Point orthogonal projection onto an algebraic surface is a very important topic in computer-aided geometric design and other fields. However, implementing this method is currently extremely challenging and difficult because it is difficult to achieve...
Fixed-point theory and symmetry are major and vigorous tools to working nonlinear analysis and applications, specially nonlinear operator theory and applications. The subject of examining the presence and inimitableness of fixed points of self-mappin...
We introduce the notion of orthogonal sets for Birkhoff orthogonality, which we will call Birkhoff orthogonal sets in this paper. As a generalization of orthogonal sets in Hilbert spaces, Birkhoff orthogonal sets are not necessarily linearly independ...
During the last two centuries, after the question asked by Euler concerning mutually orthogonal Latin squares (MOLS), essential advances have been made. MOLS are considered as a construction tool for orthogonal arrays. Although Latin squares have num...
In this publication, we establish a suitable symmetry structure for orthogonal
The theory of orthogonal polynomials is well established and detailed, covering a wide field of interesting results, as, in particular, for solving certain differential equations. On the other side the concepts and the related formalism of the theory...
In this study, we aim to construct a finite set of orthogonal matrix polynomials for the first time, along with their finite orthogonality, matrix differential equation, Rodrigues’ formula, several recurrence relations including three-term rela...
This paper builds on the notion of the so-called orthogonal derivative, where an n-th order derivative is approximated by an integral involving an orthogonal polynomial of degree n. This notion was reviewed in great detail in a paper by the author an...
This paper is a follow-up of a previous paper of the author published in Mathematics journal in 2015, which treats the so-called continuous fractional orthogonal derivative. In this paper, we treat the discrete case using the fractional orthogonal di...
A de Bruijn sequence of order k over a finite alphabet is a cyclic sequence with the property that it contains every possible k-sequence as a substring exactly once. Orthogonal de Bruijn sequences are the collections of de Bruijn sequences of the sam...
In this paper, we present a new concept of the generalized core orthogonality (called the C-S orthogonality) for two generalized core invertible matrices A and B. A is said to be C-S orthogonal to B if
In this paper, we introduce the concept of orthogonal convex structure contraction mapping and prove some fixed point theorems on orthogonal ♭-metric spaces. We adopt an example to highlight the utility of our main result. Finally, we apply our...
The aim of this paper is to extend the concept of the orthogonal derivative to provide a new integral representation of the fractional Riesz derivative. Specifically, we investigate the orthogonal derivative associated with Gegenbauer polynomials&nbs...
Frames are more stable as compared to bases under the action of a bounded linear operator. Sums of different frames under the action of a bounded linear operator are studied with the help of analysis, synthesis and frame operators. A simple construct...
A linear functional
In the paper, orthogonal transforms based on proposed symmetric, orthogonal matrices are created. These transforms can be considered as generalized Walsh–Hadamard Transforms. The simplicity of calculating the forward and inverse transforms is one of...
In this paper, we investigate how one can modify an orthogonal graph drawing to accommodate the placement of overlap-free labels with the minimum cost (i.e., minimum increase of the area and preservation of the quality of the drawing). We investigate...
This paper presents a chirp based ultrasonic positioning system (UPS) using orthogonal chirp waveforms. In the proposed method, multiple transmitters can simultaneously transmit chirp signals, as a result, it can efficiently utilize the entire availa...
For the design of computer experiments, column orthogonality and space-filling are two desirable properties. In this paper, we develop methods for constructing a new class of column-orthogonal designs (ODs) with two-dimensional stratifications on fin...
The present article studies the problem of computing empirical means on pseudo-orthogonal groups. To design numerical algorithms to compute empirical means, the pseudo-orthogonal group is endowed with a pseudo-Riemannian metric that affords the compu...
The fashionable Parr–Pearson (PP) atoms-in-molecule/bonding (AIM/AIB) approach for determining the exchanged charge necessary for acquiring an equalized electronegativity within a chemical bond is refined and generalized here by introducing the...
In this study, inspired by the concept of B-metric-like space (BMLS), we introduce the concept of orthogonal B-metric-like space (OBMLS) via a hybrid pair of operators. Additionally, we establish the concept of orthogonal dynamic system (ODS) as a ge...
In order-of-addition experiments, the full order-of-addition designs are often unaffordable due to their large run sizes. The problem of finding efficient fractional OofA designs arises. The order-of-addition orthogonal arrays are a class of optimal...
The Cholesky factorization of the moment matrix is considered for the Gauss hypergeometric discrete orthogonal polynomials. This family of discrete orthogonal polynomials has a weight with first moment given by
In this paper, we generalize the study of finite sequences of orthogonal polynomials from one to two variables. In doing so, twenty three new classes of bivariate finite orthogonal polynomials are presented, obtained from the product of a finite and...
In this paper, we first obtain the Fourier transforms of some finite bivariate orthogonal polynomials and then by using the Parseval identity, we introduce some new families of bivariate orthogonal functions.
An extreme learning machine (ELM) is an innovative algorithm for the single hidden layer feed-forward neural networks and, essentially, only exists to find the optimal output weight so as to minimize output error based on the least squares regression...
Compacting orthogonal drawings is a challenging task. Usually, algorithms try to compute drawings with small area or total edge length while preserving the underlying orthogonal shape. We suggest a moderate relaxation of the orthogonal compaction pro...
Currently, artificial intelligence and intelligent algorithms for the control of dynamic systems are the main focus for building Industry 4.0 services and developing novel, innovative industrial solutions. This paper proposes a novel intelligent cont...
In Farouki
This paper aims to answer “why-not” questions in skyline queries based on the orthogonal query range (i.e., ORSQ). These queries retrieve skyline points within a rectangular query range, which improves query efficiency. Answering why-not...
By using difference schemes, orthogonal partitions and a replacement method, some new methods to construct pure quantum error-correcting codes are provided from orthogonal arrays. As an application of these methods, we construct several infinite seri...
Nowadays, the data processing used for analyzing multifaceted disasters is based on technologies of mass observation acquisition. Terrestrial laser scanning is one of those technologies and enables the quick, non-invasive acquisition of information a...
In this paper, we are concerned with polynomials that are orthogonal with respect to the singularly perturbed Freud weight functions. By using Chen and Ismail’s ladder operator approach, we derive the difference equations and differential-diffe...
In this paper, by using the Hamming distance, we establish a relation between quantum error-correcting codes
To bring to bear the power of centrifugal microfluidics on vertical flow immunoassays, control of flow orthogonally through nanoporous membranes is essential. The on-disc approach described here leverages the rapid print-cut-laminate (PCL) disc fabri...
In this article, we modify the symmetry of orthogonal metric spaces and we prove common fixed point theorems via simulation functions in orthogonal Rectangular metric spaces. We also provide an illustrative example to support our results. The derived...
Point orthogonal projection onto a spatial algebraic curve plays an important role in computer graphics, computer-aided geometric design, etc. We propose an algorithm for point orthogonal projection onto a spatial algebraic curve based on Newton&rsqu...
ELM is an innovative learning algorithm that minimizes output error by only finding optimal output weights. Meta-learning is composed of base ELMs and exhibits good generalization. To improve its performance further by introducing orthogonal constrai...
Automatic Modulation Recognition (AMR) can obtain the modulation mode of the received signal for subsequent processing without the assistance of the transmitter. Although the existing AMR methods have been mature for the orthogonal signals, these met...
In this contribution, we propose an algorithm to compute holonomic second-order differential equations satisfied by some families of orthogonal polynomials. Such algorithm is based in three properties that orthogonal polynomials satisfy: a recurrence...
In this article, we prove an orthogonal decomposition theorem for real inner product gyrogroups, which unify some well-known gyrogroups in the literature: Einstein, Möbius, Proper Velocity, and Chen’s gyrogroups. This leads to the study of...
In the investigation of quantum entanglement, local unitary (LU) equivalence serves as a fundamental tool for distinguishing and classifying entanglement structures. Orthogonal arrays are classical combinatorial designs with applications to quantum s...
Orthogonal Linear Discriminant Analysis (OLDA) has been widely studied for dimensionality reduction, as the orthogonality constraints on its projection matrix enable more effective elimination of redundant features compared to conventional Linear Dis...
In this article, we prove fixed point results for a Meir–Keeler type contraction due to orthogonal M-metric spaces. The results of the paper improve and extend some recent developments in fixed point theory. The extension is assured by the conc...
In this study, the organization of genetic information in nucleic acids is defined using a novel orthogonal representation. Clearly defined base pairing in DNA allows the linear base chain and sequence to be mathematically transformed into an orthogo...
Some systems of univariate orthogonal polynomials can be mapped into other families by the Fourier transform. The most-studied example is related to the Hermite functions, which are eigenfunctions of the Fourier transform. For the multivariate case,...
In this paper, new formulas for the Fibonacci polynomials, including high-order derivatives and repeated integrals of them, are derived in terms of the polynomials themselves. The results are then used to solve connection problems between the Fibonac...
The orthogonality of transmitted waveforms is an important factor affecting the performance of MIMO radar systems. The orthogonal coded signal is a commonly adopted waveform in MIMO radar, and its orthogonality depends on the used orthogonal discrete...
This paper studies a new family of Angelesco multiple orthogonal polynomials with shared orthogonality conditions with respect to a system of weight functions, which are complex analogs of Pascal distributions on a legged star-like set. The emphasis...
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