Endüstri Mühendisliği Bölümü Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12469/48

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Canonical Forms for Families of Anti-Commuting Diagonalizable Linear Operators
(Elsevier Science Inc, 2012) Kumbasar, Yalcin; Bilge, Ayşe Hümeyra
It is well known that a commuting family of diagonalizable linear operators on a finite dimensional vector space is simultaneously diagonalizable. In this paper we consider a family A = {A(a)} A(a) : V -> V a = 1... N of anti-commuting (complex) linear operators on a finite dimensional vector space. We prove that if the family is diagonalizable over the complex numbers then V has an A-invariant direct sum decomposition into subspaces V(alpha) such that the restriction of the family A to V(alpha) is a representation of a Clifford algebra. Thus unlike the families of commuting diagonalizable operators diagonalizable anti-commuting families cannot be simultaneously digonalized but on each subspace they can be put simultaneously to (non-unique) canonical forms. The construction of canonical forms for complex representations is straightforward while for the real representations it follows from the results of [A.H. Bilge S. Kocak S. Uguz Canonical bases for real representations of Clifford algebras Linear Algebra Appl. 419 (2006) 417-439]. (C) 2011 Elsevier Inc. All rights reserved.
Citation - WoS: 2
Citation - Scopus: 2
Efficient Approaches for Furnace Loading of Cylindrical Parts
(Elsevier Science Inc, 2014) Osman, Mojahid Saeed; Ram, Bala; Samanlıoğlu, Funda
This paper addresses the heat treatment operation in a manufacturing plant that produces different types of cylindrical parts. The immediate prior process to heat treatment is furnace-loading where parts are loaded into baskets. The furnace-loading process is complex and involves issues relating to geometry and heterogeneity in the parts and in their processing requirements. Currently furnace-loading is accomplished by operator ingenuity ; consequently the parts loaded in heat treatment often do not use furnace capacity adequately. Efficiency in furnace operation can be achieved by improving basket utilization which is determined by the furnace-loading process. This paper describes the development of integer and mixed integer LP models for 3D loading of cylindrical parts into furnace baskets. The models consider the exact location of parts to be loaded on the basket and incorporate three models with different objectives ; the first addresses the nesting of parts within one another the second addresses the number of basket layers used and the third addresses the number of baskets used. (C) 2013 Elsevier Inc. All rights reserved.
Citation - WoS: 2
Citation - Scopus: 3
Maximal Linear Subspaces of Strong Self-Dual 2-Forms and the Bonan 4-Form
(Elsevier Science Inc, 2011) Bilge, Ayşe Hümeyra; Dereli, Tekin; Koçak, Şahin
The notion of self-duality of 2-forms in 4-dimensions plays an eminent role in many areas of mathematics and physics, but although the 2-forms have a genuine meaning related to curvature and gauge-field-strength in higher dimensions also, their "self-duality" is something which is almost avoided above 4-dimensions. We show that self-duality of 2-forms is a very natural notion in higher (even) dimensions also and we prove the equivalence of some scattered and rarely used definitions in the literature. We demonstrate the usefulness of this higher self-duality by studying it in 8-dimensions and we derive a natural expression for the Bonan form in terms of self-dual 2-forms and we give an explicit expression of the local action of SO(8) on the Bonan form. (C) 2010 Elsevier Inc. All rights reserved.

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