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DP-coloring as a generalization of list coloring was introduced by Dvořák and Postle recently. In this paper, we prove that every planar graph in which the distance between 6 − -cycles is at least 2 is DP-3-colorable, which extends the result of Yin and Yu [Discret. Math. 2019, 342, 2333–2341]. [ABSTRACT FROM AUTHOR]

DP-coloring was introduced by Dvořák and Postle [J. Comb. Theory Ser. B 2018, 129, 38–54]. In this paper, we prove that every planar graph in which the 5 − -cycles are at distance of at least 3 from each other is DP-3-colorable, which improves the result of Montassier et al. [Inform. Process. Lett. 2008, 107, 3–4] and Yin and Yu [Discret. Math. 2019, 342, 2333–2341]. [ABSTRACT FROM AUTHOR]

Kim and Kim (Russ. J. Math. Phys. 26, 2019, 40-49) introduced polyexponential function as an inverse to the polylogarithm function and by this, constructed a new type poly-Bernoulli polynomials. Recently, by using the polyexponential function, a number of generalizations of some polynomials and numbers have been presented and investigated. Motivated by these researches, in this paper, multi-poly-Euler polynomials are considered utilizing the degenerate multiple polyexponential functions and then, their properties and relations are investigated and studied. That the type 2 degenerate multi-poly-Euler polynomials equal a linear combination of the degenerate Euler polynomials of higher order and the degenerate Stirling numbers of the first kind is proved. Moreover, an addition formula and a derivative formula are derived. Furthermore, in a special case, a correlation between the type 2 degenerate multi-poly-Euler polynomials and degenerate Whitney numbers is shown. [ABSTRACT FROM AUTHOR]

It is the intention of the current study to suggest a trajectory for the advancement of prospective mathematics teachers' use of meta-cognitive skills in solving mathematics-based programming problems with Scratch. Scratch is a code-based program that can be utilized in teaching various disciplines, especially geometry and its rich range of subjects such as the topic of symmetry. The present study suggests that advancing prospective teachers' meta-cognitive skills in the Scratch environment could be done through problem solving and negotiations. The present paper analyzed the implementation of the trajectory by two pedagogic supervisors who attempted, in the frame of one-year preparation (2018–2019), to educate 18 prospective teachers to use meta-cognitive skills in mathematics-based programming activities, where this attempt was based on problem solving and negotiation processes. Data were collected through videoing and recording the learning sessions of the prospective teachers and was analyzed using deductive and inductive constant comparison methods. The deductive analysis utilized theoretical models of meta-cognitive processes and negotiation processes. The research results indicated that the negotiation processes supported the development of the prospective teachers' meta-cognitive processes in solving mathematics-based programming problems with Scratch. [ABSTRACT FROM AUTHOR]

"Number" is an important learning dimension in primary mathematics education. It covers a large proportion of mathematical topics in the primary mathematics curriculum, and teachers use most of their class time to teach fundamental number concepts and basic arithmetic operations. This paper focuses on the nature of mathematics pedagogical content knowledge (MPCK) concerning arithmetic word problems. The aim of this qualitative research was to investigate how well the future primary school teachers in Hong Kong had been prepared to teach mathematical application problems for third and sixth graders. Nineteen pre-service teachers who majored in both mathematics and primary education were interviewed using two sets of scenario-based questions. The results revealed that innovative approaches were suggested for teaching third graders while the strategies suggested for teaching sixth graders were mostly based on a profound understanding of mathematical content knowledge. Many participants demonstrated sound knowledge about the sixth grader's mathematical misconception, but most of them were unable to precisely indicate the third grader's error in presenting a complete solution for a typical mathematics word problem. A deep understanding of elementary number theory seems to be a precondition for developing pre-service teachers' MPCK in teaching arithmetic word problems. [ABSTRACT FROM AUTHOR]

Hybrid numbers are generalizations of complex, hyperbolic and dual numbers. A hyperbolic complex structure is frequently used in both pure mathematics and numerous areas of physics. In this paper we introduce a special kind of spacelike hybrid number, namely the F (p , n) -Fibonacci hybrid numbers and we give some of their properties. [ABSTRACT FROM AUTHOR]

The popularity of deep reinforcement learning (DRL) applications in economics has increased exponentially. DRL, through a wide range of capabilities from reinforcement learning (RL) to deep learning (DL), offers vast opportunities for handling sophisticated dynamic economics systems. DRL is characterized by scalability with the potential to be applied to high-dimensional problems in conjunction with noisy and nonlinear patterns of economic data. In this paper, we initially consider a brief review of DL, RL, and deep RL methods in diverse applications in economics, providing an in-depth insight into the state-of-the-art. Furthermore, the architecture of DRL applied to economic applications is investigated in order to highlight the complexity, robustness, accuracy, performance, computational tasks, risk constraints, and profitability. The survey results indicate that DRL can provide better performance and higher efficiency as compared to the traditional algorithms while facing real economic problems in the presence of risk parameters and the ever-increasing uncertainties. [ABSTRACT FROM AUTHOR]

The last two decades have witnessed an increasing interest in the use of the so-called rapid analytical methods or high throughput techniques. Most of these applications reported the use of vibrational spectroscopy methods (near infrared (NIR), mid infrared (MIR), and Raman) in a wide range of samples (e.g., food ingredients and natural products). In these applications, the analytical method is integrated with a wide range of multivariate data analysis (MVA) techniques (e.g., pattern recognition, modelling techniques, calibration, etc.) to develop the target application. The availability of modern and inexpensive instrumentation together with the access to easy to use software is determining a steady growth in the number of uses of these technologies. This paper underlines and briefly discusses the three critical pillars—the sample (e.g., sampling, variability, etc.), the spectra and the mathematics (e.g., algorithms, pre-processing, data interpretation, etc.)—that support the development and implementation of vibrational spectroscopy applications. [ABSTRACT FROM AUTHOR]

Let ST L (s) and CV L (s) denote the family of analytic and normalized functions f in the unit disk D : = z : | z | < 1 , such that the quantity z f ′ (z) / f (z) or 1 + z f ″ (z) / f ′ (z) respectively are lying in the region bounded by the limaçon (u − 1) 2 + v 2 − s 4 2 = 4 s 2 u − 1 + s 2 2 + v 2 , where 0 < s ≤ 1 / 2 . The limaçon of Pascal is a curve that possesses properties which qualify it for the several applications in mathematics, statistics (hypothesis testing problem) but also in mechanics (fluid processing applications, known limaçon technology is employed to extract electrical power from low-grade heat, etc.). In this paper we present some results concerning the behavior of f on the classes ST L (s) or CV L (s) . Some appropriate examples are given. [ABSTRACT FROM AUTHOR]

Italian domination can be described such that in an empire all cities/vertices should be stationed with at most two troops. Every city having no troops must be adjacent to at least two cities with one troop or at least one city with two troops. In such an assignment, the minimum number of troops is the Italian domination number of the empire/graph is denoted as γ I . Determining the Italian domination number of a graph is a very popular topic. Li et al. obtained γ I (C n □ C 3) and γ I (C n □ C 4) (weak {2}-domination number of Cartesian products of cycles, J. Comb. Optim. 35 (2018): 75–85). Stȩpień et al. obtained γ I (C n □ C 5) = 2 n (2-Rainbow domination number of C n □ C 5 , Discret. Appl. Math. 170 (2014): 113–116). In this paper, we study the Italian domination number of the Cartesian products of cycles C n □ C m for m ≥ 6 . For n ≡ 0 (mod 3) , m ≡ 0 (mod 3) , we obtain γ I (C n □ C m) = m n 3 . For other C n □ C m , we present a bound of γ I (C n □ C m) . Since for n = 6 k , m = 3 l or n = 3 k , m = 6 l (k , l ≥ 1) , γ r 2 (C n □ C m) = m n 3 , (the Cartesian product of cycles with small 2-rainbow domination number, J. Comb. Optim. 30 (2015): 668–674), it follows in this case that C n □ C m is an example of a graph class for which γ I = γ r 2 , which can partially answer the question presented by Brešar et al. on the 2-rainbow domination in graphs, Discret. Appl. Math. 155 (2007): 2394–2400. [ABSTRACT FROM AUTHOR]

The authors wish to make the following corrections to this paper [[1]], published recently in I Mathematics i : The coauthors Junaid Khan and Muhammad Rehan were omitted from the author list, which should read as follows: B Insaf Ullah SP 1,2, sp *, Noor Ul Amin SP 1 sp , Junaid Khan SP 3 sp , Muhammad Rehan SP 3 sp , Muhammad Naeem SP 3 sp , Hizbullah Khattak SP 1 sp , Shah Jahan Khattak SP 4 sp , and Haseen Ali SP 3 sp b The author contributions should updated as follows: B Author Contributions: b Conceptualization, I.U. and N.U.A.; methodology, I.U.; software, H.K., J.K., and M.R.; validation, I.U., J.K., M.R., N.U.A., and M.N.; formal analysis, I.U.; investigation, S.J.K.; writing - original draft preparation, I.U.; writing - review and editing, H.A.; supervision, N.U.A.; project administration, N.U.A. The authors would like to apologize for any inconvenience caused to the readers by these changes. Conflicts of Interest The authors declare no conflicts of interest. Reference 1 Ullah I., Amin N.U., Naeem M., Khattak H., Khattak S.J., Ali H. A Novel Provable Secured Signcryption Scheme PSSS: A Hyper-Elliptic Curve-Based Approach. [Extracted from the article]

The accelerated prox-level (APL) and uniform smoothing level (USL) methods recently proposed by Lan (Math Program, 149: 1–45, 2015) can achieve uniformly optimal complexity when solving black-box convex programming (CP) and structure non-smooth CP problems. In this paper, we propose two modified accelerated bundle-level type methods, namely, the modified APL (MAPL) and modified USL (MUSL) methods. Compared with the original APL and USL methods, the MAPL and MUSL methods reduce the number of subproblems by one in each iteration, thereby improving the efficiency of the algorithms. Conclusions of optimal iteration complexity of the proposed algorithms are established. Furthermore, the modified methods are applied to the two-stage stochastic programming, and numerical experiments are implemented to illustrate the advantages of our methods in terms of efficiency and accuracy. [ABSTRACT FROM AUTHOR]

In 1984, Wang and Zheng (J. Comput. Math. 1984, 1, 70–76) introduced a new fourth order iterative method for the simultaneous computation of all zeros of a polynomial. In this paper, we present new local and semilocal convergence theorems with error estimates for Wang–Zheng's method. Our results improve the earlier ones due to Wang and Wu (Computing 1987, 38, 75–87) and Petković, Petković, and Rančić (J. Comput. Appl. Math. 2007, 205, 32–52). [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new graph operation called subdivision vertex-edge join (denoted by G 1 S ▹ (G 2 V ∪ G 3 E) for short), and then the adjacency spectrum, the Laplacian spectrum and the signless Laplacian spectrum of G 1 S ▹ (G 2 V ∪ G 3 E) are respectively determined in terms of the corresponding spectra for a regular graph G 1 and two arbitrary graphs G 2 and G 3 . All the above can be viewed as the generalizations of the main results in [X. Liu, Z. Zhang, Bull. Malays. Math. Sci. Soc., 2017:1–17]. Furthermore, we also determine the normalized Laplacian spectrum of G 1 S ▹ (G 2 V ∪ G 3 E) whenever G i are regular graphs for each index i = 1 , 2 , 3 . As applications, we construct infinitely many pairs of A-cospectral mates, L-cospectral mates, Q-cospectral mates and L -cospectral mates. Finally, we give the number of spanning trees, the (degree-)Kirchhoff index and the Kemeny's constant of G 1 S ▹ (G 2 V ∪ G 3 E) , respectively. [ABSTRACT FROM AUTHOR]

The ubiquity of sensor-rich smartphones provides opportunities for a low-cost method to track indoor pedestrians. In this situation, pedestrian dead reckoning (PDR) is a widely used technology; however, its cumulative error seriously affects its accuracy. This paper presents a method of combining infrastructure-free indoor acoustic self-positioning with PDR self-positioning, which verifies the rationality of PDR results through the acoustic constraint between a sound source and its image sources. We further determine the first-order echo delay measurements, thus obtaining the mobile user position. We verify that the proposed method can achieve a continuous self-positioning median error of 0.19 m, and the error probability below 0.12 m is 54.46%, which indicates its ability to eliminate PDR error, as well as its adaptability to environmental disturbances. [ABSTRACT FROM AUTHOR]

In this paper, we bring together two concepts related to uncertainty and vagueness: fuzzy numbers and intervals. With them, we build a new structure whose elements we call interval fuzzy segments. We have undertaken this based on the conviction that the fuzzy numbers are a correct representation of the real numbers under situations of indeterminacy. We also believe that if it makes sense to consider the set of real numbers between two real bounds, then it also makes sense to consider the set of all the fuzzy numbers between two fuzzy number bounds. In this way, we extend the concept of real interval to the concept of interval fuzzy segment defined by two fuzzy bounds and a transition mapping that leads from the lower fuzzy bound to the upper fuzzy bound and this transition mapping generates the set of all the fuzzy numbers comprised between those fuzzy bounds. At the same time, this transition mapping brings the concept of interval fuzzy segment closer to the concept of line segment. [ABSTRACT FROM AUTHOR]