650 Results Found

Let $\Gamma =(V_{\Gamma },E_{\Gamma })$ be a simple undirected graph with finite vertex set $V_{\Gamma }$ and edge set $E_{\Gamma }$. A total $n$-labeling $\alpha :V_{\Gamma }\cup E_{\Gamma }\to \{1,2,\dots ,n\}$ is called a total edge irregular labeling on $\Gamma$ if for any...

Topological indices are graph invariants computed by the distance or degree of vertices of the molecular graph. In chemical graph theory, topological indices have been successfully used in describing the structures and predicting certain physicochemi...

It is known that the quasi-arithmetic means can be characterized in various ways, with an essential role of a symmetry property. In the expected utility theory, the quasi-arithmetic mean is called the certainty equivalent and it is applied, e.g., in...

In this paper, an optimization approach based on an arithmetic optimization algorithm (AOA) is proposed for specifying the optimal allocation of distribution generations/generators (DGs) and capacitor banks (CBs) in radial distribution systems. The A...

The aim of this paper is to apply the Taylor expansion method to solve the first and second kinds Volterra integral equations with Abel kernel. This study focuses on two main arithmetics: the FPA and the DSA. In order to apply the DSA, we use the CES...

In this paper, we will explore alternative varieties of integer multiplication by modifying the product axiom of Dedekind–Peano arithmetic (PA). In addition to studying the elementary properties of the new models of arithmetic that arise, we wi...

Stochastic circuits are used in applications that require low area and power consumption. The computing performed using these circuits is referred to as Stochastic computing (SC). The arithmetic operations in this computing can be realized using mini...

Developing algebraic thinking in elementary school has gained consensus among mathematics educators. The objective of this study is to understand the developmental trajectory of early algebraic thinking in elementary school students so as to assist t...

The concept of arithmetic-geometric index was recently introduced in chemical graph theory, but it has proven to be useful from both a theoretical and practical point of view. The aim of this paper is to obtain new bounds of the arithmetic-geometric...

We prove the inequalities of the weighted Hermite–Hadamard type the and Hermite–Hadamard–Mercer type for an extremely rich class of geometrically arithmetically-h-convex functions (GA-h-CFs) via generalized Hadamard–Fractional...

The utilizations of graph theory in chemistry and in the study of molecule structures are more than someone’s expectations, and, lately, it has increased exponentially. In molecular graphs, atoms are denoted by vertices and bonds by edges. In t...

The optimal integration of photovoltaic generation systems is a challenge for distribution utilities since these devices have a direct impact on company finances due to the large amount of investment required at the beginning of the planning project....

There is still much debate about the exact nature and frequency of developmental dyscalculia, and about how it should be defined. This article examines several key questions in turn: Is developmental dyscalculia a distinct disorder, or should it be s...

Approximate arithmetic circuits are an attractive alternative to accurate arithmetic circuits because they have significantly reduced delay, area, and power, albeit at the cost of some loss in accuracy. By keeping errors due to approximate computatio...

In this paper, we study some algebraic invariants of the edge ideal of generalized theta graphs, such as arithmetical rank, big height and height. We give an upper bound for the difference between the arithmetical rank and big height. Moreover, all C...

A Topological index also known as connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology a...

The large-scale integration of Distributed Generators (DGs) has significantly altered fault characteristics in distribution networks, posing challenges to conventional fault location methods. To address these limitations, this paper presents a novel...

Division remains one of the most computationally demanding operations in digital arithmetic. Traditional algorithms, such as restoring, non-restoring, and SRT (Sweeney–Robertson–Tocher) division, are limited by sequential dependencies tha...

This study introduces a novel generalization: the generalized geometric Frank matrix, which extends the classical Frank matrix and its known variants. We systematically examine its algebraic structure, providing detailed analyses of its factorization...

The family of $\alpha$-divergences including the oriented forward and reverse Kullback–Leibler divergences is often used in signal processing, pattern recognition, and machine learning, among others. Choosing a suitable $\alpha$-divergence can ei...

Multi-access edge computing implementations are ever increasing in both the number of deployments and the areas of application. In this context, the easiness in the operations of packet forwarding between two end devices being part of a particular ed...

In this paper, we address the problem of the divergent sums of general arithmetic functions over the set of primes. In classical analytic number theory, the sum of the logarithm of the prime numbers plays a crucial role. We consider the sums of power...

Parametric identification of the single diode model of a photovoltaic generator is a key element in simulation and diagnosis. Parameters’ values are often determined by using experimental data the modules manufacturers provide in the data sheet...

Previous studies have shown that the application of the M-coder in the H.264/AVC and H.265/HEVC video coding standards allows for highly parallel implementations without decreasing maximal frequencies. Although the primary limitation on throughput, o...

The moduli of the form $2^n+1$ belong to a class of low-cost odd moduli, which have been frequently selected to form the basis of various residue number systems (RNS). The most efficient computations modulo (mod) $2^n+1$ are performed using the so-called d...

The cross section is the basic data for building 3D geological models. It is inefficient to draw a large number of cross sections to build an accurate model. This paper reports the use of multi-source and heterogeneous geological data, such as geolog...

In this paper we consider a bivariate number sequence that we call Binomiacci numbers, which is constructed from the Fibonacci sequence using the rules of construction of binomial coefficients. We obtain a bivariate generating function for the Binomi...

The rapid adoption of robotic-assisted total knee arthroplasty (RATKA) has resulted in pre-operative CT scans becoming more readily available. After the segmentation and identification of landmarks by trained segmentation specialists, the Mako SmartR...

Non-Newtonian calculus naturally unifies various ideas that have occurred over the years in the field of generalized thermostatistics, or in the borderland between classical and quantum information theory. The formalism, being very general, is as sim...

In chemical graph theory, a topological index is a numerical representation of a chemical network, while a topological descriptor correlates certain physicochemical characteristics of underlying chemical compounds besides its chemical representation....

In this work, the differential evolution algorithm behavior under a fixed point arithmetic is analyzed also using half-precision floating point (FP) numbers of 16 bits, and these last numbers are known as FP16. In this paper, it is considered that it...

Traditionally, the teaching and learning of algebra has been addressed at the beginning of secondary education with a methodological approach that broke traumatically into a mathematical universe until now represented by numbers, with bad consequence...

Digital chaotic systems used in various applications such as signal processing, artificial intelligence, and communications often suffer from the issue of dynamical degradation. This paper proposes a solution to address this problem in the digital te...

It is well known that multiplication inside a computer does not follow the associative property because of roundoff effects. It is possible to use this fact to generate other different chaotic instances of chaotic maps or oscillators when a multiplic...

Nowadays, Finite Impulse Response (FIR) filters are used to change the attributes of a signal in the time or frequency domain. Among FIR filters, a reconfigurable filter has the advantage of changing the coefficient in real-time, while performing the...

Chemical graph theory plays an important role in modeling and designing any chemical structure. The molecular topological descriptors are the numerical invariants of a molecular graph and are very useful for predicting their bioactivity. In this pape...

A topological index is a numerical representation of a chemical structure, while a topological descriptor correlates certain physico-chemical characteristics of underlying chemical compounds besides its numerical representation. A large number of pro...

A hierarchical structure of isomorphic arithmetics is defined by a bijection $g_{\mathbb{R}}:\mathbb{R}\to \mathbb{R}$. It entails a hierarchy of probabilistic models, with probabilities $p_k=g^k\left(p\right)$, where g is the restriction of $g_{\mathbb{R}}$ to the interval $[0,1]$, $g^k$ is the kth iterate of g,...

In many countries, the number line (NL) is an important tool in mathematics education to develop an understanding of numbers. However, students may have difficulties using the NL. To provide students showing NL difficulties with appropriate support,...

This paper develops a positive quadratic-form approximation for expectations of globally Lipschitz functionals of conic combinations of correlated lognormal random variables. The surrogate is constructed from the same Gaussian vector as the original...

Hydro-generator cooling arrays are sparsely instrumented, limiting estimation of heat-exchanger (HX) parameters from plant data for thermal modeling. This study develops and validates a 48-state quasi-linear parameter-varying (qLPV) gray-box model fo...

The new arithmetic operations of non-normal fuzzy sets are studied in this paper by using the extension principle and considering the general aggregation function. Usually, the aggregation functions are taken to be the minimum function or t-norms. In...

In 1977, Davis et al. proposed a method to generate an arrangement of $\left[n\right]=\{1,2,\dots ,n\}$ that avoids three-term monotone arithmetic progressions. Consequently, this arrangement avoids k-term monotone arithmetic progressions in $\left[n\right]$ for $k\ge 3$. Hence, we are i...

A math word problems (MWPs) comprises mathematical logic, numbers, and natural language. To solve these problems, a solver model requires an understanding of language and the ability to reason. Since the 1960s, research on the design of a model that...

We consider the foundational relation between arithmetic and set theory. Our goal is to criticize the construction of standard arithmetic models as providing grounds for arithmetic truth. Our method is to emphasize the incomplete picture of both theo...

Arithmetic competence is crucial for navigating modern society and maintaining independence. It relies on domain-general and domain-specific cognitive skills, as well as subjective factors. Given its importance, understanding how these factors shape...

The investigation of eye movements has been shown to provide valuable insights into a variety of cognitive processes. A limited number of recent studies have adopted eye-tracking to investigate the processes underlying simple and complex arithmetic....

Wu introduced the interval range of fuzzy sets. Based on this, he defined a kind of arithmetic of fuzzy sets using a gradual number and gradual sets. From the point of view of soft computing, this definition provides a new way of handling the arithme...

In this paper, we prove large deviation results for some sequences of weighted sums of random variables. These sequences have applications to the probabilistic generalized Cramér model for products of primes in arithmetic progressions; they could lea...

We describe a general-purpose framework to design quantum algorithms. This framework relies on two pillars: a basic data structure called quantum matrix and a modular structure based on three quasi-independent modules. These latter include a loading...