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 Estimation for Lower Bounds of the Solutions of Fermat's Equation

Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.

Remarks on the lower bounds for sums of the BDH type

This paper will correct some gaps existing in the proof of a theorem written in an earlier paper by the author on the lower bounds for sums of BDH type published in 1993. Some improvements upon the previous version of that theorem will be obtained.

NEW LOWER BOUNDS FOR LEE DISCREPANCY ON TWO AND THREE MIXED LEVELS FACTORIALS

The objective of this paper is to study the issue of uniformity on asymmetrical designs with two and three mixed levels in terms of Lee discrepancy. Based on the known formulation, we present a new lower bound of Lee discrepancy of fractional factorial designs with two and three mixed levels. Our new lower bound is sharper and more valid than other existing lower bounds in literature, which is a useful complement to the lower bound theory of discrepancies.

LOWER BOUNDS OF BLOW UP TIME FOR A SYSTEM OF SEMI-LINEAR HYPERBOLIC PETROVSKY EQUATIONS

Li et al. in [3] obtained blow-up results for a system of Petrovskey equations in some different cases. In this article we obtain lower bounds for the blow up time under some considerations on initial data.

Lower bounds and modified LPT algorithm for k-partitioning problems with partition matroid constraint

In this paper, the k-partitioning problem with partition matroid constraint is considered. LPT algorithm is modified to fit the problem and its worst-ease performance is analyzed. The lower bounds of optimal solution for the min-max problem are given.

Multistatic radar analysis based on ambiguity function and Cramér-Rao lower bounds

The primary goal of this work is to characterize the impact of weighting selection strategy and multistatic geometry on the multistatic radar performance. With the relationship between the multistatic ambiguity function （AF） and the multistatie Cram6r-Rao lower bound （CRLB）, the problem of calculating the multistatic AF and the multistatic CRLB as a performance metric for multistatic radar system is studied. Exactly, based on the proper selection of the system parameters, the multistatic radar performance can be significantly improved. The simulation results illustrate that the multistatic AF and the multistatic CRLB can serve as guidelines for future multistatic fusion rule development and multistatic radars deployment.

LOWER BOUNDS ON THE MAXIMUM GENUS OF LOOPLESS MULTIGRAPHS

The lower bounds on the maximum genus of loopless graphs are obtained according to the connectivity of these graphs. This not only answers a question of Chen, Archdeacon and Gross, but also generalizes the previous known results. Thus, a picture of the lower bounds on the maximum genus of loopless multigraphs is presented.

Lower Bounds of Blow Up Time for a Class of Slow Reaction Diffusion Equations with Inner Absorption Terms

In this paper,a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied.By using the technique of improved differential inequality,the lower bounds of blow up time for the system under either homogeneous Dirichlet or nonhomogeneous Neumann boundary conditions are obtained.

Lower Bounds for Moments of Quadratic Twisted Self-dual GL(3)Central L-values

In this paper,we prove the conjectured order lower bound for the k-th moment of central values of quadratic twisted self-dual GL(3)L-functions for all k≥1,based on our recent work on the twisted first moment of central values in this family of L-functions.

Optimization of Generator Based on Gaussian Process Regression Model with Conditional Likelihood Lower Bound Search

The noise that comes from finite element simulation often causes the model to fall into the local optimal solution and over fitting during optimization of generator.Thus,this paper proposes a Gaussian Process Regression(GPR)model based on Conditional Likelihood Lower Bound Search(CLLBS)to optimize the design of the generator,which can filter the noise in the data and search for global optimization by combining the Conditional Likelihood Lower Bound Search method.Taking the efficiency optimization of 15 kW Permanent Magnet Synchronous Motor as an example.Firstly,this method uses the elementary effect analysis to choose the sensitive variables,combining the evolutionary algorithm to design the super Latin cube sampling plan;Then the generator-converter system is simulated by establishing a co-simulation platform to obtain data.A Gaussian process regression model combing the method of the conditional likelihood lower bound search is established,which combined the chi-square test to optimize the accuracy of the model globally.Secondly,after the model reaches the accuracy,the Pareto frontier is obtained through the NSGA-II algorithm by considering the maximum output torque as a constraint.Last,the constrained optimization is transformed into an unconstrained optimizing problem by introducing maximum constrained improvement expectation(CEI)optimization method based on the re-interpolation model,which cross-validated the optimization results of the Gaussian process regression model.The above method increase the efficiency of generator by 0.76%and 0.5%respectively;And this method can be used for rapid modeling and multi-objective optimization of generator systems.

Lower bounds on the periodic Hamming correlations of frequency hopping sequences with low hit zone

In this paper, several periodic Hamming correlation lower bounds for frequency hopping sequences with low hit zone, with respect to the size p of the frequency slot set, the sequence length L, the family size M, low hit zone LH （ or no hit zone NH ）, the maximum periodic Hamming autocorrelation sidelobe Ha and the maximum periodic Hamming crosscorrelation He, are established. It is shown that the new bounds include the known LempeI-Greenberger bounds, T.S. Seay bounds and Peng-Fan bounds for the conventional frequency hopping sequences as special cases.

The lower bounds of classic Ramsey number R(5,9). and R (5,10)

IT is very difficult to establish the Ramsey number, so we often use the way of getting the up-per and lower bound of the Ramsey number to near the exact value. All lower bounds of R (5,l) known so far are shown in table 1.

Lower Bounds on the(Laplacian) Spectral Radius of Weighted Graphs

The weighted graphs, where the edge weights are positive numbers, are considered. The authors obtain some lower bounds on the spectral radius and the Laplacian spectral radius of weighted graphs, and characterize the graphs for which the bounds are attained. Moreover, some known lower bounds on the spectral radius and the Laplacian spectral radius of unweighted graphs can be deduced from the bounds.

LOWER BOUNDS FOR WEAK BYZANTINE AGREEMENT

Lower bounds for Byzantine agreement obtained by Dolev and Strong are shown, by a simplermethod, also to be true for weak Byzantine agreement.

On Lower Bounds for Linear Forms in the Values of a Class of p-adic G-functions

We obtain effective lower bounds for certain linear combinations of the valuesat algebraic points of a class of p-adic G-functions defined over a completion of analgebraic closure of a p-adio field.

The correction operator for the canonical interpolation operator of the Adini element and the lower bounds of eigenvalues

In this paper,we develop a correction operator for the canonical interpolation operator of the Adini element.We use this new correction operator to analyze the discrete eigenvalues of the Adini element method for the fourth order elliptic eigenvalue problem in the three dimensions.We prove that the discrete eigenvalues are smaller than the exact ones.

On the lower bounds of the curvatures in a bounded domain

Let KD（z, z） be the Bergman kernel of a bounded domain 7P in Cn and Sect （z, ） and Ricci （z, ） be the holomorphic sectional curvature and Ricci curvature of the Bergman metric ds2 = T T：）（z,N）dzCdz respectively at the point z E T with tangent vector . It is proved by constructing suitable minimal functions that where z ∈D1 D D2, D1 is a ball contained in D and D2 is a ball containing D.

THE PERIODIC CAPACITATED ARC ROUTING PROBLEM LINEAR PROGRAMMING MODEL, METAHEURISTIC AND LOWER BOUNDS

The Periodic Capacitated Arc Routing Problem (PCARP) generalizes the well known NP-hard Capacitated Arc Routing Problem (CARP) by extending the single period to multi-period horizon. The Capacitated Arc Routing Problem (CARP) is defined on an undirected network in which a fleet of identical vehicles is based at a depot node. A subset of edges, called tasks, must be serviced by a vehicle. The CARP consists of determining a set of feasible vehicle trips that minimizes the total cost of traversed edges. The PCARP involves the assignment of tasks to periods and the determination of vehicles trips in each period, to minimize the total cost on the whole horizon. This new problem arises in various real life applications such as waste collection, mail delivery, etc. In this paper, a new linear programming model and preliminary lower bounds based on graph transformation are proposed. A meta-heuristic approach - Scatter Search (SS) is developed for the PCARP and evaluated on a large variety of instances.