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Now showing items 177 - 192 of 24623

  • INDABA CAPITAL MANAGEMENT, L. P. (Release No. 73121)

    Jill M. Peterson  

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  • Convolution Inequalities in l(p) Weighted Spaces

    Nguyen Du Vi Nhan   Dinh Thanh Duc  

    Various weighted l(p)-norm inequalities in convolutions are derived by a simple and general principle whose l(2) version was obtained by using the theory of reproducing kernels. Applications to the Riemann zeta function and a difference equation are also considered.
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  • Enantioselective degradation of diclofop-methyl in cole (Brassica chinensis L.)

    Gu, Xu   Lu, Yuele   Wang, Peng   Dang, Ziheng   Zhou, Zhiqiang  

    The stereoselective degradation of the racemic diclofop-methyl and its chiral degradation product, diclofop (the hydrolysate of diclofop-methyl), in cole has been investigated. Both enantiomers of diclofop-methyl and diclofop were extracted by organic solvent and detected by chiral high-performance liquid chromatography-diode array detector (DAD). Cellulose-tris-(3,5-dimethylphenylcarbamate)-based chiral column Was used for the chiral separation of the four enantiomers applying a mixture of n-hexane and 2-propanol (98:2) concluding 0.1% TFA as mobile phase at a flow rate of 1.0 mL/min. The assay method was linear over a range of concentrations (0.5-2.50 mg L(-1)), and the mean recovery was more than 60% for all the enantiomers. The limit of detection for all the enantiomers was 0.2 mu g g(-1) in plant. Racemic diclofop-methyl was foliar sprayed to cole. Stereoselective behaviour was observed in the diclofop-methyl degradation process. The (S)-diclofop-methyl dissipated faster than (R)-diclofop-methyl. In the case of diclofop, the generation and degradation rates of (S)-enantiomer were higher than (R)-enantiomer in the plant. (C) 2009 Elsevier Ltd. All rights reserved.
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  • L(P)-solutions of singular integro-differential equations

    Burton, T. A.   Purnaras, I. K.  

    We study a variety of scalar integro-differential equations with singular kernels including linear, nonlinear, and resolvent equations. The first result involves a type of existence theorem which uses a fixed point mapping defined by the integro-differential equation itself and produces a unique solution with a continuous derivative in a very simple way. We then construct a Liapunov functional yielding qualitative properties of solutions. The work answers questions raised by Volterra in 1928, by Levin in 1963, and by Grimmer and Seifert in 1975. Previous results had produced bounded solutions from bounded perturbations. Our results mainly concern integrable solutions from integrable perturbations. (C) 2011 Elsevier Inc. All rights reserved.
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  • Some normed binomial difference sequence spaces related to the l(p) spaces

    Song, Meimei   Meng, Jian  

    The aim of this paper is to introduce the normed binomial sequence spaces b(p)(r,s)(del) by combining the binomial transformation and difference operator, where 1 <=3D p <=3D infinity. We prove that these spaces are linearly isomorphic to the spaces l(p) and l(infinity), respectively. Furthermore, we compute Schauder bases and the alpha-, beta- and gamma-duals of these sequence spaces.
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  • LCM XIII L. P./LCM XIII LLC

    Jaiho Cho   Shannon Mooney   Winston Chang  

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  • The pl Loomis–Whitney inequality

    Ai-Jun Li   Qingzhong Huang  

    Abstract In this paper, we establish the L p Loomis–Whitney inequality for even isotropic measures in terms of the support function of L p projection bodies with complete equality conditions. This generalizes Ball's Loomis–Whitney inequality to the L p setting. In addition, the sharp upper bound of the minimal p -mean width of L p zonoids is obtained.
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  • AG BARR p. l. c./Britvic plc

    Alasdair Smith   Katherine Holmes   Alexander Johnston  

    On 14 November 2012, the boards of AG BARR p. l. c. (AG Barr) and Britvic plc (Britvic) (collectively 'the parties') announced that they had agreed the terms of an acquisition by AG Barr of Britvic by means of an all-share merger. The proposed merger was approved by shareholders on 8 January 2013 and the merged company would be named Barr Britvic Soft Drinks plc. On 13 February 2013, the Office of Fair Trading (OFT) referred the proposed acqui- sition to the Competition Commission (CC) for investigation and report. As a result of the OFT's decision to refer the merger to the CC the offer by AG Barr to purchase the entire issued and to-be-issued share capital of Britvic lapsed on 13 February. However, on 14 February both parties announced that they would work closely with the authorities to expedite clearance of the merger. We concluded that a relevant merger situation would be created by the merger and that we have the jurisdiction to consider whether the creation of that situation may be expected to result in an SLC within any market or markets in the UK for goods or services. There are two broad categories of soft drinks: carbonated soft drinks (CSDs) and still drinks. CSDs include drinks such as colas, fruit flavoured carbonates and lemonade as well as carbonated energy drinks. Still soft drinks include fruit juice, water, juice drinks, squashes and sports drinks. Soft drinks producers sell to intermediaries (ie retailers (such as supermarkets or operators of pubs or restaurants), wholesalers or cash-and-carry outlets). These customers buy products for onward sale to the consumer (ie the final purchaser of the product). Retail sales of soft drinks in the UK amounted to £11.2 billion in the year to December 2012. Of this, £7.3 billion was in the off-trade (where soft drinks are purchased from a retail outlet for consumption off the premises), and £3.9 billion in the on-trade (where soft drinks are consumed on the premises) markets. Sales in the off-trade may be further subdivided into the take- home segment (where product is purchased for consumption later at home and accounts for 75 per cent of off-trade sales) and the impulse segment (where product is purchased for immediate consumption and which accounts for 25 per cent of off- trade sales). Both companies manufacture and supply soft drinks, have a portfolio of proprietary carbonated and still brands and produce other brands under licence. IRN-BRU is the largest brand within AG Barr's portfolio. [?] per cent of IRN-BRU sales are in Scotland. AG Barr also manufactures and sells Orangina in the UK under licence from the Orangina Schweppes Group and produces and distributes Rockstar energy drinks in the UK and Republic of Ireland under a partnership arrangement with Rockstar, Inc. Britvic also manufactures and sells a number of major soft drink brands in Great Britain and has a long-standing exclusive bottling agreement with PepsiCo in Great Britain and Ireland for the manufacture and sale of Pepsi, 7UP, Gatorade, Mountain Dew and So Be V Water. We concluded that the supply of CSDs in Great Britain was an appropriate relevant market within which to assess the competitive effects of the merger. We also considered the competitive effects specifically in Scotland because AG Barr has a particularly strong presence there. We concluded that the appropriate counterfactual was a continuation of the existing situation with an independent AG Barr and Britvic both competing in the soft drink markets. We assessed three possible competitive effects of the merger: the first was that prices might rise if the merger brings together brands that are close (although not necessarily the closest) substitutes for consumers (unilateral horizontal effects); the second was that the merger may adversely impact competition by increasing the parties' bargaining power to make customers stock more of their range at the expense of the smaller brands of smaller producers (portfolio effects); and the third was that the merger may make coordination more likely post-merger if there was none pre-merger, or make coordination more stable if there was evidence of pre- existing coordination (coordinated effects). In our evaluation of unilateral horizontal effects we considered carefully the evidence on the existing level of competition between the parties and the incentive to increase prices post-merger. We noted that most customers thought there was some substitut- ability between AG Barr's and Britvic's products but they considered that the overlap was small. A survey conducted for the parties suggested there was some diversion between Orangina and Britvic brands and between IRN-BRU and Britvic brands. Another survey on customer segmentation conducted by the parties suggested that IRN-BRU was relatively distinct from other CSDs and therefore suggested that there would be low levels of substitution from IRN-BRU to other products. Our econometric analysis did not find significant results for the diversion between Orangina and Britvic brands. An analysis of Great-Britain-wide data did not show a statistically significant relation- ship for the diversion from IRN-BRU to Britvic brands. We focused our analysis on Scotland data to identify whether the greater market share of AG Barr in Scotland might make relationships between IRN-BRU and Britvic products more easily isolated statistically or whether the IRN-BRU customer and the position of IRN-BRU was different in Scotland. In our analysis of multiple retailers in Scotland we used data provided by Tesco and the Co-op.1 We also analysed two sources of data for the impulse segment in Scotland. One data set (based on Nielsen Scotland impulse data) did not produce statistically significant results for the diversion from IRN-BRU to Britvic brands. The Litmus impulse data, although this also suffered from some limitations, produced statistically significant results and suggested that in Scotland Britvic brands are to some extent a substitute for IRN-BRU. When the data from the two retailers was pooled, the data did not produce statistically significant results for the diversion between IRN-BRU and Britvic. When we looked at the data for the two retailers separately, both models appeared less reliable than when combined. The Co-op data did not produce statistically significant results but the Tesco data did. However, we were concerned about the reliability of our Tesco Scotland analysis. In general, we found that the demand estimation appeared more reliable the more that we pooled data. In our assessment of the effects of the merger we used the statistically significant result from the analysis of Litmus data in Scotland to estimate the illustrative price increase that might attend the merger. The diversion ratio of [?] per cent from IRN- BRU to Britvic brands in the Scottish impulse segment implied an illustrative price increase of [?] per cent. We also considered whether the merger might lead to a price increase for IRN-BRU to on-trade customers but noted that the merger would make little difference since AG Barr already supplies IRN-BRU to Britvic for sale in its dispensers. In our assessment of the evidence we noted that customers were in the main not concerned by the merger and said that the two companies' brands did not overlap substantially. We also noted the consumer segmentation survey, which suggested that IRN-BRU was distinct from other CSDs. In our econometric analysis we assessed a number of different sources of data and most did not produce statistically significant results for the relationship between IRN-BRU pricing and the level of Britvic sales. Overall our assessment did not suggest that the merger would create strong incentives for the parties to increase price. However, we noted that soft drinks producers and their customers negotiated on many other aspects in addition to price. These non-price factors could reduce to some extent any incentive for the parties to increase the price of IRN-BRU after the merger. We concluded that there would not be significant harm to competition resulting from the merger as a result of unilateral horizontal effects. To evaluate possible portfolio effects we examined whether a larger company was able to attain preferential distribution for its products compared with smaller com- panies. We found that although there was some evidence that on average larger companies were able to achieve somewhat better distribution for their products than would be expected simply on the basis of the sales of each brand, particularly in the impulse segment, we saw examples of smaller companies achieving high levels of distribution for their products compared with larger companies. We considered whether the merged company would be large enough to allow it to achieve levels of distribution that were more like Coca-Cola Enterprises (CCE) and, if so, whether this would be to the detriment of smaller soft drink companies or new entrants. The merged company would still be less than half the size of CCE. We concluded that the merger would make little difference and would not mean new entrants and smaller soft drink companies would be disadvantaged significantly as a result of the merger. We concluded that the merger would not result in significant harm as a result of portfolio effects. We assessed whether the merger might give rise to coordinated effects between CCE and the merged company. We did not consider that all the necessary conditions for coordination in the off-trade apply in CSD pricing: (a) soft drinks producers do not directly observe competitor pricing terms and there are substantial additional pay- ments made by soft drinks companies to customers which are highly complex and which a competitor would not be able to monitor; and (b) there is no clear coordin- ation point. We also concluded that category captaincy status (where a supplier—- usually a large supplier of branded goods—-is appointed by the retailer to exchange information with the retailer to help the retailer manage the way that products within a particular category are presented and sold to consumers) would not facilitate price coordination between soft drinks producers. We considered whether coordination would be more practical on promotions but did not find any evidence that promotions were currently the object of coordinated strategies and noted that customers, who control promotions calendars, would have an incentive and the ability to disrupt any coordination. The merged company would still be significantly smaller than CCE in the off-trade CSD market and this would continue to make coordination unlikely after the merger. We considered whether the merger would make coordination more likely in the on- trade but noted that the merger would make little difference since Britvic already supplies IRN-BRU through its dispensers in Scotland and AG Barr's market share in the on-trade is low. Therefore we concluded that the merger would not have a significant impact on coordination in the on-trade. We concluded that the merger would not result in significant harm as a result of coordinated effects. We considered whether there would be countervailing factors that might mitigate the effect of the merger. We concluded that it was unlikely that the threat of new entry of a product that would compete with IRN-BRU would act as a significant constraint on the merged entity. We did not find other significant countervailing factors that might offset the effect of the merger. We concluded that the merger would not be likely to give rise to an SLC in any market in the UK.
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  • L(p,q)-labeling of sparse graphs

    Clément Charpentier   Micka?l Montassier…  

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  • Cryptanalysis of an RSA variant with moduli N =3D p(r)q(l)

    Lu, Yao   Peng, Liqiang   Sarkar, Santanu  

    In this paper we study an RSA variant with moduli of the form N =3D p(r)q(l) (r > l >=3D 2). This variant was mentioned by Boneh, Durfee and Howgrave-Graham [2]. Later Lim, Kim, Yie and Lee [11] showed that this variant is much faster than the standard RSA moduli in the step of decryption procedure. There are two proposals of RSA variants when N =3D p(r)q(l). In the first proposal, the encryption exponent e and the decryption exponent d satisfy ed equivalent to 1 mod p(r-1)q(l-1) (p-1)(q-1), whereas in the second proposal ed equivalent to 1 mod (p-1)(q-1). We prove that for the first case if d < N1-(3r+l)(r+l)-2, one can factor N in polynomial time. We also show that polynomial time factorization is possible if d < N(7-2 root 7)/(3(r+l)) for the second case. Finally, we study the case when few bits of one prime are known to the attacker for this variant of RSA. We show that given min (l/r+l, 2(r-l)/r+l) log(2) p least significant bits of one prime, one can factor N in polynomial time.
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  • On the smoothness of\\(L^p\\)of a positive vector measure

    Agud, L.   Calabuig, J. M.   Sánchez-Pérez, E. A.  

    We investigate natural sufficient conditions for a space \(L^p(m)\) of \(p\)-integrable functions with respect to a positive vector measure to be smooth. Under some assumptions on the representation of the dual space of such a space, we prove that this is the case for instance if the Banach space where the vector measure takes its values is smooth. We give also some examples and show some applications of our results for determining norm attaining elements for operators between two spaces \(L^p(m_1)\) and \(L^q(m_2)\) of positive vector measures \(m_1\) and \(m_2\).
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  • A GLOBAL EXISTENCE RESULT FOR KORTEWEG SYSTEM IN THE CRITICAL L^P FRAMEWORK

    高真圣  

    The purpose of this work is to investigate the initial value problem for a general isothermal model of capillary fluids derived by Dunn and Serrin [12], which can be used as a phase transition model. Motivated by [9], we aim at extending the work by DanchinDesjardins [11] to a critical framework which is not related to the energy space. For small perturbations of a stable equilibrium state in the sense of suitable L^p-type Besov norms,we establish the global existence. As a consequence, like for incompressible flows, one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true.
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  • $L^p$ regularity of weighted Bergman projections

    Zeytuncu, Yunus E.  

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  • Exact recovery of sparse multiple measurement vectors by l(2,p)-minimization

    Wang, Changlong   Peng, Jigen  

    The joint sparse recovery problem is a generalization of the single measurement vector problem widely studied in compressed sensing. It aims to recover a set of jointly sparse vectors, i.e., those that have nonzero entries concentrated at a common location. Meanwhile l(p)-minimization subject to matrixes is widely used in a large number of algorithms designed for this problem, i.e., l(2,p)-minimization min(X is an element of Rnxr) parallel to X parallel to(2,p) s.t. AX =3D B. Therefore the main contribution in this paper is two theoretical results about this technique. The first one is proving that in every multiple system of linear equations there exists a constant p* such that the original unique sparse solution also can be recovered from a minimization in l(p) quasi-norm subject to matrixes whenever 0 < p < p*. The other one is showing an analytic expression of such p*. Finally, we display the results of one example to confirm the validity of our conclusions, and we use some numerical experiments to show that we increase the efficiency of these algorithms designed for l(2,p)-minimization by using our results.
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  • L^p estimates for a trilinear pseudo-differential operator with flag symbols

    Lu, Guozhen; Zhang, Lu  

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  • \(L^p\)Error Estimates of Two-Grid Method for Miscible Displacement Problem

    Chen, Yanping; Zeng, Jiaoyan; Zhou, Jie  

    This paper is concerned about the error analysis of two-grid method for incompressible miscible displacement in porous medium. A characteristics finite element method is presented for the concentration equation to handle the convection part, and standard mixed finite element is used for the pressure equation. Mixed finite element method has an advantage of approximating the unknown variable and its diffusive flux across grid-cell interfaces simultaneously, which has been proven to be an effective numerical method for solving fluid problems. Moreover, we linearize the equations based on the Newton iteration method, then, two-grid algorithm is considered in this full discrete scheme problems. It shown that coarse space can be extremely coarse and we achieve asymptotically optimal approximation. Numerical experiments are presented finally to validate the theoretical analysis.
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