A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on \({\mathbb{R}}^{n}\) is established. The valuations obtained are functional versions of the classical intrinsic volumes. For their definition, singular Hessian valuations are introduced.

We establish geometric regularity for Type I blow-up limits of the Kähler-Ricci flow based at any sequence of Ricci vertices. As a consequence, the limiting flow is continuous in time in both Gromov-Hausdorff and Gromov-W1 distances. In particular, the singular sets of each time slice and its tangent cones are closed and of codimension no less than 4.

We show that, under mild assumptions, the spectrum of a sum of independent random matrices is close to that of the Gaussian random matrix whose entries have the same mean and covariance. This nonasymptotic universality principle yields sharp matrix concentration inequalities for general sums of independent random matrices when combined with the Gaussian theory of Bandeira, Boedihardjo, and Van Handel

In this work, we obtain the first upper bound on the multiplicity of Laplacian eigenvalues for negatively curved surfaces which is sublinear in the genus g. Our proof relies on a trace argument for the heat kernel, and on the idea of leveraging an r-net in the surface to control this trace. This last idea was introduced in 2021 for similar spectral purposes in the context of graphs of bounded degree

We obtain a homological characterisation of virtually free-by-cyclic groups among groups that are hyperbolic and virtually compact special. As a consequence, we show that many groups known to be coherent actually possess the stronger property of being virtually free-by-cyclic. In particular, we show that all one-relator groups with torsion are virtually free-by-cyclic, solving a conjecture of Baumslag

Let F be a holomorphic cuspidal Hecke eigenform for \(\mathrm{Sp}_{4}({\mathbb{Z}})\) of weight k that is a Saito–Kurokawa lift. Assuming the Generalized Riemann Hypothesis (GRH), we prove that the mass of F equidistributes on the Siegel modular variety as k⟶∞. As a corollary, we show under GRH that the zero divisors of Saito–Kurokawa lifts equidistribute as their weights tend to infinity.

We prove that the cylindrical capacity of a dynamically convex domain in \({\mathbb{R}}^{4}\) agrees with the least symplectic area of a disk-like global surface of section of the Reeb flow on the boundary of the domain. Moreover, we prove the strong Viterbo conjecture for all convex domains in \({\mathbb{R}}^{4}\) which are sufficiently C3 close to the round ball. This generalizes a result of Abb

The main aim of this paper is to analyze the behavior of time-fractional Emden–Fowler (EF) equation associated with Caputo–Katugampola fractional derivative occurring in mathematical physics and astrophysics. A powerful analytical approach, which is an amalgamation of q-homotopy analysis approach and generalized Laplace transform with homotopy polynomials, is implemented to obtain approximate analytical

Let [d1(x),d2(x),…,dn(x),…] be the Lüroth expansion of x∈(0,1], and let Ln(x)=max{d1(x),…,dn(x)}. It is shown that for any α≥0, the level set x∈(0,1]:limn→∞Ln(x)loglognn=α has Hausdorff dimension one. Certain sets of points for which the sequence {Ln(x)}n≥1 grows more rapidly are also investigated.

The examination of brain responses in individuals with a pornography addiction compared to those without sheds light on the neurobiological aspects associated with this behavior. Neuroscientific studies utilizing techniques such as electroencephalography (EEG) have shown that porn-addicted individuals may exhibit alterations in neural pathways related to reward processing and impulse control. In this

In this research, we introduce a new and generalized family of convex functions, entitled the α-convex functions in the second sense with respect to a parameter and examine their important algebraic properties. Based on this novel convexity concept, we explore a new class of fractional integral inequalities for functions that are twice differentiable. These results are derived from fundamental identities

In this paper, the gas-water two-phase flow characteristics of rock media are studied based on fractal theory and the relative roughness model, and the analytical model of gas-water relative permeability of rock pores with relative roughness is derived. Through numerical simulation, it is found that the maximum flow velocity in the rough microchannel is greater than the maximum flow velocity in the

The primary aim of this work is to investigate the nonlinear fractional Schrödinger equation, which is adopted to describe the ultra-short pulses in optical fibers. A variety of new soliton solutions and periodic solutions are constructed by implementing three efficient mathematical approaches, namely, the improved fractional F-expansion method, fractional Bernoulli (G′/G)-expansion method and fractional

Based on the pseudo-order relation, we introduce the concept of left and right ℏ-preinvex interval-valued functions (LR-ℏ-PIVFs). Further, we establish the Hermite–Hadamard and Hermite–Hadamard–Fejér-type estimates for LR-ℏ-PIVFs using generalized fractional integrals. Finally, an example of interval-valued fractional integrals is provided to illustrate the validity of the results derived herein. Our

This research paper introduces a novel approach to deriving traveling wave solutions (TWSs) for the Caputo-fractional Klein–Gordon equations. This research presents a distinct methodological advancement by introducing TWSs of a particular time-fractional partial differential equation, utilizing a non-local fractional operator, specifically the Caputo derivative. To achieve our goal, a novel transformation

In gas-bearing coal seam mining projects, the pivotal considerations encompass the assessment of gas migration, emission trends, and coal seam stability, which are crucial for ensuring both the safety and efficiency of the project. The accurate evaluation of the nonlinear evolution of the fracture network, acting as the primary conduit for gas migration and influenced by mining disturbances, coal seam

This study investigates the nonlinear time-fractional Harry Dym (𝕋𝔽ℍ𝔻) equation, a model with significant applications in soliton theory and connections to various other nonlinear evolution equations. The Harry Dym (ℍ𝔻) equation describes the propagation of nonlinear waves in various physical contexts, including shallow water waves, nonlinear optics, and plasma physics. The fractional-order derivative

In this paper, we explore the price dynamics of 16 representative records of USA Education Group stocks, encompassing two non-overlapping periods (before, during, and after COVID-19). Based on information theory and cluster analysis techniques, our study provides insights into disorder, predictability, efficiency, similarity, and resilience/weakness, considering the most diverse financial stakeholders

By means of He’s fractal derivative, a new fractal (2 + 1)-dimensional Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation is extracted in this paper. The semi-inverse method is employed to establish the generalized fractal variational principle. The generalized fractal variational principle can show the conservation laws through the energy form in the fractal space. Moreover, some semi-domain solutions

Micro/nanoscale lubrication must take into account the fractal profile of the shaft and bearing surfaces. A new fractal rheological model is proposed to describe the properties of the non-Newtonian fluid, and a fractal variational principle is established by the semi-inverse method, and finally the Lagrange multipliers can be found in the obtained variational formulation. This work provides a new fractal

One of the major challenges in population economics is accurately predicting population size. Incorrect predictions can lead to ineffective population control policies. Traditional differential models assume a smooth change in population, but this assumption is invalid when measuring population on a small-time scale. To address this change, we developed two-scale fractal population dynamics that can

In this paper, we derive the Darboux solutions of Ito-type coupled KdV equation in Darboux framework which is associated with Hirota Satsuma systems. One of the main results is the generalization of Nth-fold Darboux solutions in terms of Wronskians. We also derive the exact multi-soliton solutions for the coupled field variables of that system in the background of zero seed solutions. With the addition

In this paper, we seek to find solutions of the local time fractional Telegraph equation (LTFTE) by employing the local time fractional reduced differential transform method (LTFRDTM). This method produces a numerical approximate solution having the form of an infinite series that converges to a closed form solution in many cases. We apply LTFRDTM on four different LTFTEs to examine the efficiency

In recent years, fuzzy and fractional calculus are utilized for simulating complex models with uncertainty and memory effects. This study is focused on fuzzy-fractional modeling of (2+1)-dimensional Wu–Zhang (WZ) system. Caputo-type time-fractional derivative and triangular fuzzy numbers are employed in the model to observe uncertainties in the presence of non-local and memory effects. The extended

In this research, we use a novel version of the Extended Direct Algebraic Method (EDAM) namely generalized EDAM (gEDAM) to investigate periodic soliton solutions for nonlinear systems of fractional Schrödinger equations (FSEs) with conformable fractional derivatives. The FSEs, which is the fractional abstraction of the Schrödinger equation, grasp notable relevance in quantum mechanics. The proposed

In this paper, we calculate the Hausdorff dimension of the fractal set x∈𝕋d:∏1≤i≤d|Tβin(xi)−xi|<ψ(n) for infinitely many n∈ℕ, where Tβi is the standard βi-transformation with βi>1, ψ is a positive function on ℕ and |⋅| is the usual metric on the torus 𝕋. Moreover, we investigate a modified version of the shrinking target problem, which unifies the shrinking target problems and quantitative recurrence

The short-term traffic flow prediction can help to reduce flight delays and optimize resource allocation. Using chaos dynamics theory to analyze the chaotic characteristics of en-route traffic flow is the basis of short-term en-route traffic flow prediction and ensuring the orderly and smooth state of the en-route. This paper takes the time series of en-route traffic flow extracted from Automatic-Dependent

In previous works, we have proven that there are local tetrads in four-dimensional curved Lorentzian spacetimes that can be written in terms of two kinds of local structures, the skeletons and the gauge vectors. These tetrads diagonalize locally and covariantly the stress–energy tensors for systems of differential equations of the Einstein–Maxwell kind in the Abelian electromagnetic case, or of the

In this paper, within the scope of the local fractional derivative theory, the (4+1)-dimensional local fractional Fokas equation is researched. The study of exact solutions of high-dimensional nonlinear partial differential equations plays an important role in understanding complex physical phenomena in reality. In this paper, the exact traveling wave solution of generalized functions is analyzed defined

In this paper, we propose a new program for introducing the sign of the functional equation to present the entire functions of order one in number theory. We suggest some open problems for the zeros of these entire functions related to the completed Dedekind zeta function, completed quadratic Dirichlet L-functions, completed Ramanujan zeta function and completed automorphic L-function. These lead to

Fractal geometry plays an important role in the description of the characteristics of nature. Local fractional calculus, a new branch of mathematics, is used to handle the non-differentiable problems in mathematical physics and engineering sciences. The local fractional inequalities, local fractional ODEs and local fractional PDEs via local fractional calculus are studied. Fractional calculus is also

To achieve in situ condition-preserved coring of the lunar surface and deep lunar rocks and a return mission, it is necessary to explore the mechanical properties and failure modes of simulated lunar rocks that have physical and mechanical properties approximately equivalent to those of mare basalt under simulated lunar temperature environments (−120∘C to 200∘C). To this end, real-time uniaxial compression

In this paper, we investigate solutions of telegraph, Laplace and wave equations within the local fractional derivative operator by using local fractional Sumudu decomposition method. This method is coupled by the Sumudu transform and decomposition method. The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability

In this paper, we study a class of conformal metric deformations in the quasi-radial coordinate parametrizing the three-sphere in the conformally compactified Minkowski spacetime S1×S3. Prior to reduction of the associated Laplace–Beltrami operators to a Schrödinger form, a corresponding class of exactly solvable potentials (each one containing a scalar and a gradient term) is found. In particular

This study investigated the formation and evolution of a strange star known as SAX.J1808.4–3658 in the Krori–Barua Rainbow spacetime, resulting from the collapse of string fluid. The study examined the dynamical variables derived from the field equations, taking into consideration the influence of the particle’s energy on the mass density, pressure, and string tension. Additionally, various techniques

Wormholes are considered both from the Wheeler deWitt equation, as well as from the field equations in the Euclidean background of Robertson Walker mini-superspace in R2 gravity. Quantum wormhole satisfies Hawking Page wormhole boundary condition in the Euclidean background of mini-superspace, however, in the Lorentzian background wave functional turns to the usual oscillatory function. The Euclidean

This paper aims to provide a consistent, finite-valued, and mathematically well-defined reformulation of Feynman’s path-integral measure for quantum fields obtained by studying the Wiener stochastic process in the infinite-dimensional Hilbert space of quantum states. This reformulation will undoubtedly have a crucial role in formulating quantum gravity within a mathematically well-defined framework

This research investigates the impact of modified gravity on cosmic scales, focusing on f(Q) cosmology. By applying energy conditions, the study reconstructs various f(Q) models, considering an accelerating Universe, quintessence, and a cosmological constant Λ. Using up-to-date observational data, including the Supernova Pantheon sample and cosmic chronometer data, Hubble constants H0 are estimated

In this paper, we establish a generalized Wintgen inequality for quaternionic bi-slant submanifolds and QR-submanifolds (with minimal codimension) in quaternion space forms. We also aim to characterize the second fundamental form of those submanifolds for which the equality cases can hold. Finally, we provide examples of submanifolds embedded in quaternion space forms to support our results.

By the Hirota bilinear method, some new interaction solutions with the complex perturbation for CDGKS equation are obtained. Meanwhile, with the help of the classical nonlinear KdV equation, many new exact solutions of CDGKS equation are derived through the CKdVE method, since it satisfies the CKdVE solvability. Two typical examples also show the local geometric characteristics of the parameter perturbation

We proceed to obtain an exact analytical solution of the Brans–Dicke (BD) equations for the spatially flat (k=0) Friedmann–Lamaître–Robertson–Walker (FLRW) cosmological model in both cases of the absence and presence of the cosmological constant. The solution method that we use to solve the field equations of the BD equations is called the “invariants of symmetry groups method” (ISG method). This method

This paper is devoted to observe the physical attributes of static spherically symmetric isotropic compact stellar candidates in the context of Rastall theory of gravity. In order to inspect the structural composition of compact objects, the Heintzmann ansatz is taken into account. The unknown parameters associated with Heintzmann ansatz are evaluated through matching conditions with derived values

In this study, our main focus is to investigate the mass–radius relation and several important properties of massive neutron stars to realize the nature, behavior and evolution of these kinds of compact objects at present time. Also, we want to understand the equation-of-state of the core nuclear matter precisely with their stable equilibrium configuration. We have chosen a few massive binary pulsars

The edge-Wiener index is an important topological index in Chemical Graph Theory, defined as the sum of distances among all pairs of edges. Fractal structures have received much attention from scientists because of their philosophical and aesthetic significance, and chemists have even attempted to synthesize various types of molecular fractal structures. The level-3 Sierpinski triangle is constructed

We establish the existence of a spectral gap for the transfer operator induced on \(\mathbb{P}^{k} = \mathbb{P}^{k} (\mathbb{C})\) by a generic holomorphic endomorphism and a suitable continuous weight and its perturbations on various functional spaces, which is new even in dimension one. Thanks to the spectral gap, we establish an exponential speed of convergence for the equidistribution of the backward

In this work we study the two-dimensional local fractional Boussinesq equation. Based on the basic definitions and properties of the local fractional derivatives and bilinear form, we studied the soliton solutions of non-differentiable type with the generalized functions defined on Cantor sets by using bilinear method. Meanwhile, we discuss the result when fractal dimension is 1, and compare it with

The morphological characteristics of core disking can reflect the in-situ stress field characteristics to a certain extent, but a quantitative description method for disking-induced fracture surfaces is needed. The fractal geometry was introduced to refine the three-dimensional characteristics of the core disking fracture surfaces, and the disking mechanism was explored through morphological characteristics

In this paper, we present a new encryption method based on discrete wavelet transform (DWT). This method provides a number of advantages as a pseudo randomness and sensitivity due to the variation of the initial values. We start by decomposing the image with spatial reconstruction by DWT, followed by preformation by fractional chaotic cryptovirology and Henon map keys for space encryption. Bearing

In this paper, we address the entire Fourier sine and cosine integrals related to the Mittag-Leffler function. We guess that the entire functions have the real zeros in the entire complex plane. They can be connected with the well-known conjectures in analytic number theory. They are considered as the special solutions for the time-fractional diffusion equation within the Caputo fractional derivative

In this paper, we propose a tempered xi function obtained by the recombination of the decomposable functions for the Riemann xi function for the first time. We first obtain its functional equation and series representation. We then suggest three equivalent open problems for the zeros for it. We finally consider its behaviors on the critical line.

In this paper, the scaling-law vector calculus, which is connected between the vector calculus and the scaling law in fractal geometry, is addressed based on the Leibniz derivative and Stieltjes integral for the first time. The scaling-law Gauss–Ostrogradsky-like, Stokes-like and Green-like theorems, and Green-like identities are considered in sense of the scaling-law vector calculus. The strong and

Wave–wave interaction occurs in the propagation deformation of nonlinear long waves in shallow-water. In order to further study the propagation mechanism of shallow-water long waves interaction, the exact traveling wave solutions of the local fractional generalized Hirota–Satsuma coupled Korteweg–de Vries (HS-KdV) equations defined by the Cantor sets are obtained. The non-differentiable solutions with