Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
Browse
20 results
Search Results
Article Citation - WoS: 4Relativistic Burgers and Nonlinear Schrödinger Equations(Pleiades Publishing, 2009) Pashaev, OktayWe construct relativistic complex Burgers-Schrodinger and nonlinear Schrodinger equations. In the nonrelativistic limit, they reduce to the standard Burgers and nonlinear Schrodinger equations and are integrable through all orders of relativistic corrections.Conference Object Citation - Scopus: 5Kaleidoscope of Classical Vortex Images and Quantum Coherent States(Springer, 2018) Pashaev, Oktay; Koçak, AygülThe Schrödinger cat states, constructed from Glauber coherent states and applied for description of qubits are generalized to the kaleidoscope of coherent states, related with regular n-polygon symmetry and the roots of unity. This quantum kaleidoscope is motivated by our method of classical hydrodynamics images in a wedge domain, described by q-calculus of analytic functions with q as a primitive root of unity. First we treat in detail the trinity states and the quartet states as descriptive for qutrit and ququat units of quantum information. Normalization formula for these states requires introduction of specific combinations of exponential functions with mod 3 and mod 4 symmetry, which are known also as generalized hyperbolic functions. We show that these states can be generated for an arbitrary n by the Quantum Fourier transform and can provide in general, qudit unit of quantum information. Relations of our states with quantum groups and quantum calculus are discussed. © Springer Nature Switzerland AG 2018.Article Asymptotic Behaviour of Dam Break Flow for Small Times(Institute of Computational Technologies SB RAS, 2019) Isıdıcı Demirel, Damla; Iafrati, Alessandro; Korobkin, Alexander A.; Yılmaz, OğuzTwo dimensional impulsive flow of a fluid is studied within the potential flow theory. Initially the fluid is at rest and is held on one side of a vertical plate. The plate is withdrawn suddenly and gravity driven flow of the fluid starts. Attention is paid to the singular behaviour of the velocity field at the bottom point, where the vertical free surface meets the rigid bottom. The linear problem is solved by the Fourier series method. An inner region solution is found using Mellin transform at the bottom point. The jet formation is observed at the bottom point. Also the discontinuity at the upper corner point is dealt with Lagrangian variables. For the second order outer problem, domain decomposition method is used. Comparison of the shapes of the free surfaces near the upper corner point with leading and second order solutions shows that the second order outer solution outer makes a larger difference in the vertical free surface than in the horizontal portion, compared with leading order solution.The complete picture of the shapes of the free surfaces using Lagrangian description for the upper part and Eulerian description for the bottom part at the second order is obtained. © ICT SB RAS, 2019Conference Object The Hirota Method for Reaction-Diffusion Equations With Three Distinct Roots(American Institute of Physics, 2004) Tanoğlu, Gamze; Pashaev, OktayThe Hirota Method, with modified background is applied to construct exact analytical solutions of nonlinear reaction-diffusion equations of two types. The first equation has only nonlinear reaction part, while the second one has in addition the nonlinear transport term. For both cases, the reaction part has the form of the third order polynomial with three distinct roots. We found analytic one-soliton solutions and the relationships between three simple roots and the wave speed of the soliton. For the first case, if one of the roots is the mean value of other two roots, the soliton is static.We show that the restriction on three distinct roots to obtain moving soliton is removed in the second case by, adding nonlinear transport term to the first equation.Article Citation - WoS: 1Citation - Scopus: 1Rad-supplements in injective modules(Institute of Applied Mathematics And Mechanics of the National Academy of Sciences of Ukraine, 2016) Büyükaşık, Engin; Tribak, RachidWe introduce and study the notion of Rad-sinjective modules (i.e. modules which are Rad-supplements in their injective hulls). We compare this notion with another generalization of injective modules. We show that the class of Rad-s-injective modules is closed under finite direct sums. We characterize Rads-injective modules over several type of rings, including semilocal rings, left hereditary rings and left Harada rings. © Journal “Algebra and Discrete Mathematics”.Article Citation - WoS: 20Citation - Scopus: 25Vertex-Decomposable Graphs, Codismantlability, Cohen-Macaulayness, and Castelnuoco-Mumford Regularity(Electronic Journal of Combinatorics, 2014) Biyikoglu, Turker; Civan, YusufWe call a vertex x of a graph G = (V, E) a codominated vertex if N-G[y] subset of N-G[x] for some vertex y is an element of V \{x}, and a graph G is called codismantlable if either it is an edgeless graph or it contains a codominated vertex x such that G - x is codismantlable. We show that (C-4, C-5)-free vertex-decomposable graphs are codismantlable, and prove that if G is a (C-4, C-5, C-7)-free well-covered graph, then vertex-decomposability, codismantlability and Cohen-Macaulayness for G are all equivalent. These results complement and unify many of the earlier results on bipartite, chordal and very well-covered graphs. We also study the Castelnuovo-Mumford regularity reg(G) of such graphs, and show that reg(G) = im(G) whenever G is a (C-4, C-5)-free vertex-decomposable graph, where im(G) is the induced matching number of G. Furthermore, we prove that H must be a codismantlable graph if im(H) = reg(H) = m(H), where m(H) is the matching number of H. We further describe an operation on digraphs that creates a vertex-decomposable and codismantlable graph from any acyclic digraph. By way of application, we provide an infinite family H-n (n >= 4) of sequentially Cohen-Macaulay graphs whose vertex cover numbers are half of their orders, while containing no vertex of degree-one such that they are vertex-decomposable, and reg(H-n) = im(H-n) if n >= 6. This answers a recent question of Mahmoudi, et al [12].Article Citation - WoS: 6Citation - Scopus: 5Envelope Soliton Resonances and Broer-Kaup Non-Madelung Fluids(Pleiades Publishing, 2012) Pashaev, OktayWe derive an extended nonlinear dispersion for envelope soliton equations and also find generalized equations of the nonlinear Schrödinger (NLS) type associated with this dispersion. We show that space dilatations imply hyperbolic rotation of the pair of dual equations, the NLS and resonant NLS (RNLS) equations. For the RNLS equation, in addition to the Madelung fluid representation, we find an alternative non-Madelung fluid system in the form of a Broer-Kaup system. Using the bilinear form for the RNLS equation, we construct the soliton resonances for the Broer-Kaup system and find the corresponding integrals of motion and existence conditions for the soliton resonance and also a geometric interpretation in terms of a pseudo-Riemannian surface of constant curvature. This approach can be extended to construct a resonance version and the corresponding Broer-Kaup-type representation for any envelope soliton equation. As an example, we derive a new modified Broer-Kaup system from the modified NLS equation.Article Completely Cotorsion Modules(Publishing House of the Bulgarian Academy of Sciences, 2012) Pusat, DilekWe show that any finitely generated projective cotorsion left module over a ring of left pure global dimension at most 1 is a direct sum of indecomposable direct summands. We deduce that such a ring is left cotorsion and semiperfect if and only if its left cotorsion envelope is finitely presented. Some extensions of this result are also discussed.Conference Object Citation - WoS: 9Citation - Scopus: 24Modeling Leakage of Ephemeral Secrets in Tripartite/Group Key Exchange(Springer Verlag, 2010) Manulis, Mark; Suzuki, Koutarou; Ustaoğlu, BerkantRecent advances in the design and analysis of secure two-party key exchange (2KE) such as the leakage of ephemeral secrets used during the attacked sessions remained unnoticed by the current models for group key exchange (GKE). Focusing on a special case of GKE - the tripartite key exchange (3KE) - that allows for efficient one-round protocols, we demonstrate how to incorporate these advances to the multi-party setting. From this perspective our work closes the most pronounced gap between provably secure 2KE and GKE protocols. The proposed 3KE protocol is an implicitly authenticated protocol with one communication round which remains secure even in the event of ephemeral secret leakage. It also significantly improves upon currently known 3KE protocols, many of which are insecure. An optional key confirmation round can be added to our proposal to achieve the explicitly authenticated protocol variant. © 2010 Springer-Verlag.Article Citation - WoS: 5Citation - Scopus: 8Weakly Distributive Modules. Applications To Supplement Submodules(Indian Academy of Sciences, 2010) Büyükaşık, Engin; Demirci, Yılmaz MehmetIn this paper, we define and study weakly distributive modules as a proper generalization of distributive modules. We prove that, weakly distributive supplemented modules are amply supplemented. In a weakly distributive supplemented module every submodule has a unique coclosure. This generalizes a result of Ganesan and Vanaja. We prove that π-projective duo modules, in particular commutative rings, are weakly distributive. Using this result we obtain that in a commutative ring supplements are unique. This generalizes a result of Camillo and Lima. We also prove that any weakly distributive ⊕-supplemented module is quasi-discrete. © Indian Academy of Sciences.