Search

We develop a test for deciding whether the linear spaces spanned by the factor exposures of a large cross‐section of assets toward latent systematic risk factors at two distinct points in time are the same. The test uses a panel of asset returns in local windows around the two time points. The asymptotic setup is of joint type: the number of assets and the number of return observations per asset increase asymptotically while the length of both time windows shrinks. We estimate the factor exposures, up to rotation, over the two periods using classical principal component analysis and evaluate their projection discrepancy, which is rotation invariant. This projection discrepancy is then centered with one between factor exposures computed over a partition of the pooled return data into odd and even increments. We derive the limit distribution of the statistic under the null hypothesis and develop an easy‐to‐implement bootstrap for constructing the critical region of the test. The test is applied to intraday financial data to determine whether the linear span of assets' systematic risk exposures differ during a trading day or after a release of important economic information. [ABSTRACT FROM AUTHOR]

This paper introduces a general framework of Semi-parametric TEnsor Factor Analysis (STEFA) that focuses on the methodology and theory of low-rank tensor decomposition with auxiliary covariates. Semi-parametric TEnsor Factor Analysis models extend tensor factor models by incorporating auxiliary covariates in the loading matrices. We propose an algorithm of iteratively projected singular value decomposition (IP-SVD) for the semi-parametric estimation. It iteratively projects tensor data onto the linear space spanned by the basis functions of covariates and applies singular value decomposition on matricized tensors over each mode. We establish the convergence rates of the loading matrices and the core tensor factor. The theoretical results only require a sub-exponential noise distribution, which is weaker than the assumption of sub-Gaussian tail of noise in the literature. Compared with the Tucker decomposition, IP-SVD yields more accurate estimators with a faster convergence rate. Besides estimation, we propose several prediction methods with new covariates based on the STEFA model. On both synthetic and real tensor data, we demonstrate the efficacy of the STEFA model and the IP-SVD algorithm on both the estimation and prediction tasks. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the essential pseudospectrum of bounded linear operator pencils is invariant under perturbation of each completely continuous linear operators on ultrametric Banach spaces over a spherically complete field K and we establish a characterization of the essential pseudospectrum of bounded linear operator pencils by means of the spectrum of each perturbed completely continuous operators. Furthermore, we introduce and study the notion of (n, ε)-pseudospectrum of bounded linear operators and the concept of (n, ε)-pseudospectrum of bounded linear operator pencils on ultrametric Banach spaces. We establish some results about them. Finally, several examples are provided. [ABSTRACT FROM AUTHOR]

This paper introduces a methodology to generate review-based natural language justifications supporting personalized suggestions returned by a recommender system. The hallmark of our strategy lies in the fact that natural language justifications are adapted to the different contextual situations in which the items will be consumed. In particular, our strategy relies on the following intuition: Just like the selection of the most suitable item is influenced by the contexts of usage, a justification that supports a recommendation should vary as well. As an example, depending on whether a person is going out with her friends or her family, a justification that supports a restaurant recommendation should include different concepts and aspects. Accordingly, we designed a pipeline based on distributional semantics models to generate a vector space representation of each context. Such a representation, which relies on a term-context matrix, is used to identify the most suitable review excerpts that discuss aspects that are particularly relevant for a certain context. The methodology was validated by means of two user studies, carried out in two different domains (i.e., movies and restaurants). Moreover, we also analyzed whether and how our justifications impact on the perceived transparency of the recommendation process and allow the user to make more informed choices. As shown by the results, our intuitions were supported by the user studies. [ABSTRACT FROM AUTHOR]

We introduce the function principal component regression (FPCR) forecasting method to model and forecast age-specific survival functions observed over time. The age distribution of survival functions is an example of constrained data whose values lie within a unit interval. Because of the constraint, such data do not reside in a linear vector space. A natural way to deal with such a constraint is through an invertible logit transformation that maps constrained onto unconstrained data in a linear space. With a time series of unconstrained data, we apply a functional time-series forecasting method to produce point and interval forecasts. The forecasts are then converted back to the original scale via the inverse logit transformation. Using the age- and sex-specific survival functions for Australia, we investigate the point and interval forecast accuracies for various horizons. We conclude that the functional principal component regression (FPCR) provides better forecast accuracy than the Lee–Carter (LC) method. Therefore, we apply FPCR to calculate annuity pricing and compare it with the market annuity price. [ABSTRACT FROM AUTHOR]

Flexible systems are linear systems of inclusions in which the elements of the coefficient matrix are external numbers in the sense of nonstandard analysis. External numbers represent real numbers with small, individual error terms. Using Gaussian elimination, a flexible system can be put into a row-echelon form with increasing error terms on the right-hand side. Then parameters are assigned to the error terms and the resulting system is solved by common methods of linear algebra. The solution set may have indeterminacy not only in terms of linear spaces, but also of modules. We determine maximal robustness for flexible systems. [ABSTRACT FROM AUTHOR]

The genetic code is a set of regulatory principles that control the translation of information encoded in messenger RNA (mRNA) into a sequence of amino acids. This study proposes a model starting from the relationships between its physicochemical properties of nucleobase in the codons. We employed a binary metric and the Kronecker product to represent the physicochemical properties of nucleobases in a vector space. This state space has a hierarchical order, with self-similarity and symmetry properties in the hydrogen bonds of triplets. The state space can be mapped under linear transformations to a toroidal geometry with allometric properties. Furthermore, this geometric representation highlights a charge symmetry that exists in amino acids and in the distribution of essential and non-essential amino acids. These results describe a state space between codon-anticodon interactions that can be interpreted as Bell states. This suggests that there is a quantum phenomenon involved in the mechanisms of information storage in DNA. In addition, toroidal geometry can be used to represent the sequences of codons of the mRNA that encode the sequence of amino acids of the proteins to find similarities or homologies between evolutionary related species. [ABSTRACT FROM AUTHOR]

This study employs computational fluid dynamics (CFD) simulations to investigate the effect of wall roughness on linear loss in circular pipelines. It specifically addresses hemispherical roughness, focusing on how changes in spacing influence linear loss, a critical determinant of fluid motion within pipelines. The simulations further assess the impact of these variables on flow characteristics, laying a theoretical groundwork for drag reduction and pipeline design improvement. Results indicate that increased spacing between roughness elements reduces the differential pressure at both pipeline ends. The dimensionless spacing value of 30 stabilizes this pressure, suggesting a limit to further changes. Additionally, a rise in roughness height at this spacing exacerbates differential pressure, highlighting a proportional relationship between roughness dimensions and linear loss—greater roughness leads to higher linear loss. Applying a nickel-plated coating on the inner wall significantly lowers roughness, thereby reducing linear loss. [ABSTRACT FROM AUTHOR]

This study introduces the Orbit Weighting Scheme (OWS), a novel approach aimed at enhancing the precision and efficiency of Vector Space information retrieval (IR) models, which have traditionally relied on weighting schemes like tf-idf and BM25. These conventional methods often struggle with accurately capturing document relevance, leading to inefficiencies in both retrieval performance and index size management. OWS proposes a dynamic weighting mechanism that evaluates the significance of terms based on their orbital position within the vector space, emphasizing term relationships and distribution patterns overlooked by existing models. Our research focuses on evaluating OWS's impact on model accuracy using Information Retrieval metrics like Recall, Precision, Interpolated Average Precision (IAP), and Mean Average Precision (MAP). Additionally, we assess OWS's effectiveness in reducing the inverted index size, crucial for model efficiency. We compare OWS-based retrieval models against others using different schemes, including tf-idf variations and BM25Delta. Results reveal OWS's superiority, achieving a 54% Recall and 81% MAP, and a notable 38% reduction in the inverted index size. This highlights OWS's potential in optimizing retrieval processes and underscores the need for further research in this underrepresented area to fully leverage OWS's capabilities in information retrieval methodologies. [ABSTRACT FROM AUTHOR]

In this paper, using improvement-valued maps, we define two types of E-Benson proper efficient elements for subsets within a linear space under a variable ordering map C. Consequently, we delve into studying two types of E-Benson proper efficient solutions of vector optimization problems under variable ordering structures. We establish relationships among different types of E-Benson proper efficient elements. Furthermore, we demonstrate that the two types of E-Benson proper efficiency, in relation to the ordering map C, not only unify and extend certain notions of (weakly) nondominated elements but also extend some well-known notions of Benson proper efficiency under fixed ordering structures. Lastly, under suitable assumptions, we establish linear scalarization theorems for E-Benson proper efficient solutions of vector optimization problems under variable ordering structures. Several examples are also provided to illustrate the derived results. [ABSTRACT FROM AUTHOR]

In the semialgebraic range searching problem, we are given a set of n points in ℝd, and we want to preprocess the points such that for any query range belonging to a family of constant complexity semialgebraic sets (Tarski cells), all the points intersecting the range can be reported or counted efficiently. When the ranges are composed of simplices, the problem is well-understood: It can be solved using S(n) space and with Q(n) query time with S(n)Q(n)d=Õ(nd), where the Õ(⋅) notation hides polylogarithmic factors and this trade-off is tight (up to no(1) factors). In particular, there exist “low space” structures that use O(n) space with O(n1-1/d) query time [8, 25] and “fast query” structures that use O(nd) space with O(log n) query time [9]. However, for general semialgebraic ranges, only “low space” solutions are known, but the best solutions [7] match the same trade-off curve as simplex queries, with O(n) space and Õ(n1−1/d) query time. It has been conjectured that the same could be done for the “fast query” case, but this open problem has stayed unresolved. Here, we disprove this conjecture. We give the first nontrivial lower bounds for semialgebraic range searching and other related problems. More precisely, we show that any data structure for reporting the points between two concentric circles, a problem that we call 2D annulus reporting, with Q(n) query time must use S(n)=...(n³/Q(n)5) space, where the ...(⋅) notation hides no(1) factors, meaning, for Q(n)=logO(1)n, ...(n³) space must be used. In addition, we study the problem of reporting the subset of input points in a polynomial slab defined by {(x,y)∈R²:P(x)≤y≤P(x)+w}, where P(x)=∑i=0Δaixi is a univariate polynomial of degree Δ and a0,…,aΔ,w are given at the query time, a problem that we call polynomial slab reporting. For this, we show a space lower bound of ...(nΔ+1/Q(n)(Δ+3)Δ/2), which implies that for Q(n)=logO(1)n, we must use ...(nΔ+1) space. We also consider the dual semialgebraic stabbing problems of semialgebraic range searching and present lower bounds for them. In particular, we show that in linear space, any data structure that solves 2D annulus stabbing problems must use ...(n2/3) query time. Note that this almost matches the upper bound obtained by lifting 2D annuli to 3D. Like semialgebraic range searching, we also present lower bounds for general polynomial slab stabbing problems. Again, our lower bounds are almost tight for linear size data structures in this case. [ABSTRACT FROM AUTHOR]

We continue the study of truncated matrix-valued moment problems begun in [12]. Let q ∈ N. Suppose that (X , X) is a measurable space and E is a finite-dimensional vector space of measurable mappings of X into H q , the Hermitian q × q matrices. A linear functional Λ on E is called a moment functional if there exists a positive H q -valued measure μ on (X , X) such that Λ (F) = ∫ X 〈 F , d μ 〉 for F ∈ E. In this paper a number of special topics on the truncated matricial moment problem are treated. We restate a result from [11] to obtain a matricial version of the flat extension theorem. Assuming that X is a compact space and all elements of E are continuous on X we characterize moment functionals in terms of positivity and obtain an ordered maximal mass representing measure for each moment functional. The set of masses of representing measures at a fixed point and some related sets are studied. The class of commutative matrix moment functionals is investigated. We generalize the apolar scalar product for homogeneous polynomials to the matrix case and apply this to the matricial truncated moment problem. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study the class of Lie-admissible algebras (A ,.) such that its product is a biderivation of the Lie algebra (A , [ , ]) , where [ , ] is the commutator of the algebra (A ,.). First, we provide characterizations of algebras in this class. Furthermore, we show that this class of nonassociative algebras includes Lie algebras, symmetric Leibniz algebras, Lie-admissible left (or right) Leibniz algebras, Milnor algebras, and LR-algebras. Then, we establish results on the structure of these algebras in the case that the underlying Lie algebras are perfect (in particular, semisimple Lie algebras). In addition, we then study flexible A B D -algebras, showing in particular that these algebras are extensions of Lie algebras in the category of flexible A B D -algebras. Finally, we study left-symmetric A B D -algebras, in particular we are interested in flat pseudo-Euclidean Lie algebras where the associated Levi-Civita products define A B D -algebras on the underlying vector spaces of these Lie algebras. In addition, we obtain an inductive description of all these Lie algebras and their Levi-Civita products (in particular, for all signatures in the case of real Lie algebras). [ABSTRACT FROM AUTHOR]

We describe a procedure for the generation of functional digraphs up to isomorphism; these are digraphs with uniform outdegree 1, also called mapping patterns, finite endofunctions, or finite discrete-time dynamical systems. This procedure is based on a reverse search algorithm for the generation of connected functional digraphs, which is then applied as a subroutine for the generation of arbitrary ones. Both algorithms output solutions with O (n 2) delay and require linear space with respect to the number n of vertices. [ABSTRACT FROM AUTHOR]

The document is an author index for Volume 20 (2024) of the journal "New Mathematics & Natural Computation." It provides a list of authors and their corresponding articles published in the volume. The articles cover a range of topics in mathematics and natural computation, including fuzzy sets, graph theory, optimization problems, and sustainability. The index can be a useful resource for library patrons conducting research in these areas. [Extracted from the article]

A pseudo-Euclidean left-symmetric algebra (A ,. , 〈 , 〉) is a left-symmetric algebra endowed with a non-degenerate symmetric bilinear form 〈 , 〉 such that left multiplications by any element of A are skew-symmetric with respect to 〈 , 〉. We recall that a pseudo-Euclidean Lie algebra (g , [ , ] , 〈 , 〉) is flat if and only if (g ,. , 〈 , 〉) , its underlying vector space endowed with the Levi-Civita product associated with 〈 , 〉 , is a pseudo-Euclidean left-symmetric algebra. In this paper, we study pseudo-Euclidean left-symmetric algebras (A ,. , 〈 , 〉) such that commutators of all elements of A are contained in the left annihilator of (A ,.) , these algebras will be called pseudo-Euclidean left-symmetric L -algebras. Next, we introduce and study pseudo-Euclidean modules of pseudo-Euclidean left-symmetric L -algebras. We develop double extension processes that allow us to have inductive descriptions of all pseudo-Euclidean left-symmetric L -algebras and of all its pseudo-Euclidean modules of any signature. This, in particular, improves some of the results obtained in [11]. [ABSTRACT FROM AUTHOR]

Space vector pulse width modulation (SVPWM) is widely used in three-phase inverters. As the performance requirements of inverters increase, there is a demand to suppress common-mode voltages (CMVs) generated by SVPWM. In order to suppress the CMVs, it is necessary to mathematically analyze the CMVs. By using a mathematical analysis method based on double Fourier series, general expressions of CMV harmonic amplitudes and spectra are obtained for seven-segment SVPWM and five-segment SVPWM. Comparative analyses on the CMV general expressions are performed for the two SVPWMs, and the CMV harmonics characteristics for the two SVPWMs are summarized. Simulations are carried out in an inverter-driven permanent magnet motor system, and simulation results are in good agreement with calculation ones, which verifies the correctness and validity of the mathematical analysis. Based on these analyses, a more in-depth research can be conducted on the CMV suppression. [ABSTRACT FROM AUTHOR]

In this paper, we solve a classical counting problem for non-degenerate forms of symplectic and hermitian type defined on a vector space: given a subspace π , we find the number of non-singular subspaces that are trivially intersecting with π and span a non-singular subspace with π. Lower bounds for the quantity of such pairs where π is non-singular were first studied in "Glasby, Niemeyer, Praeger (Finite Fields Appl., 2022)", which was later improved in "Glasby, Ihringer, Mattheus (Des. Codes Cryptogr., 2023)" and generalised in "Glasby, Niemeyer, Praeger (Linear Algebra Appl., 2022)". In this paper, we derive explicit formulae, which allow us to give the exact proportion and improve the known lower bounds. [ABSTRACT FROM AUTHOR]

This article proposes a fuzzy-based Unified Power Quality Conditioner (UPQC) with Wind Power Generation (WPG) and Battery Storage System (BSS). The UPQC contains a series and a shunt voltage source converters (VSC) coupled with a dc-bus. The hybrid controller adopts both the fuzzy and proportional integral (PI) controllers. The prime objectives of the present work are: (1) quick response and dc-link voltage levelling; (2) removal of supply voltage sag/swell; (3) reduction of harmonics and enhancement of power factor; (4) satisfactory performance for severe disruptions; and (5) adequate compensation for unbalanced systems. The performances of the suggested controller are examined for eight test scenarios involving various load configurations, and distorted grid voltages, and compared to those of the existing PI, sliding mode, and fuzzy logic controllers. It portrays that the proposed hybrid controller lowers the THD values to the best possible values and improves the power factor to almost unity for different loads with several power quality issues in addition to requiring very less time for reaching the steady dc-bus voltage. [ABSTRACT FROM AUTHOR]

Let K be an n-dimensional equiangular cone in a Euclidean vector space. Let 0 < ϕ < π be the common angle between any pair of vectors taken among the generators of the cone. We obtain an explicit formula for the maximum angle of K in terms of n and ϕ . We explain also how to identify a pair { u , v } of unit vectors in K achieving the maximum angle. Finally, we analyze a counterintuitive phenomenon that occurs when n is large: the equiangular cone K can be constructed so that u and v are almost opposite, whereas ϕ is near π / 2 . [ABSTRACT FROM AUTHOR]

An automorphism u of a vector space is called unipotent of index 2 whenever (u − id) 2 = 0. Let b be a non-degenerate symmetric or skewsymmetric bilinear form on a vector space V over a field F of characteristic different from 2. Here, we characterize the elements of the isometry group of b that are the product of two unipotent isometries of index 2. In particular, if b is skewsymmetric and nondegenerate we prove that an element of the symplectic group of b is the product of two unipotent isometries of index 2 if and only if it has no Jordan cell of odd size for the eigenvalue −1. As an application, we prove that every element of a symplectic group is the product of three unipotent elements of index 2 (and no fewer in general). For orthogonal groups, the classification closely matches the classification of sums of two square-zero skewselfadjoint operators that was obtained in a recent article [7]. [ABSTRACT FROM AUTHOR]

Following the definition of interval-valued fuzzy n-normed linear space given by S. Vijayabalaji et al., in this paper, notion of interval-valued generalized fuzzy n-normed linear space is introduced. The notion of convergent sequence, Cauchy sequence and their relation are studied. Some basic results are established on finite dimensional interval-valued generalized fuzzy n-normed linear space. [ABSTRACT FROM AUTHOR]

Quantum computers accelerate many algorithms based on the superposition principle of quantum mechanics. The Grover algorithm provides significant performance to malicious users attacking symmetric key systems. Since the performance of attacks using quantum computers depends on the efficiency of the quantum circuit of the encryption algorithms, research research on the implementation of quantum circuits is essential. This paper presents a new framework to construct quantum circuits of substitution boxes (S-boxes) using system modeling. We model the quantum circuits of S-boxes using two layers: Toffoli and linear layers. We generate vector spaces based on the values of qubits used in the linear layers and apply them to find quantum circuits. The framework finds the circuit by matching elements of vector spaces generated from the input and output of a given S-box, using the forward search or the meet-in-the-middle strategy. We developed a tool to apply this framework to 4-bit S-boxes. While the 4-bit S-box quantum circuit construction tool LIGHTER-R only finds circuits that can be implemented with four qubits, the proposed tool achieves the circuits with five qubits. The proposed tool can find quantum circuits of 4-bit odd permutations based on the controlled NOT, NOT, and Toffoli gates, whereas LIGHTER-R is unable to perform this task in the same environment. We expect this technique to become a critical step toward optimizing S-box quantum circuits. [ABSTRACT FROM AUTHOR]

Interpolating a density matrix from a set of known density matrices is not a trivial task. This is because a linear combination of density matrices does not necessarily correspond to another density matrix. In this Communication, density matrices are examined as objects of a Grassmann manifold. Although this manifold is not a vector space, its tangent space is a vector space. As a result, one can map the density matrices on this manifold to their corresponding vectors in the tangent space and then perform interpolations on that tangent space. The resulting interpolated vector can be mapped back to the Grassmann manifold, which can then be utilized (1) as an optimal initial guess for a self-consistent field (SCF) calculation or (2) to derive energy directly without time-consuming SCF iterations. Such a promising approach is denoted as Grassmann interpolation (G-Int). The hydrogen molecule has been used to illustrate that the described interpolated method in this work preserves the essential attributes of a density matrix. For phosphorus mononitride and ferrocene, it was demonstrated numerically that reference points for the definition of the corresponding tangent spaces can be chosen arbitrarily. In addition, the interpolated density matrices provide a superior and essentially converged initial guess for an SCF calculation to make the SCF procedure itself unnecessary. Finally, this accurate, efficient, robust, and systematically improved G-Int strategy has been used for the first time to generate highly accurate potential energy surfaces with fine details for the difficult case, ferrocene. [ABSTRACT FROM AUTHOR]

This review of movement stability, optimality, and agility is based on the theory of motor control with changes in spatial referent coordinates for the effectors, the principle of abundance, and the uncontrolled manifold hypothesis. A new optimality principle is suggested based on the concept of optimal sharing corresponding to a vector in the space of elemental variables locally orthogonal to the uncontrolled manifold. Motion along this direction is as.sociated with minimal components along the relatively unstable directions within the uncontrolled manifold leading to a minimal motor equivalent motion. For well-practiced actions, this task-specific criterion is followed in spaces of referent coordinates. Consequences of the suggested framework include trade-offs among stability, optimality, and agility, unintentional changes in performance, hand dominance, finger specialization. individual traits in performance, and movement disorders in neurological patients. [ABSTRACT FROM AUTHOR]

In this paper, we study spaces of vector functions that are holomorphic in an angular domain of the complex plane and with values in a separable Hilbert space. We show that, equipped with the appropriate norms, these spaces are Hilbert spaces. [ABSTRACT FROM AUTHOR]

AbstractLet V be a vector space over the binary field F2={0,1} with dimV≥2 . If W={W1,…,Wn} is a family of hyperplanes of V, one says that W is an irredundant covering for V provided that W covers V, that is, ∪i=1nWi=V and no proper subfamily of W covers V. We show that W is an irredundant covering for V if and only if the following three conditions are satisfied: (i) n is odd, (ii) dimV/∩i=1nWi=n−1 , and (iii) any (n−1) -fold intersection of the elements of W has codimension n – 1. Moreover, we show that for any odd integer n with 3≤n≤dimV+1 there is an irredundant hyperplane covering for V with n elements. [ABSTRACT FROM AUTHOR]

Knowledge graphs are widely used and semantically rich data representations, which is increasingly becoming a crucial technology in the field of knowledge engineering. However, real-world knowledge graphs often suffer from incompleteness and ambiguity, hindering their application performance. Knowledge graph completion techniques aim to enrich the content of knowledge graphs by predicting missing entities or relations, has been a hot research topic in recent years. In particular, embedding-based approaches have made remarkable progress in knowledge graph completion tasks. It reviews recent embedding- based static knowledge graph completion methods, categorizing them based on approaches such as translation- based models, tensor factorization, neural network models, and pre- trained language models. These methods achieve an improved semantic representation and inferential capabilities by embedding entity relations into continuous vector spaces. At the same time, it has potential advantages in capturing complex relationships between entities and utilizing graph structural information. [ABSTRACT FROM AUTHOR]

The chemical composition of individual particles can be revealed by single-particle mass spectrometers (SPMSs). With higher accuracy in the ratio of mass to charge (m/z), more detailed chemical information could be obtained. In SPMSs, the conventional standard-based calibration methods (internal/external) are constrained by the inhomogeneity of ionization lasers and the finite focusing ability of the inlet system, etc.; therefore, the mass accuracy is restricted. In this study, we obtained the detailed and reliable chemical composition of single particles utilizing a standard-free mass calibration algorithm. In the algorithm, the characteristic distributions of hundreds of ions were concluded and collected in a database denoted as prototype. Each single-particle mass spectrum was initially calibrated by a function with specific coefficients. The range of coefficients was constrained by the magnitude of mass deviation to a finite vector space. To find the optimal coefficient vector, the conformity of each initially calibrated spectrum to the prototype dataset was assessed. The optimum calibrated spectrum was obtained with maximum conformity. For more than 98 % ambient particles, a 20-fold improvement in mass accuracy, from ∼ 10 000 ppm (integer) to ∼ 500 ppm (two decimal places), was achieved. The improved mass accuracy validated the determination of adjacent ions with a m/z difference ∼ 0.05 Th. Furthermore, atmospheric particulate trace elements that were poorly studied before are specified. The obtained detailed single-particle-level chemical information could help explain the source apportionment, reaction mechanism, and mixing state of atmospheric particles. [ABSTRACT FROM AUTHOR]

This paper proposes a fault-tolerant control (FTC) strategy using the current space vectors to diagnose sensor failures and enhance the sustained operation of a field-oriented (FO) controlled induction motor drive (IMD). Three space vectors are established for the sensor fault diagnosis technique, including one converted from the measured currents and the other two calculated from the current estimation technique, respectively, measured and with reference speeds. A mixed mathematical model using three space vectors and their components is proposed to accurately determine the fault condition of each sensor in the motor drive. After determining the operating status of each sensor, if the sensor signal is in good condition, the feedback signal to the controller will be the measured signal; otherwise, the estimated signal will be used instead of the failed signal. Failure states of the various sensors were simulated to check the effectiveness of the proposed technique in the Matlab/Simulink environment. The simulation results are positive: the IMD system applying the proposed FTC technique accurately detected the failed sensor and maintained stability during the operation. [ABSTRACT FROM AUTHOR]

Let X be a set and H a collection of functions from X to { 0 , 1 } . We say that H shatters a finite set C ⊂ X if the restriction of H yields every possible function from C to { 0 , 1 } . The VC-dimension of H is the largest number d such that there exists a set of size d shattered by H , and no set of size d + 1 is shattered by H . Vapnik and Chervonenkis introduced this idea in the early 70s in the context of learning theory, and this idea has also had a significant impact on other areas of mathematics. In this paper we study the VC-dimension of a class of functions H defined on F q d , the d-dimensional vector space over the finite field with q elements. Define H t d = { h y (x) : y ∈ F q d } , where for x ∈ F q d , h y (x) = 1 if ‖ x - y ‖ = t , and 0 otherwise, where here, and throughout, ‖ x ‖ = x 1 2 + x 2 2 + ⋯ + x d 2 . Here t ∈ F q , t ≠ 0 . Define H t d (E) the same way with respect to E ⊂ F q d . The learning task here is to find a sphere of radius t centered at some point y ∈ E unknown to the learner. The learning process consists of taking random samples of elements of E of sufficiently large size. We are going to prove that when d = 2 , and | E | ⩾ C q 15 / 8 , the VC-dimension of H t 2 (E) is equal to 3. This leads to an intricate configuration problem which is interesting in its own right and requires a new approach. [ABSTRACT FROM AUTHOR]

A substitution box (S-Box) is a fundamental component used in DES and AES. This is used to achieve non-linearity in encryption. The use of S-Box also introduces the property of confusion in symmetric cipher systems. A finite field in the multiplicative inverses of GF (28) is the basis for the generation of the S-Box in the AES algorithm. This paper presents a novel approach that utilizes the XOR vector space for generating the S-Box. The XOR vector space is constructed using two-dimensional values comprising vectors of size of 2b. Following this, the resulting S-Box is employed in standard algorithms such as DES and AES to encrypt the image. Furthermore, this paper assesses the security aspects of the proposed algorithm by measuring various parameters. The result is compared with methods that generate various S-Boxes for the DES and AES algorithms. This suggests that the proposed method is relatively better. [ABSTRACT FROM AUTHOR]

We give a cohomological interpretation of the Heaviside filtration on the Varchenko–Gelfand ring of a pair |$({\mathcal{A}},{\mathcal{K}})$|⁠ , where |${\mathcal{A}}$| is a real hyperplane arrangement and |${\mathcal{K}}$| is a convex open subset of the ambient vector space. This builds on work of the first author, who studied the filtration from a purely algebraic perspective, as well as work of Moseley, who gave a cohomological interpretation in the special case where |${\mathcal{K}}$| is the ambient vector space. We also define the Gelfand–Rybnikov ring of a conditional oriented matroid, which simultaneously generalizes the Gelfand–Rybnikov ring of an oriented matroid and the aforementioned Varchenko–Gelfand ring of a pair. We give purely combinatorial presentations of the ring, its associated graded, and its Rees algebra. [ABSTRACT FROM AUTHOR]

In this paper, a symplectic structure on a Leibniz algebra is defined to be a symmetric nondegenerate bilinear form satisfying certain compatibility condition, and a phase space of a Leibniz algebra is defined to be a symplectic Leibniz algebra satisfying certain conditions. We show that a Leibniz algebra has a phase space if and only if there is a compatible Leibniz-dendriform algebra, and phase spaces of Leibniz algebras are one-to-one corresponds to Manin triples of Leibniz-dendriform algebras. Product (paracomplex) structures and complex structures on Leibniz algebras are studied in terms of decompositions of Leibniz algebras. A para-Kähler structure on a Leibniz algebra is defined to be a symplectic structure and a paracomplex structure satisfying a compatibility condition. We show that a symplectic Leibniz algebra admits a para-Kähler structure if and only if the Leibniz algebra is the direct sum of two Lagrangian subalgebras as vector spaces. A complex product structure on a Leibniz algebra consists of a complex structure and a product structure satisfying a compatibility condition. A pseudo-Kähler structure on a Leibniz algebra is defined to be a symplectic structure and a complex structure satisfying a compatibility condition. Various properties and relations of complex product structures and pseudo-Kähler structures are studied. In particular, Leibniz-dendriform algebras give rise to complex product structures and pseudo-Kähler structures naturally. [ABSTRACT FROM AUTHOR]

There are several results in the literature concerning p -groups G with a maximal elementary abelian normal subgroup of rank k due to Thompson, Mann and others. Following an idea of Sambale we obtain bounds for the number of generators etc. of a 2-group G in terms of k , which were previously known only for p > 2. We also prove a theorem that is new even for odd primes. Namely, we show that if G has a maximal elementary abelian normal subgroup of rank k , then for any abelian subgroup A the Frattini subgroup Φ (A) can be generated by 2 k elements (3 k when p = 2). The proof of this rests upon the following result of independent interest: If V is an n -dimensional vector space, then any commutative subalgebra of End (V) contains a zero algebra of codimension at most n. [ABSTRACT FROM AUTHOR]

Let 퓟n := H*((ℝP∞)n) ≅ ℤ2[x1, x2, ..., xn] be the graded polynomial algebra over ℤ2, where ℤ2 denotes the prime field of two elements. We investigate the Peterson hit problem for the polynomial algebra 퓟n, viewed as a graded left module over the mod-2 Steenrod algebra, 퓐. For n > 4, this problem is still unsolved, even in the case of n = 5 with the help of computers. In this article, we study the hit problem for the case n = 6 in the generic degree dr = 6(2r − 1) + 4.2r with r an arbitrary non-negative integer. By considering ℤ2 as a trivial 퓐-module, then the hit problem is equivalent to the problem of finding a basis of ℤ2-vector space ℤ2 ⊗퓐퓟n. The main goal of the current article is to explicitly determine an admissible monomial basis of the ℤ2 vector space ℤ2 ⊗퓐퓟6 in some degrees. As an application, the behavior of the sixth Singer algebraic transfer in the degree 6(2r − 1) + 4.2r is also discussed at the end of this paper. [ABSTRACT FROM AUTHOR]

The Sturm-Liouville eigenvalue problem is symmetric if the coefficients are even functions and the boundary conditions are symmetric. The eigenfunction is expressed in terms of orthonormal bases, which are constructed in a linear space of trial functions by using the Gram-Schmidt orthonormalization technique. Then an n-dimensional matrix eigenvalue problem is derived with a special matrix A:= [aij], that is, aij = 0 if i + j is odd. Based on the product formula, an integration method with a fictitious time, namely the fictitious time integration method (FTIM), is developed to obtain the higher-index eigenvalues. Also, we recover the symmetric potential function q(x) in the Sturm-Liouville operator by specifying a few lower-index eigenvalues, based on the product formula and the Newton iterative method. [ABSTRACT FROM AUTHOR]

In the current paper, we introduce the notion of statistical convergence of order α and strongly p-Cesàro summability of order α of sequences in the gradual normed linear spaces. We investigate several properties and a few inclusion relations of the newly introduced notions. [ABSTRACT FROM AUTHOR]

We introduce a local zeta-function for an irreducible admissible supercuspidal representation π of the metaplectic double cover of SL 2 over a non-archimedean local field of characteristic zero. We prove a functional equation of the local zeta-functions showing that the gamma factor is given by a Mellin type transform of the Bessel function of π. We obtain an expression of the gamma factor, which shows its entireness on C. Moreover, we show that, through the local theta-correspondence, the local zeta-function on the covering group is essentially identified with the local zeta-integral for spherical functions on PGL 2 ≅ SO 3 associated with the prehomogenous vector space of symmetric matrices of degree 2. [ABSTRACT FROM AUTHOR]

In the paper we utilize a new approach to the classification problem of finite-dimensional algebras. We give a complete classifications of associative and diassociative algebra structures on two-dimensional vector space over any basic field. [ABSTRACT FROM AUTHOR]

A nonlinear multivariable highly coupled system that is susceptible to both internal and external perturbations is the permanent magnet synchronous motor. A new reaching law‐based control approach that combines a sliding‐mode disturbance observer and an enhanced two‐vector model predictive current control is suggested in order to enhance the dynamic performance of the permanent magnet synchronous motor and its robustness to system disturbances. First, a new reaching law is developed in this paper to resolve the conflict between the traditional reaching law's chattering of the system and the reaching time of the sliding‐mode surface. This new reaching law not only makes the system's response more rapid but also reduces chattering; second, taking into account the possibility of systems with internal parameter uptake and external load disturbance, a sliding‐mode disturbance observer based on t is developed. Finally, the q‐axis current obtained from the speed sliding‐mode control rate is added to the model predictive current control, and an optimal duty cycle model predictive current control based on space vector modulation is designed because the traditional two‐vector model predictive current control is to optimize the duty cycle and voltage vectors separately, and the switching frequency is not fixed. The method suggested in this research may successfully suppress the sliding‐mode control system chattering and increase the resilience and dynamic response performance of the speed control system, according to simulation findings compared to the traditional reaching law and traditional duty cycle. © 2024 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]