bluuebunny/crossref_metadata_2025 huggingface dataset:
(m,ρ)-quasi-Einstein solitons on 3-dimensional trans-Sasakian manifolds and its applications in spacetimes
Authors: Sarkar Avijit , Biswas Urmila
Published: August 2023

This paper characterizes [Formula: see text]-quasi-Einstein solitons on [Formula: see text]-dimensional trans-Sasakian manifolds. It has been shown that a closed [Formula: see text]-quasi-Einstein soliton on a [Formula: see text]-dimensional trans-Sasakian manifold is either cosymplectic or Einstein under certain restrictions. Moreover, we investigate [Formula: see text]-quasi-Einstein solitons with certain potential vector fields on [Formula: see text]-dimensional trans-Sasakian manifolds. As an application of this soliton, we also analyze super quasi-Einstein spacetimes whose metrics are associated with [Formula: see text]-quasi-Einstein solitons.
Study of Yang–Mills condensate dark energy in the framework of generalized Brans–Dicke theory
Authors: Sardar Alok , Saha Pameli , Debnath Ujjal , Pradhan Anirudh
Published: August 2023

The prediction about the accelerating expansion of the universe introduced the concept of dark energy. Since then, a plethora of work has been done to explain the origin and nature of dark energy. This work deals with the possibility of obtaining cosmic acceleration of a new kind of dark energy, viz., Yang–Mills condensate dark energy in generalized Brans–Dicke theory with variable or constant [Formula: see text] (Brans–Dicke parameter) and vanishing and non-vanishing self-interacting potential. We assume the scale factor and scalar field in power law form. Then we investigate the above model to determine whether the universe is accelerating. We obtain a redshift-dependent equation of state parameter, which describes the phase transition of the universe. We notice that the equation of the state parameter meets the [Formula: see text] cold dark matter (CDM) limit in the far future. Then we study the [Formula: see text] analysis to get the thawing or freezing region. We study the stability of the model by studying the square speed of sound. Last, the nature of the scalar field and the potential are analyzed for four cases.
Quintessence scalar field of Kaniadakis holographic dark energy model with statefinder analysis
Authors: Sharma Umesh Kumar , Kumar P. Suresh , Pankaj
Published: August 2023

This paper explores the quintessence reconstruction and statefinder perspective of Kaniadakis holographic dark energy model in a flat universe with future event horizon as an IR-cutoff. The cosmological parameters of this model were re-examined from the quintessence behavior aspect. Also we reconstruct, [Formula: see text], the potential of quintessence scalar field, which shows the best fit with joint analysis data of JLA+CC+BAO for the priors [Formula: see text], [Formula: see text]. In the [Formula: see text]–[Formula: see text] phase space, the freezing-tracker model represents our canonical scalar field. This model exhibits quintessence behavior in the statefinder ([Formula: see text]–[Formula: see text]) plane for model parameters [Formula: see text] and [Formula: see text] that are close to [Formula: see text] and [Formula: see text]. The present values of deceleration [Formula: see text], statefinder [Formula: see text], jerk [Formula: see text] and model parameters [Formula: see text] are consistent with the limits of the observational data. Using the distance modulus [Formula: see text], we also fit 580 SN Type I Union2.1 data sets to our model.
Conformal perturbations of modified Novikov operators and the Kastler–Kalau–Walze type theorem
Authors: Wei Sining , Wang Yong
Published: August 2023

In this paper, we establish two Kastler–Kalau–Walze type theorems for conformal perturbations of modified Novikov operators on four-dimensional and six-dimensional compact manifolds with (respectively, without) boundary.
Classification of Killing magnetic curves in ℍ3
Authors: Kelekçi Özgür , Dündar Furkan Semih , Ayar Gülhan
Published: August 2023

In this paper, we study classification of magnetic curves corresponding to Killing vector fields of [Formula: see text]. First, we solve the geodesic equation analytically. Then we calculate the trajectories generated by all the six Killing vector fields, which are considered as magnetic field vectors, by using perturbation method up to first-order with respect to the strength of the magnetic field. We present a comparison of our solution with the numerical solution for one case. We also prove that 3-dimensional [Formula: see text]-Kenmotsu manifolds cannot have any magnetic vector field in the direction of their Reeb vector fields.
Cosmographic studies of q = α − β H parametrization in f(T) framework
Authors: Shukla Bhupendra Kumar , Bouali Amine , Chaudhary Himanshu , Tiwari Rishi Kumar , Martín Marco San
Published: August 2023

In this paper, we further investigate the cosmological tests of the deceleration parameter [Formula: see text] with [Formula: see text], where [Formula: see text] and [Formula: see text] are free parameters in [Formula: see text] framework by using 31 measurements from CC datasets, 1048 measurements of type Ia Supernovae (SNeIa) and 17 uncorrelated BAO measurements using Markov Chain Monte Carlo (MCMC). We obtained the best fit value of our model parameter and obtain the cosmological parameters of our model and analysis cosmographic studies of model. The statistical analysis revealed that our model is supported by the current Universe.
Extended constant-roll condition in non-canonical scalar field inflation
Authors: Mavoa Ferdinand , Hova Hoavo , Houndjo Stéphane , Ganiou Moussiliou , Kanfon Antonin
Published: August 2023

In this work, we apply the extended constant-roll condition to non-canonical scalar fields. We use in particular two types of non-canonical fields, namely, the tachyon field and the Dirac–Born–Infeld (DBI) field. We assume, in particular, that the tachyon scalar field satisfies the condition [Formula: see text], while the DBI scalar field satisfies the condition [Formula: see text]. We use the extended constant-roll condition to calculate the inflation indices for each of these non-canonical fields. In order to test the extended constant-roll condition, we use three types of potentials, namely chaotic potential, linear power-law potential and exponential potential, and choose power-law and exponential forms for the smooth function [Formula: see text]. It is then shown that the models under consideration are compatible with the latest Planck 2018 constraints.
Quantum heat machines enabled by twisted geometry
Authors: Filgueiras Cleverson , Rojas Moises , Silva Edilberto O. , Romero Carlos
Published: August 2023

In this paper, we analyze the operation of an Otto cycle heat machine driven by a non-interacting two-dimensional electron gas on a twisted geometry. We show that due to both the energy quantization on this structure and the adiabatic transformation of the number of complete twists per unit length of a helicoid, the machine performance in terms of output work, efficiency, and operation mode can be altered. We consider the deformations as in a spring, which is either compressed or stretched from its resting position. The realization of classically inconceivable Otto machines, with an incompressible sample, can be realized as well. The energy-level spacing of the system is the quantity that is being either compressed or stretched. These features are due to the existence of an effective geometry-induced quantum potential which is of pure quantum-mechanical origin.
The dynamical analysis of a parameterized dark energy cosmological model in the f(R,G) gravity
Authors: Rabha Dhajendra , Roy Baruah Rajshekhar
Published: August 2023

In this paper, we investigate the dynamical behavior of the universe with a flat FLRW model in [Formula: see text] gravity, where [Formula: see text] and [Formula: see text] both signify the Ricci scalar and Gauss–Bonnet invariant. Furthermore, in order to determine the model’s behavior, it must have the late-time universe’s behavior, which involves both an accelerated expansion as well as ending in a big rip. We present a model that begins with a point-type singularity, i.e. a point with zero volume and infinite energy density, by using parametrization of the scale factor [Formula: see text]. The model’s actions are accelerating and expanding at the moment, and [Formula: see text]CDM in late times. Our extensive analysis encompasses the energy conditions, dynamics of certain model solutions and additional cosmological tests through a dominant model. Finally, the proposed framework acts exactly like a quintessence dark energy model in the current time and is reliable with standard cosmology [Formula: see text]CDM in late times.
Huygens’ equations and the gradient-flow equations in information geometry
Authors: Wada Tatsuaki , Scarfone Antonio M. , Matsuzoe Hiroshi
Published: August 2023

In this paper, we revisit the relation between the gradient-flow equations and Hamilton’s equations in information geometry. By regarding the gradient-flow equations as Huygens’ equations in geometric optics, we have related the gradient flows to the geodesic flows induced by the geodesic Hamiltonian in an appropriate Riemannian geometry. The original evolution parameter [Formula: see text] in the gradient-flow equations is related to the arc-length parameter in the associated Riemannian manifold by Jacobi–Maupertuis transformation. As a by-product, the relation between the gradient-flow equation and replicator equations is found.
Parametrization of Hubble parameter in f̂(𝒯 ,𝒯G) gravity model with tachyon field
Authors: Pradhan Anirudh , Dixit Archana , Gupta Sanjeev
Published: August 2023

We look into the cosmological uses of the new modified gravitational theory [Formula: see text], which is based on the torsion invariant [Formula: see text] and the teleparallel equivalent of the Gauss–Bonnet term [Formula: see text]. The corresponding cosmology of [Formula: see text] gravity is very intriguing because it varies from both [Formula: see text] theories and the [Formula: see text] class of curvature-modified gravity. In this paper, we have investigated the applicability of an alternative gravitational theory called [Formula: see text] by applying the energy conditions. Here, we assumed the form of [Formula: see text], where [Formula: see text] and [Formula: see text] are arbitrary constants. We have examined the cosmological applications of [Formula: see text] gravity. Here, we consider two particular expressions of the time-dependent Hubble parameter. Both the model parameters are constrained jointly by the Observation Hubble dataset (OHD), the Pantheon dataset and the BAO data to constrain the model parameters using the Markov Chain Monte Carlo (MCMC) minimization technique. We determine the present values of Hubble constant for model [Formula: see text]: [Formula: see text], [Formula: see text] and [Formula: see text]; and model [Formula: see text]: [Formula: see text], [Formula: see text] and [Formula: see text] for the OHD+BAO+Pantheon dataset. Using the most recent estimated values of Hubble parameter, we properly analyzed the energy conditions and looked at the final behavior of our model. Additionally, we have explored the [Formula: see text] plane and also we have extracted the scalar field as well as potential of [Formula: see text] gravity and its relationship to the tachyon field. In addition, we find that, depending on the model parameters, the dark energy (DE) equation-of-state (EoS) parameter may be quintessence or phantom-like, or it may undergo phantom-divide crossing. Finally, we find that all the essential features of the model are satisfied successfully.
Relativistic anisotropic solution satisfying vanishing complexity condition
Authors: Al Shuali Maeen , Maurya S. K. , Al Abri Aatadal , Al Ghufaili Anad , Al Abri Budoor , Al Mayasi Buthaina , Al Saadi Amal
Published: August 2023

In this paper, we investigated anisotropic solution for a self-bound compact star model. The solution is obtained via Vaidya–Tikekar metric function [Formula: see text] and the vanishing complexity factor condition. The physical analysis of the solution has been discussed in detail which includes mass-radius ratio, and stability analysis via adiabatic index for a secondary component of the GW190814 event for different values [Formula: see text]. Furthermore, we predicted the radii and obtained the compactness factor of different self-bound compact objects for different [Formula: see text]. Moreover, the hydrostatic equilibrium condition of the solution is also checked. The physical result shows that the solution so obtained is well behaved and may be useful for modeling the self-bound compact objects as far as observational data is concerned.
New relativistic and non-relativistic investigation of deformed Klein–Gordon and Schrödinger equations for new improved screened Kratzer potential in the framework of non-commutative space
Authors: Maireche Abdelmadjid
Published: August 2023

The deformed Klein–Gordon equation has been solved in three-dimensional extended relativistic quantum mechanics (3D-ERQM) symmetries for the newly improved screened Kratzer potential (NISKP) model under the influence of the deformation space–space symmetries. The new relativistic energy eigenvalues were calculated using the parametric Bopp’s shift method and standard perturbation theory in addition to the approximation scheme suggested by Greene and Aldrich for the inverse square terms. The new relativistic energy eigenvalues of (LiH, HCl, CO and H2) molecules under the NISKP model were shown to be sensitive to the atomic quantum numbers ([Formula: see text]), mixed potential depths ([Formula: see text]), the screening parameter’s inverse [Formula: see text], control parameter [Formula: see text] and non-commutativity parameters ([Formula: see text], [Formula: see text], [Formula: see text]). In addition, we analyzed the non-relativistic energy values by applying the well-known transmission rules known in the literature. Furthermore, we studied many special cases useful to researchers in the framework of the new extended symmetries, such as the new screened cosine Kratzer potential, the new screened Kratzer potential (SKP), the new Kratzer potential, the new coshine Yukawa potential, the new coshine Yukawa potential, the new shifted improved SKP and the new shifted SKP. The study is further extended to calculate the mass spectra of mesons of the heavy quarkonium system such as charmonium [Formula: see text], bottomonium [Formula: see text], [Formula: see text] and light mesons [Formula: see text] and [Formula: see text] that have the quark and antiquark flavor within the framework of the NISKP model in 3D-ENRQM symmetries.
Structure analysis of the charged compact anisotropic systems
Authors: Ajmal M. , Bhatti M. Z.
Published: August 2023

This work deals with the investigation of several physical elements that contribute to the construction of stellar objects in the [Formula: see text] theory, where [Formula: see text] and [Formula: see text] symbolize the Ricci and Gauss–Bonnet scalars, respectively. In the presence of an anisotropic source, we offer the fundamental formalization of this modified theory. To establish the physical viability of our models, we employ various methods. Energy conditions (ECs) will be derived to ensure the physical validity of our models within the context of [Formula: see text] gravity. Moreover, we examine the physical viability through the assessment of radial and tangential sound speeds. Additionally, we analyze the equation of state (EoS) parameter and the anisotropic factor in the presence of the electromagnetic field’s influence. Dense stars are shown to be stable under anisotropy measures and exhibit their physical behavior under anisotropic stresses. We identify regions where the systems occupy high compactness and maintain stable ECs with a particular electric charge contribution.
Singularity-free anisotropic compact star in f(R,ϕ) gravity via Karmarkar condition
Authors: Malik Adnan , Naz Tayyaba , Yousaf Z. , Almas Ayesha , Saleem Komal
Published: August 2023

In this paper, we explore some emerging properties of the stellar objects in the frame of the [Formula: see text] gravity by employing the well-known Karmarkar condition, where [Formula: see text] and [Formula: see text] represent the Ricci scalar and scalar potential, respectively. We demonstrate the embedded class-I technique by using the static spherically symmetric line element along with anisotropic fluid matter distribution. Furthermore, to achieve our goal, we take a specific expression of metric potential [Formula: see text], already presented in the literature, and proceed by using the Karmarkar condition to obtain the second metric potential. To get the value of unknown parameters of the compact structures, we compare the Krori–Barua spacetime with spherically symmetric spacetime. Moreover, we examine the physical attributes of compact objects by presuming three viable [Formula: see text] models. We analyze the graphical behavior of density and pressure, the Tolman–Oppenheimer–Volkoff equation, energy conditions, mass function, surface redshift, and adiabatic index. It is recognized that all the obtained results deliver emphatic evidence for the stability of our considered realistic stars.
Hardy and Sobolev inequalities on antisymmetric functions
Authors: Hoffmann-Ostenhof Th. , Laptev A. , Shcherbakov I.
Published: August 2023

We obtain sharp Hardy inequalities on antisymmetric functions, where antisymmetry is understood for multi-dimensional particles. Partially it is an extension of the paper [Th. Hoffmann-Ostenhof and A. Laptev, Hardy inequalities with homogeneous weights, J. Funct. Anal. 268 (2015) 3278–3289], where Hardy’s inequalities were considered for the antisymmetric functions in the case of the 1D particles. As a byproduct we obtain some Sobolev and Gagliardo–Nirenberg type inequalities that are applied to the study of spectral properties of Schrödinger operators.
Acoustic Emission-Based Structural Health Prediction and Monitoring: A Comprehensive Review
Authors: Kumar Vivekanand , Kumar Vikash , Kalyan Kumar Erukala , Gangwar Ankit , Panda Subrata Kumar
Published: August 2023

In this paper, we report a detailed overview of non-destructive techniques, specifically Acoustic emission, for structural health monitoring in engineering applications. The review comprehensively covers the application of the AE technique for data related to damping and attenuation of structural components made from various material types, including conventional and non-conventional materials. Also, this paper systematically emphasizes research related to data collection processes of variable structural elements, such as stress concentration areas, sensor placement, and methodological monitoring. In addition, the analysis discussed in the review encompasses research that has utilized the AE method to examine the performance of metal and concrete building elements in risky situations, such as high temperatures and creep factors, with and without any visible signs of damage. We also examine various solution techniques, such as empirical wavelet transforms, finite element solutions, and differential quadrature for conventional materials’ damage analysis. Furthermore, the review emphasizes using waveform schemes to assess the vulnerability of damages in unconventional materials, such as laminated composite structures with different geometrical shapes. The paper concludes by presenting an overview of the current state of the AE technique in structural health monitoring and discusses potential future developments. This review is a valuable reference for professionals and researchers engaged in engineering applications related to structural health monitoring.
A Complex Mode Superposition Method Based on Hysteretic Damping Model for Mode Static Correction
Authors: Sun Panxu , Zhang Senpei , Yan Yadan , Wang Dongwei
Published: August 2023

Due to modal truncation, the dynamic responses calculated by the mode superposition method have some errors. In this paper, the source of truncation error of the complex mode superposition method for hysteretic damped systems with non-proportional characteristics is analyzed. It includes truncation errors of external excitation load and Hilbert transform term. With the increase of mode order, the ratio of excitation frequency to natural frequency gradually approaches zero. Combined with the expression of structural modal response caused by harmonic wave, the corresponding approximate expression of high-order modal response is obtained. Through quasi-static analysis, a complex mode superposition method of non-proportionally damped systems for mode static correction is proposed. Numerical examples show that when the ratios of the domain frequencies of the external excitation to the natural frequency of some high-order modes are small, the complex mode superposition method for mode static correction has a good effect.
Galois groups of n 0 + n 1 X + ⋯ + n 6 X6
Authors: Klahn Benjamin , Technau Marc
Published: August 2023

We show that the Galois group of the polynomial in the title is isomorphic to the full symmetric group on six symbols for all but finitely many [Formula: see text]. This complements earlier work of Filaseta and Moy, who studied Galois groups of [Formula: see text] for more general pairs [Formula: see text], but had to admit a possibly infinite exceptional set specifically for [Formula: see text] of at most logarithmic growth in [Formula: see text]. The proof rests upon invoking Faltings’ theorem on a suitable fibration of Galois resolvents to show that this exceptional set is, in fact, finite.
Vanishing coefficients in quotients of theta functions with odd moduli
Authors: Du Julia Q. D. , Tang Dazhao
Published: August 2023

Following recent studies of vanishing coefficients in arithmetic progressions in infinite [Formula: see text]-series products, we further prove that such phenomenon also exists in a family of quotients of theta functions with odd moduli. Moreover, we find that some arithmetic progressions with vanishing coefficients could be shared by an infinite family of quotients of theta functions. Finally, we present several related conjectures that merit further investigation.
2-Adic Galois images of isogeny-torsion graphs over ℚ with CM
Authors: Chiloyan Garen
Published: August 2023

Let [Formula: see text] be a [Formula: see text]-isogeny class of elliptic curves defined over [Formula: see text]. The isogeny graph associated to [Formula: see text] is a graph which has a vertex for each elliptic curve over [Formula: see text] of [Formula: see text] and an edge for each [Formula: see text]-isogeny of prime degree that maps one elliptic curve in [Formula: see text] to another elliptic curve in [Formula: see text], with the degree of the isogeny recorded as a label of the edge. The isogeny-torsion graph associated to [Formula: see text] is the isogeny graph associated to [Formula: see text] where, in addition, we label each vertex with the abstract group structure of the torsion subgroup over [Formula: see text] of the corresponding elliptic curve. The main result of the article is a classification of the [Formula: see text]-adic Galois image at each vertex of the isogeny-torsion graphs whose associated [Formula: see text]-isogeny class consists of elliptic curves over [Formula: see text] with complex multiplication.
Fourier coefficients of automorphic L-functions
Authors: Kim Henry H.
Published: August 2023

We prove two unconditional results on Fourier coefficients of modular forms: Let [Formula: see text] be a Hecke eigen cusp form of weight [Formula: see text] and level [Formula: see text] ([Formula: see text] square free), and [Formula: see text] be the normalized Hecke eigenvalues. Let [Formula: see text] be the least prime [Formula: see text] such that [Formula: see text]. Then we show that in a family of modular forms of weight [Formula: see text] and level [Formula: see text], except for a density zero set, [Formula: see text] for some [Formula: see text]. Second, we show that outside a density zero set, a modular form is determined by Fourier coefficients up to [Formula: see text] for some [Formula: see text].
Fourier coefficients and slopes of Drinfeld modular forms
Authors: Bandini Andrea , Valentino Maria
Published: August 2023

Let [Formula: see text] be a Drinfeld modular form of level [Formula: see text] which is an eigenform for the Hecke operator [Formula: see text] ([Formula: see text] a prime of [Formula: see text]). We study the relations between the Fourier coefficients of [Formula: see text] and the [Formula: see text]-adic valuation of its eigenvalue (slope). We use formulas for some of the Fourier coefficients of [Formula: see text] to provide bounds and estimates on the slopes and, in particular, to find necessary conditions for “large” slopes, whose existence is closely connected with conjectures on oldforms and newforms.
Paramodular groups and theta series
Authors: Böcherer Siegfried , Schulze-Pillot Rainer
Published: August 2023

For a paramodular group of any degree and square free level we study the Hecke algebra and the boundary components. We define paramodular theta series and show that for square free level and large enough weight they generate the space of cusp forms (basis problem), using the doubling or pullback of Eisenstein series method. For this we give a new geometric proof of Garrett’s double coset decomposition which works in our more general situation.
Uniformizer of the false Tate curve extension of ℚp (II)
Authors: Wang Shanwen , Yuan Yijun
Published: August 2023

In this paper, we investigate the explicit formulae for the uniformizers of the false Tate curve extension of [Formula: see text]. More precisely, we establish the formulae for the fields [Formula: see text] with [Formula: see text] and for general [Formula: see text], we prove the existence of the recurrence polynomials [Formula: see text] for general field extensions [Formula: see text] of [Formula: see text], which shows the possibility to construct the uniformizers systematically.
Arithmetic progressions in squarefull numbers
Authors: Bajpai Prajeet , Bennett Michael A. , Chan Tsz Ho
Published: August 2023

We answer a number of questions of Erdős on the existence of arithmetic progressions in [Formula: see text]-full numbers (i.e. integers with the property that every prime divisor necessarily occurs to at least the [Formula: see text]th power). Further, we deduce a variety of arithmetic constraints upon such progressions, under the assumption of the [Formula: see text]-conjecture of Masser and Oesterlé.
The sum of four squares over real quadratic number fields
Authors: Thompson Katherine
Published: August 2023

Well-known results of Lagrange and Jacobi prove that every [Formula: see text] can be expressed as a sum of four integer squares, and the number [Formula: see text] of such representations can be given by an explicit formula in [Formula: see text]. In this paper, we prove that the only real quadratic number field for which the sum of four squares is universal is [Formula: see text]. We provide explicit formulas for [Formula: see text] for [Formula: see text] and [Formula: see text]. We then consider the theta series of the sum of four squares over any real quadratic number field, providing explicit upper and lower bounds for the Eisenstein coefficients. Last, we include examples of the complete theta series decomposition of the sum of four squares over [Formula: see text], [Formula: see text] and [Formula: see text].
Modularity of Nahm sums for the tadpole diagram
Authors: Milas Antun , Wang Liuquan
Published: August 2023

We prove Rogers–Ramanujan-type identities for the Nahm sums associated with the tadpole Cartan matrix of rank 3. These identities reveal the modularity of these sums, and thereby we confirm a conjecture of Calinescu, Penn and the first author in this case. We show that these Nahm sums together with some shifted sums can be combined into a vector-valued modular function on the full modular group. We also present some conjectures for a general rank.
Newton polygons of L-functions for two-variable generalized Kloosterman sums
Authors: Wang Chunlin , Yang Liping
Published: August 2023

In this paper, we study the Newton polygon of the [Formula: see text]-function of a generalized Kloosterman polynomial with two variables over finite fields. We give the explicit form of the monomial basis of the top dimensional cohomology space of the [Formula: see text]-adic complex associated to the [Formula: see text]-function. One consequence of this result is a concrete method for computing the Hodge polygon. Using decomposition theorems of Wan, we determine when a generalized Kloosterman polynomial is ordinary and when its Newton polytope is generically ordinary.
Congruences of Galois representations attached to effective A-motives over global function fields
Authors: Okumura Yoshiaki
Published: August 2023

This paper investigates congruences of [Formula: see text]-adic representations arising from effective [Formula: see text]-motives defined over a global function field [Formula: see text]. We give a criterion for two congruent [Formula: see text]-adic representations coming from strongly semi-stable effective [Formula: see text]-motives to be isomorphic up to semi-simplification when restricted to decomposition groups of suitable places of [Formula: see text]. This is a function field analog of Ozeki–Taguchi’s criterion for [Formula: see text]-adic representations of number fields. Motivated by a non-existence conjecture on abelian varieties over number fields stated by Rasmussen and Tamagawa, we also show that there exist no strongly semi-stable effective [Formula: see text]-motives with some constrained.
Some remarks on p-adic L-functions for certain abelian varieties with complex multiplication
Authors: Li Yong-Xiong
Published: August 2023

Let [Formula: see text] be a quadratic field with prime discriminant [Formula: see text]. Let [Formula: see text] be an odd prime which splits in [Formula: see text]. In this paper, by generalizing our previous method in Iwasawa theory at the prime [Formula: see text], we construct a [Formula: see text]-adic canonical measure for the abelian varieties [Formula: see text] coming from the restriction of scalars to [Formula: see text] of quadratic twists of Gross curves. We then prove an elliptic analogue of Iwasawa’s theorem for the measure. As an application, we prove some cases of the [Formula: see text]-part Buhler–Gross conjecture for [Formula: see text] in the same spirit of Rubin.
The Mahler measure of x + 1/x + y + 1/y + 4 ± 42 and Beilinson’s conjecture
Authors: Guo Xuejun , Ji Qingzhong , Liu Hang , Qin Hourong
Published: August 2023

In this note we study the Mahler measures of reciprocal polynomials [Formula: see text] for [Formula: see text]. We prove identities relating the Mahler measure of [Formula: see text] to special values of the [Formula: see text]-functions of weight 2 cusp forms of level 64. We also express the Beilinson regulator which is a [Formula: see text] determinant of Mahler measures as special value of [Formula: see text]-function of the elliptic curve defined by [Formula: see text].
Towards a mod-p Lubin–Tate theory for GL2 over totally real fields
Authors: Banerjee Debargha , Rai Vivek
Published: August 2023

In this paper, we show that the conjectural mod [Formula: see text] local Langlands correspondence can be realized in the mod [Formula: see text] cohomology of the Lubin–Tate towers. The proof utilizes a well-known conjecture of Buzzard–Diamond–Jarvis [8, Conjecture 4.9], a study of completed cohomology of the ordinary and supersingular locus of the Shimura curves for a totally real field [Formula: see text] and of mod [Formula: see text] local Langlands correspondence as given by Emerton–Helm [20]. In the case of modular curves, a similar theorem was obtained by Chojecki [13].
Squares in recurrences using elliptic curves
Authors: Walsh P. G.
Published: August 2023

Numerous papers have studied the problem of determining upper bounds for the number of integer points on elliptic curves of the form [Formula: see text], and quartic curves of the form [Formula: see text]. Bounds for the number of integer solutions to such quartic equations typically depend on both of the coefficients [Formula: see text]. The purpose of this paper is to examine more closely how the number of integer points on such quartic curves seems to depend almost entirely on the number of prime factors of [Formula: see text]. This is done by focusing in on the problem of bounding the number of squares in certain recurrence sequences. In particular, using some arithmetic on elliptic curves, it is proved that infinitely many such sequences can have four squares, but that a fifth square remains elusive after extensive computation, suggesting that an absolute bound for the number of squares is more than likely, and also suggesting that the above assertion regarding the dependence on the number of prime factors of [Formula: see text].
Stability of certain higher degree polynomials
Authors: Laishram Shanta , Sarma Ritumoni , Sharma Himanshu
Published: August 2023

One of the interesting problems in arithmetic dynamics is to study the stability of polynomials over a field. A polynomial [Formula: see text] is stable over [Formula: see text] if irreducibility of [Formula: see text] implies that all its iterates are also irreducible over [Formula: see text], that is, [Formula: see text] is irreducible over [Formula: see text] for all [Formula: see text], where [Formula: see text] denotes the [Formula: see text]-fold composition of [Formula: see text]. In this paper, we study the stability of [Formula: see text] for [Formula: see text], [Formula: see text]. We show that for infinite families of [Formula: see text], whenever [Formula: see text] is irreducible, all its iterates are irreducible, that is, [Formula: see text] is stable. Under the assumption of explicit [Formula: see text]-conjecture, we further prove the stability of [Formula: see text] for the remaining values of [Formula: see text]. Also for [Formula: see text], if [Formula: see text] is reducible, then the number of irreducible factors of each iterate of [Formula: see text] is exactly [Formula: see text] for [Formula: see text].
On the divisibility of 7-elongated plane partition diamonds by powers of 8
Authors: Sellers J. A. , Smoot N. A.
Published: August 2023

In 2021 da Silva, Hirschhorn, and Sellers studied a wide variety of congruences for the [Formula: see text]-elongated plane partition function [Formula: see text] by various primes. They also conjectured the existence of an infinite congruence family modulo arbitrarily high powers of 2 for the function [Formula: see text]. We prove that such a congruence family exists — indeed, for powers of 8. The proof utilizes only classical methods, i.e. integer polynomial manipulations in a single function, in contrast to all other known infinite congruence families for [Formula: see text] which require more modern methods to prove.
New and simple proofs of Ramanujan’s modular equations of degree 11
Authors: Vasuki K. R. , Yathirajsharma M. V.
Published: August 2023

On pp. 243 and 244 of his second notebook, Ramanujan recorded seven modular equations of degree 11 followed by two more which he had crossed out. The first modular equation in the list was proved by Berndt using theta function identities. The same was also proved by Venkatachaliengar in a different way. To the best of our knowledge, the only available proofs to the other six modular equations in the list are by Berndt. These proofs employ the theory of modular forms. Interestingly these are the first set of modular equations, the proofs to which by Berndt take a shift from the elementary algebraic methods to the theory of modular forms. In this paper, we reprove all these modular equations of degree 11 (except the first one in the list) by elementary algebraic techniques. First, we use two series identities due to Ye and Liu to prove one of the modular equations and its reciprocal. The remaining modular equations are proved by the method of parametrization.
Cross connection compatible discrete normal categories
Authors: Rajan A. R.
Published: August 2023

The concept of normal category was introduced by Nambooripad in his theory of cross connections for describing the structure of regular semigroups. These are essentially the categories of principal left ideals and the categories of principal right ideals of regular semigroups with appropriate morphisms. These categories also have an associated partial order on the set of objects. Discrete normal categories are normal categories in which the partial order on the object set is the identity relation. A cross connection relates two normal categories [Formula: see text] and [Formula: see text] and produces a regular semigroup [Formula: see text] such that one is the category of principal left ideals and the other the category of principal right ideals of the semigroup [Formula: see text]. This paper considers the question of compatibility of two normal categories in order that they can be connected by a cross connection. It is known that given any normal category [Formula: see text] there is a normal category [Formula: see text] called the normal dual of [Formula: see text] such that [Formula: see text] is compatible with [Formula: see text]. The question of finding all normal categories [Formula: see text] that are compatible with a given normal category [Formula: see text] remains unsettled. Such categories [Formula: see text] are called compatible duals of [Formula: see text]. For the class of discrete normal categories the characterization of all compatible duals has been done here.
Solvability of an infinite system of three point BVP in c0 and ℓ1 spaces using measure of noncompactness
Authors: Das Rituparna , Sapkota Niraj , Savapondit Santonu
Published: August 2023

Various existing works in the literature have addressed the solvability of different infinite systems of boundary value problems in different types of Banach spaces. In most of these works, the authors have restricted themselves in systems of differential equations with boundary conditions defined at two points. In this work, we have addressed the solvability of an infinite system of third-order differential equations with boundary conditions defined at three points in the sequence spaces [Formula: see text] and [Formula: see text]. We have also illustrated the results for both sequence spaces with suitable examples.
A classification of endo-commutative curled algebras of dimension 2 over a nontrivial field
Authors: Takahasi Sin-Ei , Shirayanagi Kiyoshi , Tsukada Makoto
Published: August 2023

An endo-commutative algebra is a nonassociative algebra in which the square mapping preserves multiplication. In this paper, we give a complete classification of endo-commutative curled algebras of dimension 2 over an arbitrary nontrivial field, where a curled algebra satisfies the condition that the square of any element is a scalar multiple of that element. We list all multiplication tables of the algebras up to isomorphism.
Some new inequalities on the normalized signless Laplacian resolvent energy of graphs
Authors: Bozkurt Altındağ Ş. B. , Matejić M. , Milovanović I. , Milovanović E.
Published: August 2023

For a connected graph [Formula: see text] of order [Formula: see text] with normalized signless Laplacian eigenvalues [Formula: see text], the normalized signless Laplacian resolvent energy of [Formula: see text] is defined as [Formula: see text]. In this paper, we derive new inequalities on [Formula: see text] as well as relations on [Formula: see text] with Randić (normalized) incidence energy. We also deduced that some of our results improve the existing results in the literature.
On the Lie triple derivation of Hom–Lie superalgebras
Authors: Asif Sania , Wang Yao
Published: August 2023

Consider a Hom–Lie superalgebra, denoted by [Formula: see text]. In this paper, we inquire the Lie triple derivation [Formula: see text] and generalized Lie triple derivation [Formula: see text] of Hom–Lie superalgebra. Later, we address the triple centroid, triple quasi-centroid and central triple derivations of Hom–Lie superalgebra. Moreover, we attempt to show the relationship of triple centroid, triple quasi-centroid and central triple derivation with [Formula: see text] and [Formula: see text]. We give complete classification of triple derivations of Hom–Lie superalgebra, where we show that for the simple Hom–Lie superalgebras [Formula: see text].
Codes arising from directed strongly regular graphs with μ = 1
Authors: Huilgol Medha Itagi , D’Souza Grace Divya
Published: August 2023

The rank of adjacency matrix plays an important role in construction of linear codes from a directed strongly regular graph using different techniques, namely, code orthogonality, adjacency matrix determinant and adjacency matrix spectrum. The problem of computing the dimensions of such codes is an intriguing one. Several conjectures to determine the rank of adjacency matrix of a DSRG [Formula: see text] over a finite field, keep researchers working in this area. To address the same to an extent, we have considered the problem of finding the rank over a finite field of the adjacency matrix of a DSRG [Formula: see text] with [Formula: see text], including some mixed Moore graphs and corresponding codes arising from them, in this paper.
On the α-spectral radius of the k-uniform supertrees
Authors: Liu Chang , Li Jianping
Published: August 2023

Let [Formula: see text] be a [Formula: see text]-uniform hypergraph with vertex set [Formula: see text] and edge set [Formula: see text]. A connected and acyclic hypergraph is called a supertree. For [Formula: see text], the [Formula: see text]-spectral radius of [Formula: see text] is the largest [Formula: see text]-eigenvalue of [Formula: see text], where [Formula: see text] and [Formula: see text] are the diagonal tensor of the degrees and the adjacency tensor of [Formula: see text], respectively. In this paper, we determine the unique supertrees with maximum [Formula: see text]-spectral radius among all [Formula: see text]-uniform supertrees with [Formula: see text] edges and independence number [Formula: see text] for [Formula: see text], among all [Formula: see text]-uniform supertrees with given degree sequences, and among all [Formula: see text]-uniform supertrees with [Formula: see text] edges and matching number [Formula: see text] for [Formula: see text], respectively.
Stability of certified domination upon edge addition
Authors: Roushini Leely Pushpam P. , Kamalam M. , Mahavir B.
Published: August 2023

A dominating set [Formula: see text] of a graph [Formula: see text] is said to be certified, if every vertex [Formula: see text] has either 0 neighbors or at least two neighbors in [Formula: see text]. The cardinality of a minimum certified dominating set of [Formula: see text] is called the certified domination number of [Formula: see text] and is denoted by [Formula: see text]. A graph [Formula: see text] is said to be [Formula: see text]-[Formula: see text] stable if for any two vertices [Formula: see text] such that [Formula: see text], we have [Formula: see text]. In this paper, we provide upper bounds for the [Formula: see text]-value of [Formula: see text]-[Formula: see text] stable graph. We also characterize the trees and unicyclic graphs that are [Formula: see text]-[Formula: see text] stable.
EAST ASIA CLIMATE CLUB: PATHWAY TOWARD 2050 NET-ZERO
Authors: SHAW DAIGEE , FU YU-HSUAN , CHEN YA-QI
Published: August 2023

Four major and closely related economies in East Asia, i.e., China, Japan, South Korea, and Taiwan, have committed and pledged their pathway and strategies to achieve a net-zero target in the last three years. However, the net-zero pathway and strategy developed by the governments in East Asia and most countries need to be more proactive in many ways. We define four scenarios such as the business-as-usual scenario (BAU), the government pledge scenario (GOV), the East Asia climate club scenario without forming a green club fund (CLUB without the fund), and the East Asia climate club scenario (CLUB). This study first aims to apply the E3ME-FTT model to assess the net-zero pathway and strategies the governments of these four economies have already pledged under the GOV scenario. The results show that, with current pledges, we cannot achieve the net-zero target and will cause a lot of carbon debt. Then, we assess the effectiveness of forming a climate club that the four economies commit to applying four common policy instruments and programs to meet the 2050 net-zero target under the CLUB scenario. The results suggest that creating the East Asia climate club can be an excellent program to facilitate international cooperation on climate change and help to transform it into a green economy in East Asia. It can help reduce CO2 emissions, though not yet meeting the 2050 net-zero target, and have a higher positive impact on GDP. All club members would benefit both environmentally and economically. These economies with stricter environmental regulations will become more closely related as a kind of friend-shoring. As a result, the green trades between these economies increase. To fully reach the target, the four economies must formulate additional net-zero strategies across sectors based on their unique situation and invest more in emission reduction and carbon removal R&D to enhance their capacity and lower costs.
A RICARDIAN ANALYSIS OF CLIMATE CHANGE IMPACTS ON JAPAN’s AGRICULTURE: ACCOUNTING FOR SOLAR RADIATION
Authors: OKAMURA IORI , VAN PASSEL STEVEN , FABRI CHARLOTTE , SENDA TETSUJI
Published: August 2023

This study evaluates the effects of climate change on the net revenue of farmers in Japan. We adopted the Ricardian model, which implicitly accounts for farmers’ full adaptation. The main findings of this study are as follows. First, the Ricardian regression shows that changes in temperature significantly impact farmers’ net revenue. In contrast, changes in precipitation have limited effects on farmers’ net revenue. The results of future predictions showed that the effects of climate change are positive across the country, with varying degrees between north and south. These results are more optimistic than those in the existing literature, which frequently reveal negative climate change impacts in southern Japan. However, it should be noted that this model assumes full adaptation and does not consider the transition costs of farmers, and understanding the actual adaptive measures is an important remaining issue.
UNDERSTANDING THE CARBON INTENSITY OF SOUTH KOREA’S EXPORTS: A MULTIPLICATIVE STRUCTURAL DECOMPOSITION ANALYSIS
Authors: KIM TAE-JIN , TROMP NIKOLAS
Published: August 2023

Despite the large and growing role of exports in Korea’s carbon emissions, they have been largely overlooked in Korea’s carbon neutrality strategy. With this in mind, we analyze Korea’s aggregate emission intensity of exports (AEIE), an indicator of the environmental efficiency of exports, which decreased from 1.37[Formula: see text]Kt/$M to 0.74[Formula: see text]Kt/$M during 2000–2014. Using the multi-regional input-output model and two-stage multiplicative structural decomposition analysis (MSDA), we uncover drivers of changes in the AEIE. Analysis of bilateral AEIE shows that exports to developed countries had a large impact on the decline while exports to developing countries have risen in importance. MSDA shows that the carbon intensity effect contributed most to the decline but that trade in intermediate goods and trade in final goods were also important. At the sectoral level, manufacturers of basic metals, electricity, gas, steam and air conditioning supply and transportation sectors were shown to be important drivers of the decline in the AEIE. As the first study to analyze the drivers of Korea’s AEIE, this paper suggests various abatement policies to help achieve the goal of carbon neutrality by 2050.