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991.
Let $$P_n (x) = \frac{{( - 1)^n }}{{2^n n!}}\frac{{d^n }}{{dx^n }}\left[ {(1 - x^2 )^n } \right]$$ be thenth Legendre polynomial. Letx 1,x 2,…,x n andx*1,x*2,…,x* n?1 denote the roots ofP n (x) andP′ n (x), respectively. Putx 0=x*0=?1 andx* n =1. In this paper we prove the following theorem: Ify 0,y 1,…,y n andy′ 0,y′ 1, …,y′ n are two systems of arbitrary real numbers, then there exists a unique polynomialQ 2n+1(x) of degree at most 2n+1 satisfying the conditions $$Q_{2n + 1} (x_k^* ) = y_k and Q_{2n + 1}^\prime (x_k ) = y_k^\prime (k = 0,...,n).$$ . 相似文献
992.
Dapeng Liu Binod R. Giri Milán Szőri Béla Viskolcz Et-touhami Es-sebbar Aamir Farooq 《Proceedings of the Combustion Institute》2021,38(1):967-976
NOx mitigation is a central focus of combustion technologies with increasingly stringent emission regulations. NOx can also enhance the autoignition of hydrocarbon fuels and can promote soot oxidation. The reaction between allyl radical (C3H5) and NOx plays an important role in the oxidation kinetics of propene. In this work, we measured the absolute rate coefficients for the redox reaction between C3H5 and NOx over the temperature range of 1000–1252 K and pressure range of 1.5–5.0 bar using a shock tube and UV laser absorption technique. We produced C3H5 by shock heating of C3H5I behind reflected shock waves. Using a Ti:Sapphire laser system with frequency quadrupling, we monitored the kinetics of C3H5 at 220 nm. Unlike low-temperature chemistry, the two target reactions, C3H5 + NO → products (R1) and C3H5 + NO2 → products (R2), exhibited a strong positive temperature dependence for this radical-radical type reaction. However, these reactions did not show any pressure dependence over the pressure range of 1.5–5.0 bar, indicating that the measured rate coefficients are close to the high-pressure limit. The measured values of the rate coefficients resulted in the following Arrhenius expressions (in unit of cm3/molecule/s):To our knowledge, these are the first high-temperature measurements of allyl + NOx reactions. The reported data will be highly useful in understanding the interaction of NOx with resonantly stabilized radicals as well as the mutual sensitization effect of NOx on hydrocarbon fuels. 相似文献
993.
Margit Lénárd 《Acta Mathematica Hungarica》1999,84(4):317-327
Let the set of knots
(n 1) be given on the interval [-1, 1]. Find a polynomial Qm(x) of minimal degree satisfying (0, 2)-interpolational conditions at the inner knots and boundary conditions at the endpoints, that is
and
where yi
(s),O
(j), n+1
(j) are arbitrarily given real numbers, and k, l are arbitrary fixed non-negative integers. In this paper the existence and uniqueness of the polynomial Qm(x) is proved if the inner nodal points are the zeros of Jacobi polynomials Pn
2k + 1, 2l – 1 (x) or Pn
2k – 1, 2l + 1 (x). Explicit formulae for the fundamental polynomials of interpolation are also given. 相似文献
994.
R. Díaz 《Discrete and Computational Geometry》1999,21(4):581-601
We give a characterization of the Gram matrices of spherical and finite-volume hyperbolic polytopes of a given combinatorial
type. This is done in terms of the signs of certain minors of the Gram matrix.
Received June 20, 1997, and in revised form November 21, 1997. 相似文献
995.
Jesús Rodríguez Kristen Kobylus Abernathy 《Journal of Mathematical Analysis and Applications》2012,385(1):49-59
Our goal in this paper is to provide sufficient conditions for the existence of solutions to discrete, nonlinear systems subject to multipoint boundary conditions. The criteria we present depends on the size of the nonlinearity and the set of solutions to the corresponding linear, homogeneous boundary value problems. Our analysis is based on the Lyapunov–Schmidt Procedure and Brouwer?s Fixed Point Theorem. The results presented extend the previous work of D. Etheridge and J. Rodríguez (1996, 1998) [5], [6] and J. Rodríguez and P. Taylor (2007) [18], [19]. 相似文献
996.
997.
Margareth S. Alves Jaime E. Muñoz Rivera Mauricio Sepúlveda Octavio P. Vera Villagrán 《Applied Mathematics Letters》2012,25(5):884-889
In this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a mixture of two rigid solids modeling temperature and porosity. Our main result is to establish conditions which ensure the analyticity and the exponential stability of the corresponding semigroup. 相似文献
998.
Studying the algebraic structure of the YangiansY(sl(2)), andY(sl(3)) we present their boson realizations. In the case ofY(sl(2)) we give the realization by using 1-canonical boson pair and two parameters and in theY(sl(3)) with 2-canonical boson pairs, two parameters and subalgebrasl(2). Substituting the realization ofU(sl(2)), we can obtain the pure boson realization by 3-canonical pairs and three parameters.Presented at the 4th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995. 相似文献
999.
Nguy?n H. V. Hu’ng 《Mathematische Annalen》2012,353(3):827-866
The Dickson–Mùi algebra consists of all invariants in the mod p cohomology of an elementary abelian p-group under the general linear group. It is a module over the Steenrod algebra, A{\mathcal {A}} . We determine explicitly all the A{\mathcal {A}} -module homomorphisms between the (reduced) Dickson–Mùi algebras and all the A{\mathcal {A}} -module automorphisms of the (reduced) Dickson–Mùi algebras. The algebra of all A{\mathcal {A}} -module endomorphisms of the (reduced) Dickson–Mùi algebra is claimed to be isomorphic to a quotient of the polynomial algebra on one indeterminate. We prove that the reduced Dickson–Mùi algebra is atomic in the meaning that if an A{\mathcal {A}} -module endomorphism of the algebra is non-zero on the least positive degree generator, then it is an automorphism. This particularly shows that the reduced Dickson–Mùi algebra is an indecomposable A{\mathcal {A}} -module. The similar results also hold for the odd characteristic Dickson algebras. In particular, the odd characteristic reduced Dickson algebra is atomic and therefore indecomposable as a module over the Steenrod algebra. 相似文献
1000.
Eduard Krajník Vincente Montesinos Peter Zizler Václav Zizler 《Applications of Mathematics》2012,57(5):543-550
The inverse Fast Fourier Transform is a common procedure to solve a convolution equation provided the transfer function has no zeros on the unit circle. In our paper we generalize this method to the case of a singular convolution equation and prove that if the transfer function is a trigonometric polynomial with simple zeros on the unit circle, then this method can be extended. 相似文献