Sentence examples for improper problem from inspiring English sources

had posed the improper Znám problem for k = 3, and, independently of Znám, found all solutions to the improper problem for k ≤ 5. showed that Znám's problem is unsolvable for k < 5, and credited J. Janák with finding the solution {2, 3, 11, 23, 31} for k = 5.

Thus, it is a solution to the improper Znám problem, but not a solution to Znám's problem as it is usually defined.

One solution to the improper Znám problem is easily provided for any k: the first k terms of Sylvester's sequence have the required property.

Any solution to the improper Znám problem is equivalent (via division by the product of the xi's) to a solution to the equation :\sum\frac1{x_i} + \prod\frac1{x_i}=y, where y as well as each xi must be an integer, and conversely any such solution corresponds to a solution to the improper Znám problem.

Figure 4c,d illustrates the improper ROI problems for trucks and SUVs using the generation rule for sedans.

Voting machines are not without problems, in that they may marginally depress the level of voting owing to improper use, a problem that can be overcome through improved machines and voter education.

So what is P&G's problem? "Improper use of the trade marks BRAUN and Oral B in this manner is misleading to the public and could potentially result in injury".

Vocal-cord injury bears a stigma in the world of opera — it is wrongly thought to be caused invariably by improper technique, though problems can arise with the most technically proficient of singers.

"If the president believes there is a problem with improper use of sick time, her supervisors have the tools to remedy any alleged abuse.

Ron Gallagher, a deputy commissioner with the Pennsylvania Insurance Department, said, "I don't know that we have a real problem with improper claim denials".

In a ruling made public last week, Judge William Pauley III of Federal District Court refused to lift an injunction imposed last year that prevents the city from creating more job centers until it corrects the problem of improper denials.