Enhancing The Error Term of, |Np(x) – τx} For Some Special Sequence

The Adolescent and Adult Time Inventory–Time Attitudes Scale (AATI-TA) measures emotional engagement with the past, present, and future, and scores have been shown to relate meaningfully to health outcomes. For past, present, and future, five items are used to assess both positive and negative attitudes. Although evidence for the hypothesized six-factor solution has been widely reported, some studies have indicated problems with the Future Negative items. Given that a large and growing literature has emerged on the six-factor AATI-TA, and that AATI-TA scores have shown much better and more consistent fit than other temporal psychology measures, we sought to investigate the future negative factor in detail. Secondary analyses were performed on two datasets. The first was a University convenience sample ( N = 410) and the second was an adolescent sample ( N = 1,612). Confirmatory factor analyses revealed that the fit for the five Future Negative items was poor. Modification indices suggested that a correlated error term between Items 4 and 10 would result in good fit, and this was indeed the case. Models without Item 4 or Item 10 also yielded acceptable fit. Analyses using all four operationalizations of Future Negative (original scale, without Item 4 or Item 10, or with the correlated error between Items 4 and 10) to predict symptoms of anxiety and depression, and emotional self-efficacy revealed minor differences in the predictive validity coefficients. Potential ways forward, including a correlated error term or the dropping or replacement of Item 10, are discussed.

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A Sliding Surface for Controlling a Semi-Bridgeless Boost Converter with Power Factor Correction and Adaptive Hysteresis Band

Applied Sciences ◽

10.3390/app11041873 ◽

2021 ◽

Vol 11 (4) ◽

pp. 1873

Author(s):

José Robinson Ortiz-Castrillón ◽

Gabriel Eduardo Mejía-Ruiz ◽

Nicolás Muñoz-Galeano ◽

Jesús María López-Lezama ◽

Juan Bernardo Cano-Quintero

Keyword(s):

Sliding Mode Control ◽

Power Factor ◽

Error Term ◽

Sliding Mode ◽

Power Factor Correction ◽

Sliding Surface ◽

Dc Voltage ◽

Start Up ◽

Ac Current ◽

Current Error

This paper proposes a new sliding surface for controlling a Semi-Bridgeless Boost Converter (SBBC) which simultaneously performs Power Factor Correction (PFC) and DC bus regulation. The proposed sliding surface is composed of three terms: First, a normalized DC voltage error term controls the DC bus and rejects DC voltage disturbances. In this case, the normalization was performed for increasing system robustness during start-up and large disturbances. Second, an AC current error term implements a PFC scheme and guarantees fast current stabilization during disturbances. Third, an integral of the AC current error term increases stability of the overall system. In addition, an Adaptive Hysteresis Band (AHB) is implemented for keeping the switching frequency constant and reducing the distortion in zero crossings. Previous papers usually include the first and/or the second terms of the proposed sliding surface, and none consider the AHB. To be best of the author’s knowledge, the proposed Sliding Mode Control (SMC) is the first control strategy for SBBCs that does not require a cascade PI or a hybrid PI-Sliding Mode Control (PI-SMC) for simultaneously controlling AC voltage and DC current, which gives the best dynamic behavior removing DC overvoltages and responding fast to DC voltage changes or DC load current perturbations. Several simulations were carried out to compare the performance of the proposed surface with a cascade PI control, a hybrid PI-SMC and the proposed SMC. Furthermore, a stability analysis of the proposed surface in start-up and under large perturbations was performed. Experimental results for PI-SMC and SMC implemented in a SBBC prototype are also presented.

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Prime geodesics and averages of the Zagier L-series

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004121000384 ◽

2021 ◽

pp. 1-24

Author(s):

OLGA BALKANOVA ◽

DMITRY FROLENKOV ◽

MORTEN S. RISAGER

Keyword(s):

Asymptotic Expansion ◽

Asymptotic Expansions ◽

Error Term ◽

Quadratic Fields ◽

Real Quadratic Fields ◽

Prime Geodesic Theorem ◽

Error Terms ◽

Average Size ◽

Real Quadratic

Abstract The Zagier L-series encode data of real quadratic fields. We study the average size of these L-series, and prove asymptotic expansions and omega results for the expansion. We then show how the error term in the asymptotic expansion can be used to obtain error terms in the prime geodesic theorem.

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XLIX.—Generalizations of a Problem of Pillai

Proceedings of the Royal Society of Edinburgh Section A Mathematical and Physical Sciences ◽

10.1017/s0080454100006890 ◽

1949 ◽

Vol 62 (4) ◽

pp. 460-469

Author(s):

L. Mirsky

Keyword(s):

Asymptotic Formula ◽

Error Term ◽

Main Concern ◽

Positive Integers ◽

Infinite Set

I. Throughout this paper k1, …, k3 will denote s ≥ I fixed distinct positive integers. Some years ago Pillai (1936) found an asymptotic formula, with error term O(x/log x), for the number of positive integers n ≤ x such that n + k1, …, n + k3 are all square-free. I recently considered (Mirsky, 1947) the corresponding problem for r-free integers (i.e. integers not divisible by the rth power of any prime), and was able, in particular, to reduce the error term in Pillai's formula.Our present object is to discuss various generalizations and extensions of Pillai's problem. In all investigations below we shall be concerned with a set A of integers. This is any given, finite or infinite, set of integers greater than 1 and subject to certain additional restrictions which will be stated later. The elements of A will be called a-numbers, and the letter a will be reserved for them. A number which is not divisible by any a-number will be called A-free, and our main concern will be with the study of A-free numbers. Their additive properties have recently been investigated elsewhere (Mirsky, 1948), and some estimates obtained in that investigation will be quoted in the present paper.

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Testing War In the Error Term

International Organization ◽

10.1017/s0020818303572083 ◽

2003 ◽

Vol 57 (2) ◽

pp. 445-448 ◽

Cited By ~ 3

Author(s):

Damon Coletta ◽

Erik Gartzke

Keyword(s):

Incomplete Information ◽

Error Term ◽

International Organization ◽

Quantitative Studies

The proof for “War Is in the Error Term,” a piece that appeared in the Summer 1999 issue of International Organization, contains a subtle error. Once the correction is made, there are broader implications for testing theories of war using quantitative studies. Large-n tests to verify the incomplete information explanation for war will be more difficult to perform than originally anticipated.

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Bayesian Inference Method for Failure Probability of Wall Thinning Pipe in Corrosion Rate Fluctuation Model

Volume 1: Codes and Standards ◽

10.1115/pvp2008-61457 ◽

2008 ◽

Author(s):

Satoshi Okajima ◽

Satoshi Izumi ◽

Shinsuke Sakai

Keyword(s):

Corrosion Rate ◽

Failure Probability ◽

Error Term ◽

Correction Term ◽

Operational Environment ◽

Bayes Method ◽

Wall Thinning ◽

Rate Fluctuation ◽

The One ◽

Linear Bayes

To rationalize the inspection interval for the wall-thinning piping element, the linear-Bayes method was proposed in the previous paper. To derive the simple formula, the linear-Bayes method ignores the corrosion rate change against time. However, this change may be caused by the one of the operational environment. Therefore, without the sufficient monitoring of the environment, the linear-Bayes method may underestimate the failure probability. In this paper, the linear-Bayes method is extended for the wall-thinning model with the corrosion rate fluctuation, which imitates the unexpected change of the corrosion rate. The extension is carried out through following two approaches: the “correction-term” and the “error-term” approaches. The correction-term approach can evaluate the change of corrosion rate, however, it requires sufficient number of inspections. The error-term approach evaluates the failure probability conservatively.

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GENERALIZATION OF THE EFFECTIVE WIENER–IKEHARA THEOREM

International Journal of Number Theory ◽

10.1142/s1793042113500760 ◽

2013 ◽

Vol 09 (08) ◽

pp. 2091-2128 ◽

Cited By ~ 3

Author(s):

SZILÁRD GY. RÉVÉSZ ◽

ANNE de ROTON

Keyword(s):

Laplace Transform ◽

Tauberian Theorem ◽

Error Term ◽

Effective Version ◽

Slow Decrease ◽

Asymptotic Evaluation ◽

The Laplace Transform

We consider the classical Wiener–Ikehara Tauberian theorem, with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace transform. In this generality, we prove the otherwise known asymptotic evaluation of the transformed function, when the usual conditions of the Wiener–Ikehara theorem hold. However, our version also provides an effective error term, not known thus far in this generality. The crux of the proof is a proper, asymptotic variation of the lemmas of Ganelius and Tenenbaum, also constructed for the sake of an effective version of the Wiener–Ikehara theorem.

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