Narrow Results

In this paper, we consider the second-order elliptic systems with lower order terms coefficients belonging to Kato–Stummel type classes in a bounded domain $\mathrm{\Omega }\subseteq {ℝ}^n$, where $n\ge 3$. We establish the existence, global pointwise estimates and $L^p$ estimates for Green matrices. Based on these estimates, we are able to show the continuity of weak solutions for the general elliptic systems by using method of potentials. We also obtain the optimal Schauder estimates for weak solutions.

Recently, tensor complementarity problems are becoming more and more popular. There are various literatures considering all kinds of properties of tensor complementarity problems, however, the stability of solutions and the continuity of solution maps are rarely mentioned so far. In the present paper, we study these two properties for tensor complementarity problems. We propose conditions under which the solutions of tensor complementarity problems are stable with the help of the tensor variational inequality or structured tensors. We also show that the solution maps of tensor complementarity problems are upper semicontinuous with the involved tensors being $R_0$-tensors. Meanwhile, we establish the relationship between the uniqueness of solutions and the continuity of solution maps of tensor complementarity problems.

A set of perceived random events is given by a fuzzy random variable, and an estimation of real random variables is represented by a functional on real random variables. The perception-based extension of estimation regarding random events is introduced, extending the functional to a functional of fuzzy random variables. This paper discusses some conditions and various properties of the extended estimations, for example, monotonicity, continuity, linearity, sub-additivity/super-additivity, convexity/concavity. Several examples of the perception-based extended estimations are investigated. This paper analyzes the general cases, where the estimations do not have monotone properties, from the viewpoint of convexity/concavity. The results can be applicable to other estimations in engineering, economics and so on.

We give the general form of an idempotent, associative, nondecreasing and continuous binary aggregation operation in a connected order topological space. The particular case of the unit interval is studied and the choice of weights is also analized. Possible generalizations for more than two arguments are also proposed.

By focusing on family owners’ perceptions and dynamics the aim of this paper is to understand the specific goals associated to their ownership status and whether and to what extend they impact on family firms’ growth and continuity. We use survey data on Finnish family firms and identify a set of differentiated family owners’ goals. Our findings contribute to the debate on differentiating socioemotional wealth by untangling the existence of variations in family principals’ goal setting and the importance to also consider that financial motives could determine family owners’ goals.

Several fields of mathematics are relevant to computer aided design and other software systems involving solid object geometry, topology, differential and algebraic geometry being particularly important. This paper discusses some of this mathematics in order to provide a theoretical foundation for geometric modelling kernels that support non-manifold objects with an internal cellular structure and subsets of different dimensions.

The paper shows relationships between relevant concepts from topology, differential geometry and computer aided geometric design that are not widely known in the CAD community. It also discusses semialgebraic, semianalytic and subanalytic sets as candidates for object representation. Stratifications of such sets are proposed for an object's cellular structure and new stratification concepts are introduced to support candidate applications.

Current shape models are targeted at visual presentations for display and design. They lack the validity in their shape properties such as topological-, geometrical- and visual- equivalence, and even continuity. Cellular modeling is a new computational modeling that provides a computationally valid shape model. It also provides a foundation to share shapes among varied applications for extensive reuse. The implementation of cellular modeling via cell attachment tables complies with the standard relational data model. Examples are shown to demonstrate the value of cellular modeling in comparison with the existing typical shape models such as wire frame models, boundary models and solid models. Design and implementation of the cellular modeling examples using cell attachment instance tables are presented.

We discuss two issues about risk measures: we first point out an alternative interpretation of the penalty function in the dual representation of a risk measure; then we analyze the continuity properties of comonotone convex risk measures. In particular, due to the loss of convexity, local and global continuity are no more equivalent and many implications true for convex risk measures do not hold any more.

In this paper, we establish the existence of Berge's strong equilibrium for games with n persons in infinite dimensional space in the case where the payoff function of each player is quasi-concave. Moreover, we study the continuity of Berge's strong equilibria correspondence and essential games.

We prove that the -solution of the heart equation for the minimal surface with plateau boundary condition is continuous up to boundary in all variables.

We will study the dependence of λ(a, b), half-eigenvalues of the one-dimensional p-Laplacian, on potentials , 1 ≤ γ ≤ ∞, where . Two results are obtained. One is the continuity of half-eigenvalues in , where w_γ is the weak topology in space. The other is the continuous differentiability of half-eigenvalues in , where ‖ ⋅ ‖_γ is the L^γ norm of . These results will be used to study extremal problems of half-eigenvalues in future work.

Analogous to the quartic B-splines curve, a piecewise quartic trigonometric polynomial B-spline curve with two shape parameters is presented in this paper. Each curve segment is generated by three consecutive control points. The given curve posses many properties of the B-spline curve. These curves are closer to the control polygon than the different other curves considered in this paper, for different values of shape parameters for each curve. With the increase of the value of shape parameters, the curve approach to the control polygon. For nonuniform and uniform knot vector the given curves have C⁰, G³; C¹, G³; C¹, G⁷; and C³ continuity for different choice of shape parameters. A quartic trigonometric Bézier curves are also introduced as a special case of the given trigonometric spline curves. A comparison of quartic trigonometric polynomial curve is made with different other curves. In the last, quartic trigonometric spline surfaces with two shape parameters are constructed. They have most properties of the corresponding curves.

We prove that, for semi-invertible continuous cocycles, continuity of Lyapunov exponents is equivalent to continuity, in measure, of Oseledets subspaces.

Random attractors and their higher-order regularity properties are studied for stochastic reaction–diffusion equations on time-varying domains. Some new a priori estimates for the difference of solutions near the initial time and the continuous dependence in initial data in $H_0^1$ are proved. Then attraction of the random attractors in the higher integrability space $L^{2+\delta }$ for any $\delta \in [0,\infty )$ and the regular space $H_0^1$ is established.

In this paper, perturbation bounds are provided for the $W$-weighted core-EP inverse of a rectangular matrix under reasonable conditions. Perturbation bounds for the core-EP inverse could be stated as a special case. Then, the continuity of the $W$-weighted core-EP inverse is considered from the perspective of equations. Finally, we give an application to a semi-stable matrix involving an integral representation of the $W$-weighted core-EP inverse of a perturbed matrix.

In this paper, we investigate the commutativity of a Banach algebra ${𝒜}$ provided with a continuous derivation satisfying algebraic identities involving nonvoid open subsets of ${𝒜}$. Furthermore, we provide examples to show that various restrictions in the hypothesis of our theorems are not superfluous.

The discrete wavelet transform; depending of the pair of integers (m, n), applied to functions f in L²(R) with respect to an admissible function h in L²(R) of class C^∞ with compact support, is used to prove that f is continuous at x = 0, and furthermore at any x = b in R if and only if there exists the convergence of the discrete wavelet transform, as (m, n) → (-∞, n₁) for any integer n₁.

The constant generation of innovation is a major factor in explaining a firm’s long-term success. Accordingly, previous literatures have identified several organisational, processual, and cultural factors that enable firms to promote successful innovation. Although these success factors appear to be rather different, most of them revolve around continuity, competence, or cooperation. As little prior research has focused on the complexity and interdependence of these various interlinked theoretical concepts, we adopt a configurational and longitudinal approach to analyse the effect of continuity, competence, and cooperation on the innovation performance of a firm on short-, mid-, and long-term bases. Based on a longitudinal data set that captures the innovation behaviour of 220 firms from 2009 to 2015, we find that continuity is the basic requirement for constant innovation performance. In addition, cooperation is likely to be supportive of innovation performance in the short term, while competence supports innovation performance in the long term.

Drought is among the natural disasters that seriously impact the environment and human life. This study aims to explore the spatial pattern of drought using the percent of normal precipitation index (PNPI) in Fars Province, located in the Southern part of Iran. To this end, a drought risk model based on data from 42 stations in Fars province from 1990 to 2019 was evaluated. The model includes three criteria of maximum drought intensity in the period, drought trend, and a maximum number of consecutive dry years. The final drought risk map was obtained with an arithmetic mean of three indicators of intensity, continuity, and trend. The final hazard map and the 3-criteria map were interpolated by the inverse distance weighting (IDW) method and were classified into five risk classes: none, mild, moderate, severe, and very severe. The final vulnerability map shows that moderate hazard areas (5% of the region), which are observed in the Sothern parts of the region, are less widespread than areas under severe hazard (83% of the region), which are observed in almost all parts of the region. According to the final vulnerability map, about 94% of the area of Fars province is under severe and very severe conditions. Overall, this study, regarding its simplicity and considering different dimensions of drought, may be utilised as a basic framework to evaluate drought hazards for other locations worldwide. In this respect, it is necessary to study the multiple sights of this phenomenon for land use planning, resource management, and prevention of water and food crises. Therefore, this model can help users and administrations with executive initiatives.

In this paper, we examine properties of the division topology on the set of positive integers introduced by Rizza in 1993. The division topology on $\mathbb{N}$ with the division order is an example of $T_0$-Alexandroff topology. We mainly concentrate on closures of arithmetic progressions and connected and compact sets. Moreover, we show that in the division topology on $\mathbb{N}$, the continuity is equivalent to the Darboux property.