Double Representation Research Articles

Fredholm Determinant and Wronskian Representations of the Solutions to the Schrödinger Equation with a KdV-Potential

From the finite gap solutions of the KdV equation expressed in terms of abelian functions we construct solutions to the Schrödinger equation with a KdV potential in terms of fourfold Fredholm determinants. For this we establish a connection between Riemann theta functions and Fredholm determinants and we obtain multi-parametric solutions to this equation. As a consequence, a double Wronskian representation of the solutions to this equation is constructed. We also give quasi-rational solutions to this Schrödinger equation with rational KdV potentials.

GeoGebra—A great platform for experiential learning, explorations and creativity in mathematics

In this paper we are presenting some examples of how GeoGebra is used in: a) explaining concepts of the first derivative, monotony, extremums; b) studying the properties of the function (strictly increasing/decreasing); c) demonstrating the mean value theorem. The results and the conclusions are based on the experiment carried out in the teaching and learning process in the chapter of derivatives in a third-year class of a secondary school in Albania. Also, there are some encouraging facts got by the use of GeoGebra: the double representation and the dynamic features of GeoGebra allow the students to quickly grasp the mathematical concepts and properties and be actively involved in further explorations. The use of GeoGebra tools is similar to the use of the tools of virtual games, and this is a great advantage to stimulate the students to learn mathematics and master their mathematical performance the same way they play games. On the other side, using GeoGebra, it is easier for the teachers to explain mathematical concepts, the properties of algebraic objects, to discuss about different situations and aspects of the subject under study and to methodically reason the results got. GeoGebra provides a very commodious environment for the students to effectively interoperate with each other. Our results showed that GeoGebra is effective in teaching and learning mathematics. GeoGebra software contributed in enhancing students’ understanding of mathematical concepts and improved students’ interest to learn mathematics. Also, we admit that not all the stages of implementing GeoGebra software in the classroom are flowing smoothly. Based on our experience and the other researchers, it is observed that the effectiveness is dependent on the way GeoGebra is integrated in the teaching and learning process, implying that the research must continue with the commitment of many researchers of mathematics, physics and other sciences.

A Dual-Attention Learning Network With Word and Sentence Embedding for Medical Visual Question Answering.

Research in medical visual question answering (MVQA) can contribute to the development of computer-aided diagnosis. MVQA is a task that aims to predict accurate and convincing answers based on given medical images and associated natural language questions. This task requires extracting medical knowledge-rich feature content and making fine-grained understandings of them. Therefore, constructing an effective feature extraction and understanding scheme are keys to modeling. Existing MVQA question extraction schemes mainly focus on word information, ignoring medical information in the text, such as medical concepts and domain-specific terms. Meanwhile, some visual and textual feature understanding schemes cannot effectively capture the correlation between regions and keywords for reasonable visual reasoning. In this study, a dual-attention learning network with word and sentence embedding (DALNet-WSE) is proposed. We design a module, transformer with sentence embedding (TSE), to extract a double embedding representation of questions containing keywords and medical information. A dual-attention learning (DAL) module consisting of self-attention and guided attention is proposed to model intensive intramodal and intermodal interactions. With multiple DAL modules (DALs), learning visual and textual co-attention can increase the granularity of understanding and improve visual reasoning. Experimental results on the ImageCLEF 2019 VQA-MED (VQA-MED 2019) and VQA-RAD datasets demonstrate that our proposed method outperforms previous state-of-the-art methods. According to the ablation studies and Grad-CAM maps, DALNet-WSE can extract rich textual information and has strong visual reasoning ability.

End-to-End Multiview Fuzzy Clustering With Double Representation Learning and Visible-Hidden View Cooperation

End-to-End Multiview Fuzzy Clustering With Double Representation Learning and Visible-Hidden View Cooperation

Improved ant colony algorithm for the mixed-model parallel two-sided assembly lines balancing problem

ABSTRACT In response to the increasing demand for individualized products in the ‘small-lot, multi-variety’ market, there is an urgent need to enhance the efficiency and intelligence level of assembly lines. To address this, a novel solution method for the mixed-model parallel two-sided assembly lines balancing problem (MMPTSALBP) is proposed. The first step is to define the type and layout of the parallel two-sided assembly lines. Next, a mathematical model is constructed with the objective of minimizing the number of workstations required for the MMPTSALBP, proposing an improved ant colony algorithm that utilizes double string representation for the initial solution encoding method and a double pheromone matrix update to solve the model. Its efficiency is tested on benchmark datasets according to some performance measures and classifications. A study validates its effectiveness on 25 classical arithmetic cases by comparison with the solutions of an heuristic algorithm and an artificial fish swarm algorithm that had been reported to perform well.

Double quantum images encryption scheme based on chaotic system

This paper explores a double quantum images representation (DNEQR) model that allows for simultaneous storage of two digital images in a quantum superposition state. Additionally, a new type of two-dimensional hyperchaotic system based on sine and logistic maps is investigated, offering a wider parameter space and better chaotic behavior compared to the sine and logistic maps. Based on the DNEQR model and the hyperchaotic system, a double quantum images encryption algorithm is proposed. Firstly, two classical plaintext images are transformed into quantum states using the DNEQR model. Then, the proposed hyperchaotic system is employed to iteratively generate pseudo-random sequences. These chaotic sequences are utilized to perform pixel value and position operations on the quantum image, resulting in changes to both pixel values and positions. Finally, the ciphertext image can be obtained by qubit-level diffusion using two XOR operations between the position-permutated image and the pseudo-random sequences. The corresponding quantum circuits are also given. Experimental results demonstrate that the proposed scheme ensures the security of the images during transmission, improves the encryption efficiency, and enhances anti-interference and anti-attack capabilities.

“THE INTERNAL FORM OF THE VERSE” AND THE INNER WORD: OSIP MANDELSTAM’S CONVERSATION ABOUT DANTE IN THE PSYCHOLINGUISTIC PERSPECTIVE

The object of the study is Mandelstam’s article Conversation about Dante, considered in a psycholinguistic perspective. The article puts forward a hypothesis that the problem of the genesis of a poetic text in Mandelstam’s metapoetics has its ontological justification in the idea of inner word. Such a connection can be explained by the fact that the literary text is considered by Mandelstam in its genetic dimension — from the standpoint of the generation of literary speech. Mandelstam’s focus on the genetic aspect of the birth of a word leads to regular intersections of the poet’s searches with the psychological concepts of inner speech. So, firstly, the inner image of the verse, which, according to Mandelstam, stands at the beginning of the poetic text, is typologically related to the inner word. Both phenomena are correlated with pre-text / pre-speech stage, have a double representation as image and the word, and are primarily manifested in the articulatorysyntactic code. Secondly, the principles of unfolding turn out to be common to the inner word and the artistic word, taken in its genetic aspect. Just as the “clot of personal meanings” (Vygotsky) in its deployment moves from the primary ‘synsemantic’ stage to verbal differentiation, so the “compositional clot” (Mandelstam), initially arising as a single semantic impulse, unfolds in the level space of the language. Thirdly, both the inner word and the artistic integrity postulated by Mandelstam exist in a special spatial modus, which is characterized by semantic simultaneity and the absolute dominance of semantics over syntax. Fourthly, the finished speech product is understood by Mandelstam both as a result and as a process, which, on the one hand, leads to the aesthetics of a draft, and on the other hand, matches Mandelstam’s ideas with the concepts of inner speech, where the remnants of the primary semantic syntax are found.

High-Temperature Electromechanical Properties Single Crystalline Lithium Niobate-Lithium Tantalate Solid Solutions at Different Oxygen Partial Pressures

LiNbO3 (LN) is one of the most investigated electro-acoustic and electro-optical materials. Its high piezoelectric coefficients are a favorable condition for its use beyond optical applications, which includes, for example, high-temperature actuators. Compared for example to crystals of the langasite family, LN shows significantly higher piezoelectric coefficients but limited thermal stability. The latter is caused by evaporation of Li2O and related changes of e.g. electrical conductivity. As a consequence, long-term applications of LN are limited to temperatures of a few hundred degrees Celsius. A related material that offers improved thermal stability is LiNbO3 (LT). However, the Curie temperature is only about 600 °C. Furthermore, the piezoelectric coefficients are lower than for LN. The miscibility of LN and LT over the entire compositional range should allow, however, to tailor the crystal properties and, for example, to take advantage of the high piezoelectric coefficients of LT and the better thermal stability of LT. Therefore, the subject of this study are lithium niobate-lithium tantalate (LiNb1-xTaxO3, LNT) solid solutions with respect to their electroacoustic properties at temperatures between 400 and 900 °C. The objectives include the determination, understanding and correlation of defect structures, electronic and atomic transport and acoustic losses in LNT over a wide temperature range.The electromechanical properties of LNT crystals are determined as function of temperature and oxygen partial pressure (pO2) and compared with those of the congruent edge compounds LN and LT. Characterization methods include impedance spectroscopy, application of 6Li as tracer in combination with secondary ion mass spectrometry, resonant piezoelectric spectroscopy, noncontacting resonant ringdown spectroscopy and laser vibrometry. The latter reflects displacements of the sample surface even in the order of nanometers which enables the identification of the resonant modes.LNT crystals with different Nb-Ta compositions prepared by Czochralski growth and a µ-pulling down process are used to determine the overall electrical conductivity by electrical impedance spectroscopy. Further, Z- and Y-cut plates are applied as bulk acoustic wave resonators to measure the acoustic loss. When determined in air, the temperature-dependent electrical conductivity of LNT below about 600 °C is virtually independent of composition. In particular, for each sample a single activation energy is found from 400 to 600 °C which is the same for all samples within the error margins. Furthermore, the diffusive ion transport studied directly using 6Li tracers results in good agreement with the electrical conductivity when the diffusion coefficients are converted correspondingly using the Nernst-Einstein relation. Consequently lithium-ion migration can explain the overall electrical conductivity. Above about 600 °C the behavior depends on composition. At high Nb contents, a continuous increase of the slope of the electrical conductivity in an Arrhenius representation with temperature is observed, which is attributed to thermal instability.The pO2 dependent electrical conductivity shows constant values at high pO2. At sufficiently low pO2, a slope of -1/4 in a double logarithmic representation is found (see attached figure). This slope indicates electronic conduction which is caused by compensation of NbLi antisite defects. The behavior is already reported for LN by Smyth et al. (Ferroelectrics 50 (1983) 93). As the slope is independent of the composition x, it can be concluded that the same defect formation occurs in LNT. Important with respect to thermal stability is that, at a given temperature, the increase in conductivity for Ta-rich compositions starts at lower pO2 than for Nb-rich compositions.The acoustic loss is determined in a wide temperature range by the methods mentioned above. It shows some impact of the metal electrodes at low temperatures. In air and at temperatures above about 400 °C the acoustic loss is governed by the piezoelectric/carrier relaxation. It is caused by the motion of charge carriers in an oscillating piezoelectric field and, therefore, related to electrical conductivity. The finding is confirmed by modelling with independent materials data including electrical conductivity. Low pO2 result in additional loss contributions.In summary, the study leads to an understanding of the acoustic losses of LNT at high temperatures, which provides opportunities to reduce them. Furthermore, it becomes clear that Ta-rich compositions exhibit improved thermal stability. Figure 1

Similarity Measurement and Classification of Temporal Data Based on Double Mean Representation

Time series data typically exhibit high dimensionality and complexity, necessitating the use of specific approximation methods to perform computations on the data. The currently employed compression methods suffer from varying degrees of feature loss, leading to potential distortions in similarity measurement results. Considering the aforementioned challenges and concerns, this paper proposes a double mean representation method, SAX-DM (Symbolic Aggregate Approximation Based on Double Mean Representation), for time series data, along with a similarity measurement approach based on SAX-DM. Addressing the trade-off between compression ratio and accuracy in the improved SAX representation, SAX-DM utilizes the segment mean and the segment trend distance to represent corresponding segments of time series data. This method reduces the dimensionality of the original sequences while preserving the original features and trend information of the time series data, resulting in a unified representation of time series segments. Experimental results demonstrate that, under the same compression ratio, SAX-DM combined with its similarity measurement method achieves higher expression accuracy, balanced compression rate, and accuracy, compared to SAX-TD and SAX-BD, in over 80% of the UCR Time Series dataset. This approach improves the efficiency and precision of similarity calculation.

Drazin-inverse and heat capacity for driven random walkers on the ring

We apply single and double tree-like representations of Markov jump processes on ZN for obtaining their nonequilibrium heat capacity and for taking the diffusion limit N↑∞. The main tool is a graphical representation of the Drazin-inverse of the backward generator. In that way, the combination of algebraic and graph-theoretical approaches enables an exact computation of an important nonequilibrium quantity (excess heat) for Markov jump processes.

"The babbitry of professors' humble abodes": Representation of Everyday Life of the "Positivist Father" in Memoirs of Russian Symbolism

The formation of symbolism as an artistic and worldview phenomenon took place in intellectual and cultural opposition to the tradition of Russian academic positivism. In the article positivism and symbolism are viewed as two discourses competing for influence in the Russian intellectual environment, the competition of which often took on the features of a conflict between "fathers and children". One of the ways of " battle for the authority" was the construction of the image of "father-positivist" in memoirs and diary notes by symbolists. The object of the study is the representation of the everyday culture of the conventional "father" in the memoirs of A. Beliy, G. I. Chulkov, V. Y. Brusov, N. Petrovskaya, B. M. Runt and Z. N. Gippius. The subject is those discursive mechanics, through which the representation of otherness and "othering" of such everyday life are achieved. The methodology of the work is built around the optics of the translation turn, which allows us to look at the scenes from the memoirs as "third space", where the battle of discourses unfolds at the expense of representational practices. The novelty of the research is manifested both in drawing attention to this problem and in the development of an actual methodological base. Based on the results of the analysis, the following mechanics of "othering" were identified: unification and generalization, binarity and asymmetry, giving the Other the status of timelessness and non-historicity, the use of pejorative categories, the narrative technique of double representation and concealment. The aim of the fathers "othering" was the construction of personal identity and selfhood, as well as the attempt to define oneself through the constitutive Other.

Huygens' surface excitation for the finite element method applied to Maxwell's equations – A construction based on Nitsche's method

We present a Huygens' surface for the finite element method applied to Maxwell's equations, where the equivalent electric and magnetic surface currents are incorporated in the weak form by means of Nitsche's method. The proposed method preserves the reciprocity of Maxwell's equations and it allows for the computation of the total field inside the Huygens' surface, whereas on its outside only the scattered field is computed. The equivalent magnetic surface current at the Huygens' surface requires a double representation of the discontinuous tangential component of the electric field and we demonstrate that it can be efficiently combined with a previously presented higher-order brick-tetrahedron hybridization. Also, it is demonstrated that the near-to-far-field transformation can be evaluated in an accurate manner if collocated with the Huygens' surface, which allows for a compact computational domain and a reduction in the required computational resources. The proposed Huygens' surface is tested on two scattering problems with perfect electric conductor scatterers: (i) a sphere that demonstrates second-order convergence towards the analytical result for a piecewise linear approximation of the electric field; and (ii) a double ogive with two sharp tips which gives a computed monostatic radar cross section that compares well with measurements and computations in the open literature for both polarizations.

Infinite double integral representation for the polynomial set Rn(x, y)

Infinite double integral representation for the polynomial set Rn(x, y)

Exploring the Relationship between Federal Reform and the Representation of the People: The Case of the Belgian House of Representatives

Abstract Federal systems tend to have two venues of representation to ensure that both the people as a whole and the constituent units are represented at the federal level. While this double representation is put forward as a basic (normative) feature of federal systems, little to no empirical research has been conducted on this issue. This contribution therefore studies the representation of the people as a whole and of the constituent units in the Belgian House of Representatives by means of a representative claims analysis of 4,757 oral parliamentary questions. As federal systems tend to be dynamic, the analysis is based on six periods of federal reform through which Belgium decentralized. Our findings show that, over time, the representation of the constituent units increased and exceeded the representation of the people, providing unique empirical input for the debate about the idea that federalism is by definition beneficial for democracy. We problematize our results from a democratic point of view, as—despite being able to vote—the people as a whole are hardly any more represented by the House. Going beyond the Belgian case, we argue that processes of federalization should address the adequate representation of both the constituent units and the people.

Two dimension-reduction probabilistic models for simulating nonstationary turbulent wind fields

The reasonable modeling of a nonstationary stochastic turbulent wind field is an important basis and premise for the analysis of the wind-induced response and reliability of engineering structures. In the present study, two dimension-reduction probabilistic models are established for simulating the multi-dimensional and multi-variable nonstationary turbulent wind fields based on the double proper orthogonal decomposition (DPOD) and the double spectral representation method (DSRM). Among them, the DPOD, originally used to simulate a stationary turbulent wind field, is extended to a nonstationary one, and the DSRM is a newly proposed method for a nonstationary turbulent wind field with a large number of simulation points. In essence, the DPOD is a discrete method with explicit physical significance and flexible spatial location of simulation points, while the DSRM is a continuous method, of which the simulation efficiency is theoretically independent of the number of simulation points. Furthermore, by introducing the dimension-reduction methods based on random function and POD-FFT (Fast Fourier transform) technique into the DPOD and the DSRM, the nonstationary stochastic turbulent wind field can be effectively described with merely three elementary random variables. Numerical examples of the nonstationary stochastic turbulent wind fields acting on a long-span bridge and a communication tower fully verify the effectiveness and superiority of the proposed methods.

Improving generalization of double low-rank representation using Schatten-p norm

Low-rank representation reveals a highly-informative entailment of sparse matrices, where double low-rank representation (DLRR) presents an effective solution by adopting nuclear norm. However, it is a special constraint of Schatten-p norm with p=1 which equally treats all singular values, deviating from the optimal low-rank representation that considers p=0. Thus, this paper improves the DLRR generalization of DLRR by relaxing p=1 into 0<p≤1 to tighten the low-rank constraint of the Schatten-p norm. With such a relaxation, low-rank optimization is then accelerated, resulting in a lower bound on the calculation complexity. Experiments on unsupervised feature extraction and subspace clustering demonstrate that our low-rank optimization taking 0<p≤1 achieves a superior performance against state-of-the-art methods.

Double Discriminative Constraint-Based Affine Nonnegative Representation for Few-Shot Remote Sensing Scene Classification

Remote sensing scene classification (RSSC) has recently attracted more attention. However, due to restrictions in the imaging environment and equipment, it is difficult to get a large number of labeled images in remote sensing. This has led to the emergence of few-shot learning for RSSC, which aims to achieve better performance with few labeled samples. Remote sensing images’ large interclass similarity may cause classification confusion. To overcome this issue, this study proposes a double discriminative constraints-based affine nonnegative representation for few-shot RSSC. To be specific, we devise a novel representation-based classifier with two discriminative constraint terms in the objective function and utilize affine nonnegative constraints to restrict the learned parameters. These constraints reduce the correlation between classes and strengthen the class specificity of the learned parameters. Experiments on benchmark datasets demonstrate the effectiveness of our method.

Learning Double Subspace Representation for Joint Hyperspectral Anomaly Detection and Noise Removal

Efforts to enhance the detection accuracy of hyperspectral (HS) anomaly detection (AD) have been significant, but the impact of noise resulting from HS data acquisition and transmission has not been well studied. Furthermore, the separation of denoising and subsequent interpretation makes it challenging to evaluate and control the influence of noise on the detection results. To this end, we proposed a joint anomaly detection and noise removal (ADNR) paradigm called DSR-ADNR, which develops a double subspace representation method to obtain both denoised and detection results simultaneously. DSR-ADNR uses a low-dimensional orthogonal basis to represent HS images and extract distinctive features for AD. The feature matrix is represented by a dictionary-based low-rank subspace that captures the complex nature of the low-dimensional features. In each iteration, DSR-ADNR utilizes the nonlocal self-similarity of the feature matrix to remove noise and improve intermediate detection performance. Meanwhile, the progressive LR representation of the background and anomalies for the feature matrix upgrades the explicit LR expression of nonlocal self-similar patches for better denoising. The well-designed linearized alternating direction method of multipliers with an adaptive penalty (LADMAP) is utilized to solve the proposed DSR-ADNR. Extensive experiments on simulated and real-world data sets demonstrate the effectiveness of DSR-ADNR in the HS AD task under different noise cases.

On the evaluation of the Appell F2 double hypergeometric function

The transformation theory of the Appell F2(a,b1,b2;c1,c2;x,y) double hypergeometric function is developed to obtain a set of series representations of F2 which provide an efficient way to evaluate F2 for real values of its arguments x and y and generic complex values of its parameters a,b1,b2,c1 and c2 (i.e. in the nonlogarithmic case). This study rests on a classical approach where the usual double series representation of F2 and other double hypergeometric series that appear in the intermediate steps of the calculations are written as infinite sums of one variable hypergeometric series, such as the Gauss F12 or the F23, various linear transformations of the latter being then applied to derive known and new formulas. Use of the three well-known Euler transformations of F2 on these results allows us to obtain a total of 44 series which form the basis of the Mathematica package AppellF2.wl, dedicated to the evaluation of F2. A brief description of the package and of the numerical analysis that we have performed to test it is also presented. Program summaryProgram Title: AppellF2.wlCPC Library link to program files:https://doi.org/10.17632/n9v6bwpsyd.1Licensing provisions: GPLv3Programming language: Wolfram Mathematica version 11.3 and beyondNature of problem: Numerical evaluation of the double hypergeometric Appell F2 function for real values of its variables and generic complex values of its Pochhammer parametersSolution method: Mathematica implementation of a set of transformation formulas of the Appell F2 function

Roma Kolonisi Augusta Firma’daki Kraliyet Sarayı Plaza de Armas’ın Domus I Mozaikleri – Astigi (Écija, Sevilla, İspanya) - I

The Domus I of the Plaza de Armas of the Royal Alcazar of Ecija (Seville, Spain) has been object of archaeological excavations and restoration interventions since 2001, which have revealed that this luxurious urban residence was completely reformed in the Severan period, when several rooms and the central courtyard were decorated with mosaic pavements. The first one in being unearthed was the well-known mosaic of the Satyr / Silenus, with the double representation of these two companions of Dionysus in a single head, thanks to a singular visual play. In 2015 was discovered the so-called mosaic of the Loves of Zeus, which decorate the triclinium of the domus, with several scenes from this mythological cycle, along with Bacchic themes and characters, and the representation of the seasons. More recently, in 2019-2020, the monumental central peristyle of the residence was excavated, which perimetral corridor was covered with mosaic decoration. The thematic represented in the new mosaic is varied, including several planets, meteorological phenomena or the god Dyonisus himself, together with a panel which contained a scene following a hunt –unfortunately, in this case largely lost, but still recognizable–, all framed by a singular geometric pattern. In this paper is offered the first publication of the remarkable mosaic of the peristyle, just discovered.