The paper is organized as follows. In Section 2, for completeness, we review some properties of the generalized Poisson autoregressive process of **order** **1**. In Section 3, we derive the expressions for the moments estimators, the quasi-likelihood and the maximum likelihood estimators of the 3 parameters of the GPAR ( ) **1** . These methods have appeared in the literature (see Al-Nachawati, Alwasel and Alzaid [3] for the quasilike- lihood and moments method and Brännäs [4] for likelihood methods). However, asymptotic properties such as efficiencies of these methods are not discussed in those papers. In this paper (Sections 4 and 5), we study properties of these estimators such as bias and asymptotic efficiency. The last section reanalyzes a real-data example which can be modelled with a GPAR ( ) **1** process, where testing is discussed.

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(T) Computation in an external direct product of groups is easy if you know how to compute in each component group.. (F) Groups of finite order must be used to form an external direct pr[r]

Une limite de Berry-Esseen de l 0 ordre **1**/ √ n pour les martingales. Renz [13] a ´ etabli un taux de con- vergence **1**/ √ n dans le th´ eor` eme de la limite centrale pour les martingales avec certaines conditions restrictives. Dans le pr´ esent article, une modification des m´ ethodes, d´ evelopp´ ees par Bolthausen [2] et Grama et Haeusler [6], a appliqu´ e pour obtenir le mˆ eme taux de convergence pour une classe de martingales plus g´ en´ erales. Une application aux processus lin´ eaires est discut´ ee. Pour citer cet article : A. Name1, A. Name2, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

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Abstract. The present paper is a mathematical investigation into the division of unique numbers composed of digits in succession. The paper focuses on the division of a number (whose digits are written in the descending **order** in succession, starting with a two digit number) like 151413121110987654321, by its reverse counterpart number(whose digits are written in the ascending **order** in succession, ending with the same number that started the descent) which is 123456789101112131415. The author found out the values of the quotients of such divisions up till the division of the number 999897...321 by the number 123...979899, and observed a unique feature common to each division. It was realized that the quotients of two successive divisions of this nature have a constant difference between them, equal to the irrational number 0.0818181... which has been termed as the Universal Constant of Division (UCD) of the first **Order**. Similar analysis and extrapolation to even higher divisions (involving three digit numbers) reveals a startling yet similar feature about them. The quotients of such huge divisions are tedious to calculate and require computation instead of manual calculation in **order** to be evaluated. Using the value of UCD of the first **order**, the author was able to express the complex division quotients in terms of an Arithmetic Progression and thus make the calculations manual and simpler. The author finishes the paper with an introspection into the nature of the Universal Constant of Division and it’s analogy with the Ramanujan formula for Pi. The paper is a study out of sheer observation and tries to dwell deep into the realms of the fascinating operation of division and succession.

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Bounds on the curvature of level lines under certain classes of univalent and locally univalent mappings, Indian J.[r]

In this paper, the aim of the paper is to control chaos in fractional-**order** systems by using the economic, simply implemented control scheme and avoid error caused by linearization in many present literatures. Based on the stability theory of fractional-**order** differential system and the linear feedback control, chaos control of a class of chaotic fractional-**order** systems is considered, a LMI conditions is established, feedback gains could be found directly from the LMI formulation. It would be specially mentioned that control of FO system with **order** (**1**, 2) is discussed. To the best of our knowledge, there are few results on the issue. Finally, a numerical example is given to illustrate the effectiveness and usefulness of the proposed method.

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The paper is organized as follows. In Section 2, we first recall some definitions and lemmas used throughout the paper. In Section 3, the stability analysis is presented for autonomous linear fractional diﬀerential systems with **order** **1** < α < 2. The stability of nonautonomous linear fractional diﬀerential systems and the corresponding perturbed systems are studied in Sections 4 and 5, respectively. Conclusions and comments are included in Section 6.

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31. Article 9 of the **Order** requires the responsible person to carry out a “suitable and suffi cient” assessment of the risks on the premises. What form the assessment takes will be dependent on the type and size of premises or undertaking concerned. What is suitable and suffi cient for one premises will not be suffi cient for another. It will be for enforcing authorities to determine whether they consider that the risk assessment is suitable and suffi cient, taking into account such factors as the nature of the building and the type of undertaking. In each case the determining factor is likely to be whether fi re hazards have been reasonably identifi ed, risk reduction and mitigation carried out and residual risk appropriate protection measures (including management arrangements) implemented or proposed.

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The referral **order** was outlined in the final chapter of the 1997 White Paper, No More Excuses **1** . It did not feature in the initial reforms of the youth justice system provided for in the Crime and Disorder Act 1998. It was introduced upon implementation of the Youth Justice and Criminal Evidence Act 1999 and was piloted in 11 areas from March 2000 to August 2001 and, from April 2001, it was ‘rolled out’ around England and Wales. During the piloting period, legislation relating to all sentencing in criminal courts was consolidated, for greater ease of access and clarity, in the Powers of Criminal Courts (Sentencing) Act 2000 (PCC(S)A). Part III of the PCC(S)A contains the primary provisions relating to referral orders. Those provisions have been amended subsequently by The Referral **Order** (Amendment of Referral Conditions) Regulations 2003. New powers relating to the making of parenting orders (with a referral **order**) have been introduced by provisions in the Criminal Justice Act 2003.

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In **order** to determine whether features change as a generator bearing fault develops in a drivetrain, the FFT spectrum can be compared over time leading up to failure. Section 4 explains what should change in theory by introducing a fault associated with mechanical looseness, and by looking at multiple examples a sense of which features are actually observable in real wind turbine applications can be gained. Finding out to what extent these features are measurable (and in what time frame leading up to failure) is a useful exercise. Figure 7 shows examples of spectra for a wind turbine, with each classification presented leading up to failure.

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Extensive kinetic studies were performed to investigate the mechanism of the reaction between 4-methoxybenzaldehyde **1**, malononitrile 2, and dimedone 3 in the presence of fructose as a catalyst in a mixture of water and ethanol. The synthesis reaction of tetrahydrobenzo[b]pyran followed second-**order** kinetics. The partial orders with respect to **1**, 2 were one and one, respectively. Temperature effect has been investigated on the reaction rate, and relevant parameters have been determined with two linearized forms of Eyring equation. The proposed mechanism theoretical rate law were compatible with the experimental data. From the temperature, concentration and solvent studies, the activation energy (E a = 70.05 ± 1.39 kJmol -**1** ) and the related activation parameters

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In this paper, we have done quantitative structure activity relationship analysis of twenty five phenol derivatives with the help of three sets of parameter i. e. quantum chemical, topological and geometrical parameter. The values of three sets of parameter are included into three tables separately (Table **1**-3). Various QSAR models for each set of parameter are given below:

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Despite the limitations of my study mentioned above, the findings demonstrate that the **order** of the separated evaluation of the single parts of a website can influence the evaluation results under specific conditions. There was not a general halo effect in the sense that a preceding evaluation of the homepage necessarily affects the subsequent ratings of the services. Rather, the halo effect appears to be dependent on the strengths of the association between the website owner and the services. For an obvious association, there will be probably no halo effect. However, for weakly associated services, the **order** of evaluation can matter. If the association between the website owner and the service is not obvious, the preceding evaluation of the homepage can act as priming of the (good or bad) image or the website owner which in turn will probably create a halo effect that influences the subsequent ratings. Thus, in case of weak (or unclear) associations between the website owner and the components of a website, it is beneficial to test different orders of presentation. This is important in **order** to prevent a systematic bias of the usability evaluation. However, if the association with the homepage (and the website owner) is obvious for all components, it is rather unlikely that the **order** of

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The control panel for the CO 2 ventilation system is located in Basement **1**, so this was another expensive service to replace. Repairs will cost over $20,000. Not all parts of this system can be relocated, but the control panel could be. However, retrofitting this panel is expensive. In flood-prone areas buildings should have the control panel above flood levels.

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Each option will present a unique set of benefits and risks to the consumer. In **order** to choose between options, consumers will need to consider their price choices, the terms and conditions of the contract offered by the marketer, how much natural gas they use, natural gas market conditions, and their own personal risk tolerance.

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There exist other estimators of α (Resnick, 2007), but here we consider Hill and focus on **order** selection. We introduce an **order** selector that is optimal in the sense that, for a given estimation problem, it minimizes a root mean squared error (RMSE) measure for b α in an internal (i.e. within the algo- rithm) simulation loop. In our approach, the search for opti- mal k is performed in a brute force manner and adaptively for a data set. Hence, the approach is computationally intensive. Processes in complex geophysical systems may exhibit not only heavy tail behaviour, but also persistence in the time domain. Let t (i) denote a time value and { t (i), x(i) } n

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Dolch Second Grade Sight Vocabulary always around because been before best both buy call cold does don't fast first five found gave goes green its made many off or pull read right sing s[r]

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NAR(**1**) with α = .25, λ = 3 and µ = 5. . . . . . 12 It is clear that the values of the normalized bispectrum modulus given in Table 2 show that the normalized bispectrum modulus of the NSINAR(**1**) model is more flat than the non-normalized one given in Table **1** . This indicates that the test of linearity given by Subba Rao and Gabr (1980) and its modification given by Hinich (1982) can be used for integer valued time series models.

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1.00pm Friday 22 January Monday 25 January Opposition Day: subject(s) to be announced 1.00pm Monday 25 January Tuesday 26 January Environment Bill: report stage (Day 1) 1.00pm [r]

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and AI-AMRI, IBRAHIM R., "Symmetric Generating Set of the Alternating Groups A2n + 1," Journal of King Abdulaziz University, Educ.[r]