Conditional sum

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  • We discuss the proof of and systematic application of Case’s sum rules for Jacobi matrices. Of special interest is a linear combination of two of his sum rules which has strictly positive terms. Among our results are a complete classification of the spectral measures of all Jacobi matrices J for which J − J0 is Hilbert-Schmidt, and a proof of Nevai’s conjecture that the Szeg˝ condition o holds if J − J0 is trace class.

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  • We settle an old question about the existence of certain ‘sums-of-squares’ formulas over a field F , related to the composition problem for quadratic forms. A classical theorem says that if such a formula exists over a field of characteristic 0, then certain binomial coefficients must vanish. We prove that this result also holds over fields of characteristic p

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  • Much of the power of probabilistic methods in modelling language comes from their ability to compare several derivations for the same string in the language. An important starting point for the study of such cross-derivational properties is the notion of consistency. The probability model defined by a probabilistic grammar is said to be consistent if the probabilities assigned to all the strings in the language sum to one.

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  • In this chapter, we shall first consider chance experiments with a finite number of possible outcomes ω1 , ω2 , . . . , ωn . For example, we roll a die and the possible outcomes are 1, 2, 3, 4, 5, 6 corresponding to the side that turns up. We toss a coin with possible outcomes H (heads) and T (tails). It is frequently useful to be able to refer to an outcome of an experiment. For example, we might want to write the mathematical expression which gives the sum of four rolls of a die.

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  • This book is about using Microsoft Excel to analyze your data. Microsoft Excel is an electronic worksheet you can use to maintain lists; perform mathematical, financial, and statistical calculations; create charts; analyze your data with a PivotTable; and much more. Excel can help you locate data, find trends in your data, and present your data to others. Each Excel file is a workbook. Each workbook can have multiple worksheets. Worksheets are made up of rows and columns of cells you use to enter information....

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  • The King is dead; long live the King! That famous cry sums up most aspects of modern business practice. The previously existing competitive environment, scope, internal structures, and automation support needs of an enterprise have disappeared and been replaced by other sets of conditions and requirements. In time, those needs, too, will disappear and be replaced by yet another set and much more quickly than before. The concept of “Internet years” applies to most aspects of modern life.

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  • under the multiemployer insurance program, PBgC generally provides financial assistance to an insolvent plan in the form of a loan or loans, although it occasionally provides lump-sum settlements in lieu of future financial assistance. loans are usually made quarterly but sometimes monthly in an amount which, when combined with the plan’s other income, covers both the plan’s reasonable administrative expenses and its statutorily guaranteed benefits payments.

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  • Under explicit diophantine conditions on (α, β) ∈ R2 , we prove that the local two-point correlations of the sequence given by the values (m − α)2 + (n−β)2 , with (m, n) ∈ Z2 , are those of a Poisson process. This partly confirms a conjecture of Berry and Tabor [2] on spectral statistics of quantized integrable systems, and also establishes a particular case of the quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms of signature (2,2). The proof uses theta sums and Ratner’s classification of measures invariant under unipotent flows. ...

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  • Obviously, (1.2) implies the same estimate for M(Z(QN, P)). It was suggested in [2] that in this case the (1+logN) term could be omitted at the cost of multiplying by a constant. The above suggestion means that in the passage from the sum of moduli to the modulus of the sum in (1.1) essential cancellation should take place. As a contribution towards this end the authors showed that any straight line L intersects Z(QN, P) in a set FP of linear measure less than 2eP−1N. Further information about the complement of FP under certain conditions on {zk} is obtained in [1].

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  • The realisation of such a marketing strategy requires not only the existence of a he t- erogeneous consumer goods market, but also the possibility to identify market seg- ments which are internally homogeneous and externally heterogeneous with regard to the product related needs and wants of their members.

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  • Normally, any ferromagnetic or ferrimagnetic material undergoes a transition to a paramagnetic state above its Curie temperature. Superparamagnetism is different from this standard transition since it occurs below the Curie temperature of the material. Superparamagnetism occurs in nanoparticles which are single domain. This is possible when their diameter is below 3–50 nm, depending on the materials.

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  • This morning I have reviewed the outlook, the Federal Reserve’s response, and its policy options for the future should the recovery falter or inflation decline further. In sum, the pace of recovery in output and employment has slowed somewhat in recent months, in part because of slower-than-expected growth in consumer spending, as well as continued weakness in residential and nonresidential construction. Despite this recent slowing, however, it is reasonable to expect some pickup in growth in 2011 and in subsequent years.

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  • Public authorities are major consumers in Europe, spending some 16 % of the EU’s gross domestic product (which is a sum equivalent to half the GDP of Germany). By using their purchasing power to opt for goods and services that also respect the environment, they can make an important contribution towards sustainable development.

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  • Earlier research confirms this disparity in views and also the huge variation in the structures and roles of PMOs. In the tougher economic conditions and increasingly competitive business environment of today, organisations cannot afford to continue spending huge sums of money on unsuccessful projects and programmes. Neither can they afford the cost of an ineffective PMO. So it is important to evaluate and understand the value a PMO can and should deliver and what constitutes the right mix of people and processes within a PMO to make that contribution.

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  • Multiple sclerosis (MS) is not a new disease. Its effects on the brain were described in the 1830s, and it was identified as a distinct clinical entity in the 1860s. In fact, writings from the Middle Ages appear to describe individuals with this condition. MS is the most common neurological disorder of young adults; there are approximately 350,000 people with MS in the United States and an estimated 2 million patients worldwide. Research on the disorder has been energetic over recent decades. In 1996, the U.S. National Institutes of Health (NIH) spent almost $83 million on MS research.

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  • It is shown that: (1) Let R be a simple right Noetherian ring, then the following conditions are equivalent: (i) R is a right SI ring; (ii) Every cyclic singular right R - module is pseudo - injective. (2) Let R be a right artinian ring such that every finite generated right R - module is a direct sum of a projective module and a pseudo - injective module. Then: (i) R/Soc(RR ) is a semisimple artinian ring; (ii) J (R) ⊂ Soc(RR ); (iii) J 2 (R) = 0. (3) Let R be a ring with condition (∗ ),...

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  • There are also papers suggesting that the link between central bank finances and policy outcomes is not straightforward, and that other aspects are crucial, too. For example, Ueda (2004) wrote: “Summing up the experiences of insolvent central banks, my conclusion is that the maintenance of a sound balance sheet is, in general, neither a necessary nor a sufficient condition for fulfilling a central bank’s responsibility, but there have been cases where an unhealthy balance sheet became a major obstacle to price stability.

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  • The paper presents a systematic approach to find optimal maintenance strategies for pavement management systems by using the World Bank’s Highway Development and Management System (HDM-4) combined with gradient methods proposed by Tsunokawa et al (2005). The optimal maintenance strategy is defined as the set of optimal maintenance options corresponding to different traffic levels and various initial pavement conditions, which minimizes the sum of agency costs and road user costs in present value or maximizes the net benefit to society over an analysis period.

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