This study used particle swarm optimization (PSO) to determine the optimal values of effective design variables acting on the stress distribution around a quasi-triangular hole in an infinite orthotropic plate. These parameters were load angle, hole orientation, bluntness, fiber angle, and material properties, which were ascertained on the basis of an analytical method used by Lekhnitskii [3]. ...

In this paper a general analytical solution is obtained to find stress distribution in a finite elastic plate with a circular or square hole subjected to arbitrary biaxial partial loading using modified boundary condition by assuming plane stress conditions. The method employed is based on solution of circular hole in finite rectangular plate. This plate is mapped to circular ones and the parti...

We introduce a Hom-type generalization of quantum groups, called quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative analogues of Drinfel’d’s quasitriangular bialgebras, in which the non-(co)associativity is controlled by a twisting map. A family of quasi-triangular Hom-bialgebras can be constructed from any quasi-triangular bialgebra, such as Drinfel’d’s quantum env...

We prove that no triangular frame can hold a convex body, and a convex body can pass through a triangular hole ∆ if and only if the convex body can be congruently embedded in a right triangular prism with base ∆. Applying these result, we prove that a regular tetrahedron of unit edge can pass through an equilateral triangular hole if and only if the edge length of the hole is at least (1 + √ 2)...

We show that a convex body can pass through a triangular hole iff it can do so by a translation along a line perpendicular to the hole. As an application, we determine the minimum size of an equilateral triangular hole through which a regular tetrahedron with unit edge can pass. The minimum edge length of the hole is (1+ √ 2)/ √ 6 ≈ 0.9856. One of the key facts for the proof is that no triangul...

The main purpose of this paper was to evaluate the performance of the triangular vanes located on the bed and their effect on the bed topography considering different flow conditions. For this purpose, tests were carried out on a straight flume for different flow conditions (five Froude numbers of 0.18, 0.20, 0.22, 0.24 and 0.26) by installing a series of triangular vanes at a space of 4Le (Le ...

an ideal i of a ring r is called right baer-ideal if there exists an idempotent e 2 r such that r(i) = er. we know that r is quasi-baer if every ideal of r is a right baer-ideal, r is n-generalized right quasi-baer if for each i e r the ideal in is right baer-ideal, and r is right principaly quasi-baer if every principal right ideal of r is a right baer-ideal. therefore the concept of baer idea...

We prove an embedding theorem that says a convex body can pass through a triangular hole∆ if and only if the convex body can be congruently embedded in a right triangular prism with base ∆. Combining this with a known result on congruent embeddings of a regular tetrahedron in a triangular prism, we show that a regular tetrahedron with unit edge can pass through an equilateral triangular hole in...

We exhibit a family of infinite, finitely-presented, nilpotent-byabelian groups. Each member of this family is a solvable S-arithmetic group that is related to Baumslag-Solitar groups, and everyone of these groups has a quasi-isometry group that is virtually a product of a solvable real Lie group and a solvable p-adic Lie group. In addition, we propose a candidate for a polycyclic group whose q...