Tabla de Contenidos: “…4.5.1 The Case of Standard Vertex Conditions -- 4.5.2 A Counterexample -- 4.5.3 Invariance of the Quadratic Form -- 4.5.4 Positivity of the Ground State for Generalised Delta-Couplings -- 4.6 First Spectral Estimates -- 5 The Characteristic Equation -- 5.1 Characteristic Equation I: Edge Transfer Matrices -- 5.1.1 Transfer Matrix for a Single Interval -- One-Dimensional Schrödinger Equation -- Magnetic Schrödinger Equation -- 5.1.2 The Characteristic Equation -- 5.1.3 The Characteristic Equation, Second Look -- 5.2 Characteristic Equation II: Scattering Approach -- 5.2.1 On the Scattering Matrix Associated with a Compact Interval -- 5.2.2 Positive Spectrum and Scattering Matrices for Finite Compact Graphs -- 5.3 Characteristic Equation III: M-Function Approach -- 5.3.1 M-Function for a Single Interval -- 5.3.2 The Edge M-Function -- 5.3.3 Characteristic Equation via the M-Function: General Vertex Conditions -- 5.3.4 Reduction of the M-Function for Standard Vertex Conditions -- 6 Standard Laplacians and Secular Polynomials -- 6.1 Secular Polynomials -- 6.2 Secular Polynomials for Small Graphs -- 6.3 Zero Sets for Small Graphs -- Appendix 1: Singular Sets on Secular Manifolds, Proof of Lemma 6.3 -- 7 Reducibility of Secular Polynomials -- 7.1 Contraction of Graphs -- 7.2 Extensions of Graphs -- 7.3 Secular Polynomials for the Watermelon Graphand Its Closest Relatives -- 7.4 Secular Polynomials for Flower Graphs and Their Extensions -- 7.5 Reducibility of Secular Polynomials for General Graphs -- 8 The Trace Formula -- 8.1 The Characteristic Equation: Multiplicityof Positive Eigenvalues -- 8.2 Algebraic and Spectral Multiplicities of the Eigenvalue Zero -- 8.3 The Trace Formula for Standard Laplacians -- 8.4 Trace Formula for Laplacians with Scaling-InvariantVertex Conditions -- 9 Trace Formula and Inverse Problems…”

Tabla de Contenidos: “…Simón Vallejo -- Rubén Parrilla Giráldez -- Sara Macías Tejada -- Carlos Odriozola Lloret -- Juan Mayoral Valsera -- Introducción -- Objetivos del proyecto de investigación -- Metodología -- Resultados -- Conclusiones -- Bibliografía -- Las sociedades neandertales. …”

“…Lloret permaneció diez años desaparecido, sus hijos creyeron que había muerto y solo su mujer y su madre conocían su paradero. …”

“…Sofia says she does not want to leave the house as it might cause her husband to be suspicious and agrees to conduct the next few minutes of the session from her closet. The two collaboratively agree that they will discontinue the session once Sofia no longer feels comfortable inside the closet, and that they will schedule their next assessment on a day/time when her husband is not home…”

“…Manon, la hija de Jean de Florette, ha crecido. Siendo todavía una niña, fue testigo presencial de la conspiración llevada a cabo por Papet y Ugolin, cuyas fatídicas consecuencias provocaron la muerte de su padre. …”

“…During questioning, Sam reveals that his father owns a gun and that he knows that the gun is locked in his father's closet. He reports he has never desired to harm himself with a gun but has had vague thoughts about harming others…”