Search

Nexus 2018, the 12th international, interdisciplinary conference for architecture and mathematics, took place in Pisa in June 2018. From among the 43 presentations, 12 papers were selected for publication in the Nexus Network Journal. In what follows the conference directors the papers that make up vol. 22, no. 1 (2020). [ABSTRACT FROM AUTHOR]

Uncertainty theory, founded in 2007, has become a branch of mathematics to model uncertainty rather than randomness. As an indispensable part of uncertainty theory, uncertain graph and uncertain network optimization has received the wide attention of many scholars. Naturally, a series of original research achievements have been obtained on uncertain graph and uncertain network optimization. This paper aims to present a state-of-the-art review on the recent advance in uncertain graph and uncertain network optimization. Furthermore, it hopes to predict the possible future research directions. Based on Web of Science database, this paper retrieves 144 related papers from 2011 to 2021 to analyze the features of published articles. More precisely, we analyze the annual number of publications, key topics and sub-fields, journals, and most-cited articles. In addition, the main results and models for uncertain graph and uncertain network optimization are summarized. Furthermore, the limitations of existing literature and the possible development trend are discussed. [ABSTRACT FROM AUTHOR]

The paper lists the main open questions left in the area both theoretically and practically, mainly related with the inherent tension between communication efficiency and quality of assumptions in proof systems. This special issue of Designs, Codes and Cryptography on the topic Mathematics of Zero-Knowledge aims at encouraging mathematicians and computer scientists with a strong interest in Mathematics to contribute to the burgeoning topic of zero-knowledge proofs. [Extracted from the article]

Abstract Transformer differential protection is exposed to faulty operation related to abnormal operation conditions (inrush, overexcitation, etc.). In this paper a new approach to improve the relay security and dependability is proposed, based on the space-vector analysis of the differential signal, and on their time characteristic shapes in Parks plane. The approach is supported by an introductory formulation and later validated. The technique has been shown to be robust and very simple for the purpose of detecting internal faults. [ABSTRACT FROM AUTHOR]

A recent paper (hereafter referred to as the "Paper"), Bermingham (2003), presented what appeared to be an analytical review of current situation of declining population growth rates in many parts of the world. The Paper suggested that the increasing growth rates before about 1970 constituted exponential growth, but that the currently declining growth rates were not exponential growth. Hence, the paper asserted that we should not use the terms "exponential growth" and "doubling times" in describing the current situation. Many of the suggestions in the paper are contrary to established mathematics. These suggestions are examined here in some detail. [ABSTRACT FROM AUTHOR]

Very recently, Pushpa and Vasuki (Arab. J. Math. 11, 355–378, 2022) have proved Eisenstein series identities of level 5 of weight 2 due to Ramanujan and some new Eisenstein identities for level 7 by the elementary way. In their paper, they introduced seven restricted color partition functions, namely P ∗ (n) , M (n) , T ∗ (n) , L (n) , K (n) , A (n) , and B(n), and proved a few congruence properties of these functions. The main aim of this paper is to obtain several new infinite families of congruences modulo 2 a · 5 ℓ for P ∗ (n) , modulo 2 3 for M(n) and T ∗ (n) , where a = 3 , 4 and ℓ ≥ 1 . For instance, we prove that for n ≥ 0 , P ∗ (5 ℓ (4 n + 3) + 5 ℓ - 1) ≡ 0 (mod 2 3 · 5 ℓ). In addition, we prove witness identities for the following congruences due to Pushpa and Vasuki: M (5 n + 4) ≡ 0 (mod 5) , T ∗ (5 n + 3) ≡ 0 (mod 5). [ABSTRACT FROM AUTHOR]

Recent rank-based attacks have reduced the security of Rainbow, which is one of the multi-layer UOV signatures, below the NIST security requirements by speeding up iterative kernel-finding operations using classical mathematics techniques. If quantum algorithms are applied to perform these iterative operations, the rank-based attacks may be more threatening to multi-layer UOV, including Rainbow. In this paper, we propose a quantum rectangular MinRank attack called the Q-rMinRank attack, the first quantum approach to key recovery attacks on multi-layer UOV signatures. Our attack is a general model applicable to multi-layer UOV signature schemes, and in this paper, we provide examples of its application to Rainbow and the Korean TTA standard, HiMQ. We design two quantum oracle circuits to find the kernel in consideration of the depth-width trade-off of quantum circuits. One is to reduce the width of the quantum circuits using qubits as a minimum, and the other is to reduce the depth using parallelization instead of using a lot of qubits. By designing quantum circuits to find kernels with fewer quantum resources and complexity by adding mathematical techniques, we achieve quadratic speedup for the MinRank attack to recover the private keys of multi-layer UOV signatures. We also estimate quantum resources for the designed quantum circuits and analyze quantum complexity based on them. The width-optimized circuit recovers the private keys of Rainbow parameter set V with only 1089 logical qubits. The depth-optimized circuit recovers the private keys of Rainbow parameter set V with a quantum complexity of 2 174 , which is lower than the complexity of 2 221 recovering the secret key of AES-192, which provides the same security level as parameter set III. [ABSTRACT FROM AUTHOR]

Background: The purpose of this scoping review is to describe how the literature has discussed and studied disability in undergraduate-level STEM courses in the United States. A Critical Disability Studies lens informed our inclusion criteria. Results: We considered extensive lists of disability types and diagnoses and concluded that "disability" as a search term best captured educational experiences rather than medical approaches. After screening nearly 9000 abstracts, we identified a final set of 409 dissertations, articles, conference papers, commentaries, briefs and news items. Sources appeared in discipline-based education research (DBER), STEM disciplinary and education journals as well as DBER conferences. Under 10% of sources included 2-year college settings. The largest groups of sources focused on disability writ large (39%, vs. specific categories) and across STEM (38%, vs. specific disciplines). Students were the main research participants (80%). Instructors were the main target of recommendations (84%). In terms of solutions, the largest group (n = 111) advocated for Universal Design, followed by accommodations (n = 94), and technology developed or tested with persons with disabilities (n = 90). Sources which the authors framed as empirical studies less frequently disclosed positionality as a person with a disability (16%) than non-empirical sources (21%). Quantitative (n = 125), qualitative (n = 99), and mixed methods (n = 64) approaches were well-represented. The most common data collection methods were surveys, assessments or task completions (n = 161 sources), followed by interviews (n = 109), observations (n = 44), document analyses (n = 18), and institutional student records (n = 14). Conclusions: More research is needed that centers the experiences of students with disabilities, focuses on specific disability types, employs critical quantitative and qualitative methodologies, and otherwise avoids implicit deficit views of disabled students. Citations to the qualifying sources are available in a public Zotero library. [ABSTRACT FROM AUTHOR]

In this paper, we provide a simplified proof of the existence of solutions for the system of nonlinear quasi-mixed equilibrium problems studied by Suantai and Petrot (Appl. Math. Lett. 24:308–313, 2011), utilizing Banach's fixed point theorem. This result remains valid under weaker assumptions through the product space approach. Moreover, we show that the stability analysis of the iterative algorithm proposed in their work (and in (J. Inequal. Appl. 2010:437976, 2010)) contains a flaw, which we address using Ostrowski's classical result from 1967 (Z. Angew. Math. Mech. 47:77–81, 1967). Finally, we examine and improve the convergence theorem for solving a system of variational inequalities as established by Chang et al. (Appl. Math. Lett. 20:329–334, 2007). [ABSTRACT FROM AUTHOR]

Constant dimension codes (CDCs) have drawn extensive attention due to their applications in random network coding. This paper introduces a new class of codes, namely generalized bilateral Ferrers diagram rank-metric codes, to generalize the bilateral multilevel construction in Etzion and Vardy (Adv Math Commun 16:1165–1183, 2022). Combining our generalized bilateral multilevel construction and the double multilevel construction in Liu and Ji (IEEE Trans Inf Theory 69:157–168, 2023), we present an effective technique to construct CDCs. By means of bilateral identifying vectors, this approach helps us to select fewer identifying and inverse identifying vectors to construct CDCs with larger size. The new constructed CDCs have the largest size regarding known codes for many sets of parameters. Our method gives rise to at least 138 new lower bounds for CDCs. [ABSTRACT FROM AUTHOR]

The non-transferability of a designated confirmer signature scheme allows a signer to control the verification ability of a signature, hence protecting the signer's privacy. However, a designated confirmer signature is insufficient when the secret keys are damaged and incapable of collaborative signature generation. In this paper, we circumvent these limitations by introducing the notion of designated confirmer threshold signature. First, we present a formal security model, then give a generic construction, which utilizes threshold signature schemes, encryption schemes and Σ -protocols. Instantiating this generic construction, we have two specific schemes, based on threshold Schnorr and threshold ECDSA, respectively. We further design two efficient Σ -protocols for efficient proofs. We also implement these schemes, and the experiment results show that our schemes are practical with rich functionalities. Finally, we demonstrate interesting applications for blockchains, such as verifiable asset auctions in blockchain and traditional electronic bidding. [ABSTRACT FROM AUTHOR]

This paper study a class of time-space fractional reaction-diffusion equations with nonlocal initial conditions and construct an abstract theory in fractional power spaces to discuss the results related S-asymptotically ω -periodic mild solutions. When the coefficients are sufficiently small, under the condition that the nonlinear term can grow any number of orders, we discuss the existence and uniqueness of S-asymptotically ω -periodic solutions based on the theory of operator semigroups and fixed point theorem. In addition, we considered the Mittag-Leffler-Ulam-Hyers stability results using the singular type Gronwall inequality and appropriate fractional calculus. The results in the present paper extended the work of (Andrade et al. in Proc Edinb Math Soc 59:65–76, 2016) to the case of time-space fractional nonlocal reaction-diffusion equations. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to state nonexpansive Maia type fixed point theorems for Ćirić–Prešić operators in normed spaces endowed with a partial order. For this we do a thorough analysis in the hypotheses of our theorems, considering different properties of completeness, compactness, convexity and bounding. We state Maia type fixed point theorems for contraction and nonexpansive Ćirić–Prešić operators, including those defined by a multiply metric function. Fixed point theorems in spaces without a partial order, as well as, corollaries for monotone nonexpansive mappings are stated too. Our theorems generalize and improve results given by Ćirić and Prešić's (Acta Math Univ Comenian (NS) 76:143–147, 2007) and Balazs (Mathematica 10:18–31, 2018) and extend them to nonexpansive operators. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the generalization of Hermite-Hadamard-type orthogonality within skew structures. Moslehian and Rassias (Commun Math Anal 8:16–21, 2010) characterized inner product spaces by employing the parallelogram law for skew structures in their research. We introduce the concept of skew orthogonality by integrating the parallelogram law of skew structures with Hermite-Hadamard-type orthogonality and discuss its properties. Finally, we characterize inner product spaces using mappings that preserve skew orthogonality. [ABSTRACT FROM AUTHOR]

Kim (Ramanujan Math Soc Lect Notes Ser 14:157–163, 2010) introduced the overcubic partition function a ¯ (n) , which represents the number of all the overlined versions of the cubic partition counted by a(n). Let b ¯ r (n) denote the number of overcubic partitions of n with r-tuples. Several authors established many particular and infinite families of congruences for b ¯ 2 (n) . In this paper, we show that b ¯ 2 β m + t (n) ≡ b ¯ t (n) (m o d 2 β + 1) , where β ≥ 1 , m ≥ 0 , and t ≥ 1 are integers. We also prove some new congruences modulo 8, 16 and 32 for b ¯ 4 m + 2 (n) , b ¯ 4 m + 3 (n) , b ¯ 8 m + 2 (n) , b ¯ 8 m + 4 (n) and b ¯ 16 m + 4 (n) , where m is any non-negative integer. [ABSTRACT FROM AUTHOR]

Here, we systematically review research on teaching knowledge in the context of undergraduate STEM education, with particular attention to what this research reveals about knowledge that is important for evidence-based teaching. Evidence-based teaching can improve student outcomes in undergraduate STEM education. However, the enactment of promising evidence-based teaching strategies depends greatly on the instructor and potentially on the teaching knowledge they are able to deploy. The review includes an overview of prevalent teaching knowledge theory, including pedagogical content knowledge, mathematical knowledge for teaching, and pedagogical knowledge. We compare and contrast teaching knowledge theory and terminology across STEM disciplines in order to build bridges for researchers across disciplines. Our search for peer-reviewed investigations of teaching knowledge in undergraduate science, engineering and mathematics yielded 45 papers. We examined the theoretical frameworks used in each study and analyzed study approaches, comparing across disciplines. Importantly, we also synthesized findings from research conducted in the context of evidence-based teaching. Overall, teaching knowledge research is sparse and siloed by discipline, and we call for collaborative work and better bridge-building across STEM disciplines. Though disciplinary divergences are common in discipline-based education research, the effect is magnified in this research area because the theoretical frameworks are themselves siloed by discipline. Investigations of declarative knowledge were common, and we call for increased attention to knowledge used in the practice of teaching. Finally, there are not many studies examining teaching knowledge in the context of evidence-based teaching, but the existing work suggests that components of pedagogical content knowledge, pedagogical knowledge, and content knowledge influence the implementation of evidence-based teaching. We describe implications for future teaching knowledge research. We also call on those who develop and test evidence-based strategies and curriculum to consider, from the beginning, the teaching knowledge needed for effective implementation. [ABSTRACT FROM AUTHOR]

The Lean mathematical library Mathlib features extensive use of the typeclass pattern for organising mathematical structures, based on Lean's mechanism of instance parameters. Related mechanisms for typeclasses are available in other provers including Agda, Coq and Isabelle with varying degrees of adoption. This paper analyses representative examples of design patterns involving instance parameters in the finalized Lean 3 version of Mathlib, focussing on complications arising at scale and how the Mathlib community deals with them. [ABSTRACT FROM AUTHOR]

In this paper, we study the algebraic limit cycle of degree 2 for the system x ˙ = - y + a 30 x 3 + a 21 x 2 y + a 12 x y 2 + a 03 y 3 , y ˙ = x + b 30 x 3 + b 21 x 2 y + b 12 x y 2 + b 03 y 3 , which is called a linear type center plus cubic homogeneous polynomial differential system. We derive the normal form of this system with an algebraic limit cycle of degree 2. It is shown that, if an invariant algebraic curve of degree 2 is a limit cycle of the above mentioned system, then it is a unique limit cycle in the phase plane. [ABSTRACT FROM AUTHOR]

The focus of this study is to use the mixture item response theory (MixIRT) model while implementing the no-U-turn sampler as a technique for investigating the presence of latent classes (i.e., subpopulations) among eighth-grade students who were administered TIMSS 2019 mathematics subtest in paper format from the gulf cooperation council (GCC) countries. One-, two-, and constrained three-parameter logistic MixIRT models with one to four classes were used to fit to the data, where the model data fit was assessed using Bayesian fit indices. The results indicate that multiple latent classes or subpopulations can better reflect the mathematical proficiency of eighth graders from the four GCC countries, and specifically the two-class constrained three-parameter MixIRT model provides a relatively better fit to the data. The results also indicate that when a mixture of several latent classes present, the conventional unidimensional IRT model is limited in providing information for multiple latent classes and shall be avoided. In addition to adding to the existing literature on MixIRT models for international large-scale assessments such as TIMSS on its heterogenous subpopulations from a fully Bayesian approach, this study sheds light on the limitation of conventional unidimensional IRT models and subsequently directs attention to the use of the more complex MixIRT model for such assessments. [ABSTRACT FROM AUTHOR]

In this paper, we construct a symbol calculus yielding short exact sequences for the dual Toeplitz algebra generated by all bounded dual Toeplitz operators on the Hardy space associated with the polydisk D n in the unitary space C n , that have been introduced and well studied in our earlier paper (Benaissa and Guediri in Taiwan J Math 19: 31–49, 2015), as well as for the C*-subalgebra generated by dual Toeplitz operators with symbols continuous on the associated hypertorus T n . [ABSTRACT FROM AUTHOR]

Discusses the computational analysis of the Bayesian Paradigm. Determination of the traditional applied probability focus to call structural mathematics contrasts; Association of typical statistical focus on inferential mathematics; Terms of Bernouilli variables or perhaps multinomial variables; Increase in sophistication of probability models and the statistical interference.

In the present paper, we have obtained common best proximity point theorems of nonself maps in Hausdorff topological space. Further, our results extend the results due to Gerald F. Jungck, thereby proving a generalized version of Kirk's theorem (J. London Math. 1(1):107–111, 1969). [ABSTRACT FROM AUTHOR]

Reference (Ericksen in Q. J. Mech. Appl. Math. 45:545–554, 1992), a short and dense paper by J.L. Ericksen, is taken as a primary source of terms frequently used in continuum thermodynamics, in an attempt to make their significance as precise as possible. [ABSTRACT FROM AUTHOR]

This note remedies an error in our paper tilted Conormal Spaces and Whitney Stratifications (Found. Comput. Math., 2022). [ABSTRACT FROM AUTHOR]

The notion of approximate fixed point sequence, emphasized in Chidume (Geometric properties of Banach spaces and nonlinear iterations. Lecture Notes in Mathematics, 1965. Springer-Verlag London, Ltd., London, 2009), is a very useful tool in proving convergence theorems for fixed point iterative schemes in the class of nonexpansive-type mappings. In the present paper, our aim is to present simple and unified alternative proofs of some classical fixed point theorems emerging from Banach contraction principle, by using a technique based on the concepts of approximate fixed point sequence and graphic contraction. [ABSTRACT FROM AUTHOR]

In this paper, we establish some reversed dynamic inequalities of Hilbert type on time scales nabla calculus by applying reversed Hölder's inequality, chain rule on time scales, and the mean inequality. As particular cases of our results (when T = N and T = R ), we get the reversed form of discrete and continuous inequalities proved by Chang-Jian, Lian-Ying and Cheung (Math. Slovaca 61(1):15–28, 2011). [ABSTRACT FROM AUTHOR]

In the paper, we investigate the uniqueness problem of a meromorphic function and its difference operator to the most general setting via two shared set problems and thus improve a recent result of Chen–Chen (Bull Malays Math Sci Soc 35(3): 765-774, 2012). [ABSTRACT FROM AUTHOR]

In this paper, we obtain the Harary index and the hyper-Wiener index of the H-generalized join of graphs and the generalized corona product of graphs. As a consequence, we deduce some of the results in (Das et al. in J. Inequal. Appl. 2013:339, 2013) and (Khalifeh et al. in Comput. Math. Appl. 56:1402–1407, 2008). Moreover, we calculate the Harary index and the hyper-Wiener index of the ideal-based zero-divisor graph of a ring. [ABSTRACT FROM AUTHOR]

In this paper, we establish a relation-theoretic set-valued version of the fixed point result of Ćirić and Prešić (Acta Math. Univ. Comen. LXXVI(2):143–147, 2007) on metric spaces endowed with an arbitrary binary relation. The results of this paper, generalize and unify the fixed point results of Ćirić and Prešić (Acta Math. Univ. Comen. LXXVI(2):143–147, 2007), Shukla and López (Quaest. Math. 45(3):1–16, 2019), and Shukla and Radenović (An. Ştiinţ. Univ. 'Al.I. Cuza' Iaşi, Mat. 63(2):339–350, 2017) in product spaces. Some examples are provided that justify and establish the importance of our results. As applications of our main result, we have established the existence of solutions to differential inclusion problems and the weak asymptotical stability and a global attractivity of the equilibrium point of a difference inclusion problem. The use of arbitrary binary relations in our results permits us to apply the results to the differential inclusion problems and difference inclusion problems with weaker assumptions than those used in the papers mentioned above. [ABSTRACT FROM AUTHOR]

Integral inequalities with generalized convexity play an important role in both applied and theoretical mathematics. The theory of integral inequalities is currently one of the most rapidly developing areas of mathematics due to its wide range of applications. In this paper, we study the concept of higher-order strongly exponentially convex functions and establish a new Hermite–Hadamard inequality for the class of strongly exponentially convex functions of higher order. Further, we derive some new integral inequalities for Riemann–Liouville fractional integrals via higher-order strongly exponentially convex functions. These findings include several well-known results and newly obtained results as special cases. We believe that the results presented in this paper are novel and will be beneficial in encouraging future research in this field. [ABSTRACT FROM AUTHOR]

The main objective of the paper is to study the final model for the Kirchhoff-type parabolic system. Such type problems have many applications in physical and biological phenomena. Under some smoothness of the final Cauchy data, we prove that the problem has a unique mild solution. The main tool is Banach's fixed point theorem. We also consider the non-well-posed problem in the Hadamard sense. Finally, we apply truncation method to regularize our problem. The paper is motivated by the work of Tuan, Nam, and Nhat [Comput. Math. Appl. 77(1):15–33, 2019]. [ABSTRACT FROM AUTHOR]

The Markoff graphs modulo p were proven by Chen (Ann Math 199(1), 2024) to be connected for all but finitely many primes, and Baragar (The Markoff equation and equations of Hurwitz. Brown University, 1991) conjectured that they are connected for all primes, equivalently that every solution to the Markoff equation modulo p lifts to a solution over Z . In this paper, we provide an algorithmic realization of the process introduced by Bourgain et al. [arXiv:1607.01530] to test whether the Markoff graph modulo p is connected for arbitrary primes. Our algorithm runs in o (p 1 + ϵ) time for every ϵ > 0 . We demonstrate this algorithm by confirming that the Markoff graph modulo p is connected for all primes less than one million. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following Schrödinger system involving the tempered fractional p-Laplacian (- Δ - λ) p s u (x) + a u p - 1 (x) = f (u (x) , v (x)) , (- Δ - λ) p t v (x) + b v p - 1 (x) = g (u (x) , v (x)) , where n ≥ 2 , a , b > 0 , 2 < p < ∞ , 0 < s , t < 1 and λ is a sufficiently small positive constant. To effectively utilize the direct method of moving planes, we first establish the narrow region principle and the decay at infinity. Then we prove the radial symmetry and monotonicity of positive solutions for the system in the unit ball and the whole space. Our results are an extension of some content in Ma and Zhang (Appl Math J Chin Univ 37: 52–72, 2022). [ABSTRACT FROM AUTHOR]

In this article, the author presents his opinions about the article "Does demography need differential equations" by Thomas K. Burch. He agrees with Burch regarding the close association of demography to mathematical expression than other social scientific discipline. However, he warns the potential abuse of mathematics' use in population studies.

Boys in the Kingdom of Saudi Arabia consistently and significantly underperform compared to girls across different grades and subjects, forming one of the largest gender gaps in student achievement in the world. Saudi Arabia offers a unique setting in which boys and girls attend separate schools on a universal basis starting from grade 1. This means that boys and girls are educated only by male and female teachers, respectively, in effect inhabiting parallel education systems. In this context, this study examines the factors that are associated with student achievement in mathematics and science in grades 4 and 8 and the extent to which these associations are different for boys and girls, in an effort to gain insights into boys' underachievement in mathematics and science in Saudi Arabia. The paper employs data from two recent large-scale assessments of education: Trends in International Mathematics and Science Study (TIMSS) 2019 and Saudi Arabia's National Assessment of Learning Outcomes (NALO) 2018. A series of hierarchical two-level linear regression models showed that in grade 4, school climate was more strongly associated with boys' compared with girls' achievement in both mathematics and science, with boys attending schools of poorer school climate having a considerably lower performance compared with girls attending such schools. The findings also indicated that although greater literacy and numeracy readiness was linked with higher science achievement among boys and girls, grade 4 boys tended to benefit more from this readiness than girls. In addition, the results show that student absenteeism in grade 4 is particularly strongly associated with decreases in mathematics achievement among boys. In grade 8, significant interactions between gender and the extent to which students feel confident in science, the degree of schools' emphasis on academic success, and teachers' age are observed. The paper concludes by discussing some of the implications of these findings for educators and policy makers in Saudi Arabia. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the Cauchy problem of inhomogeneous convolution equations of a fairly general nature. To solve the problems posed here, we apply the operator method proposed in some earlier papers by the author. The solutions of the problems under consideration are found using an effective method in the form of well-convergent vector-valued power series. The proposed method ensures the continuity of the obtained solutions with respect to the initial data and the inhomogeneous term of the equation. [ABSTRACT FROM AUTHOR]

In this paper, by revisiting intersection rules for normal cones, we give formulas for estimating or computing the Fréchet/Mordukhovich/Moreau–Rockafellar subdifferentials of optimal value functions of constrained parametric optimization problems under metric qualification conditions. The results are then applied to derive chain rules for composite functions in both convex and nonconvex situations. Illustrative examples and comparisons to existing results, including those of Mordukhovich and Shao (Trans Amer Math Soc 348:1235–1280, 1996), Mordukhovich et al. (Math Program Ser B 116:369–396, 2009) and of An and Jourani (J Optim Theory Appl 192:82–96, 2022), are also addressed. [ABSTRACT FROM AUTHOR]

This paper proposes a new data clustering method using the advantages of metaheuristic (MH) optimization algorithms. A novel MH optimization algorithm, called arithmetic optimization algorithm (AOA), was proposed to address complex optimization tasks. Math operations inspire the AOA, and it showed significant performance in dealing with different optimization problems. However, the traditional AOA faces some limitations in its search process. Thus, we develop a new variant of the AOA, namely, Augmented AOA (AAOA), integrated with the opposition-based learning (OLB) and Lévy flight (LF) distribution. The main idea of applying OLB and LF is to improve the traditional AOA exploration and exploitation trends in order to find the best clusters. To evaluate the AAOA, we implemented extensive experiments using twenty-three well-known benchmark functions and eight data clustering datasets. We also evaluated the proposed AAOA with extensive comparisons to different optimization algorithms. The outcomes verified the superiority of the AAOA over the traditional AOA and several MH optimization algorithms. Overall, the applications of the LF and OLB have a significant impact on the performance of the conventional AOA. [ABSTRACT FROM AUTHOR]

The normalization of the combination of generalized Lommel–Wright function J κ 1 , κ 2 κ 3 , m (z) (m ∈ N , κ 3 > 0 and κ 1 , κ 2 ∈ C ) defined by J κ 1 , κ 2 κ 3 , m (z) : = Γ m (κ 1 + 1) Γ (κ 1 + κ 2 + 1) 2 2 κ 1 + κ 2 z 1 − (κ 2 / 2) − κ 1 J κ 1 , κ 2 κ 3 , m (z) , where J κ 1 , κ 2 κ 3 , m (z) : = (1 − 2 κ 1 − κ 2) J κ 1 , κ 2 κ 3 , m (z) + z (J κ 1 , κ 2 κ 3 , m (z)) ′ and J κ 1 , κ 2 κ 3 , m (z) = (z 2) 2 κ 1 + κ 2 ∑ n = 0 ∞ (− 1) n Γ m (n + κ 1 + 1) Γ (n κ 3 + κ 1 + κ 2 + 1) (z 2) 2 n , was previously introduced and some of its geometric properties have been considered. In this paper, we report conditions for J κ 1 , κ 2 κ 3 , m (z) to be starlike and convex of order α, 0 ≤ α < 1 , inside the open unit disk using some technical manipulations of the gamma and digamma functions, as well as inequality for the digamma function that has been proved (Guo and Qi in Proc. Am. Math. Soc. 141(3):1007–1015, 2013). In addition, a method presented by Lorch (J. Approx. Theory 40(2):115–120 1984) and further developed by Laforgia (Math. Compet. 42(166):597–600 1984) is applied to establish firstly sharp inequalities for the shifted factorial that will be used to obtain the order of starlikeness and convexity. We compare then the obtained orders of starlikeness and convexity with some important consequences in the literature as well as the results proposed by all techniques to demonstrate the accuracy of our approach. Ultimately, a lemma by (Fejér in Acta Litt. Sci. 8:89–115 1936) is used to prove that the modified form of the function J κ 1 , κ 2 κ 3 , m (z) defined by I κ 1 , κ 2 κ 3 , m (z) = J κ 1 , κ 2 κ 3 , m (z) ∗ z / (1 + z) is in the class of starlike and convex functions, respectively. Further work regarding the function J κ 1 , κ 2 κ 3 , m (z) is underway and will be presented in a forthcoming paper. [ABSTRACT FROM AUTHOR]

Though Bartlett has offered several constructive criticisms of the mathematical formulations that were included in my paper, Exponential Population Growth and Doubling Times, not one of them undermines either of the two basic points made in my paper—that exponential population growth is no longer being projected for any nation in the world and, this being so, writers and speakers addressing population issues no longer have reason to discuss either exponential growth or its frequent companion, "doubling times." In making my argument, included several paragraphs in which exponential growth, exponential curves, and doubling times were described. Bartlett has found these descriptions "distressing" and his paper explains his reasoning. So be it. I claim no scholarship in mathematics. In the writing of my paper believed—and still do—that my descriptions provide background material that is useful to readers not concerned with mathematical purity. [ABSTRACT FROM AUTHOR]

In this short paper we tackle two subjects. First, we provide a lower bound for the first eigenvalue of the antiperiodic problem for a Hill's equation based on L p -conditions, and as a consequence, we introduce an adjusted statement of the main result about the asymptotic stability of periodic solutions for the general Duffing equation in (Torres in Mediterr. J. Math. 1(4):479–486, 2004) (Theorem 4). This appropriate version of the result arises because of one subtlety in the proof provided in (Torres in Mediterr. J. Math. 1(4):479–486, 2004). More precisely, the lower bound of the first antiperiodic eigenvalue associated with Hill's equations of potential a (t) employed there may be negative, thus the conclusion is not completely attained. Hence, the adjustments considered here provide a mathematically correct result. On the other hand, we apply this result to obtain a lateral asymptotic stable periodic oscillation in the Comb-drive finger MEMS model with a cubic nonlinear stiffness term and linear damping. This fact is not typical in Comb-drive finger devices, thus our results could provide a new possibility; a new design principle for stabilization in Comb-drive finger MEMS. [ABSTRACT FROM AUTHOR]

This paper proposes a novel matrix rank-one decomposition for quaternion Hermitian matrices, which admits a stronger property than the previous results in Ai W et al (Math Progr 128(1):253–283, 2011), Huang Y, Zhang S (Math Oper Res 32(3):758–768, 2007), Sturm JF, Zhang S (Math Oper Res 28(2):246–267 2003). The enhanced property can be used to drive some improved results in joint numerical range, S -Procedure and quadratically constrained quadratic programming (QCQP) in the quaternion domain, demonstrating the capability of our new decomposition technique. [ABSTRACT FROM AUTHOR]

Decision-making under uncertainty involves three fundamental components: acts, states of nature, and consequences, as first introduced by Savage (The foundations of statistics, Wiley, New York, 1954). An act is uniquely determined by a number of random consequences that are associated with different states of nature. If the consequences are identical across all states of nature, then the act is state-independent. Prior research on distortion risk measures (DRMs) has primarily focused on state-independent acts. In this paper, we extend the research to state-dependent acts by introducing a state-dependent DRM (SDRM) under the Anscombe–Aumann's framework (Anscombe and Aumannin in Ann Math Stat 34(1):199–205, 1963). The proposed SDRM is the weighted average of DRMs at each state, where the weights are determined by the decision maker's (DM's) subjective probabilities of the states. In situations where there is incomplete information about the DM's true distortion function and/or the true subjective probabilities of the states, we introduce a preference robust SDRM (PRSDRM) for acts. The PRSDRM is based on the worst-case state-dependent distortion function and the worst-case subjective probabilities over a dependent joint ambiguity set constructed with partially available information. To compute the PRSDRM numerically, we show that when the distortion functions are concave, it can be formulated as a biconvex program and further as a convex program by changing some variables. As a motivation and application, we use the PRSDRM for decision-making problems and propose an alternating iterative algorithm for solving it. Finally, we conduct numerical experiments to assess the performance of our proposed model and computational scheme. [ABSTRACT FROM AUTHOR]

This paper studies decision-making in the face of two stochastically independent sources of uncertainty. It characterizes axiomatically a Subjective Expected Utility representation of preferences where subjective beliefs consist of a product probability measure. The two key axioms in this characterization both involve some behavioral notions of stochastic independence. Our result can be understood as a purely subjective version of the Anscombe and Aumann (Ann Math Stat 34:199–205, 1963) theorem that avoids the controversial use of exogenous probabilities by appealing to stochastic independence. We also obtain an extension to Choquet Expected Utility representations. [ABSTRACT FROM AUTHOR]

The paper deals with the code length distributions for which the proportion of the codewords of a given length to all words of this length is a suitable power of 1/2. We derive a lower bound and an upper bound for the number of prefix codes with the above property. We also investigate the ratio of prefix codes to all uniquely decodable codes, which relates to the more general results of Woryna (Discret Math 340(2):51–57, 2017; Discret Appl Math 244:205–213, 2018). [ABSTRACT FROM AUTHOR]

For rational functions , where is a polynomial of degree at the most and , with we use simple but elegant techniques to strengthen generalizations of certain results which extend some widely known polynomial inequalities of Erdős-Lax and Turán to rational functions . In return these reinforced results, in the limiting case, lead to the corresponding refinements of the said polynomial inequalities. As an illustration and as an application of our results, we obtain some new improvements of the Erdős-Lax and Turán type inequalities for polynomials. These improved results take into account the size of the constant term and the leading coefficient of the given polynomial. As a further factor of consideration, during the course of this paper we will demonstrate how some recently obtained results could have been proved without invoking the results of Dubinin [Distortion theorems for polynomials on the circle, Sb. Math. 191(12) (2000) 1797–1807]. [ABSTRACT FROM AUTHOR]

We consider the following problem stated in 1993 by Buttazzo and Kawohl (Math Intell 15:7–12, 1993): minimize the functional ∫ ∫ Ω (1 + | ∇ u (x , y) | 2 ) - 1 d x d y in the class of concave functions u : Ω → [0,M], where Ω ⊂ R 2 is a convex domain and M > 0. It generalizes the classical minimization problem, which was initially stated by I. Newton in 1687 in the more restricted class of radial functions. The problem is not solved until now; there is even nothing known about the structure of singular points of a solution. In this paper we, first, solve a family of auxiliary 2D least resistance problems and, second, apply the obtained results to study singular points of a solution to our original problem. More precisely, we derive a necessary condition for a point being a ridge singular point of a solution and prove, in particular, that all ridge singular points with horizontal edge lie on the top level and zero level sets. [ABSTRACT FROM AUTHOR]