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Niche segregation is a mechanism by which competition between coexisting species is reduced. The ecological niche is a multidimensional space shaped by the conditions and resources that enable the existence of species.We conducted comprehensive univariate and multidimensional analyses of phenotypic traits encompassing morphology, functional performance and ecophysiology, to investigate which phenotypic traits contribute to niche segregation and overlap in two coexisting green lizard species.Our analyses revealed that the main driver of niche segregation was body size. However, when considering size‐corrected phenotypic spaces, ecophysiological traits were still distinct, with little overlap between co‐occurring species. Such differentiation was linked mainly to preferred temperature variance and water loss, highlighting the importance of thermal and hydric niche segregation.Some particular traits such as limb length also contributed to niche segregation being maintained in the morphological space, even when the effect of size was accounted for. Instead, the phenotypic space of functional performance traits (i.e. bite force, locomotor performance) showed the greatest overlap between the two species, thus, less niche segregation was observed, once size effects were removed. Therefore, functional performance traits contribute in a minor proportion to the effective niche segregation between the two species. In light of our results, the most adequate perspective to understand niche segregation in coexisting species is through a multidimensional approach in differentiated phenotypic spaces. Our dismantling of phenotypic traits allowed us to identify niche areas in which trait overlap occurs and others that promote niche segregation, considering or not size effects.Our results suggest that differential use of structural and functional niche space promotes effective niche segregation, potentially reducing direct competition between species. We highlight the importance of studies that include the combination of several phenotypic traits that, as a whole, provide insights to better understand the mechanisms by which coexisting organisms exploit differentiated resources in multidimensional spaces. Read the free Plain Language Summary for this article on the Journal blog. [ABSTRACT FROM AUTHOR]

Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are immediate consequences of the main result. Finally, combinatorial identities involving harmonic-like numbers and other prominent sequences like hyperharmonic numbers and odd harmonic numbers are offered. [ABSTRACT FROM AUTHOR]

Mathematician and philosopher Charles Howard Hinton posited a plausible correlation between higher-dimensional spaces, also referred to as 'hyperspaces', and the allegorical concept articulated by the Ancient Greek philosopher Plato in his work, Republic, known as the 'Cave.' In Plato's allegory, individuals find themselves situated in an underground 'Cave', constrained by chains on their legs and neck, perceiving shadows and sound reflections from the 'real' world cast on the 'Cave' wall as their immediate reality. Hinton extended the interpretation of these 'shadows' through the induction method, asserting that, akin to a 3D object casting a 2D shadow, the 'shadow' of a 4D hyper-object would exhibit one dimension less, manifesting as a 3D object. Building upon this conceptual framework, the authors posit a correlation between the perceived acoustic space of the bounded individuals within the 'Cave' and the characteristics of a 4D acoustic space, a proposition substantiated mathematically by scientific inquiry. Furthermore, the authors introduce an interactive art application developed as a methodical approach to exploring the hypothetical 4D acoustic space within Plato's 'Cave', as perceived by the bounded individuals and someone liberated from his constraints navigating through the 'Cave.' [ABSTRACT FROM AUTHOR]

If f is a continuous selection for the Vietoris hyperspace F (X) of the nonempty closed subsets of a space X, then the point f (X) ∈ X is not as arbitrary as it might seem at first glance. In this paper, we will characterise these points by local properties at them. Briefly, we will show that p = f (X) is a strong butterfly point precisely when it has a countable clopen base in ⊂ for some open set U ⊂ X \ {p} with ⊂ = U ⊂ {p}. Moreover, the same is valid when X is totally disconnected at p = f (X) and p is only assumed to be a butterfly point. This gives the complete affirmative solution to a question raised previously by the author. Finally, when p = f (X) lacks the above local base-like property, we will show that F(X) has a continuous selection h with the stronger property that h(S) = p for every closed S ⊂ X with p ∈ S. [ABSTRACT FROM AUTHOR]

Given a metric continuum X, we consider the collection of all regular subcontinua of X and the collection of all meager subcontinua of X, these hyperspaces are denoted by D(X) and M(X), respectively. It is known that D(X) is compact if and only if D(X) is finite. In this way, we find some conditions related about the cardinality of D(X) and we reduce the fact to count the elements of D(X) to a Graph Theory problem, as an application of this, we prove in particular that |D(X)| G {2, 3,4, 5, 8, 9} for any continuum X. Also, we prove that D(X) is never homeomorphic to N. On the other hand, given a point p G X, we consider the meager composant and the filament composant of p in X, denoted by Mpf and FcsX (p), respectively, and we study some relations between Mpx and FcsX (p) such as the equality of them as a subset of X. Also, we construct examples showing that the collection Fcs(X) = {FcsX (p): p G X} can be homeomorphic to: any finite discrete space, the harmonic sequence, the closure of the harmonic sequence and the Cantor set. Finally, we study the contractibility of M(X); we prove the arc of pseudo-arcs, which is a no contractible continuum, satisfies that its hyperspace of meager subcontinua is contractible, given a solution to Problem 3 of [10]. Most of the results shown in this paper are focus to answer problems and questions posed in [6], [9] and [10]. Also, we rise open problems. [ABSTRACT FROM AUTHOR]

Let X ⊂ P(a0,. . ., an) be a quasi-smooth weighted Fano hypersurface of degree d and index IX such that ai | d for all i. If IX = 1, we show that, under a suitable condition, the α-invariant of X is greater than or equal to dimX/(dimX +1) and X is K-stable. This can be applied in particular to any X as above such that dimX ⩽ 3. If X is general and IX < dimX, then we show that X is K-stable. We also give a sufficient condition for the finiteness of automorphism groups of quasi-smooth Fano weighted complete intersections. [ABSTRACT FROM AUTHOR]

A topological space X is selectively highly divergent (SHD) if for every sequence of non-empty open sets {Un: n ε ω} of X, we can find points xn ε Un, for every n < ω such that the sequence {xn: n ∊ ω} has no convergent subsequences. In this note we answer four questions related to this notion that were asked by Jiménez-Flores, Ríos-Herrejón, Rojas-Sánchez and Tovar-Acosta. [ABSTRACT FROM AUTHOR]

For robots in human environments, learning complex and demanding interaction skills from humans and responding quickly to human motions are highly desirable. A common challenge for interaction tasks is that the robot has to satisfy both the task space and the joint space constraints on its motion trajectories in real time. Few studies have addressed the issue of hyperspace constraints in human-robot interaction, whereas researchers have investigated it in robot imitation learning. In this work, we propose a method of dual-space feature fusion to enhance the accuracy of the inferred trajectories in both task space and joint space; then, we introduce a linear mapping operator (LMO) to map the inferred task space trajectory to a joint space trajectory. Finally, we combine the dual-space fusion, LMO, and phase estimation into a unified probabilistic framework. We evaluate our dual-space feature fusion capability and real-time performance in the task of a robot following a human-handheld object and a ball-hitting experiment. Our inference accuracy in both task space and joint space is superior to standard Interaction Primitives (IP) which only use single-space inference (by more than 33%); the inference accuracy of the second order LMO is comparable to the kinematic-based mapping method, and the computation time of our unified inference framework is reduced by 54.87% relative to the comparison method. [ABSTRACT FROM AUTHOR]

This paper presents an investigation into the mathematical concepts of neutrosophic folding and neuretraction on neutrosophic manifolds, specifically focusing on their application in hyperspace. Through the application of specific transformations on a neutrosophic manifold situated in hyperspace, we can obtain neutrosophic manifolds in lower dimensions. Based on our research, we can accurately establish the connection between neutrosophic folding and neuretraction on a neutrosophic manifold. Furthermore, we can determine the relationship between neuretraction and neutrosophic folding. [ABSTRACT FROM AUTHOR]

The need to study boundary value problems for elliptic parabolic equations is dictated by numerous practical applications in the theoretical study of the processes of hydrodynamics, electrostatics, mechanics, heat conduction, elasticity theory, quantum physics. Let H (dimH ≥ 1) -- a finite-dimensional real Hilbert space with inner product <·,·> and norm || · ||. We will study the equation of the following form u + L (u) = g ∈ H, where L(·) is a non-linear continuous transformation, g is an element of the space H, u is the required solution of the problem from H. In this paper, we obtain two theorems on a priori estimates for solutions of nonlinear equations in a finite-dimensional Hilbert space. The work consists of four items. The conditions of the theorems are such that they can be used in the study of a certain class of initial-boundary value problems to obtain strong a priori estimates. This is the meaning of these theorems. [ABSTRACT FROM AUTHOR]

In this article, we investigate the notion of setwise betweenness, a concept introduced by P. Bankston as a generalisation of pointwise betweenness. In the context of continua, we say that a subset C of a continuum X is between distinct points a and b of X if every subcontinuum K of X containing both a and b intersects C. The notion of an interval [a,b] then arises naturally. Further interesting questions are derived from considering such intervals within an associated hyperspace on X. We explore these ideas within the context of the Vietoris topology and n-symmetric product hyperspaces on all nonempty closed subsets of a topological space X, CL(X). Moreover, an alternative pointwise interval, derived from setwise intervals, is introduced.

In this paper we continue to research relationships between closure-type properties of hyperspaces over a space X and covering properties of X. For a Hausdorff space X we denote by 2X the family of all closed subsets of X. We investigate selection properties of the bitopological space (2X, Δ1+ , Δ2+) where Δi+ is the upper Δi-topology for each i=1,2.

Over the past few decades, physicists are seeking a unifying theory that could encapsulate the theories of general relativity and quantum mechanics, our understanding of the very big and the infinitesimal small, into one all-inclusive theory. This quest led to a renewed interest in the proposal of hyperspace, which states that the structure of space and time are folded into one another, creating multiple dimensions. The author believes that the biblical confession about the resurrected Christ could be beneficial to science and theology in this respect. Biblical testimony provides insight into the apparent natural and effortless movement of Christ between the different dimensions in nature. Astrotheology, as a nexus between the different disciplines, is well equipped to describe the meaning and implications of the resurrection with regard to the fabric of space-time. The author opines that it could facilitate as a natural interface between hyperspace and the Trinity. This proposal aims to accentuate, from a scriptural point of view, that reality indeed comprises more than four dimensions and that astrotheology could make a significant epistemological contribution in the dialogue about hyperspace and God's agency in creation. [ABSTRACT FROM AUTHOR]

We determine several classes of continua whose hyperspaces of subcontinua are infinite dimensional and homeomorphic to cones over (usually) other continuum. In particular, we obtain many Peano continua with such a property. [ABSTRACT FROM AUTHOR]

Infinite Gray code has been introduced by Tsuiki [Ts02] as a redundancyfree representation of the reals. In applications the signed digit representation is mostly used which has maximal redundancy. Tsuiki presented a functional program converting signed digit code into infinite Gray code. Moreover, he showed that infinite Gray code can effectively be converted into signed digit code, but the program needs to have some non-deterministic features (see also [TS05]). Berger and Tsuiki [BT21a, BT21b] reproved the result in a system of formal first-order intuitionistic logic extended by inductive and co-inductive definitions, as well as some new logical connectives capturing concurrent behaviour. The programs extracted from the proofs are exactly the ones given by Tsuiki. In order to do so, co-inductive predicates S and G are defined and the inclusion S ⊆ G is derived. For the converse inclusion the new logical connectives are used to introduce a concurrent version S2 of S and G ⊆ S2 is shown. What one is looking for, however, is an equivalence proof of the involved concepts. One of the main aims of the present paper is to close the gap. A concurrent version G* of G and a modification S * of S2 are presented such that S * = G*. A crucial tool in [BT21a] is a formulation of the Archimedean property of the real numbers as an induction principle. We introduce a concurrent version of this principle which allows us to prove that S * and G* coincide. A further central contribution is the extension of the above results to the hyperspace of non-empty compact subsets of the reals. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a notion of shadowing property for a free semigroup action on a compact metric space, which is different of the notion of the shadowing property introduced by Bahabadi, called chain shadowing property. We study the relation between the shadowing property of a free semigroup action on a compact metric space X and the shadowing property of the induced free semigroup action on the hyperspace 2X. Specially, we not only theoretically prove that (F m + , F) ↷ X has the (chain) shadowing property if and only if (F m + , F) ↷ 2 X has the (chain) shadowing property, but also give examples to illustrate it. Finally, we compare the two notions of shadowing for free semigroup actions and obtain an interesting result that if (F m + , F) ↷ X has the shadowing property, then it has the chain shadowing property, but not vice versa. [ABSTRACT FROM AUTHOR]

In this paper, we study the relation between a space X satisfying certain generalized metric properties and the Pixley-Roy hyperspace F[X] over X satisfying the same properties. We prove that if X has a s-point-finite cn-network (resp., ck-network), then F[X] also has a s-point-finite cn-network (resp., ck-network). [ABSTRACT FROM AUTHOR]

Let X be a compact Hausdorff space. In this work we translate partial actions of X to partial actions on some hyperspaces determined by X, this gives an endofunctor 2- in the category of partial actions on compact Hausdorff spaces which generates a monad in this category. Moreover, structural relations between partial actions θ on X and partial determined by 2θ as well as their corresponding globalizations are established.

In this paper, we define the concept of pseudo-prime subhypermodules of hypermodules as a generalization of the prime hyperideal of commutative hyperrings. In particular, we examine the spectrum of the Zariski topology, which we built on the element of the pseudo-prime subhypermodules of a class of hypermodules. Moreover, we provide some relevant properties of the hypermodule in this topological hyperspace. [ABSTRACT FROM AUTHOR]

In this article, we study the space Bμ(BX,Y) of Y-valued Bloch-type functions on the unit ball BX of an infinite dimensional Hilbert space X with μ is a normal weight on BX and Y is a Banach space. We also investigate the characterizations of the space WBμ(BX) of Y-valued, locally bounded, weakly holomorphic functions associated with the Bloch-type space Bμ(BX) of scalar-valued functions in the sense that f ∈ WBμ(BX) if w ∘ f ∈ Bμ(BX) for every w ∈ W, a separating subspace of the dual Y′ of Y. [ABSTRACT FROM AUTHOR]

Let M be a semifinite von Neumann algebra on a Hilbert space H equipped with a faithful normal semifinite trace τ, S(M, τ) be the *-algebra of all τ-measurable operators. Let S0 (M, τ) be the *-algebra of all τ-compact operators and T(M, τ) = S0 (M, τ) + CI be the *-algebra of all operators X = A + λI with A ∈ S0 (M, τ) and λ ∈ C. It is proved that every operator of T (M, τ) that is left-invertible in T(M, τ) is in fact invertible in T(M, τ). It is a generalization of Sterling Berberian theorem (1982) on the subalgebra of thin operators in B(H). For the singular value function μ(t; Q) of Q = Q2 ∈ S(M, τ), the inclusion μ(t; Q) ∈ {0}⋃[1, + ∞) holds for all t > 0. It gives the positive answer to the question posed by Daniyar Mushtari in 2010. [ABSTRACT FROM AUTHOR]

Let f : M → M be a Morse–Smale diffeomorphism defined on a compact and connected manifold without boundary. Let C(M) denote the hyperspace of all subcontinua of M endowed with the Hausdorff metric and C (f) : C (M) → C (M) denote the induced homeomorphism of f. We show in this paper that if M is the unit circle S 1 then the induced map C(f) has not the shadowing property. Also we show that the topological entropy of C(f) has only two possible values: 0 or ∞ . In particular, we show that the entropy of C(f) is 0 when M is the unit circle S 1 and it is ∞ if the dimension of the manifold M is greater than two. Furthermore, we study the recurrence of the induced maps 2 f and C(f) and sufficient conditions to obtain infinite topological entropy in the hyperspace. [ABSTRACT FROM AUTHOR]

In this paper, we present translation hypersurfaces of semi-Euclidean spaces with zero scalar curvature. In addition, we prove that translation hypersurfaces with constant scalar curvature must have zero scalar curvature in the semi-Euclidean space ... . [ABSTRACT FROM AUTHOR]

In this article, we investigate the notion of setwise betweenness, a concept introduced by P. Bankston as a generalisation of pointwise betweenness. In the context of continua, we say that a subset C of a continuum X is between distinct points a and b of X if every subcontinuum K of X containing both a and b intersects C. The notion of an interval [a, b] then arises naturally. Further interesting questions are derived from considering such intervals within an associated hyperspace on X. We explore these ideas within the context of the Vietoris topology and n-fold symmetric product hyperspaces on all nonempty closed subsets of a topological space X, CL(X). Moreover, an alternative pointwise interval, derived from setwise intervals, is introduced. [ABSTRACT FROM AUTHOR]

In this paper we continue to research relationships between closure-type properties of hyperspaces over a space X and covering properties of X. For a Hausdorff space X we denote by 2X the family of all closed subsets of X. We investigate selection properties of the bitopological space (2X, Δ1+, Δ2+) where Δi+ is the upper Δi-topology for each i=1,2. [ABSTRACT FROM AUTHOR]

The aim of this paper is to review up-to-date recent results in the field of star selection principles, a rapidly growing area of topology, and to present a few new results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the following semilinear elliptic equation −∆u = uq(x)−1, in B, u > 0, in B, u = 0, in ∂B, where B is the unit ball in R N(N ≥ 3), q(x) = q(|x|) is a continuous radial function satifying 1 < minx∈Bq(x) = q− < 2 < q+ = maxx∈B q(x) < 2 ∗ = 2N/N−2, and q(0) > 2. By means of variational methods and a priori estimate, we obtain that the problem above has at least two positive radial solutions. [ABSTRACT FROM AUTHOR]

In this paper, we establish a quantum version of the Hermite-Hadamard-Mercer inequalities using the well-known Jensen-Mercer inequality. Moreover, we derive some new q-midpoint and q-trapezoidal type inequalities for differentiable functions. The newly developed inequalities are also shown to be the extensions of preexisting inequalities in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we derive a new projection algorithm by incorporating inertial effects for solving a split feasibility problem in real Hilbert spaces. We then establish a weak convergence theorem under some suitable conditions. As an application, we apply our result to image restoration. [ABSTRACT FROM AUTHOR]

Let X be a compact metric space and a continuous map f : X → X which defines a discrete dynamical system (X , f) . The map f induces two natural maps, namely f ¯ : K (X) → K (X) on the hyperspace K (X) of non-empty compact subspaces of X and the Zadeh's extension f ^ : F (X) → F (X) on the space F (X) of normal fuzzy set. In this work, we analyze the interaction of some orbit tracing dynamical properties, namely the specification and shadowing properties of the discrete dynamical system (X , f) and its induced discrete dynamical systems (K (X) , f ¯) and (F (X) , f ^) . Adding an algebraic structure yields stronger conclusions, and we obtain a full characterization of the specification property in the hyperspace, in the fuzzy space, and in the phase space X if we assume that the later is a convex compact subset of a (metrizable and complete) locally convex space and f is a linear operator. [ABSTRACT FROM AUTHOR]

This paper falls in the area of hypercompositional algebra. In particular it focuses on the class of Krasner hyperrings and it studies the regular local hyperrings. These are Krasner hyperrings R with a unique maximal hyperideal M having the dimension equal to the dimension of the vectorial hyperspace M M2. The aim of the paper is to show that any regular local hyperring is a hyperdomain. For proving this, we make use of the relationship existing between the dimension of the vectorial hyperspaces related to the hyperring R and to the quotient hyperring R = R ⟨a⟩, where a is an element in M \ M2, and of the regularity of R. [ABSTRACT FROM AUTHOR]

The introduction of renewable energy introduces operational challenges for the modern multi-energy system. To accommodate the uncertainty, this paper proposes an online probabilistic energy flow for the hydrogen-power-heat system. First, a hydrogen-power-heat system model is established to depict the interdependency of multiple energy, in which hydrogen fuel cells interconnect hydrogen, power, and heat systems by converting the hydrogen into power and heat. The probabilistic energy flow is further built considering the uncertain wind power. An efficient algorithm based on multi-parametric programming (MPP) is proposed to enhance the computational performance of probabilistic multi-energy flow for online applications. The parameter region of the probabilistic multi-energy flow in MPP model is divided into multiple critical regions (CR). Each CR reveals a unique mapping relationship from uncertain wind power to system optimal solutions. Probabilistic energy flow could be quickly calculated based on mapping relationship rather than solving optimization problem. Therefore, the proposed method could be applied in online energy flow calculation. Numerical results tested on a 6–6-8 system and an improved 40–118 − 13 system validate the accuracy and efficiency of the proposed method in probabilistic energy flow calculation. • Online rapid computational method for probabilistic energy flow is proposed for hydrogen-power-heat system. • Parameter hyperspace of uncertain wind power in multi-parametric programming is divided into a set of critical regions. • Mapping relationship is applied to quickly obtain optimal solution. • Two test systems are provided to validate effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Let S be a nonsingular projective surface. Each vector bundle V on S of rank s induces a tautological vector bundle over the Hilbert scheme of n points of S. When s = 1, the top Segre classes of the tautological bundles are given by a recently proven formula conjectured in 1999 by M. Lehn. We calculate here the Segre classes of the tautological bundles for all ranks s over all K-trivial surfaces. Furthermore, in rank s = 2, the Segre integrals are determined for all surfaces, thus establishing a full analogue of Lehn's formula. We also give conjectural formulas for certain series of Verlinde Euler characteristics over the Hilbert schemes of points. [ABSTRACT FROM AUTHOR]

Let X be a metric continuum and n 2 N. Let Fn(X) be the hyperspace of nonempty subsets of X with at most n points. If 1 ≤ m < n, we consider the quotient space Fn m(X) = Fn(X)=Fm(X). Given a mapping f: X → X, we consider the induced mappings fn: Fn(X) → Fn(X) and fn m: Fn m (X) → Fn m (X). In this paper we study relations among the dynamics of the mappings f, fn and fn m and we answer some questions, by F. Barragán, A. Santiago-Santos and J. Tenorio, related to the properties: minimality, irreducibility, strong transitivity and turbulence. [ABSTRACT FROM AUTHOR]

Let X be a compact Hausdorff space. In this work we translate partial actions of X to partial actions on some hyperspaces determined by X; this gives an endofunctor 2- in the category of partial actions on compact Hausdor-spaces which generates a monad in this category. Moreover, structural relations between partial actions θ on X and partial actions determined by 2θ as well as their corresponding globalizations are established. [ABSTRACT FROM AUTHOR]

Artificial intelligence has been widely used in the security industry. Intelligent video surveillance converts data into images on the screen. These postmodern spectacles of images involve daily life in the "image process", forming an accurate copy and representation of daily life. As a result, a postmodern hyperspace is created. Such a hyperspace, particularly in the capitalist society, produces a split between human beings and their surroundings. The postmodern body thus loses the sensibility of space coordinate and aesthetics, which veils the real in life and causes the degradation of subjects' professional skills. In aesthetic terms, hyperspace leads to the disenchantment and secularization of the meaning of space as well as the loss of the poetic in space life. The invasion into the private space and the "pollution" of the spiritual space are also negative impacts that are brought by hyperspace. Theoretical and practical solutions to these problems are indeed worth exploring. [ABSTRACT FROM AUTHOR]

In this paper, the notion of picture fuzzy sub-hyperspace of a hyper vector space is introduced and some related results are investigated on the basis of some basic operations (intersection, union, Cartesian product etc.) on picture fuzzy sets. The concept of picture fuzzy linear transformation with respect to some picture fuzzy sub-hyperspace is initiated here and some important results are studied in this regard. It is shown that with respect to some pre-assumed picture fuzzy sub-hyperspace, linear combination of two picture fuzzy linear transformations is a picture fuzzy linear transformation, composition of two picture fuzzy linear transformations is a picture fuzzy linear transformation and inverse of a bijective picture fuzzy linear transformation is a picture fuzzy linear transformation. The effect of good linear transformation on picture fuzzy sub-hyperspaces is discussed here. It is shown that the image of a picture fuzzy sub-hyperspace is a picture fuzzy sub-hyperspace under bijective good linear transformation and the inverse image of a picture fuzzy sub-hyperspace is a picture fuzzy subhyperspace under good linear transformation. Some important results on picture fuzzy sub-hyperspaces in the light of (;;)-cut of picture fuzzy set are studied here. Finally, an application of picture fuzzy sub-hyperspace conditions in decision making problem is presented here. [ABSTRACT FROM AUTHOR]

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It is well-known that some minimal (or maximal) hypersurfaces are stable. However, there is a growing recognition on unstable minimal (or maximal) hypersurfaces by introducing the concept of index of stability. Firstly, the index of stability for minimal hypersurfaces in the Euclidean n-sphere has been introduced by J. Simons [20], which is followed recently by many people (see for instance [3, 9, 18, 21]). Also, Barros and Sousa in [10] have payed attention to the concept of index of r-stability (as the r-extension of index of stability) on r-minimal hypersurfaces in the Euclidean n-sphere. They gave low bounds for r-stability index of r-minimal n-dimensional closed hypersurfaces in Sn+1. In this paper we give low bounds for the r-stability index of r-maximal closed spacelike hypersurfaces in the de Sitter space Sn+11. [ABSTRACT FROM AUTHOR]

. In the present paper proved that if for a given compact Hausdorff space X the hyperspace exp X is a contractible compact space then the space OSf (X) is also a contractible compact space. As a consequence it is established that the space OSf (X) of semi-additive functionals is absolute (neighbourhood) retract if and only if the hyperspace exp X is so. [ABSTRACT FROM AUTHOR]

Tropical forests and savannas can co-occur in a range of macro-environmental conditions. In these conditions, disturbances and resource availability are thought to control savanna and forest transitions, although the mechanisms involved are disputed. We hypothesized that, in Neotropical regions where fire activity is high, fire is the main factor controlling functional differences between savanna and forest, as well as their relative resistance to biome shifts. We sampled plant functional traits and soil and determined fire history, for 198 plots distributed across three landscapes with distinct fire frequencies (high, mid, and low). In each landscape, plots covered a woody cover gradient (from wooded grasslands to forests). We tested whether the sharpness and the magnitude of the functional distinction between savanna and forest were affected by fire. We also computed the environmental hyperspace (niche space) to evaluate how biome relative stability changed in relation to fire. Functional thresholds were detected only in the high and mid landscapes, where savanna and forest plots formed a multidimensional bimodal distribution in functional trait space. The stability of savannas in relation to forest increased abruptly with fire, whereas functional differences between forest and savanna increased gradually. Our results suggest that savanna can occur as an alternative vegetation state to forest where a fire burns every 18 years (on average), but higher frequencies are required for savannas to occupy large unique portions of the environmental niche space. [ABSTRACT FROM AUTHOR]

Physical and chemical properties of the interstellar medium (ISM) at subgalactic (∼kiloparsec) scales play an indispensable role in controlling the ability of gas to form stars. In this paper, we use the TNG50 cosmological simulation to explore the physical parameter space of eight resolved ISM properties in star-forming regions to constrain the areas of this hyperspace where most star-forming environments exist. We deconstruct our simulated galaxies spanning a wide range of mass (M⋆ = 107–1011M⊙) and redshift (0 ≤ z ≤ 3) into kiloparsec-sized regions and statistically analyze the gas/stellar surface densities, gas metallicity, vertical stellar velocity dispersion, epicyclic frequency, and dark-matter volumetric density representative of each region in the context of their star formation activity and environment (radial galactocentric location). By examining the star formation rate (SFR) weighted distributions of these properties, we show that stars primarily form in two distinct environmental regimes, which are brought about by an underlying bicomponent radial SFR profile in galaxies. We examine how the relative prominence of these regimes depends on galaxy mass and cosmic time. We also compare our findings with those from integral field spectroscopy observations and find similarities as well as departures. Further, using dimensionality reduction, we characterize the aforementioned hyperspace to reveal a high degree of multicollinearity in relationships among ISM properties that drive the distribution of star formation at kiloparsec scales. Based on this, we show that a reduced 3D representation underpinned by a multivariate radius relationship is sufficient to capture most of the variance in the original 8D space. [ABSTRACT FROM AUTHOR]

It is desirable to monitor the degradation of integrated circuits (ICs) or perform their failure analysis through their electrical characteristics [such as the voltage-transfer characteristic (VTC), of an inverter]. Such a method is nondestructive, low-cost, and can be applied to a large number of samples. Machine learning is naturally an excellent tool to perform this task. However, it is very expensive, in terms of time and cost, to generate enough experimental data with well-controlled defects to train a reliable machine. Moreover, IC defect signatures and features are usually embedded in the hyperspace of their electrical characteristics and are difficult to extract. In this article, we propose to use dimensionality reduction to extract the defect signature from the IC electrical characteristics using data generated through simulations. A CMOS inverter is used for demonstration. The drain contact resistances, which can increase due to defect or degradation, of the nMOSFET and pMOSFET in an inverter are extracted using a machine based on autoencoder (AE). The machine is trained using data generated from SPICE simulation. The machine is then tested using experimental data and high accuracy is obtained (${R}^{\,2} >0.9$). In particular, for the first time, through the analysis of the hidden variables, we demonstrate that the machine has effectively extracted the features automatically which obviates the cumbersome feature extraction process. [ABSTRACT FROM AUTHOR]

First reported in the early 2000s, a new generation of metals called 'high-entropy alloys' (HEAs) have the potential to outperform conventional alloys that rely on a primary base metal. The plethora of five or more metallic elements when alloyed in equiatomic or near equiatomic creates a vast HEA material hyperspace that can lead to exceptional technical properties. This paper provides insights into HEAdevelopment in Australia; in particular, the additive manufacturing of HEA deposits through thermal spray and laser-based methods. [ABSTRACT FROM AUTHOR]

Abstract Recently, Wu (Mathematics 6(11):219, 2018; Mathematics 6(6):90, 2018) introduced the concept of a near-fixed point and established some results on near fixed points in a metric interval space and hyperspace. Motivated by these papers, we studied the near-coincidence point theorem in these spaces via a simulation function. To show the authenticity of the established results and definitions, we also provide some examples.

Let X be a continuum and let n be a positive integer. We consider the hyperspaces Fn(X) and SFn(X). If m is an integer such that n > m ≥ 1, we consider the quotient space SFnm(X). For a given map f : X → X, we consider the induced maps Fn(f) : Fn(X) → Fn(X), SFn(f) : SFn(X) → SFn(X) and SFnm(f) : SFnm(X) → SFnm(X). In this paper, we introduce the dynamical system (SFnm(X), SFnm (f)) and we investigate some relationships between the dynamical systems (X, f), (Fn(X), Fn(f)), (SFn(X), SFn(f)) and (SFnm(X), SFnm(f)) when these systems are: exact, mixing, weakly mixing, transitive, totally transitive, strongly transitive, chaotic, irreducible, feebly open and turbulent.