Representation Of Operators Research Articles

Репрезентация специальной военной операции в печатных СМИ в контексте консолидации российского общества

Introduction. Obtaining up-to-date sociological information about the specifics of the representation of the special military operation currently being carried out by the Russian Federation in the print media is actualized by the tasks of integration and consolidation of Russian society in a hybrid reality. Considering the media as the most important institution for the formation of public opinion, the authors rely on the theory of information society and communicative action, consider the informational and communicative sphere as determining in the construction of trends in the social and political process. Methods. The empirical study was conducted by the method of quantitative and qualitative content analysis and critical discourse analysis in the period from 08/21/2022 to 10/21/2022. The general totality is 484 articles, the sample is 105 articles. Results and its discussion. Based on the quantitative and qualitative analysis of publications, the authors identified 4 thematic clusters and their content characteristics: military reports (26%), events around the special military operation (SMO) (30%), partial mobilization (28%) and peaceful life under the SMO (16%). Using the method of critical discourse analysis, the dominant discourses replicated in the media (wars, victories, everyday life and normalization of the military situation, heroization of the SMO, sacrifice, struggle, unity), as well as the main strategies for the representation of the SMO were identified, the emotional load for each cluster was revealed. It is shown that the emotional tone of publications worsened before the announcement of partial mobilization in connection with the Ukrainian counteroffensive, became positively neutral after the announcement of partial mobilization and was further characterized by instability. On the basis of the discursive strategies identified, it is concluded that the dominant image of SMO as a just and liberating action, based on an appeal to the experience of the Great Patriotic War, determines the direction of integration of Russian society and its consolidation with the authorities. Possible risks of consolidation based on the restriction of the space of free discussion may be associated with a decrease in the level of trust in the authorities and an increase in the conflict of society in the future.

Matrix representation of operations on graphs

This article considers the possibility of matrix execution of both unary and binary operations on graphs. Graphs, as an abstract mathematical construction, have a very wide range of practical applications. First of all, it is algorithmization and computer processing of information, electrical engineering, etc. Therefore, it is important to have a mathematical apparatus that allows you to transform the graphical presentation of information about objects into algebraic models for their further research using purely mathematical methods. If necessary, it is always possible to return from such an algebraic model to a graphical representation of the object (for example, to a graphical representation of a circuit diagram in electronics). For each of the considered operations on graphs, either a combination of algebraic operations or an easily programmable matrix processing algorithm is proposed, which can be used to represent any graph. Attention is also paid to the differences in such processing depending on the type of graphs involved in the considered operations. Some operations are more convenient to perform with adjacency matrices, and some - with incidence matrices. This article also considers these features of matrix execution of operations on graphs. All the proposed algorithms are illustrated with specific detailed examples. Thus, it is shown that for all operations on graphically presented objects, their matrix interpretation is possible. This result greatly facilitates the possibility of software implementation of work with such graphic objects.

Operator Representation and Class Transitions in Elementary Cellular Automata

We exploit the mirror and complementary symmetries of elementary cellular automata (ECAs) to rewrite their rules in terms of logical operators. The operator representation based on these fundamental symmetries enables us to construct a periodic table of ECAs that maps all unique rules in clusters of similar asymptotic behavior. We also expand the elementary cellular automaton (ECA) dynamics by introducing a parameter that scales the pace with which operators iterate the system. While tuning this parameter continuously, further emergent behavior in ECAs is unveiled as several rules undergo multiple phase transitions between periodic, chaotic and complex (class 4) behavior. This extension provides an environment for studying class transitions and complex behavior in ECAs. Moreover, the emergence of class 4 structures can potentially enlarge the capacity of many ECA rules for universal computation.

On Momentum Operators Given by Killing Vectors Whose Integral Curves Are Geodesics

The paper considers momentum operators on intrinsically curved manifolds. Given that momentum operators are Killing vector fields whose integral curves are geodesics, the corresponding manifold is flat or of the compact type with positive constant sectional curvature and dimensions equal to 1, 3, or 7. Explicit representations of momentum operators and the associated Casimir element are discussed for the 3-sphere S3. It is verified that the structural constants of the underlying Lie algebra are proportional to 2 ℏ/R, where R is the curvature radius of S3 and ℏ is the reduced Planck’s constant. This results in a countable energy and momentum spectrum of freely moving particles in S3. The maximal resolution of the possible momenta is given by the de Broglie wave length, λR=πR, which is identical to the diameter of the manifold. The corresponding covariant position operators are defined in terms of geodesic normal coordinates, and the associated commutator relations of position and momentum are established.

Mapping renormalized coupled cluster methods to quantum computers through a compact unitary representation of nonunitary operators

Nonunitary theories are commonly seen in the classical simulations of quantum systems. Among these theories, the method of moments of coupled cluster equations (MMCCs) and the ensuing classes of the renormalized coupled cluster (CC) approaches have evolved into one of the most accurate approaches to describe correlation effects in various quantum systems. The MMCC formalism provides an effective way for correcting the energies of approximate CC formulations (parent theories) using moments, or CC equations, that are not used to determine approximate cluster amplitudes. In this paper, we propose a quantum algorithm for computing MMCC ground-state energies that provides two main advantages over classical computing or other quantum algorithms: (i) the possibility of forming superpositions of CC moments of arbitrary ranks in the entire Hilbert space and using an arbitrary form of the parent cluster operator for MMCC expansion, and (ii) significant reduction in the number of measurements in quantum simulation through a compact unitary representation for a generally nonunitary operator. We illustrate the robustness of our approach over a broad class of test cases, including $\ensuremath{\sim}40$ molecular systems with varying basis sets encoded using 4--40 qubits, and we exhibit the detailed MMCC analysis for the 8-qubit half-filled, four-site, single impurity Anderson model and the 12-qubit hydrogen fluoride molecular system from the corresponding noise-free and noisy MMCC quantum computations. We also outline the extension of the MMCC formalism to the case of a unitary CC wave-function Ansatz.

Trace Formulas for Schrödinger Operators on a Lattice

We consider Schr\"odinger operators with periodic potentials on periodic discrete graphs. Their spectrum consists of a finite number of bands. We determine trace formulas for the Schr\"odinger operators. The proof is based on the decomposition of the Schr\"odinger operators into a direct integral and a specific representation of fiber operators. The traces of the fiber operators are expressed as finite Fourier series of the quasimomentum. The coefficients of the Fourier series are given in terms of the potentials and cycles in the quotient graph from some specific cycle sets. We also present the trace formulas for the heat kernel and the resolvent of the Schr\"odinger operators and the determinant formulas.

Financial Interpretation of Feller’s Factorization

The infinitesimal generator of a time-homogeneous univariate diffusion process is a second-order linear ordinary differential operator. Feller (1952) famously factorized this generator into successive differentiations with respect to scale and speed measure. Later, Feller (1957) also factored an extended generator that loads also on the identity operator in a particular way. We provide a novel financial interpretation of these factorization results and show that they produce an operator representation of a conditionally linear risk-return tradeoff when the conditioning variable evolves like a one-dimensional diffusion process.

A recursive formulation of one‐electron coupling coefficients for spin‐adapted configuration interaction calculations featuring many unpaired electrons

AbstractThis work reports on a novel computational approach to the efficient evaluation of one‐electron coupling coefficients as they are required during spin‐adapted electronic structure calculations of the configuration interaction type. The presented approach relies on the equivalence of the representation matrix of excitation operators in the basis of configuration state functions and the representation matrix of permutation operators in the basis of genealogical spin eigenfunctions. After the details of this connection are established for every class of one‐electron excitation operator, a recursive scheme to evaluate permutation operator representations originally introduced by Yamanouchi and Kotani is recapitulated. On the basis of this scheme we have developed an efficient algorithm that allows the evaluation of all nonredundant coupling coefficients for systems with 20 unpaired electrons and a total spin of within only a few hours on a simple Desktop‐PC. Furthermore, a full‐CI implementation that utilizes the presented approach to one‐electron coupling coefficients is shown to perform well in terms of computational timings for CASCI calculations with comparably large active spaces. More importantly, however, this work paves the way to spin‐adapted and configuration driven selected configuration interaction calculations with many unpaired electrons.

Unmanned? Military Masculinities in Filmic Representations of US Drone Operators

Drones have become the new face of American warfare, challenging institutional and cultural norms about what it means to be a soldier. In the context of military masculinities, I examine the representation of the US drone operators in three films: Drones (Rosenthal 2013), Good Kill (Niccol 2014), and Eye in the Sky (Hood 2015). The films feature a male-female team of drone operators and can partly be seen as counter-narratives to the official idealized story of drone warfare by exposing some of the moral dilemmas facing the drone operators. Yet rarely do the films address the larger ethical issues of how drone technology skirts the legal framework of war. Additionally, the films' reconfiguration of the white male drone operator as morally courageous and a potential savior of innocent women and children on the “battlefield” obscures the racialized and imperialist ideologies bound up in the US-led “war on terror.”

Which bath Hamiltonians matter for thermal operations?

In this article, we explore the set of thermal operations from a mathematical and topological point of view. First, we introduce the concept of Hamiltonians with a resonant spectrum with respect to some reference Hamiltonian, followed by proving that when defining thermal operations, it suffices to only consider bath Hamiltonians, which satisfy this resonance property. Next, we investigate the continuity of the set of thermal operations in certain parameters, such as energies of the system and temperature of the bath. We will see that the set of thermal operations changes discontinuously with respect to the Hausdorff metric at any Hamiltonian, which has the so-called degenerate Bohr spectrum, regardless of the temperature. Finally, we find a semigroup representation of (enhanced) thermal operations in two dimensions by characterizing any such operation via three real parameters, thus allowing for a visualization of this set. Using this, in the qubit case, we show commutativity of (enhanced) thermal operations and convexity of thermal operations without the closure. The latter is done by specifying the elements of this set exactly.

Quantum Error Mitigation via Matrix Product Operators

In the era of noisy intermediate-scale quantum (NISQ) devices, the number of controllable hardware qubits is insufficient to implement quantum error correction (QEC). As an alternative, quantum error mitigation (QEM) can suppress errors in measurement results via repeated experiments and postprocessing of data. Typical techniques for error mitigation, e.g., the quasi-probability decomposition method, ignore correlated errors between different gates. Here, we introduce a QEM method based on the matrix product operator (MPO) representation of a quantum circuit that can characterize the noise channel with polynomial complexity. Our technique is demonstrated on a $\rm{depth}=20$ fully parallel quantum circuit of up to $N_q=20$ qubits undergoing local and global noise. The circuit error is reduced by several times with only a small bond dimension $D^{\prime} = 1$ for the noise channel. The MPO representation increases the accuracy of modeling noise without consuming more experimental resources, which improves the QEM performance and broadens its scope of application. Our method is hopeful of being applied to circuits in higher dimensions with more qubits and deeper depth.

Towards Effective Temporary Organizing in Crises: A Tale of a Control Command in Responding to COVID-19 in China

Control commands established by Chinese local governments to tackle COVID-19 proved effective in containing its spread nationwide. The primary interest in this contribution is to uncover the mechanism underlying the effectiveness of a control command established by Qingdao municipality in managing COVID-19. We conclude that the combination of five conditions, namely, task immersion, qualified team members, flexible organizing, high swift trust, and high operational representation, is sufficient to result in effective temporary organizing. Our study contributes to the policy and governance literature through adding building blocks to the explanation regarding the effectiveness of temporary organizations in managing crises.

Struktur Grup pada Pocket Cube

The objective of this research is to examine the abstraction of a semi-direct product group that originates from a specific object, which is the pocket cube. The process involves constructing groups by identifying free groups that are produced from reduced rotation sequences with finite standard rotations within the pocket cube. Moreover, by taking the action group to the position and orientation of the cubino on the pocket cube, the set of member pairs in S_8 and Z_3^8 is derived. The investigation then focuses on various valid random patterns on the pocket cube to determine how they correspond to each element in the semi-direct product of S_8 and Z_3^8. Additionally, the study describes the randomness of the pocket cube pattern when two reduced rotation sequences are applied sequentially by analyzing the operational representation of the semi-direct product group members.Keywords: group, pocket cube, semi-direct product.

How can quantum field operators encode entanglement?

We present techniques to construct the Deutsch–Hayden representation for quantum field operators and apply them to an entangled state of identical nonrelativistic spin-1/2 fermions localized in well-separated spatial regions. Using these entangled field operators we construct operators measuring spin in localized spatial regions, and verify that matrix elements of the spin-measurement operators in the information-free Deutsch–Hayden state yield the expected correlations between pairs of both entangled and unentangled particles. The entangled Deutsch–Hayden representation field operators furnish an explicitly separable description of the entangled system.

Representation of Lipschitz Maps and Metric Coordinate Systems

Here, we prove some general results that allow us to ensure that specific representations (as well as extensions) of certain Lipschitz operators exist, provided we have some additional information about the underlying space, in the context of what we call enriched metric spaces. In this conceptual framework, we introduce some new classes of Lipschitz operators whose definition depends on the notion of metric coordinate system, which are defined by specific dominance inequalities involving summations of distances between certain points in the space. We analyze “Pietsch Theorem inspired factorizations" through subspaces of ℓ∞ and L1, which are proved to characterize when a given metric space is Lipschitz isomorphic to a metric subspace of these spaces. As an application, extension results for Lipschitz maps that are obtained by a coordinate-wise adaptation of the McShane–Whitney formulas, are also given.

Inverse spectral problems for radial Schrödinger operators and closed systems

We study an inverse eigenvalue problem for the radial Schrödinger operators on the unit interval. This problem consists in the recovery of the potential on a subinterval (0,a), a≤1, from eigenvalues corresponding to the boundary value problems with different boundary conditions. We obtain a sufficient condition for the unique specification of the radial Schrödinger operator by a set of eigenvalues and a part of the potential function on (a,1) in terms of the cosine system closedness. The Borg-type and the Hochstadt-Lieberman type results are obtained as corollaries of our main result. Furthermore, under an additional hypothetical condition, we show that our condition is not only sufficient but also necessary for the uniqueness of the inverse problem solution. The main tool of our proof technique is the singular transformation operator representation for the solution of the radial Schrödinger equation.

Revisiting the Multidimensional Work Motivation Scale (MWMS)

ABSTRACT This multi-sample study (5 samples) revisited the content and factor structure of the Multidimensional Work Motivation Scale (MWMS) through exploratory structural equation modelling. Specifically, the operational representation of, and the relations between, the types of behavioural regulation were investigated as was their relation to theoretical outcomes. Results suggest the removal of three problematic items and show that work motivation, as measured by the MWMS, is best represented by a factor structure reflecting autonomous motivation, introjected and external regulation as well as amotivation. Furthermore, introjected regulation is more strongly represented by its avoidance subscale, whereas the two types of external regulation (material and social) are not distinguishable. Lastly, autonomous motivation is linked to optimal employee functioning (e.g., vigor/vitality, satisfaction, lower turnover intention). The two controlled types of regulation have differentiated relations with performance, but are both linked to poor employee health and turnover intention, with (avoidance) introjected regulation being a particularly important predictor. By revisiting the content of the MWMS and cross-validating its structure in five samples, this study provides an empirically adequate representation of the types of regulation and their outcomes. Suggestions for future research aimed at improving the content of the MWMS are also offered.

Energy transitions driven by phase space reflection operators

Phase space reflection operators lie at the core of the Wigner–Weyl representation of density operators and observables. The role of the corresponding classical reflections is known in the construction of semiclassical approximations to Wigner functions of pure eigenstates and their coarsegrained microcanonical superpositions, which are not restricted to classically integrable systems. In their active role as unitary operators, they generate transitions between pairs of eigenstates specified by transition Wigner functions (or cross-Wigner functions): the square modulus of the transition Wigner function at each point in phase space is the transition probability for the reflection through that point.Coarsegraining the initial and final energies provides a transition probability density as a phase space path integral. It is here investigated in the simplest classical approximation involving microcanonical Wigner functions. A reflection operator generates a transition between a pair of energy shells with a probability density given by the integral of the inverse modulus of a Poisson bracket over the intersection of a shell with the reflection of its pair. The singularity of the pair of Wigner functions at their dominant caustics is nicely integrable over their intersection, except for a single degree of freedom. Even though this case is not directly relevant for future investigations of chaotic systems, it is shown here how the improved approximation of the spectral Wigner functions in terms of Airy functions resolves the singularity.

Fractal Impedance Element Synthesis Based on Multilayer Resistance-Capacitance Environment with C-R-Nc Layer Structure

The idea of fractural calculus appeared almost at the same time as the development of conventional differential calculus began. However, modern scientists became familiar with it only from pioneering works of B. Mandelbrot on fractal geometry of nature in 1980s. Since then, numerous scientific works were published on various aspects of fractural calculus and its application in science and engineering, and the interest to this area remains high. However, for physical implementation of fractural integration operators two-terminal elements with fractional power and frequency law (the fractural impedance elements - FIE) are required. Commercial FIE that could be produced industrially have not been developed so far. The greatest potential, in this case, have FIE built on the basis of multilayer resistance-capacitance element with distributed parameters (RC-distributed elements). One of the baseline designs of such FIEs with R-C-NR layer structure was manufactured as a prototype model. However, when manufacturing and testing of this element, flaws that may prevent its application were detected. The article suggests making FIE based on RC-distributed elements with dual C-R-NC layer structure where, as it is assumed, it is possible to avoid flaws found in FIE with R-C-NR layer structure. However, to solve this problem it is necessary to develop an algorithm and a program of structure synthesis of new type FIE enabling production elements with parameters not worse than those of the existing FIE with R-C-NR layer structure. For this purpose, an algorithm of frequency characteristic analysis of equivalent circuit FIE based on RC-distributed parameters having C-R-NC layer structure and being the component of synthesis algorithm, was developed. Principal stages of synthesis algorithm based on search optimization genetic algorithm were formulated. Ways of information coding of internal structure and parameter C-R-NC FIE were defined. Method of function calculation of individual fitness within population of object representation and ways of genetic operators (selection, crossing-over and mutation) realization in the process of genetic algorithm performance was described. Thereupon the synthesis program was developed and the results of its operation are given in the article. Synthesis result validity was verified by means of circuit simulation software OrCAD by application of Pspice-based C-R-NC-line model. The obtained FIE equivalent circuits integral C-R-NC structures, taking into account chosen materials and layer parameters, were designed. Comparative analysis results of synthesis program operation of C-R-NC FIE and R-C-NR FIE for synthesis FIE with the same requirements to frequency impedance FIE characteristics are given, showing that synthesizing C-R-NC FIE; the FIE with phase uniformity phase-frequency impedance characteristics from - 45° to about - 80° without galvanic coupling between poles and synthesizing R-C-NR FIE, the FIE with phase uniformity of phase-frequency impedance from -10° to about -45° with galvanic coupling between the pole are more likely to be realized.

Advancing reservoir operations modelling in SWAT to reduce socio-ecological tradeoffs

The Soil & Water Assessment Tool (SWAT) is a useful model for evaluating socio-ecological tradeoffs and analyzing coupled natural-human system dynamics in agricultural watersheds. However, reservoir operating options in SWAT are limited. This study advances the representation of reservoir operations in SWAT by adding an option for closed-loop, multi-reservoir operating policies that can be optimized using Evolutionary Multi-Objective Direct Policy Search. This enables water managers to evaluate the tradeoffs across more coordinated reservoir operations in SWAT while capitalizing on the model's ability to physically simulate hydrological processes better than traditional reservoir simulation models. Comparing our advanced reservoir operations with SWAT's existing operating options in the Omo River basin of Ethiopia, we find a wider range of policies for managing conflicting stakeholder objectives that better compromise across them and are more robust to climate change. These advances to SWAT's reservoir module show promise for informing integrated water resources management.