Volume Contents

Volume Contents

Volume Contents     

Generalized model matching and (F,G)-invariant submodules for linear systems over rings

A generalized version of the exact model matching problem (GEMMP) is considered for linear multivariable systems over an arbitrary commutative ring K with identity. Reduced forms of this problem are introduced, and a characterization of all solutions and minimal order solutions is given, both with and without the properness constraint on the solutions, in terms of linear equations over K and K-modules. An approach to the characterization of all stable solutions is presented which, under a certain Bezout condition and a freeness condition, provides a parametrization of all stable solutions. The results provide an explicit parametrization of all solutions and all stable solutions in case K is a field, without the Bezout condition. This is achieved through a very simple characterization and a generalization to an arbitrary field K of the “fixed poles” of the model matching problem in terms of invariant factors of a certain polynomial matrix. The results also show that whenever the GEMMP has a solution, there exist solutions whose poles can be chosen arbitrarily as far as they contain the “fixed poles” with the right multiplicities (in the algebraic closure of K). Implications of these results in regard to inverse systems are shown. Equivalent simpler forms (in state space form) of the problem are shown to be obtainable. A theory of finitely generated (F,G)-invariant submodules for linear systems over rings is developed, and the geometric equivalent of the model matching problem—the dynamic cover problem—is formulated, to which the results of the previous sections provide a solution in the reduced case.     

Discrete Adjoint based Sensitivity Analysis for Optimal Active Flow Control of High-Lift Configurations

Blowing and suction type of active flow control techniques can be used to delay the flow separation on the flap and to enhance the aerodynamic performance of high-lift configurations. Effective separation control and maximum enhancement in the mean lift coefficient are achieved by finding the optimal actuation parameters. The optimal set of actuation parameters can be obtained by combining the gradient based algorithms with discrete adjoints. In the present work, an unsteady discrete adjoint incompressible RANS solver is developed for the optimal active separation control. The adjoint solver is applied to the test case of active flow control on the flap of a 2D high-lift configuration. Sensitivity gradients are presented to demonstrate the accuracy of unsteady adjoint RANS solver. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Decomposition of Complete Graphs into Isomorphic Complete Bipartite Graphs

A decomposition of a complete graph into disjoint copies of a complete bipartite graph is called a ‐design of order n. The existence problem of ‐designs has been completely solved for the graphs for , for , K_{2, 3} and K_{3, 3}. In this paper, I prove that for all , if there exists a ‐design of order N, then there exists a ‐design of order n for all (mod ) and . Giving necessary direct constructions, I provide an almost complete solution for the existence problem for complete bipartite graphs with fewer than 18 edges, leaving five orders in total unsolved.     

Synthesis and biological evaluation of some 1,3-benzoxazol-2(3H)-one hybrid molecules as potential antioxidant and urease inhibitors

A new series of 1,3-benzoxazol-2(3H)-one hybrid compounds, including coumarin, isatin 1,3,4-triazole and 1,3,4-thiadiazole moieties, were synthesized and biologically evaluated for their antioxidant capacities and anti-urease properties. The synthesized benzoxazole-coumarin ( 6a–e ) and benzoxazole-isatin ( 10a–c ) hybrids showed remarkable urease inhibitory activities with IC₅₀ (μM), ranging from 0.0306 ± 0.0030 to 0.0402 ± 0.0030, while IC₅₀ of standard thiourea is 0.5027 ± 0.0293. The synthesized benzoxazole-triazole ( 8a–c ) and benzoxazole-thiadiazole ( 9a–c ) hybrids showed similar urease inhibitory activities with IC₅₀ (μM), ranging from 0.3861 ± 0.0379 to 0.5126 ± 0.0345. The antioxidant activity of the synthesized compounds was evaluated for their antioxidant activities, such as reducing power and ABTS (2,2′-azino-bis(3-ethylbenzothiazoline-6-sulphonic acid) diammonium salt) radical scavenging. The results of ABTS radical scavenging activities of some of the synthesized molecules showed higher activities than standard Trolox, SC₅₀ (μM) = 213.04 ± 18.12. One benzoxazole-coumarin ( 6f ), two benzoxazole-isothiocyanate ( 7b, 7c ), and two benzoxazole-triazole ( 8b, 8c ) derivatives showed higher activities (SC₅₀ (μM) values, 82.07 ± 10.34, 120.19 ± 7.30, 104.58 ± 10.55, 153.26 ± 7.14, and 144.82 ± 10.68, respectively) than standard Trolox, (SC₅₀ (μM) = 213.04 ± 18.12).     

Arithmetic mean of differences of Dedekind sums

Recently, Girstmair and Schoissengeier studied the asymptotic behavior of the arithmetic mean of Dedekind sums , as N → ∞. In this paper we consider the arithmetic mean of weighted differences of Dedekind sums in the form , where is a continuous function with , runs over , the set of Farey fractions of order Q in the unit interval [0,1] and are consecutive elements of . We show that the limit lim _Q→∞ A _h (Q) exists and is independent of h.     

Adsorption behavior of linear and cyclic genetically engineered platinum binding peptides

Recently, phage and cell-surface display libraries have been adapted for genetically selecting short peptides for a variety of inorganic materials. Despite the enormous number of inorganic-binding peptides reported and their bionanotechnological utility as synthesizers and molecular linkers, there is still a limited understanding of molecular mechanisms of peptide recognition of and binding to solid materials. As part of our goal of genetically designing these peptides, understanding the binding kinetics and thermodynamics, and using the peptides as molecular erectors, in this report we discuss molecular structural constraints imposed upon the quantitative binding characteristics of peptides with an affinity for inorganics. Specifically, we use a high-affinity seven amino acid Pt-binding sequence, PTSTGQA, as we reported in earlier studies and build two constructs: one is a Cys-Cys constrained "loop" sequence (CPTSTGQAC) that mimics the domain used in the pIII tail sequence of the phage library construction, and the second is the linear form, a septapeptide, without the loop. Both sequences were analyzed for their adsorption behavior on Pt thin films by surface plasmon resonance (SPR) spectroscopy and for their conformational properties by circular dichroism (CD). We find that the cyclic peptide of the integral Pt-binding sequence possesses single or 1:1 Langmuir adsorption behavior and displays equilibrium and adsorption rate constants that are significantly larger than those obtained for the linear form. Conversely, the linear form exhibits biexponential Langmuir isotherm behavior with slower and weaker binding. Furthermore, the structure of the cyclic version was found to adopt a random coil molecular conformation, whereas the linear version adopts a polyproline type II conformation in equilibrium with the random coil. The 2,2,2-trifluoroethanol titration experiments indicate that TFE has a different effect on the secondary structures of the linear and cyclic versions of the Pt binding sequence. We conclude that the presence of the Cys-Cys restraint affects both the conformation and binding behavior of the integral Pt-binding septapeptide sequence and that the presence or absence of constraints could be used to tune the adsorption and structural features of inorganic binding peptide sequences.     

Interface Conditions for a Phase Field Model with Anisotropic and Non-Local Interactions

An alternative formulation of the phase field method is utilized from an integral equation perspective. The technique allows one to derive macroscopic conditions at the interface from the microscopic potentials. Differential geometry and asymptotic analysis yield interface conditions, in arbitrary spatial dimension, for interactions that may include anisotropy as well as non-local potentials. The interface conditions can be expressed in various formulations, for example, in terms of the principal curvature directions of the interface, or the second order directional derivatives of the (signed) distance function and the Hessian of the surface tension.     

The effect of concrete slab–rockfill interface behavior on the earthquake performance of a CFR dam

Earthquake response of the concrete slab is mostly depended upon its conjunction with rockfill. This study aims to reveal the effect of concrete slab–rockfill interface behavior on the earthquake performance of a concrete-faced rockfill dam considering friction contact and welded contact. Friction contact is provided by using interface elements with five numbers of shear stiffness values. 2D finite element model of Torul concrete-faced rockfill dam is used for this purpose. Linear and materially non-linear time-history analyses considering dam–reservoir interaction are performed using ANSYS. Reservoir water is modeled using fluid finite elements by the Lagrangian approach. The Drucker–Prager model is preferred for concrete slab and rockfill in non-linear analyses. Horizontal component of 1992 Erzincan earthquake with peak ground acceleration of 0.515g is used in analyses. The maximum and minimum displacements and principal stresses are shown by the height of the concrete slab and earthquake performance of the dam is investigated considering different joint conditions for empty and full reservoir cases. In addition, potential damage situations of concrete slab are evaluated.     

On the mean square average of special values of L-functions

Let χ be a Dirichlet character and L(s,χ) be its L-function. Using weighted averages of Gauss and Ramanujan sums, we find exact formulas involving Jordan?s and Euler?s totient function for the mean square average of L(1,χ) when χ ranges over all odd characters modulo k and L(2,χ) when χ ranges over all even characters modulo k. In principle, using our method, it is always possible to find the mean square average of L(r,χ) if χ and r?1 have the same parity and χ ranges over all odd (or even) characters modulo k, though the required calculations become formidable when r?3. Consequently, we see that for almost all odd characters modulo k, |L(1,χ)|<Φ(k), where Φ(x) is any function monotonically tending to infinity.