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In this work we investigate the problem of producing iso-dual algebraic geometry (AG) codes over a finite field F q with q elements. Given a finite separable extension M / F of function fields and an iso-dual AG-code C defined over F , we provide a general method to lift the code C to another iso-dual AG-code C ~ defined over M under some assumptions on the parity of the involved different exponents. We apply this method to lift iso-dual AG-codes over the rational function field to elementary abelian p-extensions, like the maximal function fields defined by the Hermitian, Suzuki, and one covered by the GGS function field. We also obtain long binary and ternary iso-dual AG-codes defined over cyclotomic extensions. [ABSTRACT FROM AUTHOR]

In this article, we investigate a new class of convexity named inverse cosine convex functions (ICCF). We explore and examine some algebraic and geometric features by presenting the graphs of several significant ICCF functions for visual demonstration. By using this proposed class of functions, we derive the Hermite–Hadamard (HH) inequality and certain refinements applicable to functions whose first derivative in absolute value is an ICCF. To derive the main consequences, we mainly use Hölder's, Hölder–İşcan, and power‐mean integral inequalities. Furthermore, it is proved that the results obtained using Hölder–İşcan and improved power‐mean integral inequalities have better approximations compared to other techniques. This novel idea of inverse cosine convexity allows us to explore new horizons of research and may motivate researchers to investigate such classes of convexity. [ABSTRACT FROM AUTHOR]

In this paper, we show that ∞-adic multiple zeta values associated to the function field of an algebraic curve of higher genus over a finite field are not zero, under certain assumption on the gap sequence associated to the rational point ∞ on the given curve. Using arguments and results of Sheats and Thakur for the case of the projective line, we calculate the absolute values of power sums in the series defining multiple zeta values, and show that the calculation implies the non-vanishing result. [ABSTRACT FROM AUTHOR]

Let \alpha be a non-zero algebraic number. Let K be the Galois closure of \mathbb {Q}(\alpha) with Galois group G and \bar {\mathbb {Q}} be the algebraic closure of \mathbb {Q}. In this article, among the other results, we prove the following. If f\in \bar {\mathbb {Q}}[G] is a non-zero element of the group ring \bar {\mathbb {Q}}[G] and \alpha is a given algebraic number such that f(\alpha ^n) is a non-zero algebraic integer for infinitely many natural numbers n, then \alpha is an algebraic integer. This result generalises the result of Polya [Rend. Circ Mat. Palermo, 40 (1915), pp. 1–16], Corvaja and Zannier [Acta Math. 193 (2004), pp. 175–191] and Philippon and Rath [J. Number Theory 219 (2021), pp. 198–211]. We also prove the analogue of this result for rational functions with algebraic coefficients. Inspired by a result of B. de Smit [J. Number Theory 45 (1993), pp. 112–116], we prove a finite version of the Polya type result for a binary recurrence sequences of non-zero algebraic numbers. In order to prove these results, we apply the techniques of Corvaja and Zannier along with the results of Kulkarni et al. [Trans. Amer. Math. Soc. 371 (2019), pp. 3787–3804], which are applications of the Schmidt subspace theorem. [ABSTRACT FROM AUTHOR]

Supercuspidal representations are usually infinite-dimensional, so the size of such a representation cannot be measured by its dimension; the formal degree is a better alternative. Hiraga, Ichino, and Ikeda conjectured a formula for the formal degree of a supercuspidal in terms of its L-parameter only. Our first main result is to compute the formal degrees of the supercuspidal representations constructed by Yu. Our second result, using the first, is to verify that Kaletha's regular supercuspidal L-packets satisfy the conjecture. [ABSTRACT FROM AUTHOR]

The connections between parameter surfaces enable the development of various geometric designs. However, these surfaces are generally connected along their boundaries in a rectangular domain. This study investigated the methods for connecting surfaces along a curve. To this end, we introduced two-variable degenerate functions and utilized their algebraic properties to characterize the form of the parameter surfaces for practical surface construction. The results were used to deform the surfaces along the curve. For application, we presented the examples of deformations using Bézier surfaces and extended them to general surfaces. [ABSTRACT FROM AUTHOR]

Let be an uncountable field of characteristic 0. For a given function f : n → , with n ≥ 2 , we prove that f is regular if and only if the restriction f | C is a regular function for every algebraic curve C in n which is either an affine line or is isomorphic to a plane curve in 2 defined by the equation X p − Y q = 0 , where p < q are prime numbers. We also show that regularity of f can be verified on other algebraic curves in n with desired geometric properties. Furthermore, if the field is not algebraically closed, we construct a -valued function on n that is not regular, but all its restrictions to nonsingular algebraic curves in n are regular functions. [ABSTRACT FROM AUTHOR]

Statistical characterizations of complex network structures can be obtained from both the Ihara Zeta function (in terms of prime cycle frequencies) and the partition function from statistical mechanics. However, these two representations are usually regarded as separate tools for network analysis, without exploiting the potential synergies between them. In this paper, we establish a link between the Ihara Zeta function from algebraic graph theory and the partition function from statistical mechanics, and exploit this relationship to obtain a deeper structural characterisation of network structure. Specifically, the relationship allows us to explore the connection between the microscopic structure and the macroscopic characterisation of a network. We derive thermodynamic quantities describing the network, such as entropy, and show how these are related to the frequencies of prime cycles of various lengths. In particular, the n-th order partial derivative of the Ihara Zeta function can be used to compute the number of prime cycles in a network, which in turn is related to the partition function of Bose–Einstein statistics. The corresponding derived entropy allows us to explore a phase transition in the network structure with critical points at high and low-temperature limits. Numerical experiments and empirical data are presented to evaluate the qualitative and quantitative performance of the resulting structural network characterisations. [ABSTRACT FROM AUTHOR]

In the classical Geometry of Numbers, the calculation of successive minima may be quite difficult, even in R2${\bf R}^2$ using the norm coming from a distance function associated to a set. In the literature, there seem to be hardly any analogues when R${\bf R}$ is replaced by the algebraic closure of a function field in one variable and one uses a norm arising from the absolute height. Here, we calculate a one‐parameter family of examples that naturally arose in our recent paper on bounded heights. We also comment on whether the minima are attained. [ABSTRACT FROM AUTHOR]

The main concern of this paper is to study large-time behavior of solutions for an outflow problem to the reduced gravity two and a half layer model in a half space. We establish the existence of stationary solutions and further obtain the large time asymptotic stability of small-amplitude stationary solutions provided that the initial perturbation is sufficiently small. Moreover, we obtain the convergence rate of the solution toward the stationary solution in some weighted Sobolev spaces only for the supersonic case. The proof is based on the basic energy method. A key point for the proof of convergence rates is to capture the positivity of the temporal energy dissipation functional and boundary terms with suitable space weight functions either algebraic or exponential depending on whether or not the incoming far-field velocity satisfy some additional conditions. [ABSTRACT FROM AUTHOR]

Chromatic symmetric functions are well-studied symmetric functions in algebraic combinatorics that generalize the chromatic polynomial and are related to Hessenberg varieties and diagonal harmonics. Motivated by the Stanley–Stembridge conjecture, we show that the allowable coloring weights for indifference graphs of Dyck paths are the lattice points of a permutahedron P λ , and we give a formula for the dominant weight λ . Furthermore, we conjecture that such chromatic symmetric functions are Lorentzian, a property introduced by Brändén and Huh as a bridge between discrete convex analysis and concavity properties in combinatorics, and we prove this conjecture for abelian Dyck paths. We extend our results on the Newton polytope to incomparability graphs of (3 + 1) -free posets, and we give a number of conjectures and results stemming from our work, including results on the complexity of computing the coefficients and relations with the ζ map from diagonal harmonics. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel series of second-order Backward Differentiation Formulas (BDFs) specifically designed to address phase-lag and its first derivative in the numerical resolution of Initial Value Problems (IVPs) with orbital solutions. Our methodology commences with an in-depth analysis of phase-lag phenomena associated with second-order BDFs. Following this, we construct a suite of equations by embedding algebraic functions into the operational framework of the 3-step second-order BDF (SOBDF) method. Additionally, we elaborate on equations that precisely describe the phase-lag and its derivatives, with a concentrated focus on the 3-step SOBDF method. The culmination of this work is the presentation of six distinct methods, each methodically crafted to negate both the real and imaginary elements of phase-lag and its derivatives in numerical computations. The study advances with a meticulous examination of the local truncation error and the stability regions pertinent to the six phase-fitted methods introduced. Furthermore, we scrutinize their computational performance by deploying these methods across a spectrum of initial value problems, offering valuable insights into their effectiveness in varying contexts. [ABSTRACT FROM AUTHOR]

In this paper, we derive some new results for the separation of two not necessarily convex cones by a (convex) cone / conical surface in real (reflexive) normed spaces. In essence, we follow the nonlinear and nonsymmetric separation approach developed by Kasimbeyli (2010, SIAM J. Optim. 20), which is based on augmented dual cones and Bishop-Phelps type (normlinear) separating functions. Compared to Kasimbeyli's separation theorem, we formulate our theorems for the separation of two cones under weaker conditions (concerning convexity and closedness requirements) with respect to the involved cones. By a new characterization of the algebraic interior of augmented dual cones in real normed spaces, we are able to establish relationships between our cone separation results and the results derived by Kasimbeyli (2010, SIAM J. Optim. 20) and by García-Castaño, Melguizo-Padial and Parzanese (2023, Math. Meth. Oper. Res. 97). [ABSTRACT FROM AUTHOR]

The development of algebraic reasoning from the earliest educational levels is an objective that has solid support both from the point of view of research and curricular development. Effectively incorporating algebraic content to enrich mathematical activity in schools requires considering the different degrees of generality of the objects and processes involved in algebraic practices. In this article, we present an expanded version of the model of levels of algebraization proposed within the framework of the onto-semiotic approach, establishing sublevels that provide a more microscopic view of the structures involved and the processes of generalization, representation, and analytical calculation at stake. We exemplify the model with mathematical activities that can be approached from primary education, classified according to the different sublevels of algebraization. The use of this expanded model can facilitate the development of didacticmathematical knowledge of teachers in training on algebraic reasoning and its teaching. [ABSTRACT FROM AUTHOR]

Introducing initial algebraic principles poses a significant challenge, often compounded by the inherent abstract nature of algebra. This article introduces an innovative pedagogical approach that promotes the use of algebra tiles, a didactic manipulative material formed by a collection of geometric pieces symbolizing distinct algebraic monomials. Additionally, this article includes the findings of a quasi-experimental study that applied this inventive teaching method. This research was carried out across two separate classes of 15 students (10 boys and five girls) of first year of compulsory secondary education. One group of students adhered to the conventional teaching approach (the control group), while the other class embraced the proposed methodology using algebra tiles (the experimental group). The disparities in algebraic proficiency observed between these two student groups, as assessed through various examinations conducted during the intervention were statistically significant, with the experimental group consistently achieving superior results. Moreover, mathematical and algebraic errors of students were assessed using eight distinct indicators. In all cases, the experimental group demonstrated lower error percentages, and these errors showed a marked decrease as the intervention progressed. In summary, this innovative methodology markedly enhanced students' comprehension of algebra, their knowledge, and their motivation while significantly reducing mathematical errors. [ABSTRACT FROM AUTHOR]

Let |$A$| be the integral closure of the ring of polynomials |${{\mathbb {C}}}[t]$|⁠ , within the field of algebraic functions in one variable. We show that |$A$| interprets the ring of integers. This contrasts with the analogue for finite fields, proved to have a decidable theory in [ 12 ] and [ 4 ]. [ABSTRACT FROM AUTHOR]

Rotation symmetric Boolean functions are good candidates for stream ciphers because they have such advantages as simple structure, high operational speed and low implement cost. Recently, Mesnager et al. proposed for the first time an efficient method to construct balanced rotation symmetric Boolean functions with optimal algebraic immunity and good nonlinearity for an arbitrary even number of variables. However, the algebraic degree of their constructed n -variable (n > 4) function is always less than the maximum value n − 1. In this paper, by modifying the support of Boolean functions from Mesnager et al.'s construction, we present two new constructions of balanced even-variable rotation symmetric Boolean functions with optimal algebraic immunity as well as higher algebraic degree and nonlinearity. The algebraic degree of Boolean functions in the first construction reaches the maximum value n − 1 if n 2 is odd and n 2 ≠ (2 k + 1) 2 or (2 k + 1) 2 + 2 for integer k , while that of the second construction reaches the maximum value for all n. Moreover, the nonlinearities of Boolean functions in both two constructions are higher than that of Mesnager et al.'s construction. [ABSTRACT FROM AUTHOR]

Let A be the set of elements in an algebraic function field K over Fq which are integral outside a fixed place ∞. Let G = GL2(A) be a Drinfeld modular group. The normalizer of G in GL2(K), where K is the quotient field of A, gives rise to automorphisms of G, which we refer to as quasi-inner. Modulo the inner automorphisms of G, they form a group Quinn(G) which is isomorphic to Cl(A)2, the 2-torsion in the ideal class group Cl(A). The group Quinn(G) acts on all kinds of objects associated with G. For example, it acts freely on the cusps and elliptic points of G. If T is the associated Bruhat--Tits tree, the elements of Quinn(G) induce non-trivial automorphisms of the quotient graph G\T, generalizing an earlier result of Serre. It is known that the ends of G\T are in one-to-one correspondence with the cusps of G. Consequently, Quinn(G) acts freely on the ends. In addition, Quinn.G/ acts transitively on those ends which are in one-to-one correspondence with the vertices of G\T whose stabilizers are isomorphic to GL2(Fq). [ABSTRACT FROM AUTHOR]

A classical problem due to Abel is to determine if a differential equation |$y^{\prime}=\eta y$| admits a non-trivial solution |$y$| algebraic over |$\mathbb C(x)$| when |$\eta $| is a given algebraic function over |$\mathbb C(x)$|⁠. Risch designed an algorithm that, given |$\eta $|⁠ , determines whether there exists an algebraic solution or not. In this paper, we adopt a different point of view when |$\eta $| admits a Puiseux expansion with rational coefficients at some point in |$\mathbb C\cup \{\infty \}$|⁠ , which can be assumed to be 0 without loss of generality. We prove the following arithmetic characterization: there exists a non-trivial algebraic solution of |$y^{\prime}=\eta y$| if and only if the coefficients of the Puiseux expansion of |$x\eta (x)$| at |$0$| satisfy Gauss congruences for almost all prime numbers. We then apply our criterion to hypergeometric series: we completely determine the equations |$y^{\prime}=\eta y$| with an algebraic solution when |$x\eta (x)$| is an algebraic hypergeometric series with rational parameters, and this enables us to prove a prediction Golyshev made using the theory of motives. We also present two other applications, namely to diagonals of rational fractions and to directed two-dimensional walks. [ABSTRACT FROM AUTHOR]

This paper is a plea for diagonals and telescopers of rational or algebraic functions using creative telescoping, using a computer algebra experimental mathematics learn-by-examples approach. We show that diagonals of rational functions (and this is also the case with diagonals of algebraic functions) are left-invariant when one performs an infinite set of birational transformations on the rational functions. These invariance results generalize to telescopers. We cast light on the almost systematic property of homomorphism to their adjoint of the telescopers of rational or algebraic functions. We shed some light on the reason why the telescopers, annihilating the diagonals of rational functions of the form P / Q k and 1 / Q , are homomorphic. For telescopers with solutions (periods) corresponding to integration over non-vanishing cycles, we have a slight generalization of this result. We introduce some challenging examples of the generalization of diagonals of rational functions, like diagonals of transcendental functions, yielding simple F 1 2 hypergeometric functions associated with elliptic curves, or the (differentially algebraic) lambda-extension of correlation of the Ising model. [ABSTRACT FROM AUTHOR]

The present work deals with the characteristic polynomial of Laplacian matrix for circulant graphs. We show that it can be decomposed into a finite product of algebraic function evaluated at the roots of a linear combination of Chebyshev polynomials. As an important consequence of this result, we get the periodicity of characteristic polynomials evaluated at the prescribed integer values. Moreover, we can show that the characteristic polynomials of circulant graphs are always perfect squares up to explicitly given linear factors. [ABSTRACT FROM AUTHOR]

We show—to our own surprise—that total electronic energies for a family of m × n rectangular graphene flakes can be very accurately represented by a simple function of the structural parameters m and n with errors not exceeding 1 kcal/mol. The energies of these flakes, usually referred to as multiple zigzag chains Z(m,n), are computed for m, n < 21 at their optimized geometries using the DFTB3 methodology. We have discovered that the structural parameters m and n (and their simple algebraic functions) provide a much better basis for the energy decomposition scheme than the various topological invariants usually used in this context. Most terms appearing in our energy decomposition scheme seem to have simple chemical interpretations. Our observation goes against the well-established knowledge stating that many-body energies are complicated functions of molecular parameters. Our observations might have far-reaching consequences for building accurate machine learning models. [ABSTRACT FROM AUTHOR]

Symmetry is often regarded as an integral aspect about aesthetics. This motivates the pursuit of interdisciplinary studies based on the use of subjects in mathematics concerned with symmetry in conjunction with aesthetics. What is referred to as a symmetric function in the field of algebraic combinatorics is an abstraction based on polynomials that exhibit a symmetric property, and this leads us to pursue an algebraic combinatorics-inspired exploration based on aesthetics. In particular, we use different bases and transitions between them to create aesthetically pleasing visualizations of symmetric functions. We see that these visualizations in turn raise new and interesting questions. [ABSTRACT FROM AUTHOR]

Recently Vasuki and Veeresha were able to prove Dedekind η-function identities of level 14 conjectured by Somos. In this paper, we show how these Somos's identities are the consequence of Ramanujan's modular equations of degree 7. Also, in their paper authors are using a known multiplier to prove Somos's identities and we explained the method of obtaining that multiplier in this paper. [ABSTRACT FROM AUTHOR]

We give an adequate, concrete, categorical-based model for Lambda- ${\mathcal S}$ , which is a typed version of a linear-algebraic lambda calculus, extended with measurements. Lambda- ${\mathcal S}$ is an extension to first-order lambda calculus unifying two approaches of non-cloning in quantum lambda-calculi: to forbid duplication of variables and to consider all lambda-terms as algebraic linear functions. The type system of Lambda- ${\mathcal S}$ has a superposition constructor S such that a type A is considered as the base of a vector space, while SA is its span. Our model considers S as the composition of two functors in an adjunction relation between the category of sets and the category of vector spaces over $\mathbb C$. The right adjoint is a forgetful functor U , which is hidden in the language, and plays a central role in the computational reasoning. [ABSTRACT FROM AUTHOR]

Weyl group multiple Dirichlet series are Dirichlet series in r complex variables, with analytic continuation to C r and a group of functional equations isomorphic to the Weyl group of a reduced root system of rank r. Such series may be defined for any global field K , but in the case when K is an algebraic function field they are expected to be, up to a variable change, rational functions in several variables. We verify the rationality of these functions in the case when K = F q (T) , and describe the denominators and support of the numerators. [ABSTRACT FROM AUTHOR]

Here we exhibit multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or RN; N ∞ N, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We study also the case of approximation by iterated operators of the last four types. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by the algebraic sigmoid function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer. [ABSTRACT FROM AUTHOR]

This paper aims to introduce the notions of deferred Nörlund statistical Riemann integrability and statistical deferred Nörlund Riemann summability for sequence of real-valued functions and to apply them in Korovkin-type new approximations. First, we present an inclusion theorem to understand the connection between these new notions. Then, based on these potential notions we establish new versions of Korovkin-type theorems with three algebraic test functions. Finally, we compute an example, under the consideration of a positive linear operator in association with the Bernstein polynomials to exhibit the effectiveness of our findings. [ABSTRACT FROM AUTHOR]

The concepts of Dokdo sub-hoops and Dokdo filters are introduced, and their properties are investigated. The relationship between Dokdo sub-hoops and Dokdo filters is discussed, and characterizations of Dokdo sub-hoops and Dokdo filters are established. [ABSTRACT FROM AUTHOR]

Assuming that R is an associative ring with prime ideal P, this paper investigates the commutativity of the quotient ring R=P, as well as the possible forms of generalized derivations satisfying certain algebraic identities on R: We give results on strong commutativity, preserving generalized derivations of prime rings, using our theorems. Finally, an example is given to show that the restrictions on the ideal P are not super uous. [ABSTRACT FROM AUTHOR]

In this paper, we study the transfer of some alge-braic properties from the ring R to the ring of skew Hurwitz series (HR; !), where ! is an automorphism of R and vice versa. Different properties of skew Hurwitz series are studied with respect to various clean ring structures and semiclean ring structures. [ABSTRACT FROM AUTHOR]

Birational properties of generically finite morphisms X→Y$X\rightarrow Y$ of algebraic varieties can be understood locally by a valuation of the function field of X. In finite extensions of algebraic local rings in characteristic zero algebraic function fields which are dominated by a valuation, there are nice monomial forms of the mapping after blowing up enough, which reflect classical invariants of the valuation. Further, these forms are stable upon suitable further blowing up. In positive characteristic algebraic function fields, it is not always possible to find a monomial form after blowing up along a valuation, even in dimension two. In dimension two and positive characteristic, after enough blowing up, there are stable forms of the mapping which hold upon suitable sequences of blowing up. We give examples showing that even within these stable forms, the forms can vary dramatically (erratically) upon further blowing up. We construct these examples in defect Artin–Schreier extensions which can have any prescribed distance. [ABSTRACT FROM AUTHOR]

A function that is analytic on a domain of C n is holonomic if it is the solution to a holonomic system of linear homogeneous differential equations with polynomial coefficients. We define and study the Bernstein–Sato polynomial of a holonomic function on a smooth algebraic variety. We analyze the structure of certain sheaves of holonomic functions, such as the algebraic functions along a hypersurface, determining their direct sum decompositions into indecomposables, that further respect decompositions of Bernstein–Sato polynomials. When the space is endowed with the action of a linear algebraic group G, we study the class of G-finite analytic functions, i.e. functions that under the action of the Lie algebra of G generate a finite dimensional rational G-module. These are automatically algebraic functions on a variety with a dense orbit. When G is reductive, we give several representation-theoretic techniques toward the determination of Bernstein–Sato polynomials of G-finite functions. We classify the G-finite functions on all but one of the irreducible reduced prehomogeneous vector spaces, and compute the Bernstein–Sato polynomials for distinguished G-finite functions. The results can be used to construct explicitly equivariant D -modules. [ABSTRACT FROM AUTHOR]

Two Kähler manifolds are called relatives if they admit a common Kähler submanifold with the same induced metrics. In this paper, we show that a Hartogs domain over an irreducible bounded symmetric domain equipped with the Bergman metric is not a relative to the complex Euclidean space. This generalizes the results in Cheng and Hao [On the non-existence of common submanifolds of Kähler manifolds and complex space forms. Ann Glob Anal Geom. 2021;60(1):167–180] and Cheng X, Niu Y. Submanifolds of Cartan–Hartogs domains and complex Euclidean spaces. J Math Anal Appl 2017;452(2):1262–1268.] and the novelty here is that the Bergman kernel of the Hartogs domain is not necessarily Nash algebraic. [ABSTRACT FROM AUTHOR]

Symbolic 3-plithogenic sets as a generalization of classical concept of sets were applicable to algebraic structures. The symbolic 3-plithogenic rings and fields are good generalizations of classical corresponding systems. In this paper, we study the symbolic 3-plithogenic real functions with one variable by using a special algebraic function called AH-isometry. In addition, we discuss the symbolic 3-plithogenic simple differential equations and conic sections by using this isometry. Also, many examples will be presented to explain the novelty of this work. [ABSTRACT FROM AUTHOR]

Symbolic 2-plithogenic sets as a generalization of classical concept of sets were applicable to algebraic structures. The symbolic 2-plithogenic rings and fields are good generalizations of classical corresponding systems. In this paper, we study the symbolic 2-plithogenic real functions with one variable by using a special algebraic function called AH-isometry. In addition, we discuss the symbolic 2-plithogenic simple differential equations and conic sections by using this isometry. Also, many examples will be presented to explain the novelty of this work. [ABSTRACT FROM AUTHOR]

At Eurocrypt 2016, Méaux et al. presented FLIP, a new family of stream ciphers that aimed to enhance the efficiency of homomorphic encryption frameworks. Motivated by FLIP, recent research has focused on the study of Boolean functions with good cryptographic properties when restricted to subsets of the space F 2 n. If an n -variable Boolean function has the property of balancedness when restricted to each set of vectors with fixed Hamming weight between 1 and n − 1 , it is a weightwise perfectly balanced (WPB) Boolean function. In the literature, a few algebraic constructions of WPB functions are known, in which there are some constructions that use iterative method based on functions with low degrees of 1, 2, or 4. In this paper, we generalize the iterative method and contribute a unified construction of WPB functions based on functions with algebraic degrees that can be any power of 2. For any given positive integer d not larger than m , we first provide a class of 2 m -variable Boolean functions with a degree of 2 d − 1. Utilizing these functions, we then present a construction of 2 m -variable WPB functions g m ; d. In particular, g m ; d includes four former classes of WPB functions as special cases when d = 1 , 2 , 3 , m. When d takes other integer values, g m ; d has never appeared before. In addition, we prove the algebraic degree of the constructed WPB functions and compare the weightwise nonlinearity of WPB functions known so far in 8 and 16 variables. [ABSTRACT FROM AUTHOR]

The main goals of this paper are to provide an introduction to the idea of interval-valued n -polynomial s -type convex functions and to investigate the algebraic properties of this type of function. This new generalization aims to show the existence of new Hermite–Hadamard inequalities for the recently presented class of interval-valued n -polynomials of s -type convex describing the φ -fractional integral operator. In the classical sense, some special cases are figured out, and the two examples are also given. There are some recently discovered inequalities for interval-valued functions that are regulated by fractional calculus applicable to interval-valued n -polynomial s -type convexity. The results obtained show that future research will be simple to implement, highly efficient, feasible, and extremely precise in its investigation. It could also help solve modeling problems, optimization problems, and fuzzy interval-valued functions that involve both discrete and continuous variables. [ABSTRACT FROM AUTHOR]

We investigate APN functions which can be represented as rational functions and we provide non-existence results exploiting the connection between these functions and specific algebraic varieties over finite fields. This approach allows to classify families of functions when previous approaches cannot be applied. [ABSTRACT FROM AUTHOR]

The importance of empirical versus theoretical laws is a controversial issue in many scientific fields, the latter being generally accepted and the relevance of which is not discussed here. As in other areas, there are well-known theoretical and empirical formulas in geosciences that do not adequately represent the reality of a given phenomenon. Quantitative comparison of geophysical and petrophysical results with data from the other multiple fields that comprise the geosciences compels a high exigency to avoid discontinuities in existing relationships. However, the proposal of new empirical laws that more accurately reflect a given phenomenon is often considered insufficient to contradict existing formulas. The aim of this work is to defend the development of new empirical laws by showing that they constitute a true model of analysed behaviour if certain criteria are followed. This defence is especially needed when non-linearisable functions are required to fit the empirical data. To achieve this aim, this study shows the established algebraic function as a function of a single variable, whose main advantage is its application to phenomena of a geological nature that show two differentiated behaviours as the variable x is increased. A series of five examples of different phenomena related to geosciences is selected to demonstrate the level of accuracy that new empirical laws can reach in contrast to the widely accepted historical relationships. [ABSTRACT FROM AUTHOR]

In this paper, we first give a relationship between generalized algebraic geometry codes (GAG codes) and algebraic geometry codes (AG codes). More precisely, we show that a GAG code is contained (up to isomorphism) in a suitable AG code. Next we recall the concept of an N1N2-automorphism group, a subgroup of the automorphism group of a GAG code. With the use of the relation we obtained between these two classes of codes, we show that the N1N2-automorphism group is a subgroup of the automorphism group of an AG code. [ABSTRACT FROM AUTHOR]

In this study, we introduce and study the concept of strongly hyperbolic type convexity functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for the strongly hyperbolic type convex functions. After that, by using an identity, we get some inequalities for strongly hyperbolic type convex functions. In addition, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved power-mean integral inequalities. [ABSTRACT FROM AUTHOR]

The Electrical Circuits subjects constitute the fundamental basis for the training of electrical engineers, within the skills to be developed in these subjects is the analysis of the phasor diagrams of electrical circuits, an important aspect for the trainee engineer since, in practice, it is necessary to know the relationship between voltage and current in the complex plane of a given circuit. On the other hand, GeoGebra is a free interactive mathematics software that allows the graphical representation and algebraic treatment of functions. That is why the objective of the article is to propose an analytical methodology and through simulation with the GeoGebra software for the analysis of phasor diagrams that helps to improve the teaching-learning process of Electrical Circuits subjects for 2nd year students. [ABSTRACT FROM AUTHOR]

In this study, the algebraic structure of 1-absorbing ideals is first examined and applied to fuzzy sets, along with an investigation into the relationships and algebraic properties between them. The contribution to this work's literature involves examining 1-absorbing fuzzy primary ideals. Features of 1-absorbing fuzzy primary ideals are explored, and it is demonstrated, for instance, that I is deemed a 1-absorbing fuzzy primary ideal of P if I is a fuzzy primary ideal of P. Additionally, I is considered a 2-absorbing fuzzy primary ideal of P if I is a 1-absorbing fuzzy primary ideal of P. Furthermore, these theorems are elucidated through specific examples. [ABSTRACT FROM AUTHOR]

We study the existence of target patterns in oscillatory media with weak local coupling and in the presence of an impurity, or defect. We model these systems using a viscous eikonal equation posed on the plane and represent the defect as a perturbation. In contrast to previous results, we consider large defects, which we describe using a function with slow algebraic decay, i.e., g ∼ O (1 / | x | m) for m ∈ (1 , 2 ] . We prove that these defects are able to generate target patterns and that, just as in the case of strongly localized impurities, their frequency is small beyond all orders of the small parameter describing their strength. Our analysis consists of finding two approximations to target pattern solutions, one which is valid at intermediate scales and a second one which is valid in the far field. This is done using weighted Sobolev spaces, which allow us to recover Fredholm properties of the relevant linear operators, as well as the implicit function theorem, which is then used to prove existence. By matching the intermediate and far-field approximations, we then determine the frequency of the pattern that is selected by the system. [ABSTRACT FROM AUTHOR]