Search

This paper is devoted to the study of a new class of nonlinear obstacle problems involving nonhomogeneous partial differential operators and mixed boundary conditions. We provide the existence and uniqueness of the solution for the obstacle problem via applying a surjectivity theorem for set-valued mappings formulated by the sum of a set-valued pseudomonotone operator and a maximal monotone set-valued operator. Moreover, some upper bounds to the obstacle problem are established by using a regularized gap function through different norms. [ABSTRACT FROM AUTHOR]

Mining a weighted single large graph has recently attracted many researchers. The WeGraMi algorithm is considered the state-of-the-art among current approaches. It uses a MaxMin measure to calculate weights for all mined subgraphs. However, if all values in the domain have the same role and the user needs an average value of that domain, then we have to use another measure. In this paper, we introduce a novel algorithm called AWeGraMi (Average Weighted Graph Mining) to solve the above problem, and our method calculates the weight based on the average of all values in the domain. We also apply the MaxMin measure as an upper-bound to prune the search space. The new algorithm can mine all frequent weighted subgraphs effectively. Our experiments on the directed and undirected datasets have shown that AWeGraMi has better performance in comparison to post-processing GraMi for all three criteria: search space (the number of candidate subgraphs), running time, and memory consumption. [ABSTRACT FROM AUTHOR]

Discovering high utility sequences in a quantitative database is a popular data mining task. The goal is to enumerate all sequences of items (symbols) that have a high value for the user, as measured by a utility function. A representative application of high utility sequence mining is the identification of profitable sequences of purchases in transactions from online stores. Though useful, a drawback of that task is that the cost of items is not considered. However, cost is a key factor for decision-making in that domain and many others. To consider both the cost and utility of items for sequence mining, this paper defines a novel problem FLCHUSM of mining frequent sequences having a high average utility and a low average cost. Though the proposed problem is a generalization of the traditional problem of frequent sequence mining, it is more challenging because the average utility and average cost functions do not satisfy the downward-closure property traditionally used to reduce the search space. To offer a solution to this issue, this paper presents a lower bound on the cost and two novel upper bounds on the utility. Besides, four width, depth pruning, reducing and tightening strategies are devised to eliminate unpromising patterns from the search space. Taking these theoretical results as a foundation, a new CUL (Cost-Utility List) data structure is conceived for storing and quickly updating the utility and cost information of patterns, and a novel algorithm named FLCHUSPM is proposed for FLCHUSM . Results from several experiments show that FLCHUSPM is efficient in terms of memory usage and runtime, and that interesting patterns can be discovered in real data. [ABSTRACT FROM AUTHOR]

High utility sequence mining is a popular data mining task, which aims at finding sequences having a high utility (importance) in a quantitative sequence database. Though it has several applications, state-of-the-art algorithms have one or more of the following limitations: (1) they rely on a utility function that tends to be biased toward finding long patterns, (2) some algorithms do take pattern length into account using an average-utility function but they adopt an optimistic perspective that can be risky or misleading for some applications, (3) they do not let the user specify additional constraints on patterns to be found. To address these three limitations, this paper defines a novel task of mining frequent high minimum average-utility sequences (FHAUS) with constraints in a quantitative sequence database. This task has the following benefits. First, it uses the average-utility au function based on the minimum utility, which takes the length of a pattern into account to calculate its utility. This helps finding short patterns missed by traditional algorithms and it is based on more safe pessimistic utility calculations. Second, the user can specify a set of monotonic and anti-monotonic constraints C on patterns to filter irrelevant patterns and improve the performance of the mining process. To efficiently find all FHAUSs with constraints, this paper first proposes some novel upper bounds (UBs) and weak upper bounds (WUBs) on the average-utility, which satisfy downward-closure (DC) properties or DC-like properties. Then, to effectively reduce the search space, the paper designs novel width pruning, depth pruning, reducing, and tightening strategies based on the proposed bounds. These proposed novel theoretical results are integrated into an algorithm named C-FHAUSPM (Constrained Frequent High minimum Average-Utility Sequential Pattern Mining) for efficiently discovering all FHAUSs with constraints. Results from extensive experiments on both real-life and synthetic quantitative sequence databases show that C-FHAUSPM is highly efficient in terms of runtime and memory usage. [ABSTRACT FROM AUTHOR]

The Maximum Clique Problem (MCP) is a classic NP-hard problem, which has the goal of finding the largest possible clique. It is known to have direct applications in a wide spectrum of fields such as data association problems appearing in bioinformatics and computational biology, computer vision and robotics. Solutions like using brute force, backtracking and branch and bound are designed to deal with the maximum problem. In the branch and bound method, a branch is pruned if the currently found largest clique is better than its upper bound. However, the upper bound obtained by current methods is often not close enough to the ω (G) , leading to large inefficient search space. This paper discusses the branch and bound procedure to solve the maximum clique problem in large and sparse graphs and proposes a new efficient branch and bound maximum clique algorithm named SMC-BRB. SMC-BRB solves the maximum clique problem in heuristic search stage and exact search stage. It simultaneously utilizes the s + -index and color-based upper bound in heuristic search stage, which effectively reduces the number of branches in the exact search stage. This method is beneficial to the solution of MCP because it provides a scale reduction on heuristic search stage. Experimental results show that SMC-BRB has better performance than the state-of-the-art algorithm MC-BRB, which demonstrates the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we derive some upper bounds for the dominant eigenvalue of a matrix with some negative entries, which possess the Perron–Frobenius property. Numerical examples are given to illustrate the effectiveness of our new upper bounds. [ABSTRACT FROM AUTHOR]

We study extremal problems related to the best joint polynomial approximation of functions analytic in the unit disk and belonging to the Bergman space . The problem of joint approximation of periodic functions and their derivatives by trigonometric polynomials was considered by Garkavy [1] in 1960. Then, in the same year, Timan [2] considered this problem for classes of entire functions defined on the entire axis. The problem of joint approximation of functions and their derivatives is considered in more detail in Malozemov's monograph [3], where some classical theorems of the theory of approximation of functions are presented and generalized. In the present paper, a number of exact theorems are obtained and sharp upper bounds for the best joint approximations of a function and its successive derivatives by polynomials and their respective derivatives on some classes of complex functions belonging to the Bergman space are calculated. [ABSTRACT FROM AUTHOR]

The spatial behavior of solutions is studied in the model of Forchheimer equations. Using the energy estimate method and the differential inequality technology, exponential decay bounds for solutions are derived. To make the decay bounds explicit, we obtain the upper bound for the total energy. We also extend the study of spatial behavior of Forchheimer porous material in a saturated porous medium. [ABSTRACT FROM AUTHOR]

In this paper, we consider a perturbed compound Poisson risk model with stochastic premiums and constant interest force. We obtain the upper bound and Lundberg-Cramér approximation for the infinite-time ruin probability, and consider the asymptotic formula for the finite-time ruin probability when the claim size is heavy-tailed. We show that the model in our paper has similar results to the classical risk process and some existing generalized models. [ABSTRACT FROM AUTHOR]

Two efficient tree structures known as Can-tree (Leung et al., Knowledge and Information Systems, 11(3), 287–311, 2007) and FP-tree (Han et al., 2000) are used to store a database in memory for mining frequent patterns. However, there has been no discussion on tight upper bound for the number of nodes in these trees. Instead, a very loose upper bound of 2n (where n is the number of distinct items in the database) is used. In this paper, we provide a tighter upper bound for the number of nodes in Can-tree and FP-tree. The upper bound on the number of nodes is provided through a greedy algorithm for the Can-tree and a closed form solution is derived for the FP-tree. These results are illustrated by examples both in graphical and mathematical form. [ABSTRACT FROM AUTHOR]

Frameproof codes (FPCs) are widely studied as they are classic fingerprinting codes that can protect copyrighted materials. The main interests are construction methods and bounds of the number of codewords of FPCs for a fixed length when the alphabet size approaches infinity. In this paper, we focus on the upper bound of the size of FPCs when the fixed length is 4 and the strength is 2. We obtain an upper bound 2q2-2q+7 on the size of a q-ary 2-FPC of length 4 for any positive integer q>48. The best previously well known bound of this type of FPCs is 2q2-2, which is due to Blackburn (SIAM J Discret Math 16:499-510, 2003). Our new upper bound improves the previous upper bound and it is not very far from the current best lower bound 2q2-4q+3 obtained from the explicit construction due to Chee and Zhang (IEEE Trans Inf Theory 58:5449-5453, 2012). [ABSTRACT FROM AUTHOR]

This paper is concerned with the study of the nonlinear damped wave equation utt+Δ2u−Δu−ωΔut+α(t)ut=up−2u, in a bounded domain with smooth boundary. The blow-up of solutions are investigated under some conditions. Both lower and upper bounds for the blow-up time are derived when blow-up occurs. [ABSTRACT FROM AUTHOR]

High-utility itemset mining is a prominent data-mining technique where the profit or weight of itemsets plays a crucial role in defining meaningful patterns. High average-utility itemset (HAUI) mining is an advancement over high-utility itemset mining, which introduces an unbiased measure called average utility to associate the utility of itemsets with their length. Several existing HAUI mining algorithms use various upper bounds such as average-utility upper bound, revised tighter upper bound, and looser upper bound to preserve pruning methods. However, these upper bounds overestimate the average-utility of itemsets and slow down the mining process. This paper presents a fast high average-utility itemset miner (FHAIM) algorithm, which uses two improved upper bounds and several efficient pruning strategies to avoid the processing of unpromising candidate itemsets. Moreover, a novel list structure named recommended average-utility list (RAUL) is presented to store the average-utility and the required information for pruning. The RAUL for an itemset can be constructed by joining the RAULs of its subsets to avoid excessive database scans. We have performed substantial experiments on various benchmark datasets to evaluate the performance of the FHAIM in comparison with two existing HAUI mining algorithms. Experimental results show that FHAIM outperforms the existing HAUI mining algorithms in terms of runtime, memory usage, join counts, and scalability. [ABSTRACT FROM AUTHOR]

In this paper, following the Backus (in J. Geophys. Res. 67(11):4427-4440, 1962) approach, we examine expressions for elasticity parameters of a homogeneous generally anisotropic medium that is long-wave-equivalent to a stack of thin generally anisotropic layers. These expressions reduce to the results of Backus (1962) for the case of isotropic and transversely isotropic layers. In the over half-a-century since the publications of Backus (1962) there have been numerous publications applying and extending that formulation. However, neither George Backus nor the authors of the present paper are aware of further examinations of the mathematical underpinnings of the original formulation; hence this paper. We prove that-within the long-wave approximation-if the thin layers obey stability conditions, then so does the equivalent medium. We examine-within the Backus-average context-the approximation of the average of a product as the product of averages, which underlies the averaging process. In the presented examination we use the expression of Hooke's law as a tensor equation; in other words, we use Kelvin's-as opposed to Voigt's-notation. In general, the tensorial notation allows us to conveniently examine effects due to rotations of coordinate systems. [ABSTRACT FROM AUTHOR]

This paper considers the following semilinear pseudo-parabolic equation with a nonlocal source: and it explores the characters of blow-up time for solutions, obtaining a lower bound as well as an upper bound for the blow-up time under different conditions, respectively. Also, we investigate a nonblow-up criterion and compute an exact exponential decay. [ABSTRACT FROM AUTHOR]

In this paper, finite time blow-up property of solutions to a p-Kirchhoff-type parabolic equation with general nonlinearity is considered. Some sufficient conditions are given for the weak solutions to blow up in finite time. An upper bound for the blow-up time is also derived. The results partially generalize some recent ones reported by Han and Li (Comput Math Appl. 2018;75:3283–3297). [ABSTRACT FROM AUTHOR]

In this paper, we propose a joint decoding scheme called AC-MAP decoder for multiple input single output (MISO) wireless cooperative communication network that consists of single source, single relay, and single destination. The proposed scheme is based on both Alamouti combining (AC) scheme and maximum a posteriori (MAP) decoder and is used to estimate the data at the destination. The AC-MAP decoder is optimal in the sense that it minimizes the end-to-end bit error rate (BER). In order to analyze performance of the proposed decoder, we derive a closed form expression for the upper bound (UB) on the end-to-end error probability. Distances between system nodes, transmit energy, and channel noise and fading effects are considered in the derivation of the UB. Numerical results show that the closed form UB is very tight and it almost coincides with the exact BER results obtained from simulations. Therefore, we use the derived UB expression to study the effects of the relay position on the BER performance and to find the optimal location of the relay node. [ABSTRACT FROM AUTHOR]

The model of a channel that describes the transmission of information in communication systems with a single-user receiver based on order statistics is considered. The transmission of information through such a channel using a linear block code is studied. The aim of this paper is to find an upper bound on error probability for the case in which exhaustive search and a given decoding criterion are used. [ABSTRACT FROM AUTHOR]

Spectra attacks proposed recently are more data efficient than algebraic attacks against stream cipher. They are also time-and-space efficient. A measurement of the security of a stream cipher against spectra attacks is the spectral immunity, the lowest linear complexity of annihilators of the key stream. Under the restriction to binary annihilators, this paper first studies the tight upper bound on spectral immunities of periodic sequences, and sequences whose spectral immunities achieve this upper bound are corresponding to Boolean functions achieving optimal algebraic immunities. Secondly, the asymptotic behavior on spectral immunities of sequences corresponding to $$n$$ -variable balanced Boolean functions is discussed, which shows that almost all such sequences have high spectral immunities. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Central South University is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we make an attempt to introduce a new subclass of analytic functions. Using the Toeplitz determinants, we obtain the best possible upper bound for the third-order Hankel determinant associated with the kth root transform [f(zk)]1/k of the normalized analytic function f(z) when it belongs to this class, defined on the open unit disc in the complex plane. [ABSTRACT FROM AUTHOR]

In this paper, the upper bound method has been used to analyze of flat rolling process and prediction of internal defects for rigid plastic materials. The inlet and outlet shear boundaries of the deformation region are assumed to be arbitrarily curved surfaces. A unified kinematically admissible velocity field has been proposed. This field permits the possible formation of internal defects during the rolling process. A criterion has been presented to predict the occurrence of split ends and central burst defects during the flat rolling process for a given rolling condition. The corresponding results are compared with some experiments performed by authors and also with the theoretical published data. These comparisons show a good agreement. Finally, the effects of the reduction in area on the safe and unsafe zones are investigated. [ABSTRACT FROM AUTHOR]

Iterative localization algorithms are critical part in the control of mobile autonomous robots because they feed fundamental position information to the robots. In a harsh unknown environment, the estimation of environmental noise is hardly obtained during the movement of the robots. It means that the state-of-the-art methods, which increase localization accuracy using error management, are unsuitable. In this paper, we deduced an upper bound of the localization error without knowing the precise model of environment noise when the anchor nodes have position errors. Utilizing the minimum upper bound, we can construct an optimal localization linear system of iterative localization algorithms based on least square. An algorithm of generating localization linear system is proposed by using the minimum upper bound. The algorithm reduces the impact of the shortage of environmental information on localization error propagation. Our simulation results show that the algorithm is insensitive to noise and can improve the localization accuracy by constructing a proper localization linear system with a high probability. [ABSTRACT FROM AUTHOR]

Reduction of unnecessary energy consumption is becoming a major concern in green wireless sensor networks. Sleep scheduling is one of the efficient strategies to achieve energy saving. In this paper, we propose a novel scheme for the sleep scheduling, which is based on Decentralized Partially Observable Markov Decision Process (Dec-POMDP). A sleep scheduling algorithm with online planning (Dec-POP-SSA) with respect to Dec-POMDP is also presented. In Dec-POMDP, due to the hardness of obtaining the state spaces and the reward with mold-free environment, quasi-Monte Carlo is applied to collect state spaces such that the real-time acquisition of beliefs state is achieved, and the reward is evaluated in tracking reward and coverage connectivity intensity. Instead of producing the entire plan, Dec-POP-SSA need only find actions for the current step. We also give the theoretical analysis on the upper bound for Dec-POP-SSA. The numerical experiments show that Dec-POP-SSA may receive the highest reward. [ABSTRACT FROM AUTHOR]

Direction of arrival (DOA) estimation has been discussed extensively in the array signal processing field. In this paper, the authors focus on the multi-source DOA information which is defined as the mutual information between the DOA and the received signal contaminated by complex additive white Gaussian noise. A theoretical expression of DOA information with multiple sources is derived for the uniform linear array. At high SNRs and under the sparse-source assumption obtained is the upper bound of DOA information contained in K sparse sources which can be regarded as the sum of all single-source information minus the uncertainty of sources' order logK!. Moreover, because of the uncertainty of multi-sources' order, the posteriori probability distribution of DOA no longer obeys single peak Gaussian distribution so that the mean square error is unsuitable in evaluating the performance of multi-dimensional parameter estimation. Consequently, entropy error (EE) is used as a new performance evaluation metric, whose relationship with DOA information is given. [ABSTRACT FROM AUTHOR]

The objective of this paper is to obtain an upper bound to the functional | a a − a| for the function f and its inverse belonging to certain subclasses of analytic functions, using Toeplitz determinants. [ABSTRACT FROM AUTHOR]

Exact constants in Jackson–Stechkin type inequalities are found for the smoothness characteristics , , determined by averaging the norm of finite differences of th order of functions . A solution is given of the extremal problem of finding the supremum for best joint polynomial approximations of functions and their successive derivatives on some classes of functions from whose averaged norms of finite differences are bounded above by . [ABSTRACT FROM AUTHOR]

An upper bound of in-plane shear modulus for a general class of unidirectional fibrous polymeric composites of periodic structure is presented in an explicit form, according to linear elasticity approach. The fibers that reinforce the polymeric matrix are continuous, parallel to each other, and thus, no agglomeration occurs. To formulate the fiber arrangement inside the matrix, a reliable geometric body-centered model was adopted. The theoretical predictions were compared with experimental data found in the literature, together with theoretical results obtained from other workers, and a reasonable accordance was observed. [ABSTRACT FROM AUTHOR]

The concept of pattern arises in many applications comprising experimental trials with two or more possible outcomes in each trial. A binary scan of type r / k is a special pattern referring to success-failure strings of fixed length k that contain at least r-successes, where r, k are positive integers with r≤k. The multiple scan statistic Wt,k,r is defined as the enumerating random variable for the overlapping moving windows occurring until trial t which include a scan of type r / k. In the present work, we consider a sequence of independent binary trials with not necessarily equal probabilities of success and develop upper bounds for the probability of the event that the multiple scan statistic will perform a jump from ℓ to ℓ+1 (where ℓ is a nonnegative integer) in a finite time horizon. [ABSTRACT FROM AUTHOR]

For a simple graph G on n vertices and an integer k with 1 ⩽ k ⩽ n, denote by Sk+ (G) the sum of k largest signless Laplacian eigenvalues of G. It was conjectured that Sk+(G)⩽e(G)+(2k+1) (G) ⩽ e(G) + (k+1 2), where e(G) is the number of edges of G. This conjecture has been proved to be true for all graphs when k ∈ {1, 2, n − 1, n}, and for trees, unicyclic graphs, bicyclic graphs and regular graphs (for all k). In this note, this conjecture is proved to be true for all graphs when k = n − 2, and for some new classes of graphs. [ABSTRACT FROM AUTHOR]

A new mathematical model is considered related to competitive location problems where two competing parties, the Leader and the Follower, successively open their facilities and try to win customers. In the model, we consider a situation of several alternative demand scenarios which differ by the composition of customers and their preferences.We assume that the costs of opening a facility depend on its capacity; therefore, the Leader, making decisions on the placement of facilities, must determine their capacities taking into account all possible demand scenarios and the response of the Follower. For the bilevel model suggested, a problem of finding an optimistic optimal solution is formulated. We show that this problem can be represented as a problem of maximizing a pseudo- Boolean function with the number of variables equal to the number of possible locations of the Leader's facilities.We propose a novel systemof estimating the subsets that allows us to supplement the estimating problems, used to calculate the upper bounds for the constructed pseudo-Boolean function, with additional constraints which improve the upper bounds. [ABSTRACT FROM AUTHOR]

We present a method for computing an upper bound on the contact stress of elastic bodies. The continuum model of elastic bodies with contact is first modeled as a constrained optimization problem by using finite elements. An explicit formulation of the total contact force, a fraction function with the numerator as a linear function and the denominator as a quadratic convex function, is derived with only the normalized nodal contact forces as the constrained variables in a standard simplex. Then two bounds are obtained for the sum of the nodal contact forces. The first is an explicit formulation of matrices of the finite element model, derived by maximizing the fraction function under the constraint that the sum of the normalized nodal contact forces is one. The second bound is solved by first maximizing the fraction function subject to the standard simplex and then using Dinkelbach's algorithm for fractional programming to find the maximum-since the fraction function is pseudo concave in a neighborhood of the solution. These two bounds are solved with the problem dimensions being only the number of contact nodes or node pairs, which are much smaller than the dimension for the original problem, namely, the number of degrees of freedom. Next, a scheme for constructing an upper bound on the contact stress is proposed that uses the bounds on the sum of the nodal contact forces obtained on a fine finite element mesh and the nodal contact forces obtained on a coarse finite element mesh, which are problems that can be solved at a lower computational cost. Finally, the proposed method is verified through some examples concerning both frictionless and frictional contact to demonstrate the method's feasibility, efficiency, and robustness. [ABSTRACT FROM AUTHOR]

The instant system availability $$S_\tau (t)$$ of a repairable system with the renewal equation was studied. The starting point monotonicity of $$S_\tau (t)$$ was proved and the upper bound of $$S_\tau (t)$$ is also derived. It was found that the interval of instant system availability monotonically decreases. In addition, we provide examples that validate the analytically derived properties of $$S_\tau (t)$$ based on the Lognormal, Gamma and Weibull distributions and the results show that the value of T is slightly smaller than its value defined in Theorem 2. The procedure of using a bathtub as application for this article is also discussed. [ABSTRACT FROM AUTHOR]

We consider a mathematical model similar in a sense to competitive location problems. There are two competing parties that sequentially open their facilities aiming to 'capture' customers and maximize profit. In our model, we assume that facilities' capacities are bounded. The model is formulated as a bilevel integer mathematical program, and we study the problem of obtaining its optimal (cooperative) solution. It is shown that the problem can be reformulated as that of maximization of a pseudo-Boolean function with the number of arguments equal to the number of places available for facility opening. We propose an algorithm for calculating an upper bound for values that the function takes on subsets which are specified by partial (0, 1)-vectors. [ABSTRACT FROM AUTHOR]

A new upper bound for the infinity norm of inverse matrix of a strictly diagonally dominant M-matrix is given, and the lower bound for the minimum eigenvalue of the matrix is obtained. Furthermore, an upper bound for the infinity norm of inverse matrix of a strictly α-diagonally dominant M-matrix is presented. Finally, we give numerical examples to illustrate our results. [ABSTRACT FROM AUTHOR]

Incremental forming process is a method for rapid prototyping and low-volume production. Recent ideas have been introduced as 'incremental sheet metal punching.' In this study, a new analytical modeling of the process with respect to the forming mechanism and slip line field has been presented. The analysis sheet formation in this process can be divided into two stages: penetration and curve making. At the penetration stage, both approaches of the upper bound method and slip line field were used to calculate the pressure and velocity of the punch. At the second stage, the estimated slip line field was assumed for curve making. This leads to making a suitable prediction with good accordance. Furthermore, the effects of some parameters such as punch diameter and depth on the punch pressure have been evaluated. [ABSTRACT FROM AUTHOR]

Weighted sequential pattern mining has recently been discussed in the field of data mining. Different from traditional sequential pattern mining, this kind of mining considers different significances of items in real applications, such as cost or profit. Most of the related studies adopt the maximum weighted upper-bound model to find weighted sequential patterns, but they generate a large number of unpromising candidate subsequences. In this study, we thus propose an efficient approach for finding weighted sequential patterns from sequence databases. In particular, a tightening strategy in the proposed approach is proposed to obtain more accurate weighted upper-bounds for subsequences in mining. Through the experimental evaluation, the results also show the proposed approach has good performance in terms of pruning effectiveness and execution efficiency. [ABSTRACT FROM AUTHOR]

A variational solution to the eigenvalue problem for the Hamiltonian H, with orthogonality restrictions on eigenvectors of H to the vector H ∣ Φ0〉, where ∣Φ0〉 is an approximate ground-state vector, is proposed as a means to calculate excited states. The asymptotic projection (AP) method proposed previously is further developed and applied to solve this problem in a simple way. We demonstrate that the AP methodology does not require an evaluation of the matrix elements of operator H2, whereas conventional approaches—such as the elimination of off-diagonal Lagrange multipliers method, projection operator techniques, and other methods—do. It is shown, based on the results obtained for the single-electron molecular ions H2+, HeH2+, and H32+, that applying the new method to determine excited-state wavefunctions yields the upper bounds for excited-state energies. We demonstrate that regardless of whether the orthogonality constraint for states (〈Φ| Φ0〉 = 0) is applied, the zero-coupling constraint (〈Φ| H| Φ0〉 = 0) is imposed, or both of these restrictions are enforced simultaneously, practically the same excited-state energy is obtained if the basis set is almost complete. For the systems considered here, all schemes are capable of giving a sub-μhartree level of accuracy for the ground and excited states computed with different basis sets. [ABSTRACT FROM AUTHOR]