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This paper investigates a single-server queuing system with heterogeneous service, failure, and maintenance. The proposed model features a server acting as both the main and backup server. System failure can occur at any stage. When a failure happens, instead of stopping the service entirely, the main server functions as a backup, providing service at a reduced rate. Once all jobs in the system have been serviced, the backup server enters the maintenance state. Following the repair process during maintenance, the server transitions to an idle state, awaiting incoming jobs. Explicit expressions for both transient and steady-state behaviours of the system are derived. Additionally, key system performance metrics are discussed in this paper, accompanied by graphical illustrations to visualize system size probabilities and performance indices. [ABSTRACT FROM AUTHOR]

This paper investigates the thermodynamic properties of strongly interacting gravitational systems. By deriving the partition function for such systems, the authors obtain expressions for various thermodynamic quantities, including internal energy, specific heat, Helmholtz free energy, entropy, chemical potential, and pressure. The paper introduces an interaction parameter that quantifies the degree of non-ideality in the system, and explores its effects on the thermodynamic properties. The authors also calculate the moments generating function, which provides information about the distribution of particle positions. Additionally, the distribution function for the system is derived. The paper highlights the existence of an upper bound temperature beyond which the partition function becomes negative, indicating a limit on the validity of the model. [ABSTRACT FROM AUTHOR]

China, situated in the circum-Pacific seismic belt, experiences frequent seismic activity and faces diverse geological conditions, making structural stability of paramount importance, especially under seismic conditions. The majority of current earthquake generation methods do not consider the nonstationary nature of earthquakes. This paper introduces a spectral representation-random function model for generating nonstationary earthquakes, effectively simulating stochastic seismic ground motion. Furthermore, traditional slope stability analysis methods are deterministic and incapable of providing probabilistic assessments of slope instability. Therefore, this paper proposes a unified framework for static and dynamic structural reliability analysis based on the direct probability integration method, quantifying the impact of stochastic seismic ground motion on the dynamic reliability of slope stability. Finally, the proposed methods are applied to an excavation slope in Nanjing, using sliding displacement and safety factors as evaluation criteria to study the reliability of the slope under the influence of stochastic seismic events. [ABSTRACT FROM AUTHOR]

This paper presents an overview of cosine and sine Apostol-type Frobenius–Euler–Fibonacci polynomials, as well as several identities that are associated with these polynomials. By applying a partial derivative operator to the generating functions, the authors obtain derivative formulae and finite combinatorial sums involving these polynomials and numbers. Additionally, the paper establishes connections between cosine and sine Apostol-type Frobenius–Euler–Fibonacci polynomials of order α and several other polynomial sequences, such as the Apostol-type Bernoulli–Fibonacci polynomials, the Apostol-type Euler–Fibonacci polynomials, the Apostol-type Genocchi–Fibonacci polynomials, and the Stirling–Fibonacci numbers of the second kind. The authors also provide computational formulae and graphical representations of these polynomials using the Mathematica program. [ABSTRACT FROM AUTHOR]

This paper presents a general framework for simulating plot data in multienvironment field trials with one or more traits. The framework is embedded within the R package FieldSimR, whose core function generates plot errors that capture global field trend, local plot variation, and extraneous variation at a user-defined ratio. FieldSimR's capacity to simulate realistic plot data makes it a flexible and powerful tool for a wide range of improvement processes in plant breeding, such as the optimisation of experimental designs and statistical analyses of multi-environment field trials. FieldSimR provides crucial functionality that is currently missing in other software for simulating plant breeding programmes and is available on CRAN. The paper includes an example simulation of field trials that evaluate 100maize hybrids for two traits in three environments. To demonstrate FieldSimR's value as an optimisation tool, the simulated data set is then used to compare several popular spatialmodels for their ability to accurately predict the hybrids' genetic values and reliably estimate the variance parameters of interest. FieldSimR has broader applications to simulating data in other agricultural trials, such as glasshouse experiments. [ABSTRACT FROM AUTHOR]

The aim of this paper is primarily to introduce the quadra MersenneJacobsthal and quadra Mersenne-Pell sequences. Then, the Binet formulas and generating functions for these sequences are obtained. Moreover, quadra Mersenne-Jacobsthal and quadra Mersenne-Pell quaternions were defined and Binet formulas, generating functions, some quaternion sums and relations were obtained for these quaternions. [ABSTRACT FROM AUTHOR]

The Gödel–Dummett logic and Łukasiewicz one are two main many-valued logics used by the fuzzy logic community. Our goal is a quantitative comparison of these two. In this paper, we will mostly consider the 3-valued Gödel–Dummett logic as well as the 3-valued Łukasiewicz one. We shall concentrate on their implicational-negation fragments which are limited to formulas formed with a fixed finite number of variables. First, we investigate the proportion of the number of true formulas of a certain length n to the number of all formulas of such length built with exactly one variable. Then, we investigate such proportion for satisfiable formulas. Second, we generalise our investigation on formulas written with $ k\ge 1 $ k ≥ 1 variables. The primary goal of the paper is the research on the asymptotic behaviour of these fractions when the length n tends to infinity. If such limits exists, they are real numbers between 0 and 1, which are called the density of truth or the density of SAT. To compare the density of truth and the density of satisfiable formulas for both fragments of 3-valued Gödel–Dummett's and Łukasiewicz's logics we use the powerful theory of analytic combinatorics. This paper is a natural continuation of the previous brief conference note by Kostrzycka and Zaionc (2020) as well as enriched with some previous results from Kostrzycka and Zaionc (2003). In the conference note we computed analytically the density of truth and the density of SAT (with a determined precision) for 3-valued Łukasiewicz's logic restricted to a language with only one variable. In Kostrzycka and Zaionc (2003) we computed the same values for exactly the same fragment of the 3-valued Gödel–Dummett logic. This paper answers the more general questions of the existence of density of truth and density of SAT for both many-valued logics with an arbitrary finite number of variables. Therefore this paper gives an an interesting picture of two main families of finite-valued fuzzy logics problems treated quantitatively. This picture is taken from the perspective of classical logic. It shows that unexpectedly there is quantitatively a little distance between these two approaches. [ABSTRACT FROM AUTHOR]

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In this paper, we define the bi-periodic k-Pell sequence. We obtain Binet's formula, some identities of the bi-periodic k-Pell sequences like Catalan, Cassini and D'Ocagne's identities as well as some related summation formulas. [ABSTRACT FROM AUTHOR]

We consider a system of two coupled parallel queues with infinite waiting rooms. The time setting is discrete. In either queue, the service of a customer requires exactly one discrete time slot. Arrivals of new customers occur independently from slot to slot, but the numbers of arrivals into both queues within a slot may be mutually dependent. Their joint probability generating function (pgf) is indicated as A (z 1 , z 2) and characterizes the whole model. In general, determining the steady-state joint probability mass function (pmf) u (m , n) , m , n ≥ 0 or the corresponding joint pgf U (z 1 , z 2) of the numbers of customers present in both queues is a formidable task. Only for very specific choices of the arrival pgf A (z 1 , z 2) are explicit results known. In this paper, we identify a multi-parameter, generic class of arrival pgfs A (z 1 , z 2) , for which we can explicitly determine the system-content pgf U (z 1 , z 2) . We find that, for arrival pgfs of this class, U (z 1 , z 2) has a denominator that is a product, say r 1 (z 1) r 2 (z 2) , of two univariate functions. This property allows a straightforward inversion of U (z 1 , z 2) , resulting in a pmf u (m , n) which can be expressed as a finite linear combination of bivariate geometric terms. We observe that our generic model encompasses most of the previously known results as special cases. [ABSTRACT FROM AUTHOR]

In many engineering optimization problems, the number of function evaluations is severely limited by the time or cost constraints. These limitations present a significant challenge in the field of global optimization, because existing metaheuristic methods typically require a substantial number of function evaluations to find optimal solutions. This paper presents a new metaheuristic optimization algorithm that considers the information obtained by a radial basis function neural network (RBFNN) in terms of the objective function for guiding the search process. Initially, the algorithm uses the maximum design approach to strategically distribute a set of solutions across the entire search space. It then enters a cycle in which the RBFNN models the objective function values from the current solutions. The algorithm identifies and uses key neurons in the hidden layer that correspond to the highest objective function values to generate new solutions. The centroids and standard deviations of these neurons guide the sampling process, which continues until the desired number of solutions is reached. By focusing on the areas of the search space that yield high objective function values, the algorithm avoids exhaustive solution evaluations and significantly reduces the number of function evaluations. The effectiveness of the method is demonstrated through a comparison with popular metaheuristic algorithms across several test functions, where it consistently outperforms existing techniques, delivers higher-quality solutions, and improves convergence rates. [ABSTRACT FROM AUTHOR]

The present paper deals with the Durrmeyer construction of operators based on a class of orthogonal polynomials called Apostol-Genocchi polynomials. For the proposed operators, we first establish a global approximation result followed by its convergence estimate in terms of usual, r-th and weighted modulus of continuity. We further study the asymptotic type results such as the Voronovskaya theorem and quantitative Voronovskaya theorem. Moreover, we estimate the rate of pointwise convergence of the proposed operators for functions of bounded variation defined on the interval (0, ∞). Finally, the results are validated through graphical representations and an absolute error table. [ABSTRACT FROM AUTHOR]

Social scientists have long been interested in marital homogamy and its relationship with inequality. However, measuring homogamy is not straightforward, particularly when one is interested in assessing marital sorting based on multiple traits. In this paper, we argue that Separate Extreme Value (SEV) models not only generate a matching function with several desirable theoretical properties, but they are also suited for the study of multidimensional sorting. Specifically, we use rich small‐scale survey data to examine sorting among parents of school‐age children in Naples. We show that homogamy is pervasive; not only do men and women sort by age, education, and physical characteristics, but they also look for partners that share similar health‐related behavior and risk attitude. However, we also show that these marital patterns are well explained by a low number of dimensions, the most important being age cohort and human capital. In particular, human capital relates to various "outcomes" of the post‐matching relationship. Children of parents with a high human capital endowment perform better at school, although they report lower levels of subjective well‐being and of perceived quality of relationship with their mothers. [ABSTRACT FROM AUTHOR]

This paper investigates the behavior of a fluid queue driven by a non-truncated Erlangian service queue, focusing on the symmetrical properties within the system. This study determines the formulations of the steady-state distribution of both the buffer content and stationary state probabilities of a background queueing system. The efficient generating function technique is employed, utilizing a new generalization of the modified Bessel function of the second kind. Performance metrics such as mean buffer content and throughput are calculated, and server utilization is examined. The results contribute to the understanding of fluid queueing systems and offer insights into their performance in various applications, including telecommunications, manufacturing systems, healthcare operations, and ecological models, where symmetry plays a critical role in optimizing performance. [ABSTRACT FROM AUTHOR]

R. Lyons, R. Pemantle and Y. Peres (Ann. Probab. 24 (4), 1996, 1993–2006) conjectured that for a Cayley graph G with a growth rate gr(G) > 1, the speed of a biased random walk exists and is positive for the biased parameter λ ∈ (1, gr(G)). And Gabor Pete (Probability and geometry ´ on groups, Chaper 9, 2024) sheds light on the intricate relationship between the spectral radius of the graph and the speed of the biased random walk. Here, we focus on an example of a Cayley graph, a free product of complete graphs. In this paper, we establish the continuity of the spectral radius of biased random walks with respect to the bias parameter in this class of Cayley graphs. Our method relies on the Kesten-Cheeger-Dodziuk-Mohar theorem and the analysis of generating functions. [ABSTRACT FROM AUTHOR]

In this paper, the distribution function ϕ(u) = P(supn≥1∑ni=1(Xi − κ) < u), and the generating function of ϕ(u + 1) are set up. We assume that u ∈ N ∪ {0}, κ ∈ N, the random walk {∑ni=1 Xi, n ∈ N} involves N ∈ N periodically occurring distributions, and the integer-valued and nonnegative random variables X1, X2,... are independent. This research generalizes two recent works where {κ = 1, N ∈ N} and {κ ∈ N, N = 1} were considered respectively. The provided sequence of sums {∑ni=1(Xi − κ), n ∈ N} generates the socalled multi-seasonal discrete-time risk model with arbitrary natural premium and its known distribution enables to compute the ultimate time ruin probability 1 − ϕ(u) or survival probability ϕ(u). The obtained theoretical statements are verified in several computational examples where the values of the survival probability ϕ(u) and its generating function are provided when {κ = 2, N = 2}, {κ = 3, N = 2}, {κ = 5, N = 10} and Xi adopts the Poisson and some other distributions. The conjecture on the nonsingularity of certain matrices is posed. [ABSTRACT FROM AUTHOR]

Spinors are important objects in physics, which have found their place more and more after the discovery that particles have an intrinsic angular momentum shape and Cartan's mathematical expression of this situation. Recent studies using special number sequences have also revealed a new approach to the use of spinors in mathematics and have provided a different perspective for spinor research that can be used as a source for future physics studies. The purpose of this work is to expand the generalized Fibonacci quaternion polynomials to the generalized Fibonacci polynomial spinors by associating spinors with quaternions, and to introduce and investigate a new polynomial sequence that can be used to benefit from the potential advantages of spinors in physical applications, and thus, to provide mathematical arguments, such as new polynomials, for studies using spinors and quaternions in quantum mechanics. Starting from this point of view, in this paper we introduce and investigate a new family of sequences called generalized Fibospinomials (or generalized Fibonacci polynomial spinors or Horadam polynomial spinors). Being particular cases, we use (r , s) -Fibonacci and (r , s) -Lucas polynomial spinors. We present Binet's formulas, generating functions and the summation formulas for these polynomials. In addition, we obtain some special identities of these new sequences and matrices related to these polynomials. The importance of this study is that generalized Fibospinomials are currently the most generalized sequence in the literature when moving from Fibonacci quaternions to spinor structure, and that a wide variety of new spinor sequences can be obtained from this particular polynomial sequence. [ABSTRACT FROM AUTHOR]

The proliferation of the Internet of Things (IoT) propels the continuous demand for compact, low-cost, and high-performance multiband filters. This paper introduces a novel low-profile dual-band bandpass filter (BPF) constructed with a back-to-back coupled pair of shielded folded quarter-mode substrate integrated waveguide (SF-QMSIW) multimode cavities. A hybrid structure is obtained by etching a coplanar waveguide (CPW) coupling line in the folded cavity's septum layer. It serves multiple functions: generating an additional resonance, providing a separate coupling mechanism for the upper passband, and offering the flexibility to control the passbands' center frequency ratio. Additionally, the unused second higher-order mode is suppressed by integrating embedded split-ring resonators (ESRRs) with an inter-digital capacitor (IDC) structure into the feed lines. A filter prototype has been fabricated and experimentally tested. The measurements confirmed reliable operation in two passbands having center frequencies 3.6 GHz and 5.8 GHz, and exhibiting 3 dB fractional bandwidths (FBWs) of 6.4% and 5.3%, respectively. Furthermore, the group delay variation within both passbands equals only 0.62 ns and 1.00 ns, respectively. Owing to the second higher-order mode suppression, the filter demonstrated an inter-band rejection exceeding 38 dB, within a compact footprint of 0.71 λ g 2 (with λ g being the guided wavelength at the lower passband's center frequency). [ABSTRACT FROM AUTHOR]

Determining the weight distribution of all Reed-Muller codes is a huge and exciting problem that has been around since the sixties. Some progress has been made very recently, but we are still far from a solution. In this paper, we addressed the subproblem of determining as many codeword weights as possible in Reed-Muller codes of any lengths and any orders, which is decisive for determining their weight spectra (i.e., the lists of all possible weights in these codes). New approaches seem necessary for both the main problem and the subproblem. We first studied the difficulties and the limits of the approach, which consisted of using the usual primary and secondary constructions of Boolean functions for the purpose of determining as many weights as possible in Reed-Muller codes. We then introduced a way, different from the usual constructions, to generate Boolean functions in n variables having an algebraic degree bounded from above, without any restriction on n, and whose Hamming weights can be determined. This provided weights in Reed-Muller codes of any lengths 2n and any orders, allowing us to reach potentially new values in the weight spectra of Reed-Muller codes (as we illustrate with all Reed-Muller codes of lengths up to 221), with the related codewords being given with their supports and their algebraic normal forms being mathematically derived. [ABSTRACT FROM AUTHOR]

In this paper, the transformed sine Dagum distribution is proposed using the Dagum distribution as a baseline distribution in the transformed sin-G family of distributions. The purpose of this paper is to propose and explore a modified version of the Dagum distribution, based on the transformed sin-G family of distributions. The density of the transformed sine Dagum distribution shows that it can adequately model datasets that are positively skewed, approximately symmetric and decreasing. The hazard rate plot shows that the proposed distribution can adequately model both monotonic and non-monotonic hazard rate datasets. Statistical properties such quantile function, moments, inverse moments, moments generating functions, mean and median deviation and order statistics are derived. The plots of the skewness and kurtosis show that the skewness is always positive and the kurtosis is increasing. Maximum likelihood estimation is used to estimate the parameters of the transformed sine Dagum distribution. Monte Carlo simulations are performed to ascertain the behavior of the estimators. The results show that the estimators are consistent. The proposed distribution is applied to two real life datasets. The results show that the proposed distribution provide a reasonable parametric fit to the datasets compared with the other competing distribution. [ABSTRACT FROM AUTHOR]

The degenerate Changhee-Genocchi numbers (and also Changhee - Genocchi), which appear in analysis and combinatorial mathematics and play a significant role in the applications and theory of mathematics, are associated with the Daehee, Cauchy, and Stirling numbers with several extensions and have proven to be powerful tools in varied subjects in combinatorics and analysis. In combinatorics and analytic number theory, many special numbers such as degenerate Changhee-Genocchi numbers, Changhee-Genocchi numbers, derangement numbers, and Stirling numbers play an important role to solve and analyze problems of combinatorial, analytical, and many other disciplines. In this paper, we introduce generalized degenerate Changhee-Genocchi polynomials and analyze some properties by providing several relations and applications. We first attain diverse relations and formulas covering addition formulas, recurrence rules, implicit summation formulas and relations with the earlier polynomials in the literature. By using their generating function, we derive some new relations including the Stirling numbers of the first and second kinds. Moreover, we introduce generalized higher-order degenerate Changhee-Genocchi polynomials. We also derive some new identities and properties of this type of polynomials. [ABSTRACT FROM AUTHOR]

We show that certain type of generating functions allow to construct Cauchy convolutions for the Apostol-Euler and Apostol-Bernoulli polynomials and their connection with partial Bell Polynomials [ABSTRACT FROM AUTHOR]

In this paper, we construct the generalized homogeneous g-shift operator... such as: the generating function and its extension, Rogers formula and its extension, Mehler's formula and its extension, Srivastava-Agarwal type bilinear generating functions for the polynomials... [ABSTRACT FROM AUTHOR]

This paper studies an M/M/1 retrial queue with negative customers, passive breakdown, and delayed repairs. Assume that the breakdown behavior of the server during idle periods is different from that during busy periods. Passive breakdowns may occur when the server is idle, due to the lack of monitoring of the server during idle periods. When the passive breakdown occurs, the server does not get repaired immediately and enters a delayed repair phase. Negative customers arrive during the busy period, which will cause the server to break down and remove the serving customers. Under steady-state conditions, we obtain explicit expressions of the probability generating functions for the steady-state distribution, together with some important performance measures for the system. In addition, we present some numerical examples to illustrate the effects of some system parameters on important performance measures and the cost function. Finally, based on the reward-cost structure, we discuss Nash equilibrium and socially optimal strategy and numerically analyze the influence of system parameters on optimal strategies and optimal social benefits. [ABSTRACT FROM AUTHOR]

This paper is concerned with the investigation of UC and BUC plane partitions based upon the fermion calculus approach. We construct generalized the vertex operators in terms of free charged fermions and neutral fermions and present the interlacing (strict) 2-partitions. Furthermore, it is showed that the generating functions of UC and BUC plane partitions can be written as product forms. [ABSTRACT FROM AUTHOR]

In this paper we investigate locally free representations of a quiver Q over a commutative Frobenius algebra R by arithmetic Fourier transform. When the base field is finite we prove that the number of isomorphism classes of absolutely indecomposable locally free representations of fixed rank is independent of the orientation of Q. We also prove that the number of isomorphism classes of locally free absolutely indecomposable representations of the preprojective algebra of Q over R equals the number of isomorphism classes of locally free absolutely indecomposable representations of Q over R [ t ] / (t 2) . Using these results together with results of Geiss, Leclerc and Schröer we give, when k is algebraically closed, a classification of pairs (Q , R) such that the set of isomorphism classes of indecomposable locally free representations of Q over R is finite. Finally when the representation is free of rank 1 at each vertex of Q, we study the function that counts the number of isomorphism classes of absolutely indecomposable locally free representations of Q over the Frobenius algebra F q [ t ] / (t r) . We prove that they are polynomial in q and their generating function is rational and satisfies a functional equation. [ABSTRACT FROM AUTHOR]

In this paper, we construct a holomorphic Siegel modular form of weight 2 and level 2, and compute its Fourier coefficients explicitly. Moreover, we prove that this modular form equals the generating function of the representative number ρ (n , m , r) associated with the maximal order in the quaternion algebra (− 1 , − 1) ℚ . As a corollary, we can give a new proof of the famous formula for the sums of three squares. As applications, we give an explicit formula for the numbers of solutions of two systems of Diophantine equations related with Sun's "1-3-5 conjecture". Furthermore, we show that "a perfect square" in the integral condition version of Sun's conjecture can be replaced by "a power of 4". [ABSTRACT FROM AUTHOR]

This paper introduces a new simple moment-generating function (MGF) design modelling method to conclude an optimum filter to maximize the Q-factor and increase the link communication span. This approach mitigates the pulse temporal dispersion, particularly the underwater wireless optical communication (UWOC) systems. Hence, some form of equalizing filter design is highly desirable. The model solution environment includes a Double Gamma Function (DGF) water channel impulse response, intersymbol interference (ISI), stochastic Poisson process, and additive Gaussian thermal noise (AGTN). The optimal filters exhibit temporal profiles comparable to those derived by published works based on complex Chernoff Bound (CB) and Modified Chernoff Bound (MCB) methods. The results show the impact of the optimum filter at a signal level and optical receiver level utilizing Eye-Diagrams and BER vs. Q-Factor, respectively. The computation involves four different UWOC propagation channel models for Coastal and Harbor waters. One of the main conclusions indicates that the optimum filter manages the temporal dispersion due to the ISI impairment correctly. Also, the proposed optimum filter reduces eye-opening and the corresponding Q-Factor by less than 15% for a five-times increase in pulse width for the same transmitted optical power level. [ABSTRACT FROM AUTHOR]

In a previous paper, we introduced the Collatz polynomials $ P_N\left (z \right) $ P N (z) , whose coefficients are the terms of the Collatz sequence of the positive integer N. Our work in this paper expands on our previous results, using the Eneström-Kakeya Theorem to tighten our old bounds of the roots of $ P_N\left (z \right) $ P N (z) and giving precise conditions under which these new bounds are sharp. In particular, we confirm an experimental result that zeros on the circle $ \ensuremath {\{z\in \ensuremath {\mathbb {C}}:\left | z \right | = 2\}} $ { z ∈ C : | z | = 2 } are rare: the set of N such that $ P_N\left (z \right) $ P N (z) has a root of modulus 2 is sparse in the natural numbers. We close with some questions for further study. [ABSTRACT FROM AUTHOR]

Network function virtualization (NFV) implements network functions as software, which enables flexible, resource‐efficient, and rapid provision of network services. In NFV, network services are realized by the service function chain (SFC), which is a chain of virtual network functions (VNFs) linked in the proper order. Both availability and deployment cost are key concerns for network operators providing network services as SFC. This paper proposes a flexible VNF placement model on a per‐VNF instance basis that minimizes deployment costs while satisfying availability requirements that may be placed on SFC. This paper uses a multidimensional universal generating function (MUGF) method, which is a multistate system analysis method, to compute the availability of a multistate SFC system with multiple VNFs coexisting on a server. The MUGF method calculates the performance of the entire SFC by combining the performance of servers as determined by applying a continuous‐time Markov chain. To reduce the time to compute the SFC availability, we introduce operators to be applied to MUGF and develop an availability computing method. In addition, a heuristic algorithm for determining VNF placement targeting the lowest deployment cost possible while meeting availability requirements is presented. Numerical results show that the proposed model obtains VNF placement with lower cost than the conventional model in all examined cases. The proposed model achieves VNF placement at 58.5%–75.0% of the deployment cost of the conventional model for the same SFC availability requirements. [ABSTRACT FROM AUTHOR]

Let F (z 1 , ⋯ , z d) be the quotient of an analytic function with a product of linear functions. Working in the framework of analytic combinatorics in several variables, we compute asymptotic formulae for the Taylor coefficients of F using multivariate residues and saddle-point approximations. Because the singular set of F is the union of hyperplanes, we are able to make explicit the topological decompositions which arise in the multivariate singularity analysis. In addition to effective and explicit asymptotic results, we provide the first results on transitions between different asymptotic regimes, and provide the first software package to verify and compute asymptotics in non-smooth cases of analytic combinatorics in several variables. It is also our hope that this paper will serve as an entry to the more advanced corners of analytic combinatorics in several variables for combinatorialists. [ABSTRACT FROM AUTHOR]

This study evaluates the current responsibilities, skills, and knowledge sets required by marketing managers. Furthermore, it seeks to make projections about the future of the marketing management profession. Three different studies were conducted to achieve our objectives. The first analyses 600 job descriptions, the second gathers insights from marketing managers using a survey, and the third explores the perspectives of the marketing managers regarding the future of their profession. The results analyze and systematize the key activities and responsibilities of marketing managers and highlight the role of future marketing managers. The study concludes that changes in technology and big data will have a significant impact on the marketing management profession. This paper makes three primary contributions. First, it identifies the qualifications and skillsets sought among marketing managerial positions. Second, it contributes to research within the marketing domain by examining the interface between marketing management function and automation by generating insights that highlight how technology affects the role of marketing managers. Finally, it presents a snapshot of guidelines to direct companies in guiding skill development and understanding future requirements for the marketing manager position. [ABSTRACT FROM AUTHOR]

In this paper we investigate a family of bivariate orthogonal functions arising as a generalization of Koornwinder polynomials in two variables. General properties like recurrence relations and partial differential equations are introduced. Some special cases are considered and a limit relation of these functions is studied. As a consequence, a new class of bivariate orthogonal polynomials is presented. [ABSTRACT FROM AUTHOR]

The object of this paper is to study a generalized Mittag-Leffler function and a modified general class of functions which is reducible to several special functions. convergent conditions of these functions are discussed. Some results pertaining to the generalized Mittag-Leffler function and generating relations involving these functions are derived. Further, fractional integrals involving these functions are achieved. Some illustrative exclusive cases of the results are presented. [ABSTRACT FROM AUTHOR]

Motivated to find the answers to some of the questions that have occurred in recent papers dealing with Hamiltonian cycles (abbreviated HCs) in some special classes of grid graphs we started the investigation of spanning unions of cycles, the so-called 2-factors, in these graphs (as a generalizations of HCs). For all the three types of graphs from the title and for any integer m = 2 we propose an algorithm for obtaining a specially designed (transfer) digraph D* m. The problem of enumeration of 2-factors is reduced to the problem of enumerating oriented walks in this digraph. Computational results we gathered for m = 17 reveal some interesting properties both for the digraphs D* m and for the sequences of numbers of 2-factors. We prove some of them for arbitrary m = 2. [ABSTRACT FROM AUTHOR]

Related to generalized arithmetic triangle, we introduce the hyper (r, q)-Fibonacci polynomials as the sum of these elements along a finite ray starting from a specific point, which generalize the hyper-Fibonacci polynomials. We give generating function, recurrence relations and we show some properties whose application allows us to extend the notion of Cassini determinant and to study some ratios. Moreover, we derive a connection between these polynomials and the incomplete (r, q)-Fibonacci polynomials defined in this paper. [ABSTRACT FROM AUTHOR]

We extended the classical Bernoulli and Euler numbers and polynomials to introduce the Laguerre-type Bernoulli and Euler numbers and related fractional polynomials. The case of fractional Bernoulli and Euler polynomials and numbers has already been considered in a previous paper of which this article is a further generalization. Furthermore, we exploited the Laguerre-type fractional exponentials to define a generalized form of the classical Laplace transform. We show some examples of these generalized mathematical entities, which were derived using the computer algebra system Mathematica© (latest v. 14.0). [ABSTRACT FROM AUTHOR]

Recently, Appell-type polynomials have been investigated and applied in several ways. In this paper, we consider a new extension of Appell-type Changhee polynomials. We introduce two-variable generalized Appell-type λ -Changhee polynomials (2VGAT λ CHP). The generating function, series representations, and summation identities related to these polynomials are explored. Further, certain symmetry identities involving two-variable generalized Appell-type λ -Changhee polynomials are established. Finally, Mathematica was used to examine the zero distributions of two-variable truncated-exponential Appell-type Changhee polynomials. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of special polynomials called the generalized Bell polynomials, constructed by combining two-variable general polynomials with two-variable Bell polynomials. The concept of the monomiality principle was employed to establish the generating function and obtain various results for these polynomials. We explore certain related identities, properties, as well as differential and integral formulas. Further, specific members within the generalized Bell family—such as the Gould-Hopper-Bell polynomials, Laguerre-Bell polynomials, truncated-exponential-Bell polynomials, Hermite-Appell-Bell polynomials, and Fubini-Bell polynomials—were examined, unveiling analogous outcomes for each. Finally, Mathematica was utilized to investigate the zero distributions of the Gould-Hopper-Bell polynomials. [ABSTRACT FROM AUTHOR]

In this paper, a new class of distributions called the T-X θ family of distributions for bounded—(0,1)—and unbounded— (0 , ∞) —supported random variables is suggested. Some special sub-models of the proposed family are utilized. A new sub-model is selected to be studied in details. The statistical properties of the suggested family including quantile function, moments, moment generating function, order statistics and Rényi entropy are discussed. The maximum likelihood method is provided to estimate the parameters of the distribution and a Monte Carlo simulation study is used. The discretized T-X θ family provided many sub-families and sub-models. In addition, eight real data sets are utilized to demonstrate the flexibility of the proposed continuous and discrete family's multiple sub models. [ABSTRACT FROM AUTHOR]

In this paper, we consider various Stirling numbers of both kinds, including the unsigned degenerate Stirling numbers of the first kind, the degenerate Stirling numbers of the second kind, the unsigned degenerate r-Stirling numbers of the first kind and the degenerate r-Stirling numbers of the second kind. The aim of this paper is by using generating functions to further study explicit expressions, some identities and equivalent relations for those Stirling numbers. [ABSTRACT FROM AUTHOR]

In this paper, we define (k, l)--Gadovan numbers. We give the Binet-like formula, the generating functions, the exponential generating function of the (k, l)-- Gadovan numbers. Also, we derive Cassinilike identity, Catalan-like identity, Vajda-like identity, Honsberger-like identity and D'ocagne-like identity for the (k, l)--Gadovan numbers. [ABSTRACT FROM AUTHOR]

In this paper, new identities are obtained by using the generalized bivariate Fibonacci and Lucas polynomials. Firstly, several binomial summations and the closed formulas for summation of powers are investigated for these polynomials. Also, general summation formulas, different generating functions, and relations of these polynomials are presented. [ABSTRACT FROM AUTHOR]

This paper obtains the term structure technique to produce yield curves from Nigerian Eurobond by using the De Rezende parametric function. There does not seem to exist any empirical proof that Nigeria has constructed a functional model to construct its discount function from the yield curves. Therefore, the De Rezende parsimoniously parametric function is deeply examined to make this framework applicable in presenting yield curves for Nigerian Euro bond constructed through the associated positive forward curve and from where the discount function is generated. The forward rate should be continuous and at the same time generate a positive yield curve trajectory. The objective of this paper is (i) construct the yield curve trajectories and (ii) to construct the discount function from the yield curve (iii) to construct the in-sample prediction to achieve results in predicting coefficients for longer maturities. The data presented involves the daily closing of the Nigerian Eurobond yield covering January to December 2022, which is fitted to the observed Nigerian Eurobond yield curve to construct the yield function. The ordinary least square is applied to estimate the parameters used in computing the in-sample yield. A test of goodness of fit was conducted showing that the model fits in well to the observed data demonstrated by the model's high R-square adjusted through the predicted yields after obtaining the decay factors. [ABSTRACT FROM AUTHOR]

The solution to a generalized q-difference equation is described in q-operator form in this paper, which is a generalization of Fang's work [9]. We solve a general q-difference equation to get a general q-operator identity. The generalized q-polynomial φn(A,B) (b, c|q) is defined. We present two types generating function and a generalization of the transformational identity for the polynomials φn(A,B) (b, c|q) using the q-difference equation. By assigning specific values to the parameters in the findings for the polynomials φn(A,B) (b, c|q), we get two types generating functions and the transformational identity for polynomials Hn(a0, ..., as; b1, ..., bs; b, c), Pn(x, y, a), hn(x, y, a, b|q) and hn(a1,..., ar; b1,..., bs; x, y|q). [ABSTRACT FROM AUTHOR]

In this paper, we have defined new generalizations of some hypergeometric functions and fractional operators with the help of Fox-Wright function. Then, using each of the generalized fractional operators, we derived linear and bilinear generating function relations for these functions. Finally, we have shown that the newly defined hypergeometric functions and fractional operators can be reduced to functions and operators presented in many studies in the literature by giving special values for their parameters. [ABSTRACT FROM AUTHOR]

In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained. This result implies the Catalan, Cassini, Vajda, d'Ocagne and Halton identities. Moreover, generating function and matrix generators for these numbers are presented. [ABSTRACT FROM AUTHOR]

In this paper, we define Mersenne, Mersenne-Lucas hybrid quaternions. We give the Binet's formula, the generating functions, exponential generating functions and sum formula of these quaternions. We find some relations between Mersenne-Lucas hybrid quaternions, Jacobsthal hybrid quaternions, Jacobsthal-Lucas hybrid quaternions and Mersenne hybrid quaternions. [ABSTRACT FROM AUTHOR]