Under a microgravity condition, the microgravity-induced motion of a rigid pendulum has many special properties, which cannot be successfully revealed by any known theory. This work suggests a new fractal model for this purpose to describe the microgravity-induced motion by using the fractal derivative, and its variational principle is successfully established according to the semi-inverse method.

This paper considers the generalized Langevin equation involving ψ-Caputo fractional derivatives in a Banach space. The fractional derivative is generalized from the Caputo derivative (ψ(t)=t), the Caputo–Katugampola (ψ(t)=ψρ(t)=(tρ−1)/ρ, the Hadamard derivative (ψ(t)=ψH(t)=lnt). We investigate the existence of mild solutions uψ of the problem, in which the source function is assumed to satisfy some

Fractal dimension (D) is a widely used quantity to represent the irregularity of surfaces or profiles, e.g. it is often applied together with surface roughness to evaluate the quality of machined surfaces objectively and precisely. There are some conventional algorithms to calculate D values through the morphological images of measured surfaces. However, the accuracies or efficiencies of these algorithms

In this paper, the epidemic spreading was investigated from the point of view of fractal. Firstly, the real network was abstracted as a fully connected fractal network. Based on the fractal network, the fractal spreading process was studied. The fractal spreading process was simulated to analyze the change of infection density during transmission. The results showed that the infection density presented

The fractal theory has been applied to understand the transport law for the non-Newton Herschel–Bulkley (H-B) fluid grouting in fractal soil consisting of a bunch of arbitrary cross-sectional tortuous capillaries. The fractal models for the average flow velocity, starting pressure gradient and effective permeability are the functions of the cross-sectional geometric factors of capillaries, minimum

In the process of gas mining, the fracture distribution with power law length and the pore structure with adsorption effect have an important influence on the coal seam permeability. In recent years, the research on the internal structure of coal seam and the fluid flow mechanism has attracted a large number of researchers. In this paper, by considering the coal matrix deformation caused by adsorption

To study the time-delay multiscale partial cross-correlation between the high-frequency stock series SSEC and SZSE in the Chinese stock market, this paper proposes a new partial cross-correlation exponent, namely the q-order time-delay multiscale partial cross-correlation exponent (denoted by Hq(τ,s)). We integrate the time-delay factor and the multiscale range fluctuation function into partial cross-correlation

In this paper, we study the eccentric distance sum of substitution tree networks. Calculation of eccentric distance sum naturally involves calculation of average geodesic distance and it is much more complicated. We obtain the asymptotic formulas of average geodesic distance and eccentric distance sum of both symmetric and asymmetric substitution tree networks. Our result on average geodesic distance

Reliable capillary pressure data are required for reservoir simulation and fluid flow characterization in porous media. The capillary pressure is commonly measured in the laboratory, which is costly, challenging, and accompanied by measurement uncertainties, especially for low-permeability core samples. Besides laboratory measurements, two-dimensional (2D) rock images reveal another prospect to obtain

We study the stability of linear fractional order maps. We show that in the stable region, the evolution is described by Mittag-Leffler functions and a well-defined effective Lyapunov exponent can be obtained in these cases. For one-dimensional systems, this exponent can be related to the corresponding fractional differential equation. A fractional equivalent of map f(x)=ax is stable for ac(α)

In literature, the integro-differential equations (IDEs) are very much common in the engineering as well in the scientific fields for modeling of dynamical problems. There is a large number of contributions in the study of IDEs for the integer orders. But the cases in fractional order are limited and need consideration of the researchers in the area. In this paper, we initiate a study for fractional

Accurate characterization of pore-scale structures of porous media is necessary for studying their transport mechanisms and properties. An analytical model for pore and capillary structures of porous media is developed based on fractal theory in this study. The pore and tortuosity fractal dimensions are introduced to characterize the pore size distribution and tortuous flow paths. A power law scaling

The spectral and non-spectral problems of measures have been considered in recent years. For the Cantor measure μρ, Hu and Lau [Spectral property of the Bernoulli convolutions, Adv. Math.219(2) (2008) 554–567] showed that L2(μρ) contains infinite orthogonal exponentials if and only if ρ becomes some type of binomial number. In this paper, we classify the spectral number of the Cantor measure μρ except

This paper is devoted to prove the existence of mild solutions of coupled hybrid fractional order system with Caputo–Hadamard derivatives using Dhage fixed point theorem in Banach algebras. In order to confirm the applicability of obtained result an example is also presented.

For the self-affine IFS {A−1(x+di),i=1,…,m} satisfying the weak separation condition (WSC), let K be the corresponding self-affine set. It is proven in this paper that K has positive Lebesgue measure only if the interior of K is non-empty.

Under investigations into this paper is a higher-dimensional model, namely the time fractional (3+1)-dimensional Korteweg–de Vries (KdV)-type equation, which can be usually used to express shallow water wave phenomena. At the beginning, the symmetry of the time fractional (3+1)-dimensional KdV-type equation via the group analysis scheme is obtained. The definition of the fractional derivative in the

In this paper, we mainly investigate the fractional differential of a class of continuous functions. The upper Box dimension of the Marchaud fractional differential of continuous functions satisfying the Hölder condition increases at most linearly with the order of the fractional differential when they exist. Furthermore, if a continuous function satisfies the Lipschitz condition, the upper Box dimension

It is shown that every two-variable adjunction in categories enriched in a commutative quantale serves as a base for constructing Isbell adjunctions between functor categories, and Kan adjunctions are precisely Isbell adjunctions constructed from suitable associated two-variable adjunctions. Representation theorems are established for fixed points of these adjunctions.

Let (tn)n≥0 be the well-known ±1 Thue–Morse sequence +1,−1,−1,+1,−1,+1,+1,−1,…. Since the 1982–1983 work of Coquet and Dekking, it is known that ∑k

The calculus of the mixed Weyl–Marchaud fractional derivative has been investigated in this paper. We prove that the mixed Weyl–Marchaud fractional derivative of bivariate fractal interpolation functions (FIFs) is still bivariate FIFs. It is proved that the upper box dimension of the mixed Weyl–Marchaud fractional derivative having fractional order γ=(p,q) of a continuous function which satisfies μ-Hölder

It is very difficult to characterize the transport properties of porous media due to the disorder of pores distribution in porous media. In this paper, we study heat conduction through porous media with randomly fractures which are considered as tree-like networks. An expression for effective thermal conductivity (ETC) of saturated dual-porosity media is derived based on the fractal characteristics

Recently, wavelets are playing a very important role in the numerical analysis. In this paper, an investigation is made for numerical solution of a class of nonlinear fractional differential equations (FDEs) with error analysis using Haar wavelet collocation method. The proposed method is illustrated through presenting different kinds of FDEs, which gives the approximate solution and is in good agreement

The stretched Cantor product is not self-similar but rectifiable. Using the method of finite pattern, we study the mean geodesic distance on the stretched Cantor product.

In this paper, we introduce touching networks including skeleton networks of Sierpinski gasket, Sierpinski tetrahedron, Sierpinski hexagon and Lindstr öm Snowflake. For touching networks, we establish the self-similar theory of limit metric space.

This paper relates to the field of Artificial Intelligence, specifically to image recognition, and provides an innovative method to take advantage of Blockchain Convolutional Neural Networks (BCNNs) in Emotion Recognitions (ERs) using audio–visual emotion patterns to determine a healthcare emergency to be attended. BCNN architectures were used to identify emergency patterns. The results obtained indicate

We give some local moves of the Stein factorization of the product map of two Morse functions on a closed orientable smooth 3-manifold which can be realized by isotopies of the functions.

In a recent article, Cumplido and Paris studied the question of commensurability between Artin groups of spherical type. Their analysis left six cases undecided, for the following pairs of Artin groups: (F4,D4), (H4,D4), (F4,H4), (E6,D6), (E7,D7), and (E8,D8). In this note we resolve the first two of these cases, namely, we show that the Artin groups of types F4 and H4 are not commensurable with that

In this paper, a partial order and its basic properties are exploited in a fuzzy quasi-metric space in the sense of George and Veeramani (A. Gregori, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (1994) 395–399). Based on this partial order, Caristi's fixed point theorem, Ekeland's variational principle and Takahashi's maximization theorem are extended to fuzzy quasi-metric

In this paper, we investigate some versions of d-space, well-filtered space and Rudin space concerning various countability properties. It is proved that every T0 space with a first-countable sobrification is an ω-Rudin space and every first-countable T0 space is well-filtered determined. Therefore, every ω-well-filtered space with a first-countable sobrification is sober. It is also shown that every

Some sequences S of measurable sets tending to zero generate density-like topologies TS on the real line finer than the natural topology Tnat. For a topology TS we consider the metric space CS,S of S-continuous functions f:(R,TS)→(R,TS), and we consider the metric spaces Cnat,nat and C+ of continuous functions and of right continuous functions, respectively, all spaces endowed with the supremum metric

G. Debs and J. Saint Raymond in 2009 defined the Borel separation rank of an analytic ideal I (rk(I)) as minimal ordinal α<ω1 such that there is S∈Σ1+α0 with I⊆S and I⋆∩S=∅, where I⋆ is the filter dual to the ideal I. Moreover, they introduced ideals Finα, for all α<ω1, and conjectured that rk(I)≥α if and only if I contains an isomorphic copy of Finα (Finα⊑I). To define Finα in the case of limit ordinals

We discuss the monotonicity problem for the amenable category of closed manifolds under maps of non-zero degree. In dimension three this leads to a variation on a recent theorem of Capovilla, Löh and Moraschini [1].

We show that the Menger curve can be represented as a set-valued inverse limit of intervals [0,1] with a single bonding function. The graph of the function is homeomorphic to the Sierpiński carpet. This answers a question by M. Hiraki and H. Kato.

In this paper we develop a new approach to the study of uncountable fundamental groups by using Hurewicz fibrations with the unique path-lifting property (lifting spaces for short) as a replacement for covering spaces. In particular, we consider the inverse limit of a sequence of covering spaces of X. It is known that the path-connectivity of the inverse limit can be expressed by means of the derived

Using the notions of Topological dynamics, H. Furstenberg defined central sets and proved the Central Sets Theorem. Later V. Bergelson and N. Hindman characterized central sets in terms of algebra of the Stone-Čech Compactification of discrete semigroup. They found that central sets are the members of minimal idempotents of βS, the Stone-Čech Compactification of a semigroup (S,⋅). We know that any

Knotoids are open ended knot diagrams regarded up to Reidemeister moves and isotopies. The notion is introduced by Turaev in 2012. Two most important numeric characteristics of a knotoid are the crossing number and the height. The latter is the least number of intersections between a diagram and an arc connecting its endpoints, where the minimum is taken over all representative diagrams and all such

We describe two ways to define higher order Toda brackets in a pointed simplicial model category \({\mathcal {D}}\): one is a recursive definition using model categorical constructions, and the second uses the associated simplicial enrichment. We show that these two definitions agree, by providing a third, diagrammatic, description of the Toda bracket, and explain how it serves as the obstruction to

Let \({\mathcal {P}}\) be a property of subobjects relevant in a category \({\mathcal {C}}\). An object \(X\in {\mathcal {C}}\) is \({\mathcal {P}}\)-separated if the diagonal in \(X\times X\) has \({\mathcal {P}}\); thus e.g. closedness in the category of topological spaces (resp. locales) induces the Hausdorff (resp. strong Hausdorff) axiom. In this paper we study the locales (frames) in which the

In work from 2004, Cimasoni gave a geometric computation of the multivariable Conway potential function in terms of a generalization of a Seifert surface for a link called a C-complex [2]. These surfaces were introduced by Cooper [9], [10] for 2-component links and were used to compute Alexander invariants, signatures and nullities. Cooper presents a sequence of geometric moves which relate any two

In this paper, we show that the quantum disk, i.e. the quantum space corresponding to the Toeplitz C∗-algebra does not admit any compact quantum group structure. We prove that if such a structure existed the resulting compact quantum group would simultaneously be of Kac type and not of Kac type. The main tools used in the solution come from the theory of operators on Hilbert spaces.

We establish some results about countable products of spaces that are either consonant or whose complement in some compactification has the Menger Property. We use our results to answer some questions of A.Bouziad.

We prove a flatness result for entire nonlocal minimal graphs having some partial derivatives bounded from either above or below. This result generalizes fractional versions of classical theorems due to Bernstein and Moser. Our arguments rely on a general splitting result for blow-downs of nonlocal minimal graphs. Employing similar ideas, we establish that entire nonlocal minimal graphs bounded on

We develop a new approach to the conformal geometry of embedded hypersurfaces by treating them as conformal infinities of conformally compact manifolds. This involves the Loewner–Nirenberg-type problem of finding on the interior a metric that is both conformally compact and of constant scalar curvature. Our first result is an asymptotic solution to all orders. This involves log terms. We show that

In this paper, we construct Delaunay type constant mean curvature surfaces along a nondegenerate closed geodesic in a 3‑dimensional Riemannian manifold.

We provide a suitable axiomatic framework for differential cohomology in the relative case and we deduce the corresponding long exact sequences. We also construct the relative version of the generalized Cheeger–Simons characters and we define the integration map when the fibre has a boundary, generalizing to any cohomology theory the results of [13] (F. Ferrari Ruffino, “Relative Deligne cohomology

The equivalence between dg duality and Verdier duality has been established for cyclic operads earlier. We propose a generalization of this correspondence from cyclic operads and dg duality to twisted modular operads and the Feynman transform. Specifically, for each twisted modular operad \(\mathcal {P}\) (taking values in dg-vector spaces over a field k of characteristic 0), there is a certain sheaf

In this paper, we study the moduli space of frozen planet orbits in the Helium atom for an interpolation between instantaneous and mean interactions and show that this moduli space is compact.

The aim of this paper is to consider questions concerning the possible maximum cardinality of various separable pseudoradial (in short: SP) spaces. The most intriguing question here is if there is in ZFC a regular (or just Hausdorff) SP space of cardinality >c. While this question is left open, we establish a number of non-trivial results that we list below. • It is consistent with MA+c=ℵ2 that there

Given a T0 paratopological group G and a class C of continuous homomorphisms of paratopological groups, we define the C-semicompletion C[G) and C-completion C[G] of the group G that contain G as a dense subgroup, satisfy the T0-separation axiom and have certain universality properties. For special classes C, we present some necessary and sufficient conditions on G in order that the (semi)completions

A betweenness structure on a set X is a ternary relation [⋅,⋅,⋅]⊆X3 that captures a rudimentary notion of one point of X lying between two others. The interval [a,b] is the set of all points lying between a and b, and a subset C of X is convex if [a,b]⊆C whenever a,b∈C. The span of a set A is the union of all intervals [a,b], where a,b∈A; by iterating the span operator countably many times, we obtain

We denote by Cs(X) the set C(X) of real-valued continuous functions defined on X endowed with the topology of the uniform convergence on the closed separable subspaces of X. In this paper we continue the study of Cs(X) initiated in Pseudouniform topologies on C(X) given by ideals (Pichardo-Mendoza et al. (2013) [7]). We prove that Cs(X) is a k-space if and only if Cs(X) is metrizable, and that compactness

For a topologically complete space X and a family of closed covers A of X satisfying a “local refinement condition” and a “completeness condition,” we give a construction of an inverse system NA of simplicial complexes and simplicial bonding maps such that the limit space N∞=lim←NA is homotopy equivalent to X. A connection with cell structures [2], [3] is discussed.

Results in this paper concern finding a cardinal number κ, as small as possible, such that every uniformly or proximally continuous mapping from a given subspace X of a product ∏IXi into some A factorizes via a subspace of ∏JXi with |J|≤κ. In some cases we substantially improve Vidossich theorem from [12]. Influenced by investigating locally co-presentable categories in [8], also cardinals κ are found

The aim of this paper is to study the class of spaces with the FNS property and the π-FNS property. We prove that compact spaces with the FNS property for some base consisting of co-zero sets are openly generated spaces and spaces with the π-FNS property are skeletally generated spaces. We give examples of families without the Freese–Nation property.

Using the classical technique of condensation of singularities, we prove that, for every zero-dimensional, complete separable metric space G, there exists a Suslinian, chainable metric continuum whose set of end points is homeomorphic to G. This answers a question posed by R. Adikari and W. Lewis in [Houston J. Math. 45 (2019), no. 2, pp. 609–624].

Let X be a set and A⊆P(X) be a family closed under finite intersections such that ∅,X∈A. If ψ=o,ω,γ, then Ψ(A) is the family of those ψ-covers U for which U⊆A. In [3], properties (Ψ0) of a family F⊆XR of real functions have been introduced. The main result of the paper Theorem 4.1 reads as follows: if Φ=Ω,Γ and Ψ=O,Ω,Γ, then for any pair 〈Φ,Ψ〉 different from 〈Ω,O〉, X has the covering property S1(Φ(A)

The Golomb space (resp. the Kirch space) is the set N of positive integers endowed with the topology generated by the base consisting of arithmetic progressions a+bN0={a+bn:n≥0} where a,b∈N and b is a (square-free) number, coprime with a. It is known that the Golomb space (resp. the Kirch space) is connected (and locally connected). By a recent result of Banakh, Spirito and Turek, the Golomb space

As a step towards understanding the \(\mathrm {tmf}\)-based Adams spectral sequence, we compute the K(1)-local homotopy of \(\mathrm {tmf}\wedge \mathrm {tmf}\), using a small presentation of \(L_{K(1)}\mathrm {tmf}\) due to Hopkins. We also describe the K(1)-local \(\mathrm {tmf}\)-based Adams spectral sequence.

The impact of crack–cocaine dependence on the quality and microarchitecture of the mandibular bone tissue requires further investigation. This cross-sectional study evaluated the fractal dimension and panoramic radiomorphometric indices in crack–cocaine-addicted men. Panoramic radiographs were obtained from 24 addicted and 24 nonaddicted men (control individuals) between the ages of 18 years and 60

Based on high-frequency data, we study the difference in cryptocurrency market before and during the COVID-19. We analyze the multifractality of three major cryptocurrencies via the multifractal detrended fluctuation analysis (MFDFA). To investigate the source of multifractality, we construct shuffled, surrogated and truncate data. The results show that market efficiency of cryptocurrency has decreased