Projection Of Vector Research Articles

Assessing the coordination of regional water and soil resources and ecological-environment system based on speed characteristics

The evaluation of the coordination of regional water and soil resources and ecological environment systems from the perspective of speed characteristics is more conducive to decision-makers to understand the development status of water and soil resources and ecosystems in a timely manner. In this paper, taking Heilongjiang Province, the main grain producing area of China, as an example, 25 main indices are screened based on agricultural production factors and the weight of each index is determined by the information entropy, the speed characteristics of each index is characterized by the average annual growth rate. The coupling-coordination index of system development is determined by the vector angle and projection, and compare and analyze the coupling-coordination index between the result and the original data. The results show that the water and soil resources ecological environment system was in a relatively weak coupling stage of barely coordination, the coordinated development level of the system is low during the study period. In comparison with the original data results, the coupling and coordination of the system are better reflected by the calculation method using speed characteristics, and the calculation results of speed characteristics are ahead of time, which is more conducive to the timely assessment of the development of the water and soil resources ecological-environment system.

Dual Hashing Index Cancellable Finger Vein Template Based on Gaussian Random Mapping

In the existing cancellable finger vein template protection schemes, the original biometric features cannot be well protected, which results in poor security. In addition, the performance of matching recognition performances after generating a cancellable template is poor. Therefore, a dual hashing index cancellable finger vein template protection based on Gaussian random mapping is proposed in this study. The scheme is divided into an enrollment stage and a verification stage. In the two stages, symmetric data encryption technology was used to generate encryption templates for matching. In the enrollment stage, first, the extracted finger vein features were duplicated to obtain an extended feature vector; then, this extended vector was uniformly and randomly permuted to obtain a permutation feature vector. The above two vectors were combined into a two-dimensional feature matrix. The extended and permuted feature vector made full use of the original biometric features and further enhanced the non-invertibility. Second, a random Gaussian projection vector with m×q dimensions was generated, and a random orthogonal projection matrix was generated by the Schmidt orthogonalization of the previously generated random vector. This approach accurately transferred the characteristics of the biometric features to another feature space and ensured that the biological template is revocable. Finally, the inner product of the two-dimensional feature vector and random orthogonal projection matrix was obtained and superimposed into a row. The dual index values of the largest and second largest values were repeated m times to obtain a hash code for matching. The secondary maximum value index was introduced to adjust the error generated by the random matrix, which improved the recognition rate of the algorithm. In the verification stage, another hash code for matching was generated based on symmetric data encryption technology, and then the two hash codes were cross matched to obtain the final matching result. The experimental results show that this scheme attains good recognition performance with the PolyU and SDUMLA-FV databases, that it meets the design standard for cancellable biometric identification, and that it is robust to security and privacy attacks.

Gravitational memory and compact extra dimensions

We develop a general formalism for treating radiative degrees of freedom near ${\mathcal{I}}^{+}$ in theories with an arbitrary Ricci-flat internal space. These radiative modes are encoded in a generalized news tensor which decomposes into gravitational, electromagnetic, and scalar components. We find a preferred gauge which simplifies the asymptotic analysis of the full nonlinear Einstein equations and makes the asymptotic symmetry group transparent. This asymptotic symmetry group extends the Bondi--Metzner--Sachs (BMS) group to include angle-dependent isometries of the internal space. We apply this formalism to study memory effects, which are expected to be observed in future experiments, that arise from bursts of higher-dimensional gravitational radiation. We outline how measurements made by gravitational wave observatories might probe properties of the compact extra dimensions.

Ricci almost solitons with associated projective vector field

Abstract A Ricci almost soliton whose associated vector field is projective is shown to have vanishing Cotton tensor, divergence-free Bach tensor and Ricci tensor as conformal Killing. For the compact case, a sharp inequality is obtained in terms of scalar curvature.We show that every complete gradient Ricci soliton is isometric to the Riemannian product of a Euclidean space and an Einstein space. A complete K-contact Ricci almost soliton whose associated vector field is projective is compact Einstein and Sasakian.

Conjugate gradient persymmetric adaptive matched filter

The rank corresponding to interferences and clutter is commonly much smaller than the size of the covariance matrix due to the sparsity of detection environment, which results in the approximate low-rank correction structure of the transformed estimated covariance matrix in the persymmetric adaptive matched filter (PS-AMF). As a result, the conjugate gradient (CG) algorithm is an efficient iterative algorithm in the calculation of the weight vector of PS-AMF and produces the projection of PS-AMF weight vector to the Krylov subspace with the dimension increasing with the CG iterations. Therefore, we focus on the case that CG algorithm is used in PS-AMF in this paper, which leads to a family of reduced-rank detectors in Krylov subspace for PS-AMF. These detectors are referred to as the CG-PS-AMF detectors. Firstly, the expected value of the output signal-to-interference-and-noise ratio (SINR) of CG-PS-AMF detector is analyzed, and then its approximation expression is given. Finally, numerical results are presented to verify our theoretical analysis of CG-PS-AMF. Meanwhile, compared with its counterparts, CG-PS-AMF detector shows better detection performance. Besides, it is shown that CG-PS-AMF has a low computational cost.

КОНЦЕПТ БОЛЮ ЯК РЕПРЕЗЕНТАНТ ФРУСТРАЦІЙНИХ ПРОЦЕСІВ МОВНОЇ ОСОБИСТОСТІ (НА МАТЕРІАЛІ ПОЕТИЧНИХ ТВОРІВ СВІТЛАНИ ЙОВЕНКО)

The article outlines expression of the conceptual of linguistic personality in poetic works by the Ukrainian author Svitlana Yovenko. The sphere of concepts of linguistic personality is formed at the stage of conceptualization and categorization where the worldview is designed by means of language and representation of sphere of concepts finds expression at the verbal and semantic level. Decoding of the latter occurs occurs through the analysis of the character’s individual lexicon. Different physical and psychological states characteristic to the image of linguistic personality are displayed in the conceptual sphere. It was revealed that the conceptual sphere of PAIN is the basis for creating a picture of the world of her work, which comprehensively presents the negative state of the linguistic personality on both the physical and psychological levels. One of its dominant psychological states rendered on verbal and semantic level is pain as a universal sign of destructive interaction between an organism and the world around. Hence, protective mechanisms represented by introjection and extrajection become universalistic ways for overcoming it. S. Yovenko’s poetry represents construal of the linguistic personality image. It is revealed that the conceptual sphere PAIN is based on categorial and lexical semes that represent the condition of linguistic personality frustration. The conceptual sphere is formed by means of detecting protective mechanisms shown clearly through confluent and projective vectors in verses by S. Yovenko. Confluent vector of linguistic personality state which is dominating by the width of semantic expression and completeness of descriptions is revealed through substantial (lexis for space, concreteness, ontic identification) and processual lexeme semantics. Projective vector finds its reflection through substantive (ontical, abstract), processual semantics focusing on actions, signs, feelings of object.

A High-dimensional Outlier Detection Approach Based on Local Coulomb Force

Traditional outlier detections are inadequate for high-dimensional data analysis due to the interference of distance tending to be concentrated (curse of dimensionality). Inspired by the Coulombs law, we propose a new high-dimensional data similarity measure vector, which consists of outlier Coulomb force and outlier Coulomb resultant force. Outlier Coulomb force not only effectively gauges similarity measures among data objects, but also fully reflects differences among dimensions of data objects by vector projection in each dimension. More importantly, Coulomb resultant force can effectively measure deviations of data objects from a data center, making detection results interpretable. We introduce a new neighborhood outlier factor, which drives the development of a high-dimensional outlier detection algorithm. In our approach, attribute values with a high deviation degree is treated as interpretable information of outlier data. Finally, we implement and evaluate our algorithm using the UCI and synthetic datasets. Our experimental results show that the algorithm effectively alleviates the interference of Curse of Dimensionality. The findings confirm that high-dimensional outlier data originated by the algorithm are interpretable.

Multipole-moment effects in ion-molecule reactions at low temperatures: part II - charge-quadrupole-interaction-induced suppression of the He+ + N2 reaction at collision energies below kB·10 K.

We report on an experimental and theoretical investigation of the He+ + N2 reaction at collision energies in the range between 0 and kB·10 K. The reaction is studied within the orbit of a highly excited Rydberg electron after merging a beam of He Rydberg atoms (He(n), n is the principal quantum number), with a supersonic beam of ground-state N2 molecules using a surface-electrode Rydberg–Stark decelerator and deflector. The collision energy Ecoll is varied by changing the velocity of the He(n) atoms for a fixed velocity of the N2 beam and the relative yields of the ionic reaction products N+ and N2+ are monitored in a time-of-flight mass spectrometer. We observe a reduction of the total reaction-product yield of ∼30% as Ecoll is reduced from ≈kB·10 K to zero. An adiabatic capture model is used to calculate the rotational-state-dependent interaction potentials experienced by the N2 molecules in the electric field of the He+ ion and the corresponding collision-energy-dependent capture rate coefficients. The total collision-energy-dependent capture rate coefficient is then determined by summing over the contributions of the N2 rotational states populated at the 7.0 K rotational temperature of the supersonic beam. The measured and calculated rate coefficients are in good agreement, which enables us to attribute the observed reduction of the reaction rate at low collision energies to the negative quadrupole moment, Qzz, of the N2 molecules. The effect of the sign of the quadrupole moment is illustrated by calculations of the rotational-state-dependent capture rate coefficients for ion–molecule reactions involving N2 (negative Qzz value) and H2 (positive Qzz value) for |J, M〉 rotational states with J ≤ 5 (M is the quantum number associated with the projection of the rotational angular momentum vector J⃑ on the collision axis). With decreasing value of |M|, J⃑ gradually aligns perpendicularly to the collision axis, leading to increasingly repulsive (attractive) interaction potentials for diatomic molecules with positive (negative) Qzz values and to reaction rate coefficients that decrease (increase) with decreasing collision energies.

Interpretation of Λ hyperon spin polarization measurements

A new global polarization measurement method based on the projection of the polarization vector on the properly defined system’s orbital angular momentum in the Λ hyperon’s rest frame is briefly described. The advantages of the new method over the standard procedure are discussed.

A moment closure based on a projection on the boundary of the realizability domain: Extension and analysis

<p style='text-indent:20px;'>A closure relation for moments equations in kinetic theory was recently introduced in [<xref ref-type="bibr" rid="b38">38</xref>], based on the study of the geometry of the set of moments. This relation was constructed from a projection of a moment vector toward the boundary of the set of moments and corresponds to approximating the underlying kinetic distribution as a sum of a chosen equilibrium distribution plus a sum of purely anisotropic Dirac distributions.</p><p style='text-indent:20px;'>The present work generalizes this construction for kinetic equations involving unbounded velocities, i.e. to the Hamburger problem, and provides a deeper analysis of the resulting moment system. Especially, we provide representation results for moment vectors along the boundary of the moment set that implies the well-definition of the model. And the resulting moment model is shown to be weakly hyperbolic with peculiar properties of hyperbolicity and entropy of two subsystems, corresponding respectively to the equilibrium and to the purely anisotropic parts of the underlying kinetic distribution.</p>

The generalized Wiener–Hopf equations for the elastic wave motion in angular regions

In this work, we introduce a general method to deduce spectral functional equations in elasticity and thus, the generalized Wiener–Hopf equations (GWHEs), for the wave motion in angular regions filled by arbitrary linear homogeneous media and illuminated by sources localized at infinity. The work extends the methodology used in electromagnetic applications and proposes for the first time a complete theory to get the GWHEs in elasticity. In particular, we introduce a vector differential equation of first-order characterized by a matrix that depends on the medium filling the angular region. The functional equations are easily obtained by a projection of the reciprocal vectors of this matrix on the elastic field present on the faces of the angular region. The application of the boundary conditions to the functional equations yields GWHEs for practical problems. This paper extends and applies the general theory to the challenging canonical problem of elastic scattering in angular regions.

Berry–Esseen bounds for random projections of $\ell _p^n$-balls

We study the rate of convergence in the central limit theorem for the Euclidean norm of random orthogonal projections of vectors chosen at random from an $\ell _p^n$-ball which has been obtained in [D. Alonso-Gutiérrez et al., Bernoulli 25 (2019)]. More p

Metric connection on tangent bundle with Berger-type deformed Sasaki metric

Let $TM$ be the tangent bundle over an almost antipara-Hermitian manifold endowed with Berger-type deformed Sasaki metric $% ^{BS}g$. In this paper, we introduce the deformed Sasaki metric which Berger-type and study the metric connection of this metric on the tangent bundle. We give some curvature properties of this metric and characterization of projective vector field which preserving the fiber of $\left( TM, ^{BS}g\right) $. Next, we present some geometric results concerning them.

A new fuzzy and Gaussian distribution induced two-directional inverse FDA for feature extraction and face recognition

In the area of face recognition research, the high dimensionality of the data is indeed a crucial problem. This paper proposes a new fuzzy and Gaussian distribution induced two-directional inverse Fisher's discriminant analysis (FGD-2DIFDA) which computes the fuzzy and Gaussian distribution membership values and thereby combined the values with the training samples to obtain the class-wise mean and the global mean. These fuzzy and Gaussian function induced membership values are incorporated in inter- and intra-class scatter matrices for diminishing the effect of uncertainty formed by variation of light facial expression and pose. Finally, the eigenvalue problems of the inverse Fisher's criteria are solved to finds the optimal inverse projection vectors. The uncertainty associated in the image region is efficiently managed by the FGD-2DIFDA method than fuzzy generalised 2DFLD (FG-2DFLD) method as two membership values are employed in the former case while the later one uses only one membership value to handle such situation. The FGD-2DIFDA method has been evaluated on the AT&T (formally known as ORL), UMIST and FERET face databases using support vector machine (SVM) as classifier. Simulation results demonstrate that the proposed FGD-2DIFDA method can obtain higher recognition rate than some state-of-the-art face recognition methods.

Фразеографический потенциал «Большого универсального словаря русского языка»

The article presents the results of a study of the phraseological parameter of the Big Universal Dictionary of the Russian Language (V.V. Morkovkin, G.F. Bogacheva, N.M. Lutskaya, 2016) in paper format. Phraseological units (henceforth PUs) as the content of the phraseological zone marked in the structure of the dictionary entry by a rhombus (◊) served as the basis for the study. The aim is to reveal features of the headword representativeness as a key structural-semantic component of the phraseological zone and determine the research potential of the phraseological array of the Dictionary. A wide projection of phraseography is one of the characteristics of the Dictionary’s universality. The phraseological zones of the Dictionary are represented as PUs with different degrees of idiomaticity, as well as nominative and communicative units with the capacity for reproducibility in an unchanged composition. This approach is justified by the expansion of the phraseological base in modern lexicographic projects. The structural-semantic multiplicity of the headword as a component of a PU determines the universality of the phraseological zone’s content representativeness. The use of “multipath” references to a variety of dictionary entries, how many components a PU has, determines the vector projection to a wider range of types of figurative nominations. At the same time, the phraseological definition is presented only in the structure of a single dictionary entry where the headword acts as a key structural-semantic component of a PU. In phraseological zones as part of a peculiar linguistic corpus of the Russian language, a set of PUs has many aspects. Optional lexical and variant components of PUs are indicated. Words a PU usually collocates with are given. There are notes indicating the expressive-stylistic and evaluative functions of a PU; grammatical notes describing some morphological properties of the lexical components of a PU. An interpretation/meaning of a PU, or a reference to the headword in which the content of the PU is considered, is given. If there is a semantic identity, synonyms are provided. The phraseological zone may contain examples of a PU’s uses in speech and commentaries of a cognitive nature. The phraseographic objectification of the receptivity of the lexicalsemantic variant of the headword is strongly represented by compound terms and names that objectify human discursive activity. Phraseological zones in the structure of entries in which homonymic units act as headwords can become one of the potential vectors of studying phraseology. A single presentation of a phraseological definition in the dictionary shows a typical situation/situations of using PUs and is a potential linguistic material for studies in the cognitivediscursive direction.

An accurate full-dimensional H4O potential energy surface and dynamics of an exchange reaction.

H2O and H2 are ubiquitous in the universe and their collisions play a crucial role in astrophysical processes. The reaction between the two also provides a prototype for understanding dynamics through four-center transition states. In this work, we adopted a strategy of combing two ab initio methods, CCSD(T)-F12a/AVTZ and MRCI-F12 + Qrot/AVTZ, to provide a balanced description for all regions of the configuration space, including one hydrogen exchange channel and two dissociation channels, namely H2 + H2O, H + H + H2O, and H + OH + H2. About 40 500 points were sampled to cover all dynamically relevant space, and the permutation invariant polynomial-neural network (PIP-NN) method was employed to develop a high-precision full-dimensional potential energy surface (PES), with a total fitting error of 0.055 kcal mol-1. Using a quasi-classical trajectory (QCT) method, the reaction dynamics and mode specificity of the hydrogen exchange channel were studied on the PES. It has been found that the stretching mode of H2, the bending, the symmetric stretching, the asymmetric stretching mode of H2O, and the translational mode can all promote reactivity. The strongest promotion effect comes from the H-H stretching mode. The Sudden Vector Projection (SVP) model was applied to predict mode specificity effects and rationalize the product energy partitioning. In both cases, the QCT and SVP results are generally consistent with each other. Furthermore, the hydrogen exchange channel was found to be dominated by sideways scattering.

Broadband reduction of phase noise in a spatially extended tunnel‐diode oscillator through multiple self‐injection locking

SummaryA self‐injection locking scheme is proposed to reduce phase noise in a spatially extended oscillator that uses a tunnel‐diode (TD) transmission line. When a linear transmission line is connected to each cell of the TD line, a part of the oscillating edge flows through the linear line. This wave on the linear line is reflected at its far end and flows back to the point of connection of the TD and linear transmission lines. By matching the time taken by the reflected wave on the linear transmission line to reach the point of connection with the time taken by the forward‐moving oscillating edge to return to the point, the edge can be synchronized with the wave that flows back through each linear line. This multiple self‐injection locking significantly reduces the phase noise of the oscillating edge. In this work, the technique of phase noise reduction is explained through numerical phase noise analysis using the perturbation projection vector of the system. Several experimental observations were made to validate the reduction of the phase noise in the oscillating edge traveling on the TD line.

CONSTRUCTION OF ROTOR ANGLE IDENTIFIER IN VECTOR CONTROL SYSTEMS OF DOUBLE FEED MACHINES

In asynchronous electric drives with vector control on the rotor, it is necessary to calculate the value of the sine and cosine of the angle of rotation of the rotor relative to the stator to form control actions. When using angle sensors, complex structural tasks can arise — placement and reliable mounting of the sensor on the shaft and, accordingly, the task of the overall layout of the unit. For high-power machines, the tasks of developing and creating the design of the sensor itself arise. If serial rotor angular position sensors can be used, the task of placing and mounting the sensor is no less difficult. In these cases it is necessary to deduce the second end of a shaft from the case of the engine with contact rings that complicates its design. Therefore, the urgent need to create more reliable electric drives with vector control systems on the rotor is the synthesis of identifiers of the angle of rotation of the rotor.
 Identifiers are known whose calculation algorithms are based on determining the projections of the flow coupling vectors. In the work with the use of coordinate transducers of projections of stator or rotor current vectors and equations of electromagnetic circuits of an asynchronous machine, the synthesis and subsequent analysis of the properties of the rotor position angle identifier in vector control systems of dual power machines is performed. New equations of the identifier of flux couplings are received, its stability is investigated and on conditions of stability types of electric drives in which it is possible to apply the offered identifier are defined. The stability of the vector control system and sufficient identification accuracy when using the proposed equations and functions are confirmed by the method of mathematical modeling of the recommended electric drive systems in different operating modes.

Wave-optical study of the Einstein cross formed by a quadrupole gravitational lens

We study imaging of point sources with a quadrupole gravitational lens while focusing on the formation and evolution of the Einstein cross formed on the image sensor of an imaging telescope. We use a new type of a diffraction integral that we developed to study generic, opaque, weakly aspherical gravitational lenses. To evaluate this integral, we use the method of stationary phase that yields a quartic equation with respect to a Cartesian projection of the observer's position vector with respect to the vector of the impact parameter. The resulting quartic equation can be solved analytically using the method first published by Cardano in 1545. We find that the resulting solution provides a good approximation of the electromagnetic (EM) field almost everywhere in the image plane, yielding the well-known astroid caustic of the quadrupole lens. The sole exception is the immediate vicinity of the caustic boundary, where a numerical treatment of the diffraction integral yields better results. We also convolve the quartic solution for the EM field on the image plane with the point-spread function of a thin lens imaging telescope. By doing so, we are able to explore the direct relationship between the algebraic properties of the quartic solution for the EM field, the geometry of the astroid caustic, and the geometry and shape of the resulting Einstein-cross that appear on the image plane of the thin lens telescope. The new quartic solution leads to significant improvements in numerical modeling as evaluation of this solution is computationally far less expensive than a direct numerical treatment of the new diffraction integral. In the case of the solar gravitational lens (SGL), the new results drastically improve the speed of numerical simulations related to sensitivity analysis performed in the context of high-resolution imaging of exoplanets.

An asymptotic thin shell condition and large deviations for random multidimensional projections

It is well known that fluctuations of marginals of high-dimensional random vectors that satisfy a certain concentration estimate called the thin shell condition are approximately Gaussian. In this article we identify a general condition on a sequence of high-dimensional random vectors under which one can identify the exponential decay rate of large deviation probabilities of the corresponding sequence of marginals. More precisely, consider the projection of an n-dimensional random vector onto a random kn-dimensional basis, kn≤n, drawn uniformly from the Haar measure on the Stiefel manifold of orthonormal kn-frames in Rn, in three different asymptotic regimes as n→∞: “constant” (kn=k), “sublinear” (kn→∞ but kn/n→0) and “linear” (kn/n→λ with 0<λ≤1). When the sequence of random vectors satisfies a certain “asymptotic thin shell condition”, we establish large deviation principles for the corresponding sequence of random projections in the constant regime, and for the sequence of empirical measures of the coordinates of the random projections in the sublinear and linear regimes. We also establish large deviation principles for scaled ℓq norms of the random projections in all three regimes. Moreover, we show that the asymptotic thin shell condition holds for various sequences of random vectors of interest, including the uniform measure on suitably scaled ℓpn balls, for p∈[1,∞), and generalized Orlicz balls defined via a superquadratic function, as well as a class of Gibbs measures with superquadratic interaction potential. Along the way, we obtain logarithmic asymptotics of volumes of high-dimensional Orlicz balls, which may be of independent interest. We also show that the decay rate of large deviation probabilities of Euclidean norms of multi-dimensional projections of ℓpn balls, when p∈[1,2), exhibits an unexpected phase transition in the sublinear regime, thus disproving an earlier conjecture due to Alonso-Gutiérrez et al. Random projections of high-dimensional random vectors are of interest in a range of fields including asymptotic convex geometry and high-dimensional statistics.