Error bounds for spatial discretization and waveform relaxation applied to parabolic functional differential equations

The process of semi-discretization and waveform relaxation are applied to general nonlinear parabolic functional differential equations. Two new theorems are presented, which extend and improve some of the classical results. The first of these theorems gives an upper bound for the norm of the error of finite difference semi-discretization. This upper bound is sharper than the classical error bound. The second of these theorems gives an upper bound for the norm of the error, which is caused by both semi-discretization and waveform relaxation. The focus in the paper is on estimating this error directly without using the upper bound for the error, which is caused by the process of semi-discretization and the upper bound for the error, which is caused by the waveform relaxation method. Such estimating gives sharper error bound than the bound, which is obtained by estimating both errors separately.     

Estimates of the rate of convergence of a dynamic reconstruction algorithm under incomplete information about the phase state

In this paper, we study a dynamic reconstruction algorithm which reconstructs the unknown unbounded input and all unobservable phase coordinates from the results of measurements of part of the coordinates. An upper and a lower bound for the accuracy of the reconstruction is obtained. We determine the class of inputs for which the upper bound is uniform. We give a condition for optimally matching the algorithm parameters, ensuring the highest order of the upper bound and equating the orders of the upper and lower bounds. Thus, we establish the sharpness of the upper bound.     

Maximal amplitudes of hyperelliptic solutions of the derivative nonlinear Schrödinger equation

A simple formula is proven for an upper bound for amplitudes of hyperelliptic (finite-gap or N-phase) solutions of the derivative nonlinear Schrödinger equation. The upper bound is sharp, viz, it is attained for some initial conditions. The method used to prove the upper bound is the same method, with necessary modifications, used to prove the corresponding bound for solutions of the focusing NLS equation (Wright OC, III. Sharp upper bound for amplitudes of hyperelliptic solutions of the focusing nonlinear Schrödinger equation. Nonlinearity. 2019;32:1929-1966).     

On field extensions given by periods of Drinfeld modules

In this short note, we answer a question raised by M. Papikian on a universal upper bound for the degree of the extension of $$K_\infty $$ given by adjoining the periods of a Drinfeld module of rank 2. We show that contrary to the rank 1 case such a universal upper bound does not exist, and the proof generalies to higher rank. Moreover, we give an upper and lower bound for the extension degree depending on the valuations of the defining coefficients of the Drinfeld module. In particular, the lower bound shows the non-existence of a universal upper bound.     

A new upper bound for unconstrained two-dimensional cutting and packing

A new upper bound for the unconstrained two-dimensional cutting or packing problem is proposed in this paper. The proposed upper bound can be calculated for any size of plate by solving just two knapsack problems at the beginning of the algorithm. In this research, the proposed upper bound was applied to the well known exact cutting algorithm, although it can be used for both cutting and packing applications. The experimental results demonstrate that the new upper bound is very efficient, and reduces the search time required to find an optimal solution.     

An upper bound for the number of matroids

An upper bound for the number of matroids is obtained. This upper bound complements the lower bound obtained by Piff and Welsh in [1].     

相关随机利率下的双二项模型的破产概率

研究带有相关随机利率的双二项风险模型,得到了破产概率的积分表达式,并利用鞅分析的方法得到了破产概率的经典Lundberg上界,另外给出了一个破产概率的比经典Lundberg上界更精确的上界.     

A note on construction of upper bound graphs

In this paper, we consider construction of upper bound graphs. An upper bound graph can be transformed into a nova by contractions and a nova can be transformed into an upper bound graph by splits. These results include a characterization on upper bound graphs.     

Inequality for the Moment of a Function of a Random Variable

ＩｎｅｑｕａｌｉｔｙｆｏｒｔｈｅＭｏｍｅｎｔｏｆａＦｕｎｃｔｉｏｎｏｆａＲａｎｄｏｍＶａｒｉａｂｌｅ￥ＬｉＢａｉｎｉａｎＨｕＳｈｕｈｅ（李柏年，胡舒合）（ＡｎｈｕｉＩｎｓｔｉｔｕｔｅｏｆＦｉｎａｎｃｅａｎｄＴｒａｄｅ）（ＡｎｈｕｉＵｎｉｖｅｒｓｉｔｙ...     

A degree bound for families of rational curves on surfaces

We give an upper bound for the degree of rational curves in a family that covers a given birationally ruled surface in projective space. The upper bound is stated in terms of the degree, sectional genus and arithmetic genus of the surface. We introduce an algorithm for constructing examples where the upper bound is tight. As an application of our methods we improve an inequality on lattice polygons.     

An improved balanced job bound analysis of closed queuing networks

Balanced job bounds (BJB) is a technique for obtaining lower and upper bounds on the throughput of a separable closed queuing network. The conceptual simplicity and the low computational complexity of this technique make these bounds very attractive. However, whereas the lower bound is usually quite good, the upper bound may be loose. In this paper, we present an improved BJB analysis for obtaining a tight upper bound.     

Approximation of differentiation operator in the space L 2 on semiaxis

We establish an upper bound for the error of the best approximation of the first order differentiation operator by linear bounded operators on the set of twice differentiable functions in the space L ₂ on the half-line. This upper bound is close to a known lower bound and improves the previously known upper bound due to E. E. Berdysheva. We use a specific operator that is introduced and studied in the paper.     

Multidimensional van der Corput and sublevel set estimates

Van der Corput's lemma gives an upper bound for one-dimensional oscillatory integrals that depends only on a lower bound for some derivative of the phase, not on any upper bound of any sort. We establish generalizations to higher dimensions, in which the only hypothesis is that a partial derivative of the phase is assumed bounded below by a positive constant. Analogous upper bounds for measures of sublevel sets are also obtained. The analysis, particularly for the sublevel set estimates, has a more combinatorial flavour than in the one-dimensional case.

     

On the Trace of Algebraic Integers of Small Height

We give an upper bound for the modulus of the first non–zero trace among natural powers of an algebraic integer of small house. An upper bound for this power is obtained for the Pisot and Salem numbers. Although the house of these numbers is not at all small, similar bounds for the first non–zero trace are also established. Finally, we give an upper bound for the trace of an algebraic number with the Mahler measure bounded above by the square root of the degree.     

Dynamic programming algorithms for the bi-objective integer knapsack problem

This paper presents two new dynamic programming (DP) algorithms to find the exact Pareto frontier for the bi-objective integer knapsack problem. First, a property of the traditional DP algorithm for the multi-objective integer knapsack problem is identified. The first algorithm is developed by directly using the property. The second algorithm is a hybrid DP approach using the concept of the bound sets. The property is used in conjunction with the bound sets. Next, the numerical experiments showed that a promising partial solution can be sometimes discarded if the solutions of the linear relaxation for the subproblem associated with the partial solution are directly used to estimate an upper bound set. It means that the upper bound set is underestimated. Then, an extended upper bound set is proposed on the basis of the set of linear relaxation solutions. The efficiency of the hybrid algorithm is improved by tightening the proposed upper bound set. The numerical results obtained from different types of bi-objective instances show the effectiveness of the proposed approach.     

算术级数中的奇数Goldbach问题

本文给出了算术级数的模的精确数值上界,在该算术级数中奇数Goldbach问题可解。我们的结果蕴含了Linnik常数的一个数值上界。     

A quadratic programming approach to the determination of an upper bound on the weighted stability number

In a previous work, the authors have introduced an upper bound on the stability number of a graph and several of its properties were given. The determination of this upper bound was done by a quadratic programming approach whose implementation has given good computational results. We now extend this bound to the weighted case, i.e., an upper bound on the weighted stability of an arbitrary graph with node weights is presented. Similarly to the non-weighted case, the deduced bound allows us to give a necessary and sufficient condition to a weighted graph that attains the given bound. Also a heuristic for determining the maximum weight stable set is proposed which is based on an integrality property of a convex quadratic problem that produces the bound. Some comments about the proposed approach will conclude the paper.     

Inside S-inner product sets and Euclidean designs

A finite set X in the Euclidean space is called an s-inner product set if the set of the usual inner products of any two distinct points in X has size s. First, we give a special upper bound for the cardinality of an s-inner product set on concentric spheres. The upper bound coincides with the known lower bound for the size of a Euclidean 2s-design. Secondly, we prove the non-existence of 2- or 3-inner product sets on two concentric spheres attaining the upper bound for any d>1. The efficient property needed to prove the upper bound for an s-inner product set gives the new concept, inside s-inner product sets. We characterize the most known tight Euclidean designs as inside s-inner product sets attaining the upper bound.     

On finding a worst-case optimal Fourth Normal Form database decomposition

Although several Fourth Normal Form (4NF) decomposition algorithms have been published, the problem's computational complexity remains an open question. Part of the difficulty is that no one has established an upper bound on the size of a 4NF decomposition scheme for a given number of attributes. We prove such an upper bound and we present an algorithm which is worst-case optimal: it never produces a 4NF decomposition scheme that is larger than the upper bound.     

HARVEST PLANNING UNDER UNCERTAIN EXTINCTION TIME

ABSTRACT. Harvesting a targeted commercial species results in impacts on an endangered species which may have no direct market value but may need protection as mandated by environmental laws. A vigorous harvest path might drive the endangered species to extinction. This paper studies harvest planning when the endangered species is subject to an uncertain extinction time. It is shown that the optimal static harvest level under certainty can be used as an upper bound for the entire dynamic harvest time path under uncertainty. The paper also develops an explicit upper bound for the entire harvest path under uncertain extinction time of the endangered species. It is demonstrated that an increase in the hazard rate of the endangered species will shift down the upper bound for the entire harvest path, whereas an increase in the growth rate of the commercial species will shift up the upper bound for the entire harvest path.