Computer Calculations of the Gasbuggy Event

A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary circle at the ends of each chord. Variations of this construction are considered here, where bands are possibly attached to the outer boundary circle of the annulus. The genus range of a chord diagram is the genus values over all such variations of surfaces thus obtained from a given chord diagram. Genus ranges of chord diagrams for a fixed number of chords are studied. Integer intervals that can be, and those that cannot be, realized as genus ranges are investigated. Computer calculations are presented, and play a key role in discovering and proving the properties of genus ranges.

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Study of the Convergence of Muller's Sequence Computer Calculations

10.1109/ukrcon53503.2021.9575546 ◽

2021 ◽

Author(s):

Oleh Vietrov ◽

Rostyslav Bilous

Keyword(s):

Computer Calculations

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Development of a Mathematical Model for a Workpiece Heating and Cooling in a Protective Medium while Treatment under Pressure

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.410.115 ◽

2021 ◽

Vol 410 ◽

pp. 115-122

Author(s):

Victoria V. Devyatiarova ◽

Eugenia E. Balakhnina ◽

Lilya M. Valeeva

Keyword(s):

Mathematical Model ◽

Cross Section ◽

Arbitrary Shape ◽

Thermal Conductivity Coefficient ◽

Regression Equations ◽

Heating And Cooling ◽

Temperature Problem ◽

Protective Medium ◽

Computer Calculations ◽

The Mathematical Model

The paper reviews and develops the mathematical model of plastic flow during the hot-forming processes. A flat non-stationary temperature problem for a cross-section of a long solid (rolled product) of arbitrary shape with different heat transfer conditions along the perimeter of the cross-section was considered. Equations for calculation of the thermal conductivity coefficient and heat capacity of tungsten billets were obtained in the temperature range of 700 - 1500°C, based on the literature data. Analytical dependences in form of regression equations were obtained, allowing for computer calculations of physical specifications of 11x11 mm VA grade tungsten billets in form of temperature functions with accuracy sufficient for practical calculations.

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Small Degree Representations of Finite Chevalley Groups in Defining Characteristic

LMS Journal of Computation and Mathematics ◽

10.1112/s1461157000000838 ◽

2001 ◽

Vol 4 ◽

pp. 135-169 ◽

Cited By ~ 72

Author(s):

Frank Lübeck

Keyword(s):

Algebraic Groups ◽

Small Degree ◽

Irreducible Representations ◽

Simple Groups ◽

Finite Simple Groups ◽

Linear Algebraic Groups ◽

Large Rank ◽

Projective Representations ◽

Computer Calculations ◽

Simply Connected

AbstractThe author has determined, for all simple simply connected reductive linear algebraic groups defined over a finite field, all the irreducible representations in their defining characteristic of degree below some bound. These also give the small degree projective representations in defining characteristic for the corresponding finite simple groups. For large rank l, this bound is proportional to l3, and for rank less than or equal to 11 much higher. The small rank cases are based on extensive computer calculations.

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