Complete Theory Research Articles

Spectrally accurate numerical quadrature formulas for a class of algebraically singular periodic Hadamard finite part integrals by regularization

We consider the numerical computation of Hadamard Finite Part (HFP) integrals Hσ(t;u)=⨎0T|sinπ(x−t)T|σu(x)dx,0<t<T,σ<−1,σ⁄∈Z,u(x) being sufficiently differentiable and T-periodic on R. Thus σ=−(m+δ), m∈{1,2,3,…}, 0<δ<1. For each such σ, we regularize Hσ(t;u), and show that Hσ(t;u)=Hσ+2r(t;Uσ),r=⌊(m+1)/2⌋, where Uσ(x)=∑k=0raku(2k)(x) for some constants ak, Hσ+2r(t;Uσ) being a regular integral. We then propose to approximate Hσ(t;u) by the quadrature formula Qσ,n(t;u)≡Hσ(t;ϕn), where ϕn(x) is the nth-order balanced trigonometric polynomial that interpolates u(x) on [0,T] at the 2n equidistant points xn,k=kT2n, k=0,1,…,2n−1. The implementation of Qσ,n(t;u) is simple, the only input needed for this being the 2n function values u(xn,k), k=0,1,…,2n−1. Using Fourier analysis techniques, we develop a complete convergence theory for Qσ,n(t;u) as n→∞ and prove that it enjoys spectral convergence when u∈C∞(R).We also show that the theoretical developments and numerical quadrature formulas developed for the HFP integrals Hσ(t;u) with σ<−1 and σ⁄∈Z apply, with no changes, to the regular singular integrals Hσ(t;u) with σ>−1 and σ⁄∈Z.We illustrate the effectiveness of Qσ,n(t;u) with numerical examples both for σ<−1 and σ>−1.Finally, we show that the HFP or regular integral ⨎0Tf(x)dx of any T-periodic integrand f(x) that has algebraic singularities of the form |x−t+kT|σ, 0<t<T, k=0,±1,±2,…, with σ⁄∈Z, but is sufficiently differentiable in x on R∖{t±kT}k=0∞, can be expressed as Hσ(t;u), where u(x) is a T-periodic and sufficiently differentiable function of x on R that can be computed from f(x). Therefore, ⨎0Tf(x)dx can be computed efficiently using our new numerical quadrature formulas Qσ,n(t;u) on the individual Hσ(t;u). Again, only 2n function evaluations, namely, u(xn,k), k=0,1,…,2n−1, are needed for the whole process.

An embedded cluster CASPT2 study of the Ce:YVO4 spectrum.

Multiconfigurational theory, in combination with the embedded cluster approach, is a precise and abinitio approach to describe the electronic structure of solids. In this work, the spectrum of a Ce(III) dopant in YVO4 has been studied by complete active space perturbation theory of the second order (CASPT2), with the host material represented as a set of abinitio model potentials and point-charges. We assess the sensitivity of the spectrum to the size of both the embedded cluster size as well as the size of the electronic basis set. A comparison of our best computational model with experimental results shows that the embedding approach is robust and can accurately model the spectrum of low-concentration dopants in complex host materials.

Superrosiness and dense pairs of geometric structures

Let T be a complete geometric theory and let TP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_P$$\\end{document} be the theory of dense pairs of models of T. We show that if T is superrosy with -rank 1 then TP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_P$$\\end{document} is superrosy with -rank at most ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}.

Qualitative properties, bifurcations and chaos of a discrete predator–prey system with weak Allee effect on the predator

In this work, the qualitative properties of the fixed points in the non-hyperbolic and degenerate cases, codimension-one bifurcations and Marotto’s chaos of a discrete predator–prey system with weak Allee effect on the predator are investigated. Utilizing the center manifold theorem and the reduction principle, the qualitative property of each fixed point in the non-hyperbolic case is explored. Based on the approximate flow theory, the qualitative property of the boundary fixed point in the degenerate case is investigated. Making use of the center manifold theorem and the bifurcation theory, all the potential codimension-one bifurcation types of the co-existence fixed point are explored, including flip bifurcation and Neimark–Sacker bifurcation. For each type of these bifurcations, not only the concise non-degenerate condition expressed by the system parameters is given, but also the analytical expression of the system orbit caused by the bifurcation is derived. Based on the non-negativity of the bifurcation critical values, the non-resonant and non-degenerate conditions for the occurrence of these bifurcations, the system parameter plane is divided into several regions using tools such as the polynomial complete discriminant system theory, real root separation theory, dichotomy method, implicit function theorem and Cardan’s formula. In each region, the direction and stability of these bifurcations are studied, which helps to theoretically explain the impact of Allee effect on the system. By proving that the co-existence fixed point is a snap-back repeller under appropriate conditions, it is obtained that the system is chaotic. Numerical simulations are completely consistent with all the theoretical analyses. The research results show that the impact of Allee effect on the population system depends not only on the assumption and construction of the system, but also on the system parameter and initial value of the system.

Starobinsky inflation from string theory?

Starobinsky inflation is currently one of the best models concerning agreement with cosmological data. Despite this observational success, it is still lacking a robust embedding into a UV complete theory. Previous efforts to derive Starobinsky inflation from string theory have been based on the derivation of higher derivative curvature terms from the low-energy limit of ten-dimensional string theory. This approach is however known to fail due to the difficulty to tame the effect of contributions proportional to the Ricci scalar to a power larger than two. In this paper we investigate an alternative attempt which exploits instead the ubiquitous presence of scalar fields in string compactifications combined with the fact that Starobinsky inflation can be recast as Einstein gravity coupled to a scalar field with a precise potential and conformal coupling to matter fermions. After showing that the dilaton does not feature the right Yukawa coupling to matter, we focus in particular on type IIB Kähler moduli since they have shown to lead to exponential potentials with a Starobinsky-like plateau. We consider three classes of moduli with a different topological origin: the volume modulus, bulk fibre moduli, and blow-up modes. The only modulus with the correct coupling to matter is the volume mode but its potential does not feature any plateau at large field values. Fibre moduli admit instead a potential very similar to Starobinsky inflation with a natural suppression of higher curvature corrections, but they cannot reproduce the correct conformal coupling to matter. Blow-up modes have both a wrong potential and a wrong coupling. Our analysis implies therefore that embedding Starobinsky inflation into string theory seems rather hard. Finally, it provides a detailed derivation of the coupling to matter of fibre moduli which could be used as a way to discriminate Starobinsky from fibre inflation.

COUNTABLE MODELS OF COMPLETE ORDERED THEORIES

The article consists of observations regarding complete theories of countable signatures and their countable models. We provide a construction of a countable linearly ordered theory which has the same number of countable non-isomorphic models as the given countable, not necessarily linearly ordered, theory.

Complete Equational Theories for the Sum-Over-Paths with Unbalanced Amplitudes

Complete Equational Theories for the Sum-Over-Paths with Unbalanced Amplitudes

Information and Theoretical Foundations for Control of the State of Agrocenoses in Real Time

Objective: Presentation of a complete theory of management of the state of agrocenoses, including sowing crops and weeds. This theory makes it possible to obtain a given crop yield with the required reliability. Such management is formed on the basis of estimates of the parameters of the state of crops, soil environment and weeds, formed according to the data of Earth remote sensing in real time. Methods: The presented theory is based on new mathematical models of the parameters of the state of agricultural crops, soil environment, weeds, as well as models of the relationship of these parameters with remote sensing (RS) data. Control factors in agricultural technology are doses of mineral fertilizers, herbicides and irrigation rates. Therefore, the parameters of the state in the management system under consideration, in addition to the parameters of the biomass of agricultural crops and weeds, are the chemical parameters of the soil environment. All technological operations are carried out at the onset of certain phenological phases of the development of crop sowing. RS data are entered precisely at such moments of time when the parameters of the state of crops and weeds are estimated on their basis. The presented theory is based on classical control principles used in modern dynamic systems. The most important feature of the proposed approach to solving the problem of agrocenoses management is the development of the principle of spatial distribution of agricultural technology parameters. It consists in using models with spatial variables, which are complemented by models of spatial approximation of controls in the form of multidimensional power polynomials. The parameters of the approximation models are evaluated according to the optimal parameters of technological operations obtained on 15-20 test sites of the field. Results: In accordance with the proposed theory, mathematical models of agrocenoses, a real-time control algorithm using RS data and a specialized software package were developed, with the help of which the control system was tested on the example of spring wheat sowing. Conclusion: As a result of testing a specialized software package for the implementation of the proposed theory, the operability of the proposed theory of agrocenoses control in real time and the possibility of using it in practical systems for automated control of agricultural technologies were established.

Effect of geometrical and electronic alteration on the n → π* vertical excitation energy and thermodynamic stability of locked azobenzene (LAB) with protein confinement

AbstractLocked azobenzenes (LAB) derivatives are recognized as photoswitchable potassium ion channel blockers. Here we report the effect of tetraethyl ammonium ion (TEA) substituent and KcsA K+‐ion channel protein environment on the thermodynamic stability and vertical excitation energy of locked azobenzene. The complete active space self‐consistent field (CASSCF and state‐averaged CASSCF, SA2‐CAS) with complete active space perturbation theory (state‐averaged CASPT2, SA2‐CASPT2) and our own n‐layered integrated molecular orbital and molecular mechanics—mechanical embedding (ONIOM‐ME) followed by electronic embedding (ONIOM‐EE) methods were employed for the study. The Z‐isomer of LAB is thermodynamically more stable as compared to E‐isomer. The substitution of tetraethyl ammonium ion does not influence the thermodynamic stability. On the other hand, the thermodynamic stability is reversed in the protein environment. Furthermore, the vertical excitation energies (VEE) and geometrical parameters show that the photochemistry of LAB is unaffected by para‐substituted TEA. However, geometrical changes imposed by the protein on the confined LAB‐TEA decreases the VEE.

Analyzing Multivariate Generalizability Theory Designs within Structural Equation Modeling Frameworks

We demonstrate how to analyze complete multivariate generalizability theory (GT) designs within structural equation modeling frameworks that encompass both individual subscale scores and composites formed from those scores. Results from numerous analyses of observed scores obtained from respondents who completed the recently updated form of the Big Five Inventory (BFI-2) revealed that the lavaan SEM package in R produced results virtually identical to those obtained from the mGENOVA package, which historically has served as the gold standard for conducting multivariate GT analyses. We further extended lavaan analyses beyond what mGENOVA allows to produce Monte Carlo based confidence intervals for key GT parameters and correct score consistency and correlational indices for effects of scale coarseness characteristic of binary and ordinal data. Our comprehensive online Supplemental Material includes code for performing all illustrated analyses using lavaan and mGENOVA.

Virtual design of a measuring device integrated in electroacupuncture stimulator on Arduino

The object of research is the electrical conductivity of biologically active points. Biologically active points as a method of non-traditional medical procedures and diagnostics, as well as being used for therapeutic purposes. Although this method has become the subject of mass research, a complete theory of the method has not yet been formed. Based on research, it is possible to say that there are different approaches to explaining the mechanism of action. These independent studies suggest the existence of unique electrical properties in the areas of the skin where biologically active points are located. However, due to technical and methodological problems, it was not in the interest of the scientific community, and as a result of solving the problem mentioned in recent history, interest in research in this field has increased. Nerve endings, called biologically active points or acupuncture points, are widely used in alternative medicine. The first step in electrostimulation of acupuncture points is the localization of the point. Localization is based on measuring the electrical conductivity of acupuncture points. The article discusses the virtual design of the measuring device, which is expected to be integrated with electrostimulators. As a result of the simulation, measurements were made and the accuracy class of the device was determined. Thus, it is possible to accurately measure electrical conductivity in biological objects through this device. The proposed device is designed on the basis of a modern element base. The basic element of the device is Arduino. A voltage divider scheme was used to determine the electrical conductivity of Arduino-based biologically active points. The purpose of using a voltage divider circuit is to protect the Arduino's analog input from overvoltage. Based on the measurements, the accuracy class of the proposed device was determined. As a result of the simulations, it was determined that the absolute error of the device is 0.463056, the relative error is 0.005742, and the accuracy class is 0.0463056.

Poor Man’s Memristor: Chua Corsage Memristor

Chua Corsage Memristor (CCM) can accurately emulate the neuromorphic behaviors of biological neurons. Recently, we built a working CCM circuit board using only inexpensive and off-the-shelf electronic components. When this poor-mans memristor is connected to a linear passive L and C circuit, the resulting circuit can generate action potentials and chaos. This paper presents the complete theory for deriving the electronic circuit realization of the poor-mans memristor, and also displays more additional neuromorphic waveforms, measured experimentally from the poor-mans memristor, further verifying the neuromorphic dynamics of the CCM.

Contributions toward Understanding the Acquisition of Eight Aspects of Vocabulary Knowledge

With the intent of adding to the literature leading toward a more complete theory of second language vocabulary acquisition, this study elicited accuracy data from 110 ESL learners ranging from novice high to advanced low on 64 words randomly selected in the 2K–3K range of Corpus of Contemporary American English (COCA) (32 verbs, 24 nouns, 8 adjectives) covering eight aspects of word knowledge. These included spelling based on hearing the spoken form, selecting collocations based on the written form, pronunciation based on the written form, selecting inflections based on the written context, selecting the definition based on hearing the spoken form, selecting the written definition based on the written form, selecting appropriate derivations based on the written form, and selecting the written form based on the written definition. ANOVA results show accuracy levels varied across word knowledge aspects and that implicational scaling was possible with some but not all aspects of word knowledge examined simultaneously. In aggregation with other current and future studies, this has important implication for developing L2 vocabulary acquisition theory.

Companionability characterization for the expansion of an o-minimal theory by a dense subgroup

This paper provides a full characterization for when the expansion of a complete o-minimal theory, one that extends the theory of ordered divisible abelian groups, by a unary predicate that picks out a divisible, dense and codense group has a model companion. This result is motivated by criteria and questions introduced in the recent works [14] and [10] concerning the existence of model companions, as well as preservation results for some neostability properties when passing to the model companion. Examples are included both in which the predicate is an additive subgroup of a real ordered vector space, and where it is a multiplicative subgroup of the nonzero elements of an o-minimal expansion of a real closed field. The paper concludes with a brief discussion of neostability properties and examples that illustrate the lack of preservation (from the base o-minimal theory to the model companion of the expansion we define) for properties such as strong, NIP, and NTP2, though there are also examples for which some or all three of those properties are preserved.

Keeping quantifier meaning in mind: Connecting semantics, cognition, and pragmatics

A complete theory of the meaning of linguistic expressions needs to explain their semantic properties, their links to non-linguistic cognition, and their use in communication. Even though in principle interconnected, these areas are generally not pursued in tandem. We present a novel take on the semantics-cognition-pragmatics interface. We propose that formal semantic differences in expressions’ meanings lead those meanings to activate distinct cognitive systems, which in turn have downstream effects on when speakers prefer to use those expressions. As a case study, we focus on the quantifiers “each” and “every”, which can be used to talk about the same state of the world, but have been argued to differ in meaning. In particular, we adopt a mentalistic proposal about these quantifiers on which “each” has a purely individualistic meaning that interfaces with the psychological system for representing object-files, whereas “every” has a meaning that implicates a group and interfaces with the psychological system for representing ensembles. In seven experiments, we demonstrate that this account correctly predicts both known and newly-observed constraints on how “each” and “every” are pragmatically used. More generally, this integrated approach to semantics, cognition, and pragmatics suggests that canonical patterns of language use can be affected in predictable ways by fine-grained differences in semantic meanings and the cognitive systems to which those meanings connect.

What Are the Balanced and Unbalanced Dynamics of a Tropical Cyclone?

Abstract Recently, Ji and Qiao took into account the unbalanced components and derived an extended Sawyer–Eliassen (SE) equation. This study developed a new derivation of this extended SE equation from the perspective of restoring forces, and gives a physical interpretation for the coefficients that appear in the SE equation. For an unbalanced vortex, we demonstrated that the thermodynamic fields are only determined by the distribution of gradient wind, and thus, the gradient wind and thermodynamic fields always remain in balance as the unbalanced vortex evolves. Consequently, we attributed the gradient wind imbalance to the agradient wind rather than to the thermodynamic fields. Subsequently, we explored the effect of the agradient wind on the secondary circulation, and showed that the agradient wind strengthens the secondary circulation in its vicinity, which can be explained as a consequence of the restoring forces and mass continuity. Furthermore, we speculated that the SE equation, together with the radial velocity equation, could reproduce the primary characteristic of the axisymmetric boundary layer dynamics by prescribing the parameterization of subgrid-scale turbulent mixing. Specifically, the noU_BL and noVa_BL experiments conducted by Fei et al. in an article published in 2021 were reinterpreted, and the oscillation wavelength of the agradient wind in the eyewall was approximated based on this framework. Additionally, a new numerical solution algorithm to overcome the hyperbolicity near the boundary layer was proposed. This study attempts to develop a complete dynamic theory for tropical cyclones in both qualitative and quantitative perspectives.

Going all the way in the search for WIMP dark matter at the muon collider through precision measurements

Dark Matter is a necessary ingredient for a complete theory of Nature, which has so far remained elusive in laboratory searches for new particles. Searches at current and future colliders are in principle a promising way to search for electroweak charged dark matter particles, but the sensitivity of experiments at the LHC and future pp colliders falls short to fully probe the whole mass range allowed for electroweak charged dark matter particles, which extends in principle up to the O(0.1) PeV. In this work we examine the effect of on-shell and off-shell propagation of electroweak charged thermal dark matter particles on integrated and differential rates of several Standard Model final states at the muon collider, considering candidates from weak 2-plet at the TeV scale up to 7-plet and 9-plet in the O(0.1) PeV ballpark. For fermionic WIMPs we find that all dark matter candidates with nle 5, corresponding to a thermal mass up to 14 TeV, can be probed at the high-energy muon collider for some center-of-mass energy at or below 14 TeV. For the n>5 WIMPs our results show that higher energy muon colliders offer a route to conclusively probe both scalar and fermionic WIMPs off-shell production all the way up to the perturbativity bound for WIMP dark matter at O(0.1) PeV. Our results bring WIMPs over the whole allowed mass range in the realm of collider searches and motivate research and development for the realization of a high energy muon collider.

Federalism as an institutional doctrine

Federalism as an institutional doctrine

The structure of accounting theory. Part 2

Subject. This article examines the main approaches to the construction of the theory of accounting, namely the inductive and deductive ones. Objectives. The article aims to identify the advantages and disadvantages of each of the approaches, analyze the structure of the theory of accounting in detail, and identify it at the present stage of development of accounting as a science discipline. Methods. For the study, I used combinations of analysis and synthesis, induction and deduction, and historical and logical research methods. Results. The article defines the structure of the theory of accounting that includes the objectives of financial reporting, postulates and theoretical concepts of accounting, as well as the principles and techniques of accounting. Conclusions and Relevance. The article concludes that of the two existing approaches to the construction of the theory of accounting, the inductive approach has a number of significant drawbacks that do not allow building a full-fledged theory of accounting. The deductive approach also has a number of drawbacks associated with understanding the axiomatic basis and the inference rules, but it helps lay the scientific foundations for building a complete and consistent theory of accounting. The results obtained can be used to create the theory of accounting.

Nonadiabatic Potential Energy Surfaces for a Molecule on a Surface as Found by Constrained Complete Active Space Theory.

In order to study electron-transfer mediated chemical processes on a metal surface, one requires not one but two potential energy surfaces (one ground state and one excited state) as in Marcus theory. In this letter, we report that a novel, dynamically weighted, state-averaged constrained CASSCF(2,2) (DW-SA-cCASSCF(2,2)) can produce such surfaces for the Anderson impurity model. Both ground and excited state potentials are smooth, they incorporate states with a charge transfer character, and the accuracy of the ground state surface can be verified for some model problems by renormalization group theory. Future development of gradients and nonadiabatic derivative couplings should allow for the study of nonadiabatic dynamics for molecules near metal surfaces.