In this paper, by using the p-adic q-integral on Zp which was defined by Kim, we define the weighted Carlitz q-Bernoulli polynomials and investigate some identities of these polynomials. In particular, we define the weighted degenerate Carlitz’s q-Bernoulli polynomials and numbers and give some interesting properties that are associated with these numbers and polynomials. AMS subject classifica...

We give a formula that expresses a sum of products of poly-Bernoulli numbers of negative index as a linear combination of poly-Bernoulli numbers. More generally, we show that if a two-variable formal power series satisfies a certain partial differential equation, then its coefficients satisfy this type of formula. As an appendix, we solve this partial differential equation.

This paper proposed a new regression model called l1regularized outlier isolation and regression (LOIRE) and a fast algorithm based on block coordinate descent to solve this model. Besides, assuming outliers are gross errors following a Bernoulli process, this paper also presented a Bernoulli estimate model which, in theory, should be very accurate and robust due to its complete elimination of ...

As deep neural networks (DNNs) are applied to increasingly challenging problems, they will need to be able to represent their own uncertainty. Modelling uncertainty is one of the key features of Bayesian methods. Using Bernoulli dropout with sampling at prediction time has recently been proposed as an efficient and well performing variational inference method for DNNs. However, sampling from ot...

The aim of this paper is to give a congruence on universal Bernoulli numbers which congruence is the same type of Kummer’s original paper [K]. The remakable thing is the index of prime power that is the modulus of the congruence is half of the original one. We mention in this paper that this estimate is best possible. It is suprising fact for the author that the critical index is not less than ...

BACKGROUND The assessment of the severity of aortic valve stenosis is done by either invasive catheterization or non-invasive Doppler Echocardiography in conjunction with the simplified Bernoulli equation. The catheter measurement is generally considered more accurate, but the procedure is also more likely to have dangerous complications. OBJECTIVE The focus here is on examining computational...

Geometrically simple Bernoulli generators are constructed for certain ergodic endomorphisms of solenoids. An arbitrary ergodic solenoidal group automorphism is obtained as the limit of a sequence of such Bernoulli factors and hence, by a theorem of D. S. Ornstein, must be measuretheoretically isomorphic to a Bernoulli shift. In his survey paper [6], B. Weiss stated that, using Y. Katznelson's m...

In the wake of D. Ornstein's proof five years ago that Bernoulli shifts with the same entropy are isomorphic came a flood of new results concerned in one way or another with Bernoulli shifts. Perhaps most surprising has been the discovery that so many of the classical examples of ergodic theory, as well as many "physical" systems, are isomorphic to Bernoulli shifts. We shall not discuss this as...

We present a relationship between the generalized hyperharmonic numbers and poly-Bernoulli polynomials, motivated from connections harmonic Bernoulli numbers. This yields numerous identities for hyper-sums several congruences.