Bronstein, I.N., Semendjajev, K.A., Musiol, G., Mhlig, H.: Taschenbuch der Mathematik (in german). 5th edn. Thun, Frankfurt/M.: Verlag Harry Deutsch 2001 Home/Search Document Not in Database Summary Related Articles Check |
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Efficient Symbolic Analysis for Parallelizing Compilers and.. - Fahringer (1997) (5 citations) (Correct)
....of integers. They are described in [13] and reviewed in [21] For i 0 there are no closed forms known. However, for i = Gamma1 and 2 n it has been shown [13] that (ln is the natural logarithm) ln(n) ln(n) 1 Gammaln(n) Gamma 1 Gamman Gammaln(n) 13) and also [5] that 2 = 1:65. Based on this approximation it can be shown that for all i 2 the following holds: 2 i , and finally v i 6 if i 2 i 6 if i 2 and i is even i Gamma1 if i 2 and i is odd (14) 11 4.4 Miscellaneous In this section we ....
I. Bronstein and K. Semendjajev. Taschenbuch der Mathematik. Verlag Harri Deutsch, Frankfurt, Germany, ISBN 3 87144492 8, 1989.
Modelling Conditional Probability Densities with Neural Networks - Husmeier (1997) (2 citations) (Correct)
.... Gamma k ] exp ( Gamma fi k [y Gamma k ] 1 Gamma ) exp( Gammafi k y) 1 Gamma exp( Gammafi k k ) exp(sy) exp(s k ) the moment generating function becomes exp(sy)d = d : Now Gamma(1 s=fi k ) Gamma(1 Gamma s=fi k ) Gamma(2) e.g. [10], p.70) where Gamma( is the gamma function Gamma(x) Gammau x Gamma1 du; which has the following properties: Gamma(1) 1; x 6= 0 ) Gamma(x 1) x Gamma(x) Gamma(x) Gamma(1 Gamma x) sin(x) e.g. 10] p.103) Hence and M(s) thus reduces to In order to ....
.... Gamma(1 s=fi k ) Gamma(1 Gamma s=fi k ) Gamma(2) e.g. 10] p. 70) where Gamma( is the gamma function Gamma(x) Gammau x Gamma1 du; which has the following properties: Gamma(1) 1; x 6= 0 ) Gamma(x 1) x Gamma(x) Gamma(x) Gamma(1 Gamma x) sin(x) e.g. [10] p.103) Hence and M(s) thus reduces to In order to obtain the first two moments from M(s) by use of (2.21) M(s) is expanded in a power series up to second order in s, using exp(x) 1 x : and sin (x) for 0 jxj , see [10] p.33) This leads to 1 ....
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Bronstein I.N., Semendjajew, K.A. (1984): Taschenbuch der Mathematik. Thun: Verlag Harri Deutsch. 301
Model Equations And Instability Regions For The.. - Bürger, Karlsen.. (Correct)
....in a simil way as I, whose sign determines the instability region. Namely, for N = 3 the chacteristic polynomial of the Jacobian r( tes the form p, X; x (o)x (o)x t(o) 69) where the leading coefficient has been r r( tr Jf( s = o o It is well known [14] that the equation solutions if and only if with normalized to one and the functions r, s and t are given by (o 0 2 o 3 2 3] t = t( I) der Jf ( I) o o o o o2 o o3 o2 5 P3 (A; I) 0 has one real and one pair of complex conjugate i 2 2 3 1 p p(q) s r , ....
BRONSTEIN, I.N.; SEMENDJAJEW, K.A.: Taschenbuch der Mathematik. Verlag Harri Deutsch, Thun/Frankfurt am Main, 23rd edition, 1987.
The Monogenic Scale-Space: A Unifying Approach to.. - Felsberg, Sommer (2003) (Correct)
.... Kernel The spread in the spatial domain reads (see [15] #x = x = # ( x 3 dx dy ( x 2 s 2 ) 3 dx dy # change to polar coordinates r = x : r 2 s 2 ) 3 dr (r 3 dr # 4s = s where the integrals are evaluated according to [6] 19.5.1.3 integral 63 and 71. The spread in the frequency domain is obtained as ## = change to polar coordinates q = # : q exp( 4#qs) dq o q exp( 4#qs) dq (4#s) 4 (4#s) 4#s where the integrals are evaluated according to [6] 19.6.1 integral ....
....according to [6] 19.5.1.3 integral 63 and 71. The spread in the frequency domain is obtained as ## = change to polar coordinates q = # : q exp( 4#qs) dq o q exp( 4#qs) dq (4#s) 4 (4#s) 4#s where the integrals are evaluated according to [6] 19.6.1 integral 1. Hence (#x) ##) 4# in the case of the Poisson kernel which means that the uncertainty is slightly worse than for the 2D Gaussian kernel (factor # 1.5) Acknowledgments We appreciate the help of Nils Madeja for translating parts of [29] for finding the error in the original ....
Bronstein, I., Semendjajew, K., Musiol, G., and M uhlig, H. Taschenbuch der Mathematik. Verlag Harri Deutsch, Frankfurt, 1993.
Scale Adaptive Filtering Derived from the Laplace Equation - Felsberg, Sommer (2001) (1 citation) (Correct)
....11 A. 3 Uncertainty of the Poisson Kernel The spread in the spatial domain reads x = x = g(x; y; s) g(x; y; s) 1=2 change to polar coordinates r = R = s where the integrals are evaluated according to [2] 19.5.1.3 integral 63 and 71. The spread in the frequency domain is obtained as u = u = G(u; v; s) G(u; v; s) RR exp( 4 change to polar coordinates q = exp( 4 qs) dq q exp( 4 qs) dq 4 s where the integrals are evaluated ....
....63 and 71. The spread in the frequency domain is obtained as u = u = G(u; v; s) G(u; v; s) RR exp( 4 change to polar coordinates q = exp( 4 qs) dq q exp( 4 qs) dq 4 s where the integrals are evaluated according to [2] 19.6.1 integral 1. Hence ( x) u) which means that the uncertainty is slightly worse than for the 2D Gaussian kernel (factor 1:5) 12 ....
BRONSTEIN, I., SEMENDJAJEW, K., MUSIOL, G., AND M UHLIG, H. Taschenbuch der Mathematik. Verlag Harri Deutsch, Frankfurt, 1993.
A novel generalized optimization criterion for transmit.. - Meurer, Tröger, Jotten (Correct)
....the identity matrix of dimension #K#S###K#S#. 17) represents an optimization problem with the side condition (11) and complex valued unknowns. This kind of optimization problem can be transformed into an optimization problem without side condition by employing the Lagrange multiplier technique [14]. This proceeding leads to the Lagrange cost function E# # # #; 19) which has to be minimized. # in (19) is termed Lagrange multiplier. With the complex Nabla operator # 6 6 6 . 7 7 7 (20) originally introduced as Wirtinger derivative in [15] the cost ....
....of directions of departure The average energy T ###### radiated in the azimuth should be minimized. Utilizing the weighting function (38) to describe the omnidirectional uniform distribution, with (33) the corresponding spatial covariance matrix # # # # # (39) with the elements [14] ## # # ### ## # # ;i;j ##: K # ; 40) can be obtained. # # ### in (40) denotes the Bessel function of first kind and zero order. 40) shows that each element ## # # ### , i ##: K # , j ##: K #,o f# # only depends on the wavelength and the distance ## # between two AEs i and j. ....
I.N. Bronstein and K.A. Semendjajew, Taschenbuch der Mathematik, Verlag Harry Deutsch, Frankfurt/Main, 1985.
Modelling Conditional Probability - Densities With Neural (Correct)
....probability density from (2.17) into (2.20) gives Using the substitution y y( with 1 t exp( y ] 1 q exp( y) exp( the moment generating function becomes M(s) al exp(sy)dq k 0 1 alexp(lls) 1 ) s kd. Now d z r(1 s k)r(1 s k) r(2) e.g. [10], p.70) where F( is the gamma function r(x) f e UuX ldu which has the following properties: r(1) l, x 0 r(x l) xr( re)r(1 ) sin(rx) e.g. 10] p.103) Hence = sin( sMk) and M(s) thus reduces to M(s) yakexp( S)sij ) In order to obtain the first two moments ....
....function becomes M(s) al exp(sy)dq k 0 1 alexp(lls) 1 ) s kd. Now d z r(1 s k)r(1 s k) r(2) e.g. 10] p. 70) where F( is the gamma function r(x) f e UuX ldu which has the following properties: r(1) l, x 0 r(x l) xr( re)r(1 ) sin(rx) e.g. [10] p.103) Hence = sin( sMk) and M(s) thus reduces to M(s) yakexp( S)sij ) In order to obtain the first two moments from M(s) by use of (2.21) M(s) is expanded in a power series up to second order in s, using x 2 exp(x) 1 q x q q . sin l(x) 1 x (for 0 Il , see [10] ....
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Bronstein I.N., Semendjajew, K.A. (1984): Taschenbuch der Mathematik. Thun:
Design and Analysis of Low-Complexity Interference.. - Müller, Verdú (2001) (Correct)
....to the MMSE detector would be meaningless if there were no simple ways to implement them. A fast structure to implement a linear th order detector for fixed weights has been found in [27] There, the computations are accelerated compared to (7) using a generalization of Horner s scheme [28]: 67) Fig. 8. Block structure for first order approximate linear MMSE detection [27] This means that multiplications between matrices are avoided by subsequent respreading and matched filtering. In effect, only multiplications between matrices and vectors are required. For , the receiver is ....
I. N. Bronstein and K. A. Semendjajew, Taschenbuch der Mathematik, 22nd ed., B. G. Teubner, Ed. Frankfurt, Germany, 1985.
Multi-Lingual Prosodic Processing - Buckow, Huber, Warnke, Batliner.. (1999) (Correct)
....be interpreted as a transformation of a fea ture F (u) with mean F (I) F (X) and standard deviation F (I)oe F (X) to a feature with mean 0 and standard deviation 1. If we assume that the F (u) are independent random variables then F (u 1 ) oe F (u 2 ) oe F (u 1 ) F (u 2 ) see e.g. [5]) Thus, we can compute the mean F (w) and the standard deviation oe F (w) for a word w = p1 ; p2 ; p3 ; pn) with phonemes p i as shown in Equations 3 and 4 as long as F (w) F (p1) F (p2) F (pn) F (w) F (p i ) 3) oe F (w) q F (p 1 ) F (p 2 ) F (pn ) v ....
I.N. Bronstein and K.A. Semendjajew. Taschenbuch der Mathematik. Verlag Harri Deutsch, Thun und Frankfurt /Main, 24 edition, 1989.
Fast and Robust Features for Prosodic Classification - Buckow, Warnke, Huber.. (1999) (Correct)
....2 can be interpreted as a transformation of a feature with mean F (I) F (X) and standard deviation F (I)oe F (X) to a feature with mean 0 and standard deviation 1. If we assume that the F (u) are independent random variables then oe F (u1 ) oe F (u2 ) oe F (u1 ) F (u2 ) see e.g. [4]) Thus, we can compute the mean F (w) and the standard deviation oe F (w) for a word w = p 1 ; p 2 ; p 3 ; pn ) with phonemes p i as shown in Equations 3 and 4 (if F (w) F (p 1 ) F (p 2 ) F (p n ) F (w) F (p i ) 3) oe F (w) q F (p1 ) F (p2 ) F (pn ) ....
I.N. Bronstein and K.A. Semendjajew. Taschenbuch der Mathematik. Verlag Harri Deutsch, Thun und Frankfurt/Main, 24 edition, 1989.
Backing up a Truck in Real-Time - Zöbel, Polock (2000) (Correct)
.... aa cos(u v) 8) aa y = r zk sin(u) l aa sin(u v) 9) Dragging from position zk lead to changes of position aa: d(aa x ) d(aa y ) tan(u v) 10) For a functional description of the maneuver we are interested in a relation between u and v which can be derived in several steps (see [3], pages 55 and 284 in the case of r zk l aa ) u = 2r zk # r 2 zk l 2 aa arctan # r zk l aa # r 2 zk l 2 aa tan(v 2) # (11) Decisive for our purposes is only a small range of angles. For a maneuver from a straight line to a right arc the steering wheels are set to ....
I. N. Bronstein and K. A. Semendjajew. Taschenbuch der Mathematik, volume 25. Auflage. B. G. Teubner, Leipzig, 1991.
Z-Transform Package for REDUCE - Koepf, Temme (1995) (Correct)
.... 2 2 2 a b a c a b a c b c b c 6 EXAMPLES 6 11: invztrans(z log(z (z a) z,n) n a a n 1 12: invztrans(e (1 (a z) z,n) 1 n a factorial(n) 13: invztrans(z (z cosh(a) z 2 2 z cosh(a) 1) z,n) cosh(a n) Examples: Solutions of Di#erence Equations I (See [1], p. 651, Example 1) Consider the homogeneous linear di#erence equation f n 5 2f n 3 2f n 2 3f n 1 2f n = 0 with initial conditions f 0 = 0, f 1 = 0, f 2 = 9, f 3 = 2, f 4 = 23. The Z Transform of the left hand side can be written as F (z) P (z) Q(z) where P (z) 9z 3 2z ....
.... 2 z (9 z 2 z 5) ztransresult : ztrans(f(n) n,z) 5 3 2 z 2 z 2 z 3 z 2 22: result: invztrans(part(first(ztransresult) 2) z,n) n n n n 2 ( 2) i ( 1) i 4 n result : 2 II (See [1], p. 651, Example 2) Consider the inhomogeneous di#erence equation: f n 2 4f n 1 3f n = 1 with initial conditions f 0 = 0, f 1 = 1. Giving 6 EXAMPLES 8 F (z) Z 1 # 1 z 2 4z 3 z z 2 4z 3 # = z z 1 # 1 z 2 4z 3 z z 2 4z 3 # . The Inverse Z Transform results ....
Bronstein, I.N. and Semedjajew, K.A., Taschenbuch der Mathematik, Verlag Harri Deutsch, Thun und Frankfurt(Main), 1981. ISBN 3 87144 492 8.
On linear constraints with uncertain coefficients (Extended.. - Seelisch (2001) (Correct)
....to I J def = f i j : i 2 I; j 2 J g; 3) where is de ned only if 0 62 J . It is easy to see that the resulting subsets of R are again bounded, closed real intervals. Now, having de ned the four basic arithmetic operations also for uncertain coecients, Gauss s Elimination Algorithm (see [BS2]) can immediately be applied to linear equations with uncertain coecients. Runtimes have shown to be similar to runtimes obtained for ordinary linear equations. The price for good runtime results is incompleteness of the computational results, due to the incompleteness of naiv interval calculus. ....
Bronstein-Semendjajew, Taschenbuch Der Mathematik, Verlag Nauka, Moskau, BSB B. G. Teubner Verlagsgesellschaft, Leipzig, pp. 157-158, 1989
Visualising deformation fields computed by non-linear image.. - Tittgemeyer, al. (2002) (2 citations) (Correct)
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Bronstein, I.N., Semendjajev, K.A., Musiol, G., Mhlig, H.: Taschenbuch der Mathematik (in german). 5th edn. Thun, Frankfurt/M.: Verlag Harry Deutsch 2001
Monitoring Structural Change in the Brain: Application .. - Tittgemeyer, Wollny.. (2002) (Correct)
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I. N. Bronstein, K. A. Semendjajev, G. Musiol, and H. M uhlig. Taschenbuch der Mathematik (in german). Verlag Harry Deutsch, Thun
Multivariate Fractionally Integrated CARMA Processes - Marquardt (2006) (Correct)
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Bronstein, I. N., Semendjajew, K. A., Musiol, G. & Muhlig, H. (1999). Taschenbuch der Mathematik, 4 edn, Verlag Harri Deutsch.
A Model-Based Framework for Optimal Measurements in Machine.. - Brunn, Hanebeck (2005) (Correct)
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I. Bronstein, K. Semendjajew, G. Musiol, and G. M uhlig, Taschenbuch der Mathematik, 3rd ed. Harry Deutsch Verlag, 1998.
Efficient Symbolic Analysis for Parallelizing Compilers and.. - Fahringer (1998) (5 citations) (Correct)
No context found.
I. Bronstein and K. Semendjajev. Taschenbuch der Mathematik. Verlag Harri Deutsch, Frankfurt, Germany, ISBN 3 87144492 8, 1989.
Representing Orientation in N-Dimensional Spaces - Rieger, van Vliet (2003) (Correct)
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I.N. Bronstein, K.A.Semendjajew, G. Musiol, and H. Muhlig. Taschenbuch der Mathematik. Verlag Harri Deutsch, Thun, Frankfurt (Main), 4th edition, 1999.
Basic morphological operations, band-limited images and.. - Pattern Recog Nition (2003) (Correct)
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Bronstein, I.N., Semendjaev, K.A., Musiol, G., Muhlig , H.: Taschenbuch der Math ematik. 4th edn. Verlag Harri Deutsch, Thun, Frankfurt am Main (1999)
The Effect of Imperfect SNR Knowledge on Multiantenna - Multiuser Systems With (2003) (Correct)
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I. Bronstein, K. Semendjajew, G. Musiol, H. Muhlig, Taschenbuch der Mathematik, Verlag Harri Deutsch, 1999.
Grouping based on Projective Geometry Constraints and Uncertainty - Utcke (1997) (5 citations) (Correct)
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I. N. Bronstein and K. A. Semendjajew. Taschenbuch der Mathematik. G. Grosche and V. Ziegler and D. Ziegler, Harri Deutsch, Thun und Frankfurt (Main), 23. edition, 1987.
Application of the Multiple Space-Time Scale Analysis on a.. - Schiller (1998) (Correct)
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Il'ja N. Bronstein and Konstantin A. Semendjaev. Taschenbuch der Mathematik. Harry Deutsch, Thun, 24. edition 1989.
Representation of Unique Sequences in Libraries of.. - Tabler, Benos, Dörr (1996) (Correct)
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Bronstein,I.N. and Semendjajew,K.A. (1979) Taschenbuch der Mathematik. Verlag Harri Deutsch, Thun und Frankfurt/Main, Germany.
Querying Semistructured Data Based On Schema Matching - Bergholz (1999) (1 citation) (Correct)
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I. N. Bronstein, K. A. Semendjajew, G. Musiol, and H. Muhlig. Taschenbuch der Mathematik. Harri Deutsch, Thun, Frankfurt, Germany, 1993.
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