lacunary造句

• Thus lacunary sequences are  canonical examples of " bad universal sequences ".
• When an exception exists, it is called a lacunary value of the function.
• Note, for example, that 0 is the only lacunary value of the complex exponential function.
• The two Picard theorems limit the number of possible lacunary values of certain types of holomorphic functions.
• The possibility of a lacunary value is illustrated by the exponential function, which never takes on the value 0.
• The species [ PW 11 O 39 ] 7 & minus; is a lacunary, or defective Keggin ion.
• As with the little theorem, the ( at most two ) points that are not attained are lacunary values of the function.
• Bellow showed that every lacunary sequence of integers is in fact a " bad universal sequence " in " L " 1.
• Because is symmetric, the lacunary part is determined by its terms containing only the variables, i . e ., which do not contain.
• The first known examples of lacunary functions involved Taylor series with large gaps, or lacunae, between the non-zero coefficients of their expansions.
• In the case where the values of " f " are missing a single point, this point is called a lacunary value of the function.
• Greater insight into the underlying question that motivates the investigation of lacunary power series and lacunary trigonometric series can be gained by re-examining the simple example above.
• Greater insight into the underlying question that motivates the investigation of lacunary power series and lacunary trigonometric series can be gained by re-examining the simple example above.
• As evidenced by his publications ( see next ), he focused on complex analysis and harmonic analysis, with an emphasis on Dirichlet series, lacunary series, and entire functions.
• There is a slight ambiguity in the modern usage of the term "'lacunary series "', which may be used to refer to either Taylor series or Fourier series.
• What is not so evident is that the gaps between the powers of " z " can expand much more slowly, and the resulting series will still define a lacunary function.
• The functions exp, cos, and sin so defined have infinite Picard's theorem, which asserts that the range of a nonconstant entire function is either all of \ mathbb { C }, or \ mathbb { C } excluding one lacunary value.
• From this perspective, then, mathematicians who investigate lacunary series are asking the question : How much does the geometric series have to be distorted & ndash; by chopping big sections out, and by introducing coefficients " a " " k " & ne; 1 & ndash; before the resulting mathematical object is transformed from a nice smooth meromorphic function into something that exhibits a primitive form of chaotic behavior?
• More precisely : If and are two homogeneous symmetric polynomials in having the same degree, and if the coefficient of before each monomial which contains only the variables equals the corresponding coefficient of, then and have equal lacunary parts . ( This is because every monomial which can appear in a lacunary part must lack at least one variable, and thus can be transformed by a permutation of the variables into a monomial which contains only the variables .)
• More precisely : If and are two homogeneous symmetric polynomials in having the same degree, and if the coefficient of before each monomial which contains only the variables equals the corresponding coefficient of, then and have equal lacunary parts . ( This is because every monomial which can appear in a lacunary part must lack at least one variable, and thus can be transformed by a permutation of the variables into a monomial which contains only the variables .)