On the monoids of transformations that preserve the order and a uniform partition

In this article we consider the monoid O(mxn) of all order-preserving full transformations on a chain with mn elements that preserve a uniformm-partition and its submonoids O(mxn)(+) and O(mxn)(-) of all extensive transformations and of all co-extensive transformations, respectively. We determine their ranks and construct a bilateral semidirect product decomposition of O(mxn) in terms of O(mxn)(-) and O(mxn)(+).

Bilateral semidirect product decompositions of transformation monoids

In this paper we consider the monoid OR(n) of all full transformations on a chain with n elements that preserve or reverse the orientation, as well as its submonoids OD(n) of all order-preserving or order-reversing elements, OP(n) of all orientation-preserving elements and O(n) of all order-preserving elements. By making use of some well known presentations, we show that each of these four monoids is a quotient of a bilateral semidirectproduct of two of its remarkable submonoids.

On semigroups of endomorphisms of a chain with restricted range

Let X be a finite or infinite chain and let be the monoid of all endomorphisms of X. In this paper, we describe the largest regular subsemigroup of and Green's relations on. In fact, more generally, if Y is a nonempty subset of X and is the subsemigroup of of all elements with range contained in Y, we characterize the largest regular subsemigroup of and Green's relations on. Moreover for finite chains, we determine when two semigroups of the type are isomorphic and calculate their ranks.

On the ranks of certain monoids of transformations that preserve a uniform partition

The rank of a semigroup, an important and relevant concept in Semigroup Theory, is the cardinality of a least-size generating set. Semigroups of transformations that preserve or reverse the order or the orientation as well as semigroups of transformations preserving an equivalence relation have been widely studied over the past decades by many authors. The purpose of this article is to compute the ranks of the monoid

A numerical analysis of generalized Boussinesq-type equation using continuos/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time-dependent varying seabed are included. Thus, high-order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher-order models, an extra O(mu 2n+2) term (n ??? N) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth-order models. The discretization of the spatial variables is made using continuous P2 Lagrange elements. A predictor-corrector scheme with an initialization given by an explicit RungeKutta method is also used for the time-variable integration. Moreover, a CFL-type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved.

The cardinal of various monoids of transformations that preserve a uniform partition

In this paper we give formulas for the number of elements of the monoids ORm x n of all full transformations on it finite chain with tun elements that preserve it uniform m-partition and preserve or reverse the orientation and for its submonoids ODm x n of all order-preserving or order-reversing elements, OPm x n of all orientation-preserving elements, O-m x n of all order-preserving elements, O-m x n(+) of all extensive order-preserving elements and O-m x n(-) of all co-extensive order-preserving elements.

Presentations for monoids of finite partial isometries

In this paper we give presentations for the monoid DPn of all partial isometries on {1,..., n} and for its submonoid ODPn of all order-preserving partial isometries.

On differentiability and analyticity of positive definite functions

We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is real-analytic and consequently extends holomorphically to a maximal horizontal strip of the complex plane.

Node adaptation for global collocation with radial basis functions using direct multisearch for multiobjective optimization

Meshless methods are used for their capability of producing excellent solutions without requiring a mesh, avoiding mesh related problems encountered in other numerical methods, such as finite elements. However, node placement is still an open question, specially in strong form collocation meshless methods. The number of used nodes can have a big influence on matrix size and therefore produce ill-conditioned matrices. In order to optimize node position and number, a direct multisearch technique for multiobjective optimization is used to optimize node distribution in the global collocation method using radial basis functions. The optimization method is applied to the bending of isotropic simply supported plates. Using as a starting condition a uniformly distributed grid, results show that the method is capable of reducing the number of nodes in the grid without compromising the accuracy of the solution. (C) 2013 Elsevier Ltd. All rights reserved.

Analysis of sandwich beam structures using kriging based higher order models

Functionally graded composite materials can provide continuously varying properties, which distribution can vary according to a specific location within the composite. More frequently, functionally graded materials consider a through thickness variation law, which can be more or less smoother, possessing however an important characteristic which is the continuous properties variation profiles, which eliminate the abrupt stresses discontinuities found on laminated composites. This study aims to analyze the transient dynamic behavior of sandwich structures, having a metallic core and functionally graded outer layers. To this purpose, the properties of the particulate composite metal-ceramic outer layers, are estimated using Mod-Tanaka scheme and the dynamic analyses considers first order and higher order shear deformation theories implemented though kriging finite element method. The transient dynamic response of these structures is carried out through Bossak-Newmark method. The illustrative cases presented in this work, consider the influence of the shape functions interpolation domain, the properties through-thickness distribution, the influence of considering different materials, aspect ratios and boundary conditions. (C) 2014 Elsevier Ltd. All rights reserved.

Estimation of rotational frequency response functions

As it is widely known, in structural dynamic applications, ranging from structural coupling to model updating, the incompatibility between measured and simulated data is inevitable, due to the problem of coordinate incompleteness. Usually, the experimental data from conventional vibration testing is collected at a few translational degrees of freedom (DOF) due to applied forces, using hammer or shaker exciters, over a limited frequency range. Hence, one can only measure a portion of the receptance matrix, few columns, related to the forced DOFs, and rows, related to the measured DOFs. In contrast, by finite element modeling, one can obtain a full data set, both in terms of DOFs and identified modes. Over the years, several model reduction techniques have been proposed, as well as data expansion ones. However, the latter are significantly fewer and the demand for efficient techniques is still an issue. In this work, one proposes a technique for expanding measured frequency response functions (FRF) over the entire set of DOFs. This technique is based upon a modified Kidder's method and the principle of reciprocity, and it avoids the need for modal identification, as it uses the measured FRFs directly. In order to illustrate the performance of the proposed technique, a set of simulated experimental translational FRFs is taken as reference to estimate rotational FRFs, including those that are due to applied moments.

Deuterium NMR Study of Orientational Order in Cellulosic Network Microfibers

Deuterium NMR was used to investigate the orientational order in a composite cellulosic formed by liquid crystalline acetoxypropylcellulose (A PC) and demented nematic 4'-penty1-4-cyanobiphenyl (5CB-4 alpha d(2)) with the per centage of 85% A PC by weight Three forms of the composite including electro spun microfibers, thin film and bulk samples were analyzed The NMR results initially suggest two distinct scenarios, one whet e the 503-alpha d(2), is confined to small droplets with dimensions smaller than the magnetic coherence length and the other where the 503-alpha d(2) molecules arc aligned with the A PC network chains Polarized optical microscopy (POW from thin film samples along with all the NMR results show the presence of 5CB-alpha d(2) droplets in the composite systems with a nematic wetting layer at the APC-5CB-alpha d(2) interface that experiences and order disorder transition driven by the polymer network N-I transition The characterization of the APC network I-N transition shows a pronounced subcritical behavior within a heterogeneity scenario.

Equilibrium self-assembly of colloids with distinct interaction sites: Thermodynamics, percolation, and cluster distribution functions

We calculate the equilibrium thermodynamic properties, percolation threshold, and cluster distribution functions for a model of associating colloids, which consists of hard spherical particles having on their surfaces three short-ranged attractive sites (sticky spots) of two different types, A and B. The thermodynamic properties are calculated using Wertheim's perturbation theory of associating fluids. This also allows us to find the onset of self-assembly, which can be quantified by the maxima of the specific heat at constant volume. The percolation threshold is derived, under the no-loop assumption, for the correlated bond model: In all cases it is two percolated phases that become identical at a critical point, when one exists. Finally, the cluster size distributions are calculated by mapping the model onto an effective model, characterized by a-state-dependent-functionality (f) over bar and unique bonding probability (p) over bar. The mapping is based on the asymptotic limit of the cluster distributions functions of the generic model and the effective parameters are defined through the requirement that the equilibrium cluster distributions of the true and effective models have the same number-averaged and weight-averaged sizes at all densities and temperatures. We also study the model numerically in the case where BB interactions are missing. In this limit, AB bonds either provide branching between A-chains (Y-junctions) if epsilon(AB)/epsilon(AA) is small, or drive the formation of a hyperbranched polymer if epsilon(AB)/epsilon(AA) is large. We find that the theoretical predictions describe quite accurately the numerical data, especially in the region where Y-junctions are present. There is fairly good agreement between theoretical and numerical results both for the thermodynamic (number of bonds and phase coexistence) and the connectivity properties of the model (cluster size distributions and percolation locus).

Solutions of second-order and fourth-order ODEs on the half-line

We start by studying the existence of positive solutions for the differential equation u '' = a(x)u - g(u), with u ''(0) = u(+infinity) = 0, where a is a positive function, and g is a power or a bounded function. In other words, we are concerned with even positive homoclinics of the differential equation. The main motivation is to check that some well-known results concerning the existence of homoclinics for the autonomous case (where a is constant) are also true for the non-autonomous equation. This also motivates us to study the analogous fourth-order boundary value problem {u((4)) - cu '' + a(x)u = vertical bar u vertical bar(p-1)u u'(0) = u'''(0) = 0, u(+infinity) = u'(+infinity) = 0 for which we also find nontrivial (and, in some instances, positive) solutions.

A Pitch Control Malfunction Analysis for Wind Turbines with Permanent Magnet Synchronous Generator and Full-power Converters: Proportional Integral Versus Fractional-order Controllers

A transient analysis for two full-power converter wind turbines equipped with a permanent magnet synchronous generator is studied in this article, taking into consideration, as a new contribution to earlier studies, a pitch control malfunction. The two full-power converters considered are, respectively, a two-level and a multi-level converter. Moreover, a novel control strategy based on fractional-order controllers for wind turbines is studied. Simulation results are presented; conclusions are in favor of the novel control strategy, improving the quality of the energy injected into the electric grid.