Related papers: The Generalized Law of Total Covariance

We present a complete theory, which is a generalization of Bargmann's theory of factors for ray representations. We apply the theory to the generally covariant formulation of the Quantum Mechanics.

A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.

We prove a generalized Gauss-Kuzmin-L\'evy theorem for the $p$-numerated generalized Gauss transformation $$T_p(x)=\{\frac{p}{x}\}.$$ In addition, we give an estimate for the constant that appears in the theorem.

In this paper we give a generalization of Iseki's formula and use it to prove the transformation law of $\theta_1(z, \tau)$.

One of the variants to proof the generalized Ito-Wentzell's formula is introduced and examined in this paper. The relationship between different representations of the generalized Ito-Wentzell's formula/ is considered.

Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.

We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

We prove some new results related to Tanaka's formula.

We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.

In this paper, we propose a generalization of a congruence due to Carlitz.

The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, and there have been reservations about…

In the present note a generalization of Borel-Cantelli Lemma is proposed.

A vector variational principle is proved.

The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].

This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.

In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…

In this paper we study a group theoretical generalization of the well-known Gauss's formula that uses the generalized Euler's totient function introduced in [11].

A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…