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developed to higher analogues of these categories, so called m -cluster categories, for m ⩾ 2 {m\geqslant 2} , and led to the systematic study of positive CY triangulated categories, which reveal many interesting and important homological and combinatorial properties. Not much is known, however, about negative CY triangulated categories, although there is recent progress in [ 5 , 6 , 7 , 8 , 13 ]. We study w -simple-minded objects in triangulated categories 𝖳 w {\mathsf{T}_{w}} generated by a w -spherical object. These categories, which can be defined for any

Abstract

Spherical shaped objects are some of the most interesting and difficult to measure objects in dimensional metrology. Made of steel, alloys, ceramics, glass, rubber or plastics, they are important elements of precision bearings, pumps, valves, flow meters, medical, measuring, automotive, aerospace and other equipment, used for polishing, grinding, etc. Quality requirements, including their geometric accuracy, are high. A spherical object is defined geometrically by a centre, radius, and spherical spatial surface. There are no uniform rules and definitions for measuring these characteristics, and there is no standard definition of a form deviation. A number of solutions and publications are known to address the problem in practice, which, for the time being, do not allow a uniquely substantiated definition of the derived geometric elements and methods for their measurement. Full measurement of the deviation from sphericity, for example, is impossible. The question of the type of its associated element satisfying certain standard criteria remains open. The accuracy and reliability of measuring spherical objects is related to finding a reasonable solution to the outlined issues.

The designation of spherical objects in five European languages: an essay in contrastive semantics* Dietrich Nehls The starting point of my investigation is the divergence between English and German with regard to the designation of spherical objects. As is well- known, E. ball has two German translation equivalents: Ball and Kugel. If the spherical object ball· is elastic and bounces it has to be rendered into German by the etymologically related lexeme Ball. If the round object ball is not elastic and does not bounce it has to be rendered by Kugel. Thus E. ball

Abstract

This paper shows a new phenomenon in higher cluster tilting theory. For each positive integer d, we exhibit a triangulated category 𝖢 with the following properties.

On the one hand, the d-cluster tilting subcategories of 𝖢 have very simple mutation behaviour: Each indecomposable object has exactly d mutations. On the other hand, the weakly d-cluster tilting subcategories of 𝖢 which lack functorial finiteness can have much more complicated mutation behaviour: For each 0 ≤ ℓ ≤ d - 1, we show a weakly d-cluster tilting subcategory 𝖳 which has an indecomposable object with precisely ℓ mutations.

The category 𝖢 is the algebraic triangulated category generated by a (d + 1)-spherical object and can be thought of as a higher cluster category of Dynkin type A .

Abstract

In this paper, the adhesive contact of elastic solids with flat surfaces with an edge radius is studied within the framework of Johnson – Kendall – Roberts theory. Solutions are obtained for the stresses at the contacting surfaces and for the relative displacement of the two bodies due to adhesion and applied load. Results are given for flat-ended punches with rounded edges of small radius to nearly spherical objects with small flat areas (truncated spheres) on their surfaces. The classical Johnson – Kendall – Roberts-model for adhesion and contact between spherical surfaces arises as a limiting case of the results. The pull-off force between the adhering bodies is deduced for the flat-surfaced geometries studied. For small flats, the numerical solutions are similar to the classical Johnson – Kendall – Roberts solution for a sphere.

Abstract

The collision of two elastic or viscoelastic spherical shells is investigated as a model for the dynamic response of a human head impacted by another head or by some spherical object. Determination of the impact force that is actually being transmitted to bone will require the model for the shock interaction of the impactor and human head. This model is indended to be used in simulating crash scenarios in frontal impacts, and provide an effective tool to estimate the severity of effect on the human head and to estimate brain injury risks. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. It is assumed that the viscoelastic features of the shells are exhibited only in the contact domain, while the remaining parts retain their elastic properties. In this case, the contact spot is assumed to be a plane disk with constant radius, and the viscoelastic features of the shells are described by the fractional derivative standard linear solid model. In the case under consideration, the governing differential equations are solved analytically by the Laplace transform technique. It is shown that the fractional parameter of the fractional derivative model plays very important role, since its variation allows one to take into account the age-related changes in the mechanical properties of bone.

Sphere A and Sphere C of Figure 174, a square encloses the true circle; the built-up section is in a direction away from the ob- server, as the two spheres are at the left and right of the vertical through the center of vision, and above and below the horizon line, respectively. SPHERE. B Experience and practice will enable the student to judge the proper size of the built-up section. 122- (Tlie Sphere) Fig. 175 (above). Elevation of rings on a sphere Fig. 176. Per- spective view of a spherical object, below horizon line but centered on vertical line

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(t)-caloric method 1039 Raquel Coelho Simões Mutations of simple-minded systems in Calabi–Yau categories generated by a spherical object 1065 Kevin Coulembier, Volodymyr Mazorchuk Some homological properties of categoryO. IV 1083 Maria Ferrer, Salvador Hernández, Dmitri Shakhmatov Subgroups of direct products closely approximated by direct sums 1125 Mário J. J. Branco, Gracinda M. S. Gomes, Pedro V. Silva Takahasi semigroups 1145 Yu Ito Integration of controlled rough paths via fractional calculus 1163 Yutian Lei Qualitative properties of positive solutions of quasilinear

nitride ceramics sintered with Al2O3 and Y2O3 sintering additives were crystallized at 1400 °C for 50 h. This crystallization should lead to the enhancement of the creep resistance of these materials. In contrary, the creep behavior of crystallized material was worse compared to those as sin- tered. The crystallized phases were mainly the Y2Si2O7 and Y2SiO5 phases. Transmission electron microscopy (TEM) analysis, shown in Fig. 6, revealed the presence of spherical objects containing Fe, Ti, and Cr. These elements were not detected in the original glassy-phase triple

coordinates but rather the language of structural science while symmetry itself is the principal language of the crystallographer. Crystallography transcends the traditional disciplines and offers broad in- sights into the materials world. For example, H2, N2, C60 and a number of virus structures all crystallise in space group Pa3 or its non-centred sub-group P213. Why? Sim- ply because all consist of cubic-close-packed arrays of al- most spherical objects whose asphericity can be described in terms of the same irreducible representation. In a simi- lar vein, many diffuse