Principal Realization Research Articles

The dialogue between a government and society in the digital age

A dialogue between a government and society is the principal realization of which is declared in many of modern states. Though such dialogue can occur only when authorities make it possible for the mechanisms and channels of political feedback to function successfully which allows to identify, analyze, understand and take into account social demands and the current problematic field of the society while working out a political course. In the era of digitalization when the new technologies continue to permanently change the basic spheres of the society this question has become more urgent. Political-administrative sphere is not an exception and today digital technologies of political participation and governmental services providing. Though the question to what extent these steps change the essence of policy, political governing and political regimes (primarily the democracies) and the dialogue between government and society. Particularly the statement that digitalization of the political-administrative process is a step towards establishing democracy of a new type raises doubts. The latter creates opportunities for fundamentally different significant opportunities for citizens to participate in public decision-making. For answering the question, the article looks into the nature and peculiarities of a social-governmental dialogue, the gist and the principals of democracy, the limits of modifying democracy towards factual increasing of the role of the society in taking part of political administrative decision making; the possibility of realization of the principles of a deliberative democracy is being considered.

A new hybrid approach for speech synthesis: application to the Arabic language

This research is part of the automatic speech synthesis (ASS) field; it addresses a study on the voice production based on a text written in the Arabic language. Our principal purpose is the design of a new hybrid approach that integrates the advantages of artificial intelligence in the field of ASS using expert systems (ES). We describe the methodology tackled for the approach design, and we present its principal realization steps, which are summarized as follows; (1) the sound base creation based on the elaborated corpus; (2) the linguistic processing, which is responsible for the conversion of the written form of the text to its spoken form; and (3) the acoustic generation corresponding to the pre-acquired Text. The adopted approach is based on a conceptual analysis of the principal steps needed for the design of our speech synthesis ES. Finally, we present the system evaluation report and we explain the obtained results.

An equivalence between truncations of categorified quantum groups and Heisenberg categories

We introduce a simple diagrammatic 2-category $\mathscr{A}$ that categorifies the image of the Fock space representation of the Heisenberg algebra and the basic representation of $\mathfrak{sl}_\infty$. We show that $\mathscr{A}$ is equivalent to a truncation of the Khovanov--Lauda categorified quantum group $\mathscr{U}$ of type $A_\infty$, and also to a truncation of Khovanov's Heisenberg 2-category $\mathscr{H}$. This equivalence is a categorification of the principal realization of the basic representation of $\mathfrak{sl}_\infty$. As a result of the categorical equivalences described above, certain actions of $\mathscr{H}$ induce actions of $\mathscr{U}$, and vice versa. In particular, we obtain an explicit action of $\mathscr{U}$ on representations of symmetric groups. We also explicitly compute the Grothendieck group of the truncation of $\mathscr{H}$. The 2-category $\mathscr{A}$ can be viewed as a graphical calculus describing the functors of $i$-induction and $i$-restriction for symmetric groups, together with the natural transformations between their compositions. The resulting computational tool is used to give simple diagrammatic proofs of (apparently new) representation theoretic identities.

On principal realization of modules for the affine Lie algebra 𝐴₁⁽¹⁾ at the critical level

We present complete realization of irreducible A 1 ( 1 ) A_1^{(1)} –modules at the critical level in the principal gradation. Our construction uses vertex algebraic techniques, the theory of twisted modules and representations of Lie conformal superalgebras. We also provide an alternative Z-algebra approach to this construction. All irreducible highest weight A 1 ( 1 ) A_1^{(1)} –modules at the critical level are realized on the vector space M 1 2 + Z ( 1 ) ⊗ 2 M_{\tfrac {1}{2}+\mathbb {Z}}(1)^{\otimes 2} where M 1 2 + Z ( 1 ) M_{\tfrac {1}{2} + \mathbb {Z}}(1) is the polynomial ring C [ α ( − 1 / 2 ) , α ( − 3 / 2 ) , … ] {\mathbb {C}}[\alpha (-1/2), \alpha (-3/2),\dots ] . Explicit combinatorial bases for these modules are also given.

Tau functions and Virasoro symmetries for Drinfeld–Sokolov hierarchies

For each Drinfeld–Sokolov integrable hierarchy associated to affine Kac–Moody algebra, we obtain a uniform construction of tau function by using tau-symmetric Hamiltonian densities, moreover, we represent its Virasoro symmetries as linear/nonlinear actions on the tau function. The relations between the tau function constructed in this paper and those defined for particular cases of Drinfeld–Sokolov hierarchies in the literature are clarified. We also show that, whenever the affine Kac–Moody algebra is simply-laced or twisted, the tau function of the Drinfeld–Sokolov hierarchy coincides with the solution of the corresponding Kac–Wakimoto hierarchy constructed from the principal vertex operator realization of the affine algebra.

METHODOLOGY OF CONSTRUCTION OF CLASSIFIER OF THREATS TO STATE INFORMATIVE RESOURCES

On the base of the conducted analysis and research of the existent normatively-legal and Legislative providing, domestic and international standards of industry "Informative security" the question of approach of the systems is considered and the methodology of construction of general "Classifier of threats to the State informative resources" is presented. Authors are offer methodological approach, in relation to forming of classifier of threats to the state informative resources on the base of the offered method of so-called : the "Double three of defense". The informatively-analytical model of method of "double three of defense" is offered, as basis of forming of methodology taking into account the constituents of process of defense of informative resources. It is based on a modern domestic and international normatively-legal base and own scientifically-professional experience, principal conceptual items or component realization of process of "Informative security. Basic conceptual approaches of classification of threats of state informative resources (after character, type, aspiration, methods of code of threats, and others like that) are presented, the types of threats to the state informative resources of normatively-legal aspiration are exposed more in detail. Examples of classification and methods of code of threats to the state informative resources of normatively-legal aspiration are made.

Generalized Bell states and principal realization of the Yangian $Y(\mathfrak {sl}_{N})$Y(slN)

We prove that the action of the Yangian algebra $Y(\mathfrak {sl}_N)$Y(slN) is better described by the principal generators on the tensor product of the fundamental representation and its dual. The generalized Bell states or maximally entangled states are permuted by the principal generators in a dramatically simple manner on the tensor product. Under the Yangian symmetry the new quantum number $\bf J^2$J2 is also explicitly computed, which gives an explanation for these maximally entangled states.

Principal Realization of Twisted Yangian $${Y(\mathfrak{g}_{N})}$$

We give the principal realization of the twisted Yangians of orthogonal and symplectic types. The new bases are interpreted in terms of discrete Fourier transform over the cyclic group \({\mathbb Z_N}\) .

Method for Preceding Vehicle Type Classification Based on Sparse Representation

This paper proposes a novel vehicle-type classifier named SRCVT that uses video data collected from video detection units. The SRCVT uses the sparse representation classifier (SRC) technique without the requirement of an additional training procedure to construct the classification model. It classifies preceding vehicles directly from the testing samples’ sparse representation, without the need for explicit model selection. The SRCVT consists of four steps: data preparation, principal component analysis transformation, realization, and classification output. The classifier has been compared with the traditional method of using a supported vector machine. The results show that the SRCVT is more promising for vehicle-type classification in terms of classification accuracy and ease of use.

Soliton equations, vertex operators, and simple singularities

We prove the equivalence of two hierarchies of soliton equations associated to a simply-laced finite Dynkin diagram. The first was defined by Kac and Wakimoto (Proc. Symp. Pure Math. 48:138–177, 1989) using the principal realization of the basic representations of the corresponding affine Kac–Moody algebra. The second was defined in Givental and Milanov (The Breadth of Symplectic and Poisson Geometry, Progress in Mathematics, vol. 232, pp. 173–201, Birkhäuser, Basel, 2005) using the Frobenius structure on the local ring of the corresponding simple singularity. We also obtain a deformation of the principal realization of the basic representation over the space of miniversal deformations of the corresponding singularity. As a by-product, we compute the operator product expansions of pairs of vertex operators defined in terms of Picard–Lefschetz periods for more general singularities. Thus, we establish a surprising link between twisted vertex operators and deformation theory of singularities.

A remark on Kac–Wakimoto hierarchies of D-type

For the Kac–Wakimoto hierarchy constructed from the principal vertex operator realization of the basic representation of the affine Lie algebra D(1)n, we compute the coefficients of the corresponding Hirota bilinear equations, and verify the coincidence of these bilinear equations with the ones that are satisfied by Givental's total descendant potential of the Dn singularity, as conjectured by Givental and Milanov (2005 Simple singularities and integrable hierarchies The Breadth of Symplectic and Poisson Geometry (Prog. Math. vol 232) (Boston: Birkhäuser) pp 173–201).

Acoustic vowel space in pre‐/r/ contexts: Shetland and American English.

The acoustic space available to vowel systems in pre‐/r/ contexts commonly differs from that of other phonetic contexts. In English this space has gradually shrunk, which relates to changes in the phonetic nature of /r/, having gone from more consonantal articulations (tap, trill) to approximant and often complex articulations that have a stronger effect on the production and perception of adjacent vowels (e.g., “bunched” and retroflex /r/). This paper contains an acoustic study of pre‐/r/ vowel systems in Shetland and American English. F1–F3 values were obtained from steady state vowel portions from words spoken in isolation. The acoustic vowel spaces and the positions of contrastive items within these are compared and discussed in relation to the phonetic nature of /r/ and its effects on vowel formants. In contrast to American English, Shetland maintains a trill or tap as the principal realization of /r/, and the full range of vowel contrasts found elsewhere is supported before /r/. As Shetland is one of the most conservative English dialects in this respect, the study may also offer some insight into the acoustic characteristics of English pre‐/r/ vowel systems of earlier periods and the pressures affecting such systems.

Principal realization of the Yangian Y(gl(n))

Motivated to simplify the structure of tensor representations we give a new set of generators for the Yangian Y(sl(n)) using the principal realization in simple Lie algebras. The isomorphism between our new basis and the standard Cartan–Weyl basis is also given. We show by example that the principal basis simplifies the Yangian action significantly in the tensor product of the fundamental representation and its dual.

Calculation of vibration reduction design for underground sources

The problems of ecology situation control near intensive underground acoustical sources is considered. Studied vibration absorbers are modeled by multi-component system of connected oscillators with damping. Obtained oscillatory equation system was investigated numerically. Frequency dependencies of absorbers efficiency have been calculated. An influence of the physical-mechanical parameters of the surrounding ground on the value of vibration reduction has been determined. Some variants of principal realization of vibration absorbers for the case of underground railway are discussed. [Work supported by Russian Foundation for Basic Researches Grants Nos. 01-02-16127, 02-02-17143.]

Representations of Extended Affine Lie Algebras Coordinatized by Certain Quantum Tori

An irreducible representation of the extended affine Lie algebra of type An-1 coordinatized by a quantum torus of ν variables is constructed by using the Fock space for the principal vertex operator realization of the affine Lie algebra \(\widehat{gl}_N \).

Hirota bilinear forms with 2-toroidal symmetry

We compute Hirota bilinear forms arising from both homogeneous and principal realization of vertex representations of 2-toroidal Lie algebras of type A l , D l , E l .

Combinatorial description of the Fock representation of the affine lie algebra go(?)

Symmetric function techniques are applied to the vertex operator of the BKP hierarchy to give a combinatorial interpretation of the Fock representation of go(∞). From this follows a combinatorial description of the basic representations of the ‘twisted’ affine Lie algebrasA2n(2) andDn+1(2) in the principal realization. The Fock representation of go(∞) is easily converted to a representation of the quantum enveloping algebra Uq(go(∞)).

On a new hierarchy associated with the W 3(2) conformal algebra

In a realization of the Kac-Moody algebra A 2 (1) intermediate between the homogeneous and the principal realization, an integrable hierarchy of differential equations is constructed. The hierarchy shares features of both the AKNS and the KdV hierarchies. The same hierarchy can also be constructed using the Drinfeld-Sokolov approach in terms of zero curvature conditions, with as hamiltonian structure the W 3 (2) algebra of Polyakov and Bershadsky. It provides evidence for the conjecture that there exists a general relation between hierarchies constructed in some intermediate realization and the covariantly coupled chiral algebras of Bais, Tjin and van Driel.

Norms of principal axis realizations: Application of abstract realization theory

Principal axis realizations are an important class of implementations, associated with good numerical properties. The spectral (l/sub 2/) norm of the principal axis realization matrices of arbitrary transfer functions is studied. In particular, it is shown that if the transfer function is contractive, then its principal axis realization matrices have a norm less than square root 2, while the internally balanced realization is conjectured to have a norm of less than 1. Furthermore, if the transfer function is an all-pass transfer function, then the three principal axis realizations become identical and equal to an orthogonal matrix. Abstract realization theory is used to prove these results. >

On endomorphism rings of non-separable abelian p-groups

There have been spectacular advances in recent years in the so-called realization problem for certain classes of abelian groups and modules. The advances have derived mainly from powerful combinatorial set-theoretic tools pioneered by Shelah. In the case of separable abelian p-groups these results appear, e.g., in [ 1,4, 51. For non-separable abelian p-groups the most significant contribution has been [2]. Our objective in this paper is to extend the results in [2] and derive analogous results to those obtained in [4, 51. It is perhaps worth pointing out that our methods are entirely algebraic; the necessary set-theoretical work has been carried out in the separable case and no further set-theoretical arguments are needed. In this the work is reminiscent of [S]. All our set theory (with one exception) is in ZFC and this is not acknowledged in the statement of individual results. In the exceptional case where we work in Godel’s Constructible Universe (V= L) this is acknowledged by appending (V= L) after the statement number. The principal realization result can be stated as: