Uniqueness Properties Research Articles

On Delocalization in the Six-Vertex Model

We show that the six-vertex model with parameter $c\in[\sqrt 3, 2]$ on a square lattice torus has an ergodic infinite-volume limit as the size of the torus grows to infinity. Moreover we prove that for $c\in[\sqrt{2+\sqrt 2}, 2]$, the associated height function on $\mathbb Z^2$ has unbounded variance. The proof relies on an extension of the Baxter-Kelland-Wu representation of the six-vertex model to multi-point correlation functions of the associated spin model. Other crucial ingredients are the uniqueness and percolation properties of the critical random cluster measure for $q\in[1,4]$, and recent results relating the decay of correlations in the spin model with the delocalization of the height function.

Lie generalized derivations on bound quiver algebras

In this paper, we investigate Lie generalized derivations on bound quiver algebras associated with a finite acyclic quiver. The first main result shows that every bound quiver algebra associated with a finite acyclic quiver has the properness Lie generalized derivation property. The second main result investigates the uniqueness property. Namely, among other things, we show that a bound quiver algebra associated with a finite acyclic quiver E has the uniqueness Lie generalized derivation property if and only if the quiver E does not contain any isolated vertex.

Simple preference intensity comparisons

We propose and analyze a general model of simple preference intensity comparisons. The model encompasses those that belong to the utility-difference class, has transparent behavioural underpinnings and features purely ordinal uniqueness properties. Its empirical content is characterized by an easily testable condition on dual behavioural data that include choices and additional observables with intensity-revealing potential that are often elicited in experimental/empirical work, such as survey ratings, response times or willingness to pay.

Normality and Uniqueness Property of Meromorphic Function in Terms of Some Differential Polynomials

In this paper, we will consider normality and uniqueness property of a family $\mathcal {F}$ of meromorphic functions when [Q(f)](k) and [Q(g)](k) share α ignoring multiplicities, for any $f,g\in \mathcal {F}$ , where Q is a polynomial and α is a small function. Our results do not need all of zeros of Q have large order as other authors’ results.

Uniqueness property for 2-dimensional minimal cones in $\mathbb{R}^3$

In this article we treat two closely related problems: 1) the upper semicontinuity property for Almgren minimal sets in regions with regular boundary; and 2) the uniqueness property for all the 2-dimensional minimal cones in R3 . Given an open set Ω ⊂ Rn, a closed set E ⊂ Ω is said to be Almgren minimal of dimension d in Ω if it minimizes the d-Hausdorff measure among all its Lipschitz deformations in Ω. We say that a d-dimensional minimal set E in an open set Ω admits upper semi-continuity if, whenever {fn(E)}n is a sequence of deformations of E in Ω that converges to a set F, then we have Hd(F) ≥ lim supn Hd(fn(E)). This guarantees in particular that E minimizes the d-Hausdorff measure, not only among all its deformations, but also among limits of its deformations. As proved in [19], when several 2-dimensional minimal cones are all translational and sliding stable, and admit the uniqueness property, then their almost orthogonal union stays minimal. As a consequence, the uniqueness property obtained in the present paper, together with the translational and sliding stability properties proved in [18] and [20] permit us to use all known 2-dimensional minimal cones in Rn to generate new families of minimal cones by taking their almost orthogonal unions. The upper semi-continuity property is also helpful in various circumstances: when we have to carry on arguments using Hausdorff limits and some properties do not pass to the limit, the upper semi-continuity can serve as a link. As an example, it plays a very important role throughout [19].

The regularity properties and blow-up of the solutions for improved Boussinesq equations

In this paper, we study the Cauchy problem for linear and nonlinear Boussinesq type equations that include the general differential operators. First, by virtue of the Fourier multipliers, embedding theorems in Sobolev and Besov spaces, the existence, uniqueness, and regularity properties of the solution of the Cauchy problem for the corresponding linear equation are established. Here,Lp-estimates for a~solution with respect to space variables are obtained uniformly in time depending on the given data functions. Then, the estimates for the solution of linearized equation and perturbation of operators can be used to obtain the existence, uniqueness, regularity properties, and blow-up of solution at the finite time of the Cauchy for nonlinear for same classes of Boussinesq equations. Here, the existence, uniqueness,Lp-regularity, and blow-up properties of the solution of the Cauchy problem for Boussinesq equations with differential operators coefficients are handled associated with the growth nature of symbols of these differential operators and their interrelationships. We can obtain the existence, uniqueness, and qualitative properties of different classes of improved Boussinesq equations by choosing the given differential operators, which occur in a wide variety of physical systems.

Uniqueness properties of the KAM curve

<p style='text-indent:20px;'>Classical KAM theory guarantees the existence of a positive measure set of invariant tori for sufficiently smooth non-degenerate near-integrable systems. When seen as a function of the frequency this invariant collection of tori is called the KAM curve of the system. Restricted to analytic regularity, we obtain strong uniqueness properties for these objects. In particular, we prove that KAM curves completely characterize the underlying systems. We also show some of the dynamical implications on systems whose KAM curves share certain common features.</p>

Dynamics of Leslie–Gower model with double Allee effect on prey and mutual interference among predators

In this paper, a Leslie–Gower-type model is proposed to study a diffusive predator–prey system with multiple Allee effects acting on the growth rate of the prey population. Crowley–Martin-type functional response is considered to describe mutual interference among predators. Preliminary analysis includes uniqueness, dissipation and persistence property of the proposed model system. Detailed equilibrium analysis suggests that proposed system has rich dynamics in the sense that it can have four to eight equilibrium points. Multistability behavior is observed which is an interesting phenomenon. Parametric conditions are established for stability and Hopf bifurcation in both the local and diffusive systems. We investigate the emergence of complex patterns through Turing instability phenomenon of coupled reaction–diffusion system. A variety of patterns is obtained such as flower, square, circle and rhombus. Comparative analysis of patterns between weak and strong Allee effect is the novelty of this study. It is found that prey population uses its agility in aggregation. Bond between prey populations becomes stronger when the system experiences strong Allee effect which forces the predator population to remain united despite mutual interference. A highly significant result has been found that for slow prey population, predators decide the hunting strategy in a short time, while it takes more time for the predators to form a strategy to encircle the more dynamic prey.

Uniqueness and sign properties of minimizers in a quasilinear indefinite problem

<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M1">\begin{document}$ 1&lt;q&lt;p $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ a\in C(\overline{\Omega}) $\end{document}</tex-math></inline-formula> be sign-changing, where <inline-formula><tex-math id="M3">\begin{document}$ \Omega $\end{document}</tex-math></inline-formula> is a bounded and smooth domain of <inline-formula><tex-math id="M4">\begin{document}$ \mathbb{R}^{N} $\end{document}</tex-math></inline-formula>. We show that the functional <p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ I_{q}(u): = \int_{\Omega}\left( \frac{1}{p}|\nabla u|^{p}-\frac{1}{q}a(x)|u|^{q}\right) , $\end{document} </tex-math></disp-formula> <p style='text-indent:20px;'>has exactly one nonnegative minimizer <inline-formula><tex-math id="M5">\begin{document}$ U_{q} $\end{document}</tex-math></inline-formula> (in <inline-formula><tex-math id="M6">\begin{document}$ W_{0}^{1,p}(\Omega) $\end{document}</tex-math></inline-formula> or <inline-formula><tex-math id="M7">\begin{document}$ W^{1,p}(\Omega) $\end{document}</tex-math></inline-formula>). In addition, we prove that <inline-formula><tex-math id="M8">\begin{document}$ U_{q} $\end{document}</tex-math></inline-formula> is the only possible <i>positive</i> solution of the associated Euler-Lagrange equation, which shows that this equation has at most one positive solution. Furthermore, we show that if <inline-formula><tex-math id="M9">\begin{document}$ q $\end{document}</tex-math></inline-formula> is close enough to <inline-formula><tex-math id="M10">\begin{document}$ p $\end{document}</tex-math></inline-formula> then <inline-formula><tex-math id="M11">\begin{document}$ U_{q} $\end{document}</tex-math></inline-formula> is positive, which also guarantees that minimizers of <inline-formula><tex-math id="M12">\begin{document}$ I_{q} $\end{document}</tex-math></inline-formula> do not change sign. Several of these results are new even for <inline-formula><tex-math id="M13">\begin{document}$ p = 2 $\end{document}</tex-math></inline-formula>.

Global stability of age-of-infection multiscale HCV model with therapy.

In order to treat the diseases caused by hepatitis C virus (HCV) more efficiently, the concentration of HCV in blood, cells, tissues and the body has attracted widespread attention from related scholars. This paper studies a dynamic dependent HCV model (more specifically, including age structure and treatment methods model) that concludes states of infection-free and infected equilibrium. Through eigenvalue analysis and Volterra integral formula, it proves that $E_0$ is globally asymptotically stable when $\mathcal{R}<1$. After explaining the existence, uniqueness and positive properties of the solution of the system, we have proved the global asymptotic stability of $E^*$ when $\mathcal{R}>1$ by constructing a suitable Lyapunov function. Through the above proofs, it can be concluded that effective treatment measures can significantly reduce the number of HCVs, so many related researchers are aware of the importance of highly efficient nursing methods and are committed to applying relevant methods to practice.

The time fractional Schrödinger equation with a nonlinearity of Hartree type

The aim of this work is to show existence, uniqueness and regularity properties of local in time mild solutions for the nonlinear space-time fractional Schrodinger equation (1.1), with a fractional time derivative of order $$\alpha \in (0,1),$$ and with a nonlinear term of Hartree type.

Existence, uniqueness and qualitative properties of heteroclinic solutions to nonlinear second-order ordinary differential equations

Existence, uniqueness and qualitative properties of heteroclinic solutions to nonlinear second-order ordinary differential equations

Recipes and Properties of Multicomponent Systems "Aspiration Dust - Mineral Powder - Na&lt;sub&gt;2&lt;/sub&gt;SiO&lt;sub&gt;3&lt;/sub&gt;"

The paper presents the results of studies of the effect of the concentration of binder components on the properties of cement alkaline stone. Formulations of clinker-free binders of alkaline activation with the level of filling the system of 20 and 40% have been developed, the properties of the cement paste of the binding binder "aspiration dust - mineral powder - liquid glass" have been studied, the dynamics of a set of strength indicators has been studied, both for bending and compressive forces. The received results allow to estimate uniqueness of properties of a binding binder "a mineral powder - Na2SiO3" and to create new materials on resource saving and energy saving technology. The results presented in this article were obtained within the framework of studies on the implementation of scientific project No. 05. 607.21.0320. "Development of technology for new building composites based on clinkerless cement of alkaline activation using substandard natural and secondary raw materials" supported by the Federal Target Program "Research and Development in Priority Areas of Development of the Scientific and Technological Complex of Russia for 2014-2020". The unique identifier for the agreement is RFMTFI60719X0320.

Lp-Variational solutions of multivalued backward stochastic differential equations

We prove the existence and uniqueness of the Lp-variational solution, with p &gt; 1, of the following multivalued backward stochastic differential equation with p-integrable data: {−dYt + ∂yΨ(t,Yt)dQt∋H(t,Yt,Zt)dQt−ZtdBt,0≤t&lt;τ, Yτ = η, where τ is a stopping time, Q is a progressively measurable increasing continuous stochastic process and ∂yΨ is the subdifferential of the convex lower semicontinuous function y↦Ψ(t, y). In the framework of [14] (the case p ≥ 2), the strong solution found it there is the unique variational solution, via the uniqueness property proved in the present article.

Existence and monotonicity of nonlocal boundary value problems: the one-dimensional case

We consider nonlocal equations of the general form\begin{equation} \left(a*u''\right)(\cdot)+\lambda f\big(\cdot,u(\cdot)\big)=0.\nonumber \end{equation}By developing a Green's function representation for the solution of the boundary value problem we study existence, uniqueness, and qualitative properties (e.g., positivity or monotonicity) of solutions to these problems. We apply our methods to fractional order differential equations. We also demonstrate an application of our methodology both to convolution equations with nonlocal boundary conditions as well as those with a nonlocal term in the convolution equation itself.

Forearm Orientation and Contraction Force Independent Method for EMG-Based Myoelectric Prosthetic Hand

An accurate and robust pattern recognition system is crucial for advanced electromyography-based upper limb prosthetics. Variations in the user’s forearm orientation and contraction force varies the electromyography features for the same movement. It degrades the performance of electromyography-based movement classification. Few attempts reported to increase the classification accuracy under such dynamic factors include utilizing multi-stage classifiers, multi-modal sensory data, high-dimensional data, or set of power spectral descriptors. This work aims to overcome limitations in the existing methods through a novel feature set. The combined effect of forearm orientations and contraction force levels on the classification of six hand movements are considered in this study. In this paper, a novel feature set extracted from electromyography’s wavelet bispectrum, obtained as the combination of continuous wavelet transform and bispectrum, is proposed. The proposed method remains independent of the multiple dynamic factors due to its invariant and uniqueness properties. Linear discriminant analysis classifier with the proposed wavelet bispectrum feature set showed superiority (classification accuracy=86.43±3.67%) over conventional time-domain feature set (classification accuracy=75.92±5.41%) when trained with data from single orientation and force level. When trained with data from appropriate variations (three orientations and medium force), the accuracy with the proposed method increased to 90.35±2.01%. Further, by training with data from all three orientations and force levels, this method achieved an accuracy of 96.11% ±1.34%. The statistical significance of the higher classification accuracy achieved with the proposed feature set compared to other conventional feature sets is proven (repeated measure one-way ANOVA, p < 0.05).

On The Solution And Stability Analysis Of 6thorder Bvp By Special Multistep Methods

An effective method of solving a 6th order nonlinear BVP based on the numerical differentiation is presented in this article. The Uniqueness and existence properties of the solution are established. A more accurate and reliable process is derived to know the solution of 6th order BVPs. The procedure is verified on nonlinear problem. The solutions are matched with exact solutions and absolute errors obtained in this method are compared with that of Galerkin method.

Wave Propagation Dynamics in a Fractional Zener Model with Stochastic Excitation

Abstract Equations of motion for a Zener model describing a viscoelastic rod are investigated and conditions ensuring the existence, uniqueness and regularity properties of solutions are obtained. Restrictions on the coefficients in the constitutive equation are determined by a weak form of the dissipation inequality. Various stochastic processes related to the Karhunen-Loéve expansion theorem are presented as a model for random perturbances. Results show that displacement disturbances propagate with an infinite speed. Some corrections of already published results for a non-stochastic model are also provided.

Component-based 2-/3-dimensional nearest neighbor search based on Elias method to GPU parallel 2D/3D Euclidean Minimum Spanning Tree Problem

We present improved data parallel approaches working on graphics processing unit (GPU) compute unified device architecture (CUDA) platform to build hierarchical Euclidean minimum spanning forest or tree (EMSF/EMST) for applications whose input only contains N points with arbitrary data distribution in 2D/3D Euclidean space. Characteristic of the proposed parallel algorithms follows “data parallelism, decentralized control and O(1) local memory occupied by each GPU thread”. This research has to solve GPU parallelism of component-based nearest neighbor search (component-based NNS), tree traversal, and other graph operations like union-find. For exact NNS, instead of using classical K-d tree search or brute-force computing method, we propose a K-d search method working based on dividing the Euclidean K-dimensional space into congruent and non-overlapping square/cubic cells where size of points in each cell is bounded. For component-based NNS, with the uniqueness property based on 2D/3D square/cubic space partition, we propose dynamic and static pruning techniques to prune unnecessary neighbor cells’ search. For tree traversal, instead of using breadth-first-search, this paper proposes CUDA kernels working with a distributed dynamic link list for selecting a local spanning tree’s shortest outgoing edge since size of local EMSTs in EMSF cannot be predicted. Source code is provided online and experimental comparisons are conducted on both 2D and 3D benchmarks with up to 107 points to build final EMST. Results show that applying K-d search with static pruning technique and the proposed operators totally working in parallel on GPU, our current implementation runs faster than our previous work and current optimal sequential dual-tree mlpack EMST library.

Translational and Sliding Stability for Two-Dimensional Minimal Cones in Euclidean Spaces

Abstract In this article, we prove the translational stability for all two-dimensional Almgren minimal cones in ${\mathbb{R}}^n$ and the Almgren (resp. topological) sliding stability for the two-dimensional Almgren (resp. topological) minimal cones in ${\mathbb{R}}^3$. As proved in [ 19], when several two-dimensional Almgren (resp. topological) minimal cones are translational, Almgren (resp. topological) sliding stable, and Almgren (resp. topological) unique, their almost orthogonal union stays minimal. As a consequence, the results of this article, together with the uniqueness properties proved in [ 14], permit us to use all two-dimensional minimal cones in ${\mathbb{R}}^3$ to generate new families of minimal cones by taking their almost orthogonal unions.