Given this kind of business climate, what competitive marketing problems will your company face in the next 10 yrs.??

Given our formula φ, we group strings of quantifiers of one kind together in blocks:

Given the structure of the experiment, it may or may not be possible to actually perform it, and, in the case that it is possible for it to be performed, there need be no intention of any kind to actually perform the experiment in question.

Given that he refers to clothes as food and considers them a kind of delicacy, it may be that Decapodians themselves consume clothes.

Given the massing of the Muslim armies at Yarmouk, however, Vahan had little choice but to respond in kind.

Given a Riemannian manifold with metric tensor, we can compute the Ricci tensor, which collects averages of sectional curvatures into a kind of " trace " of the Riemann curvature tensor.

Given that the derivatives as Schwartz distributions are symmetric, this kind of example belongs in the ' fine ' theory of real analysis.

Given a set of data and the desire to produce some kind of “ model ” of those data ( model, in this case, meaning a function fitted through the data ), there are a variety of functions that can be chosen for the fit.

Given that their orders were to capture the ship intact at all costs, that kind of opposition proved most frustrating.

Given two integer parameters P and Q, the Lucas sequences of the first kind U < sub > n </ sub >( P, Q ) and of the second kind V < sub > n </ sub >( P, Q ) are defined by the recurrence relations:

Given the controversy surrounding her grave site, it is possible that she may have been initially interred at Kaithal and then later at Delhi but this remains purely a speculation with no evidence of any kind.

Given the nature of most Assassins ' Guild traditions, this could be seen as a kind of impromptu " pass or fail " examination ( see bitter almonds for the reason why ).

Given a complex manifold M, a differential of the first kind ω is therefore the same thing as a 1-form that is everywhere holomorphic ; on an algebraic variety V that is non-singular it would be a global section of the coherent sheaf Ω < sup > 1 </ sup > of Kähler differentials.

Given a graph, one may write for the largest book ( of the kind being considered ) contained within.

Given some encrypted data (" ciphertext "), the goal of the cryptanalyst is to gain as much information as possible about the original, unencrypted data (" plaintext ").

Given a particular query, the DBMS ' query optimizer is responsible for devising the most efficient strategy for finding matching data.

Given a particular query, the DBMS ' query optimizer is responsible for devising the most efficient strategy for finding matching data.

Given the widespread expansion in the tenth revision, it is not possible to convert ICD-9 data sets directly into ICD-10 data sets, although some tools are available to help guide users.

Given the repeated failures and frustrations of workers ' revolutions and movements, Marx also sought to understand capitalism, and spent a great deal of time in the reading room of the British Museum studying and reflecting on the works of political economists and on economic data.

Given fixed resources, it is often better to spend more time collecting additional training data and more informative features than it is to spend extra time tuning the learning algorithms.

Given a model of some atomic positions, these positions and their respective Debye-Waller factors ( or B-factors, accounting for the thermal motion of the atom ) can be refined to fit the observed diffraction data, ideally yielding a better set of phases.

Given that radio communication channels are allocated by agencies such as the Federal Communication Commission giving a prescribed ( maximum ) bandwidth, the advantage of QPSK over BPSK becomes evident: QPSK transmits twice the data rate in a given bandwidth compared to BPSK-at the same BER.

Given the CIA's purposeful destruction of most records, its failure to follow informed consent protocols with thousands of participants, the uncontrolled nature of the experiments, and the lack of follow-up data, the full impact of MKUltra experiments, including deaths, will never be known.

Given inconsistencies and the lack of reliable data and completely contradicting and unpredictable behavior, the true nature of ball lightning is still unknown and was often regarded as a fantasy or a hoax.

Given some training data, a set of n points of the form

Formally, the problem of supervised pattern recognition can be stated as follows: Given an unknown function ( the ground truth ) that maps input instances to output labels, along with training data assumed to represent accurate examples of the mapping, produce a function that approximates as closely as possible the correct mapping.

Given a table of costs and revenues at each quantity, we can either compute equations or plot the data directly on a graph.

Given a grid point field of geopotential height, storm tracks can be visualized by contouring its average standard deviation, after the data has been band-pass filtered.

* Point location: Given a partitioning of the space into cells, produce a data structure that efficiently tells in which cell a query point is located.

* Ray tracing: Given a set of objects in space, produce a data structure that efficiently tells which object a query ray intersects first.

Given inconsistencies and the lack of reliable data, the true nature of ball lightning is still unknown.

Given a set of n + 1 data points ( x < sub > i </ sub >, y < sub > i </ sub >) where no two x < sub > i </ sub > are the same, one is looking for a polynomial p of degree at most n with the property

Given a set of k + 1 data points

Given a set of k + 1 data points

Given the shortcomings of the beneficial acclimation hypothesis, researchers are continuing to search for a theory that will be supported by empirical data.

Given a set of objects in d-dimensional space, preprocess them into a data structure so that for each query ray the first object hit by the ray can be found quickly.

Given the then GDP ($ 7. 095 bln ) of the country, military spending is roughly estimated to be about $ 300 million.

Given current trends in the UMC — with overseas churches growing, especially in Africa, and U. S. churches collectively losing about 1, 000 members a week — it has been estimated that Africans will make up at least 30 % of the delegates at the 2012 General Conference, and it is also possible that 40 % of the delegates will be from outside the U. S. One Congolese bishop has estimated that typical Sunday attendance of the UMC is higher in his country than in the entire United States.

Given the current estimated mass of the black hole, the progenitor star must have lost over 30 solar masses of material.

Given the Russian historical experiences of frequent invasions and the immense death toll ( estimated at 27 million ) and the destruction the Soviet Union sustained during World War II, the Soviet Union sought to increase security by dominating the internal affairs of countries that bordered it.

Given the newness of such technologies, product lifespan can only be estimated, varieties are limited, and distribution is sporadic.

Given the estimation of from, the error bars of can be estimated by the sample variance using the unbiased estimate of the variance:

Given a mean AGB lifetime of one Myr and an outer velocity of, its maximum radius can be estimated to be roughly ( 30 light years ).

Given those conditions, estimated population size is:

Given that the Tenn-Tom Waterway has an estimated lifetime of well over 50 years, the Waterway is expected to play a significant role in southern interstate trade for years to come.

Given those statistics, it is estimated that the population of Nakasongola District in 2010, was approximately 163, 600.

Given those statistics, it is estimated that in 2010, the population of the district was approximately 466, 300.

Given those statistics, it is estimated that the population of the district in 2010 was approximately 332, 900.

Given those statistics, it is estimated that the population of Busia District in 2010 was approximately 287, 800.

Given those statistics, it is estimated that the population of Lira District in 2010, was about 368, 100.

Given the sample mean () and sample coefficient of variation () the parameters and can be estimated:

Given the amount of debt that Manchester United is saddled with, some analysts have estimated that any takeover bid would have to total more than £ 2 billion, of which around £ 1. 6 billion would be needed to match the Glazers ' valuation of the club – double what they paid for the club in 2005.

Given any two estimated models, the model with the lower value of BIC is the one to be preferred.

Given the temperature of the CMB, the temperature of the CνB can be estimated.