Developing a Tool for the Location Optimization of the Alert Aircraft with Changing Threat Anticipation

The threat to the airspace is posed by the outside world in conventional terms as well as hostilities from within the airspace such as hijacked aircraft. Alert aircraft are located with the sole responsibility of responding to any incident. Different regions of the airspace may have different alert states depending on current intelligence input. Due to non-constant states of threat level, the Turkish Air Force must deploy aircraft to cover the more sensitive regions with a greater number of aircraft with a relatively short response time. This research deals with the problem by developing a tool for the location optimization of the alert aircraft. The tool can adapt to changes in threat anticipation while meeting the objectives of the alert network. Thus, a new location model with backup coverage requirements was formulated, and an interactive tool is developed that is capable of generating the aircraft locations for different user-defined threat anticipation

Commutativity and structure of Gamma rings

Bu tezin amacı, karakteristi˘gi 2 den farklı olan türevli gamma halkalarda de˘gismelilik kosullarını arastırmaktır. Bunun için gamma halkalarda g-Lie idealleri tanımlanmıs ve gamma halkalarda yeni bazı özellikler elde edilmistir. Çalısma temel olarak bes bölümden olusmaktadır. ˙Ilk bölümde, gamma halkaların ortaya çıkısı özetlenmis ve gamma halkalarla ilgili literatürde yer alan bazı çalısmalardan bahsedilmistir. ˙Ikinci bölümde, halkalar ve gamma halkalar ile ilgili bu çalısmanın temelini olusturan bazı tanımlar ve özellikler verilmistir. Üçüncü bölümde, gamma halkalar için bazı yeni kavramlar tanıtılmıstır ve bu kavramlar yardımıyla gamma halkalarda yeni özellikler elde edilmistir. Dördüncü bölümde, türevli gamma halkalarda g-Lie idealler üzerindeki özellikler yardımıyla gamma halkanın yapısı ile ilgili bazı sonuçlara yer verilmistir. Son bölümde, gamma halkalar ile gamma halkaya ba˘glı olarak tanımlanan halkalar arasında iliskiler kurulmus ve gamma halkalarda literatürde var olan radikaller ile gamma halkanın g-radikalleri arasındaki iliskiler arastırılmıstır.The objective of this thesis is to find commutativity conditions in prime gamma rings with derivation of characteristic not 2. For this reason, a g-Lie ideal of a gamma ring is introduced and some new properties have been obtained in gamma rings. The study consists of five sections basically. In the first chapter, the emergence of the gamma ring is summarized and and some works which have been done in the literature about the gamma rings have been mentioned. In the second chapter, some definitions and properties have been given which are the basis of this work. In the third chapter, some new notions have been introduced and get new properties in gamma rings with the help of these notions. In the forth chapter, some results have been given about the structure of the gamma rings by the help of the properties of g-Lie ideals in the gamma rings with derivation. In the last chapter, the relations between the rings and the gamma rings have been established and the relations between the radicals and the g-radicals of gamma rings have been investigated

Finitary permutation groups and S-groups

This thesis is a survey of A. O. Asar's and M. R. Dixon, M. J. Evans, V. N. Obraztsov, J. Wiegold's papers that are \On Finitary Permutation Groups" and \Groups that are Covered by Non-Abelian Simple Groups". A group G is called FC-group if the conjugacy class of every element is ¯nite. G is called minimal non-FC-group if G is not an FC-group, but every proper subgroup of G is an FC-group. All minimal non-FC-groups that are di®erent from their commutator subgroups are classi¯ed by Belyaev in 1978. Belyaev proved that if there exists a locally ¯nite minimal non-FC-group G that is equal to its commutator subgroup is either G=Z (G) is simple or G is a p-group for some prime p. In 1989, Kuzucuo¸glu and Phillips showed that G=Z (G) can not be simple. Therefore, if there exists a locally ¯nite minimal non-FC-group G with G = G0 then it is a p-group for some prime p. But, existence of a perfect locally ¯nite minimal non-FC-group has been a problem for 30 years. vi F. Leinen and V. V. Belyaev are proved independently that if there exists such a group then it has a non-trivial representation into the group of ¯nitary permutations on some in¯nite set ­. So the existence problem of a perfect locally ¯nite minimal non-FC-group turns out to investige to ¯nitary permutation groups. Asar, in this paper, proved that there exist no such group if the following holds: If G is a locally ¯nite minimal non-FC-group and for every ¯nite non-normal subgroup F of G there exists y 2 GnNG(F) such that yp 2 FCG(F), then G can not be perfect. Let S denote the class of all groups that are the set theoretic union of their non-abelian simple subgroups. In chapter 4, some properties of such groups are examined. In this chapter, it is showed that if G is locally graded group, M is torsion-free radical of G and N is the normal subgroup of G generated by all the elements of ¯nite order and if N 6= 1, then M · N · G, G=N torsion-free, N=M simple. In addition, if also M 6= 1, then every ¯nite subgroup of G is cyclic or metacyclic.Bu tez; A. O. Asar'ın "On Finitary Permutation Groups" ve M. R. Dixon, M. J. Evans, V. N. Obraztsov, J. Wiegold'un "Groups That Are Covered By Non-Abelian Simple Groups" adlı makalelerinin bir derlemesidir. Bir G grubunun her elemanının eşlenik sınıfı sonlu ise G ye FC-grup denir. Kendisi FC-grup olmayan ancak her özalt grubu FC-grup olan gruplara minimal FC-olmayan grup denir. Komütatör grubu kendisinden farklı olan minimal FC-olmayan gruplar V. V. Belyaev tarafından 1978 yılında sınıflandırılmıştır. Belyaev, komütatör grubu kendisine eşit olan minimal FC-olmayan yerel sonlu bir G grubu var ise ya G/Z(G) basit bir grup ya da p asal olmak üzere G nin bir p-grup olduğunu kanıtlamıştır. 1989 da Kuzucuoğlu ve Phillips G/Z(G) nin basit olamayacağını göstermişlerdir. Dolayısıyla G=G? özelliğini sağlayan yerel sonlu minimal FC-olmayan bir grup var ise bu grup bir p-gruptur. Ancak böyle bir grubun var olup olmadığı 30 yıldır açık bir problemdir. F. Leinen ve V. V. Belyaev birbirlerinden bağımsız olarak böyle bir grup var ise bu grubun sonsuz bir ? kümesi üzerindeki sonlumsu permütasyon grubunun bir altgrubuna izomorfik olacağını kanıtlamışlardır. Bu durumda G=G' özelliğini sağlayan yerel sonlu minimal FC-olmayan bir grubun var olup olmadığını incelemek sonlumsu permütasyon grubun altgruplarını incelemekten geçmektedir. Asar bu makalesinde aşağıdaki şartların var olması durumunda böyle bir grubun olamayacağını kanıtlamıştır: Yerel sonlu minimal FC olmayan bir G grubunun normal olmayan sonlu her F altgrubu için y^{p}?FC_{G}(F) olacak şekilde en az bir y?G\N_{G}(F) varsa G mükemmel olamaz. Değişmeli olmayan basit altgruplarının birleşimi ile oluşturulan bütün grupların oluşturduğu sınıfı S ile gösterelim. Bölüm 4 te, bu özellikte olan grupların(S-gruplar) temel özellikleri verilmiştir. Bu bölümde; G yerel derecelendirilmiş bir S-grup, M grubu G nin serbest periyodik radikali ve G nin tüm sonlu mertebeden elemanları tarafından üretilen normal altgrubu N olmak üzere N?1 ise M?N?G, G/N serbest periyodik, N/M basit olduğu gösterilmiştir. Bununla birlikte M de birimden farklı bir eleman varsa G nin sonlu her altgrubunun ya devirli ya da metadevirli olduğu kanıtlanmıştır

γ-Lie structures in γ-prime gamma rings with derivations

Let $M$ be a $\gamma$-prime weak Nobusawa $\Gamma$-ring and $d\neq 0$ be a $k$-derivation of $M$ such that $k\left( \gamma \right) =0$ and $U$ be a $\gamma$-Lie ideal of $M$. In this paper, we introduce definitions of $\gamma$-subring, $\gamma$-ideal, $\gamma$-prime $\Gamma$-ring and $\gamma$-Lie ideal of M and prove that if $U\nsubseteq C_{\gamma}$, $char$M$\neq2$ and $d^3\neq0$, then the $\gamma$-subring generated by $d(U)$ contains a nonzero ideal of $M$. We also prove that if $[u,d(u)]_{\gamma}\in C_{\gamma}$ for all $u\in U$, then $U$ is contained in the $\gamma$-center of $M$ when char$M\neq2$ or $3$. And if $[u,d(u)]_{\gamma}\in C_{\gamma}$ for all $u\in U$ and $U$ is also a $\gamma$-subring, then $U$ is $\gamma$-commutative when char$M=2$

Origami in Mathematics Education: The Development and Validation of an Origami-Related Self-Efficacy Scale

The current study aims to develop and validate a scale in order to measure preservice and/or in-service teachers’ self-efficacy beliefs regarding the use of origami in mathematics education. In line with this purpose, Origami in Mathematics Education Self-Efficacy Scale (OMESS) is developed and administered to 143 preservice teachers in the pilot study. Exploratory factor analysis results indicate that single dimension explains 73 percent of the total variance. In the main study, OMESS is administered to 299 preservice teachers. Obtained data is analyzed with confirmatory factor analysis techniques, and RMSEA is found to be 0.068, NC is found to be 2.37, CFI and NFI are found to be 0.99. Furthermore, Cronbach alpha coefficient for the single dimension is calculated as 0.94. Followed by the additional validation studies, OMESS might serve as a valuable tool in order to measure self-efficacy beliefs on the use of origami in mathematics education

Exact solution of the evasive flow capturing problem

The Evasive Flow Capturing Problem is defined as the problem of locating a set of law enforcement facilities on the arcs of a road network to intercept unlawful vehicle flows traveling between origin-destination pairs, who in turn deviate from their route to avoid any encounter with such facilities. Such deviations are bounded by a given tolerance. We first propose a bilevel program that, in contrast to previous studies, does not require a priori route generation. We then transform this bilevel model into a single-stage equivalent model using duality theory to yield a compact formulation. We finally reformulate the problem by describing the extreme rays of the polyhedral cone of the compact formulation and by projecting out the auxiliary variables, which leads to facet-defining inequalities and a cut formulation with an exponential number of constraints. We develop a branch-and-cut algorithm for the resulting model, as well as two separation algorithms to solve the cut formulation. Through extensive experiments on real and randomly generated networks, we demonstrate that our best model and algorithm accelerate the solution process by at least two orders of magnitude compared with the best published algorithm. Furthermore, our best model significantly increases the size of the instances that can be solved optimally.</p

Exact solution of the evasive flow capturing problem

The Evasive Flow Capturing Problem is defined as the problem of locating a set of law enforcement facilities on the arcs of a road network to intercept unlawful vehicle flows traveling between origin-destination pairs, who in turn deviate from their route to avoid any encounter with such facilities. Such deviations are bounded by a given tolerance. We first propose a bilevel program that, in contrast to previous studies, does not require a priori route generation. We then transform this bilevel model into a single-stage equivalent model using duality theory to yield a compact formulation. We finally reformulate the problem by describing the extreme rays of the polyhedral cone of the compact formulation and by projecting out the auxiliary variables, which leads to facet-defining inequalities and a cut formulation with an exponential number of constraints. We develop a branch-and-cut algorithm for the resulting model, as well as two separation algorithms to solve the cut formulation. Through extensive experiments on real and randomly generated networks, we demonstrate that our best model and algorithm accelerate the solution process by at least two orders of magnitude compared with the best published algorithm. Furthermore, our best model significantly increases the size of the instances that can be solved optimally

A Flexible, Natural Formulation for the Network Design Problem with Vulnerability Constraints

Given a graph, a set of origin-destination (OD) pairs with communication requirements, and an integer k 2, the network design problem with vulnerability constraints (NDPVC) is to identify a subgraph with the minimum total edge costs such that, between each OD pair, there exist a hop-constrained primary path and a hop-constrained backup path after any k â' 1 edges of the graph fail. Formulations exist for single-edge failures (i.e., k = 2). To solve the NDPVC for an arbitrary number of edge failures, we develop two natural formulations based on the notion of length-bounded cuts. We compare their strengths and flexibilities in solving the problem for k 3. We study different methods to separate infeasible solutions by computing length-bounded cuts of a given size. Experimental results show that, for single-edge failures, our formulation increases the number of solved benchmark instances from 61% (obtained within a two-hour limit by the best published algorithm) to more than 95%, thus increasing the number of solved instances by 1,065. Our formulation also accelerates the solution process for larger hop limits and efficiently solves the NDPVC for general k. We test our best algorithm for two to five simultaneous edge failures and investigate the impact of multiple failures on the network design. Â</p

A Flexible, Natural Formulation for the Network Design Problem with Vulnerability Constraints

Given a graph, a set of origin-destination (OD) pairs with communication requirements, and an integer k &gt;= 2, the network design problem with vulnerability constraints (NDPVC) is to identify a subgraph with the minimum total edge costs such that, between each OD pair, there exist a hop-constrained primary path and a hop-constrained backup path after any k - 1 edges of the graph fail. Formulations exist for single-edge failures (i.e., k = 2). To solve the NDPVC for an arbitrary number of edge failures, we develop two natural formulations based on the notion of length-bounded cuts. We compare their strengths and flexibilities in solving the problem for k &gt;= 3. We study different methods to separate infeasible solutions by computing length-bounded cuts of a given size. Experimental results show that, for single-edge failures, our formulation increases the number of solved benchmark instances from 61% (obtained within a two-hour limit by the best published algorithm) to more than 95%, thus increasing the number of solved instances by 1,065. Our formulation also accelerates the solution process for larger hop limits and efficiently solves the NDPVC for general k. We test our best algorithm for two to five simultaneous edge failures and investigate the impact of multiple failures on the network design

Single Allocation Hub Location with Heterogeneous Economies of Scale

We study the single allocation hub location problem with heterogeneous economies of scale (SAHLP-h). The SAHLP-h is a generalization of the classical single allocation hub location problem (SAHLP), in which the hub-hub connection costs are piecewise linear functions of the amounts of flow. We model the problem as an integer nonlinear program, which we then reformulate as a mixed integer linear program (MILP) and as a mixed integer quadratically constrained program (MIQCP). We exploit the special structures of these models to develop Benders-type decomposition methods with integer subproblems. We use an integer L-shaped decomposition to solve the MILP formulation. For the MIQCP, we dualize a set of complicating constraints to generate a Lagrangian function, which offers us a subproblem decomposition and a tight lower bound. We develop linear dual functions to underestimate the integer subproblem, which helps us obtain optimality cuts with a convergence guarantee by solving a linear program. Moreover, we develop a specialized polynomial-time algorithm to generate enhanced cuts. To evaluate the efficiency of our models and solution approaches, we perform extensive computational experiments on both uncapacitated and capacitated SAHLP-h instances derived from the classical Australian Post data set. The results confirm the efficacy of our solution methods in solving large-scale instances