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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 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.

While the UN’s proclaimed decade of family farming (2019-2029) unfolds, management research has still not sufficiently explored the enterprising family in agriculture. Our article aims at exploring the literature on agricultural family businesses in the field of management sciences, towards suggesting future research directions. We present an overview of the definitional efforts and specificities of these family businesses, followed by a systematic literature review over the past decade. Our analysis identifies three clusters of dimensions that underpin the existing knowledge: entrepreneurial behavior, succession process, and psychological dynamics, in relation with three major outcomes that are growth, resilience, and continuity. Building on the existing research limitations and the current research trends, we craft a comprehensive agenda for scholars to advance our understanding of enterprising families in agriculture.

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.

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, a condition which implies the continuity of an $h$-convex function is investigated. In fact, any $h$-convex function bounded from above is continuous if the function $h$ satisfies a certain condition which is called pre-continuity condition.

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.

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.

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

Discrete Level of Detail (LOD) strategy is an effective solution for balancing the inherent contradiction between quality and speed in computer graphics. However, application of this strategy requires both the appropriate selection approach and the visually comfortable transition procedure to reduce the popping effects introduced by switching between different levels. In this paper, a novel automatic LOD selection method based on viewpoint entropy was proposed. Firstly, the traditional calculation method of viewpoint entropy contained in a scene was improved for the preprocessing of LOD models. Then, the runtime rendering scheme combined with our selection method was designed for balance of frame rate during real-time rendering, and a novel smoothing LOD transition strategy based on Alternate Frame Rendered (ALR) was put forward for elimination of popping effects. Finally, an example of complex scene combined with our proposal was researched to verify its real-time performance and ability in holding continuity of rendered images. Experimental studies show the effectiveness for stabilizing frame rate and improvements in reducing loss of continuity.

We give the definition of uniform symmetric continuity for functions defined on a nonempty subset of the real line. Then we investigate the properties of uniformly symmetrically continuous functions and compare them with those of symmetrically continuous functions and uniformly continuous functions. We obtain some characterizations of uniformly symmetrically continuous functions. Several examples are also given.

A class of quartic Said-Ball type blending functions with two shape parameters α, β is presented in this paper, which is an extension of quartic Said-Ball blending functions. Based on Said-Ball type blending functions, the quintic Said-Ball type curves and surfaces with two shape parameters are defined. This class of curves inherits the outstanding properties of the quartic Ball curve. The properties of the blending functions and curves, and the geometrical property of shape parameters are analyzed. The G⁰ -continuity, G¹ -continuity and G² -continuity conditions of two pieces of curves are also given. Some examples illustrate that this method of constructing curves and surfaces is useful for curves and surfaces design.

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.

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.

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.

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 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.

Fuzzy doubly labeled transition systems are fuzzy extension of doubly labeled transition systems in which the propositions and transitions take values from the unit interval [0,1], and the set of actions is equipped with a fuzzy equivalence relation. The notion of bisimulations that have been proven in the boolean setting is generalized to fuzzy setting. Some interesting results on perturbation and continuity properties of fuzzy bisimulation under some fuzzy connectives are proven.

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.