Generic Stability Research Articles

Generic Stabilizers in Actions of Simple Algebraic Groups

In this paper we treat faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties. By explicit calculation, we show that in each case, with essentially one exception, there is a dense open subset any point of which has stabilizer conjugate to a fixed subgroup, called the generic stabilizer. We provide tables listing generic stabilizers in the cases where they are non-trivial; in addition we decide whether or not there is a dense orbit, or a regular orbit for the action on the module.

The spectral boundary of block structured random matrices

Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple interacting dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define and study an interesting new matrix ensemble with extensive correlations, generalising the elliptic ensemble. We determine analytically the boundary of its eigenvalue spectrum in the complex plane, as a function of the correlations determined by the model at hand. We solve numerically our equations in several cases of interest, and show that the resulting spectra can take a surprisingly wide variety of shapes.

Moduli spaces of ℤ/kℤ-constellations over 𝔸2

Let [Formula: see text] be a representation of a finite abelian group and let [Formula: see text] be the space of generic stability conditions on the set of [Formula: see text]-constellations. We provide a combinatorial description of all the chambers [Formula: see text] and prove that there are [Formula: see text] of them. Moreover, we introduce the notion of simple chamber and we show that, in order to know all toric [Formula: see text]-constellations, it is enough to build all simple chambers. We also prove that there are [Formula: see text] simple chambers. Finally, we provide an explicit formula for the tautological bundles [Formula: see text] over the moduli spaces [Formula: see text] for all chambers [Formula: see text] which only depends upon the chamber stair which is a combinatorial object attached to the chamber [Formula: see text].

Birational classification of toric orbifolds

We give a complete classification of the torus-equivariant birational equivalence classes of smooth proper toric Deligne–Mumford stacks with trivial generic stabilizer in terms of their associated stacky fans.

Pollution simulation of heavy metal in saturated porous media using CFD

Visualizing contaminant transport can play a significant role in better understanding the fate of contaminants in soil. The present study aimed to evaluate contamination of aluminium and mercury in the soil through the use of computational fluid dynamics (CFD) to obtain an estimate of degraded zones. A leak from a generic stabilization pond measuring 40 m (length) and 20 m (width) was developed for the simulations. The simulations were carried out for a period of 10 years with different leak speeds, water inlet flow rates and different values of aluminum and mercury volume fractions. All governing equations was solved with the transient mode. The flow characterized as laminar, and the multiphase model was employed through the Mixture method. The time required for contamination to reach its maximum value was directly influenced by the change in speed values. The concentration of the pollutant increases as the water inlet and leakage speeds increase, however, it reduces the time needed to reach the highest pollutant value, indicating that the degree of pollution of the porous medium was greater. The study shows that contamination can be seen as a potential contaminant source for groundwater.

Generic Stability Independence and Treeless Theories

Abstract We initiate a systematic study of generic stability independence and introduce the class of treeless theories in which this notion of independence is particularly well behaved. We show that the class of treeless theories contains both binary theories and stable theories and give several applications of the theory of independence for treeless theories. As a corollary, we show that every binary NSOP $_{3}$ theory is simple.

Facultative Mutualisms and θ-Logistic Growth: How Larger Exponents Promote Global Stability of Co-Existence Equilibria

We investigate the stability of co-existence equilibria for two-species models of facultative mutualism for which birth and death are modeled as separate processes, with possibly distinct types of density dependence, and the mutualistic contributions are either linear or saturating. To provide a unifying perspective, we first introduce and discuss a generic stability framework, finding sufficient stability conditions expressed in terms of reproductive numbers computed at high population densities. To this purpose, an approach based on the theory of monotone dynamical systems is employed. The outcomes of the generic stability framework are then used to characterize the dynamics of the two-species models of concern, delineating between decelerating (lower-powered) and accelerating (higher-powered) density dependences. It is subsequently seen that accelerating density dependences promote the stability of co-existence equilibria, while decelerating density dependences either completely destabilize the system via promoting the unboundedness of solutions or create multiple co-existence equilibria.

Existence and generic stability of open-loop Nash equilibria for noncooperative fuzzy differential games

Differential game is a critical area of study not only in theory but also in application. Based on the concept of the fuzzy process introduced by Liu, a fuzzy differential game model described using fuzzy differential equations is studied. Firstly, the existence theorem of open-loop Nash equilibrium for fuzzy differential games is given using Ky Fan inequality, and an example shows the applicability of the theorem. Secondly, the fuzzy differential game space Γ1 is constructed, and the stability of open-loop Nash equilibria of the fuzzy differential game γ∈Γ1 is studied. The conclusion shows that the fuzzy differential games whose all the open-loop Nash equilibria are stable form a dense residual set, i.e., most of the fuzzy differential games are stable in the sense of Baire classification.

Existence results and equilibrium stability conditions to fuzzy [formula omitted]-player generalized multiobjective games with application to economic equilibrium models

The purpose of this article is to study existence conditions and generic stability of solution sets to the fuzzy generalized multiobjective games in infinite dimensional spaces. First, we revisit a new class of the fuzzy generalized multiobjective games. Second, we introduce the concept of the extended Ci-quasi-concavity and establish existence conditions for fuzzy generalized multiobjective games using Browder type fixed point theorem in the noncompact cases. Third, we establish some sufficient conditions for generic solution stability conditions to such n-player multiobjective games under uncertainty. Finally, as a real-world application, we consider the special case of economic equilibrium models. Existence conditions and generic stability of solution sets for these real models are also obtained. The results obtained in this paper are new and different from the main results given by some authors in the literature.

Growth and development of seedlings of Robinia pseudoacacia (L.) for the production of planting material in conditions of chestnut soils south of the Russian Federation

Robinia (R. pseudoacacia) is distinguished by a high level of ecological plasticity and is able to grow in different agroforestry areas under conditions of chestnut soils in southern Russia. The research was carried out in cluster collection sites of the Federal Research Center of Agroecology of the Russian Academy of Sciences (Lower Volga Station) and on the basis of the Volgograd Forestry State Educational Institution according to generally accepted methods in 2022. The purpose of the research was to analyze the technological features of the dynamics of growth and development of seedlings of R. pseudoacacia, to conduct a bioinformatic analysis of the gene sequence and to assess the prospects of their use for the production of planting material. Physiological indicators for assessing the Robinia generic complex stability have been identified. The economically valuable signs identified were morphological characteristics to the method of the Federal Scientific Center of Agroecology of the Russian Academy of Sciences, features of nitrogen fixation and the pigment complex. All the studied seedlings of R. pseudoacacia were at a sufficient level of nitrogen nutrition. On the territory of the Lower Volga station, plants formed a larger growth and biomass with the largest number of nodules than Robinia seedlings on the territory of the Volgograd Forestry State Budgetary Institution. However, the mass of nodules on the roots decreased with an increase in the humus content of the experimental site in Kamyshin (0.93%), which was explained by favourable weather conditions for the development of this plant during the growing season of seedlings and a sufficient amount of nutrients for the formation of these nodules – nitrogen and its compounds. This plantation planting material Robinia pseudoacacia (L.) had the property of adapting to the type of soil, thereby being a potential breed for growing in protective plantings and landscaping plantings of various functional purposes on chestnut soils of Russian Federation.

Fixed-Time Synchronization of Reaction-Diffusion Fuzzy Neural Networks with Stochastic Perturbations

In this paper, we investigated the fixed-time synchronization problem of a type of reaction-diffusion fuzzy neural networks with stochastic perturbations by developing simple control schemes. First, some generalized fixed-time stability results are introduced for stochastic nonlinear systems. Based on these results, some generic fixed-time stability criteria are established and upper bounds of settling time are directly calculated by using several special functions. Then, the fixed-time synchronization of a type of reaction-diffusion fuzzy neural networks with stochastic perturbations is analysed by designing a type of controller which is more simple and thus have a better applicability. Finally, one numerical example with its Matlab simulations is provided to show the feasibility of developed theoretical results.

Controlled-source electromagnetic modeling using a high-order finite-difference time-domain method on a nonuniform grid

Simulation of 3D low-frequency electromagnetic (EM) fields propagating in the earth is computationally expensive. We have developed a fictitious wave-domain high-order finite-difference time-domain (FDTD) modeling method on nonuniform grids to compute frequency-domain 3D controlled-source EM data. The method overcomes the inconsistency issue widely present in the conventional second-order staggered-grid finite-difference scheme over a nonuniform grid, achieving high accuracy with an arbitrarily high-order scheme. The finite-difference coefficients adaptive to the node spacings can be accurately computed by inverting a Vandermonde matrix system using an efficient algorithm. A generic stability condition applicable to nonuniform grids is established, revealing the dependence of the time step and these finite-difference coefficients. A recursion scheme using fixed-point iterations is designed to determine the stretching factor to generate the optimal nonuniform grid. The grid stretching in our method reduces the number of grid points required in the discretization, making it more efficient than the standard high-order FDTD with a densely sampled uniform grid. Instead of stretching in vertical and horizontal directions, better accuracy of our method is observed when the grid is stretched along the depth without horizontal stretching. The efficiency and accuracy of our method are demonstrated by numerical examples.

Smooth Compactifications of the Abel-Jacobi Section

Abstract For $\theta $ a small generic universal stability condition of degree $0$ and A a vector of integers adding up to $-k(2g-2+n)$ , the spaces $\overline {\mathcal {M}}_{g,A}^\theta $ constructed in [AP21, HMP+22] are observed to lie inside the space $\textbf {Div}$ of [MW20], and their pullback under $\textbf {Rub} \to \textbf {Div}$ of loc. cit. to be smooth. This provides smooth and modular modifications $\widetilde {\mathcal {M}}_{g,A}^\theta $ of $\overline {\mathcal {M}}_{g,n}$ on which the logarithmic double ramification cycle can be calculated by several methods.

Generic Stability of the Weakly Pareto-Nash Equilibrium with Strategy Transformational Barriers

The object of this paper is to establish a new model with strategy transformational barriers for a class of generalized multileader multifollower multiple objective games (GMLMFMOG) and further deduce some new results of the weakly Pareto-Nash equilibrium (WPNE) with strategy transformational barriers for the GMLMFMOG. First, we investigate the existence of the WPNE with strategy transformational barriers for the GMLMFMOG by using the Kakutani-Fan-Glicksberg fixed point theory. Next, we study the generic stability of the GMLMFMOG with strategy transformational barriers in Hausdorff space. Finally, we obtain that the majority of the WPNE with strategy transformational barriers for the GMLMFMOG are essential on the meaning of Baire’s category. In addition, we demonstrate that there is at least an essential component for the GMLMFMOG with strategy transformational barriers.

Generic Stability Criteria for Switched Nonlinear Systems With Switching-Signal-Based Lyapunov Functions Using Takagi–Sugeno Fuzzy Model

The aim of this article is to establish generic stability conditions for switched nonlinear systems with mode-dependent average dwell-time (MDADT) switching rules via Takagi–Sugeno (T–S) fuzzy modeling, which cover all unstable modes, all stable modes, and partially unstable modes as special cases. Different from traditional multiple and multiple discontinuous Lyapunov function (MDLF) methods, the proposed novel switching-signal-based multiple discontinuous Lyapunov function (SMDLF) approach divides each mode-running interval dynamically according to the actual switching of the system. The developed approach can not only yield less conservative bounds on the MDADT but can also handle all unstable subsystems, which cannot be done by means of the traditional MDLF. A class of SMDLF is constructed for continuous-time switched T–S fuzzy systems, and relaxed stability conditions are presented for the system with both stable and unstable subsystems, using a larger switching signal space. Then, novel stability conditions are deduced for all stable and unstable subsystems in terms of slow and fast MDADT switching signals, respectively. Finally, comparative simulation examples are provided to verify the advantages and effectiveness of the proposed approach.

The Evasion of Literary History

The Evasion of Literary History

Generic Stabilizers for Simple Algebraic Groups

We prove a myriad of results related to the stabilizer in an algebraic group G of a generic vector in a representation V of G over an algebraically closed field k. Our results are on the level of group schemes, which carries more information than considering both the Lie algebra of G and the group G(k) of k-points. For G simple and V faithful and irreducible, we prove the existence of a stabilizer in general position, sometimes called a principal orbit type. We determine those G and V for which the stabilizer in general position is smooth, or dimV/G<dimG, or there is a v∈V whose stabilizer in G is trivial.

The law review paper between the Kingdom of the law and the realms of academia: A systemic functional analysis of adverbial clauses

Legal discourse has long been classified among those genres that defy generic changes the most (Gocić 2012). Recently, however, hybrid legal genres have been challenging this generic stability by imposing their own norms to coin a novel kind of ‘legal culture’ (Goźdź-Roszkowski 2011: 11). The law review article is a case in point for it combines both legal and academic standards of writing which make it “far richer in intertextuality and interdiscursivity” (Bhatia 2006: 6) than the traditional set of legal genres. This generic subversion can be traced in the lexico-grammatical choices made by the authors to turn their papers into influential legal sources rather than mere descriptions of the law. In this context, this study aspires to scrutinize the use of adverbial clauses as one specific lexico-grammatical choice in a corpus of 44 accredited law review papers with the aim of showing how this hybrid genre strives to evolve beyond the stagnation of what is termed ‘language of the law’. Specifically, a Systemic Functional Linguistics analysis of the semantic, structural and thematic uses of these structures is conducted to demonstrate how the hybridity of contexts in a single genre can make for unprecedented generic breaches. The quantitative and qualitative analyses revealed an uneven distribution of adverbial patterns in favor of non-finite purpose and finite condition, concession and reason clauses. Additionally, the positional distribution of these patterns is manipulated whenever the need arises to hedge claims as a form of allegiance to the communal demands of the law and academia. These choices are found to comply with the authors’ needs to balance both legal and academic rituals of writing while observing at the same time their personal needs to be highly acclaimed as legal scholars and to “publish or perish” (Christensen &amp; Oseid 2008: 1).

Collapse of arbitrary-shaped soft microfluidics

Soft epidermal microfluidics gain momentum because of their unique capabilities to collect and analyze the sweat or interstitial fluid for health monitoring and disease diagnostics. However, they are susceptible to structural instability or self-collapse due to their high mechanical compliance and strong adhesion between layers. Here, a generic mechanical stability model that combines a geometric optimization approach and superelliptical plate theory is established to analyze the structural stability of arbitrary-shaped soft microfluidic components. The established model not only reduces to the existing models for circle chambers and infinite channels, but also results in a simplified anti-collapse criterion to evaluate the stability of soft microfluidic devices. The result from the model indicates that there exists a shape-specific upper bounds critical value for the normalized work of adhesion to ensure mechanical stability, which combines the effects of the minimum enclosed geometry, interfacial work of adhesion, uniform height and effective bending stiffness of top and bottom plates in microfluidic components. The obtained design theory validated by extensive experimental data provides essential guidelines to design epidermal microfluidic devices free of self-collapse issues.

New techniques for bounding stabilizer rank

In this work, we present number-theoretic and algebraic-geometric techniques for bounding the stabilizer rank of quantum states. First, we refine a number-theoretic theorem of Moulton to exhibit an explicit sequence of product states with exponential stabilizer rank but constant approximate stabilizer rank, and to provide alternate (and simplified) proofs of the best-known asymptotic lower bounds on stabilizer rank and approximate stabilizer rank, up to a log factor. Second, we find the first non-trivial examples of quantum states with multiplicative stabilizer rank under the tensor product. Third, we introduce and study the generic stabilizer rank using algebraic-geometric techniques.