http://publications.mfo.de/handle/mfo/1343 Tue, 07 Apr 2026 02:07:20 GMT 2026-04-07T02:07:20Z http://publications.mfo.de/handle/mfo/1250 Second Main Theorems and Unicity of Meromorphic Mappings with Moving Hypersurfaces Si, Duc Quang In this article, we establish some new second main theorems for meromorphic mappings of $\mathbf{C}^m$ into $\mathbf{P}^n(\mathbf{C})$ and moving hypersurfaces with truncated counting functions. As an application, we prove a uniqueness theorem for these mappings sharing few moving hypersurfaces without counting multiplicity. This result is an improvement of the results of Dulock - Min Ru [2] and Dethloff - Tan [4]. Moreover the meromorphic mappings maybe algebraically degenerate. OWLF 2011 Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/1250 2011-01-01T00:00:00Z Si, Duc Quang In this article, we establish some new second main theorems for meromorphic mappings of $\mathbf{C}^m$ into $\mathbf{P}^n(\mathbf{C})$ and moving hypersurfaces with truncated counting functions. As an application, we prove a uniqueness theorem for these mappings sharing few moving hypersurfaces without counting multiplicity. This result is an improvement of the results of Dulock - Min Ru [2] and Dethloff - Tan [4]. Moreover the meromorphic mappings maybe algebraically degenerate. http://publications.mfo.de/handle/mfo/1249 The Cleavage Operad and String Topology of Higher Dimension Bargheer, Tarje OWLF 2011 Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/1249 2011-01-01T00:00:00Z Bargheer, Tarje http://publications.mfo.de/handle/mfo/1248 The T-Graph of a Multigraded Hilbert Scheme Hering, Milena; Maclagan, Diane The $T$-graph of a multigraded Hilbert scheme records the zero and one-dimensional orbits of the $T=(K^*)^n$ action on the Hilbert scheme induced from the $T$-action on $\mathbb{A}^n$. It has vertices the $T$-fixed points, and edges the onedimensional $T$-orbits. We give a combinatorial necessary condition for the existence of an edge between two vertices in this graph. For the Hilbert scheme of points in the plane, we give an explicit combinatorial description of the equations defining the scheme parameterizing all one-dimensional torus orbits whose closures contain two given monomial ideals. For this Hilbert scheme we show that the $T$-graph depends on the ground field, resolving a question of Altmann and Sturmfels. OWLF 2010 Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/1248 2011-01-01T00:00:00Z Hering, Milena Maclagan, Diane The $T$-graph of a multigraded Hilbert scheme records the zero and one-dimensional orbits of the $T=(K^*)^n$ action on the Hilbert scheme induced from the $T$-action on $\mathbb{A}^n$. It has vertices the $T$-fixed points, and edges the onedimensional $T$-orbits. We give a combinatorial necessary condition for the existence of an edge between two vertices in this graph. For the Hilbert scheme of points in the plane, we give an explicit combinatorial description of the equations defining the scheme parameterizing all one-dimensional torus orbits whose closures contain two given monomial ideals. For this Hilbert scheme we show that the $T$-graph depends on the ground field, resolving a question of Altmann and Sturmfels. http://publications.mfo.de/handle/mfo/1247 Analytic Varieties with Finite Volume Amoebas are Algebraic Madani, Farid; Nisse, Mounir In this paper, we study the amoeba volume of a given $k$-dimensional generic analytic variety $V$ of the complex algebraic torus $(C^*)^n$. When $n>=2k$, we show that $V$ is algebraic if and only if the volume of its amoeba is finite. Moreover, in this case, we establish a comparison theorem for the volume of the amoeba and the coamoeba. Examples and applications to the $k$-linear spaces will be given. OWLF 2011 Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/1247 2011-01-01T00:00:00Z Madani, Farid Nisse, Mounir In this paper, we study the amoeba volume of a given $k$-dimensional generic analytic variety $V$ of the complex algebraic torus $(C^*)^n$. When $n>=2k$, we show that $V$ is algebraic if and only if the volume of its amoeba is finite. Moreover, in this case, we establish a comparison theorem for the volume of the amoeba and the coamoeba. Examples and applications to the $k$-linear spaces will be given. http://publications.mfo.de/handle/mfo/1246 Products of pairs of Dehn twists and maximal real Lefschetz fibrations Degtyarev, Alex; Salepci, Nermin We address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic Lefschetz bration is algebraic. OWLF 2011 Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/1246 2011-01-01T00:00:00Z Degtyarev, Alex Salepci, Nermin We address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic Lefschetz bration is algebraic. http://publications.mfo.de/handle/mfo/1245 Positive recurrence of piecewise Orntein-Uhlenbeck processes and common quadratic Lyapunov functions Dieker, A. B.; Gao, Xuefeng We study the positive recurrence of piecewise Ornstein-Uhlenbeck (OU) diffusion processes, which arise from many-server queueing systems with phase-type service requirements. These diffusion processes exhibit different behavior in two regions of the state space, corresponding to `overload' and `underload'. The two regimes cause standard techniques for proving positive recurrence to fail. Using and extending the framework of common quadratic Lyapunov functions from the theory of control, we construct Lyapunov functions for the diffusion approximations corresponding to systems with and without abandonment. With these Lyapunov functions, we prove that piecewise OU processes have a unique stationary distribution. OWLF 2011 Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/1245 2011-01-01T00:00:00Z Dieker, A. B. Gao, Xuefeng We study the positive recurrence of piecewise Ornstein-Uhlenbeck (OU) diffusion processes, which arise from many-server queueing systems with phase-type service requirements. These diffusion processes exhibit different behavior in two regions of the state space, corresponding to `overload' and `underload'. The two regimes cause standard techniques for proving positive recurrence to fail. Using and extending the framework of common quadratic Lyapunov functions from the theory of control, we construct Lyapunov functions for the diffusion approximations corresponding to systems with and without abandonment. With these Lyapunov functions, we prove that piecewise OU processes have a unique stationary distribution. http://publications.mfo.de/handle/mfo/1244 Upper bounds for the number of solutions to quartic thue equations Akhtari, Shabnam We will give upper bounds for the number of integral solutions to quartic Thue equations. Our main tool here is a logarithmic curve $\phi(x,y)$ that allows us to use the theory of linear forms in logarithms. This manuscript improves the results of author's earlier work with Okazaki [2] by giving special treatments to forms with respect to their signature. OWLF 2011 Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/1244 2011-01-01T00:00:00Z Akhtari, Shabnam We will give upper bounds for the number of integral solutions to quartic Thue equations. Our main tool here is a logarithmic curve $\phi(x,y)$ that allows us to use the theory of linear forms in logarithms. This manuscript improves the results of author's earlier work with Okazaki [2] by giving special treatments to forms with respect to their signature. http://publications.mfo.de/handle/mfo/1243 New representations of matroids and generalizations Izhakian, Zur; Rhodes, John L. We extend the notion of matroid representations by matrices over fields by considering new representations of matroids by matrices over finite semirings, more precisely over the boolean and the superboolean semirings. This idea of representations is naturally generalized to include hereditary collections (also known as abstract simplicial complexes). We show that a matroid that can be directly decomposed as matroids, each of which is representable over a field, has a boolean representation, and more generally that any arbitrary hereditary collection is superboolean-representable. OWLF 2011 Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/1243 2011-01-01T00:00:00Z Izhakian, Zur Rhodes, John L. We extend the notion of matroid representations by matrices over fields by considering new representations of matroids by matrices over finite semirings, more precisely over the boolean and the superboolean semirings. This idea of representations is naturally generalized to include hereditary collections (also known as abstract simplicial complexes). We show that a matroid that can be directly decomposed as matroids, each of which is representable over a field, has a boolean representation, and more generally that any arbitrary hereditary collection is superboolean-representable. http://publications.mfo.de/handle/mfo/1242 Monoid valuations and value ordered supervaluations Izhakian, Zur; Knebusch, Manfred; Rowen, Louis We complement two papers on supertropical valuation theory ([IKR1], [IKR2]) by providing natural examples of m-valuations (= monoid valuations), after that of supervaluations and transmissions between them. The supervaluations discussed have values in totally ordered supertropical semirings, and the transmissions discussed respect the orderings. Basics of a theory of such semirings and transmissions are developed as far as needed. OWLF 2011 Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/1242 2011-01-01T00:00:00Z Izhakian, Zur Knebusch, Manfred Rowen, Louis We complement two papers on supertropical valuation theory ([IKR1], [IKR2]) by providing natural examples of m-valuations (= monoid valuations), after that of supervaluations and transmissions between them. The supervaluations discussed have values in totally ordered supertropical semirings, and the transmissions discussed respect the orderings. Basics of a theory of such semirings and transmissions are developed as far as needed. http://publications.mfo.de/handle/mfo/1241 Classification of totally real elliptic Lefschetz fibrations via necklace diagrams Salepci, Nermin We show that totally real elliptic Lefschetz brations that admit a real section are classified by their "real loci" which is nothing but an $S^1$-valued Morse function on the real part of the total space. We assign to each such real locus a certain combinatorial object that we call a $necklace diagram$. On the one hand, each necklace diagram corresponds to an isomorphism class of a totally real elliptic Lefschetz fibration that admits a real section, and on the other hand, it refers to a decomposition of the identity into a product of certain matrices in $PSL(2,Z)$. Using an algorithm to find such decompositions, we obtain an explicit list of necklace diagrams associated with certain classes of totally real elliptic Lefschetz fibrations. Moreover, we introduce refinements of necklace diagrams and show that refined necklace diagrams determine uniquely the isomorphism classes of the totally real elliptic Lefschetz fibrations which may not have a real section. By means of necklace diagrams we observe some interesting phenomena underlying special feature of real fibrations. OWLF 2011 Sat, 01 Jan 2011 00:00:00 GMT http://publications.mfo.de/handle/mfo/1241 2011-01-01T00:00:00Z Salepci, Nermin We show that totally real elliptic Lefschetz brations that admit a real section are classified by their "real loci" which is nothing but an $S^1$-valued Morse function on the real part of the total space. We assign to each such real locus a certain combinatorial object that we call a $necklace diagram$. On the one hand, each necklace diagram corresponds to an isomorphism class of a totally real elliptic Lefschetz fibration that admits a real section, and on the other hand, it refers to a decomposition of the identity into a product of certain matrices in $PSL(2,Z)$. Using an algorithm to find such decompositions, we obtain an explicit list of necklace diagrams associated with certain classes of totally real elliptic Lefschetz fibrations. Moreover, we introduce refinements of necklace diagrams and show that refined necklace diagrams determine uniquely the isomorphism classes of the totally real elliptic Lefschetz fibrations which may not have a real section. By means of necklace diagrams we observe some interesting phenomena underlying special feature of real fibrations.