Lower Bounds of Decay Rates for Solution to the Single-Layer Quasi-Geostrophic Model

In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizing the Fourier splitting method, under suitable assumptions on the initial data, for any multi-index α, we show that the solution Ψ satisfies .

LOWER BOUNDS ESTIMATE FOR THE BLOW-UP TIME OF A NONLINEAR NONLOCAL POROUS MEDIUM EQUATION

The lower bounds for the blow-up time of blow-up solutions to the nonlinear nolocal porous equation ut=△u^m＋u^p∫Ωu^qdxwith either null Dirichlet boundary condition or homogeneous Neumann boundary condi- tion is given in this article by using a differential inequality technique.

THE ENERGY CONSERVATIONS AND LOWER BOUNDS FOR POSSIBLE SINGULAR SOLUTIONS TO THE 3D INCOMPRESSIBLE MHD EQUATIONS

In this note,we give a new proof to the energy conservation for the weak solutions of the incompressible 3D MHD equations.Moreover,we give the lower bounds for possible singular solutions to the incompressible 3D MHD equations.

A PRIORI BOUNDS AND THE EXISTENCE OF POSITIVE SOLUTIONS FOR WEIGHTED FRACTIONAL SYSTEMS

In this paper,we prove the existence of positive solutions to the following weighted fractional system involving distinct weighted fractional Laplacians with gradient terms:{(−Δ)_(a/1)^(α/2)u1(x)=u_(1)^(q11)(x)+u_(2)^(q12)(x)+h_(1)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,(−Δ)_(a2)^(β/2)u2(x)=u_(1)^(q21)(x)+u_(2)^(q22)(x)+h_(2)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,u_(1)(x)=0,u_(2)(x)=0,x∈R^(n)∖Ω.Here(−Δ)_(a1)^(α/2) and(−Δ)_(a2)^(β/2) denote weighted fractional Laplacians andΩ⊂R^(n) is a C^(2) bounded domain.It is shown that under some assumptions on h_(i)(i=1,2),the problem admits at least one positive solution(u_(1)(x),u_(2)(x)).We first obtain the{a priori}bounds of solutions to the system by using the direct blow-up method of Chen,Li and Li.Then the proof of existence is based on a topological degree theory.

The Relationship between Energy Consumption and Economic Growth in the USA: A Non-Linear ARDL Bounds Test Approach

We study the relationship between energy consumption and economic growth in the case of USA by using an asymmetric ARDL bounds test approach to achieve the actual model. The quarterly data set covers the period of 1973:1- 2013:4. The findings indicate that the effect of energy consumption is asymmetric in the long term but not in the short term. In the long run, the effect of negative component of energy consumption on economic growth is small and statistically insignificant. The coefficient of the positive component of energy consumption is found about 0.9 and statistically significant at 1% level. We conclude that energy saving policies such as technological progress and organizational rearrangements may have the dimmer effect for the impact of a negative component of energy consumption and the booster effect for impact of the positive component of energy consumption. Thus, energy saving policy should be tightly followed by the goal of high economic growth.

A NEW METHOD FOR ESTIMATING BOUNDS OF EIGENVALUES

A new method for estimating the bounds of eigenvalues ispresented. In order to show that the method proposed is as effectiveas Qiu's an undamping spring-mass system with 5 nodes and 5 degrees ofreedom is given. To illustrate that the present method can beapplied to structures which cannot be treated by non-negativedecomposition, a plane frame with 202 nodes and 357 beam elements isgiven. The results show that the present method is effective forestimating the bounds of eigenvalues and is more common than Qiu's.

Bounds for the Zeros of a Polynomial with Restricted Coefficients

In this paper we shall obtain some interesting extensions and generalizations of a well-known theorem due to Enestrom and Kakeya according to which all the zeros of a polynomial P(Z =αnZn+...+α1Z+α0satisfying the restriction αn≥αn-1≥...≥α1≥α0≥0 lie in the closed unit disk.

Estimated Bounds for Zeros of Polynomials from Traces of Graeffe Matrices

In this paper, we combine Graeffe matrices with the classical numerical method of Dandelin-Graeffe to estimate bounds for the moduli of the zeros of polynomials. Furthermore, we give some examples showing significant gain for the convergence towards the polynomials dominant zeros moduli.

Bounds for Polynomial’s Roots from Fiedler and Sparse Companion Matrices for Submultiplicative Matrix Norms

We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial P(X) over the field C[X]. From a n×n Fiedler companion matrix C, sparse companion matrices and triangular Hessenberg matrices are introduced. Then, we identify a special triangular Hessenberg matrix Lr, supposed to provide a good estimation of the roots. By application of Gershgorin’s theorems to this special matrix in case of submultiplicative matrix norms, some estimations of bounds for roots are made. The obtained bounds have been compared to known ones from the literature precisely Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds. According to the starting formel of Lr, we see that the more we have coefficients closed to zero with a norm less than 1, the more the Sparse method is useful.

Bounds on the overall properties of composites with ellipsoidal inclusions

A new model is put forward to bound the effective elastic moduli of composites with ellipsoidal inclusions. In the present paper, transition layer for each ellipsoidal inclusion is introduced to make the trial displacement field for the upper bound and the trial stress field for the lower bound satisfy the continuous interface conditions which are absolutely necessary for the application of variational principles. According to the principles of minimum potential energy and minimum complementary energy, the upper and lower bounds on the effective elastic moduli of composites with ellipsoidal inclusions are rigorously derived. The effects of the distribution and geometric parameters of ellipsoidal in- clusions on the bounds of the effective elastic moduli are an- alyzed in details. The present upper and lower bounds are still finite when the bulk and shear moduli of ellipsoidal inclusions tend to infinity and zero, respectively. It should be mentioned that the present method is simple and needs not calculate the complex integrals of multi-point correlation functions. Meanwhile, the present paper provides an entirely different way to bound the effective elastic moduli of composites with ellipsoidal inclusions, which can be developed to obtain a series of bounds by taking different trial displacement and stress fields.

The Bounds for Eigenvalues of Normalized Laplacian Matrices and Signless Laplacian Matrices

In this paper, we found the bounds of the extreme eigenvalues of normalized Laplacian matrices and signless Laplacian matrices by using their traces. In addition, we found the bounds for k-th eigenvalues of normalized Laplacian matrix and signless Laplacian matrix.

ASYMPTOTIC EXPANSIONS OF ZEROS FOR KRAWTCHOUK POLYNOMIALS WITH ERROR BOUNDS

Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and uniform asymptotic expansions are got. Furthermore, the asymptotic expansions of the zeros for Krawtchouk polynomials are again deduced by using the property of the zeros of Airy function, and their corresponding error bounds axe discussed. The obtained results give the asymptotic property of Krawtchouk polynomials with their zeros, which are better than the results educed by Li and Wong.

BOUNDS OF THE EXPANSION COEFFICIENTS OF COMPOSITES REINFORCED BY SPHERICALLY ISOTROPIC PARTICLES

The present paper is devoted to the study of expansional behaviours of a composite reinforced by spherically isotropic particles. An exact relation is derived between the effective expansion coefficient and bulk modulus of the composite by using the concept of uniform fields in the matrix which is proposed here. Through obtaining the Paul-type bounds of the bulk modulus by using the extreme principle of energy, bounds of the effective expansion coefficient are also derivded.

Generalized gap functions and error bounds for generalized variational inequalities

We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz.

Derivation of FFT numerical bounds of the effective properties ofcomposites and polycristals

In this paper,we provide exact fast Fourier transform(FFT)-based numerical bounds for the elastic prop-erties of composites having arbitrary microstructures.Two bounds,an upper and a lower,are derivedby considering usual variational principles based on the strain and the stress potentials.The bounds arecomputed by solving the Lippmann-Schwinger equation together with the shape coefficients which al-low an exact description of the microstructure of the composite.These coefficients are the exact Fouriertransform of the characteristic functions of the phases.In this study,the geometry of the microstructureis approximated by polygonals(two-dimensional,2D objects)and by polyhedrons(three-dimensional,3Dobjects)for which exact expressions of the shape coefficients are available.Various applications are pre-sented in the paper showing the relevance of the approach.In the first benchmark example,we considerthe case of a composite with fibers.The effective elastic coefficients ares derived and compared,consider-ing the exact shape coefficient of the circular inclusion and its approximation with a polygonal.Next,thehomogenized elastic coefficients are derived for a composite reinforced by 2D flower-shaped inclusionsand with 3D toroidal-shaped inclusions.Finally,the method is applied to polycristals considering Voronoitessellations for which the description with polygonals and polyhedrons becomes exact.The comparisonwith the original FFT method of Moulinec and Suquet is provided in order to show the relevance of thesenumerical bounds.

BOUNDS FOR THE ZEROS OF POLYNOMIALS

Let P(z)= be a polynomial of degree n. In this paper we prove a more general result whichinteralia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrom-Kakeya theorem.

WEAK TYPE(1,1)BOUNDS FOR A MARCINKIEWICZ INTEGRAL

In this paper, the two-dimensional Marcinkewicz integral introduced by Stein μ(f)(x)=(∫_0~x|∫_(|x-y|≤1) _(|x-y|)^(Ω(x-y))f(y)dy|~2t^(-3)dt)~2 is shown to be of weak type (1,1) and weighted weak type (1,1) with respect to power weight |x|~' if - 1< α< 0, where Ω is homogeneous of degree 0. has mean value 0 and belongs to Llog^+L(S^1).

Novel Bounds for Solutions of Nonlinear Differential Equations

In this paper the estimates for norms of solutions to nonlinear systems are obtained via an integral inequality. As an application we considered affine control systems and systems of equations for synchronization of motions.

BOUNDS FOR SINGULAR INTEGRALS ASSOCIATED WITH A CLASS OF HYPERSURFACES

For the hypersurface Γ=(y,γ(y)), the singular integral operator along Γ is defined by. Kf(x,x_n)=P.V.∫_R^(nl), f(x-y,x_n-γ(y))_(|y|^(n-1))^(Ω(y))dy, where Ω is homogeneous of order 0, ∫_∑_(1)Ω(y')dy'=0, For a certain class of hypersurfaces. T is shown to be bounded on L^p(R^n) provided Ω∈L_α~l(Σ_(n-2)),P>1.

OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS(1)

In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.