Ideal Criteria for both Ideal Criteria for both X2-dy2 = M1 And X2-dy2 = M2 to have Primitive Solutions for any Integers M1, M2 Prime to D > 0

This article provides necessary and sufficient conditions for both of the Diophantine equations X^2 − DY^2 = m1 and x^2 − Dy^2 = m2 to have primitive solutions when m1 , m2 ∈ Z, and D ∈ N is not a perfect square. This is given in terms of the ideal theory of the underlying real quadratic order Z[√D].

General electromagnetic simulation tool to predict the microwave nonlinear response of planar, arbitrarily-shaped HTS structures

This work describes a simulation tool being developed at UPC to predict the microwave nonlinear behavior of planar superconducting structures with very few restrictions on the geometry of the planar layout. The software is intended to be applicable to most structures used in planar HTS circuits, including line, patch, and quasi-lumped microstrip resonators. The tool combines Method of Moments (MoM) algorithms for general electromagnetic simulation with Harmonic Balance algorithms to take into account the nonlinearities in the HTS material. The Method of Moments code is based on discretization of the Electric Field Integral Equation in Rao, Wilton and Glisson Basis Functions. The multilayer dyadic Green's function is used with Sommerfeld integral formulation. The Harmonic Balance algorithm has been adapted to this application where the nonlinearity is distributed and where compatibility with the MoM algorithm is required. Tests of the algorithm in TM010 disk resonators agree with closed-form equations for both the fundamental and third-order intermodulation currents. Simulations of hairpin resonators show good qualitative agreement with previously published results, but it is found that a finer meshing would be necessary to get correct quantitative results. Possible improvements are suggested.

Study of the Compressive Strength of Aluminum Curved Elements

Currently, the Specification for Aluminum Structures (Aluminum Association, 2010) shows thin-walled aluminum plate sections with radii greater than eight inches have a lower compressive strength capacity than a flat plate with the same width and thickness. This inconsistency with intuition, which suggests any degree of folding a plate should increase its elastic buckling strength, inspired this study. A wide range of curvatures are studied—from a nearly flat plate to semi-circular. To quantify the curvature, a single non-dimensional parameter is used to represent all combinations of width, thickness and radius. Using the finite strip method (CU-FSM), elastic local buckling stresses are investigated. Using the ratio of stress values of curved plates compared to flat plates of the same size, equivalent plate-buckling coefficients are calculated. Using this data, nonlinear regression analyses are performed to develop closed form equations for five different edge support conditions. These equations can be used to calculate the elastic critical buckling stress for any curved aluminum section when the geometric properties (width, thickness, and radius) and the material properties (elastic modulus and Poisson’s ratio) are known. This procedure is illustrated in examples, each showing the applicability of the derived equations to geometries other than those investigated in this study and also providing comparisons with theoretically exact numerical analysis results.

Effect of child care subsidies on price and quality of care for low -income families

This dissertation examines the effect of regulations, resource and referral agencies, and subsidies on price and quality of care in child care centers. This research is based on a carefully developed conceptual framework that incorporates the factors affecting the demand and supply of child care. The first step in developing this framework is sketching out the structural equations. The structural equations help us understand the underlying behavior of individuals and firms making a decision. The exogenous variables are vector of attributes relating to family characteristics, child characteristics, regulations, subsidy, community characteristics and prices of inputs. Based on the structural equations, reduced form equations are estimated to find the effect of each of the exogenous variables on each of the endogenous variables. Reduced form equations help us answer public policy questions. The sample for this study is from the 1990 Profile of Child Care Settings (PCCS) data in which 2,089 center based programs were interviewed.^ Child/Staff Ratio (Group Level). Results indicate that among subsidies, only the state subsidy per child in poverty has a significant effect on the child/staff ratio at the group level. Presence of resource and referral agencies also increase the child/staff ratio at the group level. Also when the maximum center group size regulation for 25-36 months becomes more stringent, the child/staff ratio at the group level decreases.^ Child/Staff Ratio (Center Level). When the regulations for the maximum child/staff ratio for age groups 13-24 months and 37-60 months become lax, the child/staff ratio for the center increases. As the regulation for maximum group size for infants becomes stringent, the child/staff ratio decreases. An interesting finding is that as the regulations for maximum group size for age groups 13-24 months and 25-36 months become stringent, the child/staff ratio for the center increases. Another significant finding is that when a center is located in a rural area the child/staff ratio is significantly lower.^ Center Weighted Average Hourly Fees. Maximum group size regulations for age groups 25-36 months and 37-60 months have a negative effect on center hourly fee. Maximum child staff regulations for age groups 13-24 months and 37-60 months have a negative effect on center hourly fee. Maximum child staff regulations for age groups 0-12 months and 25-36 months have a positive effect on center hourly fee. Findings also indicate that the center average hourly price is lower when there is a resource and referral agency present. Cost adjusted prekindergarten funds and JOBS child care subsidies have a negative effect on average hourly fee. Cost adjusted social services block grant and state subsidy per child in poverty have a positive effect on the average hourly price. A major finding of this dissertation is the interaction of subsidy and regulatory variables.^ Another major finding is that child/staff ratio at the group level is lower when there is an interaction between geographic location and nature of center sponsorship. ^

Effect of child care subsidies on price and quality of care for low -income families

This dissertation examines the effect of regulations, resource and referral agencies, and subsidies on price and quality of care in child care centers. This research is based on a carefully developed conceptual framework that incorporates the factors affecting the demand and supply of child care. The first step in developing this framework is sketching out the structural equations. The structural equations help us understand the underlying behavior of individuals and firms making a decision. The exogenous variables are vector of attributes relating to family characteristics, child characteristics, regulations, subsidy, community characteristics and prices of inputs. Based on the structural equations, reduced form equations are estimated to find the effect of each of the exogenous variables on each of the endogenous variables. Reduced form equations help us answer public policy questions. The sample for this study is from the 1990 Profile of Child Care Settings (PCCS) data in which 2,089 center based programs were interviewed. Child/Staff Ratio (Group Level): Results indicate that among subsidies, only the state subsidy per child in poverty has a significant effect on the child/staff ratio at the group level. Presence of resource and referral agencies also increase the child/staff ratio at the group level. Also when the maximum center group size regulation for 25-36 months becomes more stringent, the child/staff ratio at the group level decreases. Child/Staff Ratio (Center Level): When the regulations for the maximum child/staff ratio for age groups 13-24 months and 37-60 months become lax, the child/staff ratio for the center increases. As the regulation for maximum group size for infants becomes stringent, the child/staff ratio decreases. An interesting finding is that as the regulations for maximum group size for age groups 13-24 months and 25-36 months become stringent, the child/staff ratio for the center increases. Another significant finding is that when a center is located in a rural area the child/staff ratio is significantly lower. Center Weighted Average Hourly Fees: Maximum group size regulations for age groups 25-36 months and 37-60 months have a negative effect on center hourly fee. Maximum child staff regulations for age groups 13-24 months and 37-60 months have a negative effect on center hourly fee. Maximum child staff regulations for age groups 0-12 months and 25-36 months have a positive effect on center hourly fee. Findings also indicate that the center average hourly price is lower when there is a resource and referral agency present. Cost adjusted prekindergarten funds and JOBS child care subsidies have a negative effect on average hourly fee. Cost adjusted social services block grant and state subsidy per child in poverty have a positive effect on the average hourly price. A major finding of this dissertation is the interaction of subsidy and regulatory variables. Another major finding is that child/staff ratio at the group level is lower when there is an interaction between geographic location and nature of center sponsorship.

Identification of structural damage in flexible structures using system norm and neural networks

Nowadays there is great interest in damage identification using non destructive tests. Predictive maintenance is one of the most important techniques that are based on analysis of vibrations and it consists basically of monitoring the condition of structures or machines. A complete procedure should be able to detect the damage, to foresee the probable time of occurrence and to diagnosis the type of fault in order to plan the maintenance operation in a convenient form and occasion. In practical problems, it is frequent the necessity of getting the solution of non linear equations. These processes have been studied for a long time due to its great utility. Among the methods, there are different approaches, as for instance numerical methods (classic), intelligent methods (artificial neural networks), evolutions methods (genetic algorithms), and others. The characterization of damages, for better agreement, can be classified by levels. A new one uses seven levels of classification: detect the existence of the damage; detect and locate the damage; detect, locate and quantify the damages; predict the equipment's working life; auto-diagnoses; control for auto structural repair; and system of simultaneous control and monitoring. The neural networks are computational models or systems for information processing that, in a general way, can be thought as a device black box that accepts an input and produces an output. Artificial neural nets (ANN) are based on the biological neural nets and possess habilities for identification of functions and classification of standards. In this paper a methodology for structural damages location is presented. This procedure can be divided on two phases. The first one uses norms of systems to localize the damage positions. The second one uses ANN to quantify the severity of the damage. The paper concludes with a numerical application in a beam like structure with five cases of structural damages with different levels of severities. The results show the applicability of the presented methodology. A great advantage is the possibility of to apply this approach for identification of simultaneous damages.

Integral form of Yang-Mills equations and its gauge invariant conserved charges

Despite the fact that the integral form of the equations of classical electrodynamics is well known, the same is not true for non-Abelian gauge theories. The aim of the present paper is threefold. First, we present the integral form of the classical Yang-Mills equations in the presence of sources and then use it to solve the long-standing problem of constructing conserved charges, for any field configuration, which are invariant under general gauge transformations and not only under transformations that go to a constant at spatial infinity. The construction is based on concepts in loop spaces and on a generalization of the non-Abelian Stokes theorem for two-form connections. The third goal of the paper is to present the integral form of the self-dual Yang-Mills equations and calculate the conserved charges associated with them. The charges are explicitly evaluated for the cases of monopoles, dyons, instantons and merons, and we show that in many cases those charges must be quantized. Our results are important in the understanding of global properties of non-Abelian gauge theories.

Closed Form Solutions of Integrable Nonlinear Evolution Equations

2010 Mathematics Subject Classification: 35Q55.

On Principle Eigenvalue for Linear Second Order Elliptic Equations in Divergence Form

2002 Mathematics Subject Classification: 35J15, 35J25, 35B05, 35B50

The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form

2000 Mathematics Subject Classification: 35J70, 35P15.

A Note on the L2-norm of the Second Fundamental Form of Algebraic Manifolds

2000 Mathematics Subject Classification: 53C42, 53C55.

Quantitative Derivation of Effective Evolution Equations for the Dynamics of Bose-Einstein Condensates

This thesis proves certain results concerning an important question in non-equilibrium quantum statistical mechanics which is the derivation of effective evolution equations approximating the dynamics of a system of large number of bosons initially at equilibrium (ground state at very low temperatures). The dynamics of such systems are governed by the time-dependent linear many-body Schroedinger equation from which it is typically difficult to extract useful information due to the number of particles being large. We will study quantitatively (i.e. with explicit bounds on the error) how a suitable one particle non-linear Schroedinger equation arises in the mean field limit as number of particles N → ∞ and how the appropriate corrections to the mean field will provide better approximations of the exact dynamics. In the first part of this thesis we consider the evolution of N bosons, where N is large, with two-body interactions of the form N³ᵝv(Nᵝ⋅), 0≤β≤1. The parameter β measures the strength and the range of interactions. We compare the exact evolution with an approximation which considers the evolution of a mean field coupled with an appropriate description of pair excitations, see [18,19] by Grillakis-Machedon-Margetis. We extend the results for 0 ≤ β < 1/3 in [19, 20] to the case of β < 1/2 and obtain an error bound of the form p(t)/Nᵅ, where α>0 and p(t) is a polynomial, which implies a specific rate of convergence as N → ∞. In the second part, utilizing estimates of the type discussed in the first part, we compare the exact evolution with the mean field approximation in the sense of marginals. We prove that the exact evolution is close to the approximate in trace norm for times of the order o(1)√N compared to log(o(1)N) as obtained in Chen-Lee-Schlein [6] for the Hartree evolution. Estimates of similar type are obtained for stronger interactions as well.

Weighted S-Asymptotically omega-Periodic Solutions of a Class of Fractional Differential Equations

We study the existence of weighted S-asymptotically omega-periodic mild solutions for a class of abstract fractional differential equations of the form u' = partial derivative (alpha vertical bar 1)Au + f(t, u), 1 < alpha < 2, where A is a linear sectorial operator of negative type.

LOCAL WELL POSEDNESS, ASYMPTOTIC BEHAVIOR AND ASYMPTOTIC BOOTSTRAPPING FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS OF THE SECOND ORDER IN TIME

A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques.

Experimental results on the nonlinear H(infinity) control via quasi-LPV representation and game theory for wheeled mobile robots

In this paper, nonlinear dynamic equations of a wheeled mobile robot are described in the state-space form where the parameters are part of the state (angular velocities of the wheels). This representation, known as quasi-linear parameter varying, is useful for control designs based on nonlinear H(infinity) approaches. Two nonlinear H(infinity) controllers that guarantee induced L(2)-norm, between input (disturbances) and output signals, bounded by an attenuation level gamma, are used to control a wheeled mobile robot. These controllers are solved via linear matrix inequalities and algebraic Riccati equation. Experimental results are presented, with a comparative study among these robust control strategies and the standard computed torque, plus proportional-derivative, controller.