This article deals with the problems of model-theoretic characterization of J-superstable Jonsson theories. The characteristic features of such theories are analyzed in terms of J-stability, J-P-superstability, and J-nonmultidimensionality. The need to generalize classical stability notions to the framework of Jonsson theories is identified and justified. The concepts of J-stationary and J-orthogonal types are introduced, and their role in describing the dimensional structure of existentially closed models is examined. It is shown that every JFλα-saturated model embeds as a submodel of the semantic model of a Jonsson theory T. Based on the notion of J-stationarity, a theory of independence for existential types is developed, and the notions of J-basis and J-dimension are defined. The equivalence between J-nonmultidimensionality, J-P-superstability, and J-P-stability is established, providing precise criteria for the model-theoretic classification of Jonsson theories. The results contribute to the refinement of model-theoretic tools for analyzing stability and dimensionality within the framework of Jonsson theories and place these findings in the broader context of modern classification theory, highlighting Jonsson theories as a natural generalization of elementary theories. These results clarify the interaction between saturation, independence, and dimensionality in Jonsson theories and provide a unified framework for further developments in their model-theoretic classification.
The aim of this paper is to offer an analytic theory of the shear banding instability in amorphous solids that are subjected to athermal quasi-static shear. To this aim we derive nonlinear equations for the displacement field, including the consequences of plastic deformation on the mechanical response of amorphous solids. The plastic events collectively induce distributed dipoles that are responsible for screening effects and the creation of typical length-scales that are absent in classical elasticity theory. The nonlinear theory exposes an instability that results in the creation of shear bands. By solving the weakly nonlinear amplitude equation we present analytic expressions for the displacement fields that is associated with shear bands, explaining the role of the elastic moduli that determine the width of a shear band from ductile to brittle characteristics. We derive an energy functional whose Hessian possesses an eigenvalue that goes to zero at the shear-banding instability, providing a prediction for the critical value of the accumulated stress that results in an instability.
In the paper, the Gagliardo–Nirenberg type inequalities for smoothness spaces Bpqsτ(Tn) of Nikol’skii–Besov type and spaces Fpqsτ(Tn) of Lizorkin–Triebel type both related to Morrey spaces over n-dimensional torus for some range of the parameters s, p, q, τ were proved. These spaces are natural analogues of the spaces Bpqsτ(Rn) and Fpqsτ(Rn) in the case of multidimensional torus Tn. The main results of the article are two theorems, each of which proves the Gagliardo–Nirenberg type inequality for the Lizorkin–Triebel type spaces or the Nikol’skii–Besov type spaces respectively.
An existing approach for deriving analytical expressions for slip-flow properties of Stokes flow is generalised and applied to a range of micro and nanoscale applications. The technique, which exploits the reciprocal theorem, can generate first-order predictions of the impact of Navier or Maxwell slip boundary conditions on surface moments of the traction force (e.g. on drag and torque). This article brings dedicated focus to the technique, generalises it to predict first-order slip effects on arbitrary moments of the surface traction, numerically verifies the technique on a number of cases and applies the method to a range of micro and nano-scale applications. Applications include predicting: the drag on translating spheres with varying slip length; the efficiency of a micro journal bearing; the speed of a self-propelled particle (a ‘squirmer’); and the pressure drop required to drive flow through long, straight micro/nano channels. Certain general results are also obtained. For example, for low-slip Stokes flow: any surface distribution of positive slip length will reduce the drag on any translating particle; and any perimetric distribution of positive slip length will reduce the pressure loss through a straight channel flow of arbitrary cross-section.
This paper examines para-Sasakian manifolds that satisfy a hyper-generalized weakly symmetric curvature condition. The conditions under which such a manifold with a hyper-generalized weakly symmetric curvature condition satisfies the η-Einstein manifold are established. Furthermore, the geometric behavior of a hyper-generalized weakly symmetric para-Sasakian manifold admitting quarter-symmetric metric connection is analyzed.
In a rectangular domain, the second boundary value problem for the Viscous Transonic Equation is considered. The uniqueness of the solution to the problem is proved using the energy integral method. The existence of a solution is proved by the method of separation of variables, i.e. it is sought in the form of a product of two functions X (x) and Y (y). For definition Y (y), an ordinary differential equation of the second order with two boundary conditions on the boundaries of segment [0,q] is obtained. For this problem, the eigenvalues and the corresponding eigenfunctions are found at n ∈ N. For definition X (x), an ordinary differential equation of the third order with three boundary conditions on the boundaries of segment [0,q] is obtained. The solution to this problem is found in the form of an infinite series, uniform convergence, and the possibility of term-by-term differentiation under certain conditions on the given functions is proven. The convergence of the second-order derivative of the solution with respect to variable y is proved using the Cauchy-Bunyakovsky and Bessel inequalities. When substantiating the uniform convergence of the solution, the absence of a “small denominator” is proved.
Abstract The evolution of solitary waves governed by perturbations of the Korteweg-de Vries (KdV) equation is considered, focussing in particular on the Burgers-Korteweg-de Vries (BKdV) equation. Using matched asymptotic expansions the structure of the wave is determined for all timescales. A tail appears behind the main waveform, the structure of which is determined in the form of a convolution integral. Numerical results are presented using a pseudospectral scheme but modified so that linear terms are incorporated into an integrating factor. All details of the asymptotic structure of the waveform are validated by numerical results. Comparisons are made with earlier asymptotic analyses of decaying solitary waves.
M.Sh. Mamatov, J.T. Nuritdinov, Kh.Sh. Turakulov
et al.
This article is about Minkowski difference of sets, which is one of the Minkowski operators. The necessary and sufficient conditions for the existence of the Minkowski difference of given regular polygons in the plane were derived. The method of finding the Minkowski difference of given regular tetrahedrons in the Euclidean space R3 was explained. At the end of the article, the obtained results were summarized and a geometric method for finding the Minkowski difference of the convex set M and compact set N given in Rn was shown. The theory of foliations was applied to find the Minkowski difference of sets. New geometric concepts such as “dense embedding” and “completely dense embedding” were introduced. An important geometric property of the Minkowski operator was introduced and proved as a theorem.
We study a source identification boundary value problem for a parabolic partial differential equation with multi-point Neumann type boundary condition. Stability estimates for the solution of the overdetermined mixed BVP for multi-dimensional parabolic equation were established. The first and second order of accuracy difference schemes for the approximate solution of this problem were proposed. Stability estimates for both difference schemes were obtained. The result of numerical illustration in test example was given.
In this study, we present an investigation of the asymptotic behavior of solutions of sum-difference equations. Based on some mathematical inequalities, we have obtained our results. The obtained results can apply to some fractional type difference equations as well.
In this work, we study two boundary value problems for involutary parabolic equation with the first and second kind conditions. We propose absolute stable difference schemes for numerical solutions of these boundary value problems. Actually the stability estimates for solutions of difference schemes are proved. Later error analysis for the numerical solution of both difference schemes are illustrated by test examples.
We review the progress on the applications of the vortex-surface field (VSF). The VSF isosurface is a vortex surface consisting of vortex lines. Based on the generalized Helmholtz theorem, the VSF isosurfaces of the same threshold at different times have strong coherence. As a general flow diagnostic tool for studying vortex evolution, the numerical VSF solution is first constructed in a given flow field by solving a pseudo-transport equation driven by the instantaneous frozen vorticity, and then the VSF evolution is calculated by the two-time method. From the database of numerical simulations or experiments, the VSF can elucidate mechanisms in the flows with essential vortex dynamics, such as isotropic turbulence, wall flow transition, flow past a flapping plate and turbulence–flame interaction. The characterization of VSFs reveals the correlation between robust statistical features and the critical quantities needed to be predicted in engineering applications, such as the friction coefficient in transition, thrust in bio-propulsion and growth rate in interface instability. Since the VSF evolution captures the essential Lagrangian-based dynamics of vortical flows, it inspires novel numerical methods on cutting-edge hardware, e.g. graphic and quantum processors.
The overseas market expansion strategy is important for achieving competitive advantage and sustainable growth of global electronic component companies. Although the global electronic component market has grown rapidly recently, research focusing on the innovation strategy of global electronic component companies’ expansion into overseas markets is scarce. This paper defines the key factors that influence the success of a global electronic component company’s overseas market expansion strategy based on the Technology, Organization, and Environment (TOE) framework and quantitatively identifies the relative importance of factors at the technology, organization, and environmental levels through Analytic Hierarchy Process (AHP) analysis. As a case study, we analyze Samsung Electro-Mechanics, which has grown as a global electronic components company through an overseas market expansion strategy in recent decades. As a result of the analysis, among the three top factors defined as key factors, the technology factor was evaluated as the most important factor, and among the subfactors of the technology factor, “R&D Availability”, and “Production Availability” were analyzed as the most important influencing factors. These analysis results suggest that global electronic component companies can achieve successful results when they pursue overseas market expansion strategies by prioritizing technology development and focusing on growth strategies suited to the market environment. This study is meaningful as an academic study focusing on the overseas market expansion strategies of global electronic component companies and makes a practical contribution by providing management implications that can be taken by electronic component companies seeking to expand overseas markets.
This paper investigates inner boundary value problems with a shift for a second-order mixed-hyperbolic equation consisting of a wave operator in one part of the domain and a degenerate hyperbolic operator of the first kind in the other part. We find sufficient conditions for the given functions to ensure the existence of a unique regular solution to the problems under study. In some special cases, solutions are obtained explicitly.
L. Y. Aaron Yung, Rachel S. Somerville, Henry C. Ferguson
et al.
In anticipation of the new era of high-redshift exploration marked by the commissioning of the James Webb Space Telescope (JWST), we present two sets of galaxy catalogues that are designed to aid the planning and interpretation of observing programs. We provide a set of 40 wide-field lightcones with footprints spanning approximately ~ 1,000 sq. arcmin, containing galaxies up to z = 10, and a new set of 8 ultra-deep lightcones with 132 sq. arcmin footprints, containing galaxies up to z ~ 12 down to the magnitudes expected to be reached in the deepest JWST surveys. These mock lightcones are extracted from dissipationless N-body simulations and populated with galaxies using the well-established, computationally efficient Santa Cruz semi-analytic model for galaxy formation. We provide a wide range of predicted physical properties, and simulated photometry from NIRCam and many other instruments. We explore the predicted counts and luminosity functions and angular two-point correlation functions for galaxies in these simulated lightcones. We also explore the predicted field-to-field variance using multiple lightcone realizations. We find that these lightcones reproduce the available measurements of observed clustering from 0.2 < z < 7.5 very well. We provide predictions for galaxy clustering at high redshift that may be obtained from future JWST observations. All of the lightcones presented here are made available through a web-based, interactive data release portal https://flathub.flatironinstitute.org/group/sam-forecasts.
Philip Lindner, Philip Lindner, Jonas Ramnerö
et al.
Introduction: Online gambling, popular among both problem and recreational gamblers, simultaneously entails both heightened addiction risks as well as unique opportunities for prevention and intervention. There is a need to bridge the growing literature on learning and extinction mechanisms of gambling behavior, with account tracking studies using real-life gambling data. In this study, we describe the development and validation of the Frescati Online Research Casino (FORC): a simulated online casino where games, visual themes, outcome sizes, probabilities, and other variables of interest can be experimentally manipulated to conduct behavioral analytic studies and evaluate the efficacy of responsible gambling tools.Methods: FORC features an initial survey for self-reporting of gambling and gambling problems, along with several games resembling regular real-life casino games, designed to allow Pavlovian and instrumental learning. FORC was developed with maximum flexibility in mind, allowing detailed experiment specification by setting parameters using an online interface, including the display of messages. To allow convenient and rapid data collection from diverse samples, FORC is independently hosted yet integrated with the popular crowdsourcing platform Amazon Mechanical Turk through a reimbursement key mechanism. To validate the survey data quality and game mechanics of FORC, n = 101 participants were recruited, who answered an questionnaire on gambling habits and problems, then played both slot machine and card-draw type games. Questionnaire and trial-by-trial behavioral data were analyzed using standard psychometric tests, and outcome distribution modeling.Results: The expected associations among variables in the introductory questionnaire were found along with good psychometric properties, suggestive of good quality data. Only 6% of participants provided seemingly poor behavioral data. Game mechanics worked as intended: gambling outcomes showed the expected pattern of random sampling with replacement and were normally distributed around the set percentages, while balances developed according to the set return to player rate.Conclusions: FORC appears to be a valid paradigm for simulating online gambling and for collecting survey and behavioral data, offering a valuable compromise between stringent experimental paradigms with lower external validity, and real-world gambling account tracking data with lower internal validity.
The coupling effects affecting the vibrations of two close nanostructures (e.g., two metal nanoplates or nanospheres separated by a thin dielectric layer) may considerably alter their vibrational eigenfrequencies, as demonstrated by several recent experimental studies. In this work, we present theoretical investigations of these coupling processes based on a continuum mechanics approach, considering various systems composed by two identical nanostructures mechanically coupled by a spacer made of a different material and computing their eigenfrequencies as a function of the spacer thickness. We first discuss the vibrations of stacked slabs, a one-dimensional problem which can be treated analytically. The more complex configurations of dimers of rods or spheres coupled by a finite cylindrical spacer are then treated numerically. In all cases, the frequency shifts occurring for thin spacers can be simply interpreted as a modification of the boundary conditions of the problem as compared to the single nanostructure case, while those predicted near specific spacer thicknesses are ascribed to an avoided crossing effect, happening when the individual building blocks of the dimers (nanostructures and spacer) present common eigenfrequencies.
James Wells, Rachel Henderson, Adrienne Traxler
et al.
Investigating student learning and understanding of conceptual physics is a primary research area within physics education research. Multiple quantitative methods have been employed to analyze commonly used mechanics conceptual inventories: the Force Concept Inventory (FCI) and the Force and Motion Conceptual Evaluation (FMCE). Recently, researchers have applied network analytic techniques to explore the structure of the incorrect responses to the FCI identifying communities of incorrect responses which could be mapped on to common misconceptions. In this study, the method used to analyze the FCI, modified module analysis was applied to a large sample of FMCE pretest and post-test responses (N_{pre}=3956, N_{post}=3719). The communities of incorrect responses identified were consistent with the item groups described in previous works. As in the work with the FCI, the network was simplified by only retaining nodes selected by a substantial number of students. Retaining as nodes only those incorrect answer choices selected by at least 20% of the students produced communities associated with only four misconceptions. The incorrect response communities identified for men and women were substantially different, as was the change in these communities from pretest to post-test. The 20% threshold was far more restrictive than the 4% threshold applied to the FCI in the prior work that generated similar structures. Retaining nodes selected by 5% or 10% of students generated a large number of complex communities. The communities identified at the 10% threshold were generally associated with common misconceptions producing a far richer set of incorrect communities than the FCI; this may indicate that the FMCE is a superior instrument for characterizing the breadth of student misconceptions about Newtonian mechanics.
Let $z$ be the activity of point particles described by classical equilibrium statistical mechanics in ${\bf R}^ν$. The correlation functions $ρ^z(x_1,\dots,x_k)$ denote the probability densities of finding $k$ particles at $x_1,\dots,x_k$. Letting $φ^z(x_1,\dots,x_k)$ be the cluster functions corresponding to the $ρ^z(x_1,\dots,x_k)/z^k$ we prove identities of the type $$ φ^{z_0+z'}(x_1,\dots,x_k) $$ $$ =\sum_{n=0}^\infty{z'^n\over n!}\int dx_{k+1}\dots\int dx_{k+n}\,φ^{z_0}(x_1,\dots,x_{k+n}) $$ It is then non-rigorously argued that, assuming a suitable cluster property (decay of correlations) for a crystal state, the pressure and the translation invariant correlation functions \- $ρ^z(x_1,\dots,x_k)$ are real analytic functions of $z$.