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Showing 1 to 20 of 77 for “"generating function"”.
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Expressions for the generating function of the Donaldson invariants for CP²
… theory by Moore and Witten. We derive the generating function for the Donaldson invariants of CP2 as the stationary phase approximation of the low-energy effective U(I)-gauge theory on CP2 thus obtaining an interpretation of the u-plane integral in terms of determinant line bundles. For the …
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Differential algebraic methods for obtaining approximate numerical solutions to the Hamilton-Jacobi equation
… a perturbative expansion of Hamilton’s principle function about some reference trajectory (RT) through the system. The HJ/DA method also extracts the equations of motion for the RT itself. Hamilton’s principle function generates the canonical transformation, or mapping, between the initial and …
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A sequence related to the Stern sequence
… the Stern sequence. In particular, we derive the generating function for the general bow sequence, and give interpretations of the generating function for two basic cases. We also determine properties of the bow sequences modulo 2 and 3, and give conjectures for the behavior of the bow sequences …
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Weighted Inverse Weibull and Beta-Inverse Weibull Distribution
… Weibull distribution including the hazard function, reverse hazard function, moments, moment generating function, coefficient of variation, coefficient of skewness, coefficient of kurtosis, Fisher information and Shanon entropy are studied. The estimation for the parameters of the …
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The Zero-Truncated Poisson-Weighted Exponential Distribution with Applications
… (the theoretical part), the probability mass function is derived from two methods. Then theoretical properties of the zero-truncated Poisson weighted exponential distribution are discussed: such as probability generating function, moment generating function, characteristic function, and …
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Random Walks with Pheromone
… from each vertex depend on values of a function, f, at neighboring nodes. The work is motivated by applications that arise in bio-inspired models wherein questions of dynamics are effected by pheromone trails. In Chapter 2, we discuss when the graph is the n-cycle, and the set of …
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Counting coloured boxes
… conjecture of Kenyon/Szendroi by computing the generating function for pyramid partitions. Pyramid partitions are closely related to Aztec Diamonds; their generating function turns out to be the partition function for the Donaldson-Thomas theory of a non-commutative resolution of the conifold …
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Algebraic and combinatorial properties of minimal border strip tableaux
… expansion of Schur's Q[sub][lambda] symmetric functions in terms of the power sum symmetric functions. The second result gives a basis for the space spanned by the lowest degree terms in the expansion of the Schur symmetric functions in terms of the power sum symmetric functions. These lowest …
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Combinatorics in Schubert varieties and Specht modules
… certain hyperplane arrangement. We show that the generating function for regions of this arrangement coincides with the Poincaré polynomial if and only if the Schubert variety is rationally smooth. For classical types the arrangements are (signed) graphical arrangements coning from (signed) …
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Practical Aspects Of Kernel Smoothing For Binary Regression And Density Estimation
… This knowledge is encapsulated in the moment generating function, and it is demonstrated that, in most circumstances, the use of the empirical moment generating function and related functions is superior to kernel smoothed estimates.
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Discriminants: calculation, properties, and connection to the root distribution of polynomials with rational generating functions
… and the discriminant of the denominator of its generating function. A more specialized aspect of this area of this research concerns the root distribution and the generating functions of the discriminants of polynomials related to Chebyshev polynomials. Other areas involve the factorization …
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ΜΕΓΙΣΤΟ ΜΗΚΟΣ ΡΟΗΣ ΕΠΙΤΥΧΙΩΝ ΚΑΙ ΠΟΛΥΩΝΥΜΑ ΤΥΠΟΥ-FIBONACCI
… (LN=K) AND P (LN<K) (1<K<N). WE ALSO DERIVE THE GENERATING FUNCTION AND FACTORIAL MOMENTS OF LN. OUR FORMULAS ARE IN TERMS OF FIBONACCI-TYPE POLYNOMIALS OF ORDER K. WE INTRODUCE AND STUDY A NEW DISTRIBUTION, THE BINOMIAL DISTRIBUTION OF ORDER K AND DERIVE THE EXACT DISTRIBUTION OF IT. …
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Discrete Small Sample Asymptotics
Random variables defined on the natural numbers may often be approximated by Poisson variables. Just as normal approximations may be improved by saddlepoint methods, Poisson approximations may be substantially improved by tilting, expansion, and other related methods. This work will develop and …
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Average Cayley genus for Cayley maps with dihedral groups
Let Gamma be a finite group and let Delta be a generating set for Gamma. A Cayley map associated with Gamma and Delta is an oriented 2-cell embedding of the Cayley graph GDelta (Gamma) such that the rotation of arcs emanating from each vertex is determined by a unique cyclic permutation of …
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A new approach in the transient analysis of ATM multiplexers with bursty sources
… derivation of the transient joint probability generating function of the buffer content and the number of active sources. From this, time-dependent performance measures such as mean, variance and distribution of the queue length can be derived. Further, the transient analysis allows us to …
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Laplace transforms, probabilities and queues.
… of the Laplace transform of probability density functions (p.d.f.) for waiting times in queues. We interpret the Laplace transform of a p.d.f. as the probability that the corresponding random variable wins a race against (i.e., is less than) an exponential random variable. This interpretation is …
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Root distribution of polynomials and distance sums on the unit circle
… minimal polynomial of the maximum value and its generating function.
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The joint distribution of the maximum and duration of stochastic events driven by Pareto II observations
… derivations of the joint probability density function, cumulative distribution function, conditional and marginal distributions, conditional survival function, moment-generating function, Laplace transforms, and covariance matrix. We also address the problem of parameter estimation using the …
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Asymptotics of the Rough Heston Model
… small-time asymptotic formulae for the cumulant generating function of the Fractional Heston model as presented in Guennoun et al. (2018). These formulae and their effectiveness for small-time pricing are interrogated and compared against the Rough Heston model proposed in El Euch and Rosenbaum …
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Partition identity bijections related to sign-balance and rank
… generalize Andrews' product formula for the generating function for partitions with respect number of odd parts and number of odd parts of the conjugate. The parameters which we use are related to Stanley's work on the sign-balance of a partition.
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