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We propose an efficient version of ensemble Hartree–Fock/density functional theory to calculate a set of two charge-transfer states for systems with odd-numbers of electrons. The approach does require definitions of donor/acceptor fragments; however, the approach is not very sensitive to such definitions—even in the limit of very strong electronic coupling. The key ansatz is that, by mandating that the vector space spanned by the active orbitals projects equally onto the donor and acceptor fragments, such a constraint eliminates all intra-molecular local excitations and makes it far easier to generate potential energy surfaces that are smooth over a wide region of configuration space. The method is fast, working with only two electron configurations, and should be useful for ab initio non-adiabatic dynamics in the near future. [ABSTRACT FROM AUTHOR]

Multipoint evaluation is the computational task of evaluating a polynomial given as a list of coefficients at a given set of inputs. Besides being a natural and fundamental question in computer algebra on its own, fast algorithms for this problem are also closely related to fast algorithms for other natural algebraic questions such as polynomial factorization and modular composition. And while nearly linear time algorithms have been known for the univariate instance of multipoint evaluation for close to five decades due to a work of Borodin and Moenck [7], fast algorithms for the multivariate version have been much harder to come by. In a significant improvement to the state-of-the-art for this problem, Umans [25] and Kedlaya & Umans [16] gave nearly linear time algorithms for this problem over field of small characteristic and over all finite fields, respectively, provided that the number of variables n is at most do(1) where the degree of the input polynomial in every variable is less than d. They also stated the question of designing fast algorithms for the large variable case (i.e., n x do(1)) as an open problem. In this work, we show that there is a deterministic algorithm for multivariate multipoint evaluation over a field Fq of characteristic p, which evaluates an n-variate polynomial of degree less than d in each variable on N inputs in time provided that p is at most do(1), and q is at most (exp(exp(exp(· · · (exp(d))))), where the height of this tower of exponentials is fixed. When the number of variables is large (e.g., n x do(1)), this is the first nearly linear time algorithm for this problem over any (large enough) field. Our algorithm is based on elementary algebraic ideas, and this algebraic structure naturally leads to the following two independently interesting applications: --We show that there is an algebraic data structure for univariate polynomial evaluation with nearly linear space complexity and sublinear time complexity over finite fields of small characteristic and quasipolynomially bounded size. This provides a counterexample to a conjecture of Miltersen [21] who conjectured that over small finite fields, any algebraic data structure for polynomial evaluation using polynomial space must have linear query complexity. We also show that over finite fields of small characteristic and quasipolynomially bounded size, Vandermonde matrices are not rigid enough to yield size-depth tradeoffs for linear circuits via the current quantitative bounds in Valiant's program [26]. More precisely, for every fixed prime p, we show that for every constant e > 0, and large enough n, the rank of any n × n Vandermonde matrix V over the field Fpa can be reduced to (n/exp(O(poly(e)log0.53 n))) by changing at most nT(e) entries in every row of V, provided a = poly(logn). Prior to this work, similar upper bounds on rigidity were known only for special Vandermonde matrices. For instance, the Discrete Fourier Transform matrices and Vandermonde matrices with generators in a geometric progression [9]. [ABSTRACT FROM AUTHOR]

If C$C$ is a smooth projective curve over an algebraically closed field F$\mathbb {F}$ and G$G$ is a group of automorphisms of C$C$, the canonical representation of C$C$ is given by the induced F$\mathbb {F}$‐linear action of G$G$ on the vector space H0C,ΩC$H^0\left(C,\Omega _C\right)$ of holomorphic differentials on C$C$. Computing it is still an open problem in general when the cover C→C/G$C \rightarrow C/G$ is wildly ramified. In this paper, we fix a prime power q$q$, we consider the Drinfeld curve, that is, the curve C$C$ given by the equation XYq−XqY−Zq+1=0${XY^q-X^qY-Z^{q+1}=0}$ over F=Fq¯$\mathbb {F}=\hspace{0.83328pt}\overline{\hspace{-0.83328pt}\mathbb {F}_q\hspace{-0.83328pt}}\hspace{0.83328pt}$ together with its standard action by G=SL2Fq${G=SL_2\left(\mathbb {F}_q\right)}$, and decompose H0C,ΩC$H^0\left(C,\Omega _C\right)$ as a direct sum of indecomposable representations of G$G$, thus solving the aforementioned problem in this case. [ABSTRACT FROM AUTHOR]

In computational homogenization approaches, data-driven methods entail advantages due to their ability to capture complex behavior without assuming a specific material model. Within this domain, constitutive model-based and model-free data-driven methods are distinguished. The former employ artificial neural networks as models to approximate a constitutive relation, whereas the latter directly incorporate stress–strain data in the analysis. Neural network-based constitutive descriptions are one of the most widely used data-driven approaches in computational mechanics. In contrast, distance-minimizing data-driven computational mechanics enables substituting the material modeling step entirely by iteratively obtaining a physically consistent solution close to the material behavior represented by the data. The maximum entropy data-driven solver is a generalization of this method, providing increased robustness concerning outliers in the underlying data set. Additionally, a tensor voting enhancement based on incorporating locally linear tangent spaces enables interpolating in regions of sparse sampling. In this contribution, a comparison of neural network-based constitutive models and data-driven computational mechanics is made. General differences between machine learning, distance minimizing, and entropy maximizing data-driven methods are explored. These include the pre-processing of data and the required computational effort for optimization as well as evaluation. Numerical examples with synthetically generated datasets obtained by numerical material tests are employed to demonstrate the capabilities of the investigated methods. An anisotropic nonlinear elastic constitutive law is chosen for the investigation. The resulting constitutive representations are then applied in structural simulations. Thereby, differences in the solution procedure as well as use-case accuracy of the methods are investigated. [ABSTRACT FROM AUTHOR]

The Distributed power flow controller can be considered as advance power flow controller which is combination of series and shunt compensator without DC link. In this paper Space vector Pulse width Modulation employs in Distributed power flow Controller for Harmonics Reduction and power quality improvement. A new technique SVPWM adopted which reduces the harmonics and the same time improves power quality and increase transient stability. In this paper a new technique of Multi objective Grey wolf algorithm used to optimize the controller parameter of DPFC. For the design of PI controller GWO algorithm can be used for better optimistic performance of DPFC. As a result of that power quality and voltage profile improves drastically and the same time harmonics also reduced remarkable level of 4.62% of Voltage THD and 1.8% of current THD. The simulation result and hardware model Prove the feasibility of proposed Configuration. [ABSTRACT FROM AUTHOR]

Hyperdimensional (HD) computing (also referred to as vector symbolic architectures, VSAs) offers a method for encoding symbols into vectors, allowing for those symbols to be combined in different ways to form other vectors in the same vector space. The vectors and operators form a compositional algebra, such that composite vectors can be decomposed back to their constituent vectors. Many useful algorithms have implementations in HD computing, such as classification, spatial navigation, language modeling, and logic. In this letter, we propose a spiking implementation of Fourier holographic reduced representation (FHRR), one of the most versatile VSAs. The phase of each complex number of an FHRR vector is encoded as a spike time within a cycle. Neuron models derived from these spiking phasors can perform the requisite vector operations to implement an FHRR. We demonstrate the power and versatility of our spiking networks in a number of foundational problem domains, including symbol binding and unbinding, spatial representation, function representation, function integration, and memory (i.e., signal delay). [ABSTRACT FROM AUTHOR]

This paper is dedicated to defining and studying for the first time the concept of fuzzy metric spaces based on two-fold fuzzy algebras, where the elementary properties of this new concept will be studied and presented by many theorems and related examples that explain the validity of our work. Also, many different types of open and closed balls will be discussed, as well as the relationships between these metric substructures. Keywords: fuzzy metric space, two-fold algebra, open ball, closed ball, torus Introduction and basic concepts The applications of neutrosophic sets and fuzzy sets are very wide and open research areas. In the literature, we can find many neutrosophic and fuzzy algebraic structures with deep connection with applied mathematics and number theory [5-11]. The concept of two-fold algebra was presented by Smarandache in [4], where many suggestions for the algebraic structure related to this algebra were defined and presented. This new idea has been used in [1] to study the two-fold algebra based on the standard fuzzy number theoretical system [3]. In [2], Hatip et.al. proposed the two-fold vector space and two-fold algebraic module based on fuzzy mappings, where they have studied the elementary properties of these new generalizations with many interesting examples. This work is motivated by the modern idea of two-fold algebra, and metric spaces, where we can combine those to different structures in one algebraic structure called two-fold. [ABSTRACT FROM AUTHOR]

The performance of neutral‐point‐clamped (NPC) converters is subject to the regulation of neutral point balance. In the literature, researchers have addressed two main modulation methods: the active space vector PWM (SVPWM) technique and the virtual SVPWM (VSVPWM) method. However, those two approaches respectively suffer from reduced DC‐link voltage utilization and poor active regulation capability. To address this, an improved VSVPWM modulation scheme with actively strong voltage regulation capability is proposed in this paper. The fast and precise control of capacitor voltages is achieved by optimizing the synthesis scheme of the virtual vectors. When there is a voltage imbalance, the proposed technique can quickly restore and maintain the capacitor voltage balance till the full DC‐link voltage utilization without affecting the converter output quality. The experimental validation results on the NPC converter have demonstrated the benefits of the proposed active VSVPWM method. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

We consider bounded linear operators from the view of functional reproducing property. For some bounded linear operators associated with orthogonal polynomials we define an inner product space associated with a kernel constructed with orthogonal polynomials, show that it is a functional reproducing kernel Hilbert space (FRKHS) associated with these bounded linear operators and give decay rate for the best FRKHS approximation with a K -functional associated with the FRKHS. On this basis, we provide a learning rate for kernel regularized regression whose hypothesis space is the defined FRKHS. As applications, we define some concrete FRKHSs associated with polynomial operators such as the Bernstein–Durrmeyer operators, the de la Vallée Poussin operators on both the unit sphere S d − 1 and the unit ball B d . We show that these polynomial operators have reproducing property with respect to the corresponding concrete FRKHSs and show the learning rate for the kernel regularized regression. In short, we provide a way of constructing FRKHS operators with Fourier multipliers and show a learning framework from the view of operator approximation. [ABSTRACT FROM AUTHOR]

Summary: This paper targets to minimize the peak common mode voltage (CMV) in ultra sparse matrix converters (USMC) by applying new zero vectors for the space vector modulation technique (SVM). Conventional zero vectors in the SVM raise the peak CMV by 42.23%. An increased magnitude of CMV is associated with the occurrence of leakage current, hence resulting in insulation degradation. So, the reduction of peak CMV is necessary for USMC. The proposed method offers suitable switching arrangements using auxiliary shoot through (AST) switches to minimize the peak‐to‐peak CMV. This proposed method holds the advantages of the conventional method, like a wide range of modulation index and zero current switching at the rectifier side, and also reduces the CMV problem. This paper also provides a comparative analysis of the existing reported methods and the proposed method. The effectiveness of the proposed method is validated through both simulation and experimental results. [ABSTRACT FROM AUTHOR]

We prove the strong Lefschetz property for Artinian Gorenstein algebras generated by the relative invariants of prehomogeneous vector spaces of commutative parabolic type. [ABSTRACT FROM AUTHOR]

A new concept known as the orthogonal component graph associated with a finite-dimensional vector space over a finite field has been recently added as another class of algebraic graphs. In these types of graphs, the vertices will be all the possible non-zero linear combinations of orthogonal basis vectors, and any two vertices will be adjacent if the corresponding vectors are orthogonal. In this paper, we discuss the various colorings and structural properties of orthogonal component graphs. [ABSTRACT FROM AUTHOR]

Let X be an irreducible 2 n-dimensional holomorphic symplectic manifold. A reflexive sheaf F is very modular if its Azumaya algebra End (F) deforms with X to every Kähler deformation of X. We show that if F is a slope-stable reflexive sheaf of positive rank and the obstruction map HH² (X) → Ext 2 (F, F) has rank 1, then F is very modular. We associate to such a sheaf a vector in the Looijenga-Lunts-Verbitsky lattice of rank b 2 (X) + 2. Three sources of examples of such modular sheaves emerge. The first source consists of slope-stable reflexive sheaves F of positive rank that are isomorphic to the image Φ (O X) of the structure sheaf via an equivalence Φ: Db (X) → Db (Y) of the derived categories of two irreducible holomorphic symplectic manifolds. The second source consists of such F, which are isomorphic to the image of a skyscraper sheaf via a derived equivalence. The third source consists of images Φ (L) of torsion sheaves L supported as line bundles on holomorphic lagrangian submanifolds Z such that Z deforms with X in codimension 1 in moduli, and L is a rational power of the canonical line bundle of Z. An example of the first source is constructed using a stable and rigid vector bundle G on a K 3 surface X to get the very modular vector bundle F on the Hilbert scheme X [n] associated to the equivariant vector bundle G ⊠ ⋯ ⊠ G on X n via the Bridgeland-King-Reid (BKR) correspondence. This builds upon and partially generalizes results of O'Grady for n = 2. A construction of the second source associates to a set {Gi}ni = 1 of n distinct stable vector bundles in the same two-dimensional moduli space of vector bundles on a K3 surface X the very modular vector bundle F on X [n] corresponding to the equivariant bundle ⊕ σ ∈ S n [Gσ(1)...Gσ(n)] on Xn. [ABSTRACT FROM AUTHOR]

Let 픽 q d be the d-dimensional vector space over the finite field 픽 q with q elements. For each non-zero r in 픽 q and E ⊂ 픽 q d , we define W ⁢ (r) as the number of quadruples (x , y , z , w) ∈ E 4 such that Q ⁢ (x - y) Q ⁢ (z - w) = r , where Q is a non-degenerate quadratic form in d variables over 픽 q . When Q ⁢ (α) = ∑ i = 1 d α i 2 with α = (α 1 , ... , α d) ∈ 픽 q d , Pham (2022) recently used the machinery of group actions and proved that if E ⊂ 픽 q 2 with q ≡ 3 ⁢ (mod ⁡ 4) and | E | ≥ C ⁢ q , then we have W ⁢ (r) ≥ c ⁢ | E | 4 q for any non-zero square number r ∈ 픽 q , where C is a sufficiently large constant, c is some number between 0 and 1, and | E | denotes the cardinality of the set E. In this article, we improve and extend Pham's result in two dimensions to arbitrary dimensions with general non-degenerate quadratic distances. As a corollary of our results, we also generalize the sharp results on the Falconer-type problem for the quotient set of distance set due to the first two authors and Parshall (2019). Furthermore, we provide improved constants for the size conditions of the underlying sets. The key new ingredient is to relate the estimate of the W ⁢ (r) to a quadratic homogeneous variety in 2 ⁢ d -dimensional vector space. This approach is fruitful because it allows us to take advantage of Gauss sums which are more handleable than the Kloosterman sums appearing in the standard distance-type problems. [ABSTRACT FROM AUTHOR]

Let h = ∏ i = 1 t p i s i be its decomposition into a product of powers of distinct primes, and ℤ h be the residue class ring modulo h. Let ℤ h n be the n -dimensional row vector space over ℤ h . A generalized Grassmann graph over ℤ h , denoted by G r (m , n , ℤ h) ( G r for short), has all m -subspaces of ℤ h n as its vertices, and two distinct vertices are adjacent if their intersection is of dimension > m − r , where 2 ≤ r ≤ m + 1 ≤ n. In this paper, we determine the clique number and geometric structures of maximum cliques of G r . As a result, we obtain the Erdős–Ko–Rado theorem for ℤ h n . [ABSTRACT FROM AUTHOR]

Roos' direct sum decomposition of a cyclic convolutional code based upon a suitable construction of a minimal encoder is extended to a broader class of convolutional codes endowed with additional algebraic structure. The two (equivalent) usual concepts of a convolutional code are taken into account, as a vector space and as a module. [ABSTRACT FROM AUTHOR]

In this paper, we first strengthen a few results about the order of solvable linear groups of odd order. We then use these results to bound the product of the orders of odd-order composition factors in a composition series of an arbitrary finite linear group. [ABSTRACT FROM AUTHOR]

This paper studies a notion of directed homology for preordered spaces, called the homology digraph. We show that the homology digraph is a directed homotopy invariant and establish variants of the main results of ordinary singular homology theory for the homology digraph. In particular, we prove a Künneth formula, which enables one to compute the homology digraph of a product of preordered spaces from the homology digraphs of the components. [ABSTRACT FROM AUTHOR]

Hyper‐redundant manipulators have strong flexibility that benefits from their redundant limb structure. However, a large number of redundant degrees of freedom will also lead the solution of inverse kinematics much more difficult, which restricts their motion performance to some extent. Inspired by the FABRIK (Forward and Backward Reaching Inverse Kinematics) method, an improved inverse kinematics solution method for the hyper‐redundant manipulator is proposed. Based on the space vector method, the kinematic model of the manipulator is established to dynamically acquire its endpoint position, and the workspace is further obtained by using the Monte Carlo method. The original search method is optimized, the include angle decoupling mechanism between adjacent links is established to obtain the rotation angles of each joint, and the joint angle limitation is introduced to meet the actual manipulator structural restriction. On this basis, the pose constraint mechanism is established to realize the control of the end‐link pose, and the linear degree of freedom is introduced to realize the solution after the directional expansion of the manipulator's workspace. A series of simulation experiments are carried out. In the experiments, the position error of the manipulator's endpoint is always less than 10−6 mm. Meanwhile, the comparative experimental results show that compared with the original method, the proposed method exhibits higher position accuracy under the condition that the computation time is almost the same. In addition, in the end‐link pose constraint experiment and path motion experiments, the pose error of the end‐link is always less than 10−7°, indicating that the end‐link pose can also meet the high accuracy requirements under the premise of ensuring high position accuracy. Finally, the prototype experiment further verifies its performance. [ABSTRACT FROM AUTHOR]

This paper investigates second-order optimality conditions for general constrained set-valued optimization problems in normed vector spaces under the set criterion. To this aim we introduce several new concepts of second-order directional derivatives for set-valued maps by means of excess from a set to another one, and discuss some of their properties. By virtue of these directional derivatives and by adopting the notion of set criterion intoduced by Kuroiwa, we obtain second-order necessary and sufficient optimality conditions in the primal form. Moreover, under some additional assumptions we obtain dual second-order necessary optimality conditions in terms of Lagrange–Fritz–John and in terms of Lagrange–Karush–Kuhn–Tucker multipliers. [ABSTRACT FROM AUTHOR]

Some programmers have difficulty when they are debugging or developing a new feature. Program comprehension is an activity to understand the behavior of a specific code. A prior understanding of a code could help the performance of a programmer. The feature location is the activity to identify which part of the source code correlated with a specific feature. The feature location mostly uses information retrieval and text processing. The usage of known structure was limited to the model on a specific domain. The proposed method combines textual-based information retrieval and class structure extraction (TESA) of elements of codes to help increase the precision and recall of feature location. The textual processing includes natural language processing and indexing using Vector Space Model (VSM)-Lucene to determine what the best token as the query. The structural extraction process was done by extracting the class member from the class relationship to determine where the correct class to expand the direction. The class relationship is used as the base of searching feature location expansion. The dataset was based on Java and using Model View Controller (MVC) design. The proposed method achieved 91% of precision and 95% of recall. [ABSTRACT FROM AUTHOR]

Essays are one of the most used exams to assess students. Universitas Terbuka Indonesia (Open University) conducts three online essay exams within a week for each first-year course, accounting for 30% of the mid-test score. The university has over 500.000 students and hundreds of courses. However, the limited number of correctors resulted in a time-consuming and ineffective process of checking and scoring each student's essay response. Even score results can be subjective, unfair, lack detailed feedback from students, miss contextual and creative aspects, and be less reliable with complex or non-standard writing. This research proposes a hybrid approach of deep learning models and natural semantic grammar to improve and optimize an AES system, with the following steps: First, the datasets are collected from hundreds of students' answers, each representing a single question. The datasets are pre-processed and augmented to enhance the quantity and variety of the original data and scores. Second, the BERT approach was utilized to transform each text dataset into vector feature spaces using pre-trained model weights. Finally, a prediction score model was generated using the BiLSTM method. The experiment's results show that the model had an average Cohen's Kappa score of 0.749 and the highest Cohen's Kappa score of 0.91. This BERT-BiLSTM optimization model also has a better Cohen's Kappa Score average (0.820) than the ATT-CNN-LSTM, BERT-XLNET, R2BERT, and CNNBiLSTM models. After conducting a test on 46 lecturers, the results showed that the average time taken to examine one course for each student decreased to 1 minute and 2 seconds. Additionally, 92.75% of the lecturers found the process of checking responses to be fairer and more objective. In the results of the trial with 200 students, the mean percentage of question indications related to UI/UX, fairness, responsiveness, rubric, feedback, and transparency across students was 93.72%. [ABSTRACT FROM AUTHOR]

Feature fusion for multimodal sentiment analysis is a challenging but worthwhile research topic. With the extension of the time dimension, there are interactions between multimodal signals and the lack of control over the target modal representations during the fusion process leads to erroneous shifts of vectors in the feature space. Moreover, ignoring the representation of target modal features under different fusion orders may lead to insufficient fusion of complementary information. To address the above issues, this paper proposes a transformer-encoder-based multimodal multi-attention fusion network model. The model constructs a multi-attention fusion transformer-encoder to learn inter-modal consistent features and enhance the representation of target modal features. Meanwhile, for each target modality, we construct multi-attention fusion transformer-encoder with different fusion orders in the model to capture the complementary features among the sequences with different fusion orders. Then, the three target modal representations containing consistent features and complementary features are fused with initial features through residual connections to guide the final sentiment analysis. We conduct extensive experiments on three public multimodal datasets. The results show that our approach outperforms the compared multimodal sentiment analysis methods on most metrics and can explain the contributions of inter- and intra-modal interactions in multiple modalities. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the existence of solutions of set-valued quasiequilibrium problems in real Banach spaces. We introduce a concept of Brezis pseudomonotonicity for set-valued mappings. By constructing appropriate constraint conditions for the weak coercive function and the objective mapping, we obtain a solution-existence result for usual set-valued equilibrium problems. By a sequence of penalized set-valued equilibrium problems, we obtain a solution-existence result for set-valued quasi-equilibrium problems. These results do not require the assumption of compactness of the constraint set, and improve the corresponding ones in the literature. [ABSTRACT FROM AUTHOR]

A new concept known as the orthogonal component graph associated with a finite-dimensional vector space over a finite field has been recently added as another class of algebraic graphs. In these types of graphs, the vertices will be all the possible non-zero linear combinations of orthogonal basis vectors, and any two vertices will be adjacent if the corresponding vectors are orthogonal. In this paper, we discuss the various colorings and structural properties of orthogonal component graphs. [ABSTRACT FROM AUTHOR]

The identification of cancer driver genes is crucial for early detection, effective therapy, and precision medicine of cancer. Cancer is caused by the dysregulation of several genes at various levels of regulation. However, current techniques only capture a limited amount of regulatory information, which may hinder their efficacy. In this study, we present IMI-driver, a model that integrates multi-omics data into eight biological networks and applies Multi-view Collaborative Network Embedding to embed the gene regulation information from the biological networks into a low-dimensional vector space to identify cancer drivers. We apply IMI-driver to 29 cancer types from The Cancer Genome Atlas (TCGA) and compare its performance with nine other methods on nine benchmark datasets. IMI-driver outperforms the other methods, demonstrating that multi-level network integration enhances prediction accuracy. We also perform a pan-cancer analysis using the genes identified by IMI-driver, which confirms almost all our selected candidate genes as known or potential drivers. Case studies of the new positive genes suggest their roles in cancer development and progression. Author summary: Cancer driver identification is of great value in cancer research. Recent advancements have demonstrated that incorporating the intricate regulatory relationships among genes can facilitate driver genes identification. However, current methods do not fully capture the regulatory relationships at different layers. In this study, we propose a new method for predicting cancer driver genes (IMI-driver), which integrates multi-omics data into eight biological networks (including common networks such as protein-protein interaction networks and various cancer-specific networks) and embeds multi-level network information as features to predict driver gene sets. Experiment demonstrates that our method outperforms mainstream tools, and can discover new drivers. [ABSTRACT FROM AUTHOR]

The three-level (3-L) neutral-point-clamped (NPC) converter has found widespread applications in various fields, due to its simple structure, low failure rate and high efficiency. However, the 3-L NPC converter suffers the issue of unbalanced neutral-point (NP) voltage due to the divided two dc-side capacitors. The large NP voltage ripple and offset Based on the detailed analysis of the effects of vectors and clamping patterns on the NP voltage, a discontinuous optimized modulation method for NPC grid-connected inverter with both low switching loss and ability to balance NP voltage is presented. By measuring NP voltage and utilizing the property that superfluous clamping patterns have opposing effects on the NP voltage, the modulation method adjusts the NP voltage with the injection of various zero sequence voltages (ZSV) into the original sinusoidal waves. The results of this study demonstrate that the CB-DPWM can control the NP voltage balanced and decrease switching loss compared to conventional DPWM and SVPWM strategies. Moreover, the CB-DPWM strategy does not need to identify sectors and subsectors or calculate dwelling times. This modulation strategy effectively suppresses low-frequency fluctuations and deviations of the NP voltage with the injection of a simple ZSV, and improves the power quality of the output voltages and currents. Compared to the traditional SVPWM scheme, the suggested CB-DPWM has a 27 % lower overall IGBT loss. Moreover, this method is implemented through carrier waves, which is simpler than modulation schemes based on space vector, greatly shortens the program running time, and is conducive to engineering implementation. [ABSTRACT FROM AUTHOR]

We introduce the variety B sup of bicommutative superalgebras over an arbitrary field of characteristic different from 2. The variety consists of all nonassociative Z 2 -graded algebras satisfying the polynomial super-identities of super- left- and right-commutativity x (y z) = (− 1) x ‾ y ‾ y (x z) and (x y) z = (− 1) y ‾ z ‾ (x z) y , where u ‾ ∈ { 0 , 1 } is the parity of the homogeneous element u. We present an explicit construction of the free bicommutative superalgebras, find their bases as vector spaces and show that they share many properties typical for ordinary bicommutative algebras and super-commutative associative superalgebras. In particular, in the case of free algebras of finite rank we compute the Hilbert series and find explicitly its coefficients. As a consequence we give a formula for the codimension sequence. We establish an analogue of the classical Hilbert Basissatz for two-sided ideals. We see that the Gröbner-Shirshov bases of these ideals are finite, the Gelfand-Kirillov dimensions of finitely generated bicommutative superalgebras are nonnegative integers and the Hilbert series of finitely generated graded bicommutative superalgebras are rational functions. Concerning problems studied in the theory of varieties of algebraic systems, we prove that the variety of bicommutative superalgebras satisfies the Specht property. In the case of characteristic 0 we compute the sequence of cocharacters. [ABSTRACT FROM AUTHOR]

We study the determination of a holomorphic function from its absolute value. Given a parameter θ∈R$\theta \in \mathbb {R}$, we derive the following characterization of uniqueness in terms of rigidity of a set Λ⊆R$\Lambda \subseteq \mathbb {R}$: if F$\mathcal {F}$ is a vector space of entire functions containing all exponentials eξz,ξ∈C∖{0}$e^{\xi z}, \, \xi \in \mathbb {C} \setminus \lbrace 0 \rbrace$, then every F∈F$F \in \mathcal {F}$ is uniquely determined up to a unimodular phase factor by {|F(z)|:z∈eiθ(R+iΛ)}$\lbrace |F(z)|: z \in e^{i\theta }({\mathbb {R}}+ i \Lambda) \rbrace$ if and only if Λ$\Lambda$ is not contained in an arithmetic progression aZ+b$a\mathbb {Z}+b$. Leveraging this insight, we establish a series of consequences for Gabor phase retrieval and Pauli‐type uniqueness problems. For instance, Z×Z∼${\mathbb {Z}}\times \tilde{{\mathbb {Z}}}$ is a uniqueness set for the Gabor phase retrieval problem in L2(R+)$L^2({\mathbb {R}}_+)$, provided that Z∼$\tilde{{\mathbb {Z}}}$ is a suitable perturbation of the integers. [ABSTRACT FROM AUTHOR]

Power losses in semiconductor devices present a significant impediment to advancing power electronics systems for achieving higher frequencies, improved efficiency, and greater integration. A major challenge lies in directly coupling power losses with various control strategies, considering the variations in manufacturers, packaging, and process structures within the power electronics field. This paper introduces a field‐circuit coupling simulation methodology of the insulated gate bipolar transistor (IGBT) within the Simulink/COMSOL environment, using a conventional three‐phase six‐switch voltage source inverter (VSI) IGBT module as a case study. A composite transfer function interconnects the electrical and thermal aspects, enabling bidirectional coupling between IGBT temperature and losses. This study aims to comprehensively compare the effects of various control strategies, namely, single‐vector, dual‐vector, and three‐vector current model predictive control (CMPC) and space vector pulse width modulation (SVPWM), on the losses and temperature of IGBT power modules. The findings emphasize that losses are significantly influenced by the selection of weighting factor coefficients and power factor settings under the same CMPC control strategy with a fixed switching frequency. Additionally, the selection of control strategies, such as CMPC and SVPWM, substantially impacts power losses in power electronic devices. [ABSTRACT FROM AUTHOR]

Marcinkiewicz spaces with variable exponents are defined and some basic properties are given. [ABSTRACT FROM AUTHOR]

The non-zero component graph of a finite dimensional vector space V over a finite field F is the graph G(Va) = (V, E), where vertices of G(Va) are the non-zero vectors in V, two of which are adjacent if they share at least one basis vector with non-zero coefficient in their basic representation. In this paper, we study the various types of colorings of non-zero component graph. [ABSTRACT FROM AUTHOR]

We introduce a polynomial extremal function Φ (E , F , z) which is one of possible generalizations of the classical Siciak extremal function, restricted to subspaces F of the linear space of all polynomials of N variables that are invariant under differentiation. We show that the so-called HCP condition in this situation: log Φ (E , F , z) ≤ A dist (z , E) s , z ∈ C N is equivalent to a generalization of the classical V. Markov's inequality: | | D α P | | E ≤ A 1 | α | (deg P) m | α | (| α | !) m - 1 | | P | | E , P ∈ F with dependence m = 1 / s . The situation is similar to the basic case (cf. [8]) F = K [ z 1 , ⋯ , z N ] , where a V. Markov's type inequality was introduced and the above-mentioned equivalence was proved. As a byproduct, we prove new results related to V. Markov's inequality for an important class of subsets of R N , which are then applied to obtain the first versions of this inequality for some thin sets, such as spheres in R N + 1 and Euclidean spheres in particular. Furthermore, we prove an interesting fact on the polynomial convex hull of the circle S 1 , as a subset of R 2 . [ABSTRACT FROM AUTHOR]

Sequences formed by symbols are found in diverse fields, including genome sequences, written texts and computer codes. An interesting question is whether a sequence of symbols contains correlated structures. Existing methods to characterize correlations require a numerical representation of the sequence. In this regard, mapping a sequence of text into a sequence of numerical values is a key step for assessing correlation analysis. This work proposes a methodology to study correlations in a sequence of symbols. In the first step, the sequence of symbols is mapped in a multivariate numerical sequence formed by unit vectors in a vectorial space. The main feature of such mapping is that symbols are equally weighted, thus avoiding the numerical overrepresentation of symbols. In the second step, a multivariate version of the detrended fluctuation analysis is used to quantify correlations in the numerical sequence. Genome sequences (first COVID-19), written English texts and comovements between Bitcoin and gold markets were used to illustrate the proposed methodology's performance. The results showed that the balanced numerical mapping of symbolic sequences and the multivariate DFA provides valuable insights into the correlations in a sequence of symbols. [ABSTRACT FROM AUTHOR]

In these notes we generalize the notion of a (pseudo) metric measuring the distance of two points, to a (pseudo) n-metric which assigns a value to a tuple of n ≥ 2 points. Some elementary properties of pseudo n-metrics are provided and their construction via exterior products is investigated. We discuss some examples from the geometry of Euclidean vector spaces leading to pseudo n-metrics on the unit sphere, on the Stiefel manifold, and on the Grassmann manifold. Further, we construct a pseudo n-metric on hypergraphs and discuss the problem of generalizing the Hausdorff metric for closed sets to a pseudo n-metric. [ABSTRACT FROM AUTHOR]

The concept of summability is crucial in deriving formal solutions to partial differential equations. This paper explores the connection between the methods of statistical convergence of sequences and statistical Cesàro summability in intuitionistic fuzzy n-normed linear space (IFnNLS). While the existing literature covers Cesàro summability and its statistical variant in fuzzy, intuitionistic fuzzy, and classical normed spaces, this study stands out not only for its methodology but also for its comprehensive approach, encompassing a broader range of spaces and detailing the pathway from the statistical Cesàro summability method to statistical convergence. These results will lead us to Tauberian theorems in IFnNLS. [ABSTRACT FROM AUTHOR]

In this paper, three discrete transforms related to vector spaces over finite fields are studied. For our purposes, and according to the properties of the finite fields, the most suitable transforms are as follows: for binary fields, this is the Walsh–Hadamard transform; for odd prime fields, the Vilenkin–Chrestenson transform; and for composite fields, the trace transform. A factorization of the transform matrices using Kronecker power is given so that the considered discrete transforms are reduced to the fast discrete transforms. Examples and applications are also presented of the considered transforms in coding theory for calculating the weight distribution of a linear code. [ABSTRACT FROM AUTHOR]

For a curve in positive characteristic, the Cartier operator acts on the vector space of its regular differentials. The a-number is defined to be the dimension of the kernel of the Cartier operator. In [a-numbers of curves in Artin–Schreier covers, Algebra Number Theory 14(3) (2020) 587–641], Booher and Cais use a sheaf-theoretic approach to give bounds on the a-numbers of Artin–Schreier covers. In this paper, I generalize that approach to arbitrary powers of the Cartier operator, yielding bounds for the dimension of the kernel. These bounds give new restrictions on the Ekedahl-Oort type of Artin–Schreier covers. [ABSTRACT FROM AUTHOR]

Similarity metrics are critical to identifying the relationships between patents. While many bibliometric methods such as co-citation and co-classification fail to use the vast majority of technical information existing in the text, most text mining methods focus on keywords in only one text field of the patent document. This article aims to leverage various text fields to measure pairwise patent similarity according to their technological bases. A novel approach called semantic embedding with attention for patent similarity (SEA-PS) is proposed. First, the method identifies technological bases and models the semantic relatedness. To achieve this, we put forward an additional patent stop-word list to help extract technical terms with an n -gram-based statistical method. The technical terms are then mapped into a vector space using word embedding. Second, we propose a graph-based method to allocate weights to distinguish the technical focus, considering the linkages between technologies. Finally, we assess the feasibility of the text fields, and integrate their semantics at the patent-level with an attention layer to conduct similarity metrics. The validations are from two perspectives: content validity (coverage of technical information, the validity of semantic representations and effectiveness of text field combinations), and external validity against existing methods via an expert panel. The results demonstrate the superiority of SEA-PS to existing methods, and suggest that 'abstracts', 'claims' and 'technical descriptions' are more effective than 'titles'. SEA-PS is a fundamental tool for patent retrieval and classification. It also has a broad range of practical applications in innovation and strategy studies, including identifying technological frontiers and studying knowledge spillovers. [ABSTRACT FROM AUTHOR]

Knowledge embedding for geographic knowledge graphs can effectively improve computational efficiency and provide support for knowledge reasoning, knowledge answering and other applications of knowledge graphs. To maintain a more comprehensive understanding of spatial features through knowledge embedding, it is crucial to integrate the representation and computation of various entity types, encompassing points, lines, and polygons. This article proposes a geographic entities uniformly explicit knowledge embedding model (GEUKE). In GEUKE, spatial data of point, line, and polygon‐type geographic entities are expressed in the form of subgraphs, and space embedding is generated using a SubGNN‐based uniform spatial feature encoder. GEUKE improves the energy function in TransE to train spatial feature‐based embedding and structural‐based embedding of geographic entities into a unified vector space. Experimental results show that GEUKE has higher performance than TransE, TransH, TransD, and TransE‐GDR on link prediction and triple classification task. Within the spatial feature embedding process, GEUKE effectively preserves the inherent features of entities, encompassing location, neighborhood, and structural attributes, while simultaneously ensuring a coherent spatial data representation across all three entity types: points, lines, and polygons. By maintaining the spatial features of geographic entities and their interrelations, this capability unleashes the full potential of applications such as knowledge reasoning and geospatial question answering in a manner that is conducive to diverse geospatial scenarios. [ABSTRACT FROM AUTHOR]

Let F be a non-archimedean local field of characteristic zero and (π , V) a depth zero, irreducible, supercuspidal representation of GSp (4 , F). We calculate the dimensions of the spaces of Klingen-invariant vectors in V of level p n for all n ≥ 0. [ABSTRACT FROM AUTHOR]

We introduce a new class of division algebras, the hyperpolyadic algebras, which correspond to the binary division algebras R , C , H , O without considering new elements. First, we use the matrix polyadization procedure proposed earlier which increases the dimension of the algebra. The algebras obtained in this way obey binary addition and a nonderived n-ary multiplication and their subalgebras are division n-ary algebras. For each invertible element, we define a new norm which is polyadically multiplicative, and the corresponding map is a n-ary homomorphism. We define a polyadic analog of the Cayley–Dickson construction which corresponds to the consequent embedding of monomial matrices from the polyadization procedure. We then obtain another series of n-ary algebras corresponding to the binary division algebras which have a higher dimension, which is proportional to the intermediate arities, and which are not isomorphic to those obtained by the previous constructions. Second, a new polyadic product of vectors in any vector space is defined, which is consistent with the polyadization procedure using vectorization. Endowed with this introduced product, the vector space becomes a polyadic algebra which is a division algebra under some invertibility conditions, and its structure constants are computed. Third, we propose a new iterative process (we call it the "imaginary tower"), which leads to nonunital nonderived ternary division algebras of half the dimension, which we call "half-quaternions" and "half-octonions". The latter are not the subalgebras of the binary division algebras, but subsets only, since they have different arity. Nevertheless, they are actually ternary division algebras, because they allow division, and their nonzero elements are invertible. From the multiplicativity of the introduced "half-quaternion" norm, we obtain the ternary analog of the sum of two squares identity. We show that the ternary division algebra of imaginary "half-octonions" is unitless and totally associative. [ABSTRACT FROM AUTHOR]

Summary: Traditional electric drive control methodologies, such as field oriented control (FOC) and direct torque and flux control (DTFC), predominantly rely on multiple proportional‐integral (PI) controllers that demand complex tuning. While model predictive current control (MPCC) omits PI controllers, it has inherent challenges including high computational burden and tempered dynamics. Although two‐level inverters (2LI) are prevalent in many applications, their performance wanes in high‐power applications like high performance industrial drives and marine propulsions. Multilevel inverters (MLIs) are more efficient, but combined with space vector modulation (SVM), they add computational complexity, particularly at higher levels, limiting drive sampling frequencies and causing torque ripples and harmonics, affecting performance. To address the above drawbacks, this manuscript presents a deadbeat predictive current control of five‐level inverter fed permanent magnet synchronous motor (PMSM) drive with a novel generalized SVM algorithm with reduced computational burden and improved performance. The proposed method is validated through MATLAB/Simulink‐based simulation study and experimental implementation. The results are presented and discussed. The results are compared with DTFC and MPCC where it is observed that the proposed method offers superior performance with reduced computational burden and streamlined implementation. [ABSTRACT FROM AUTHOR]

Given a semifinite von Neumann algebra \mathcal M equipped with a faithful normal semifinite trace \tau, we prove that the spaces L^0(\mathcal M,\tau) and \mathcal R_\tau are complete with respect to pointwise—almost uniform and bilaterally almost uniform—convergences in L^0(\mathcal M,\tau). Then we show that the pointwise Cauchy property for a special class of nets of linear operators in the space L^1(\mathcal M,\tau) can be extended to pointwise convergence of such nets in any fully symmetric space E\subset \mathcal R_\tau, in particular, in any space L^p(\mathcal M,\tau), 1\leq p<\infty. Some applications of these results in the noncommutative ergodic theory are discussed. [ABSTRACT FROM AUTHOR]

Dual-output three-level converters are widely used in multiphase motor drives, and their common-mode voltage (CMV) and neutral point (NP) balance problems can affect the safe and stable operation of systems. Owing to their unique structure, certain disabled switching states exist. Suppressing the CMV to comply with operational constraints is worthy of further investigation. In this paper, an improved time-sharing virtual space vector (ITVSV) modulation strategy is proposed. In addition, the working principle of the converter is analyzed and divided into two effective working modes. The proposed strategy defines two kinds of virtual vector synthesis methods, using virtual vectors instead of the basic small vector of large CMV to reduce the degrees of freedom of voltage fluctuation. The switching loss can be reduced by adjusting the switching sequence in some areas. Furthermore, it is demonstrated that the NP voltage is self-balancing within one primitive period. Finally, the effectiveness of the ITVSV for suppressing CMV and NP voltage balance is verified by experimental results. [ABSTRACT FROM AUTHOR]

Let r and s be positive integers such that r ⩾ 3. Let U 1 , ... , U r be vector spaces over a field F and V 1 , ... , V s be vector spaces over a field K such that dim ⁡ U i , dim ⁡ V j ⩾ 2 for all i , j. In this paper, we characterize maps ψ : ⨂ i = 1 r U i → ⨂ i = 1 s V i that preserve adjacency in both directions, which extends Hua's fundamental theorem of geometry of rectangular matrices. We also characterize related results concerning locally full maps preserving adjacency in both directions between tensor spaces, maps preserving adjacency in both directions between tensor spaces over a field all whose nonzero endomorphisms are automorphisms, and injective continuous adjacency preserving maps on finite dimensional tensor spaces over the real field. [ABSTRACT FROM AUTHOR]

We study a matrix analog of the Erdős-Falconer distance problems in vector spaces over finite fields. We provide lower bounds for the cardinality of a subset of the matrix algebra over a finite field such that its distance set is the whole matrix algebra. There arises an interesting analysis of certain quadratic matrix Gauss sums. [ABSTRACT FROM AUTHOR]