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Abstract: For Cylindrical Hex on a board with circumference 3, we give a winning strategy for the end-to-end player. This is the first known winning strategy for odd circumference at least 3, answering a question of David Gale. [Copyright &y& Elsevier]

Abstract: We show that for finite , every first-order axiomatisation of the varieties of representable n-dimensional cylindric algebras, diagonal-free cylindric algebras, polyadic algebras, and polyadic equality algebras contains an infinite number of non-canonical formulas. We also show that the class of structures for each of these varieties is non-elementary. The proofs employ algebras derived from random graphs. [Copyright &y& Elsevier]

Abstract: The lateral boundary differentiability with respect to is shown for solutions of parabolic differential equations in nondivergence form on cylindrical convex domains. [Copyright &y& Elsevier]

Abstract: During the last decade the spectral vanishing viscosity (SVV) method has been adopted successfully for large-eddy-type simulations (LES) with high-order discretizations in both Cartesian and cylindrical coordinate systems. For the latter case, however, previous studies were confined to annular domains. In the present work, we examine the applicability of SVV in cylindrical coordinates to flows in which the axis region is included, within the setting of an exponentially convergent spectral element–Fourier discretization. In addition to the ‘standard’ SVV viscosity kernel, two modified kernels with enhanced stabilization in the axis region are considered. Three fluid flow examples are considered, including turbulent pipe flow. The results, on the one hand, show a surprisingly small influence of the SVV kernel, while on the other, they reveal the importance of spatial resolution in the axis region. [Copyright &y& Elsevier]

Using techniques developed by Comer on sheaf-theoretic duality for cylindric algebras, we refine a result of Judit Madarász by showing that epimorphisms are not surjective even in the class of simple infinite dimensional cylindric algebras. [ABSTRACT FROM PUBLISHER]

Abstract: A necessary and sufficient condition of càdlàg modification of Ornstein–Uhlenbeck process with cylindrical stable noise in a Hilbert space is given in this Note. Applying this result, some questions in Time irregularity of generalized Ornstein–Uhlenbeck processes [C. R. Acad. Sci. Paris, Ser. I 348 (2010) 273–276] and Structural properties of semilinear SPDEs driven by cylindrical stable process [Probab. Theory Related Fields 149 (2011) 97–137] are answered. [Copyright &y& Elsevier]

We show that the representability of cylindric algebras by relativized set algebras depends on the scope of the operation transposition which can be defined on the algebra. The existence of 'partial transposition' assures this kind of representability of the cylindric algebra (while the existence of transposition assures polyadic representation). Further we characterize those cylindric algebras in which the operator transposition can be introduced (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Neat embedding theorems yield an abstract algebraic characterization for the representability of a given class of algebras by set algebras. Resek and Thompson's theorem called attention to a new kind of representation in the theory of cylindric algebras, to the representation by cylindric relativised set algebras. In this paper, we present the algebraic characterization of this kind of representation; we formulate neat embedding theorems for this representation. [ABSTRACT FROM AUTHOR]

This is a survey article on the concept of neat reducts. An old venerable idea in algebraic logic, in this paper we show why it is regaining momentum. [ABSTRACT FROM AUTHOR]

Abstract: Large time behavior of solutions to the linearized compressible Navier–Stokes equation around the motionless state in a cylindrical domain is investigated. The decay estimates of the associated semigroup are established for all . It is also shown that the time-asymptotic leading part of the semigroup is given by a one-dimensional heat semigroup. [Copyright &y& Elsevier]

Nonlinear corrections to some classical solutions of the linear diffusion equation in cylindrical coordinates are studied within quadratic approximation. When cylindrical coordinates are used, we try to find a nonlinear correction using quadratic polynomials of Bessel functions whose coefficients are Laurent polynomials of radius. This usual perturbation technique inevitably leads to a series of overdetermined systems of linear algebraic equations for the unknown coefficients (in contrast with the Cartesian coordinates). Using a computer algebra system, we show that all these overdetermined systems become compatible if we formally add one function on radius W( r). Solutions can be constructed as linear combinations of these quadratic polynomials of the Bessel functions and the functions W( r) and W′( r). This gives a series of solutions to the nonlinear diffusion equation; these are found with the same accuracy as the equation is derived. [ABSTRACT FROM AUTHOR]

Letn > 2. A weakly representable relation algebra that is not strongly representable is constructed. It is proved that the set of all n by n basic matrices forms a cylindric basis that is also a weakly but not a strongly representable atom structure. This gives an example of a binary generated atomic representable cylindric algebra with no complete representation. An application to first order logic is given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Some properties of finite diagonal-free two-dimensional cylindric algebras, or Df2-algebras, are studied. In particular, a connection between Df2-algebras and pairs formed by a monadic Boolean algebra and a subalgebra of this algebra is exhibited. Finally, these results are applied to obtain a formula to determine the number of monadic subalgebras of a given monadic Boolean algebra. [ABSTRACT FROM PUBLISHER]

Catastrophe theory was used to investigate the fracture behavior of thin-wall cylindrical tubes subjected to internal explosive pressure. Based on the energy theory and catastrophe theory, a cusp catastrophe model for the fracture was established, and a critical condition associated with the model is given. [ABSTRACT FROM AUTHOR]

We show that certain properties of dimension complemented cylindric algebras, concerning neat embeddings, do not generalize much further. Let α ≥ ω. There are non-isomorphic representable cylindric algebras of dimension α each of which is a generating subreduct of the same β dimensional cylindric algebra. We also show that there exists a representable cylindric algebra 𝔄 of dimension α, such that 𝔄 is a generating subreduct of 𝔅 and 𝔅′, both in CAα +ω, however 𝔅 and 𝔅′ are not isomorphic. This settle questions raised by Henkin, Monk and Tarski (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Within the framework of the well-known curvature models, a fluid lipid bilayer membrane is regarded as a surface embedded in the three-dimensional Euclidean space whose equilibrium shapes are described in terms of its mean and Gaussian curvatures by the so-called membrane shape equation. In the present paper, all solutions to this equation determining cylindrical membrane shapes are found and presented, together with the expressions for the corresponding position vectors, in explicit analytic form. The necessary and sufficient conditions for such a surface to be closed are derived and several sufficient conditions for its directrix to be simple or self-intersecting are given. [ABSTRACT FROM AUTHOR]

A discussion on the article "Dissipation-induced Heteroclinic Orbits in Tippe Tops" by N. Bou-Rabee, J. Marsden and L. Romero, is presented. A tippe top is described as a sphere with small cylindrical stem, and a tippe top inversion refers to a classical problem in applied mathematics. According to the author, the article demonstrated that the stabilities of the noninverted and inverted states of a tippe top can be analyzed through modified Maxwell-Bloch equations. It also offered a look at the world of dynamical systems via a classical problem.

In [2] we investigated the lattice ?( Df 2) of all subvarieties of the variety Df 2 of two-dimensional diagonal free cylindric algebras. In the present paper we investigate the lattice ?( CA 2) of all subvarieties of the variety CA 2 of two-dimensional cylindric algebras. We prove that the cardinality of ?( CA 2) is that of the continuum, give a criterion for a subvariety of CA 2 to be locally finite, and describe the only pre locally nite subvariety of CA2. We also characterize nitely generated subvarieties of CA2 by describing all fteen pre nitely generated subvarieties of CA 2. Finally, we give a rough picture of ?( CA 2), and investigate algebraic properties preserved and reected by the reduct functors $$ \mathbb{F}: \mathbf{CA}_2 and \Phi : \Lambda (\mathbf{CA}_2) \rightarrow (\Lambda (\mathbf{Df}_2) $$ . [ABSTRACT FROM AUTHOR]