On a Theorem by A.S. Cherny for Semilinear Stochastic Partial Differential Equations

We consider analytically weak solutions to semilinear stochastic partial differential equations with non-anticipating coefficients driven by a cylindrical Brownian motion. The solutions are allowed to take values in Banach spaces. We show that weak uniqueness is equivalent to weak joint uniqueness, and thereby generalize a theorem by A.S. Cherny to an infinite dimensional setting. Our proof for the technical key step is different from Cherny’s and uses cylindrical martingale problems. As an application, we deduce a dual version of the Yamada–Watanabe theorem, i.e. we show that strong existence and weak uniqueness imply weak existence and strong uniqueness.

Tachyon condensation in magnetic compactifications

Intersecting D-brane models and their T-dual magnetic compactifications provide an attractive framework for particle physics, allowing for chiral fermions and supersymmetry breaking. Generically, magnetic compactifications have tachyons that are usually removed by Wilson lines. However, quantum corrections prevent local minima for Wilson lines. We therefore study tachyon condensation in the simplest case, the magnetic compactification of type I string theory on a torus to eight dimensions. We find that tachyon condensation restores supersymmetry, which is broken by the magnetic flux, and we compute the Kaluza-Klein mass spectrum. The gauge group SO(32) is broken to USp(16). We give arguments that the vacuum reached by tachyon condensation corresponds to the unique 8d superstring theory already known in the literature, with discrete Bab background or, in the T-dual version, the type IIB orientifold with three O7−-planes, one O7+-plane and eight D7-branes coincident with the O7+-plane. The ground state after tachyon condensation is supersymmetric and has no chiral fermions.

F-theory from fundamental five-branes

We describe the worldvolume for the bosonic sector of the lower-dimensional F-theory that embeds 4D, N=1 M-theory and the 3D Type II superstring. The worldvolume (5-brane) theory is that of a single 6D gauge 2-form XMN(σP) whose field strength is selfdual. Thus unlike string theory, the spacetime indices are tied to the worldsheet ones: in the Hamiltonian formalism, the spacetime coordinates are a 10 of the GL(5) of the 5 σ’s (neglecting τ). The current algebra gives a rederivation of the F-bracket. The background-independent subalgebra of the Virasoro algebra gives the usual section condition, while a new type of section condition follows from Gauß’s law, tying the worldvolume to spacetime: solving just the old condition yields M-theory, while solving only the new one gives the manifestly T-dual version of the string, and the combination produces the usual string. We also find a covariant form of the condition that dimensionally reduces the string coordinates.

Relación teoría-práctica y actividad común como focos para resolver problemas de educación: la significación del conocimiento de la educación no ampara el modelo dual (Versión en castellano)

Este trabajo insiste en la importancia del estudio de la relación teoría-práctica para obtener el conocimiento especializado y específico de la educación: el conocimiento pedagógico. Se establece una relación entre significación y conocimiento de la educación por medio de la capacidad de resolución de problemas para la intervención, y se debate su estructura y utilidad para la intervención a través de la relación teoría-práctica en cada corriente del conocimiento de la educación (marginal, subalternada y autónoma). La significación como principio de metodología es un problema derivado de cómo se entiende la relación teoría-práctica en cada corriente del conocimiento de la educación para justificar el conocimiento válido. Al ejecutar la actividad común externa, mejoramos y entrenamos las actividades-capacidades internas: sin la actividad es imposible educar y gracias a ella se hace posible que el educando sea agente actor y cada vez mejor agente autor de su propios proyectos y actos. Veremos cómo la función pedagógica genera intervención desde las actividades comunes. Y podremos concluir que la actividad común y la relación teoría-práctica son focos para resolver problemas de educación desde la intervención pedagógica, que siempre implica conocimiento y acción.

¿Quién Es Tají­n? Reflexiones Sobre La Deidad Y Su Relación Con Otros Dioses

ResumenSe presenta en este artí­culo un análisis de El Tají­n, dios principal de los totonacos contemporáneos, en su relación con otras deidades del panteón mesoamericano. Se revisa su relación con Tláloc, dios del agua y la lluvia, y con Quetzalcóatl, dios del viento, así­ como la versión dual de estos dos dioses; se revisa así­ mismo su relación con el dios Huracán, de larga tradición circuncaribe, y con su versión mesoamericana en Tezcatlipoca: ”El espejo humeante”, análoga a El Tají­n: ”El poderoso humo”. Se emplean en la discusión datos arqueológicos, iconográficos, lingüí­sticos y etnográficos. Este es solo un breve ensayo de un problema poco abordado y que aún requiere mayor trabajo de investigación e interpretación.Palabras clave: El Tají­n, deidades mesoamericanas, Tláloc, Quetzalcóatl, Tezcatlipoca.AbstractIn this work, I present an analysis of El Tají­n -The main deity of the contemporary Totonac people - and it´s relation with other deities of Mesoamerican pantheon. I revise it´s relation to two gods: Tláloc, the god of the water and rain; and Quetzalcóatl, good of the wind. As well as the dual version of these two deities. It´s relation with the god Huracán, of long circum-caribean tradition, is also revised, and with it´s Mesoamerican version: Tezcatlipoca, ”El espejo humeante” (”The smoky mirror”), analogous to Tají­n, ”El poderoso humo” (The powerful smoke). In this discussion, I make use of archeological, iconographic, linguistic and ethnographic dat. This is just a brief essay on a little-addressed problem, which requires more research and interpretation work.Keywords: El Tají­n, Mesoamerican deities, Tláloc, Quetzalcóatl, Tezcatlipoca. [1] Licenciado en Antropologí­a Social por la Universidad Autónoma Metropolitana Iztapalapa. Maestro en Ciencias en Agroecosistemas Tropicales por el Colegio de Posgraduados. Doctor en Estudios Mesoamericanos por la Universidad Nacional Autónoma de México. Investigador del Centro Veracruz del Instituto Nacional de Antropologí­a e Historia.

On a Dual Direct Cosine Simplex Type Algorithm and Its Computational Behavior

The goal of this paper is to propose a dual version of the direct cosine simplex algorithm (DDCA) for general linear problems. The proposed method has not artificial variables, so it is different from both the two-phase method and big-M method. Our technique solves the dual Klee–Minty problem via two iterations and solves the dual Clausen problem via four iterations. The power of the proposed algorithm is evident from the extensive experimental results on benchmark problems adapted from NETLIB. Preliminary results indicate that this dual direct cosine simplex algorithm (DDCA) reduces the number of iterations of the two-phase method.

The Dual Baer Criterion for non-perfect rings

Baer’s Criterion for Injectivity is a useful tool of the theory of modules. Its dual version (DBC) is known to hold for all right perfect rings, but its validity for the non-right perfect ones is a complex problem (first formulated by C. Faith [Algebra. II. Ring Theory, Springer, Berlin, 1976]). Recently, it has turned out that there are two classes of non-right perfect rings: (1) those for which DBC fails in ZFC, and (2) those for which DBC is independent of ZFC. First examples of rings in the latter class were constructed in [J. Trlifaj, Faith’s problem on R-projectivity is undecidable, Proc. Amer. Math. Soc. 147 2019, 2, 497–504]; here, we show that this class contains all small semiartinian von Neumann regular rings with primitive factors artinian.

Rota–Baxter cosystems and coquasitriangular mixed bialgebras

In this paper, we present a dual version of T. Brzeziński’s results about Rota–Baxter systems which appeared in [Rota–Baxter systems, dendriform algebras and covariant bialgebras, J. Algebra 460 (2016) 1–25]. Then as a generalization to bialgebras, we introduce the notion of Rota–Baxter bisystem and construct various examples of Rota–Baxter bialgebras and bisystems in dimensions 2, 3 and 4. On the other hand, we introduce a new type of bialgebras (named mixed bialgebras) which consist of an associative algebra and a coassociative coalgebra satisfying the compatible condition determined by two coderivations. We investigate coquasitriangular mixed bialgebras and the particular case of coquasitriangular infinitesimal bialgebras, where we give the double construction. Also, we show in some cases that Rota–Baxter cosystems can be obtained from a coquasitriangular mixed bialgebras.

Existence of Small-Energy Solutions to Nonlocal Schrödinger-Type Equations for Integrodifferential Operators in ℝN

We are concerned with the following elliptic equations: ( − Δ ) p , K s u + V ( x ) | u | p − 2 u = λ f ( x , u ) in R N , where ( − Δ ) p , K s is the nonlocal integrodifferential equation with 0 < s < 1 < p < + ∞ , s p < N the potential function V : R N → ( 0 , ∞ ) is continuous, and f : R N × R → R satisfies a Carathéodory condition. The present paper is devoted to the study of the L ∞ -bound of solutions to the above problem by employing De Giorgi’s iteration method and the localization method. Using this, we provide a sequence of infinitely many small-energy solutions whose L ∞ -norms converge to zero. The main tools were the modified functional method and the dual version of the fountain theorem, which is a generalization of the symmetric mountain-pass theorem.

On a Dual Direct Cosine Simplex Type Algorithm and Its Computational Behavior

The goal of this paper is to propose a dual version of the direct cosine simplex algorithm (DDCA) for general linear problems. Unlike the two-phase and the big-M methods, our technique does not involve artificial variables. Our technique solves the dual Klee-Minty problem in two iterations and solves the dual Clausen&rsquo;s problem in four iterations. The utility of the proposed method is evident from the extensive computational results on test problems adapted from NETLIB. Preliminary results indicate that this dual direct cosine simplex algorithm (DDCA) reduces the number of iterations of two-phase method.