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#### Existence of nonabelian free subgroups in the maximal subgroups of GL n(D)

, Article Algebra Colloquium ; Vol. 21, issue. 3 , 2014 , p. 483-496 ; Fallah-Moghaddam, R ; Mahdavi-Hezavehi, M ; Sharif University of Technology
Abstract

Given a non-commutative finite dimensional F-central division algebra D, we study conditions under which every non-abelian maximal subgroup M of GL n(D) contains a non-cyclic free subgroup. In general, it is shown that either M contains a non-cyclic free subgroup or there exists a unique maximal subfield K of Mn(D) such that NGLn<(D) (K*)=M, K* M, K/F is Galois with Gal(K/F) ≅ M/K*, and F[M]=Mn(D). In particular, when F is global or local, it is proved that if ([D:F],Char(F))=1, then every non-abelian maximal subgroup of GL 1(D) contains a non-cyclic free subgroup. Furthermore, it is also shown that GLn(F) contains no solvable maximal subgroups provided that F is local or global and n ≥ 5. ©...

#### Frattini subgroup of the unit group of central simple algebras

, Article Journal of Algebra and its Applications ; Volume 11, Issue 3 , 2012 ; 02194988 (ISSN) ; Mahdavi Hezavehi, M ; Sharif University of Technology
2012

Abstract

Given an F-central simple algebra A = M n(D), denote by A′ the derived group of its unit group A*. Here, the Frattini subgroup Φ(A*) of A* for various fields F is investigated. For global fields, it is proved that when F is a real global field, then Φ(A*) = Φ(F*)Z(A′), otherwise Φ(A*) = ∩ pdoes not dividedeg(A) F *p. Furthermore, it is also shown that Φ(A*) = k* whenever F is either a field of rational functions over a divisible field k or a finitely generated extension of an algebraically closed field k

#### Hyperbolic involutions and quadratic extensions

, Article Communications in Algebra ; Volume 39, Issue 1 , Jan , 2011 , Pages 125-132 ; 00927872 (ISSN) ; Sharif University of Technology
Abstract

This is a variation on a theme of Bayer-Fluckiger, Shapiro, and Tignol related to hyperbolic involutions. More precisely, criteria for the hyperbolicity of involutions of quadratic extensions of simple algebras and involutions of the form σ ⊗ τ and σ ⊗ ρ, where σ is an involution of a central simple algebra A, τ is the nontrivial automorphism of a quadratic extension of the center of A, and ρ is an involution of a quaternion algebra are obtained

#### Efficient visibility maintenance of a moving segment observer inside a simple polygon

, Article 19th Annual Canadian Conference on Computational Geometry, CCCG 2007, Ottawa, ON, 20 August 2007 through 22 August 2007 ; 2007 , Pages 249-252 ; Zarei, A ; Ghodsi, M ; Sharif University of Technology
2007

Abstract

In this paper we consider maintaining the visibility of a segment observer moving inside a simple polygon. A practical instance of this problem is to identify the regions of a planar scene illuminated by a fluorescent lamp while the lamp moves around. We consider both strong and weak visibility in this paper. Our method is based on the shortest path tree which builds a linear-sized data structure in O(n) time, where n is the number of the vertices of the underlying simple polygon P. We first compute VP(st̄), the initial view of the segment observer st̄. Then, as st̄ moves, each change of VP(st̄) can be computed in O(log2(|V P(st̄)|)) time when the observer is allowed to change its direction,...

#### On the distortion value of elections with abstention

, Article Journal of Artificial Intelligence Research ; Volume 70 , 2021 , Pages 567-595 ; 10769757 (ISSN) ; Latifian, M ; Ghodsi, M ; Sharif University of Technology
AI Access Foundation
2021

Abstract

In Spatial Voting Theory, distortion is a measure of how good the winner is. It has been proved that no deterministic voting mechanism can guarantee a distortion better than 3, even for simple metrics such as a line. In this study, we wish to answer the following question: How does the distortion value change if we allow less motivated agents to abstain from the election? We consider an election with two candidates and suggest an abstention model, which is a general form of the abstention model proposed by Kirchgässner. Our results characterize the distortion value and provide a rather complete picture of the model. ©2021 AI Access Foundation

#### Weak visibility queries of line segments in simple polygons and polygonal domains

, Article International Journal of Computer Mathematics ; 2017 , Pages 1-18 ; 00207160 (ISSN) ; Ghodsi, M ; Sharif University of Technology
Taylor and Francis Ltd
2017

Abstract

In this paper we consider the problem of computing the weak visibility polygon of a query line segment pq (or (Formula presented.)) inside a given polygon (Formula presented.). Our first algorithm runs in simple polygons and needs (Formula presented.) time and (Formula presented.) space in the preprocessing phase to report (Formula presented.) of any query line segment pq in time (Formula presented.). We also give an algorithm to compute the weak visibility polygon of a query line segment in a non-simple polygon with (Formula presented.) pairwise-disjoint polygonal obstacles with a total of n vertices. Our algorithm needs (Formula presented.) time and (Formula presented.) space in the...

#### Weak visibility queries of line segments in simple polygons and polygonal domains

, Article International Journal of Computer Mathematics ; Volume 95, Issue 4 , 2018 , Pages 721-738 ; 00207160 (ISSN) ; Ghodsi, M ; Sharif University of Technology
Taylor and Francis Ltd
2018

Abstract

In this paper we consider the problem of computing the weak visibility polygon of a query line segment pq (or WVP(pq)) inside a given polygon P. Our first algorithm runs in simple polygons and needs O(n3 log n) time and O(n3) space in the preprocessing phase to report WVP(pq) of any query line segment pq in time O(log n + |WVP(pq)|).. We also give an algorithm to compute the weak visibility polygon of a query line segment in a non-simple polygon with h ≥ 1 pairwise-disjoint polygonal obstacles with a total of n vertices. Our algorithm needs O(n2 log n) time and O(n2) space in the preprocessing phase and WVP(pq) in query time of O(nh’ log n + k), in which h’ is an output sensitive parameter...

#### Weak visibility queries in simple polygons

, Article Proceedings of the 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011 ; 2011 ; Ghodsi, M ; Sharif University of Technology
Abstract

In this paper, we consider the problem of computing the weak visibility (WV ) of a query line segment in- side a simple polygon. Our algorithm first preprocesses the polygon and creates data structures from which any WV query is answered efficiently in an output sensitive manner. In our solution, the preprocessing is performed in time O(n3 log n) and the size of the constructed data structure is O(n3). It is then possible to report the WV polygon of any query line segment in time O(log n+k), where k is the size of the output. Our algorithm im- proves the current results for this problem

#### On totally decomposable algebras with involution in characteristic two

, Article Journal of Algebra ; Volume 451 , 2016 , Pages 208-231 ; 00218693 (ISSN) ; Nokhodkar, A. H ; Sharif University of Technology
Abstract

A necessary and sufficient condition for a central simple algebra with involution over a field of characteristic two to be decomposable as a tensor product of quaternion algebras with involution, in terms of its Frobenius subalgebras, is given. It is also proved that a bilinear Pfister form, recently introduced by A. Dolphin, can classify totally decomposable central simple algebras of orthogonal type

#### How to extend visibility polygons by mirrors to cover invisible segments

, Article 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017, 29 March 2017 through 31 March 2017 ; Volume 10167 LNCS , 2017 , Pages 42-53 ; 03029743 (ISSN); 9783319539249 (ISBN) ; Ghodsi, M ; Sharif University of Technology
Springer Verlag
2017

Abstract

Given a simple polygon P with n vertices, the visibility polygon (V P) of a point q (V P(q)), or a segment (formula present) (V P(pq)) inside P can be computed in linear time. We propose a linear time algorithm to extend V P of a viewer (point or segment), by converting some edges of P into mirrors, such that a given non-visible segment (formula present) can also be seen from the viewer. Various definitions for the visibility of a segment, such as weak, strong, or complete visibility are considered. Our algorithm finds every edge such that, when converted to a mirror, makes (formula present) visible to our viewer. We find out exactly which interval of (formula present) becomes visible, by...

#### Commuting graphs of some subsets in simple rings

, Article Linear Algebra and Its Applications ; Volume 416, Issue 2-3 , 2006 , Pages 1038-1047 ; 00243795 (ISSN) ; Raja, P ; Sharif University of Technology
2006

Abstract

Let D be a division ring with center F and n {greater than or slanted equal to} 1 a natural number. For S ⊆ Mn(D) the commuting graph of S, denoted by Γ(S), is the graph with vertex set S{minus 45 degree rule}Z(S) such that distinct vertices a and b are adjacent if and only if ab = ba. In this paper we prove that if n > 2 and A, N, I, T are the sets of all non-invertible, nilpotent, idempotent matrices, and involutions, respectively, then for any division ring D, Γ ( A ), Γ ( N ), Γ ( I ), and Γ ( T ) are connected graphs. We show that if n > 2 and U is the set of all upper triangular matrices, then for every algebraic division ring D, Γ ( U ) is a connected graph. Also it is shown that if R...

#### Multiple-shift acquisition algorithm in ultra-wide bandwidth frame time-hopping wireless CDMA systems

, Article 13th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC 2002, Lisboa, 15 September 2002 through 18 September 2002 ; Volume 4 , 2002 , Pages 1824-1828 ; 0780375890 (ISBN); 9780780375895 (ISBN) ; Salehi, J. A ; Sharif University of Technology
2002

Abstract

In this paper we study and analyze multiple-shift algorithms in the context of ultrawideband radio frame time-hopping CDMA system (UWB-FTH-CDMA). In our analysis we consider major sources of noise, namely multiaccess interference and the additive white Gaussian noise. For multiaccess interference we consider a model in which mutual interference due to each user is based on frame asynchronous but half-chip synchronous. Since simple serial-search is a special case of the multiple-shift algorithm, we can analyze the advantage of multiple-shift algorithm. It is shown that multiple-shift algorithm is superior than simple serial-search algorithm in reducing the required average acquisition time by...

#### Using satisfiability for non-optimal temporal planning

, Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ; Volume 7519 Lnai , 2012 , Pages 176-188 ; 03029743 (ISSN) ; 9783642333521 (ISBN) ; Mahjoob, A ; Ghassem-Sani, G ; Sharif University of Technology
Springer
2012

Abstract

AI planning is one of the research fields that has benefited from employing satisfiability checking methods. These methods have been proved to be very effective in finding optimal plans for both classical and temporal planning. It is also known that by using planning-based heuristic information in solving SAT formulae, one can develop SAT-based planners that are competitive with state-of-the-art non-optimal planners in classical planning domains. However, using satisfiability for non-optimal temporal planning has not been investigated so far. The main difficulty in using satisfiability in temporal planning is the representation of time, which is a continuous concept. Previously introduced...

#### Nonlinear oscillation analysis of a pendulum wrapping on a cylinder

, Article Scientia Iranica ; Volume 19, Issue 2 , 2012 , Pages 335-340 ; 10263098 (ISSN) ; Hosseinzadeh, A ; Ahmadian, M. T ; Sharif University of Technology
2012

Abstract

In this paper, the nonlinear oscillation of a pendulum wrapping and unwrapping on two cylindrical bases is studied, and an analytical solution is obtained using the multiple scales method. The equation of motion is derived based on an energy conservation technique. By applying the perturbation method to the differential equation, the nonlinear natural frequency of the system is calculated, along with its time response. Analytical results are compared with numerical findings and good agreement is found. The effect of large amplitude and radius of cylinders on system frequency is evaluated. The results indicate that as the radius of the cylinder increases, the system frequency is increased....

#### A complete state-space based temporal planner

, Article Proceedings - International Conference on Tools with Artificial Intelligence, ICTAI, 7 November 2011 through 9 November 2011, Boca Raton, FL ; 2011 , Pages 297-304 ; 10823409 (ISSN) ; 9780769545967 (ISBN) ; Ghassem Sani, G ; Sharif University of Technology
Abstract

Since that heuristic state space planners have been very successful in classical planning, this approach is currently the most popular strategy in dealing with temporal planning, too. However, all current state-space temporal planners use a search method known as decision epoch planning, which is not complete for problems with required concurrency. In theory, this flaw can be overcome by employing another search method, called temporally lifted progression planning. In this paper, we show that there are two major problems which, if not tackled properly, can cause the latter method to be very inefficient in practice. The first problem is dealing with the remarkably large state space of...

#### Effect of Non-Plastic Fine on Liquefaction Resistance of Sand Using Cyclic Simple Shear Test

, M.Sc. Thesis Sharif University of Technology ; Ahmadi, Mohammad Mehdi (Supervisor)
Abstract

Soil Liquefaction is a phenomenon corresponding to earthquake in which granular soil loses most of its strength in seismic loading. In this study, cyclic simple shear tests were performed for evaluating the effect of non-plastic fines on liquefaction resistance of Firuzkouh sand. Firuzkouh sand is uniform and is classified as SP in USCS. Firuzkouh silt was used as Non-plastic fine. Tests were performed under constant vertical load and undrained conditions on cylindrical specimens 7 cm in diameter and 2.2 cm in height. Samples were prepared using wet tamping method. All specimens were saturated following the standard back pressure method until the Skempton B-value was at least 0.96. Samples...

#### Unit Groups Of Central Simple Algebras And Their Frattini Subgroups

, M.Sc. Thesis Sharif University of Technology ; Mahdavi Hezavehi, Mohammad (Supervisor)
Abstract

Given a finite dimensional F-central simple algebra A = Mn(D),the connection between the Ferattini subgroup (A) and (F) via Z(A′), the center of the derived group of A , is investigated. Setting G = F \(A), it is shown that (F)Z(A′ ) G (\pFp)Z(A′)where the intersection is taken over primes p not dividing the degree of A. Furthermore ,when F is a local or global field, the group G is completely determined. Using the above connection, (A) is also calculated for some particular division rings D

#### Dynamic Parameters of Saturated and Unsaturated Sand at Different Range of Shear Strain Levels in Cyclic Simple Shear Test

, M.Sc. Thesis Sharif University of Technology ; Jafarzadeh, Fardin (Supervisor)
Abstract

In this investigation, a series of cyclic simple shear tests were carried out in order to evaluate dynamic parameters of Babolsar and Toyoura sand at levels of saturation 25, 50, 75 and 100%. 96 tests were conducted using SGI type cyclic simple shear device. The specimens were cylindrical, with 7cm diameter and 2.2 cm height. The tests were performed under both drained condition (constant-load) at levels of saturation 25, 50%, and undrained condition at levels of saturation 75, 100%. All tests were performed under vertical consolidation stress of 50 and 150 kPa, relative density of 30 and 70% and cyclic shear strain of 0.5, 5 and 10%. The tests were shear strain-controlled with an...

#### Subgraphs Associated with Lists in Graphs and Digraphs

, M.Sc. Thesis Sharif University of Technology ; Akbari, Saeed (Supervisor)
Abstract

Let G be a graph and F : V (G) ...! 2N be a function. The graph G is said to be F-avoiding if there exists an orientation O of G such that d+ O(v) =2 F(v) for every v 2 V (G), where d+O(v) denotes the out-degree of v in the directed graph G with respect to O. In this thesis it is shown that if G is bipartite and jF(v)j dG(v) 2 for every v 2 V (G), then G is F-avoiding. The bound jF(v)j dG(v) 2 is best possible. For every graph G, we conjecture that if jF(v)j dG(v) 1 2 for every v 2 V (G), then G is F-avoiding. We also argue this conjecture; the best possibility and some partial solutions, e.g. for the complete graphs. For graph G, we say the set f(d+ i ; d i ); i = 1; : : : ; ng of...

#### Touring a sequence of disjoint polygons: Complexity and extension

, Article Theoretical Computer Science ; Vol. 556, Issue. C , October , 2014 , pp. 45-54 ; ISSN: 03043975 ; Mozafari, A ; Zarei, A ; Sharif University of Technology
Abstract

In the Touring Polygons Problem (TPP) there is a start point s, a sequence of simple polygons P=(P1,. . .,Pk) and a target point t in the plane. The goal is to obtain a path of minimum possible length that starts from s, visits in order each of the polygons in P and ends at t. This problem was introduced by Dror, Efrat, Lubiw and Mitchell in STOC '03. They proposed a polynomial time algorithm for the problem when the polygons in P are convex and proved its NP-hardness for intersecting and non-convex polygons. They asked as an open problem whether TPP is NP-hard when the polygons are pairwise disjoint. In this paper, we prove that TPP is also NP-hard when the polygons are pairwise disjoint in...