bluuebunny/crossref_metadata_2025 huggingface dataset:
Yamabe and gradient Yamabe solitons in the complex hyperbolic two-plane Grassmannians
Authors: Suh Young Jin
Published: May 2022

First, we want to give a complete classification of Yamabe solitons and gradient Yamabe solitons for real hypersurfaces in the complex hyperbolic two-plane Grassmannians [Formula: see text]. Next, as an application we also give a complete classification of quasi-Yamabe and gradient quasi-Yamabe solitons on real hypersurfaces in the complex hyperbolic two-plane Grassmannians [Formula: see text].
Orthogonal decompositions and twisted isometries
Authors: Rakshit Narayan , Sarkar Jaydeb , Suryawanshi Mansi
Published: May 2022

Let [Formula: see text]. Let [Formula: see text] be [Formula: see text] commuting unitaries on some Hilbert space [Formula: see text], and suppose [Formula: see text], [Formula: see text]. An [Formula: see text]-tuple of isometries [Formula: see text] on [Formula: see text] is called [Formula: see text]-twisted isometry with respect to [Formula: see text] (or simply [Formula: see text]-twisted isometry if [Formula: see text] is clear from the context) if [Formula: see text]’s are in the commutator [Formula: see text], and [Formula: see text], [Formula: see text]

We prove that each [Formula: see text]-twisted isometry admits a von Neumann–Wold type orthogonal decomposition, and prove that the universal [Formula: see text]-algebra generated by [Formula: see text]-twisted isometries is nuclear. We exhibit concrete analytic models of [Formula: see text]-twisted isometries, and establish connections between unitary equivalence classes of the irreducible representations of the [Formula: see text]-algebras generated by [Formula: see text]-twisted isometries and the unitary equivalence classes of the nonzero irreducible representations of twisted noncommutative tori. Our motivation of [Formula: see text]-twisted isometries stems from the classical rotation [Formula: see text]-algebras and Heisenberg group [Formula: see text]-algebras.
On the fixed point spaces of some completely positive maps
Authors: Hayashi Tomohiro
Published: May 2022

In this paper, we generalize some results shown by Das and Peterson. Let [Formula: see text] be a [Formula: see text]-factor acting on [Formula: see text]. We consider certain unital normal completely positive maps on [Formula: see text] which are identity on [Formula: see text]. We investigate their fixed point spaces and obtain a rigidity result. As an application, we show some results of subfactors.
Possible connection between time-splitting parameter and surface tension in Casimir-type problems
Authors: Brevik Iver
Published: May 2022

We discuss four different, though related, fundamental topics related to the Casimir effect: (1) We suggest that the application of Casimir theory to real dielectric materials, thus implying the atomic spacing as a course-grained length parameter, makes it natural to assume that this parameter is of the same order of magnitude as the QFT time-splitting parameter multiplied with the velocity of light. (2) We show that application of Casimir theory to a thick fluid shell (apparently a closed mechanical system) leads actually to an unstable situation if no extra mechanical forces, typically surface tension forces, are brought into consideration. (3) We analyze how the presence of a radial Casimir repulsive pressure modifies the filling process of a spherical vacuum hole in an infinite fluid (the Reynolds problem), with the result that a bounce occurs at a finite though very small radius. (4) As a comment on an apparently similar situation in general relativity, we consider the gravitational collapse of a singular shell. It might seem natural to allow for the presence of a repulsive Casimir pressure in this case also, thereby obtaining a bounce-like situation again. However, we have to conclude that such a procedure implies an omission of the Casimir field’s gravitational energy, and is therefore hardly tenable, although it is in our opinion worth mentioning.
Ultraperipheral production of lepton pairs (perturbative and nonperturbative effects)
Authors: Dremin I. M.
Published: May 2022

Perturbative and nonperturbative terms of the cross-sections of ultraperipheral production of lepton pairs in ion collisions are taken into account. It is shown that production of low-mass [Formula: see text] pairs is strongly enhanced (compared to perturbative estimates) due to the nonperturbative Sommerfeld–Gamow–Sakharov (SGS) factor. Coulomb attraction of the nonrelativistic components of those pairs leads to the finite value of their mass distribution at lowest masses. Their annihilation can result in an increased intensity of 511 keV photons. It can be recorded at the NICA collider and is especially crucial in astrophysical implications regarding the 511 keV line emitted from the Galactic center. The analogous effect can be observed in lepton pairs production at LHC. Energy spectra of lepton pairs created in ultraperipheral nuclear collisions and their transverse momenta are calculated.
Evolution of Labor Relations in the Development of Human Resources Based on Improved Genetic Algorithm
Authors: Qin Min
Published: May 2022

This paper systematically constructs a multi-project and a multi-objective human resource scheduling mathematical model in construction projects and puts forward an improved genetic algorithm to solve it by aiming at the problems existing in the process of human resource scheduling and optimization. Specifically, first, the basic mathematical models of GPRs and resource-constrained construction project human resource scheduling problem (RCWSP/GPRs) are established, and the multi-project equilibrium problem is extended. Then, an improved inter-cluster separation (ICS) algorithm is proposed and used to solve the RCWSP/GPRs problem. Finally, on this basis, the mathematical model of multi-project and multi-objective human resource scheduling problem and the solution method based on multi-objective-integrated circuit are proposed. At the same time, the resource-constrained multi-project and multi-skill human resource scheduling problem and the integer programming mathematical model under the generalized priority relationship are proposed. Also, the simulation results verify the accuracy of the proposed algorithm and model.
Alexander and Markov theorems for generalized knots, II generalized braids
Authors: Bartholomew Andrew , Fenn Roger
Published: May 2022

In the first of this series of papers, we looked at various generalized knot theories. In this follow up paper, we look at the theory of generalized braids and show how they are related to generalized knots. The twin groups are related to the theory of planar doodles and we prove a Markov-type theorem for them. An example and invariants are given to show that this is best possible. We also give conditions for when an exchange move is dependent on the other moves.
Antikaon condensation in magnetized neutron stars
Authors: Kumari Manisha , Kumar Arvind
Published: May 2022

This study investigates the possibility of antikaon condensation in strongly magnetized neutron stars (NSs) with [Formula: see text]-equilibrium condition using chiral [Formula: see text] model and chiral perturbation theory (ChPT). We explore the effect of finite strong magnetic field on particle fraction, effective masses of kaon/antikaon, and equation of state (EoS). The longitudinal EoS gets softened; whereas in transverse EoS, stiffness is observed as the magnetic field strength increases. The presence of antikaon condensation causes softness in both the longitudinal and transverse EoS. Finally, we investigate the structure of NSs through the mass–radius relation, tidal deformability, and Love number and present possible comparison with recent work in the field. The presence of antikaon condensed phase decreases the mass of NSs corresponding to both EoS (longitudinal and transverse). For longitudinal pressure, the mass–radius shows decrement with increase in magnetic field strength; whereas transverse pressure causes an increment.
MATHEMATICAL INSIGHTS INTO THE DYNAMICS OF INNATE IMMUNE RESPONSE DURING INFLAMMATION
Authors: TREJO IMELDA , LAFCI BÜYÜKKAHRAMAN MEHTAP , KOJOUHAROV HRISTO V.
Published: May 2022

Innate immune system cells activate in response to infection and trigger an acute inflammatory reaction to restore tissue homeostasis and promote subsequent tissue repair. Their activation and functions must be very well regulated to avoid tissue damage, organ dysfunction, or even death. In this work, a new set of mathematical models is presented to examine the dynamics of the innate immune system response to tissue damage and provide further understanding of the role of the innate immune system during the early stages of an inflammatory response. Different damaged cells production functions are proposed to represent the effect of secondary tissue damage by the innate immune system. The stability and bifurcation analyses of the model reveal that there is an important threshold parameter that can be controlled in order to avoid sustained chronic inflammation and secure a successful healing outcome. A set of numerical simulations is also performed to support the presented theoretical results and demonstrate the medical applicability of the new mathematical model.
CONVERGENCE INVESTIGATION OF MULTIFRACTAL ANALYSIS BASED ON Lp-NORM CONSTRAINT
Authors: WANG JIAN , JIANG WENJING , SHAO WEI
Published: May 2022

In this paper, we propose the multifractal detrending fluctuation analysis based on [Formula: see text]-norm constrain (MF-DFN). We assess the performance of the proposed algorithm by constructing a [Formula: see text]-model based multiplicative cascades time series. We calculate the generalized [Formula: see text] exponent [Formula: see text], [Formula: see text] exponent [Formula: see text], singularity exponent [Formula: see text] and multifractal spectrum [Formula: see text] for multifractal detrended fluctuation analysis (MF-DFA) and MF-DFN, respectively. We notice that under different norm constraints, the distribution of multifractal characteristics is quite different. Appropriate norm constraints can make the multifractal characteristics of time series described more accurately. Based on the analytical solution curve, the distribution of different multifractal numerical curves determines the correct selection of norm constraint value. In this study, using a combination of norms [Formula: see text] and [Formula: see text], the depicted numerical curves almost overlap the theoretical curve, which shows that the proposed MF-DFN is superior to MF-DFA. To eliminate the influence of specific time series, we reset parameters [Formula: see text] and [Formula: see text] in [Formula: see text]-model. Various experimental results also show the effectiveness of the proposed MF-DFN. In addition, we also verify the efficiency of the proposed MF-DFN by using the practical application. The experimental results show that our proposed method plays a significant role in ECG classification.
NEW INEQUALITIES ON GENERALIZED m-CONVEXITY ON FRACTAL SETS
Authors: SÁNCHEZ C. RAINIER V. , SANABRIA JOSÉ E. , TROUSSELOT EDUARD
Published: May 2022

In this research, we study some algebraic and topological properties of generalized [Formula: see text]-convex functions on fractal sets and establish a new Jensen type inequality. Also, we obtain some new Hermite–Hadamard type inequalities for local fractional integrals of this class of functions. As applications, we present some inequalities with generalized special means and generalized probability density functions.
NOVEL RESULTS ON BIFURCATIONS FOR A FRACTIONAL-ORDER NEURAL NETWORK WITH NEUTRAL DELAYS
Authors: HUANG CHENGDAI , MO SHANSONG , WU ZENGBAO
Published: May 2022

In comparison with numerous available results with regard to bifurcations on account of fractional-order neural networks (FONNs) with the retarded delays, this paper is concerned with the stability and bifurcation of FONN with neutral delays. Delay-induced bifurcation results are firstly, procured and the bifurcation diagrams with respect to different delays are nicely plotted. Then it reveals that both time delay and fractional order have important effects in affecting the stability and bifurcation of the developed FONN. It further detects that FONN involving neutral delays can postpone the onset of bifurcations of the developed FONN compared with FONN with the retarded delays. It hints that neutral delays have a vital impact on the dynamics of FONNs in comparison with FONN with the retarded delays, which has outstanding performance in maintaining stability of FONNs. Eventually, numerical examples are addressed to check the availability of the developed results. The obtained criterion can be evaluated as an important contribution to the stability issue of the considered neural networks (NNs).
A FRACTAL MODIFICATION OF THE SHARMA–TASSO–OLVER EQUATION AND ITS FRACTAL GENERALIZED VARIATIONAL PRINCIPLE
Authors: WANG KANG-JIA , SHI FENG , LIU JING-HUA
Published: May 2022

The Sharma–Tasso–Olver equation can well describe the wave motion in physics, however, it becomes ineffective when the boundary is non-smooth, so a modification of the equation is urgently needed. In this study, we derive a new fractal Sharma–Tasso–Olver equation that can model the wave motion with the non-smooth boundary by applying He’s fractal derivative. By means of the semi-inverse method, we successfully establish its fractal generalized variational principle, which provides the conservation laws in an energy form in the fractal space and reveals the possible solution structures of the equation. The obtained generalized variational principle can be used for the numerical and analytical studies of the solitary wave properties in the fractal PDEs.
FRACTAL CHARACTERIZATION ON FRACTURE VOLUME IN COAL BASED ON CT SCANNING: PRINCIPLE, METHODOLOGY, AND IMPLICATION
Authors: ZHANG ZHEN , LIU GAOFENG , WANG XIAOMING , LI BAOLIN , LIU HUAN
Published: May 2022

This paper proposes a method for the fractal characterization on fracture volume in coal based on CT scanning experiment, and derives the relation among the fractal dimension [Formula: see text], fracture volume and length scale. The principle and methodology were deduced in detail, and the rationality was examined by the classical Mandelbrot fractal equation on fractal structure in porous media. The results demonstrate fracture volume is the comprehensive embodiment of the height, length, and aperture of fracture. Consequently, the estimated fractal dimension [Formula: see text] can more comprehensively symbolize the fractal characteristic on fracture volume of coal in three-dimensional space than the fractal dimension for fracture number. Therefore, it is worth to be further studied on establishing the analytical equation for fluids transport characteristic parameters in porous media based on [Formula: see text].
IMAGE FEATURE EXTRACTION AND FRACTALITY EVALUATION BASED ON TWO-DIMENSIONAL CONTINUOUS WAVELET TRANSFORM: APPLICATION TO DIGITAL ELEVATION MODEL DATA
Authors: SONG MAN HYOK , KIM CHOL , HO JIN GYONG , CHOE IL YONG , LIM GWANG JIN
Published: May 2022

A new method to extract image features and to evaluate fractality is proposed based on two-dimensional (2D) continuous wavelet transform (CWT). Multi-directional 2D CWT coefficients are used to determine the direction and magnitude of image intensity gradients directly unlike other methods using gradient components in the horizontal and vertical directions. Image feature points are detected by comparing candidate directional 2D CWT coefficients at candidate points and their neighbors instead of gradient magnitudes or 2D CWT moduli used by traditional methods. It enables us to extract multiscale image features including line singularities such as corners which are recognized to be hardly extracted by traditional methods. This offers an advantage condition to study fractal objects consisting of lots of line singularities. It is suggested that the detected multiscale image features can reflect multiscale fractal measures to be used to evaluate fractality, that is, self-similarity across scales. From this suggestion, the method to evaluate fractality and calculate fractal dimensions using multiscale image features is proposed. The proposed method is applied to theoretical fractal models to show that the method is convenient and effective in extracting image features of them consisting of many line singularities and calculating their fractal dimensions. Finally, the method is validated using a case study dealing with fractality evaluation of geoscientific objects such as coastlines and stream networks from the digital elevation model (DEM) data.
RINGS AROUND SIERPINSKI HOLES
Authors: JANG HYEGYONG , PAK SINHYOK , RI SONGIL
Published: May 2022

For the family of rational maps [Formula: see text] where [Formula: see text] it is known that there are infinitely many Mandelpiński necklaces [Formula: see text] with [Formula: see text] around the McMullen domain surrounding the origin in the parameter [Formula: see text]-plane. In this paper, we prove the existence of infinitely many these rings with a number of [Formula: see text] for fixed [Formula: see text] outside the Mandelpiński necklace [Formula: see text]. The ring [Formula: see text] is a simple closed curve meeting [Formula: see text] at [Formula: see text] points, such that it passes through exactly [Formula: see text] centers of Sierpinski holes and [Formula: see text] superstable parameter values. For each [Formula: see text], [Formula: see text] passes through precisely alternating [Formula: see text] superstable parameter values and the same number of centers of Sierpiński holes. There exist [Formula: see text] disjoint rings [Formula: see text] not meeting [Formula: see text] and surrounding the centers of Sierpiński holes lying on [Formula: see text], in the exterior and interior of a curve [Formula: see text], respectively. The number of such rings [Formula: see text] for fixed [Formula: see text] is [Formula: see text].
A Shapley Value Index for Market Basket Analysis: Efficient Computation Using an Harsanyi Dividend Representation
Authors: Fitzsimon Jayden , Agrawal Shrikant , Khade Kirti , Shellshear Evan , Allport Jonathon , Chapman Archie C.
Published: May 2022

Market basket analysis (MBA) aims to discover purchasing patterns and item associations from customer transaction data. A major drawback of current techniques for MBA is a lack of quantitative metrics to measure the real value associated with basket items. This paper addresses this gap by deriving a practical game-theoretic measure for MBA based on the Shapley value of cooperative games, which we call Shapley value index for MBA (SIMBA). The SIMBA of an item represents the average revenue it earns, including its influence on the revenue earned from sales of other items. A significant challenge when applying Shapley value-inspired approaches in practical domains is the exponential complexity of Shapley value computation. However, for the MBA domain, we show that SIMBA admits a scalable exact computation method that does not require sampling or other approximations. Specifically, a characteristic function for the MBA game is constructed so that the transaction dataset input corresponds to the game’s Harsanyi dividends. The relationship between Harsanyi dividends and the Shapley value is then exploited to efficiently compute SIMBA. This approach scales linearly in the number of transactions, making SIMBA a feasible approach for quantitative MBA. SIMBA can be used to screen conventional MBA techniques, such as association rules, to identify significant rules based on the items’ cross-selling capacity. This combination of existing MBA methods and SIMBA will generate rules based not only on frequency of co-occurrence, but also on the significance of the items. We demonstrate the working of the algorithm by analyzing openly available transaction data from an online retail store. To the best of our knowledge, this is the first time Shapley value is used in this way to solve market basket analyses of a practical size.
Kähler tori with almost non-negative scalar curvature
Authors: Chu Jianchun , Lee Man-Chun
Published: May 2022

Motivated by the torus stability problem, in this work, we study Kähler metrics with almost non-negative scalar curvature on complex torus. We prove that after passing to a subsequence, non-collapsing sequence of Kähler metrics with almost non-negative scalar curvature will converge to flat torus weakly.
Reduced arc schemes for Veronese embeddings and global Demazure modules
Authors: Dumanski Ilya , Feigin Evgeny
Published: May 2022

We consider arc spaces for the compositions of Plücker and Veronese embeddings of the flag varieties for simple Lie groups of types ADE. The arc spaces are not reduced and we consider the homogeneous coordinate rings of the corresponding reduced schemes. We show that each graded component of a homogeneous coordinate ring is a cocyclic module over the current algebra and is acted upon by the algebra of symmetric polynomials. We show that the action of the polynomial algebra is free and that the fiber at the special point of a graded component is isomorphic to an affine Demazure module whose level is the degree of the Veronese embedding. In type A1 (which corresponds to the Veronese curve), we give the precise list of generators of the reduced arc space. In general type, we introduce the notion of global higher level Demazure modules, which generalizes the standard notion of the global Weyl modules, and identify the graded components of the homogeneous coordinate rings with these modules.
Characteristic properties of σ-A-nuclei of a quasigroup
Authors: Chauhan Dimpy , Gupta Indivar , Verma Rashmi
Published: May 2022

In this paper, we investigate the properties of [Formula: see text]-A-nuclei of a quasigroup including relations between them and relations between their respective component sets, where [Formula: see text]. We also find connections between components of [Formula: see text]-A-nuclei of a quasigroup and components of [Formula: see text]-A-nuclei of the isostrophic images. Further, we investigate the properties of various inverse quasigroups using the derived connections. These properties will not only make the study of [Formula: see text]-A-nuclei of a quasigroup simple but also reduce the time required in the computation of [Formula: see text]-A-nuclei of a quasigroup for different values of [Formula: see text].
Categorification of a set relation geometry induced by rough operators
Authors: Infusino Federico
Published: May 2022

In this paper, we investigate Pawlak’s rough set theory from a categorical point of view, by introducing specific categories of lower and upper operators in order to analyze in a generalized setting the usual approximant operators of rough set theory. We determine several embeddings and isomorphisms between these categories and suitable categories of finitary matroids, set partitions and equivalence relations, some of which already investigated in recent papers. Using the aforementioned isomorphic categories, we exhibit several categorical properties of lower and upper operators. In addition, as one of the main applications of rough set theory concerns Pawlak’s information systems and Granular Computing, in the last part of the paper we translate in categorical terms the occurrence of rough sets in Granular Computing and, to this end, we need to work with a category PR of pairings (i.e. generalizations of Pawlak’s information systems) and pairing homomorphisms. More specifically, we exhibit several categorical properties of pairings, such as balancedness, completeness, exactness, (RegEpi,Mono-Source)-factorizability and prove that PR is Heyting but, in general, it does not admit coproducts.
Stable [64Cu]-labelled phthalocyanine choline bioconjugate for development of a potential cancer PET probe. In vivo biodistribution evaluation
Authors: Tomé Vanessa A. , Neves Ângela C. B. , Pinto Sara M. A. , Rodrigues Fábio M. S. , Calvete Mário J. F. , Alves Vítor H. P. , Sereno José , Abrunhosa Antero J. , Pereira Mariette M.
Published: May 2022

The development of stable vectorized probes for application in medical imaging, particularly in PET, has been of great interest over the last few years. In this work, we report an efficient and straightforward (5 minute) radiolabeling methodology using [[Formula: see text]Ni](p,n)[[Formula: see text]Cu], produced in ICNAS medical cyclotron, using water as solvent. The new [[Formula: see text]Cu]-radiolabelled phthalocyanine complex, bearing choline moieties, a known key vector for breast cancer, was obtained with a RCC (radiochemical conversion) of 99%, presenting a high radiochemical stability. In vivo PET imaging/biodistribution studies, performed in BALB/c mice showed that the main excretion pathway was via the hepatobiliary pathway.
On a sum involving small arithmetic functions
Authors: Zhai Wenguang
Published: May 2022

Let [Formula: see text] be any arithmetic function and define [Formula: see text]. If the function [Formula: see text] is small, namely, [Formula: see text] then the error term in the asymptotic formula of [Formula: see text] has the form [Formula: see text] In this paper, we shall prove that if a small arithmetic function [Formula: see text] has a binary additive property, then we can break the barrier [Formula: see text] in the asymptotic formula of [Formula: see text].
On certain sums of number theory
Authors: Bordellès Olivier
Published: May 2022

We study sums of the shape [Formula: see text] where [Formula: see text] is either the von Mangoldt function or the Dirichlet–Piltz divisor functions. We improve previous estimates when [Formula: see text] and [Formula: see text], and provide new results when [Formula: see text] with [Formula: see text], breaking the [Formula: see text]-barrier in each case. The functions [Formula: see text], [Formula: see text] and [Formula: see text] are also investigated.
The Barban–Davenport–Halberstam theorem for a restricted set of arithmetic progressions
Authors: Bauer Claus
Published: May 2022

We consider the asymptotic version of the Barban–Davenport–Halberstam theorem in the form proved first by Hooley. Instead of averaging the expected error term over all reduced residue classes to modules in a given range, here we only consider those reduced arithmetic progressions that satisfy an additional congruence condition and provide an asymptotic approximation.
Rational points on Del Pezzo surfaces of degree four
Authors: Mitankin Vladimir , Salgado Cecília
Published: May 2022

We study the distribution of the Brauer group and the frequency of the Brauer–Manin obstruction to the Hasse principle and weak approximation in a family of smooth del Pezzo surfaces of degree four over the rationals.
On the properties of Northcott and Narkiewicz for elliptic curves
Authors: Mello Jorge , Sha Min
Published: May 2022

In this paper, as an analog of the number field case, for an elliptic curve [Formula: see text] defined over the algebraic numbers and for any subfield [Formula: see text] of algebraic numbers, we say that [Formula: see text] has the Northcott property over [Formula: see text] if there are at most finitely many [Formula: see text]-rational points on [Formula: see text] of uniformly bounded height, and we say that [Formula: see text] has the property (P) over [Formula: see text] if for any infinite subset [Formula: see text] of [Formula: see text]-rational points on [Formula: see text], [Formula: see text] for an [Formula: see text]-endomorphism [Formula: see text] of [Formula: see text] implies that [Formula: see text] is an automorphism. We establish some criteria for both properties and provide typical examples. We also show that the Northcott property implies the property (P), but the converse is not true.
On abelian covers of the projective line with fixed gonality and many rational points
Authors: Faber Xander , Vermeulen Floris
Published: May 2022

A smooth geometrically connected curve over the finite field [Formula: see text] with gonality [Formula: see text] has at most [Formula: see text] rational points. Faber and Grantham conjectured that there exist curves of every sufficiently large genus with gonality [Formula: see text] that achieve this bound. In this paper, we show that this bound can be achieved for an infinite sequence of genera using abelian covers of the projective line. We also argue that abelian covers will not suffice to prove the full conjecture.
Solubility of additive quartic forms over ramified quadratic extensions of ℚ2
Authors: Duncan Drew , Leep David B.
Published: May 2022

In this paper, we determine the minimal number of variables [Formula: see text] which guarantees a nontrivial solution for every additive form of degree [Formula: see text] over the four ramified quadratic extensions [Formula: see text] of [Formula: see text]. In all four fields, we prove that [Formula: see text]. This is the first example of such a computation for a proper ramified extension of [Formula: see text] where the degree is a power of [Formula: see text] greater than [Formula: see text].
The smallest parts function associated with ω(q)
Authors: Wang Liuquan , Yang Yifan
Published: May 2022

We establish two families of congruences modulo powers of 5 for the Fourier coefficients of [Formula: see text], where [Formula: see text] is the weight 2 Eisenstein series and [Formula: see text] is the Dedekind eta function. This allows us to prove similar congruences for two smallest parts functions. The first function is [Formula: see text], which was introduced by Andrews, Dixit and Yee and is associated with Ramanujan/Watson’s third-order mock theta function [Formula: see text]. The second one is [Formula: see text], which appeared in the work of Garvan and Jennings-Shaffer. Moreover, we confirm two conjectural congruences of Wang.
Frobenius finds non-monogenic division fields of abelian varieties
Authors: Smith Hanson
Published: May 2022

Let [Formula: see text] be an abelian variety over a finite field [Formula: see text] with [Formula: see text]. Let [Formula: see text] denote the Frobenius and let [Formula: see text] denote Verschiebung. Suppose the Weil [Formula: see text]-polynomial of [Formula: see text] is irreducible. When [Formula: see text], we construct a matrix which describes the action of [Formula: see text] on the prime-to-[Formula: see text]-torsion points of [Formula: see text]. We employ this matrix in an algorithm that detects when [Formula: see text] is an obstruction to the monogenicity of division fields of certain abelian varieties.
Inhomogeneous additive equations
Authors: Knapp Michael P.
Published: May 2022

In this paper, we study the function [Formula: see text], which we define as the smallest number [Formula: see text] of variables needed to guarantee that the equation [Formula: see text] has nontrivial solutions in each of the [Formula: see text]-adic fields [Formula: see text], regardless of the rational integer coefficients. This generalizes the [Formula: see text] function of Davenport and Lewis. In this paper, we give a sharp upper bound for [Formula: see text] and compute its value for various choices of the degrees.
On the exponential Diophantine equation Fnx ± Fmx = a with a ∈{Fr,Lr}
Authors: Şiar Zafer
Published: May 2022

In this paper, we will answer the question of when the sum or the difference of [Formula: see text]th powers of any two Fibonacci numbers becomes a Fibonacci number or a Lucas number. We prove that if this is possible with [Formula: see text], then [Formula: see text] may be only 3,4,5, or 10. Also, we give the result that the Diophantine equation in the title with [Formula: see text] has no solutions for [Formula: see text]
On the problem of Pillai with Pell numbers, Pell–Lucas numbers and powers of 3
Authors: Faye Bernadette , Edjeou Bilizimbéyé
Published: May 2022

Let [Formula: see text] be the sequence of Pell numbers defined by [Formula: see text], [Formula: see text] and [Formula: see text] for all [Formula: see text] and let [Formula: see text] be its companion sequence, the Pell–Lucas numbers defined by [Formula: see text] and [Formula: see text] for all [Formula: see text]. In this paper, we find all integers [Formula: see text] admitting at least two representations as a difference between a Pell number or a Pell–Lucas number and a power of [Formula: see text]
Efficient congruencing in ellipsephic sets: the general case
Authors: Biggs Kirsti D.
Published: May 2022

In this paper, we bound the number of solutions to a general Vinogradov system of equations [Formula: see text] as well as other related systems, in which the variables are required to satisfy digital restrictions in a given base. Specifically, our sets of permitted digits have the property that there are few representations of a natural number as sums of elements of the digit set — the set of squares serving as a key example. We obtain better bounds using this additive structure than could be deduced purely from the size of the set of variables. In particular, when the digits are required to be squares, we obtain diagonal behavior with [Formula: see text] variables.
Extensions of Watson’s theorem and the Ramanujan–Guinand formula
Authors: Kumar Rahul
Published: May 2022

Ramanujan provided several results involving the modified Bessel function [Formula: see text] in his Lost Notebook. One of them is the famous Ramanujan–Guinand formula, equivalent to the functional equation of the non-holomorphic Eisenstein series on SL[Formula: see text]. Recently, this formula was generalized by Dixit, Kesarwani, and Moll. In this paper, we first obtain a generalization of a theorem of Watson and, as an application of it, give a new proof of the result of Dixit, Kesarwani, and Moll. Watson’s theorem is also generalized in a different direction using [Formula: see text] which is itself a generalization of [Formula: see text]. Analytic continuation of all these results are also given.
On the Shimura lift modulo 2
Authors: Kohnen Winfried
Published: May 2022

We study the kernel of the Shimura lifting from modular forms of half-integral weight to integral weight.
Numerical Modeling of Generation of Landslide Tsunamis: A Review
Authors: Lee Cheng-Hsien , Lo Peter H.-Y. , Shi Huabin , Huang Zhenhua
Published: May 2022

Depth-integrated wave models are widely used for simulating large-scale propagation of landslide tsunamis, with the generation of tsunami being simulated separately by various generation models to provide the required initial conditions. For a given problem, the selection of a proper tsunami generation model is an important aspect for tsunami hazard analysis. The generation of tsunamis by submarine or subaerial landslides is a transient multiphase process which involves important fine-scale physics. Depth-integrated generation models, while relatively easy to use, cannot simulate these fine-scale physics. Depth-resolved generation models can overcome the shortcomings of depth-integrated generation models but are computationally demanding. This paper first reviews existing depth-integrated generation models to show the need for depth-resolved generation models. Four classes of depth-resolved generation models are reviewed: computational fluid dynamics (CFD) models, approaches coupling CFD and discrete element method, multiphase flow models, and meshless particle models. Multiphase flow models, which are relatively new, can consider complex interactions between landslide materials and its surrounding fluids. Meshless particle models are appealing for simulating landslide tsunamis because of their convenience to deal with the violent motion of the water surface and ability to run on graphics processing units. The main strengths, weaknesses, and future research directions of the reviewed models are briefly discussed. The literature reviewed, which is by no means complete, aims to provide researchers updated and practical guidelines on numerical modeling techniques for simulating the generation process of landslide tsunamis.
Stability and bifurcation analysis of a tri-trophic food chain model with intraguild predation
Authors: Giricheva Evgeniya
Published: May 2022

The dynamics of a three-component model for food web with intraguild predation is considered. The model is based on the collection of ordinary differential equations that describe the interactions among prey, intermediate predator and top predator. First, the model without self-limitation of the predators is studied. Boundedness of the system and existence of non-negative solutions are established. The local stability analysis of the equilibria is carried out to examine the behavior of the system. The possibility of Hopf bifurcation around non-negative equilibria with consumption rates as bifurcation parameters is studied. Center manifold theorem and the normal form theory are applied to obtain the formulas for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions. Numerical simulations support the analytical findings, which show that the extinction of one of the predators can occur under certain restrictions on the predation rate of the top predator. Subsequently, numerical analysis of the model with self-limitation of the predators is carried out. Simulations reveal that the system with intraspecific competition in the predator populations can reproduce coexistence between the three species in resource-rich environment.
Diagnosis of knee osteoarthritis by OCT and surface-enhanced Raman spectroscopy
Authors: An Ran , Gu Huaimin , Guo Zhouyi , Zhong Huiqing , Wei Huajiang , Wu Guoyong , He Yonghong , Xie Shusen , Yang Hongqin
Published: May 2022

In this paper, optical coherence tomography (OCT) and surface-enhanced Raman spectroscopy (SERS) were used to characterize normal knee joint (NKJ) tissue and knee osteoarthritis (KOA) tissue ex vivo. OCT images show that there is a clear hierarchical structure in NKJ tissue, including surface layer, transitional layer, radiation layer and cartilage matrix calcification layer tissue structure, while the hierarchical structure of KOA tissue is not clear and unevenly distributed, and the pathological tissues at different stages also show significant differences. SERS shows that NKJ tissue and mild osteoarthritic knee cartilage (MiKOA) tissue have strong characteristic Raman peaks at 964, 1073 (1086), 1271, 1305, 1442, 1660 and 1763[Formula: see text]cm[Formula: see text]. Compared with the Raman spectrum of NKJ tissue, the Raman characteristic peaks of MiKOA tissue have some shifts, moving from 1073[Formula: see text]cm[Formula: see text] to 1086[Formula: see text]cm[Formula: see text] and from 1542[Formula: see text]cm[Formula: see text] to 1442[Formula: see text]cm[Formula: see text]. There is a characteristic Raman peak of 1271[Formula: see text]cm[Formula: see text] in MiKOA tissue, but not in NKJ tissue. Compared with NKJ tissue, severely degenerated cartilage (SdKOA) tissues show some new SERS peaks at 1008, 1245, 1285, 1311 and 1321[Formula: see text]cm[Formula: see text], which are not seen in SERS spectra of NKJ tissue. Principal component analysis (PCA) was used to analyze the Raman spectra of 1245–1345[Formula: see text]cm[Formula: see text] region. The results show that PCA can distinguish NKJ, MiKOA and SdKOA tissues and the accuracy is about 90%. These results indicate that OCT can clearly distinguish NKJ, MiKOA, moderate osteoarthritic knee cartilage (MoKOA) and SdKOA tissue, while SERS can provide further judgment basis. The results also prove that the contents of protein and polysaccharide in knee tissue are changed during the pathological process of knee tissue, which is the cause of pain caused by poor friction in knee joint during movement.
TECHNOLOGY TREATIES AND CLIMATE CHANGE
Authors: GERSBACH HANS , RIEKHOF MARIE-CATHERINE
Published: May 2022

We introduce an international technology treaty (‘Tech Treaty’) that couples the funding of research for a more advanced abatement technology with an international emissions permit market. While each country decides on domestic permit issuance, a fraction of these permits is auctioned by an international agency. Auction revenues scale up license revenues for the innovators of abatement technologies. We show that such a treaty increases innovations and decreases emissions under plausible conditions compared to an emissions trading system without additional technology agreement. Finally, we discuss how a Tech Treaty may inspire next steps in existing technology programs.
AN ECONOMY-WIDE FRAMEWORK FOR ASSESSING THE STRANDED ASSETS OF ENERGY PRODUCTION SECTOR UNDER CLIMATE POLICIES
Authors: CHEN YEN-HENG HENRY , LANDRY ERIK , REILLY JOHN M.
Published: May 2022

Climate change mitigation efforts, which require the transition away from carbon-intensive activities, can pose financial risks for owners of fossil fuel assets and investors that the finance companies are engaged in greenhouse gas-emitting activities. For instance, fossil fuel extraction may be significantly scaled-back, and coal-power plants may be idled or even phased out prematurely, thus becoming stranded assets for the shareholders. Using a global general equilibrium model with detailed energy sector and capital stock structures, we estimate the corresponding stranded assets under various emissions mitigation scenarios. Our findings reveal that, depending on the policy scenario, the global net present value of unrealized fossil fuel output through 2050 relative to a “no policy” scenario is between 21.5 and 30.6 trillion USD, and that of stranded assets in coal power generation is between 1.3 and 2.3 trillion USD. The analytical framework presented in our study complements existing research, in which macroeconomic variables required for estimating the stranded assets are often derived from models with more simplified assumptions. Therefore, individual firms and financial institutions can combine our economy-wide analysis with details on their own investment portfolios to determine their climate-related transition risk exposure.
Multiscale modeling of fracture in 2D materials
Authors: Robert Kerlin P. , Lee James D.
Published: May 2022

Research on two-dimensional (2D) materials, such as graphene and molybdenum disulfide (MoS2), now involves researchers worldwide, implementing cutting edge technology to study them. However, when considering using 2D materials in such promising applications, one of the major concerns is the mechanical failure, which remains heavily underexplored. In this work, we demonstrate the use of sequential and concurrent multiscale modeling to study the effect of various fracture modes on graphene and molybdenum disulfide (MoS2). Some of the fracture modes explored are pure tensile loading, shear loading, and a combination of tensile and shear loading and cyclic loading to investigate fatigue.
3D Viscoelastic Finite-Difference Analysis of the Monopole Acoustic Logs in Cylindrical Coordinates
Authors: Pan Yue , He Xiao , Wang Xiuming
Published: May 2022

In this paper, a model of the heterogeneous anelastic seismic wave problem is proposed in three-dimensional (3D) cylindrical coordinates. We use the velocity-stress formula to describe the realistic attenuation properties of viscoelastic materials, derived from a rheological model of the generalized standard linear solid (GSLS). The equation system is completed by additional equations for the anelastic functions including the strain history of the material. We apply the staggered grid finite-difference (FD) method in 3D cylindrical coordinates to solve the equations. Moreover, to avoid the effect of gradual expansion of the grid size as the radius increases, we use a variable grid method to achieve compensation. In real drilling operations, the mud injected in the borehole is a fluid with viscous properties. The actual formation is also not elastic. In the synthetic data of acoustic logging while drilling (LWD), we find that the drill collar wave is not affected by the viscoelastic parameters of the formation. In contrast, the Stoneley wave is more sensitive to the viscosity of the drilling fluid. The phase and amplitude of the received waveform are affected by the drilling fluid as well as the formation viscoelasticity. Therefore, the development of the cylindrical variable-grid FD method provides a flexible and efficient numerical technique to solve 3D viscoelastic wave propagation problems, including realistic attenuation and complex geometry.
Drug-Induced Lupus: A Forgotten Cause of Prolonged Pyrexia of Unknown Origin
Authors: Sivalingam Varsha , Dinning Hillary , Fang Johnny , Prasad Yashneel , Jones Peter , Senanayake Sanjaya
Published: May 2022

The causes of a pyrexia of unknown origin (PUO) are broadly spread across infectious, malignant, or inflammatory conditions. The authors report a case of a 43-year-old female who initially presented with hypoxia and fevers secondary to a presumed acute viral or bacterial infectious pulmonary insult. However, fevers persisted despite pulmonary imaging remaining normal. The case subsequently evolved into a PUO with multiple lines of investigation proving inconclusive. No definitive diagnosis was made at the time of discharge; however, cessation of hydralazine was noted to coincide with the last of the patient’s fevers. Following the discharge, her anti-histone antibodies returned a positive result, and the diagnosis of drug-induced lupus was made with hydralazine as the presumed trigger.
From Industry 4.0 to Supply Chain 4.0: A systematic review
Authors: Lee C. K. M. , Chung S. Y.
Published: May 2022

The latest development of advanced manufacturing technology drives the manufacturing paradigm shift as Industry 4.0. The supply chain and logistics play important roles to increase the operational efficiency so as to further boost the overall productivity of the holistic production system. The latest technologies, such as Machine Learning, Big Data, the Internet of Things, and Cloud platforms, enable manufacturers to overcome the challenges and enhance their competitive advantages. The purpose of this paper is to review how the latest technologies for Industry 4.0 can incorporate into inbound and outbound logistics to meet the latest requirements of customers. Having reviewed around 500 papers from the Web of Science database, a comprehensive supply chain framework that supports Industry 4.0 is proposed. The paper provides the managerial implications and insights for future research work for Supply Chain 4.0.
Optimal Energy-Centric Resource Allocation and Offloading Scheme for Green Internet of Things Using Machine Learning
Authors: Manogaran Gunasekaran , Rawal Bharat S. , Song Houbing , Wang Huihui , Hsu Chinghsien , Saravanan Vijayalakshmi , Kadry Seifedine Nimer , Shakeel P. Mohamed
Published: May 2022

Resource allocation and offloading in green
Internet of Things (IoT)
relies on the multi-level heterogeneous platforms. The energy expenses of the platform determine the reliability of green IoT based services and applications. This manuscript introduces a decisive energy management scheme for optimal resource allocation and offloading along with energy constraints. This scheme handles both the allocation and energy-cost in a balanced manner through deterministic task offloading. In particular, resource allocation solution for non-delay tolerant green IoT applications is focused by confining the failures of discrete tasks through neural learning. The dropout process augmented with the learning process improves the feasible conditions for resource handling and task offloading among the active IoT service providers. Through extensive simulations the performance of the proposed scheme is analyzed and energy consumption, failure rate, processing, and completion time metrics are used for a comparative study. Further, the optimal utilization and on-demand dissipation of such stored resources help to improve the sustainability of green power and communication technologies in the smart city environment.