Quadratic Type Research Articles

On an Extended Time-Varying Beverton–Holt Equation Subject to Harvesting Monitoring and Population Excess Penalty

This paper considers a more general eventually time-varying Beverton–Holt equation for species evolution which can include a harvesting action and a penalty for overpopulation numbers. The harvesting action may be positive (typically consisting of hunting or fishing) or negative which refers to repopulation within the environment. One considers also a penalty of quadratic type on the overpopulation and the introduction of a term related to Allee effect to take account of small levels of population. The intrinsic growth rate is assumed either to exceed unity or to be under unity. In the second case, the extinction point is a locally stable attractor while the other positive equilibrium point is unstable contrarily to the commonly studied case of intrinsic growth rate exceeding unity where the above roles are inverted. This consequence implies that the extinction point is also globally asymptotically stable for any given finite initial condition. In the case when the eventual overpopulation is penalized with a sufficiently large coefficient which exceeds a prescribed threshold, to quantify such an excess, only a globally asymptotically stable extinction attractor is present and no other positive equilibrium points exist. In the case of a positive moderate quadratic evaluation term for such an overpopulation, one or two positive equilibrium points coexist with the extinction one. The smaller one is unstable contrarily to the extinction equilibrium which is locally asymptotically stable. If it exists a second largest positive equilibrium point, being distinct to the above-given one, then it can be unstable or locally stable depending on the parameterization. Also, some methods of monitoring the population evolution through control laws on the harvesting action are discussed.

Optimal Selection of Capacitors for a Low Energy Storage Quadratic Boost Converter (LES-QBC)

This article studies a recently proposed dc-dc converter and its optimization in terms of capacitors selection through the Particle Swarm Optimization (PSO) algorithm. The converter under study is the so-called Low Energy Storage Quadratic Boost Converter (LES-QBC), a quadratic type of converter that offers a smaller Output Voltage Ripple (OVR) compared to the traditional quadratic boost topology with capacitors of the same characteristics. This study presents a way to select the capacitors for minimizing the OVR while achieving a constraint of a maximum stored energy in capacitors. The capacitor’s stored energy is given as a design specification. The results are compared against the traditional quadratic boost converter and the LES-QBC without optimization (equal capacitance in capacitors). The optimization algorithm used was the so-called Particle Swarm Optimization (PSO). The experimental results demonstrate the effectiveness of the proposition. For the design exercise used for the results, the capacitor’s stored energy was kept almost the same, and a reduction in the OVR was achieved versus the non-optimized LES-QBC.

Finite Block Method with Chebyshev Polynomials Applied to Cracked Plate in Functionally Graded Materials

The finite block method (FBM) with Chebyshev polynomials is developed in this paper for the functionally graded material (FGM) of two-dimensional fracture problem. The main idea is to divide domain into few blocks. By introducing the mapping technique, a block of quadratic type is transformed from Cartesian coordinate to normalised coordinate with eight seeds two dimensions. The differential matrices in physical domain are determined from that in the normalised transformed system. The accuracy of the FBM with Chebyshev polynomials is demonstrated with two examples and comparisons have been implemented with different numerical approaches.

Approximation Solution of Fuzzy Singular Volterra Integral Equation by Non-Polynomial Spline

A non-polynomial spline (NPS) is an approximation method that relies on the triangular and polynomial parts, so the method has infinite derivatives of the triangular part of the NPS to compensate for the loss of smoothness inherited by the polynomial. In this paper, we propose polynomial-free linear and quadratic spline types to solve fuzzy Volterra integral equations (FVIE) of the 2nd kind with the weakly singular kernel (FVIEWSK) and Abel's type kernel. The linear type algorithm gives four parameters to form a linear spline. In comparison, the quadratic type algorithm gives five parameters to create a quadratic spline, which is more of a credit for the exact solution. These algorithms process kernel singularities with a simple technique. Illustrative examples use MathCad software to deal with upper and lower-bound solutions to fuzzy problems. The method provides a reliable way to ensure that an exact solution is approximated. Also, figures and tables show the potential of the method.

Risk-sensitive mean field games with major and minor players

We investigate a class of mean field games containing a large number of major and minor players. Each player minimizes a quadratic-tracking type risk-sensitive cost functional, where the reference signal is a function of the state average term of the major and minor players. To reduce the complexity for solving the problem, we design a sequence of decentralized strategies by the Nash certainty equivalence principle. Firstly, for the optimal control problems with quadratic type risk-sensitive cost functionals, we propose a new verification theorem. Secondly, we apply the two-layer state aggregation method to construct the fixed-point equations for the estimations of the state average terms and give the conditions for the existence and uniqueness of the fixed points. Then, we design a sequence of decentralized strategies by the estimations of the state average terms based on local information. It is shown that the estimations of the state average terms are consistent with the true values for the closed-loop systems, and the sequence of strategies designed is a decentralized asymptotic Nash equilibrium. Finally, the effectiveness of the theoretical analysis is demonstrated by a numerical example.

Generalized Stability of the Quadratic Type λ-Functional Equation with 3k-Variables in Non-Archimedean Banach Space and Non-Archimedean Random Normed Space

Generalized Stability of the Quadratic Type λ-Functional Equation with 3k-Variables in Non-Archimedean Banach Space and Non-Archimedean Random Normed Space

Dispatching Arrays with Tasks of Equal Resource Measure in GRID Systems

The role of computing and time resource management of parallel systems when dispatching multiprocessor tasks increases significantly in Grid systems consisting of multiple sites with multiprocessor computing systems, with multisite execution of a parallel task on several sites simultaneously. Such Grid systems of centralized architecture are modeled by the resource quadrant. User's request for maintenance by the Grid system dispatcher is modeled by a resource rectangle with horizontal and vertical dimensions, respectively, equal to the number of time and processor resource units required to fulfill the request. Examples of the exponential complexity of dispatching resource rectangles are the stacking of consecutive resource squares and consecutive resource rectangles of equal perimeter into an enclosing rectangle of the minimum area. Heuristic algorithms of polynomial labor intensity based on the operations of dynamic integration of resource rectangles in the environment of resource rectangles are of practical value. The quality of dispatching is assessed by a non-Euclidean heuristic measure that takes into account the area and shape of the occupied resource area. The quality of dispatching arrays with requests of the same resource measure equal to the product of the number of required processors and runtime is analyzed. In this paper, the quality of three polynomial level algorithms in height and three polynomial level algorithms in length (with the nearest approach to the level, with exceeding of the level and with minimum deviation) is evaluated when dispatching arrays with requests of equal resource measure. Such arrays belong to the parabolic quadratic type and contain user's tasks of circular, hyperbolic and parabolic type. On five test arrays, it is shown that H-finite-level algorithms with a with the nearest approach to the level and with minimum deviation have the smallest value of the maximum of the heuristic measure of 8.45. When servicing arrays with user's tasks of the same resource measure in Grid systems, it is recommended to use the polynomial Н- finite-level algorithm in length with the nearest approach to the level which is introduced in this paper.

Extensions, crossed modules and pseudo quadratic Lie type superalgebras

Extensions and crossed modules of Lie type superalgebras are introduced and studied. We construct homology and cohomology theories of Lie-type superalgebras. The notion of left super-invariance for a bilinear form is defined and we consider Lie type superalgebras endowed with nondegenerate, supersymmetric and left super-invariant bilinear form. Such Lie type superalgebras are called pseudo quadratic Lie type superalgebras. We show that any pseudo quadratic Lie type superalgebra induces a Jacobi-Jordan superalgebra. By using the method of double extension, we study pseudo quadratic Lie type superalgebras and theirs associated Jacobi-Jordan superalgebras.

Classification of a class of systems of cubic ordinary differential equations

In this article, we consider the classification of the systems of two ordinary differential equations with a complex-valued unknown and gauge-invariant cubic nonlinearities of polynomial type. The class of systems of ODEs arises in the study of the large time behavior of a system of cubic nonlinear Schrödinger equations or that of cubic nonlinear Klein-Gordon equations. We give the complete classification of the systems which possess a conserved quantity of quadratic type. Our argument is based on the representation of a system in terms of a pair of a matrix and a vector.

Connection between State Funding and International Sporting Success: The Case of Croatia

Abstract The aim of this paper is to determine the types and intensity of connection between the amount of state funding for various programmes in sport invested by Croatian Olympic Committee from 2001 until 2016 and international sporting success of Croatian athletes. A connection between 12 independent variables (funds invested in 33 summer Olympic sports (24 individual and 9 team sports) broken down in 8 specific programmes, as well as the number of athletes and coaches in different programmes) and international sporting success was tested using regression analysis. The results show statistically significant logarithm connection between success and total funds invested (ACR=0.160, R 2 =0.319, p=0.001). Additionally, three variables showed linear, eight logarithm and one quadratic type of connection. Applying different regression models contributes to better understanding of connection between the amount and direction of investments in high performance sport and result of those investments in the form of achieved international sporting success.

Asymmetric and robust loss function driven least squares support vector machine

Least squares support vector machine (LSSVM) considerably simplifies problem solving, however, there are restrictions. The first is that it treats samples on both sides of the proximal hyperplane equally and does not differentiate them based on locations; the second is that it is sensitive to noise and outliers. To address the aforementioned issues, this paper proposes an asymmetric robust least squares support vector machine termed QTLS by combining Quadratic Type Squared Error Loss Function (QTSELF) with LSSVM, in which QTSELF is introduced into machine learning for the first time. On the one hand, QTLS can impose various penalties on samples according to their locations and place greater emphasis on samples that are susceptible to misclassification. On the other hand, it improves the model robustness by imposing a tiny penalty on noise or outliers located far from the proximal hyperplane. Using Rademacher complexity theory, we investigate the generalization capacity of QTLS. The RMSProp technique is utilized to solve both linear and nonlinear QTLS. Extensive experiments indicate the effectiveness of QTLS in addressing binary classification problems.

The effect of varying levels of purified condensed tannins on performance, blood profile, meat quality and methane emission in male Bapedi sheep fed grass hay and pellet-based diet

This study determined the effect of purified condensed tannin inclusion levels in a diet on production, haematological indices, blood biochemical components, meat quality and methane emission by yearling indigenous male Bapedi sheep on a grass hay and sheep pellet-based diet in a 28-day trial. The diets contained similar (P > 0.05) nutrients but with different (P < 0.05) purified condensed tannin supplementation levels. A complete randomized design was used. Twenty-four yearling male Bapedi sheep were assigned to four dietary treatments having different purified condensed tannin levels of 0 (GH80P20PCT0), 30 (GH80P20PCT30), 40 (GH80P20PCT40) and 50 (GH80P20PCT50) g/kg DM. A quadratic type of equation was also used to determine condensed tannin supplementation levels for optimal performance and methane emission reduction by sheep. Supplementing diets with purified condensed tannins did not affect (P > 0.05) diet intake, digestibility and live weight gain of male Bapedi sheep. Supplementing diets with purified condensed tannins did not affect (P > 0.05) blood components of male Bapedi sheep. Inclusion of condensed tannins in the diets did not affect (P > 0.05) Bapedi sheep meat pH and sensory attributes. However, supplementing diets with purified condensed tannins decreased (P < 0.05) methane emission by 51 to 60%. A 49.08 g supplementation level with purified condensed tannins per kg DM diet was calculated, with the use of quadratic equations, to result in the lowest methane emission by male Bapedi sheep. The meat of male Bapedi rams on diets containing 30, 40 or 50 g of purified condensed tannins per kg DM contained higher (P < 0.05) antioxidant activities than those from rams fed a diet without purified condensed tannins. These results indicate that purified condensed tannin supplementation levels of 0, 30, 40 or 50 g/kg DM diet had no adverse effects on growth performance, blood profiles and meat sensory attributes of male Bapedi sheep. However, supplementation levels of 30, 40 or 50 g of purified condensed tannins per kg DM diet reduced methane emission by 51 to 60%, and increased sheep meat antioxidant activity values. Supplementing diets with purified condensed tannins has the potential to reduce methane production and emission by sheep. However, long-term studies are recommended to ascertain the present findings.

Stability for Semilinear Parabolic Optimal Control Problems with Respect to Initial Data

A distributed optimal control problem for a semilinear parabolic partial differential equation is investigated. The stability of locally optimal solutions with respect to perturbations of the initial data is studied. Based on different types of sufficient optimality conditions for a local solution of the unperturbed problem, Lipschitz or Hölder stability with respect to perturbations are proved. Moreover, a particular example with semilinear equation, constant initial data, and standard quadratic tracking type objective functional is constructed that has at least two different locally optimal solutions. By the perturbation analysis, the existence of a problem with non-constant initial data is shown that also has at least two different locally optimal solutions.

Characteristics and Prediction of Fatigue Resistance between Asphalt Pavement Layers Based on Shear Stiffness Decay Rate

Abstract The evaluation of fatigue performance between asphalt pavement layers highly depends on fatigue life and shear stiffness. However, fatigue life and shear stiffness are comprehensive evaluation indexes. In the study of the formation mechanism and decay process of fatigue resistance, both of them cannot provide effective theoretical support. In this study, the shear stiffness decay curve was obtained through a four-point shear fatigue test under different loading conditions. The initial shear stiffness and the shear stiffness decay rate of interlayers were chosen to evaluate the initial resistance and process resistance. The effects of temperature, loading frequency, compressive stress, and shear stress on the evolution of interlayer fatigue performance were investigated. The findings of this study revealed that first, with the increase of the compressive stress perpendicular to the interlayer interface, the interlayer shear stiffness decay curve transitions from a cubic curve type to a quadratic curve type and gradually changes to a linear equation. Second, the ranking of influence degree of four factors on initial resistance and process resistance was obtained, and the influence mechanism analysis was carried out based on the variance analysis result. Finally, a multiple nonlinear regression model was established successfully to predict the fatigue life and to explain the internal connection between the initial shear stiffness, shear stiffness decay rate, and fatigue life.

Asymptotics and statistics on Fishburn matrices: Dimension distribution and a conjecture of Stoimenow

AbstractWe establish the asymptotic normality of the dimension of large‐size random Fishburn matrices by a complex‐analytic approach. The corresponding dual problem of size distribution under large dimension is also addressed and follows a quadratic type normal limit law. These results represent the first of their kind and solve two open questions raised in the combinatorial literature. They are presented in a general framework where the entries of the Fishburn matrices are not limited to or nonnegative integers . The analytic saddle‐point approach we apply, based on a powerful transformation for ‐series due to Andrews and Jelínek, is also useful in solving a conjecture of Stoimenow in Vassiliev invariants.

Homogenization of discrete thin structures

We consider graphs parameterized on a portion X⊂Zd×{1,…,M}k of a cylindrical subset of the lattice Zd×Zk, and perform a discrete-to-continuum dimension-reduction process for energies defined on X of quadratic type. Our only assumptions are that X be connected as a graph and periodic in the first d-directions. We show that, upon scaling of the domain and of the energies by a small parameter ɛ, the scaled energies converge to a d-dimensional limit energy. The main technical points are a dimension-reducing coarse-graining process and a discrete version of the p-connectedness approach by Zhikov.

Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities* *S Lu is supported by NSFC (No. 11925104), Science and Technology Commission of Shanghai Municipality (19XD1420500, 21JC1400500). M Salo is supported by the Academy of Finland (Finnish Centre of Excellence in Inverse Modelling and Imaging, Grant 284715) and by the European Research Council under Horizon 2020 (ERC

We consider increasing stability in the inverse Schrödinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential function, are proposed and their performance on the inverse Schrödinger potential problem is investigated. It can be observed that higher order linearization for small boundary data can provide an increasing stability for an arbitrary power type nonlinearity term if the wavenumber is chosen large. Meanwhile, linearization with respect to the potential function leads to increasing stability for a quadratic nonlinearity term, which highlights the advantage of nonlinearity in solving the inverse Schrödinger potential problem. Noticing that both linearization approaches can be numerically approximated, we provide several reconstruction algorithms for the quadratic and general power type nonlinearity terms, where one of these algorithms is designed based on boundary measurements of multiple wavenumbers. Several numerical examples shed light on the efficiency of our proposed algorithms.

Spectral splitting method for nonlinear Schrödinger equations with quadratic potential

In this paper we propose a modified Lie-type spectral splitting approximation where the external potential is of quadratic type. It is proved that we can approximate the solution to a one-dimensional nonlinear Schrödinger equation by solving the linear problem and treating the nonlinear term separately, with a rigorous estimate of the remainder term. Furthermore, we show by means of numerical experiments that such a modified approximation is more efficient than the standard one.

Parabolic Approximation of Quasilinear Wave Equations with Applications in Nonlinear Acoustics

This work deals with the convergence analysis of parabolic perturbations to quasilinear wave equations on smooth bounded domains. In particular, we consider wave equations with nonlinearities of quadratic type, which cover the two classical models of nonlinear acoustics, the Westervelt and Kuznetsov equations. By employing a high-order energy analysis, we obtain convergence of their solutions to the corresponding inviscid equations' solutions in the standard energy norm with a linear rate, assuming small data and a sufficiently short time. The smallness of initial data can, however, be imposed in a lower-order norm than the one needed in the energy analysis. It arises only from ensuring the nondegeneracy of the studied wave equations. In addition, we address the open questions of local well-posedness of the two classical models on bounded domains with a nonnegative, possibly vanishing sound diffusivity.

The combined Shepard operator of inverse quadratic and inverse multiquadric type

"Starting with the classical, the modified and the iterative Shepard methods, we construct some new Shepard type operators, using the inverse quadratic and the inverse multiquadric radial basis functions. Given some sets of points, we compute some representative subsets of knot points following an algorithm described by J.R. McMahon in 1986."