Search

We study the relations between two consequences of the Continuum Hypothesis discovered by Wacław Sierpiński, concerning uniform continuity of continuous functions and uniform convergence of sequences of real-valued functions, defined on subsets of the real line of cardinality continuum. [ABSTRACT FROM AUTHOR]

In this paper, we demonstrate some zero-r laws related to the analyticity of fractional resolvent families. Using these findings, we establish a zero-r law for the uniform continuity of fractional resolvent families. Additionally, we provide a similar result to the previous one by utilizing the algebraic characteristic of fractional resolvent families. Here, r is taken to be greater than 1. In particular, we prove a zero-r law on the scalar of fractional resolvent families, which offers a positive response to the question raised by F.L. Schwenninger and H. Zwart. [ABSTRACT FROM AUTHOR]

It is known that the Sorites paradox can be resolved by working in fuzzy logic and making one of the premises of the argument close to true rather than fully true [2]. We call this premise the Principle of Charity and introduce an additional condition on it, desiring for it to be "almost true" and not just close to true. We proceed to analyze the resolution of the Sorites paradox under various monoidal t-norm based fuzzy logics and determine which of these logics establishes the Principle of Charity as "almost true". In particular, we desire the Principle of Charity to be "almost true" iff the function mapping objects to their truth values is uniformly continuous. We prove that this relationship holds exactly when the underlying t-norm is nilpotent. This result provides a characterization of both nilpotent t-norms and uniformly continuous functions onto [0, 1]. [ABSTRACT FROM AUTHOR]

The fast reconstruction of the ship hull nonuniform rational B-spline (NURBS) surface with uniform continuity is essential for calculating hydrostatic elements such as waterplane area and molded volume in real time. Thus, this study proposes a fast reconstruction model with uniform continuity to solve the problem of uniform continuity and splicing in the separate model of hull bow and stern surfaces. The proposed model includes the NURBS curve generation (UCG) algorithm with uniform continuity and the hybrid NURBS surface generation (HSG) algorithm. The UCG algorithm initially fits the feature points using the global interpolation algorithm and then precisely constructs straight-line segments in the curve using the improved flattening algorithm. In comparison, the HSG algorithm adaptively selects the surface knot vectors according to the parameters of the section curves. In this study, the profile of discontinuous compartments is uniformly expressed, effectively avoiding various articulation problems in separation modeling. The results of comparative experiments show that the NURBS surface generated using the HSG algorithm can accurately express the characteristics of various parts of the hull with uniform continuity, and the calculation speed of the proposed model can be increased by up to 8.314% compared with the existing best-performing algorithms. Thus, the proposed model is effective and can improve computational efficiency to a certain extent. The NURBS surfaces generated by the proposed model can be further applied to calculating the hydrostatic elements of hulls and compartments. [ABSTRACT FROM AUTHOR]

Extending and completing earlier results on lifting certain continuity properties of aggregation functions by super- and sub-additive transformations (J. Mahani Math. Res. Center 8 (2019) 37–51, and Iranian J. Fuzzy Sets 17 (2020) 2, 165–168), we prove that uniform continuity of multi-dimensional aggregation functions is preserved under super-additive transformations. [ABSTRACT FROM AUTHOR]

The purpose of this study is to introduce an inertial algorithm for approximating a solution of the split equality Hammerstein type equation problem in general reflexive real Banach spaces. Strong convergence results are established under the assumption that the associated mappings are monotone and uniformly continuous. The results in this paper generalize and improve many of the existing results in the literature in the sense that the underlying mappings are relaxed from Lipschitz continuous to uniformly continuous and the spaces under consideration are extended from Hilbert spaces to reflexive real Banach spaces with a more general problem which includes the Hammerstein type equation problems. [ABSTRACT FROM AUTHOR]

The fast reconstruction of the ship hull nonuniform rational B-spline (NURBS) surface with uniform continuity is essential for calculating hydrostatic elements such as waterplane area and molded volume in real time. Thus, this study proposes a fast reconstruction model with uniform continuity to solve the problem of uniform continuity and splicing in the separate model of hull bow and stern surfaces. The proposed model includes the NURBS curve generation (UCG) algorithm with uniform continuity and the hybrid NURBS surface generation (HSG) algorithm. The UCG algorithm initially fits the feature points using the global interpolation algorithm and then precisely constructs straight-line segments in the curve using the improved flattening algorithm. In comparison, the HSG algorithm adaptively selects the surface knot vectors according to the parameters of the section curves. In this study, the profile of discontinuous compartments is uniformly expressed, effectively avoiding various articulation problems in separation modeling. The results of comparative experiments show that the NURBS surface generated using the HSG algorithm can accurately express the characteristics of various parts of the hull with uniform continuity, and the calculation speed of the proposed model can be increased by up to 8.314% compared with the existing best-performing algorithms. Thus, the proposed model is effective and can improve computational efficiency to a certain extent. The NURBS surfaces generated by the proposed model can be further applied to calculating the hydrostatic elements of hulls and compartments.

It is the purpose of this paper that uniform continuity of fractional order integral of fractal interpolation function (FIF) is researched. First, FIF generated by affine transformation is constructed. Second, the combination between Riemann–Liouville fractional order integral and FIF is defined. Finally, the continuity and the uniform continuity of fractional order integral of FIF are proved by compactness theorem of numbers sequence or finite covering theorem. The result shows that fractional order integral of FIF is uniformly continuous on a closed interval. [ABSTRACT FROM AUTHOR]

In this paper the properties of space of the G-permutation degree, like: weight, uniform connectedness and index boundedness are studied. It is proved that: (1) If (X, U) is a uniform space, then the mapping π s n, G : (X n , U n ) → (SP n GX, SP n GU) is uniformly continuous and uniformly open, moreover w (U) = w (SP n GU); (2) If the mapping f : (X, U) → (Y, V) is a uniformly continuous (open), then the mapping SP n Gf : (SP n GX, SP n GU) → (SP n GY, SP n GV) is also uniformly continuous (open); (3) If the uniform space (X, U) is uniformly connected, then the uniform space (SP n GX, SP n GU) is also uniformly connected.

We show how two fundamental sequential criteria for real functions, namely the sequential criterion for continuity and the sequential criterion for uniform continuity, are relaxed. Further, we derive a global continuity criterion, as an immediate consequence of the relaxed sequential criterion for continuity, and a fundamental property of uniformly continuous functions, as an application of the relaxed sequential criterion for uniform continuity. [ABSTRACT FROM AUTHOR]

In this paper we aim to characterize uniformly continuous real functions and pseudometrics on metric spaces, having uniformly continuous extension. For functions we use a very similar approach as McShane in [7] using moduli of continuity. By doing that we obtain an explicit formula for the extension. We also show that our characterization for functions is equivalent to one proposed in [8] for uniform spaces. We then show that a similar approach can be done for uniformly continuous pseudometrics. To do so we use the notion of chainable metric spaces and intrinsic metrics defined in [9]. A somewhat similar approach has been studied in [6] for normed linear spaces. [ABSTRACT FROM AUTHOR]

In this paper the properties of space of the G-permutation degree, like: weight, uniform connectedness and index boundedness are studied. It is proved that: (1) If (X, U) is a uniform space, then the mapping s n,G: (Xn, Un) ! (SPn GX, SPn GU) is uniformly continuous and uniformly open, moreover w (U) = w (SPn GU); (2) If the mapping f: (X, U) ! (Y, V) is a uniformly continuous (open), then the mapping SPn Gf: (SPn GX, SPn GU) ! (SPn GY, SPn GV) is also uniformly continuous (open); (3) If the uniform space (X, U) is uniformly connected, then the uniform space (SPn GX, SPn GU) is also uniformly connected. [ABSTRACT FROM AUTHOR]

In this note we study the differentiability with respect to the time-parameter of semicocycles over differentiable semigroups on a domain in a Banach space. [ABSTRACT FROM AUTHOR]

Using concentration-compactness arguments, we prove a variant of the Brézis–Lieb-Lemma under weaker assumptions on the nonlinearity than known before. An intermediate result on the uniform continuity of superposition operators in Sobolev space is of independent interest.

The first sentence in the abstract should be replaced with the sentence "A sequence $(x_{k})$ is called arithmetically convergent if for each $\varepsilon > 0$ there is an integer $n_{0}$ such that $|x_{m} - x_{}| \geq n_{0}$, where the symbol $< m, n >$ denotes the greatest common divisor of the integers $m$ and $n$".

In this paper, we start with establishing the existence of a minimal (maximal) Lp (1 < p ⩽ 2) solution to a one-dimensional backward stochastic differential equation (BSDE), where the generator g satisfies a p-order weak monotonicity condition together with a general growth condition in y and a linear growth condition in z. Then, we propose and prove a comparison theorem of Lp (1 < p ⩽ 2) solutions to one-dimensional BSDEs with q-order (1 ⩽ q < p) weak monotonicity and uniform continuity generators. As a consequence, an existence and uniqueness result of Lp (1 < p ⩽ 2) solutions is also given for BSDEs whose generator g is q-order (1 ⩽ q < p) weakly monotonic with a general growth in y and uniformly continuous in z. [ABSTRACT FROM AUTHOR]

In this note we show that the Axiom of Countable Choice is equivalent to two statements from the theory of pseudometric spaces: the first of them is a well-known characterization of uniform continuity for functions between (pseudo)metric spaces, and the second declares that sequentially compact pseudometric spaces are UC—meaning that all real valued, continuous functions defined on these spaces are necessarily uniformly continuous. [ABSTRACT FROM AUTHOR]

In this paper we investigate the problem of uniform continuity of nonautonomous superposition operators acting between spaces of functions of bounded Λ-variation. In particular, we give the sufficient conditions for nonautonomous superposition operators to continuously map a space of functions of bounded Λ-variation into itself. The conditions cover the generators being functions of C1-class (in view of two variables), but also allow for less regular functions, including discontinuous generators. [ABSTRACT FROM AUTHOR]

Abstract Let X be a uniform space and U (X) the linear space of real-valued uniformly continuous functions on X. Our main objective is to give a number of properties characterizing the fact that U (X) is stable under pointwise product in case X is a metric space. Some of these characterizations hold in much more general circumstances. [ABSTRACT FROM AUTHOR]