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and Applied Analysis 3 rate of convergence under some additional assumptions, and it should be noted that we only use the approximate values of the objective function and its subgradients which makes the algorithm easier to implement. Some notations are listed below for presenting the algorithm. (i) ∂f(x) = {ξ ∈ Rn | f(z) ≥ f(x) + ξT(z − x), ∀z ∈ R}, the subdifferential of f at x, and each such...
and Applied Analysis 3 In fact for r 2, Sr x is the classical sine function sinx. It is straightforward to show that Sr x also satisfies 1.3 for the whole real line. With this in mind, we introduce the half-linear cotangent function cotr x as cotrx Sr x Sr x , x ∈ 0, πr . 1.8 Throughout the paper s will be the conjugate number of r, that is, 1/r 1/s 1. It is straightforward to show that s − 1 r...
In the first section the lattice of subsets of distinct set is introduced. The join and meet operations are, respectively, union and intersection of sets, and the ordering relation is inclusion. It is shown that this lattice is Boolean, i.e. distributive and complimentary. The socond section introduced the poset generated in a distinct lattice by its ordering relation. Besides, it is proved tha...
In this section, we discuss the numerical implementation of obtaining our proposed sieve estimators. The estimation procedure is based on the EM algorithm. In particular, we describe the special considerations regarding efficient optimization of the constrained maximization problem in each maximization step. Let’s start from the model (3.4) in Section 3.2 where the target variable X is approxim...
We report observation of the electroweak production of single top quarks in pp[over ] collisions at sqrt[s]=1.96 TeV based on 2.3 fb(-1) of data collected by the D0 detector at the Fermilab Tevatron Collider. Using events containing an isolated electron or muon and missing transverse energy, together with jets originating from the fragmentation of b quarks, we measure a cross section of sigma(p...
This article is an attempt to generalize the classical theory of reversible computing, principally developed by Bennet [IBM J. Res. Develop., 17(1973)] and by Fredkin and Toffoli [Internat. J. Theoret. Phys., 21(1982)], to the quantum case. This is a fundamental step towards the construction of a quantum computer because a time efficient quantum computation is a reversible physical process. The...
Let M be a closed almost complex manifold on which a compact connected Lie group G acts non-trivially. If the first Chern class of M is divisible by an integer N greater than 1, then its equivariant elliptic genus φ(M) of level N is rigid, i.e., it is constant as a virtual character of G. This result was predicted by Witten [W] and proved by Taubes [T], Bott-Taubes [BT] and Hirzebruch [H]. Elli...
are starting to build their applications as extensions to scripting language interpreters or component frameworks. This often involves shared libraries and dynamically load-able modules. However, the inner workings of shared libraries and dynamic loading are some of the least understood and most mysterious areas of software development. In this installment of Scientific Programming, we tour the...
We study projective non-degenerate closed subschemes X ⊆ P having degenerate general hyperplane section, continuing our earlier work. We find inequalities involving three relevant integers, namely: the dimensions of the spans of Xred and of the general hyperplane section of X, and a measure of the “fatness” of X, which is introduced in this paper. We prove our results first for curves and then ...
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