<p>Modern data collection, storage, and processing rely on diverse techniques to handle various types of information, ranging from structured tables to free-form text. This paper explores the captivating application of Natural Language Processing (NLP) for categorizing titles from Google Forms or any other textual data. The process of training an NLP model will be demonstrated through a specific example. Just as we learn from our past experiences, NLP models need to be fed with relevant data and labels. This ensures accurate and efficient processing even when new titles are introduced. We will conclude with a fascinating demonstration of how NLP algorithms analyze the structure and meaning of titles. By identifying keywords and understanding the context, they can automatically classify titles into relevant categories. This dramatically simplifies data organization and analysis, empowering us to extract valuable insights faster.</p>

IP devices are ubiquitously spread, for both residential and industrial purposes, thanks to the low integration costs and rapid development cycle of all-IP-based 5G+ technologies. As a consequence, the engineering community now considers their automatization and energy scheduling/management as relevant research fields. These topics have a striking relevance also for the development of smart city networks. As a drawback, most ID-device applications produce a large amount of data (high-frequency complexity), requiring supervised machine learning algorithms to be properly analyzed. In this research, we focus on the performance of vehicular mobility and imaging systems, recognizing scenarios (with powered-on devices) in real-time, with the help of a simple convolutional neural network, proving the effectiveness of such an innovative low-cost approach.

In this paper $X$ is a Banach space, $\left( {S(t)}\right) _{t\geq 0}$ is non-dege\-ne\-ra\-te $\alpha -$times integrated, exponentially bounded semigroup on $X$ $(\alpha \in \mathbb{R}^{+}),$ $M\geq 0$ and $\omega _{0}\in \mathbb{R}$ are constants such that $\left\| {S(t)}\right\| \leqslant Me^{\omega _{0}t}$ for all $t\geq 0,$ $\gamma $ is any positive constant greater than $\omega _{0},$ $\Gamma $ is the Gamma-function, $(C,\beta )-\lim $ is the Ces\`{a}ro-$\beta $ limit. Here we prove that\begin{equation*}\mathop {\lim }\limits_{n\rightarrow \infty }\frac{1}{{\Gamma(\alpha )}} \int\limits_{0}^{T}{(T-s)^{\alpha -1}\left({\frac{{n+1}}{s}}\right) ^{n+1}R^{n+1}\left({\frac{{n+1}}{s},A}\right) x\,ds=S(T)x,}\end{equation*}for every $x\in X,$ and the limit is uniform in $T>0$ on any bounded interval. Also we prove that\begin{equation*}S(t)x=\frac{1}{{2\pi i}}(C,\beta )-\mathop {\lim }\limits_{\omega\rightarrow \infty }\int\limits_{\gamma -i\omega }^{\gamma+i\omega }{ e^{\lambda t}\frac{{R(\lambda ,A)x}}{{\lambda^{\alpha }}}\,d\lambda },\end{equation*}for every $x\in X,\,\,\beta >0$ and $t\geq 0.$   2000 Mathematics Subject Classification. 47D06, 47D60, 47D62

In this paper $\left( S(t)\right) _{t\geq 0}$ is an exponentially bounded integrated semigroup on a Banach space $X,$ with generator $A.$ We present some relations between an integrated semigroup and its generator $A,$ or its resolvent.   2000 Mathematics Subject Classification. 47D60, 47D62

In this paper we investigate measure-theoretic properties of the class of all weakly mixing transformations on a finite measure space which preserve measurability. The main result in this paper is the following theorem: If $\phi $ is a weakly mixing transformation on a finite measure space $( S, \mathcal A , \mu )$ with the property that $\phi (\mathcal A ) \subseteq \mathcal A ,$ then for every $A, B $ in $\mathcal A$ there is a subset $J(A,B)$ of the set of non-negative integers of density zero such that $\lim _{m \to \infty ,m \notin J(A,B)} \mu (A \cap \phi ^m(B)) = (\mu (A) / \mu (S))\lim _{n \to \infty } \mu \,(\phi^n(B)).$ Furthermore, we show that for most useful measure spaces we can strengthen the preceding statement to obtain a set of density zero that works for all pairs of measurable sets $A$ and $ B.$ As corollaries we obtain a number of inclusion theorems. The results presented here extend the well-known classical results (for invertible weakly mixing transformations), results of R. E. Rice [17] (for strongly mixing), a result of C. Sempi [19] (for weakly mixing) and previous results of the author [8, 10] (for weakly mixing and ergodicity).   2000 Mathematics Subject Classification. Primary: 28D05, 37A25; Secondary: 37A05, 47A35

We consider the following system of rational difference equations in the plane: $$\left\{\begin{aligned}%{rcl}x_{n+1} &= \frac{\alpha_1}{A_1+B_1 x_n+ C_1y_n} \\[0.2cm]y_{n+1} &= \frac{\alpha_2}{A_2+B_2 x_n+ C_2y_n}\end{aligned}\right. \, , \quad n=0,1,2,\ldots $$ where the parameters $\alpha_1, \alpha_2, A_1, A_2, B_1, B_2, C_1, C_2$ are positive numbers and initial conditions $x_0$ and $y_0$ are nonnegative numbers. We prove that the unique positive equilibrium of this system is globally asymptotically stable. Also, we determine the rate of convergence of a solution that converges to the equilibrium $E=(\bar{x},\bar{y})$ of this systems.   2000 Mathematics Subject Classification. 39A10, 39A11, 39A20

We investigate the global character of the difference equation of the form $$ x_{n+1} = f(x_n, x_{n-1},\ldots, x_{n-k+1}), \quadn=0,1, \ldots $$ with several equilibrium points, where $f$ is increasing in all its variables. We show that a considerable number of well known difference equations can be embeded into this equation through the iteration process. We also show that a negative feedback condition can be used to determine a part of the basin of attraction of different equilibrium points, and that the boundaries of the basins of attractions of different locally asymptotically stable equilibrium points are in fact the global stable manifolds of neighboring saddle or non-hyperbolic equilibrium points.   2000 Mathematics Subject Classification. 39A10, 39A11

We investigate the period-two trichotomies of solutions of the equation $$x_{n+1} = f(x_{n}, x_{n-1},x_{n-2}), \quad n=0, 1, \ldots $$ where the function $f$ satisfies certain monotonicity conditions. We give fairly general conditions for period-two trichotomies to occur and illustrate the results with numerous examples.   1991 Mathematics Subject Classification. 39A10, 39A11

Motivated with Hille's first exponential formula for $C_{0}$ semigroups, we prove a formula for $n-$times integrated semigroups. At first we prove a formula for twice integrated semigroup, and, later, we generalize this formula for $n-$times integrated semigroups.   2000 Mathematics Subject Classification. 47D60, 47D62

Enterprise resource planning (ERP) is widely used to boost the total market power of businesses. The wrong selection is one of the key reasons why ERP installations fail. Due to the complexity of the business environment and the range of ERP systems, choosing an ERP system is a complex and time-consuming procedure. ERP alternatives may be assessed using several criteria, so the ERP selection process may be considered a multi-criteria decision-making (MCDM) problem. In this study, the rough best worst method (BWM) was used to determine criteria weights, while the newly developed rough integrated simple weighted sum product (WISP) was used to rank ERP alternatives. Results suggest that the SFT-4 coded software is regarded as the best option, followed by SFT-5, SFT-6, SFT-2, SFT-3, and SFT-1. Results of the newly developed rough WISP method are compared to those of existing rough techniques in the sensitivity analysis. The differences between them have been found to be negligible. The outcomes show how effectively developed rough BWM and WISP integrated method performs in terms of ERP selection with usability, accuracy, ease of use, and consistency. This study will help decision-makers in a context where ERP is implemented choose the best ERP software for different sectors.

In this paper we analyze the values and the properties of the function $S(n,l):=\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}(n-k)^{l}\ \(n,l\in \mathbb{N\cup }\left\{ 0\right\} ),$ for $n<l.$ At first, we obtain two recurrence relations. Namely, we prove that forevery $n\in \mathbb{N\cup } \left\{ 0\right\} $ and every $l\in \mathbb{N}$ such that $l>n,$ we have\begin{equation*}S(n+1,l)=\sum_{k=1}^{l-n}\binom{l}{k}S(n,l-k),\end{equation*}and also, for every $n\in \mathbb{N\cup }\left\{ 0\right\} $and every $l\in \mathbb{N}$, we have\begin{equation*}S(n+1,l)=(n+1)S(n,l-1)+(n+1)S(n+1,l-1).\end{equation*}Further, we conclude that for every $n\geq 2$ and every $l\geq n$ the following representation formula holds\begin{multline*}S(n,l) =\sum\limits_{k_{1}=1}^{l-(n-1)}\binom{l}{k_{1}}\sum\limits_{k_{2}=1}^{l-k_{1}-(n-2)}\binom{l-k_{1}}{k_{2}}\\\cdot\sum\limits_{k_{3}=1}^{l-k_{1}-k_{2}-(n-3)}\binom{l-k_{1}-k_{2}}{k_{3}}\dots\sum\limits_{k_{n-1}=1}^{l-\sum\limits_{i=1}^{n-2}k_{i}-1}\binom{l-\sum\limits_{i=1}^{n-2}k_{i}}{k_{n-1}}.\end{multline*}We obtain an explicit formula for the calculation $S(n,l),$ especially for $ l=n+1,\dots,n+5,$ and later we give a general result.   2000 Mathematics Subject Classification. 40B05, 11Y55, 05A10

In this paper we describe five methods for the calculation of the moments\begin{equation*}\label{Momenti}\mathbb{M}_{n,m}=\int_{0}^{m}\varphi_{m}(t)t^{n}dt,n\in\mathbb{N}_{0},\end{equation*}where weight function $\varphi_{m}(\cdot)$ is the cardinal B-spline of order $m,m\in\mathbb{N}.$   2000 Mathematics Subject Classification. 65D07, 41A15

Single axis trackers have their application in the efficiency improvement process of photovoltaic systems. In spite of large investment costs, their application is necessary in the areas with a low amount of available solar irradiation. This is applicable only if it is required to exploit all available energy sources at any cost. With optimization and improvement of these systems it is possible to increase their efficiency, reduce energy usage for their movement and improve system reliability. Motion parameters are significant for the optimization of the system. It is necessary to set and monitor the right parameters as a prerequisite for system optimization. The process of calibration of single axis tracker prototype is shown in this paper. It is shown that proper calibration and system adjustment could improve efficiency of the system.

This paper introduces a novel chaotic strategy for controlling the acceleration coefficients within the particle swarm optimization (PSO) algorithm. The PSO algorithm with chaotic exponential-based acceleration coefficients is developed to enhance the exploration of the search space and avoid premature convergence, a common issue associated with the standard PSO algorithm. The PSO algorithm with chaotic exponential-based acceleration coefficients is applied to multilevel image thresholding. The attained experimental results demonstrate that the PSO algorithm utilizing the chaotic strategy to control the cognitive and social acceleration coefficients can be successfully utilized for the selection of image thresholds across a variety of images.