Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Article Citation - Scopus: 1Level Set Estimates for the Discrete Frequency Function(Springer Verlag, 2019) Temur, FarukWe introduce the discrete frequency function as a possible new approach to understanding the discrete Hardy-Littlewood maximal function. Considering that the discrete Hardy-Littlewood maximal function is given at each integer by the supremum of averages over intervals of integer length, we define the discrete frequency function at that integer as the value at which the supremum is attained. After verifying that the function is well-defined, we investigate size and smoothness properties of this function.Article On the Structure of Modules Defined by Opposites of Fp Injectivity(Springer Verlag, 2019) Büyükaşık, Engin; Kafkas Demirci, GizemLet R be a ring with unity and let MR and RN be right and left modules,respectively. The module MR is said to be absolutely RN-pure if M circle times NL circle times N is amonomorphism for every extension LR of MR. For a module MR, the subpurity domain of MR is defined to be the collection of all modules RN, such that MR is absolutely RN-pure. Clearly, MR is absolutely RF-pure for every flat module RF and that MR is FP-injective if the subpurity domain of M is the entire class of left modules. As an opposite of FP-injective modules, MR is said to be a test for flatness by subpurity (or t.f.b.s. for short) if its subpurity domain is as small as possible, namely, consisting of exactly the flat left modules. We characterize the structure of t.f.b.s. modules over commutative hereditary Noetherian rings. We prove that a module M is t.f.b.s. over a commutative hereditary Noetherian ring if and only if M/Z(M) is t.f.b.s. if and only if Hom(M/Z(M),S)0 for each singular simple module S. Prufer domains are characterized as those domains all of whose nonzero finitely generated ideals are t.f.b.s.Article Citation - WoS: 30Citation - Scopus: 33The Initial Stage of Dam-Break Flow(Springer Verlag, 2009) Korobkin, Alexandre; Yılmaz, OğuzThe liquid flow and the free surface shape during the initial stage of dam breaking are investigated. The method of matched asymptotic expansions is used to derive the leading-order uniform solution of the classical dam-break problem. The asymptotic analysis is performed with respect to a small parameter which characterizes the short duration of the stage under consideration. The second-order outer solution is obtained in the main flow region. This solution is not valid in a small vicinity of the intersection point between the initially vertical free surface and the horizontal rigid bottom. The dimension of this vicinity is estimated with the help of a local analysis of the outer solution close to the intersection point. Stretched local coordinates are used in this vicinity to resolve the flow singularity and to derive the leading-order inner solution, which describes the formation of the jet flow along the bottom. It is shown that the inner solution is self-similar and the corresponding boundary-value problem can be reduced to the well-known Cauchy-Poisson problem for water waves generated by a given pressure distribution along the free surface. An analysis of the inner solution reveals the complex shape of the jet head, which would be difficult to simulate numerically. The asymptotic solution obtained is expected to be helpful in the analysis of developed gravity-driven flows.Article Citation - WoS: 23Citation - Scopus: 26Travelling Wave Solutions To Nonlinear Physical Models by Means of the First Integral Method(Springer Verlag, 2011) Aslan, İsmailThis paper presents the first integral method to carry out the integration of nonlinear partial differential equations in terms of travelling wave solutions. For illustration, three important equations of mathematical physics are analytically investigated. Through the established first integrals, exact solutions are successfully constructed for the equations considered. © Indian Academy of Sciences.Article Citation - WoS: 1Citation - Scopus: 4A Practical Privacy-Preserving Targeted Advertising Scheme for Iptv Users(Springer Verlag, 2016) Khayati, Leyli Javid; Örencik, Cengiz; Savaş, Erkay; Ustaoğlu, BerkantIn this work, we present a privacy-preserving scheme for targeted advertising via the Internet Protocol TV (IPTV). The scheme uses a communication model involving a collection of subscribers, a content provider (IPTV), advertisers and a semi-trusted server. To target potential customers, the advertiser can utilize not only demographic information of subscribers, but also their watching habits. The latter includes watching history, preferences for IPTV content and watching rate, which are periodically (e.g., weekly) published on a semi-trusted server (e.g., cloud server) along with anonymized demographics. Since the published data may leak sensitive information about subscribers, it is safeguarded using cryptographic techniques in addition to the anonymization of demographics. The techniques used by the advertiser, which can be manifested in its queries to the server, are considered (trade) secrets and therefore are protected as well. The server is oblivious to the published data and the queries of the advertiser as well as its own responses to these queries. Only a legitimate advertiser, endorsed with so-called trapdoors by the IPTV, can query the cloud server and access the query results. Even when some background information about users is available, query responses do not leak sensitive information about the IPTV users. The performance of the proposed scheme is evaluated with experiments, which show that the scheme is practical. The algorithms demonstrate both weak and strong scaling property and take advantage of high level of parallelism. The scheme can also be applied as a recommendation system. © 2015, Springer-Verlag Berlin Heidelberg.Article Citation - WoS: 7Integrating Identity-Based and Certificate-Based Authenticated Key Exchange Protocols(Springer Verlag, 2011) Ustaoğlu, BerkantKey establishment is becoming a widely deployed cryptographic primitive. As such, there has been extensive research on designing algorithms that produce shared secret keys. These protocols require parties to either hold certificates or rely on identity (ID)-based primitives to achieve authentication. Chain and cross certifications allow users trusting different certification authorities to interact. Similarly, there are methods to extend ID-based solutions across multiple key generation centers (KGC). However, there has been no dedicated work on interoperability between the two settings. A straightforward solution would require each user to maintain certificates and ID-based static keys to accommodate all peers. The cost of maintaining many secret keys; matching keys with protocols; and preventing undesired interference would arguably make such a solution impractical. In this work, we offer an alternative where a user needs to keep a single static key pair and can subsequently engage in a session key establishment with peers holding certificates or identity-based keys. Thus, the proposed solution has none of disadvantages of maintaining multiple static private keys. © 2011 Springer-Verlag.Article Citation - WoS: 4Citation - Scopus: 4Power-Series Solution for the Two-Dimensional Inviscid Flow With a Vortex and Multiple Cylinders(Springer Verlag, 2009) Pashaev, Oktay; Yılmaz, OğuzThe problem of a point vortex and N fixed cylinders in a two-dimensional inviscid fluid is studied and an analytical-numerical solution in the form of an infinite power series for the velocity field is obtained using complex analysis. The velocity distribution for the case of two cylinders is compared with the existing results of the problem of a vortex in an annular region which is conformally mapped onto the exterior of two cylinders. Limiting cases of N cylinders and the vortex, being far away from each other are studied. In these cases, "the dipole approximation" or "the point-island approximation" is derived, and its region of validity is established by numerical tests. The velocity distribution for a geometry of four cylinders placed at the vertices of a square and a vortex is presented. The problem of vortex motion with N cylinders addressed in the paper attracted attention recently owing to its importance in many applications. However, existing solutions using Abelian function theory are sophisticated and the theory is not one of the standard techniques used by applied mathematicians and engineers. Moreover, in the N ≥ 3 cylinder problem, the infinite product involved in the presentation of the Schottky-Klein prime function must also be truncated. So, the approach used in the paper is simple and an alternative to existing methods. This is the main motivation for this study.Article Citation - WoS: 9Citation - Scopus: 10Relation Between Relativistic and Non-Relativistic Quantum Mechanics as Integral Transformation(Springer Verlag, 2002) Mir-Kasimov, Rufat M.A formulation of quantum mechanics (QM) in the relativistic configurational space (RCS) is considered. A transformation connecting the non-relativistic QM and relativistic QM (RQM) has been found in an explicit form. This transformation is a direct generalization of the Kontorovich-Lebedev transformation. It is shown also that RCS gives an example of non-commutative geometry over the commutative algebra of functions.