We study maxima of linear processes with heavy-tailed innovations and random coefficients. Using the point process approach we derive functional convergence of the partial maxima stochastic process in the space of cadlag functions on $[0,1]$ endowed with the Skorohod $M_{1}$ topology.
By utilizing integral arithmetic mean $F$ defined as
$$
F(x,y)=\left\{\begin{array}{cc}
\frac{1}{y-x}\int_{x}^{y}f(t)dt, & x,y\in I,~x\neq y,\\
f(x), & x=y\in I
\end{array}\right.
$$
and applying a generalized form of Niezgoda's inequalty, we present new proofs concerning the $(m,n)$-convexity of the integral arithmetic mean function. This paper aims to contribute novel proofs to D. E....
The bicentric $n$-gon is a polygon with $n$ sides that are tangential for incircle and chordal for circumcircle. The connection between the radius ($R$) of circumcirle, the radius ($r$) of incircle and the distance ($d$) of their centers represents the Fuss' relation for the certain bicentric $n$-gon. According to Poncelet's porism, there exist infinitely many bicentric $n$-gons with these...
Digital game-based learning (DGBL) is regarded as a engaging teaching approach that has attracted the interest of researchers and has become prominent as a research topic. However, the potential benefits of gaming on students' academic achievement, motivation, and skills are still a topic of debate.
Given the relatively limited adoption of digital games in upper secondary education,...
Considering the Gaussian mixture model the restriction-based iterative method is developed. The proposed method applied the conditional expectations for parameter re-estimation in an iterative process, where the rejection of the model component's tails of low probabilities is considered. In order to study the proposed method, continuous and discrete random variable cases are observed, where...
In proportional electoral systems, party vote counts must be converted to seat allocations within a parliament of fixed size. Divisor methods are the most common approach to this problem, but different divisor methods often give different seat allocations. To highlight these differences, the effects of various divisor methods on a party’s seat allocation are expressed as intervals of the...
The stochastic version of the SIRV (susceptible-infected-recovered-vaccinated) epidemic model in the population of non-constant size and finite period of immunity is considered. Among many parameters influencing the dynamics of this model, the most important parameter is the contact rate, i.e. the average number of adequate contacts of an infective person, where an adequate contact is one...
We use the one-point integral formula to obtain identities that are related to the classical Steffensen inequality. We give some new weight inequalities of the Hermite-Hadamard type for these identities. At the end, we present Hermite-Hadamard type bounds for the obtained identities by applying convex/concave functions of the form $|f^{(n)}|^q$.
Let $n\neq0$ be an integer. A set of $m$ distinct positive integers is called a $D(n)$-$m$-tuple if the product of any two of its distinct elements increased by $n$ is a perfect square. We present known results and mention open problems and conjectures related to $D(4)$-$m$-tuples. Also, the latest results from $[1]$ are shown.
References:
$[1]$ Bliznac Trebješanin, Marija; Radić, Pavao,...
The classical Ostrowski inequality states:
$
\left\vert f(x)-\frac{1}{b-a}\int_{a}^{b}f(t)dt\right\vert \leq\left[
\frac{1}{4}+\frac{\left( x-\frac{a+b}{2}\right) ^{2}}{\left( b-a\right)
^{2}}\right] \left( b-a\right) \left\Vert f^{\prime}\right\Vert _{\infty
},
$
for all $x \in \left[a,b\right]$, where $f:\left[a,b\right]\to \mathbb{R}$ is continuous on $\left[a,b\right]$ and...
Gyroscopic systems are mechanical systems described by the equation:
$$M \ddot x(t) + G\dot x(t) + K x(t) = 0,$$
where the mass matrix $M\in\mathbb{R}^{n\times n}$ is symmetric positive definite, the gyroscopic matrix $G \in\mathbb{R}^{n\times n}$ is skew-symmetric, the stiffness matrix $K\in\mathbb{R}^{n\times n}$ is symmetric, and $x=x(t)$ is a time-dependent displacement vector. The...
A clique is a fully connected subset of an undirected graph. Finding the largest clique is NP complete problem (it takes exponential time to solve the problem).
However, if we know that the largest clique is not too large, then it is a polynomial problem. If the graph is also very sparse, then it does not have to be a polynomial of high degree, and it can be solved up to some predetermined...
We propose a fractional diffusion process based on the (non-fractional) Bessel process with constant negative drift. The model is obtained as stochastically time-changed Bessel process with constant negative drift through inverse stable subordinator of order $0<\alpha <1$. Spectral representation of the transition density of fractional Bessel process is calculated. Based on this...
We use the tools of topological data analysis to detect some features of random sets in order to detect outliers or do goodness of fit testing. Persistence diagram is a key object of our interest and we view it as an empirical measure. Statistical depth can be defined on that (random) measure, for example by using support functions of corresponding lift zonoid and applying methods for...
Green functions are very interesting from different aspects and are used
for solving wide variety of problems in many fields, specifically in
quantum field theory, aerodynamics, aeroacoustics, electrodynamics and
seismology. Considering Green functions, we obtain new results on the
Hardy-type inequality in the general context, in terms of measure spaces
with positive $\sigma$-finite...
We study the properties of a complete quadrangle in the Euclidean plane. Many of them are known from earlier, published in different journals and periods and proved each using different methods. Hereby, we use rectangular coordinates symmetrically on four vertices and four parameters $a, b, c, d$ and prove all properties by the same analytical method. We put the complete quadrangle into such...
We study 3-convex functions, which are characterized by the third order divided differences, and for them we derive a class of inequalities of the Jensen and Edmundson-Lah-Ribarič type involving positive linear functionals that does not require convexity in the classical sense. A
great number of theoretic divergences, i.e. measures of distance between two probability distributions, are...
A generalized helix is a space curve whose tangent vectors make a constant angle with a fixed straight line, called the axis of a generalized helix. Among such curves, the ones that lay on a sphere show interesting geometric properties.
In Euclidean space, spherical generalized helices have a property that their orthogonal projections onto a plane normal to their axis appear as epicycloids,...
We assume that the one-dimensional diffusion $X$ satisfies a stochastic differential equation of the form:
$dX_t=\mu(X_t)dt+\nu(X_t)dW_t$, $X_0=x_0$, $t\geq 0$.
Let $(X_{i\Delta_n},0\leq i\leq n)$ be discrete observations along fixed time interval $[0,T]$. We prove that the random vectors which $j$-th component is...
