We propose two algorithms for sampling from two gamma variates possessing a negative correlation. The case of positive correlation is easily solved, so we just mention it. The main problem is the lowest value of the correlation coefficient that can be reached. The starting point of both algorithms is generation from a bivariate density with uniform negatively correlated marginals. Actually the ...

A traditional method of Monte Carlo computer simulation is to obtain uniformly distributed random numbers on the interval from zero one a linear congruential generator (LCG) or other methods. Random variates can then be obtained by inverse transformation technique applied numbers. The used as input simulation. response variable results. may biased for various reasons. One reason presence small ...

Abstract This paper proposes a numerical model of the network of two-Chinese-character compound words (two-character network, for short). In this network, a Chinese character is a node and a twoChinese-character compound word links two nodes. The basic framework of the model is that an important character gets many edges. As the importance of a character, we use the frequency of each character ...

Problem 2. (a) For any ring R, define a ring structure on the abelian group R̃ = R×Z such that (0, 1) is the identity of R̃ and the inclusion map R ↪→ R̃, r 7→ (r, 0) is a rng homomorphism. (b) Let C be the category of rings without identity. Show that the functor F : C → Rings such that F (R) = R̃ is a left adjoint to the forgetful functor G : Rings→ C taking a ring with identity R to R considered...

We prove that the solution of the Kac analogue of Boltzmann’s equation can be viewed as a probability distribution of a sum of a random number of random variables. This fact allows us to study convergence to equilibrium by means of a few classical statements pertaining to the central limit theorem. In particular, a new proof of the convergence to the Maxwellian distribution is provided, with a ...

The goal of the paper is to study asymptotic behavior of the number of lost messages. Long messages are assumed to be divided into a random number of packets which are transmitted independently of one another. An error in transmission of a packet results in the loss of the entire message. Messages arrive to the M/GI/1 finite buffer model and can be lost in two cases as either at least one of it...

In this paper X denotes a set, R, R1, R2 denote binary relations, x, y, z denote sets, and n, m, k denote natural numbers. Let us consider a binary relation R on X. Now we state the propositions: (1) fieldR ⊆ X. (2) If x, y ∈ R, then x, y ∈ X. Now we state the propositions: (3) Let us consider sets X, Y . Then (idX)Y = X ∩ Y . (4) 〈x, y〉 ∈ R |2 X if and only if x, y ∈ X and 〈x, y〉 ∈ R. (5) dom(...

We study a model describing the spread of a globalized culture in a population of individuals localized at the nodes of a social network. The influence of this globalized culture, assumed to be foreign to the local culture, is measured by a probability to convince each individual to adopt its cultural traits. This probability depends upon the degree s—a real between 0 and 1—of “wise” skepticism...

In this paper n is a natural number. One can prove the following propositions: (1) For every non empty subset X of E2 T and for every compact subset Y of E2 T such that X ⊆ Y holds N-boundX ¬ N-boundY. (2) For every non empty subset X of E2 T and for every compact subset Y of E2 T such that X ⊆ Y holds E-boundX ¬ E-boundY. (3) For every non empty subset X of E2 T and for every compact subset Y ...

We consider the occupancy problem where balls are thrown independently at infinitely many boxes with fixed positive frequencies. It is well known that the random number of boxes occupied by the first n balls is asymptotically normal if its variance Vn tends to infinity. In this work, we mainly focus on the opposite case where Vn is bounded, and derive a simple necessary and sufficient condition...