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We propose a new symmetric variational functional-algebraic statement of the eigenvalue problem in a Hilbert space with a linear dependence on the spectral parameter for a class of mathematical models of thin-walled structures with an attached oscillator. The existence of eigenvalues and eigenvectors is established. A new symmetric approximation of the problem in a finite-dimensional subspace with a linear dependence on the spectral parameter is constructed. Error estimates are obtained for the approximate eigenvalues and eigenvectors. The theoretical results are illustrated with an example of a structural mechanics problem. [ABSTRACT FROM AUTHOR]

Wind power systems, which are currently being constructed for the electricity worldwide market, are mostly based on Doubly Fed Induction Generators (DFIGs). To control such systems, multilevel converters are increasingly preferred due to the well-known benefits they provide. This paper deals with the control of a standalone DFIG-based Wind Energy Conversion System (WECS) by using a three-level Neutral-Point-Clamped (NPC) converter. The frequency and magnitude of the stator output voltage of the DFIG are controlled and fixed at nominal values despite the variable rotor speed, ensuring a continuous AC supply for three-phase loads. This task is achieved by controlling the DFIG rotor currents via a PI controller combined with a new Simplified Direct Space Vector Modulation strategy (SDSVM), which is applied to the three-level NPC converter. This strategy is based on the use of a line-to-line three-level converter space vector diagram without using Park transformation and then simplifying it to that of a two-level converter. The performance of the proposed SDSVM technique in terms of controlling the three-level NPC-converter-based standalone WECS is demonstrated through simulation results. The whole WECS control and the SDSVM strategy are implemented on a dSPACE DS 1104 board that drives a DFIG-based wind system test bench. The obtained experimental results confirm the validity and performance in terms of control. [ABSTRACT FROM AUTHOR]

Assume that we are given a filtration (Fn)$(\mathcal F_n)$ on a probability space (Ω,F,P)$(\Omega,\mathcal F,\mathbb {P})$ of the form that each Fn$\mathcal F_n$ is generated by the partition of one atom of Fn−1$\mathcal F_{n-1}$ into two atoms of Fn$\mathcal F_n$ having positive measure. Additionally, assume that we are given a finite‐dimensional linear space S$S$ of F$\mathcal F$‐measurable, bounded functions on Ω$\Omega$ so that on each atom A$A$ of any σ$\sigma$‐algebra Fn$\mathcal F_n$, all Lp$L^p$‐norms of functions in S$S$ are comparable independently of n$n$ or A$A$. Denote by Sn$S_n$ the space of functions that are given locally, on atoms of Fn$\mathcal F_n$, by functions in S$S$ and by Pn$P_n$ the orthoprojector (with respect to the inner product in L2(Ω)$L^2(\Omega)$) onto Sn$S_n$. Since S=span{1Ω}$S = \operatorname{span}\lbrace \mathbbm 1_\Omega \rbrace$ satisfies the above assumption and Pn$P_n$ is then the conditional expectation En$\mathbb {E}_n$ with respect to Fn$\mathcal F_n$, for such filtrations, martingales (Enf)$(\mathbb {E}_n f)$ are special cases of our setting. We show in this article that certain convergence results that are known for martingales (or rather martingale differences) are also true in the general framework described above. More precisely, we show that the differences (Pn−Pn−1)f$(P_n - P_{n-1})f$ form an unconditionally convergent series and are democratic in Lp$L^p$ for 1

The transformation formula under the action of a general linear fractional transformation for a generalized Dedekind eta function has been the subject of intensive study since the works of Rademacher, Dieter, Meyer, and Schoenberg et al. However, the (Hecke) modular relation structure was not recognized until the work of Goldstein-de la Torre, where the modular relations mean equivalent assertions to the functional equation for the relevant zeta functions. The Hecke modular relation is a special case of this, with a single gamma factor and the corresponding modular form (or in the form of Lambert series). This has been the strongest motivation for research in the theory of modular forms since Hecke's work in the 1930s. Our main aim is to restore the fundamental work of Rademacher (1932) by locating the functional equation hidden in the argument and to reveal the Hecke correspondence in all subsequent works (which depend on the method of Rademacher) as well as in the work of Rademacher. By our elucidation many of the subsequent works will be made clear and put in their proper positions. [ABSTRACT FROM AUTHOR]

We obtain an asymptotic upper bound for the product of the p -parts of the orders of certain composition factors of a finite group acting completely reducibly and faithfully on a finite vector space of order divisible by a prime p. This enables us to give a new bound for the diameter of a nondiagonal orbital graph of an affine primitive permutation group. [ABSTRACT FROM AUTHOR]

This paper presents a novel multiphase hybrid matrix converter topology dedicated to grid-connected five-phase wind generation. The proposed converter, named Five-phase Ultra-Sparse Series Z-source Matrix Converter (FUSSZMC), aims to facilitate the integration of the five-phase wind turbine generators. This is done by taking into account the improvement of the injected power quality and allowing the fixed output converter voltage level to that of the grid, thanks to the use of the series Z-source, under the variable voltage magnitude of the wind turbine generator, which depends on the wind speed. The proposed space vector modulation as a control strategy for FUSSZMC was detailed, where it was demonstrated that a suitable use of both large and small current vectors improves the input current waveforms. The global model of the proposed system was tested by simulation under Matlab/Simpowersys environment. The obtained results demonstrate clearly the advantages of using FUSSZMC and its modulation strategie. These benefits includea good input and output current waveforms, as reflected by the obtained total harmonic distortion (THD) values, that fall within the range prescribed by international standards. Additionally, FUSSZMC is capable of operating with unity input power factor, regulating input voltages and improving the quality of injected power into the grid. [ABSTRACT FROM AUTHOR]

We prove that the linear syzygy spaces of a general canonical curve are spanned by syzygies of minimal rank. [ABSTRACT FROM AUTHOR]

Similarity of point patterns is critical to geographic information retrieval. Many methods depend on measuring the similarity between point patterns within the spatial database. However, previous researches mainly focus on point density which is only one aspect of point patterns. A point distribution can be complex by its numerous alignments of point groups, which usually imply different geographical meanings in reality. In this paper, we propose a new method that uses image analysis techniques to comprehensively consider the characteristics of a point pattern. Specifically, given a set of point datasets falling in the same region, our method first generates the point intensity surfaces to transform the original vector space to raster space; then, the method constructs a matrix to describe all the pattern-related information. Finally, the point pattern similarity is calculated by decomposing this matrix into the lower-order representation and the factorized basis features. Due to the use of matrix decomposition, the proposed method has the merits that it can eliminate noises from the original data and assess the similarity of two patterns with emphasis on their major features. As a case study, our method is effective in discovering regularity from the taxi pick-up/drop-off point datasets. [ABSTRACT FROM AUTHOR]

The article reveals concept of lpN(X), 1 ≤ p < ∞, the p – absolutely summable neutrosophic valued sequence space. We have proved that it is a neutrosophic normed linear space valued sequence space. We have studied its different algebraic and topological properties. We have also established some inclusion results. The main aim is to introduce the notion of neutrosophic normed linear space lpN(X), 1 ≤ p < ∞, and to show that it is a complete neutrosophic sequence space. [ABSTRACT FROM AUTHOR]

A new approach to finite elasto-plasticity of crystalline materials, with a differential geometry point of view toward the material description, is proposed. In order to define the plastic and elastic distortions, traditionally it is accepted the existence of an intermediate configuration, which is endowed with a differential manifold structure. A more restrictive but physically and mathematically well-motivated structure is assigned to the intermediate configuration, namely, a vector bundle structure. Two approaches to multiplicative decomposition of the deformation gradient can be rebuilt if on the same total space (intermediate configuration) the vector bundle structures are considered, but either the reference configuration, B (i.e., plastic assumption) or the deformed configuration, B t (i.e., elastic assumption) stands for the base space. As the base spaces are homeomorphic, a pullback vector bundle over one base space is provided by the other one through the motion diffeomorphism. Thus, the total space is endowed with different differential manifold structures. The plastic distortion and the inverse elastic distortion, respectively, are defined for any material points as linear, invertible, and non-integrable maps from the tangent vector space at their material points, with the value on the attached vector fiber. The multiplicative decompositions into their non-integrable components are derived, based on the associate inverse elastic distortion and plastic distortion, respectively. When the plastic and elastic assumptions are simultaneously accepted, then a three-term multiplicative decomposition of the deformation gradient is achieved. The transition functions, which characterize the compatibility of the overlapping charts which belong to these different structures, namely of the vector bundle and of the pullback vector bundle over the same configuration, say B define the non-uniqueness of the two-term multiplicative decomposition. The material symmetry transformation is defined for elastic-type materials. The compatibility of the models and examples of the bundle vector structures are also discussed. [ABSTRACT FROM AUTHOR]

In this research paper, we investigate the controllability in the α -norm of a coupled system of integrodifferential equations with state-dependent nonlocal conditions in generalized Banach spaces. We establish sufficient conditions for the system's controllability using resolvent operator theory introduced by Grimmer, fractional power operators, and fixed-point theorems associated with generalized measures of noncompactness for condensing operators in vector Banach spaces. Finally, we present an application example to validate the proposed methodology in this research. [ABSTRACT FROM AUTHOR]

The units of a number field k act naturally on the real vector space k ⊗ Q R , and so on open subsets of (k ⊗ Q R) ⁎ that are stable under the units. A Shintani domain for this action consists of a finite number of polyhedral cones, all having generators in k , whose union is a fundamental domain. Aside from the trivial case of imaginary quadratic fields, no practical method for computing Shintani domains for totally complex number fields has been published. Here we give a quick way to compute Shintani domains for totally complex quartic number fields. To construct these domains we exploit the existence of a forward attractor and backward repeller set for this action. We prove that the number of polyhedral cones needed for the Shintani domain is bounded by an absolute constant, a fact previously known only for cubic or quadratic fields. We also show that our algorithm for finding a Shintani domain runs in polynomial time and we give a table describing the results of running the algorithm on more than 168,000 fields. [ABSTRACT FROM AUTHOR]

As a social institution, a border simultaneously divides and connects. When thinking about state borders, or borderlands, scholars tend to view them as either linear or zonal spaces, distinguishing as well as linking one state with another. My article argues for an alternative interpretation and explores the geopolitical and cultural meanings of a historical border region from both domestic and inter-state perspectives. The border of China and Korea along the Yalu and the Tumen Rivers, is arguably one of the oldest state boundaries that is still effective today. The history of the border river region as a "buffer space" can be traced back to the seventeenth century when Qing China and Chosŏn Korea established the border along their northern frontiers. However, the geopolitical function of this border went beyond considerations of defence or communications. From the mid-seventeenth century to the mid-nineteenth century, both the Manchu-Qing court and the Chosŏn court implemented strict laws to control domestic population flows to their northeastern and northern frontiers. Such policies, I argue, must be understood in the context of domestic politics in the two courts. Internal anxiety over preserving Manchu and Korean identity, coupled with strategy to control the border against an external power, contributed to the making of this borderland. Hence, the Qing-Chosŏn border region served as a "dual buffer". Employing historical records and local gazettes in the two countries, my article reveals a subtler layer of "buffer" from a case study in early modern East Asia. [ABSTRACT FROM AUTHOR]

In this article, a particular approach to deriving recursive state estimators for linear state space models is generalised, namely the weighted least-squares approach introduced by Duncan and Horn in 1972, for the case of the two noise processes arising in such models being cross-correlated; in this context, the fact that in the available literature two different non-equivalent recursive algorithms are presented for the task of state estimation in the aforementioned case is discussed. Although the origin of the difference between these two algorithms can easily be identified, the issue has only rarely been discussed so far. Then the situations in which each of the two algorithms apply are explored, and a generalised Kalman filter which represents a merger of the two original algorithms is proposed. While, strictly speaking, optimal state estimates can be obtained only through the non-recursive weighted least-squares approach, in examples of modelling simulated and real-world data, the recursive generalised Kalman filter shows almost as good performance as the optimal non-recursive filter. [ABSTRACT FROM AUTHOR]

This note addresses the problem of recovering a convex set of homogeneous polynomials from the subset of its extreme points, i.e., the justification of a polynomial version of the classical Krein–Milman theorem. Not much was done in this direction. The existing papers deal mostly with the description of the extreme points of the unit ball in the space of homogeneous polynomials in various special cases. Even in the case of linear operators, the classical Krein–Milman theorem does not work, since closed convex sets of operators turn out to be compact in some natural topology only in rather special cases. In the 1980s, a new approach to the study of the extremal structure of convex sets of linear operators was proposed on the basis of the theory of Kantorovich spaces, which led to an operator form of the Krein–Milman theorem. Combining the approach with the linearization method for homogeneous polynomials, we obtain a version of the Krein–Milman theorem for homogeneous polynomials. Namely, a weakly order bounded, operator convex, and pointwise order closed set of homogeneous polynomials from an arbitrary vector space to a Kantorovich space is the pointwise order closure of the operator convex hull of the extreme points of . We also establish Milman's converse of the Krein–Milman theorem for homogeneous polynomials: The extreme points of the smallest operator convex pointwise order closed set including a given set of homogeneous polynomials are pointwise uniform limits of appropriate nets of mixings in . A mixing of a family of polynomials with the values in a Kantorovich space is understood as the (infinite) sum of these polynomials multiplied by pairwise disjoint order projections with sum the identity operator in the Kantorovich space. [ABSTRACT FROM AUTHOR]

This paper works with functions defined in metric spaces and takes values in complete paranormed vector spaces or in Banach spaces, and proves some necessary and sufficient conditions for weak convergence of probability measures. Our main result is as follows: Let X be a complete paranormed vector space and Ω an arbitrary metric space, then a sequence { μ n } of probability measures is weakly convergent to a probability measure μ if and only if lim n → ∞ ∫ Ω g (s) d μ n = ∫ Ω g (s) d μ for every bounded continuous function g: Ω → X. A special case is as the following: if X is a Banach space, Ω an arbitrary metric space, then { μ n } is weakly convergent to μ if and only if lim n → ∞ ∫ Ω g (s) d μ n = ∫ Ω g (s) d μ for every bounded continuous function g: Ω → X. Our theorems and corollaries in the article modified or generalized some recent results regarding the convergence of sequences of measures. [ABSTRACT FROM AUTHOR]

We study the theory of K-vector spaces with a predicate for the union X of an infinite family of independent subspaces. We show that if K is infinite then the theory is complete and admits quantifier elimination in the language of K-vector spaces with predicates for the n-fold sums of X with itself. If K is finite this is no longer true, but we still have that a natural completion is near-model-complete. [ABSTRACT FROM AUTHOR]

We consider the predecessor problem on the ultra-wide word RAM model of computation, which extends the word RAM model with ultrawords consisting of w 2 bits (TAMC, 2015). The model supports arithmetic and boolean operations on ultrawords, in addition to scattered memory operations that access or modify w (potentially non-contiguous) memory addresses simultaneously. The ultra-wide word RAM model captures (and idealizes) modern vector processor architectures. Our main result is a simple, linear space data structure that supports predecessor in constant time and updates in amortized, expected constant time. This improves the space of the previous constant time solution that uses space in the order of the size of the universe. Our result holds even in a weaker model where ultrawords consist of w 1 + ϵ bits for any ϵ > 0 . It is based on a new implementation of the classic x-fast trie data structure of Willard (Inform Process Lett 17(2):81–84, https://doi.org/10.1016/0020-0190(83)90075-3, 1983) combined with a new dictionary data structure that supports fast parallel lookups. [ABSTRACT FROM AUTHOR]

In this paper, we are following the plane time-harmonic waves propagation in an entire linear thermoelastic space, knowing the wavelength. Concerning the thermodynamic response, we fit the dual phase-lag model, while the effect of porosity on elasticity is given by Cowin–Nunziato theory. We obtain two shear waves and five longitudinal waves as: quasi-elastic wave, quasi-microrotational wave quasi-micropolar wave, quasi thermal mode, quasi-phase-lag thermal mode. The purpose of numerical simulations and of graphs is to identify the influence of connection between thermoelasticity, microrotation and porosity. [ABSTRACT FROM AUTHOR]

Currently, many inverters employ inductors to boost the AC voltage. However, this leads to increased current distortion and limits the voltage boosting capability of the inverter. To address the above issue, a triple two-level inverter is proposed in this paper. The proposed inverter adopts a switched-capacitor boost circuit to boost the AC output voltage and to generate a multi-level voltage. Simultaneously, a three-phase full-bridge circuit is assigned to convert the DC voltage into AC voltage. In addition, a novel space vector modulation strategy is introduced to achieve capacitor voltage self-balance. Finally, simulation and experimental platforms have been established to verify the effectiveness of proposed inverter. The obtained results show that the proposed inverter meets the requirements for the expected inverter. [ABSTRACT FROM AUTHOR]

For linear non-uniform cellular automata (NUCA) which are global perturbations of CA over an arbitrary universe, we introduce and investigate their dual linear NUCA, which are also endomorphisms over a generally infinite dimensional vector space. Generalizing results for linear CA, we show that dynamical properties namely pre-injectivity, resp. injectivity, resp. stably injectivity, resp. invertibility of a linear NUCA is equivalent to surjectivity, resp. post-surjectivity, resp. stably post-surjectivity, resp. invertibility of the dual linear NUCA. However, while bijectivity is a dual property for linear CA, it is no longer the case for linear NUCA. We prove that for linear NUCA, stable injectivity and stable post-surjectivity are precisely characterized respectively by left invertibility and right invertibility and that a linear NUCA is invertible if and only if it is pre-injective and stably post-surjective. Surprisingly, we show that linear NUCA with finite memory satisfy the shadowing property also known as the pseudo-orbit tracing property. Thus, linear NUCA can be useful for fault-tolerant computation. Applications on the dual surjunctivity are also obtained. [ABSTRACT FROM AUTHOR]

Due to the rapid adoption of Deep Neural Networks (DNNs) into larger software systems, testing of DNN-based systems has received much attention recently. While many different test adequacy criteria have been suggested, we lack effective test input generation techniques. Inputs such as images of real-world objects and scenes are not only expensive to collect but also difficult to randomly sample. Consequently, current testing techniques for DNNs tend to apply small local perturbations to existing inputs to generate new inputs. We propose SINVAD (Search-based Input space Navigation using Variational AutoencoDers), a way to sample from, and navigate over, a space of realistic inputs that resembles the true distribution in the training data. Our input space is constructed using Variational Autoencoders (VAEs), and navigated through their latent vector space. Our analysis shows that the VAE-based input space is well-aligned with human perception of what constitutes realistic inputs. Further, we show that this space can be effectively searched to achieve various testing scenarios, such as boundary testing of two different DNNs or analyzing class labels that are difficult for the given DNN to distinguish. Guidelines on how to design VAE architectures are presented as well. Our results have the potential to open the field to meaningful exploration through the space of highly structured images. [ABSTRACT FROM AUTHOR]

Motivated by the work, in which the author studied the convexity of nonlinear mappings defined between bounded linear operator spaces, our research extends this inquiry. In this work, we continue the study of the convexity of nonlinear mappings defined between bounded linear operator spaces and we establish a characterization in terms of the second order directional derivative. We apply the main result to prove the convexity and the nonconvexity of well-known nonlinear mappings. The case of nondifferentiable mappings is also treated in the last section. [ABSTRACT FROM AUTHOR]

PWM (pulse width modulation) is the most widely applied current conversion technology, but the high-frequency harmonics it causes have a significant negative impact on inverter system performance. This paper focuses on the three-phase T-type three-level inverter as the research object and addresses existing PWM voltage noise and midpoint potential imbalance issues by proposing an improved random SVPWM strategy, named Neutral Point Potential Balance Random Space Vector PWM (NPB–RSVPWM). The NPB–RSVPWM strategy includes three main steps: (1) introducing a midpoint potential balancing control loop to adjust the synthesis timing of the effective vectors to generate pulse signals, optimizing midpoint potential balance; (2) employing a randomly varying carrier frequency in place of the carrier used in the SVPWM strategy to generate the driving signals for switching devices; and (3) controlling the inverter through the driving pulse signals. This strategy optimizes the synthesis sequence of traditional SVPWM strategy vectors and incorporates random frequency modulation techniques. The mathematical model analyzes PWM harmonic expressions corresponding to fixed switching frequencies, and a random frequency carrier is chosen to suppress these PWM harmonics. The effective vector's equivalent circuit is analyzed, proposing a technique for optimized vector synthesis timing. The simulation and experimental results verify that the NPB–RSVPWM technique can disperse PWM harmonic energy, reduce voltage noise, and optimize midpoint potential balance. Under the NPB–RSVPWM strategy, the line voltage spectrum becomes uniform, the maximum harmonic content is greatly reduced, and the fluctuation in the DC side midpoint potential is significantly improved. Compared with the traditional SVPWM strategy and random PWM strategy, the NPB–RSVPWM strategy has a lower voltage noise, smaller total harmonic distortion, and a more stable midpoint potential. The effectiveness and feasibility of the NPB–RSVPWM strategy are verified by simulation and experimental results. [ABSTRACT FROM AUTHOR]

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For d⩾2$d\geqslant 2$ and an odd prime power q$q$, consider the vector space Fqd$\mathbb {F}_q^d$ over the finite field Fq$\mathbb {F}_q$, where the distance between two points (x1,...,xd)$(x_1,\ldots ,x_d)$ and (y1,...,yd)$(y_1,\ldots ,y_d)$ is defined as ∑i=1d(xi−yi)2$\sum _{i=1}^d (x_i-y_i)^2$. A distance graph is a graph associated with a nonzero distance to each of its edges. We show that large subsets of vector spaces over finite fields contain every nearly spanning distance tree with bounded degree in each distance. This quantitatively improves results by Bennett, Chapman, Covert, Hart, Iosevich, and Pakianathan on finding distance paths, and results by Pham, Senger, Tait, and Thu on finding distance trees. A key ingredient in proving our main result is to obtain a colorful generalization of a classical result of Haxell about finding nearly spanning bounded‐degree trees in an expander. [ABSTRACT FROM AUTHOR]

The growth of medical record documents is increasing over time, and the various types of diseases and therapies needed are increasing. However, this has not been followed by an effective and efficient search process. This study aims to deal with search problems that often take a long time with search results that are not necessarily as expected by building a search model for medical record documents using the vector space model (VSM) and TF-IDF methods. The VSM method allows retrieval of results that are not the same as the search queries entered by the user but are expected to provide still results relevant to the user's desired needs. The model development process was taken based on the data in the FS_ANAMNESA and FS_DIAGNOSA columns, followed by preprocessing, which consists of deleting blank lines, lowercase, removing punctuation marks, HTML tags, stop words, excess spaces between words, and normalizing typo words, then forming a TF-IDF matrix based on the frequency of occurrence of each word feature, and followed by the calculation of the similarity value of the search query compared to medical record documents based on the cosine similarity formula. The retrieval results were all columns of each existing medical record document and were sorted based on 10 rows with the highest similarity value. The model evaluation results were based on 1000 medical record documents and tested with 20 search queries in this study, which gave an average precision value of 0.548 and an average recall value of 0.796. [ABSTRACT FROM AUTHOR]

Let 0 < ρ ≤ 2 and w ρ (X) be the operator radius of a bounded linear Hilbert space operator X. In this paper we present characterizations of operators satisfying w ρ (X) ≤ 1. We also give an expression for the ρ -radii based on the numerical radius of a certain 2 × 2 block matrix. This enables us to investigate the properties of the operator radii w ρ (⋅). In particular, we obtain lower and upper bounds for the operator radii. In addition, we define a norm on Hilbert space operators, which generalizes the operator radii and prove some basic properties of this norm. Our results extend or improve some theorems due to Ando [4] , Bhatia–Jain [9] and Kittaneh [19]. [ABSTRACT FROM AUTHOR]

The voltage of the battery system is increased to increase the efficiency of the electric motor drive system. Additionally, the space vector pulse width modulation (SVPWM) technique is used to ensure high controllability. However, high-voltage and high-speed PWM switching controls for system efficiency generate high common mode voltage (CMV), and shaft voltage is induced in the bearing. This results in a shortened bearing life and potential damage. Therefore, this paper proposes a method to reduce the shaft voltage of the motor through a novel hybrid shield ring structure. It also analyzes how to improve the cooling performance of the motor using a shield ring. First, the parasitic capacitance inside the motor is analyzed. Then, the shaft voltage reduction technology is analyzed according to the material of the shield ring. Finally, experiments validate the proposed method. Additionally, the temperature characteristics of the main part of the motor are analyzed through an experiment in consideration of the shield ring. [ABSTRACT FROM AUTHOR]

This study presents a sparse grid interpolation and ensemble Kalman filter (EnKF)-based Markov Chain Monte Carlo (MCMC) method (SG-EnMCMC). Initiating with the formulation of a recursive equation for the state space vector, derived from the structural dynamic equation, this study adopts a dimensionality reduction strategy. This approach involves a separation of physical parameters and the state space vector. The acquisition of physical parameters is accomplished through sampling, utilizing sample moments to substitute population moments, thereby mitigating the need for computationally high-dimensional covariance matrix calculations. To further streamline the recursive equation of the state space vector, a sparse grid method is employed for interpolation. This step simplifies the process while ensuring superior accuracy compared to the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). Subsequent to this, acceptance rates and the final parameter posterior distribution within the MCMC framework are derived. The efficiency of the proposed method is assessed through validation in two shaking table experiments. [ABSTRACT FROM AUTHOR]

In this paper, we consider a hypervector space (in the sense of Tallini) V over a field K. We use the fundamental relation ε* over V, as the smallest equivalence relation on V, to derived the fundamental vector space V/ε*. In this regards, we prove that if V is a (resp. quasi) topological hypervector space, then the fundamental vector space V/ε* with the property that each open subset of it is a complete part, then its fundamental vector space V/ε* is a topological vector space. Finally, we prove that for a topological vector space (V, +, ·, K) and every subspace W of V, the hypervector space (..., +, º, K) is a topological hypervector space and we will prove .../ε* and V/W are homeomorphic, where ... = V. [ABSTRACT FROM AUTHOR]

With tremendous evolution in the internet world, the internet has become a household thing. Internet users use search engines or personal assistants to request information from the internet. Search results are greatly dependent on the entered keywords. Casual users may enter a vague query due to lack of knowledge of the domain-specific words. We propose a query reformulation system that determines the context of the query, decides on keywords to be replaced and outputs a better-modified query. We propose strategies for keyword replacements and metrics for query betterment checks. We have found that if we project keywords into the vector space of word projection using word embedding techniques and if the keyword replacement is correct, clusters of a new set of keywords become more cohesive. This assumption forms the basis of our proposed work. To prove the effectiveness of the proposed system, we applied it to the ad-hoc retrieval tasks over two benchmark corpora viz TREC-CDS 2014 and OHSUMED corpus. We indexed Whoosh search engine on these corpora and evaluated based on the given queries provided along with the corpus. Experimental results show that the proposed techniques achieved 9 to 11% improvement in precision and recall scores. Using Google's popularity index, we also prove that the reformulated queries are not only more accurate but also more popular. The proposed system also applies to Conversational AI chatbots like ChatGPT, where users must rephrase their queries to obtain better results. [ABSTRACT FROM AUTHOR]

Due to the polysemy and complexity of the Chinese language, Chinese machine reading comprehension has always been a challenging task. To improve the semantic understanding and robustness of Chinese machine reading comprehension models, we propose a model that utilizes adversarial training algorithms and Permuted Language Model (PERT). Firstly, we employ the PERT pre-training model to embed paragraphs and questions into vector space to obtain corresponding sequential representations. Secondly, we use a multi-head self-attention mechanism to extract key textual information from the sequence and employ a Bi-GRU network to semantically fuse the output feature vectors, aiming to learn deep semantic representations in the text. Finally, we introduce perturbations into the model training process. We achieve this by utilizing adversarial training algorithms such as Fast Gradient Method (FGM) and Projected Gradient Descent (PGD). These algorithms generate adversarial samples to enhance the model's robustness and stability when facing diverse inputs. We conducted comparative experiments on the publicly available Chinese reading comprehension datasets CMRC2018 and DRCD. The experimental results show that our proposed model has achieved significant improvements in both EM and F1-Score compared to the baseline model. To validate the model's generalization and robustness, we utilized ChatGPT to construct a scientific dataset that includes a large number of domain-specific terms, sentences with mixed Chinese and English, and complex comprehension tasks. Our model also performed remarkably well on the self-built dataset. In conclusion, the proposed model not only effectively enhances the understanding of semantic information in Chinese text but also demonstrates a certain level of generalization capability. [ABSTRACT FROM AUTHOR]

To address this storage issue, we propose a Content-Aware Deduplication Clustering Analysis for Cloud Storage Optimization (CADC-FPRLE) based on a file partitioning running length encoder. At first, preprocessing was done by indexing, counting terms, cleansing, and tokenizing. Further multi-objective clustering points are analysed based on the bisecting divisible partition block, which divides a set of documents. The count terms are filtered from the divisible blocks and make up the count terms content block. Using Content-Aware Multi-Hash Ensemble Clustering (CAMH-EC) to group the similar blocks into clusters. This creates a high-dimensional Euclidean interval to create the number of clusters, and points are performed randomly to set the initial collection. Then, the Magnitude Vector Space Rate (MVSR) estimates the similarity distance between the groups to select the highest scatter value content for indexing. Finally, the Running Block Parity Encoder (RBPE) generates similarity parity in order to reduce the content to a redundant, singularized file in order to optimise storage. This implementation proves a higher level of storage optimization compared to the previous system than other methods. [ABSTRACT FROM AUTHOR]

An innovative method for synthesizing optimum difference patterns of the spherical sensor array is introduced, along with a sidelobe tapering technique. Firstly, we suggest employing the spherical harmonics of degree ±1 to synthesize the spherical array difference pattern; secondly, we study the mapping relationship between the difference pattern of the spherical sensor array and the difference pattern of the uniformly spaced linear array (ULA) with odd-numbered elements; finally, we enhance the Zolotarev difference pattern, which is a counterpart to the Dolph–Chebyshev sum pattern that traditionally allows synthesis only for ULA with even-numbered elements. Our modification extends its applicability to synthesize difference patterns for ULA with odd-numbered elements. Leveraging the optimal difference pattern, a generalized Bayliss difference pattern synthesis method designed for the ULA with odd-numbered elements is further proposed. To illustrate the effectiveness of our approach, we present several design examples through experimental simulation. [ABSTRACT FROM AUTHOR]

In general, most of the clustering algorithms deal with high-dimensional data. Therefore, the resulting clusters are high-dimensional geometrical objects, which are difficult to analyse, visualize and interpret. Principal component analysis (PCA) is a widely used classical technique for unsupervised dimensional reduction of datasets which extracts smaller uncorrelated data from the original high dimensional data space. The methodology of classical PCA is based on orthogonal projection defined in convex vector space. Thus, a norm between two projected vectors is unavoidably smaller than the norm between any two objects before implementation of PCA. Due to this, in some cases when the PCA cannot capture the data structure, its implementation does not necessarily confirm the real similarity of data in the higher dimensional space making the results unacceptable. Furthermore, when applied with fuzzy clustering algorithms, it demonstrates its weakness in capturing the data structure what affects the PCA mapping quality. In this research we propose a new fuzzy PCA algorithm (FuzPCA) combining FCM and PCA which builds not only fuzzy similarity measures based on the membership functions calculated by FCM but also a measure corresponding to the rate of dissimilarities between the clustering structures of the dataset objects and their dimensions. We formulated the respective new fuzzy covariance matrix which is processed by the PCA during subsequent iterations. FuzPCA demonstrates higher clustering discriminatory ability and visualization accuracy than regular FCM when applied to high-dimensional datasets, in cases when clusters’ sizes or densities are different as well as in discovering small clusters. The function integrated with FuzPCA Silhouette provides preliminary information and visualization allowing faster choice of number of clusters which is additionally refined after implementation of fuzzy clustering validation metrics. The projected 2- and 3-D topologies of FuzPCA are more reliable, significantly improve the visualization results and demonstrate high mapping quality. [ABSTRACT FROM AUTHOR]

We discuss various applications of a uniform vanishing result for the graded components of the finite length Koszul module associated to a subspace K ⊆ ⋀ 2 V , where V is a vector space. Previously Koszul modules of finite length have been used to give a proof of Green's Conjecture on syzygies of generic canonical curves. We now give applications to effective stabilization of cohomology of thickenings of algebraic varieties, divisors on moduli spaces of curves, enumerative geometry of curves on K3 surfaces and to skew-symmetric degeneracy loci. We also show that the instability of sufficiently positive rank 2 vector bundles on curves is governed by resonance and give a splitting criterion. [ABSTRACT FROM AUTHOR]

We present a reformulation of optimization problems over the Stiefel manifold by using a Cayley-type transform, named the generalized left-localized Cayley transform, for the Stiefel manifold. The reformulated optimization problem is defined over a vector space, whereby we can apply directly powerful computational arts designed for optimization over a vector space. The proposed Cayley-type transform enjoys several key properties which are useful to (i) study relations between the original problem and the proposed problem; (ii) check the conditions to guarantee the global convergence of optimization algorithms. Numerical experiments demonstrate that the proposed algorithm outperforms the standard algorithms designed with a retraction on the Stiefel manifold. [ABSTRACT FROM AUTHOR]

In this paper, we discuss various consequences of Hahn-Banach theorem for bounded b-linear functional in linear n-normed space and describe the notion of reexivity of linear n-normed space with respect to bounded b-linear functional. The concepts of strong convergence and weak convergence of a sequence of vectors with respect to bounded b-linear functionals in linear n-normed space have been introduced and some of their properties are being discussed. [ABSTRACT FROM AUTHOR]

This paper proposes a differential evolution modified with adaptive ε-constraint handling and whale optimization algorithm (ε-WOA-DE) for the synthesis of unequally spaced linear arrays under array layout constraints and array pattern characteristics constraints. In particular, the success history based adaptive differential evolution with linear population reduction (LSHADE) serves as the basic search engine in this study. To ensure the searching ability of LSHADE under multiple constraints, an adaptive ε-constraint handling technique is implemented in LSHADE, in which the epsilon level is adjusted dynamically to make the solution scalable to the feasible region when it is in the infeasible region. In addition, theWOA mutation is implemented in the LSHADE to enhance the local search capability. Two array synthesis examples with multiple constraints are chosen to demonstrate the effectiveness of the proposed algorithm. The simulation results comparison and the convergence analysis of the ε-WOA-DE illustrate the superior capability of the proposed method. [ABSTRACT FROM AUTHOR]

According to the principles of compositional verification, verifying that lower-level components satisfy their specification ensures that the whole system satisfies its top-level specification. The key step is to ensure that the lower-level specifications constitute a correct decomposition of the top-level specification. In a non-stochastic context, such decomposition can be analyzed using techniques of theorem proving. In industrial applications, especially in safety-critical systems, specifications are often of stochastic nature, for example, giving a bound on the probability that a system failure will occur before a given time. A decomposition of such a specification requires techniques beyond traditional theorem proving. The first contribution of the paper is a theoretical framework that allows the representation of, and reasoning about, stochastic and timed behavior of systems as well as specifications for such behavior. The framework is based on traces that describe the continuous-time evolution of a system, and specifications are formulated using timed automata combined with probabilistic acceptance conditions. The second contribution is a novel approach to verifying decompositions of such specifications by reducing the problem to checking emptiness of the solution space for a system of linear inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we study a nonlinear scalarization function for a variable domination structure in an arbitrary linear space without assuming any particular topology. Conditions are provided under which the nonlinear scalarization function possesses several useful properties such as finiteness, properness, positive homogeneity, subadditivity, (strict) monotonicity, convexity or continuity. These properties are employed to characterize approximate efficiency in linear spaces. [ABSTRACT FROM AUTHOR]

Least Squares Support Vector Regression (LSSVR) which is a least squares version of the Support Vector Regression (SVR) is defined with a regularized squared loss without epsilon-insensitiveness. LSSVR is formulated in the dual space as a linear equality constrained quadratic minimization which can be transformed into solution of a linear algebraic equation system. As a consequence of this system where the number of Lagrange multipliers is half that of classical SVR, LSSVR has much less time consumption compared to the classical SVR. Despite this computationally attractive feature, it lacks the sparsity characteristic of SVR due to epsilon-insensitiveness. In LSSVR, every (training) input data is treated as a support vector, yielding extremely poor generalization performance. To overcome these drawbacks, the epsilon-insensitive LSSVR with epsilon-insensitivity at quadratic loss, in which sparsity is directly controlled by the epsilon parameter, is derived in this paper. Since the quadratic loss is sensitive to outliers, its weighted version (epsilon insensitive WLSSVR) has also been developed. Finally, the performances of epsilon-insensitive LSSVR and epsilon-insensitive WLSSVR are quantitatively compared in detail with those commonly used in the literature, pruning-based LSSVR and weighted pruning-based LSSVR. Experimental results on simulated and 8 different real-life data show that epsilon-insensitive LSSVR and epsilon-insensitive WLSSVR are superior in terms of computation time, generalization ability, and sparsity. [ABSTRACT FROM AUTHOR]

U (n) is a semi-direct product group characterized by nontrivial homomorphisms mapping U (1) into the automorphism group of S U (n) . For U (3) , there are three nontrivial homomorphisms that induce three separate defining representations. In a toy model of U (3) Yang–Mills (endowed with a suitable inner product) coupled to massive fermions, this renders three distinct covariant derivatives acting on a single matter field. Employing a mod 3 permutation induced by a large gauge transformation acting on the defining representation vector space, the three covariant derivatives and one matter field can alternatively be expressed as a single covariant derivative acting on three distinct species of matter fields possessing the same U (3) quantum numbers. One can interpret this as three species of matter fields in the defining representation. [ABSTRACT FROM AUTHOR]

Currently, power trains based on an Open-End Winding Induction Machine fed by a Dual Inverter (DI-OEWIM) are attracting a great deal of interest in various modern industrial applications. However, applying symmetrical control to this system (DI-OEWIM), which is symmetrical in nature, will lead to malfunction. Therefore, the objective of this paper is to explore the influence of asymmetric control on the performance of this system. The principle of this study is to create an asymmetrical control by integrating a phase-shift angle in the Space Vector Pulse Width Modulation (SVPWM) strategy. We then evaluate the impact of these angles on various performances, such as the Total Harmonic Distortion (THD), power losses, Common Mode Voltage (CMV), Zero-Sequence Voltage (ZSV), rotation speed and torque ripple of this system. This study was carried out in the Matlab/Simulink environment and was validated experimentally using the dSPACE 1104 board. The results show that the different angles have significant effects on the overall performance of this system. [ABSTRACT FROM AUTHOR]

Analyzing point clouds with neural networks is a current research hotspot. In order to analyze the 3D geometric features of point clouds, most neural networks improve the network performance by adding local geometric operators and trainable parameters. However, deep learning usually requires a large amount of computational resources for training and inference, which poses challenges to hardware devices and energy consumption. Therefore, some researches have started to try to use a nonparametric approach to extract features. Point-NN combines nonparametric modules to build a nonparametric network for 3D point cloud analysis, and the nonparametric components include operations such as trigonometric embedding, farthest point sampling (FPS), k-nearest neighbor (k-NN), and pooling. However, Point-NN has some blindness in feature embedding using the trigonometric function during feature extraction. To eliminate this blindness as much as possible, we utilize a nonparametric energy function-based attention mechanism (ResSimAM). The embedded features are enhanced by calculating the energy of the features by the energy function, and then the ResSimAM is used to enhance the weights of the embedded features by the energy to enhance the features without adding any parameters to the original network; Point-NN needs to compute the similarity between each feature at the naive feature similarity matching stage; however, the magnitude difference of the features in vector space during the feature extraction stage may affect the final matching result. We use the Squash operation to squeeze the features. This nonlinear operation can make the features squeeze to a certain range without changing the original direction in the vector space, thus eliminating the effect of feature magnitude, and we can ultimately better complete the naive feature matching in the vector space. We inserted these modules into the network and build a nonparametric network, Point-Sim, which performs well in 3D classification tasks. Based on this, we extend the lightweight neural network Point-SimP by adding some trainable parameters for the point cloud classification task, which requires only 0.8 M parameters for high performance analysis. Experimental results demonstrate the effectiveness of our proposed algorithm in the point cloud shape classification task. The corresponding results on ModelNet40 and ScanObjectNN are 83.9% and 66.3% for 0 M parameters—without any training—and 93.3% and 86.6% for 0.8 M parameters. The Point-SimP reaches a test speed of 962 samples per second on the ModelNet40 dataset. The experimental results show that our proposed method effectively improves the performance on point cloud classification networks. [ABSTRACT FROM AUTHOR]

Recently, generative artificial intelligence (GAI) has impressed the world with its ability to create text, images, and videos. However, there are still areas in which GAI produces undesirable or unintended results due to being "uncertain". Before wider use of AI-generated content, it is important to identify concepts where GAI is uncertain to ensure the usage thereof is ethical and to direct efforts for improvement. This study proposes a general pipeline to automatically quantify uncertainty within GAI. To measure uncertainty, the textual prompt to a text-to-image model is compared to captions supplied by four image-to-text models (GIT, BLIP, BLIP-2, and InstructBLIP). Its evaluation is based on machine translation metrics (BLEU, ROUGE, METEOR, and SPICE) and word embedding's cosine similarity (Word2Vec, GloVe, FastText, DistilRoBERTa, MiniLM-6, and MiniLM-12). The generative AI models performed consistently across the metrics; however, the vector space models yielded the highest average similarity, close to 80%, which suggests more ideal and "certain" results. Suggested future work includes identifying metrics that best align with a human baseline to ensure quality and consideration for more GAI models. The work within can be used to automatically identify concepts in which GAI is "uncertain" to drive research aimed at increasing confidence in these areas. [ABSTRACT FROM AUTHOR]

A generalized construction procedure for algebraic number systems is hereby presented. This procedure offers an efficient representation and computation method for complex numbers, quaternions, and other algebraic structures. The construction method is then illustrated across a range of examples. In particular, the novel developments reported herein provide a generalized form of the Cayley–Dickson construction through involutive dimagmas, thereby allowing for the treatment of more general spaces other than vector spaces, which underlie the associated algebra structure. [ABSTRACT FROM AUTHOR]

There is a growing interest in defining specific tools on correlation matrices which depart from those suited to SPD matrices. Several geometries have been defined on the open elliptope of full-rank correlation matrices: some are permutation-invariant, some others are log-Euclidean, i.e., diffeomorphic to a Euclidean space. In this work, we prove the existence of permutation-invariant log-Euclidean metrics by defining the families of off-log metrics and log-scaled metrics. First, we prove that the recently introduced off-log bijection is a smooth diffeomorphism, allowing pullback of (permutation-invariant) inner products. We introduce the "cor-inverse" involution on the open ellip- tope, which can be seen as analogous to the inversion of SPD matrices. We show that off-log metrics are not inverse-consistent. That is why, second, we define the log-scaling smooth diffeomorphism between the open elliptope and the vector space of symmetric matrices with null row sums. This map is based on the congruence action of positive diagonal matrices on SPD matrices, more precisely on the existence and uniqueness of a "scaling," i.e., an SPD matrix with unit row sums within an orbit. Thanks to this multiplicative approach, log-scaled metrics are inverse-consistent. We provide the main Riemannian operations in closed form for the two families modulo the computation of the respective bijections. [ABSTRACT FROM AUTHOR]

The conventional approach of predictive torque control (PTC) is frequently employed in the control of permanent magnet synchronous motors (PMSMs) driven by a two-level voltage source inverter (2L-VSI). This technique offers low complexity and reduced torque ripples in the low-speed region by minimizing the duty-cycle of the applied voltage vector (VV) compared to the complete utilization of the DC-link voltage. However, it has its limitations, including slow torque dynamics, restricted modulation index (MI), and an inability to select zero VV, which would be useful for minimizing ripples in multilevel VSI drives. Additionally, it can lead to an unbalanced DC link due to the restricted VV selection, especially at low MI. To address these limitations, a modified PTC based on space vector pulse-width modulation approach is proposed for three-level neutral-point-clamped (3L-NPC) VSI-fed PMSM. The proposed 3L-PTC method can reduce torque and flux ripples at low MI, improve dynamic response, and maintain a balanced DC link regardless of operating conditions. Intensive numerical and experimental evaluations are carried out to validate the effectiveness of the proposed 3L-PTC. [ABSTRACT FROM AUTHOR]