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A Continuous Cusp Closing Process for Negative Kähler-Einstein Metrics Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-03-04
Xin Fu, Hans-Joachim Hein, Xumin JiangWe give an example of a family of smooth complex algebraic surfaces of degree 6 in \(\mathbb{CP}^{3}\) developing an isolated elliptic singularity. We show via a gluing construction that the unique Kähler-Einstein metrics of Ricci curvature −1 on these sextics develop a complex hyperbolic cusp in the limit, and that near the tip of the forming cusp a Tian-Yau gravitational instanton bubbles off.
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On the Shapes of Rational Lemniscates Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-02-18
Christopher J. Bishop, Alexandre Eremenko, Kirill LazebnikA rational lemniscate is a level set of |r| where \(r: \widehat {\mathbb{C}}\rightarrow \widehat {\mathbb{C}}\) is rational. We prove that any planar Euler graph can be approximated, in a strong sense, by a homeomorphic rational lemniscate. This generalizes Hilbert’s lemniscate theorem; he proved that any Jordan curve can be approximated (in the same strong sense) by a polynomial lemniscate that is
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Suppression of Chemotactic Singularity by Buoyancy Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-02-13
Zhongtian Hu, Alexander Kiselev, Yao YaoChemotactic singularity formation in the context of the Patlak-Keller-Segel equation is an extensively studied phenomenon. In recent years, it has been shown that the presence of fluid advection can arrest the singularity formation given that the fluid flow possesses mixing or diffusion enhancing properties and its amplitude is sufficiently strong - this effect is conjectured to hold for more general
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Uniqueness of Tangent Flows at Infinity for Finite-Entropy Shortening Curves Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-02-13
Kyeongsu Choi, Dong-Hwi Seo, Wei-Bo Su, Kai-Wei ZhaoIn this paper, we prove that an ancient smooth curve-shortening flow with finite entropy embedded in \(\mathbb{R}^{2}\) has a unique tangent flow at infinity. To this end, we show that its rescaled flows backwardly converge to a line with multiplicity m≥3 exponentially fast in any compact region, unless the flow is a shrinking circle, a static line, a paper clip, or a translating grim reaper. In addition
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On the Spielman-Teng Conjecture Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-02-13
Ashwin Sah, Julian Sahasrabudhe, Mehtaab SawhneyLet M be an n×n matrix with iid subgaussian entries with mean 0 and variance 1 and let σn(M) denote the least singular value of M. We prove that $$ \mathbb{P}\big( \sigma _{n}(M) \leqslant \varepsilon n^{-1/2} \big) = (1+o(1)) \varepsilon + e^{- \Omega (n)} $$ for all 0⩽ε≪1. This resolves, up to a 1+o(1) factor, a seminal conjecture of Spielman and Teng.
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Geometric Langlands Duality for Periods Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-02-06
Tony Feng, Jonathan WangWe study conjectures of Ben-Zvi–Sakellaridis–Venkatesh that categorify the relationship between automorphic periods and L-functions in the context of the Geometric Langlands equivalence. We provide evidence for these conjectures in some low-rank examples, by using derived Fourier analysis and the theory of chiral algebras to categorify the Rankin-Selberg unfolding method.
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Optimal Rigidity and Maximum of the Characteristic Polynomial of Wigner Matrices Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-02-05
Paul Bourgade, Patrick Lopatto, Ofer ZeitouniWe determine to leading order the maximum of the characteristic polynomial for Wigner matrices and β-ensembles. In the special case of Gaussian-divisible Wigner matrices, our method provides universality of the maximum up to tightness. These are the first universal results on the Fyodorov–Hiary–Keating conjectures for these models, and in particular answer the question of optimal rigidity for the spectrum
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Invariant Subvarieties of Minimal Homological Dimension, Zero Lyapunov Exponents, and Monodromy Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-02-03
Paul ApisaWe classify the \(\mathrm{GL}(2,\mathbb{R})\)-invariant subvarieties \(\mathcal{M}\) in strata of Abelian differentials for which any two \(\mathcal{M}\)-parallel cylinders have homologous core curves. As a corollary we show that outside of an explicit list of exceptions, if \(\mathcal{M}\) is a \(\mathrm{GL}(2,\mathbb{R})\)-invariant subvariety, then the Kontsevich-Zorich cocycle has nonzero Lyapunov
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Unit and Distinct Distances in Typical Norms Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-01-24
Noga Alon, Matija Bucić, Lisa SauermannErdős’ unit distance problem and Erdős’ distinct distances problem are among the most classical and well-known open problems in discrete mathematics. They ask for the maximum number of unit distances, or the minimum number of distinct distances, respectively, determined by n points in the Euclidean plane. The question of what happens in these problems if one considers normed spaces other than the Euclidean
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Optimal Transport Between Algebraic Hypersurfaces Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-01-22
Paolo Antonini, Fabio Cavalletti, Antonio LerarioWhat is the optimal way to deform a projective hypersurface into another one? In this paper we will answer this question adopting the point of view of measure theory, introducing the optimal transport problem between complex algebraic projective hypersurfaces. First, a natural topological embedding of the space of hypersurfaces of a given degree into the space of measures on the projective space is
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Lagrangian Subvarieties of Hyperspherical Varieties Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-01-22
Michael Finkelberg, Victor Ginzburg, Roman TravkinGiven a hyperspherical G-variety 𝒳 we consider the zero moment level Λ𝒳⊂𝒳 of the action of a Borel subgroup B⊂G. We conjecture that Λ𝒳 is Lagrangian. For the dual G∨-variety 𝒳∨, we conjecture that that there is a bijection between the sets of irreducible components \(\operatorname {Irr}\Lambda _{{\mathscr{X}}}\) and \(\operatorname {Irr}\Lambda _{{\mathscr{X}}^{\vee }}\). We check this conjecture
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On the Distance Sets Spanned by Sets of Dimension d/2 in $\mathbb{R}^{d}$ Geom. Funct. Anal. (IF 2.4) Pub Date : 2025-01-09
Pablo Shmerkin, Hong WangWe establish the dimension version of Falconer’s distance set conjecture for sets of equal Hausdorff and packing dimension (in particular, for Ahlfors-regular sets) in all ambient dimensions. In dimensions d=2 or 3, we obtain the first explicit improvements over the classical 1/2 bound for the dimensions of distance sets of general Borel sets of dimension d/2. For example, we show that the set of distances
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The Hadwiger Theorem on Convex Functions, I Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-10-16
Andrea Colesanti, Monika Ludwig, Fabian MussnigA 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.
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Geometric Regularity of Blow-up Limits of the Kähler-Ricci Flow Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-10-16
Max Hallgren, Wangjian Jian, Jian Song, Gang TianWe 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.
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Universality and Sharp Matrix Concentration Inequalities Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-10-10
Tatiana Brailovskaya, Ramon van HandelWe 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
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Birkhoff Conjecture for Nearly Centrally Symmetric Domains Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-10-10
V. Kaloshin, C. E. Koudjinan, Ke Zhang -
Gromov-Witten Invariants in Complex and Morava-Local K-Theories Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-10-07
Mohammed Abouzaid, Mark McLean, Ivan Smith -
Direct Products of Free Groups in Aut(FN) Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-08-05
Martin R. Bridson, Richard D. Wade -
Maximal Multiplicity of Laplacian Eigenvalues in Negatively Curved Surfaces Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-07-25
Cyril Letrouit, Simon MachadoIn 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
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Virtually Free-by-Cyclic Groups Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-07-22
Dawid Kielak, Marco LintonWe 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
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Mass Equidistribution for Saito-Kurokawa Lifts Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-07-23
Jesse Jääsaari, Stephen Lester, Abhishek SahaLet 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.
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Disk-Like Surfaces of Section and Symplectic Capacities Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-07-16
O. EdtmairWe 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
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The Singular Support of Sheaves Is γ-Coisotropic Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-07-01
Stéphane Guillermou, Claude Viterbo -
Fusion and Positivity in Chiral Conformal Field Theory Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-06-27
James E. Tener -
Growth of k-Dimensional Systoles in Congruence Coverings Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-06-05
Mikhail Belolipetsky, Shmuel Weinberger -
FORECASTING THE BEHAVIOR OF FRACTIONAL MODEL OF EMDEN–FOWLER EQUATION WITH CAPUTO–KATUGAMPOLA MEMORY Fractals (IF 3.3) Pub Date : 2024-06-04
JAGDEV SINGH, ARPITA GUPTA, JUAN J. NIETOThe 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
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SOME FRACTALS RELATED TO PARTIAL MAXIMAL DIGITS IN LÜROTH EXPANSION Fractals (IF 3.3) Pub Date : 2024-06-04
JIANG DENG, JIHUA MA, KUNKUN SONG, ZHONGQUAN XIELet [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.
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COMPLEXITY-BASED ANALYSIS OF THE VARIATIONS IN THE BRAIN RESPONSE OF PORN-ADDICTED AND HEALTHY INDIVIDUALS UNDER DIFFERENT FUNCTION TASKS Fractals (IF 3.3) Pub Date : 2024-05-31
NAJMEH PAKNIYAT, JANARTHANAN RAMADOSS, ANITHA KARTHIKEYAN, PENHAKER MAREK, ONDREJ KREJCAR, HAMIDREZA NAMAZIThe 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
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ON A NEW α-CONVEXITY WITH RESPECT TO A PARAMETER: APPLICATIONS ON THE MEANS AND FRACTIONAL INEQUALITIES Fractals (IF 3.3) Pub Date : 2024-05-30
MUHAMMAD SAMRAIZ, TAHIRA ATTA, HOSSAM A. NABWEY, SAIMA NAHEED, SINA ETEMADIn 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
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RELATIVE PERMEABILITY MODEL OF TWO-PHASE FLOW IN ROUGH CAPILLARY ROCK MEDIA BASED ON FRACTAL THEORY Fractals (IF 3.3) Pub Date : 2024-05-30
SHANSHAN YANG, SHUAIYIN CHEN, XIANBAO YUAN, MINGQING ZOU, QIAN ZHENGIn 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
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NEW OPTICAL SOLITONS FOR NONLINEAR FRACTIONAL SCHRÖDINGER EQUATION VIA DIFFERENT ANALYTICAL APPROACHES Fractals (IF 3.3) Pub Date : 2024-05-30
KANG-LE WANGThe 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
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NEW FRACTIONAL INTEGRAL INEQUALITIES FORLR-ℏ-PREINVEX INTERVAL-VALUED FUNCTIONS Fractals (IF 3.3) Pub Date : 2024-05-29
YUN TAN, DAFANG ZHAOBased 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
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A MODERN TRAVELING WAVE SOLUTION FOR CAPUTO-FRACTIONAL KLEIN–GORDON EQUATIONS Fractals (IF 3.3) Pub Date : 2024-05-29
AHMAD EL-AJOU, RANIA SAADEH, ALIAA BURQAN, MAHMOUD ABDEL-ATYThis 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
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QUANTIFYING ROUGH FRACTURE BEHAVIORS IN GAS-BEARING COAL SEAM: A FULLY COUPLED FRACTAL ANALYSIS Fractals (IF 3.3) Pub Date : 2024-05-29
ZHOU ZHOU, WAN ZHIJUN, LIU GUANNAN, YU BOMING, YE DAYU, WEI MINGYAOIn 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
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Rigidity Theorems for Higher Rank Lattice Actions Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-05-29
Homin Lee -
The Parabolic U(1)-Higgs Equations and Codimension-Two Mean Curvature Flows Geom. Funct. Anal. (IF 2.4) Pub Date : 2024-05-29
Davide Parise, Alessandro Pigati, Daniel Stern -
NONLINEARITY AND MEMORY EFFECTS: THE INTERPLAY BETWEEN THESE TWO CRUCIAL FACTORS IN THE HARRY DYM MODEL Fractals (IF 3.3) Pub Date : 2024-05-23
MOSTAFA M. A. KHATER, SULEMAN H. ALFALQIThis 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
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SPILLOVER EFFECTS OF COVID-19 ON USA EDUCATION GROUP STOCKS Fractals (IF 3.3) Pub Date : 2024-05-23
LEONARDO H. S. FERNANDES, FERNANDO H. A. DE ARAUJO, JOSÉ W. L. SILVA, JOSÉ P. V. FERNANDES, URBANNO P. S. LEITE, LUCAS M. MUNIZ, RANILSON O. A. PAIVA, IBSEN M. B. S. PINTO, BENJAMIN MIRANDA TABAKIn 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
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THE FRACTAL ZAKHAROV–KUZNETSOV–BENJAMIN–BONA–MAHONY EQUATION: GENERALIZED VARIATIONAL PRINCIPLE AND THE SEMI-DOMAIN SOLUTIONS Fractals (IF 3.3) Pub Date : 2024-05-23
KANG-JIA WANG, FENG SHI, SHUAI LI, PENG XUBy 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
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VARIATIONAL PRINCIPLE FOR A FRACTAL LUBRICATION PROBLEM Fractals (IF 3.3) Pub Date : 2024-05-23
YU-TING ZUOMicro/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
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FAST AND ACCURATE POPULATION FORECASTING WITH TWO-SCALE FRACTAL POPULATION DYNAMICS AND ITS APPLICATION TO POPULATION ECONOMICS Fractals (IF 3.3) Pub Date : 2024-05-23
YARONG ZHANG, NAVEED ANJUM, DAN TIAN, ABDULRAHMAN ALI ALSOLAMIOne 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
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Multi-soliton solutions of Ito-type coupled KdV equation with conservation laws in Darboux framework Int. J. Geom. Methods Mod. Phys. (IF 2.1) Pub Date : 2024-05-21
Irfan Mahmood, Zhao Li, Hira Sohail, Allah Ditta, Hosam O. Elansary, Ejaz HussainIn 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
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LOCAL TIME FRACTIONAL REDUCED DIFFERENTIAL TRANSFORM METHOD FOR SOLVING LOCAL TIME FRACTIONAL TELEGRAPH EQUATIONS Fractals (IF 3.3) Pub Date : 2024-05-21
YU-MING CHU, MAHER JNEID, ABIR CHAOUK, MUSTAFA INC, HADI REZAZADEH, ALPHONSE HOUWEIn 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
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DESIGN AND IMPLEMENTATION OF FUZZY-FRACTIONAL WU–ZHANG SYSTEM USING HE–MOHAND ALGORITHM Fractals (IF 3.3) Pub Date : 2024-05-21
MUBASHIR QAYYUM, EFAZA AHMAD, MUHAMMAD SOHAIL, NADIA SARHAN, EMAD MAHROUS AWWAD, AMJAD IQBALIn 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
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ON THE PERIODIC SOLITON SOLUTIONS FOR FRACTIONAL SCHRÖDINGER EQUATIONS Fractals (IF 3.3) Pub Date : 2024-05-21
RASHID ALI, DEVENDRA KUMAR, ALI AKGÜL, ALI ALTALBEIn 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
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MODIFIED SHRINKING TARGET PROBLEM FOR MATRIX TRANSFORMATIONS OF TORI Fractals (IF 3.3) Pub Date : 2024-05-21
NA YUAN, SHUAILING WANGIn 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
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RESEARCH ON CHAOTIC CHARACTERISTICS AND SHORT-TERM PREDICTION OF EN-ROUTE TRAFFIC FLOW USING ADS-B DATA Fractals (IF 3.3) Pub Date : 2024-05-17
ZHAOYUE ZHANG, ZHE CUI, ZHISEN WANG, LINGKAI MENGThe 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
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Tetrad extremal field-gauge vector structure Int. J. Geom. Methods Mod. Phys. (IF 2.1) Pub Date : 2024-05-17
Alcides GaratIn 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
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EXACT TRAVELING WAVE SOLUTION OF GENERALIZED (4+1)-DIMENSIONAL LOCAL FRACTIONAL FOKAS EQUATION Fractals (IF 3.3) Pub Date : 2024-05-15
ZHUO JIANG, ZONG-GUO ZHANG, XIAO-FENG HANIn 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
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A NEW PROGRAM FOR THE ENTIRE FUNCTIONS IN NUMBER THEORY Fractals (IF 3.3) Pub Date : 2024-05-15
XIAO-JUN YANGIn 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
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PREFACE — SPECIAL ISSUE ON FRACTALS AND LOCAL FRACTIONAL CALCULUS: RECENT ADVANCES AND FUTURE CHALLENGES Fractals (IF 3.3) Pub Date : 2024-05-15
XIAO-JUN YANG, DUMITRU BALEANU, J. A. TENREIRO MACHADO, CARLO CATTANIFractal 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
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THE MECHANICAL PROPERTIES AND FAILURE MODE OF SIMULATED LUNAR ROCK BY IN SITU TEMPERATURE REAL-TIME ACTION OF LUNAR-BASED Fractals (IF 3.3) Pub Date : 2024-05-15
HAI-CHUN HAO, MING-ZHONG GAO, YAN WU, XUE-MIN ZHOU, XUAN WANG, ZHENG GAO, ZHAO-YING YANGTo 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
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LOCAL FRACTIONAL SUMUDU DECOMPOSITION METHOD TO SOLVE FRACTAL PDEs ARISING IN MATHEMATICAL PHYSICS Fractals (IF 3.3) Pub Date : 2024-05-15
PING CUI, HASSAN KAMIL JASSIMIn 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
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Potentials on the conformally compactified Minkowski spacetime and their application to quark deconfinement Int. J. Geom. Methods Mod. Phys. (IF 2.1) Pub Date : 2024-05-15
M. Kirchbach, J. A. VallejoIn 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
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Exploring the physical properties of strange star SAXJ1808.4–3658 in rainbow gravity Int. J. Geom. Methods Mod. Phys. (IF 2.1) Pub Date : 2024-05-15
Wasib Ali, Umber Sheikh, Sarfraz Ali, Muhammad Jamil AmirThis 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
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Wormhole inducing exponential expansion in R2 gravity Int. J. Geom. Methods Mod. Phys. (IF 2.1) Pub Date : 2024-05-15
B Modak, Gargi BiswasWormholes 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
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Brownian motion in the Hilbert space of quantum states and the stochastically emergent Lorentz symmetry: A fractal geometric approach from Wiener process to formulating Feynman’s path-integral measure for relativistic quantum fields Int. J. Geom. Methods Mod. Phys. (IF 2.1) Pub Date : 2024-05-15
Amir Abbass VarshoviThis 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
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Reconstruction of symmetric teleparallel gravity with energy conditions Int. J. Geom. Methods Mod. Phys. (IF 2.1) Pub Date : 2024-05-15
Irfan Mahmood, Hira Sohail, Allah Ditta, S. H. Shekh, Anil Kumar YadavThis 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
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A generalized Wintgen inequality in quaternion Kähler geometry Int. J. Geom. Methods Mod. Phys. (IF 2.1) Pub Date : 2024-05-11
Mohd. Danish Siddiqi, Aliya Naaz Siddiqui, Kamran AhmadIn 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.
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Two-wave interaction solutions of perturbation and CKdVE integrability for (2+1)-D CDGKS equation Int. J. Geom. Methods Mod. Phys. (IF 2.1) Pub Date : 2024-05-09
Xiaorong Kang, Daquan Xian, Lizhu Xian, Kelong ZhengBy 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