Lithuanian private forest owners (PFOs), state forest managers, forest management planners and other local forest stakeholders. We find a considerable increase of environmental consideration since 1990, with emphasis on forestland zoning at landscape level. Most of the interviewed forest managers and PFOs are aware of and compliant with the legal demands, however, their judgement of environmental consideration appears to be strongly affected by the degree of the faced restrictions. Informants who manage forest areas with a high share of non-commercial forest zones assess the current restrictions as excessive. Though the Lithuanian forestland zoning overall can be seen as a successful example of implementing multiple use forestry at landscape level, deep qualitative interviews expose several critical issues. Hastily performed zoning entails many mistakes, where the forest or landscape characteristics do not match the intended purpose. Even more critically, severe forest management restrictions around the nests of rare birds lead to widespread destructions of nests in private forests. The most important recommendations of our study are: (i) introducing a fair system of compensations for the economic losses inflicted on PFOs; and (ii) gradual rezoning of forestland, with radically improved consideration of local specifics, including on site assessments and genuine involvement of the local stakeholdersVilniaus universitetasVytauto Didžiojo universitetasŽemės ūkio akademij