scholarly journals LIMIT DISTRIBUTIONS OF SOME STEREOLOGICAL ESTIMATORS IN WICKSELL'S CORPUSCLE PROBLEM

2011 ◽  
Vol 26 (2) ◽  
pp. 63 ◽  
Author(s):  
Lothar Heinrich
Keyword(s):  
Analytical Solution ◽  
Asymptotic Behaviour ◽  
Point Process ◽  
Cross Section ◽  
Homogeneous System ◽  
Spherical Particles ◽  
Limit Distributions ◽  
The Common ◽  
Special Case ◽  
Independent Identically Distributed

Suppose that a homogeneous system of spherical particles (d-spheres) with independent identically distributed radii is contained in some opaque d-dimensional body, and one is interested to estimate the common radius distribution. The only information one can get is by making a cross-section of that body with an s-flat (1 ≤ s ≤ d -1) and measuring the radii of the s-spheres and their midpoints. The analytical solution of (the hyper-stereological version of) Wicksell's corpuscle problem is used to construct an empirical radius distribution of the d-spheres. In this paper we study the asymptotic behaviour of this empirical radius distribution for s = d -1 and s = d - 2 under the assumption that the s-dimensional intersection volume becomes unboundedly large and the point process of the midpoints of the d-spheres is Brillinger-mixing. Of course, in stereological practice the only relevant cases are d = 3; s = 2 or s = 1 and d = 2; s = 1. Among others we generalize and extend some results obtained in Franklin (1981) and Groeneboom and Jongbloed (1995) under the Poisson assumption for the special case d = 3; s = 2.

scholarly journals Analytical solution for torsion of cylindrical orthotropic annular wedge-shaped bars reinforced by thin shells

2021 ◽  
Author(s):  
István Ecsedi ◽  
Attila Baksa
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Analytical Method ◽  
Torsional Rigidity ◽  
Circular Ring ◽  
Thin Shells ◽  
Elastic Wedge ◽  
Curved Boundary ◽  
Cylindrically Orthotropic ◽  
Boundary Surfaces

AbstractThis paper deals with the Saint-Venant torsion of elastic, cylindrically orthotropic bar whose cross section is a sector of a circular ring shaped bar. The cylindrically orthotropic homogeneous elastic wedge-shaped bar strengthened by on its curved boundary surfaces by thin isotropic elastic shells. An analytical method is presented to obtain the Prandtl’s stress function, torsion function, torsional rigidity and shearing stresses. A numerical example illustrates the application of the developed analytical method.

The Uniform Flexure of an Incomplete Tore

1949 ◽  
Vol 2 (4) ◽  
pp. 469
Author(s):  
W Freiberger ◽  
RCT Smith
Keyword(s):  
General Solution ◽  
Cross Section ◽  
Harmonic Functions ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Derivatives Of ◽  
Special Case

In this paper we discuss the flexure of an incomplete tore in the plane of its circular centre-line. We reduce the problem to the determination of two harmonic functions, subject to boundary conditions on the surface of the tore which involve the first two derivatives of the functions. We point out the relation of this solution to the general solution of three-dimensional elasticity problems. The special case of a narrow rectangular cross-section is solved exactly in Appendix II.

Free Vibration Analysis for Tapered Cross-Section Steel-Concrete Composite Material Beam

2017 ◽  
Vol 893 ◽  
pp. 380-383
Author(s):  
Jun Xia ◽  
Z. Shen ◽  
Kun Liu
Keyword(s):  
Finite Element ◽  
Composite Material ◽  
Cross Section ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Composite Beams ◽  
Shear Connection ◽  
The Common ◽  
Interlayer Slip

The tapered cross-section beams made of steel-concrete composite material are widely used in engineering constructions and their dynamic behavior is strongly influenced by the type of shear connection jointing the two different materials. The 1D high order finite element model for tapered cross-section steel-concrete composite material beam with interlayer slip was established in this paper. The Numerical results for vibration nature frequencies of the composite beams with two typical boundary conditions were compared with ANSYS using 2D plane stress element. The 1D element is more efficient and economical for the common tapered cross-section steel-concrete composite material beams in engineering.

MATHEMATICAL MODEL OF TWO-DIMENSIONAL LAYERED PRESSURE FLOW IN THE AUGER CHANNEL

2018 ◽  
Author(s):  
А.В. ГУКАСЯН ◽  
В.С. КОСАЧЕВ ◽  
Е.П. КОШЕВОЙ
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Cross Section ◽  
Dynamic Pressure ◽  
Two Dimensional ◽  
Flow Dynamic ◽  
Pressure Flow ◽  
Rectangular Channels ◽  
Wide Range ◽  
Pressure Characteristics

Получено аналитическое решение двумерного слоистого напорного течения в канале шнека, позволяющее моделировать расходно-напорные характеристики прямоугольных каналов шнековых прессов с учетом гидравлического сопротивления формующих устройств и рассчитывать расходно-напорные характеристики экструдеров в широком диапазоне геометрии витков как в поперечном сечении, так и по длине канала. Obtained the analytical solution of two-dimensional layered pressure flow in the screw channel, allow to simulate the flow-dynamic pressure characteristics of rectangular channels screw presses taking into account the hydraulic resistance of the forming device and calculate the mass flow-dynamic pressure characteristics of the extruders in a wide range of the geometry of the coils, as in its cross section and along the length of the channel.

Graphic Satire and the Printed Image in Shakespeare’s London

2016 ◽  
Author(s):  
Helen Pierce
Keyword(s):  
Seventeenth Century ◽  
Cross Section ◽  
Commercial Practice ◽  
Graphic Satire ◽  
Single Sheet ◽  
The Common ◽  
Broad Cross Section ◽  
Print Market

How was the multiplied, printed image encountered in Shakespeare’s London? This chapter examines a range of genres and themes for single sheet, illustrated broadsides in an emerging, specialist print market. It discusses how such images were used to persuade and to entertain a potentially broad cross-section of society along moral, political and religious lines, and according to both topical and commercial interests. The mimetic nature of the English print in both engraved and woodcut form is highlighted, with its frequent adaptation of continental models to suit more local concerns. Consideration is also given to the survival of certain images in later seventeenth-century impressions, indicative of popularity and the common commercial practice of reprinting stock from aging plates and blocks, and the sporadic nature of censorship upon the illustrated broadside.

scholarly journals Derivation of Equations for a Size Distribution of Spherical Particles in Non-Transparent Materials

2021 ◽  
Vol 5 (4) ◽  
pp. 53-60
Author(s):  
Daniel Gurgul ◽  
Andriy Burbelko ◽  
Tomasz Wiktor
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Size Distribution ◽  
Density Function ◽  
Cross Section ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Two Dimensional ◽  
Mathematical Formulas ◽  
Transparent Materials

This paper presents a new proposition on how to derive mathematical formulas that describe an unknown Probability Density Function (PDF3) of the spherical radii (r3) of particles randomly placed in non-transparent materials. We have presented two attempts here, both of which are based on data collected from a random planar cross-section passed through space containing three-dimensional nodules. The first attempt uses a Probability Density Function (PDF2) the form of which is experimentally obtained on the basis of a set containing two-dimensional radii (r2). These radii are produced by an intersection of the space by a random plane. In turn, the second solution also uses an experimentally obtained Probability Density Function (PDF1). But the form of PDF1 has been created on the basis of a set containing chord lengths collected from a cross-section.The most important finding presented in this paper is the conclusion that if the PDF1 has proportional scopes, the PDF3 must have a constant value in these scopes. This fact allows stating that there are no nodules in the sample space that have particular radii belonging to the proportional ranges the PDF1.

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