contexts including **finite** geometry, the inverse Galois problem [1], the construction of difference sets with Singer parameters [8], determining cross-correlation between m-sequences [11, 14] and to construct error- correcting codes [4], as well as to speed up the index calculus method for computing discrete logarithms on **finite** fields [12, 13] and on algebraic curves [21].

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Between grains segmented by the Watershed transforma- tion, there are boundaries having the label number zero and of one voxel in thickness, i.e. grain boundaries, as shown in Fig. 5 (a). Voxels with label number zero were extracted **from** the image data shown in Fig. 4 as grain boundaries, and then, the label numbers of neighbor grains were checked on each grain boundary (GB) voxel. In the case that a GB voxel has two kinds of label numbers among the neighbor grains, the GB voxel constitutes a grain boundary. If the same combina- tion of label number was found, the same GB label was as- signed to a GB voxel, if not, a new GB label was assigned. Further, **when** a GB voxel has three kinds of label among the neighbor grains, the GB voxel means the edge of the three grains. Therefore, an edge label number was assigned to each voxel. Similarly, if four labels were found, it is a vertex com- posed by four grains. A vertex label number was assigned to each voxel in the same way. A three dimensional image of grain boundaries which are colored by GB label is shown in Fig. 5(b).

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the following conditions: (1) card(**X**) is greater than a huge positive **integer** and it is conjectured that **X** is infinite, (2) we do not know any algorithm deciding the finiteness of **X**, (3) a **known** and short algorithm for every **n** ∈ **N** decides whether or not **n** ∈ **X**, (4) a **known** and short algorithm returns an **integer** **n** such that **X** is infinite if and only if **X** contains an element greater than **n**. The following problem is open: simply define a set **X** ⊆ **N** such that **X** satisfies conditions (1)-(4), and we do not know any representation of **X** as a **finite** union of sets whose definitions are simpler than the definition of **X** (5). Let f (1) = 2, f (2) = 4, and let f (**n** + 1) = f (**n**)! for every **integer** **n** > 2. For a positive **integer** **n**, let Ψ **n** denote the following statement: if a system of equations

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and similar summations derived **from** this one. This allows the mutual inductance of two thin cylindrical solenoids to be evaluated as a single integral not significantly more complex than Equation (5). The mutual inductance of two thick coils can then obtained by summing over the various combinations of thin solenoids. With current knowledge, it does not seem to be possible to sum analytically in the radial direction in the same manner as in the axial direction.

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1. Introduction. We denote by π (**x**) the number of all prime numbers ≤ **x**. We denote also f (**x**) = **x**/π (**x**) for **x** ≥ 2. Since π (**x**) ∼ **x**/logx, it follows that f (**x**) ∼ log **x**. We could expect that the function f (**x**) behaves like log **x**. However, we will see that log **x** possesses several properties that f (**x**) does not possess.

In the following, we let Ᏸ be the space of infinitely diﬀerentiable functions with compact support, let Ᏸa,b be the space of infinitely diﬀerentiable functions with support contained in [r]

Until now individual techniques have been applied in each section. For instance, we usually used substitution in Exercises 5.5, integration by parts in Exercises 5.6, and partial fractions in Exercises 5.7 and Appendix G. But in this section we present a collection of miscellaneous integrals in random order and the main challenge is to recognize which technique or formula to use. No hard and fast rules can be given as to which method applies in a given situation, but we give some advice on strategy that you may find useful. A prerequisite for strategy selection is a knowledge of the basic integration formulas. In the following table we have collected the integrals **from** our previous list together with several additional formulas that we have learned in this chapter. Most of them should be memorized. It is useful to know them all, but the ones marked with an asterisk need not be memorized since they are easily derived. Formula 19 can be avoided by using partial frac- tions, and trigonometric substitutions can be used in place of Formula 20.

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Classically, a short circuit is defined as a circuit element across which the voltage is zero, regardless of the current flowing through it [45]. Consequences include excessive electric current flow, causing circuit damage, overheating, fire or explosion. **From** a safety point of view, internal or external short circuits of Li-ion batteries [46] are very important because they can cause a sudden increase in heat generation, called thermal runaway [47]. Recently many researchers have focused on graphite-based anodes for LIBs with varying suc- cess, depending on the treatments employed. In this study we provide new approaches of graphene/ (h-BN) **n** /**X**-doped graphene in LIB anode applica-

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if separated **from** the substrate, i.e., “free” NWs. To calcu- late this internal strain, we apply the approach described in [9] where the elastic strain of GaN and AlN layers of an GaN/AlN superlattice is calculated considering the mini- mum elastic energy of one period of the superlattice. Ac- cordingly, we divide the entire Al **x** Ga 1− **x** **N** NW into

D 4.1 General. Table D 4.1 lists the discharge capacity of rectangular roof scuppers of various widths with various heads of water. The maximum allowable level of water on the roof shall be obtained **from** the structural engineer, based on the design of the roof.

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E12.5. Suppose that µ is a measure on a set S. A subset A of S is a µ-atom iff µ(A) > 0 and for every **X** ⊆ A, either µ(**X**) = 0 or µ(**X** ) = µ(A). Show that if κ is a real- valued measurable cardinal, µ is a κ-additive measure on κ, and A ⊆ κ is a µ-atom, then {**X** ⊆ A : µ(**X** ) = µ(A)} is a κ-complete nonprincipal ultrafilter on A. Conclude that κ is a measurable cardinal if there exist such µ and A.

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An updated ephemeris and expanded UV spectroscopy with better orbital coverage are needed to better con- strain the implications of the UV emission lines and the characteristics of this XRB system. In this paper, we revisit LMC **X**-3 with a new ephemeris and new UV ob- servations. We update the ephemeris of LMC **X**-3 based on high-resolution optical spectroscopy recently obtained with the 6.5m Magellan-Clay telescope. We also report new ultraviolet observations of LMC **X**-3 **from** two high- resolution instruments. First, we present temporal moni- toring of the O vi emission using FUSE data with a much longer time baseline that provides more than three quar- ters of the LMC **X**-3 orbit. With the extended FUSE data, we detect narrow O vi emission **from** the binary system and measure the variations in velocity and in- tensity of the emission as a function of orbital phase. Second, we complement the O vi analysis with new ob- servations of the **N** v λλ1238.8,1242.8 doublet obtained with the Cosmic Origins Spectrograph (COS) on board the Hubble Space Telescope (HST). The **N** v emission is detected at high significance in the COS data and pro- vides corroborating evidence of the velocity and inten- sity variations of the highly ionized emission. During the time of the FUSE observations in 2004, LMC **X**-3 was also observed quasi-simultaneously in the **X**-ray band- pass with Chandra and the Rossi **X**-ray Timing Exper- iment (RXTE); see Wang et al. (2005) for full details. While our emphasis in this paper is on the UV emission lines, we also briefly comment on the affiliated **X**-ray ob-

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Join Fr. Jason and fellow parishioners for Bible study, live, on-line, on Monday nights (except the weeks we have Parish Night). The first book we will explore is First Peter. Our study will be **from** 7:30 to 8:30 p.m. starting Monday, September 14. Zoom information was sent in an e-mail last Thursday - don’t delete it! Add it to your Google or Outlook calendar. We will explore how the Bible applies to our own lives. We will also consider the theological, cultural, linguistic, histor- ical, and social contexts of the Bible, in an easy-to-understand way. We will also look at how Church Fathers understood various passages. Please contact Fr. Jason with any questions:

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The **above** results prove the efficacy of CDR267F018 and CDR134F194 in ameliorating insulin resistant conditions as seen in the 3T3L1 adipocyte, skeletal muscle model and fructose fed models. This is the first study to report about the existence of insulin resistance reversal property of active fractions obtained **from** **X**. molluccensis and **X**. granatum, which could be of clinical interest. Further the efficacy of the fractions in management of type 2 diabetes and dyslipidemia can be proved by conducting clinical studies. Further work is in progress to identify the active constituents **from** the fractions CDR267F018 and CDR134F194, which are responsible for these activities.

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[43] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuse- ria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery, Jr., R. E. Stratmann, J. C. Burant, S. Dap- prich, J. M. Millam, A. D. Daniels, K. **N**. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, **N**. Rega, P. Salvador, J. J. Dannenberg, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, A. G. Baboul, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J. L. Andres, C. Gonzalez, M. Head-Gordon, E. S. Replogle and J. A. Pople, “Revision A.11.2,” Gaussian, Inc., Pitts- burgh, 2001.

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Rochester Institute of Technology RIT Scholar Works Theses Thesis/Dissertation Collections 11-2-2005 Long term behavior of the positive solutions of the non-autonomous difference equatio[r]

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PTCR * NOT USED ON NOT USED ON SOME MODELS SOME MODELS RED WHT WHT WHT WHT BRN GRN/YEL GRN/YEL RED YEL BLK 3105052.017 BLU RED * START CAP * Wiring Diagram Early Version Later Version * [r]

The crosses designed to test segregation were made between the segregating amphiploids (for short Ws W s ws ws) and Ws ws hetero- zygotes of N. The observed segregation ratio[r]

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We illustrate this here with the Metropolis-Hastings (MH) update, but it should be stressed at this point that the results presented in this paper apply to much more general settings (including in particular hybrid samplers, sequential or population Monte Carlo samplers). The MH algorithm requires the choice of a proposal distribution q. In order to simplify the discussion, we will here assume that π and q admit densities with respect to the Lebesgue measure λ Leb , denoted with an abuse of notation π and q hereafter. The rˆ ole of the distribution q consists of proposing potential transitions for the Markov chain {**X** k }. Given that the chain is currently at **x**, a candidate y is accepted with probability α(**x**, y) defined as

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