Wyniki wyszukiwania - Biblioteka Nauki

1

Continuous bending of minimal surfaces, formed by means of plane curves of complex curvature

100%

Pylypaka S. , Mukvich M.

Motrol. Motoryzacja i Energetyka Rolnictwa

|

2017

|

tom 19

|

nr 3

2

ОРГАНІЗАЦІЯ ДОСЛІДНИЦЬКОЇ ДІЯЛЬНОСТІ СТУДЕНТІВ ПРИ ВИВЧЕННІ ВИЩОЇ МАТЕМАТИКИ

63%

Грицик Т.

Педагогічні науки: теорія, історія, інноваційні технології

|

2016

|

nr 2(56)

218-227

EN

Effective organization of research activity of students is an urgent task of the teacher of mathematics. Modern educational process at the university is focused on the usage of reproductive techniques and little training is provided with appropriate means for the development of creativity and research skills. Article aims to offer a method of teaching students of educational organization to study the prominent curves (for example, academic research on «logarithmic spiral»). We have used the scientific and pedagogical research methods, among which theoretical and empirical methods, including analysis of the literature on the issue of research, systematization and generalization of pedagogical experience, the theoretical modeling of the development of research capabilities, its experimental realization. Research activity of a student is an independent academic work, which involves the «discovery» of knowledge, has a subjective significance and originality, creativity and independent study of the topic. It is proved that the educational research is a process and the result of the student’s research activity. The technique of the organization of research activity of students for the study of prominent curves is proposed; an example of academic research on «logarithmic spiral» is also present; outstanding curves which have practical application are considered. The research work of students of a technical college for the study of outstanding curves connects the study of higher mathematics course with mastering the fundamentals of professional activity. We believe that the discovery of properties of prominent curves integrates the knowledge of students from different academic areas and encourages a comprehensive analysis of the objects of research. During the research increases an interest in mathematics and the motivation of learning, and as a result comes the development of student’s individuality. Further scientific development of the considered problems can be associated with the creation of methodological maintenance of independent research, writing of guidelines, containing a set of professionally-oriented tasks of research character on higher mathematics.

3

Кручение призматического составного стержня из материалов с различными свойствами анизотропии

63%

Aleksanan R. K. , Edoan V. A. , Aleksanan D. R.

Zeszyty Naukowe Politechniki Częstochowskiej. Budownictwo

|

2015

|

tom Z. 21 (171)

9--16

RU

Рассматривается задача кручения призматического стержня, составленного из двух призматических частей, соединяемых по общей части боковых поверхностей. Материалы составных частей стержня обладают различными свойствами цилиндрической анизотропии, имеют плоскости упругой симметрии, совпадающие с плоскостью поперечного сечения составного стержня. Получено точное решение задачи, когда непрямолинейные края замыкающей части поперечного сечения стержня являются дугами логарифмических спиралей, определяемые упругими постоянными материалов соответствующих частей. В ходе решения задачи получено характеристическое уравнение относительно собственных значений λ краевой задачи. Когда в интервале (0;1) существуют корни характеристического уравнения, то напряжение в угловой точке r = 0 поперечного сечения составного стержня имеет особенности. Порядок особенностей равен 1 - λ1, где λ1 - наименьший корень в интервале (0;1).

EN

In this paper the torsion problem of a prismatic rod made up of two prismatic parts connected by a common part of the lateral surfaces is considered. Materials of component parts of the rod are of different features of cylindrical anisotropy and they have planes of elastic symmetry coinciding with the plane of the cross-section of the rod. An exact solution of the problem has been obtained in a case when the non-rectilinear edges of the closing part of the cross-section of the rod are arcs of logarithmic spirals defined by the elastic constants of materials of respective parts. While solving the problem a characteristic equation with respect to eigenvalues λ of the boundary problem has been derived. If the roots of the characteristic equation exist in the interval (0;1), then the stress at the vertex angle r = 0 of the cross-sections of a composite rod has a singularity. The order of singularity is equal to 1 - λ1, where λ1 is the smallest root in the interval (0;1).

4

Spira Mirabilis in the selected models of Bittner operational calculus

51%

Wysocki H.

Zeszyty Naukowe Akademii Marynarki Wojennej

|

2015

|

tom R. 56 nr 4 (203)

65--96

EN

Parametric descriptions of spirals being analogues of the logarithmic spiral are determined using the concept of the exponential element in the non-classical Bittner operational calculus and applying the chosen models of it.

PL

Korzystając z pojęcia elementu wykładniczego w nieklasycznym rachunku operatorów Bittnera oraz stosując wybrane modele tego rachunku, wyznaczono opisy parametryczne spiral będących odpowiednikami spirali logarytmicznej.