On the asymptotic behavior of a linear viscoelastic fluid

We study the asymptotic behavior of an incompressible viscoelastic fluid and prove that the temporal decay of the energy is similar to one of the memory kernel. The innovative aspect of this research lies in considering the evolutive problem with non‐zero external sources and/or initial histories. Copyright © 2012 John Wiley & Sons, Ltd.     

On the asymptotic behavior of the quasi-static problem for a linear viscoelastic fluid

In this paper we study the quasi-static problem for a viscoelastic fluid by means of the concept of minimal state. This implies the use of a different free energy defined in a wider space of data. The existence and uniqueness is proved in this new space and the asymptotic decay for the problem with non vanishing supplies is obtained for a large class of memory kernels, including those presenting an exponential or polynomial decay.     

On the existence of a cyclic code with rate R

In this paper a short proof is given of the existence of a cyclic, q-ary code with rate R, for any rational number R, 0 ? R ? 1.     

On a Kaehler hypersurface with the cyclic Ricci semi-symmetric tensor

The purpose of the present paper is to prove that a Kaehler hypersurface with the cyclic Ricci semi-symmetric tensor is locally symmetric.     

Two-component device for cyclic tests under a complex load

The design of a device, measurement scheme, and method of testing plastic specimens are described.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 141–147, January–February, 1972.     

On the longtime behavior of a 2D hydrodynamic model for chemically reacting binary fluid mixtures

Two dimensional diffuse interface model for a chemically reacting incompressible binary fluid in a bounded domain is considered. The corresponding evolution system consists of the Navier–Stokes equations for the (averaged) fluid velocity that are nonlinearly coupled with a convective Cahn–Hilliard–Oono type equation for the difference ψ of two fluid concentrations. The effects of a (reversible) chemical reaction is represented in the latter equation by an additional term of the form ε(ψ ? c₀), ε > 0. Here, c₀ is the stationary spatial average of ψ, provided that, for example, no‐slip and no‐flux boundary conditions are considered. The mass is not necessarily conserved unless the spatial average of the initial datum for ψ coincides with c₀. When ε = 0 (i.e., no chemical reaction), the model reduces to the well‐known Cahn–Hilliard–Navier–Stokes system, which has been investigated by several authors. Here, we want to show that the global dynamic behavior of the system is robust with respect to ε. More precisely, we construct a family of exponential attractors, which is continuous with respect to ε. Copyright © 2013 John Wiley & Sons, Ltd.     

On the three diagonals of a cyclic quadrilateral

If the side lengths of a non-degenerate cyclic quadrilateral are given, but not necessarily in cyclic order, then three diagonal lengths arise in the resulting three cyclic quadrilaterals, just as three possible pairs of supplementary angles arise as opposite vertices, and where the diagonals intersect, in each of the three configurations. We obtain a formula for the sum of the lengths of the three diagonals minus the sum of the four sides which enables us to deduce the geometric inequality that the sum of the side lengths is less than the sum of the lengths of the three diagonals. We obtain another formula when these lengths are replaced by their squares, and this yields a similar inequality. A proof of both formulas is given which uses algebraic geometry, but which proceeds by analysis of degenerate situations. Two alternative proofs of the linear version of the inequality (which implies the quadratic version) are supplied which use trigonometry and Lagrange multipliers respectively. An unusual feature of these results is that they refer not to one configuration, but rather concern three possible configurations.     

On a generalization of cyclic semifields

A new construction is given of cyclic semifields of orders q ²ⁿ , n odd, with kernel (left nucleus) and right and middle nuclei isomorphic to , and the isotopism classes are determined. Furthermore, this construction is generalized to produce potentially new semifields of the same general type that are not isotopic to cyclic semifields. In particular, a new semifield plane of order 4⁵ and new semifield planes of order 16⁵ are constructed by this method.     

On the number of cyclic subgroups of a group

Abstract

There has been some interest in understanding the relationship between the number of cyclic subgroups of a group and its order. This relationship is controlled in many cases by the size of the set of non-squares of the group. We improve upon previously established bounds and classify groups that obtain our new bound.     

Numerical investigation of the behavior of thin flexible membranes in interaction with a fluid domain

With the increasing concern over massive damage ensuing from flood, the application of flood protection systems has aroused growing interest. As part of an interdisciplinary project regarding the development of a temporary installable textile protective system against flood, we study, how the thin flexible membrane behaves in interaction with a fluid domain numerically and experimentally. The numerical research was carried out by means of the FV solver available in Star CCM+ based on both morphing motion model and on the basis of overset mesh and morphing motion model, with the help of a FEM solver available in Abaqus and finally through FSI Star CCM+ and Abaqus Co-Simulation (interconnection between FV solver for fluid domain analysis and FEM solver for solid domain analysis). A key challenge facing us was the implementation of proper damping models to address the problem with oscillation of the membrane. We have examined, how the change in water level affects the behavior of the thin flexible membrane. A comparable physical validation with respect to experimental model has been achieved through numerical analysis. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On simple groups with a cyclic maximal 2-Sylow intersection

Finite simple groupsG with a cyclic maximal 2-Sylow intersectionV are classified under the assumption that [G: N _G (V)] is odd.     

On a generalization of the master cyclic group polyhedron

We study the master equality polyhedron (MEP) which generalizes the master cyclic group polyhedron (MCGP) and the master knapsack polyhedron (MKP). We present an explicit characterization of the polar of the nontrivial facet-defining inequalities for MEP. This result generalizes similar results for the MCGP by Gomory (1969) and for the MKP by Araóz (1974). Furthermore, this characterization gives a polynomial time algorithm for separating an arbitrary point from MEP. We describe how facet-defining inequalities for the MCGP can be lifted to obtain facet-defining inequalities for MEP, and also present facet-defining inequalities for MEP that cannot be obtained in such a way. Finally, we study the mixed-integer extension of MEP and present an interpolation theorem that produces valid inequalities for general mixed integer programming problems using facets of MEP.     

On cyclic strings avoiding a pattern

We count the number of cyclic strings over an alphabet that avoid a single pattern under two different assumptions. In the first case, we assume that the symbols of the alphabet are on numbered positions on a circle, while in the second case we assume that the symbols can be freely rotated on the circle (i.e., we deal with necklaces). In each case, we provide a generating function, and we explain how these two cases are related. For the situation of avoiding more than one pattern, we formulate a general conjecture for the first case, and a conditional result for the second case. We also explain the differences between our theory and the theory of Edlin and Zeilberger (2000) by emphasizing how we modified the definition of the enumeration of cyclic strings that avoid one or more patterns when their lengths are less than the length of the longest pattern.     

On a composition of cyclic 2-designs

A CB(v,k,λ) means a cyclic 2-design of block size k coincidence number λ, and with v points. In this paper, a recursive construction of a CB(v,k,λ) from two or three cyclic 2-designs is given.