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In recent years, slash and skew slash distributions have been employed, as flexible models, in various fields. In this paper, we study several properties of these distributions in both univariate and multivariate cases. Some recurrence relations for the probability density functions are derived and the behavior of reliability measures, such as hazard rate and mean residual life, associated to these distributions are investigated.

A ring *R* is called *NLI* (rings whose nilpotent elements form a Lie ideal) if for each *a* ∈ *N*(*R*) and *b* ∈ *R*, *ab* − *ba* ∈ *N*(*R*). Clearly, *NI* rings are *NLI*. In this note, many properties of *NLI* rings are studied. The main results we obtain are the following: (1) *NLI* rings are directly finite and left min-abel; (2) If *R* is a *NLI* ring, then (a) *R* is a strongly regular ring if and only if *R* is a Von Neumann regular ring; (b) *R* is (weakly) exchange if and only if *R* is (weakly) clean; (c) *R* is a reduced ring if and only if *R* is a *n*-regular ring; (3) If *R* is a *NLI* left *MC*2 ring whose singular simple left modules are *Wnil*-injective, then *R* is reduced.

A recently published paper [6] considered the total graph of commutative ring *R*. In this paper, we compute Wiener, hyper-Wiener, reverse Wiener, Randić, Zagreb, *ABC* and *GA* indices of zero-divisor graph.

The classification of Bruce and Gaffney respectively Gibson and Hobbs for simple plane curve singularities respectively simple space curve singularities is characterized in terms of invariants. This is the basis for the implementation of a classifier in the computer algebra system singular.

The maximal Orlicz spaces such that the mixed logarithmic means of multiple Walsh-Fourier series for the functions from these spaces converge in measure and in norm are found.

*V*be the 2-dimensional column vector space over a finite field

*q*is necessarily a power of a prime number) and let ℙ

_{q}be the projective line over

*GL*

_{2}(

*q*), for

*q*≠ 3, and

*SL*

_{2}(

*q*) acting on

*V*− {0} have the strict EKR property and

*GL*

_{2}(3) has the EKR property, but it does not have the strict EKR property. Also, we show that

*GL*

_{n}(

*q*) acting on

*PSL*

_{2}(

*q*) acting on ℙ

_{q}, where

*q*≡ −1 (mod 4), has a clique of size

*q*+ 1.

We study basic properties of the generalized ideal transforms *D*
_{I} (*M*, *N*) and the set of associated primes of the modules *R*
^{i}
*D*
_{I} (*M*, *N*).

*G*be a finite group. A subgroup

*H*of

*G*is called an

*G*if

*N*

_{G}(

*H*) ∩

*H*

^{g}≤

*H*for all

*g*∈

*G*. A subgroup

*H*of

*G*is called a weakly

*G*if there exists a normal subgroup

*K*of

*G*such that

*G*=

*HK*and

*H*∩

*K*is an

*G*. In this article, we investigate the structure of a group

*G*in which every subgroup with order

*p*

^{m}of a Sylow

*p*-subgroup

*P*of

*G*is a weakly

*G*, where

*m*is a fixed positive integer. Our results improve and extend the main results of Skiba [13], Jaraden and Skiba [11], Guo and Wei [8], Tong-Veit [15] and Li et al. [12].

A new generalization of the logarithmic series distribution has been obtained as a limiting case of the zero-truncated Mishra’s [10] generalized negative binomial distribution (GNBD). This distribution has an advantage over the Mishra’s [9] quasi logarithmic series distribution (QLSD) as its moments appear in compact forms unlike the QLSD. This makes the estimation of parameters easier by the method of moments. The first four moments of this distribution have been obtained and the distribution has been fitted to some well known data-sets to test its goodness of fit.

An upper bound is given on the size of a *k*-fan-free 3-graph, and an infinite family reaching this bound is also described.