sums and products
Sums and products of indirect utility functions
... and Products of Indirect Utility Functions DENIS CONNIFFE* NIRSA and NUI, Maynooth Abstract: There are relatively few known demand systems that are theoretically satisfactory and practically ...considering ...
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Correlation kernels for sums and products of random matrices
... of sums and products of random matrices can be described under fairly general conditions using free probability techniques ...the sums and products of random matri- ces, until recently there ...
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Correlation kernels for sums and products of random matrices
... of sums and products of random matrices can be described under fairly general conditions using free probability techniques ...the sums and products of random matri- ces, until recently there ...
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Simultaneous Determination Of Adjusted Ranks Of Sample Observations And Their Sums And Products
... Intrinsically, Sums of ...rank sums, products, sums of squares and breaking of ties between sample observations in their rankings (Gibbons ...
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Almost sure central limit theorem for products of sums of partial sums
... 6. Wu, QY: Almost sure central limit theory for products of sums of partial sums. Appl. Math. J. Chin. Univ. Ser. B 27, 169-180 (2012) 7. Petrov, V: Sums of Independent Random Variables. ...
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Sums of Products of Euler Polynomials and Numbers
... Recommended by Vijay Gupta We derive formulae for the sums of products of the q-Euler polynomials and numbers using the multivariate fermionic p-adic q-Volkenborn integral on Z p . Copyright q 2009 ...
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Sums of finite products of Genocchi functions
... Abstract In a previous work, it was shown that Faber-Pandharipande-Zagier and Miki’s identities can be derived from a polynomial identity which in turn follows from a Fourier series expansion of sums of ...
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Sums of finite products of Bernoulli functions
... Full list of author information is available at the end of the article Abstract In this paper, we consider three types of functions given by sums of finite products of Bernoulli functions and derive their ...
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Sums of products of the degenerate Euler numbers
... Abstract The paper focuses on the degenerate Euler numbers, the degenerate Euler polynomials and the degenerate Bernoulli polynomials. By adopting the method of recurrences, two explicit expressions have been established ...
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Sum-of-Products and Product-of-Sums expressions
... Notes 3 Even if your students have never heard of Boolean algebra before, they should still be able to determine which of the first four expressions are SOP and which are POS. If there is any confusion on this point, ask ...
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Sums of finite products of Legendre and Laguerre polynomials
... study sums of finite products of Legendre and Laguerre polynomials and derive Fourier series expansions of functions associated with ...those sums of finite products as linear combinations of ...
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Sums of products of two reciprocal Fibonacci numbers
... reciprocal sums of the products of two Fibonacci numbers in several ...the sums of the reciprocals of the products of two Fibonacci numbers and establish ...
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Series of sums of products of higher order Bernoulli functions
... Full list of author information is available at the end of the article Abstract It is shown in a previous work that Faber-Pandharipande-Zagier’s and Miki’s identities can be derived from a polynomial identity, which in ...
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Some results for sums of products of Chebyshev and Legendre polynomials
... Abstract In this paper, we perform a further investigation of the Gegenbauer polynomials, the Chebyshev polynomials of the first and second kinds and the Legendre polynomials. By making use of some analytic and ...
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Sums of products of Apostol Bernoulli and Apostol Euler polynomials
... of sums of products of any number of Apostol-Bernoulli and Apostol-Euler polynomials and numbers are established by applying the generating function methods and some summation transform ...
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Finite rank sums of products of Toeplitz and Hankel operators
... and products of Toeplitz operators or Hankel ...are sums of any two of the form T u H v or H u T v and characterize such operators to have finite rank; see Theorem ...
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Sums of finite products of Chebyshev polynomials of the third and fourth kinds
... study sums of finite products of Chebyshev polynomials of the third and fourth kinds and obtain Fourier series expansions of functions associated with ...those sums of finite products as linear ...
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Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials
... consider sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials and derive Fourier series expansions of functions associated with ...those sums of finite ...
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Fourier series of sums of products of ordered Bell and poly Bernoulli functions
... 5 Results and discussion In this paper, we study three types of sums of products of ordered Bell and poly-Bernoulli functions and derive their Fourier series expansion. In addition, we express those func- ...
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A parallel algorithm for the calculation of Kronecker products/sums on hypercube processor topologies
... paper shows that Kronecker products/sums can be viewed as simple algebraic operations performed on the elements residing on (n,b,k)-hypercubes.This technique provides a [r] ...
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