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We present a simple implicit solution for the time-dependent trajectory of a thin Asay foil ejecta diagnostic for the general case where the impinging ejecta cloud is generated by a source function characterized by an arbitrary (sustained) time dependence and a time-independent (stationary) particle velocity distribution. In the limit that the source function time dependence becomes a delta function, this solution—which is amenable to rapid numerical calculations of arbitrary accuracy—exactly recovers a previously published solution for the special case of instantaneous ejecta production. We also derive simple expressions for the free-surface arrival (catch-up) time as well as the true ejecta areal mass accumulation on the accelerating foil and place bounds on the level of error incurred when applying instant-production mass solutions to a sustained-production trajectory. We demonstrate these solutions with example calculations for hypothetical source functions spanning a wide range of ejecta production durations, velocity distributions, and temporal behaviors. These calculations demonstrate how the foil trajectory is often insensitive to the temporal dependence of the source function, instead being dominated by the velocity distribution. We quantify this insensitivity using a "compatibility score" metric. Under certain conditions, one may capitalize upon this insensitivity to obtain a good approximation of the second integral of the velocity distribution from the observed foil trajectory. [ABSTRACT FROM AUTHOR]

The Graph Minors Structure Theorem of Robertson and Seymour asserts that, for every graph H, every H-minor-free graph can be obtained by clique-sums of "almost embeddable" graphs. Here a graph is "almost embeddable" if it can be obtained from a graph of bounded Euler-genus by pasting graphs of bounded pathwidth in an "orderly fashion" into a bounded number of faces, called the vortices, and then adding a bounded number of additional vertices, called apices, with arbitrary neighborhoods. Our main result is a full classification of all graphs H for which the use of vortices in the theorem above can be avoided. To this end, we identify a (parametric) graph \(\mathscr{S}_{t}\) and prove that all \(\mathscr{S}_{t}\) -minor-free graphs can be obtained by clique-sums of graphs embeddable in a surface of bounded Euler-genus after deleting a bounded number of vertices. We show that this result is tight in the sense that the appearance of vortices cannot be avoided for H-minor-free graphs, whenever H is not a minor of \(\mathscr{S}_{t}\) for some \(t\in \mathbb {N}\). Using our new structure theorem, we design an algorithm that, given an \(\mathscr{S}_{t}\) -minor-free graph G, computes the generating function of all perfect matchings of G in polynomial time. Our results, combined with known complexity results, imply a complete characterization of minor-closed graph classes where the number of perfect matchings is polynomially computable: They are exactly those graph classes that do not contain every \(\mathscr{S}_{t}\) as a minor. This provides a sharp complexity dichotomy for the problem of counting perfect matchings in minor-closed classes. [ABSTRACT FROM AUTHOR]

In this paper, a multi-objective prediction and optimization integration method combining response surface method (RSM) and non-dominated sorting genetic algorithm-II (NSGA-II) was proposed to improve the overhead low-power pulsed laser-MAG (metal active gas) hybrid welding quality. A four-factor with a five-level experiment matrix considering the weld current(I), weld speed(V), laser power(P), and assembly clearance(C) was established based on te central composite design method. The relationship between weld parameters and back weld width (BW) and weld reinforcement (WR) was approximated by RSM. The significance and adequacies were validated by the analysis of variance and validation experiments, and the average error of validation experiments between predict and actual value is less than 5%, indicating that the model exhibits high predictive accuracy. The individual effect of a single parameter and the interaction of multiple parameters on BW and WR were studied, and the weld current and assembly clearance are the most significant parameters influencing BW and WR, respectively. NSGA-II was used for multi-objective optimization taking the constructed RSM models as objective functions and generating the Pareto-optimal front composed of optimal solutions. Finally, the verification experiments show that the optimal solutions of different fronts can obtain the desired welding morphology without any defect. [ABSTRACT FROM AUTHOR]

The Horadam polynomials unify many well-known polynomials, such as the Fibonacci polynomials, the Lucas polynomials, the Pell polynomials, the Jacobsthal polynomials and the Chebyshev polynomials. We investigate some properties of various combinatorial triangles related to Horadam polynomials, including their properties as almost-Riordan arrays and Riordan arrays, their total positivity, the real-rootedness of the generating functions of their rows, and the asymptotic normality (by central and local limit theorems). [ABSTRACT FROM AUTHOR]

We show that if a group contains ℤn × F m as a finite-index subgroup, then its cogrowth series is the diagonal of a rational function for every generating set. This answers a question of Pak and Soukup on the cogrowth of virtually abelian groups; and generalizes a result by Elder, Rechnitzer, Janse van Rensburg, and Wong on the cogrowth series of the Baumslag–Solitar groups BS(N,N). [ABSTRACT FROM AUTHOR]

Part 2 of this article is devoted to the analysis of a new class of combination rules on belief functions generated by conditioning w.r.t. random sets and their linear convex combinations. Each such rule obeys two requirements: the consensus requirement with the conjunction rule means that this rule coincides with Dempster's rule on non-conflicting sources of information, and the consensus requirement with a mixture rule means that the result must be a specialization of their mixture combination. We show that this new class of combination rules is closed under convex combinations of such rules and their compositions. This allows us to implement the conflict management using the introduced functionals for measuring the specialization relation on belief functions. We also introduce similar rules for idempotent combination rules on credal sets obeying the similar consensus requirements and study the results obtained using various examples. [ABSTRACT FROM AUTHOR]

In the article, the problem of multi-criteria optimization of quality control mechanisms is analyzed. The presented method assumes the use of the NPGA genetic algorithm to simultaneously manage costs and the level of detecting non-conformities. The main assumption of the presented approach is to treat individual quality control procedures as vectors, whose elements are probability generating functions of defect detection. Each of these procedures generates certain operational costs and covers specific types of defects within its scope. The task of the presented algorithm is to indicate which procedure and to what extent should operate to ensure an appropriate level of non-conformity detection while minimizing costs. The article presents the theoretical foundations of the developed algorithm and the results of its implementation. The software has been developed in C++ with a particular focus on performance aspects. Its essence lies in the implementation of data structures introduced in the theoretical part, as well as methods for their rapid processing. Thanks to this approach, the entire program is scalable and can be used to solve multidimensional optimization problems. The presented approach may also find application in other areas of enterprise management. This will be possible primarily in cases where the effectiveness of procedures or devices is primarily evaluated based on probability. Therefore, the presented methods can provide effective optimization of other areas related to enterprise management. [ABSTRACT FROM AUTHOR]

Copyright of Baghdad Science Journal is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A set of regions of a link projection is said to be isolated if any pair of regions in the set share no crossings. The isolate-region number of a link projection is the maximum value of the cardinality for isolated sets of regions of the link projection. In this paper, all the link projections of isolate-region number one are determined. Also, estimations for welded unknotting number and a combinatorial way to find the isolate-region number are discussed, and a formula of the generating function of isolated-region sets is given for the standard projections of (2,n)-torus links. [ABSTRACT FROM AUTHOR]

The generating function for polygons on the square lattice has been known for many decades and is closely related to the path integral formulation of a free fermion model. On the cubic and hypercubic lattices the generating function is still unknown and the problem remains open. It has been conjectured that the three-dimensional (3D) and higher dimensional problems are not solvable—or, to be more precise, that there are no differentiably finite (D-finite) solutions. In this context, very recently a Berezin integral of an exponentiated Grassmann action was found for the polygon generating function on the cubic lattice, making explicit the connection between 3D polygons and a model of interacting fermions. Here we address the problem of how to generalize the 3D result to higher dimensions. We derive a Grassmann representation in terms of a Berezin integral for the generating function of polygons on d-dimensional hypercubic lattices. On the one hand, this new result admittedly brings us no closer to the problem of finding an explicit analytic expression for the desired generating function for polygons. On the other hand, however, the significant advance reported here precisely quantifies the remarkable mathematical difficulty of finding the explicit generating function. Indeed, the non-quadratic functional form of the Grassmann action that we derive here provides a very clear picture of the formidable mathematical obstruction that would need to be overcome. Specifically, in d dimensions, the Grassmann action contains terms of degree 2 (d - 1) , so the model describes interacting rather than free fermions. It is an open problem whether or not these models of interacting fermions can in principle be free fermionized through some still undiscovered algebraic method, but it is widely believed that this goal is mathematically impossible. [ABSTRACT FROM AUTHOR]

Very recently, Baruah et al. refined a result of Andrews and Newman on the sum of minimal excludants over all the partitions of a positive integer n by establishing the generating functions of two functions σomex(n) and σemex(n) which denote the sum of odd minimal excludants and the sum of even minimal excludants, respectively. They proved some congruences on σomex(n) and σemex(n) modulo 4 and 8 and posed a conjecture on σomex(n) and σemex(n) at the end of their paper. In this paper, we confirm this conjecture by using theta function identities. [ABSTRACT FROM AUTHOR]

Let Y be a random variable whose moment generating function exists in some neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Whitney numbers of the second kind and those of the degenerate Dowling polynomials, namely, the probabilistic degenerate Whitney numbers of the second kind associated with Y$$ Y $$ and the probabilistic degenerate Dowling polynomials associated with Y$$ Y $$. We derive some properties, explicit expressions, certain identities, recurrence relations and generating functions for those numbers and polynomials. In addition, we investigate their generalizations, namely, the probabilistic degenerate r$$ r $$‐Whitney numbers of the second kind associated with Y$$ Y $$ and the probabilistic degenerate r$$ r $$‐Dowling polynomials associated with Y$$ Y $$, and get similar results to the aforementioned numbers and polynomials. [ABSTRACT FROM AUTHOR]

The numerical method developed in Nour and Zeidan (IEEE Control Syst. Lett. 6:1190-1195, 2022) via the exponential penalization technique for optimal control problems involving sweeping processes with sweeping set C generated by onesmooth function, is generalized in this paper to the case where C is nonsmooth. That is, C is the intersection of a finite number (greater than one) of sublevel sets of smooth functions. The change from one to greater than one generating smooth functions is quite challenging. Indeed, while in the latter case C could be reformulated as being generated by one function, however, this function is only Lipschitz, and hence, the method established for one generating smooth function is not applicable to this framework. Therefore, this general setting requires a new approach, which represents the novelty of this paper. [ABSTRACT FROM AUTHOR]

Nowadays, efficient spectrum usage is one of the most important design principles to take into account in wireless communications due to the exponential growth of mobile devices. In that sense, solutions such as Non-Orthogonal Multiple Access (NOMA) and cognitive radio (CR) have been proposed. In essence, NOMA allows some interference level by using non-orthogonal resource allocation with a tolerable increase in receiver complexity employing successive interference cancellation (SIC). In this work, a novel mathematical model of teletraffic for users performing accessment, simultaneously, by means of Orthogonal Multiple Access (OMA) and NOMA, is developed using a Markovian process that considers bursts of arrivals to model the access schemes. This novel procedure implies a closed-form solution of the proposed system compared to other works where these parameters are estimated assuming the moment generating function obtained with approximation models. The model is validated with a discrete event simulator, considering different scenarios and simulation conditions. The simulation results are in agreement with the mathematical solution proposed. [ABSTRACT FROM AUTHOR]

This study introduces two new sequences: the incomplete Edouard and the incomplete Edouard–Lucas numbers. In addition, we establish some of the properties, identities, and recurrence relations of these sequences. The relations of these new sequences with balancing, Lucas-balancing, incomplete balancing, and incomplete Lucas-balancing numbers are explored, and some new identities are provided. Moreover, the functions for generating the incomplete Edouard and incomplete Edouard–Lucas numbers are stated. [ABSTRACT FROM AUTHOR]

Semantic segmentation often suffers from class imbalance, where the label ratio for each class in the dataset is not uniform. Recent studies have addressed the issue of class imbalance in semantic segmentation by leveraging the neural collapse phenomenon in conjunction with an Equiangular Tight Frame (ETF). While the use of ETF aids in enhancing the discriminability of minor classes, class correlation is another crucial factor that must be taken into account. However, managing the balance between class correlation and discrimination through neural collapse remains challenging, as these properties inherently conflict with one another. Moreover, this control is established during the training stage, resulting in a fixed classifier. There is no guarantee that this classifier will consistently perform well with different input images. To address this problem, we propose an Equiangular Tight Frame Transformer (ETFT), a transformer-based model that jointly processes the features and classifier using ETF structure, and dynamically generates the classifier as a function of the input for imbalanced semantic segmentation. Specifically, the classifier initialized with the ETF structure is jointly processed with the input patch tokens during the attention process. As a result, the transformed patch tokens, aided by the ETF structure, achieve discriminability between classes while preserving contextual correlation. The classifier, initially structured as an ETF, is adjusted to incorporate the correlation information, benefiting from the attention mechanism. Furthermore, the learned classifier is combined with the fixed ETF classifier, leveraging the advantages of both. Extensive experiments demonstrate that the proposed method outperforms state-of-the-art methods for imbalanced semantic segmentation on both the ADE20K and Cityscapes datasets. [ABSTRACT FROM AUTHOR]

It is known that the following five counting problems lead to the same integer sequence f t (n) : the number of nonequivalent compact Huffman codes of length n over an alphabet of t letters, the number of "nonequivalent" complete rooted t-ary trees (level-greedy trees) with n leaves, the number of "proper" words (in the sense of Even and Lempel), the number of bounded degree sequences (in the sense of Komlós, Moser, and Nemetz), and the number of ways of writing 1 = 1 t x 1 + ⋯ + 1 t x n with integers 0 ≤ x 1 ≤ x 2 ≤ ⋯ ≤ x n . In this work, we show that one can compute this sequence for all n < N with essentially one power series division. In total we need at most N 1 + ε additions and multiplications of integers of cN bits (for a positive constant c < 1 depending on t only) or N 2 + ε bit operations, respectively, for any ε > 0 . This improves an earlier bound by Even and Lempel who needed O (N 3) operations in the integer ring or O (N 4) bit operations, respectively. [ABSTRACT FROM AUTHOR]

Multiplication by a given modular form can be viewed as a linear map on the space of modular forms. By computing its adjoint operator, one can obtain certain cusp forms whose Fourier coefficients are special values of Dirichlet series of Rankin-Selberg type associated to modular forms. We generalize this idea to the space of almost holomorphic modular forms with some cuspidal conditions. We prove that the generating function of special values of the Dirichlet series at certain points is a quasi-modular form. [ABSTRACT FROM AUTHOR]

In this article, we study the M/M/1 queueing systems with negative customers and unreliable repairers. The arrival of a negative customer causes the failure of the server, and the server is repaired immediately. The repairers may successfully repair the server with probability p, and the server continues to serve customers in the system. Otherwise, once the repair fails, the system will be cleared and all customers are forced to leave the system. By analyzing the quasi-birth-and-death process and using the probability generating function method, we obtain the steady-state probability and some performance measures of the system. Then, based on the reward-cost structure, we discuss the strategic behavior of customers and consider the equilibrium strategy. Finally, the effects of system parameters on the performance measures, individual benefit, and social benefit are analyzed by numerical examples. [ABSTRACT FROM AUTHOR]

We prove that for any graph G of maximum degree at most Δ, the zeros of its chromatic polynomial χ G (x) (in C) lie inside the disc of radius 5.94Δ centered at 0. This improves on the previously best known bound of approximately 6.91Δ. We also obtain improved bounds for graphs of high girth. We prove that for every g there is a constant K g such that for any graph G of maximum degree at most Δ and girth at least g , the zeros of its chromatic polynomial χ G (x) lie inside the disc of radius K g Δ centered at 0, where K g is the solution to a certain optimization problem. In particular, K g < 5 when g ≥ 5 and K g < 4 when g ≥ 25 and K g tends to approximately 3.86 as g → ∞. Key to the proof is a classical theorem of Whitney which allows us to relate the chromatic polynomial of a graph G to the generating function of so-called broken-circuit-free forests in G. We also establish a zero-free disc for the generating function of all forests in G (aka the partition function of the arboreal gas) which may be of independent interest. [ABSTRACT FROM AUTHOR]

In this article, we study hook lengths of ordinary partitions and t -regular partitions. We establish hook length biases for the ordinary partitions and motivated by them we find a few interesting hook length biases in 2-regular partitions. For a positive integer k , let p (k) (n) denote the number of hooks of length k in all the partitions of n. We prove that p (k) (n) ≥ p (k + 1) (n) for all n ≥ 0 and n ≠ k + 1 ; and p (k) (k + 1) − p (k + 1) (k + 1) = − 1 for k ≥ 2. For integers t ≥ 2 and k ≥ 1 , let b t , k (n) denote the number of hooks of length k in all the t -regular partitions of n. We find generating functions of b t , k (n) for certain values of t and k. Exploring hook length biases for b t , k (n) , we observe that in certain cases biases are opposite to the biases for ordinary partitions. We prove that b 2 , 2 (n) ≥ b 2 , 1 (n) for all n > 4 , whereas b 2 , 2 (n) ≥ b 2 , 3 (n) for all n ≥ 0. We also propose some conjectures on biases among b t , k (n). [ABSTRACT FROM AUTHOR]

This manuscript proposed a hybrid system for enhancing the control strategy of a unified power quality conditioner connected to a wind energy conversion system. The proposed method is combined with honey badger algorithm (HBA) and reptile search algorithm (RSA). Therefore, it is known as the Enhanced HBA (EnHBA) technique. The key aim of the EnHBA technique is to alleviating the PQ issue exhibited in the WECS. The EnHBA approach is utilized in the non‐linear load condition to find the best solutions from the available searching space in light of the goal function and generates the output. During the load variation conditions the EnHBA technique manages the loss of power, total harmonic distortion (THD), and voltage instability issue respectively. In this way, the PQ system performances improved and moreover, the various qualities decreased with the support of the EnHBA method. The EnHBA techniques' performance is validated through the MATLAB platform and the implementation is calculated with the existing techniques. The method EnHBA technique displays better outcomes in all approaches like, particle swarm optimization, whale optimization algorithm and singular spectrum analysis (SSA). The proposed method's voltage sag and swell are lowered to 14% and 15%, respectively. The THD of the En HBA method is 10%, which is lesser than other existing PSO, WOA, and SSA methods. [ABSTRACT FROM AUTHOR]

Although flow mixing and cooling can be greatly enhanced when considering the use of fluidic oscillators (FOs), they are more commonly employed in active flow control (AFC) applications where the injected pulsating flow interacts with the boundary layer, usually in order to delay its separation. In fact, prior to any FO implementation in a given application, it is essential to study the range of frequencies and amplitudes it can generate as a function of the incoming mass flow and its dimensions. This is what is being performed in the present manuscript for a rather novel FO configuration. A numerical study of a standard three-dimensional (3D) FO configuration, and also using a two-dimensional (2D) approach, is initially presented. After comparing the 3D and the 2D results and analyzing the main differences, we modified some of the internal dimensions of the FO in order to evaluate the variation in its dynamic performance. The present results clarify which internal dimensional modifications are more effective in generating larger output frequencies and velocity field variations. Care is taken to analyze the origin of self-sustained oscillations. This paper links, for the first time, the origin of the pressure force oscillations at the feedback channel's outlet, with the interaction of the mixing chamber central jet and the reverse feedback channel flow at the mixing chamber's converging walls. A novel equation relating the FO outlet mass flow frequency with the time-averaged FC reverse flow is presented and discussed. In fact, the present study needs to be seen as the continuation of a former one, recently published by authors, where the effects of several Reynolds numbers as well as some different internal dimensions were considered. [ABSTRACT FROM AUTHOR]

In this paper, we describe a systematic way of obtaining the exact generating functions for p ¯ (2 n) , p ¯ (4 n) (first proved by Fortin et al.), p ¯ (8 n) , p ¯ (16 n) , etc. where p ¯ (n) denotes the number of overpartitions of n. We further establish several new infinite families of congruences modulo 2 4 and 2 5 for p ¯ (n) . For example, we prove that for all n , α , β ≥ 0 and primes p ≥ 5 , p ¯ 3 4 α + 1 p 2 β + 1 24 p n + 24 j + 7 p ≡ 0 (mod 2 5) and p ¯ 3 2 α + 1 (24 n + 23) ≡ 0 (mod 2 5) , where ( - 6 p) = - 1 and 1 ≤ j ≤ p - 1 . The last congruence was proved by Xiong (Int J Number Theory 12:1195–1208, 2016) for modulo 2 4 . [ABSTRACT FROM AUTHOR]

A partition is said to be ℓ-regular if none of its parts is a multiple of ℓ. Let b5′(n) denote the number of 5-regular partitions into distinct parts (equivalently, into odd parts) of n. This function has also close connections to representation theory and combinatorics. In this paper, we study arithmetic properties of b5′(n). We provide full characterization of the parity of b5′(2n + 1), present several congruences modulo 4, and prove that the generating function of the sequence (b5′(5n + 1)) is lacunary modulo any arbitrary positive powers of 5. [ABSTRACT FROM AUTHOR]

Cell‐based microarrays are widely used in the fields of drug discovery and toxicology. Precise gradient generation and automated drug feeding are essential for high‐throughput screening of live cells in tiny droplets. However, most existing technologies either require sophisticated robotic equipment or cause mechanical/physiological interference with cells. Here, a heterogeneous organohydrogel is presented for automated gradient drug feeding, while ensuring minimal interference with cells. The heterogeneous organohydrogel comprises three crucial components. The bottom surface can automatically generate gradients functioning as a gradient generator, the organohydrogel bulk allows unidirectional transport of drugs without backflow, and the top surface with hydrophilic arrays can firmly anchor the cell‐based droplet array to evaluate the concentration‐dependent bioeffects of drugs accurately. Such a unique structure enables universal screening of different cell types and drugs dissolved in different solvents, requiring neither additional accessories nor arduous drug functionalization. The heterogeneous organohydrogel with unprecedented automation and non‐interference possesses the enormous potential to be a next‐generation platform for drug screening. [ABSTRACT FROM AUTHOR]

We consider a one-dimensional variant of a recently introduced settlement planning problem in which houses can be built on finite portions of the rectangular integer lattice subject to certain requirements on the amount of insolation they receive. In our model, each house occupies a unit square on a 1 × n strip, with the restriction that at least one of the neighboring squares must be free. We are interested mostly in situations in which no further building is possible, i.e. in maximal configurations of houses in the strip. We reinterpret the problem as a problem of restricted packing of vertices in a path graph and then apply the transfer matrix method in order to compute the bivariate generating functions for the sequences enumerating all maximal configurations of a given length with respect to the number of houses. This allows us to determine the asymptotic behavior of the enumerating sequences and to compute some interesting statistics. Along the way, we establish close connections between our maximal configurations and several other types of combinatorial objects, including restricted permutations and walks on certain small oriented graphs. We then generalize our results in several directions by considering multi-story houses, by varying the insolation restrictions, and, finally, by considering strips of width 2 and 3. At the end we comment on several possible directions of future research. [ABSTRACT FROM AUTHOR]

The Priority Arbiter-based Physical Unclonable Function (PA-PUF) is a one-way function implemented in hardware, where output or response bits, corresponding to a given set of challenge bits, are influenced by the device-specific parameters. An n -length PA-PUF can be represented as an n -variable Boolean function. The research we conducted demonstrates the exploration of Boolean functions obtained by implementing a PA-PUF construction with randomly selected delay parameters. We observe that the set of Boolean functions generated from PA-PUF is significantly larger than the set of Boolean functions generated from classical Arbiter-based PUF. Further, we look into the bias estimation of the response bit generated from PA-PUF towards the impact of changing specific bits in the challenge input. Finally, we perform a comparative analysis on PA-PUF to study its cryptographic properties and a detailed analysis of the machine learning attacks. [ABSTRACT FROM AUTHOR]

An alternative closed‐form expression for the marginal joint probability distribution of item scores under the random effects generalized partial credit model is presented. The closed‐form expression involves a cumulant generating function and is therefore subjected to convexity constraints. As a consequence, complicated moment inequalities are taken into account in maximum likelihood estimation of the parameters of the model, so that the estimation solution is always proper. Another important favorable consequence is that the likelihood function has a single local extreme point, the global maximum. Furthermore, attention is paid to expected a posteriori person parameter estimation, generalizations of the model, and testing the goodness‐of‐fit of the model. Procedures proposed are demonstrated in an illustrative example. [ABSTRACT FROM AUTHOR]

In this paper, we attempt to use the Dunkl analog to study the convergence properties of q-Phillips operators by using the q-Appell polynomials. By applying the new sequences of continuous functions ν s , q (z) = (z − 1 2 [ s ] q ) ϱ on [ 0 , ∞) , we construct an improved version of the q-Phillips operators. We calculate the qualitative outcomes in weighted Korovkin spaces to better understand the Phillips operators' uniform convergence results. We obtain the approximation properties by use of the modulus of continuity and functions belonging to the Lipschitz class. Moreover, we give some direct theorems for the function belonging to Peetre's K-functional. [ABSTRACT FROM AUTHOR]

AbstractThis paper characterises the shape of the Young diagram associated with integer partitions in terms of two newly invented statistics which are defined in the text: namely interior vertices and horizontal edges. Generating functions and associated asymptotic results are developed for both interior vertices and horizontal edges. [ABSTRACT FROM AUTHOR]

We introduce a new flexible count distribution by combining Bernoulli and Poisson moment exponential (PMEx) distributions. The new model named the Bernoulli PMEx distribution. Some mathematical properties are studied, including the hazard rate function, moments, moment generating function, probability generating function, and dispersion index. A count regression model is also proposed based on this distribution. The maximum likelihood estimation method is used to estimate the model parameters. In the end, three datasets from different fields are utilized for application purposes. The findings show that the new model efficiently analyzed these datasets as compared to Poisson, discrete Pareto, discrete Rayleigh, discrete Burr‐Hatke, and discrete inverted Topp–Leone distributions. [ABSTRACT FROM AUTHOR]

We examine the diffusive dynamics of a lattice random walk subject to resetting in a one-dimensional spatially heterogeneous environment composed of two media separated by an interface. At random times the walker may reset its position to the interface, but only when in the left medium. In addition the spatial heterogeneity results from having unequal diffusivities and biases in the two media. We construct the Master equation for the dynamics of the walker occupation probability in unbounded space, solve it exactly in terms of generating functions, and analyse the dynamics of the first and second moment. Making use of the closed form solution in the unbounded case, we build the analytic solution of the Master equation in finite and semi-infinite domains. By bounding the space on the right with a reflecting boundary we study the first-passage dynamics to a single fully absorbing target placed in the left medium away from the interface. As reset strongly increases the time to reach the target, we find that the first-passage dynamics enter the motion-limited regime even for relative small resetting probability. We also identify a surprising non-monotonic dependence of the first-passage probability mode as a function of the bias. By deriving an analytic expression for the mean first-passage time, we show when its value is independent of the diffusivity and bias in the left medium, uncovering another example of the so-called mean disorder indifference phenomenon. [ABSTRACT FROM AUTHOR]

Stochastic population models with mild catastrophes have gained much attention in recent years due to their wide application in a variety of areas including computer-communications systems. This article considers a population model in which both the arrival process of individuals and catastrophes occur as per the Markovian arrival process (MAP) and are independent of each other. The killing mechanism takes place according to the binomial distribution. The steady-state analysis of the model is carried out using the vector generating function approach and the population size distributions at an arbitrary, post-catastrophe, and pre-arrival epochs are presented in terms of the roots of the characteristic equation. Several performance measures of the system are studied in detail, and the impact of critical parameters is duly investigated. [ABSTRACT FROM AUTHOR]

It is known that the generating function associated with the enumeration of non-backtracking walks on finite graphs is a rational matrix-valued function of the parameter; such function is also closely related to graph-theoretical results such as Ihara's theorem and the zeta function on graphs. In Grindrod et al. [13] , the radius of convergence of the generating function was studied for simple (i.e., undirected, unweighted and with no loops) graphs, and shown to depend on the number of cycles in the graph. In this paper, we use technologies from the theory of polynomial and rational matrices to greatly extend these results by studying the radius of convergence of the corresponding generating function for general, possibly directed and/or weighted, graphs. We give an analogous characterization of the radius of convergence for directed (unweighted or weighted) graphs, showing that it depends on the number of cycles in the undirectization of the graph. We also consider backtrack-downweighted walks on unweighted digraphs, and we prove a version of Ihara's theorem in that case. Finally, for weighted directed graphs, we provide for the first time an exact formula for the radius of convergence, improving a previous result that exhibited a lower bound, and we also prove a version of Ihara's theorem. [ABSTRACT FROM AUTHOR]

This paper presents a sensitivity analysis to assess the impact of random rail unevenness profiles on the generation of ground-borne vibrations. The random profiles are generated from a power spectral density function, assuming that the uneven rail surface is governed by a stationary Gaussian random process in space. Different proposals are employed to generate these profiles. A previously validated PiP model is used to perform a set of parametric studies, involving the dynamic simulation of a train–track–tunnel–ground system. It was found that the number of harmonics in generating ground-borne vibrations has a residual impact on the evaluated vibration levels. The main differences observed, although not significant, are attributed to the stochastic nature of the rail unevenness profile. More critically, it is important to highlight that different existing approaches for generating the PSD function have a pronounced impact on the evaluated vibration levels. [ABSTRACT FROM AUTHOR]

Background: Network meta-analysis is developed to compare all available treatments; therefore it enriches evidence for clinical decision-making, offering insights into treatment effectiveness and safety when faced with multiple options. However, the complexity and numerous treatment comparisons in network meta-analysis can challenge healthcare providers and patients. The purpose of this study aimed to introduce a graphic design to present complex rankings of multiple interventions comprehensively. Methods: Our team members developed a "beading plot" to summary probability of achieving the best treatment (P-best) and global metrics including surface under the cumulative ranking curve (SUCRA) and P-score. Implemented via the "rankinma" R package, this tool summarizes rankings across diverse outcomes in network meta-analyses, and the package received an official release on the Comprehensive R Archive Network (CRAN). It includes the 'PlotBead()' function for generating beading plots, which represent treatment rankings among various outcomes. Results: Beading plot has been designed based on number line plot, which effectively displays collective metrics for each treatment across various outcomes. Order on the -axis is derived from ranking metrics like P-best, SUCRA, and P-score. Continuous lines represent outcomes, and color-coded beads signify treatments. Conclusion: The beading plot is a valuable graphic that intuitively displays treatment rankings across diverse outcomes, enhancing reader-friendliness and aiding decision-making in complex network evidence scenarios. While empowering clinicians and patients to identify optimal treatments, it should be used cautiously, alongside an assessment of the overall evidence certainty. [ABSTRACT FROM AUTHOR]

We report an in-depth study of the reductive activation of O2 by the nonheme [FeII(L 25)(MeCN)]2+ complex carried out by cyclic voltammetry. Experimental evidence is obtained for the slow coordination of dioxygen to the ferrous center yielding an FeII/O2 adduct with a strong FeII–O2 character rather than an FeIII–superoxo one. Electron injection in the FeII–O2 species occurs at a potential of ca. −700 mV vs. SCE, i.e. 200 mV above the O2 to O2˙− reduction, leading to the formation of a FeIII–peroxo intermediate and then FeIII–hydroperoxo upon protonation by residual water. The experimental CVs recorded at variable scan rate or variable FeII concentration are well simulated taking into account a detailed mechanism initiated by the competitive reduction of O2 and the FeII–O2 adduct. Analysis of the concentration of the reaction intermediates generated as a function of the applied potential indicates that the FeIII–peroxo intermediate significantly accumulates at a potential of −650 mV. Oxidative bromination of anisole is assayed under electrolytic conditions at this potential to yield bromoanisole products. The low faradaic yields observed reveal that deleterious reactions such as direct reduction of reaction intermediates likely occur. Based on the detailed mechanism elucidated, a number of improvements to achieve more efficient catalytic reactions can be proposed. [ABSTRACT FROM AUTHOR]

Real-world complex systems demonstrated temporal features, i.e., the network topology varies with time and should be described as temporal networks since the traditional static networks cannot accurately characterize. To describe the deliberate attack events in the temporal networks, we propose an activity-based targeted attack on the activity-driven network to investigate temporal networks' temporal percolation properties and resilience. Based on the node activity and network mapping framework, the giant component and temporal percolation threshold are solved according to percolation theory and generating function. The theoretical results coincide with the simulation results near the thresholds. We find that targeted attacks can affect the temporal network, while random attacks cannot. As the probability of a highly active node being deleted increases, the temporal percolation threshold increases, and the giant component increases, thus enhancing robustness. When the network's activity distribution is extremely heterogeneous, network robustness decreases consequently. These findings help us to analyze and understand real-world temporal networks. [ABSTRACT FROM AUTHOR]

In this paper, we consider constructions of first derivative approximations using the generating function. The weights of the approximations contain the powers of a parameter whose modulus is less than one. The values of the initial weights are determined, and the convergence and order of the approximations are proved. The paper discusses applications of approximations of the first derivative for the numerical solution of ordinary and partial differential equations and proposes an algorithm for fast computation of the numerical solution. Proofs of the convergence and accuracy of the numerical solutions are presented and the performance of the numerical methods considered is compared with the Euler method. The main goal of constructing approximations for integer-order derivatives of this type is their application in deriving high-order approximations for fractional derivatives, whose weights have specific properties. The paper proposes the construction of an approximation for the fractional derivative and its application for numerically solving fractional differential equations. The theoretical results for the accuracy and order of the numerical methods are confirmed by the experimental results presented in the paper. [ABSTRACT FROM AUTHOR]

In recent decades, the study of discrete distributions has received increasing attention in the field of statistics, mainly because discrete distributions can model a wide range of count data. One common distribution used for modeling count data, for instance, is the negative binomial distribution (NBD), which performs well with over-dispersed data. In this paper, a new count distribution is introduced, called the conflation of negative binomial and logarithmic distributions, which is formed by conflating the negative binomial and logarithmic distributions, resulting in a distribution that possesses some of the properties of negative binomial and logarithmic distributions. The distribution has two parameters and is verified by a positive integer. Two modifications are proposed to the distribution, which includes zero as a support point. The new distribution is valuable from a theoretical perspective since it is a member of the weighted negative binomial distribution family. In addition, the distribution differs from the NBD in the sense that the probability of lower counts is inflated. This study discusses the characteristics of the proposed distribution and its modified versions, such as moments, probability generating functions, likelihood stochastic ordering, log-concavity, and unimodality properties. Real-world data are used to evaluate the performance of the proposed models against other models. All computations shown in this paper were produced using the R programming language. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new Orlicz function, namely a b-Orlicz function, which is not necessarily convex. The Orlicz spaces L Φ generated by the b-Orlicz function Φ equipped with a Luxemburg quasi-norm contain both classical spaces L p (p ≥ 1) and L p (0 < p < 1) . The Orlicz spaces L Φ are quasi-Banach spaces. Some basic properties in quasi-normed Orlicz spaces are discussed, and the criteria that a quasi-normed Orlicz space is strictly monotonic and lower (upper) locally uniformly monotonic are given. [ABSTRACT FROM AUTHOR]

In this paper, by using q-integers and higher-order generalized Fibonacci numbers, we define the higher-order generalized Fibonacci quaternions with q-integer components. We give some special cases of these newly established quaternions. This article examines q-calculus and quaternions together. We obtain a Binet-like formula, some new identities, a generating function, a recurrence relation, an exponential generating function, and sum properties of quaternions with quantum integer coefficients. In addition, we obtain some new identities for these types of quaternions by using three new special matrices. [ABSTRACT FROM AUTHOR]

The present article proposes a novel hybrid approach for addressing the synthesis problem of rectangular planar arrays under multiple constraints, through joint optimization of the weight function and the improved grey wolf optimization (IGWO) algorithm. Firstly, the grey wolf optimization (GWO) algorithm is improved by using tent chaotic mapping, nonlinear convergence factor, dominant wolf dynamic belief strategy, and opposition‐based learning strategy to increase the population diversity and the ability to jump out of the local optimum. Secondly, the array elements are weighted using the weight function to generate the position distribution matrix, which reduces the thinned matrix optimization time and improves the optimization efficiency. Finally, the position distribution matrix is used to generate the thinned array, and the IGWO algorithm is applied to perform the sparse optimization with multiple constraints. The effectiveness of the method is verified through numerical simulation and full‐wave simulation experiments, demonstrating its capability to enhance array antenna performance and reduce peak sidelobe level (PSLL). These experimental results hold significant engineering implications and provide valuable references for addressing the array distribution problem under multiple constraints. [ABSTRACT FROM AUTHOR]

Navigation safety is critical for many autonomous systems such as self-driving vehicles in an urban environment. It requires an explicit consideration of boundary constraints that describe the borders of any infeasible, non-navigable, or unsafe regions. We propose a principled boundary-aware safe stochastic planning framework with promising results. Our method generates a value function that can strictly distinguish the state values between free (safe) and non-navigable (boundary) spaces in the continuous state, naturally leading to a safe boundary-aware policy. At the core of our solution lies a seamless integration of finite elements and kernel-based functions, where the finite elements allow us to characterize safety-critical states' borders accurately, and the kernel-based function speeds up computation for the non-safety-critical states. The proposed method was evaluated through extensive simulations and demonstrated safe navigation behaviors in mobile navigation tasks. Additionally, we demonstrate that our approach can maneuver safely and efficiently in cluttered real-world environments using a ground vehicle with strong external disturbances, such as navigating on a slippery floor and against external human intervention. [ABSTRACT FROM AUTHOR]

Denote by N ℓ (n) the number of ℓ -tuples of elements in the symmetric group S n with commuting components, normalized by the order of S n . In this paper, we prove asymptotic formulas for N ℓ (n) . In addition, general criteria for log-concavity are shown, which can be applied to N ℓ (n) among other examples. Moreover, we obtain a Bessenrodt-Ono type theorem which gives an inequality of the form c (a) c (b) > c (a + b) for certain families of sequences c(n). [ABSTRACT FROM AUTHOR]

In this paper, we introduce an R package EATME, which is known as Exponentially weighted moving average (EWMA) control chart with Adjustments To Measurement Error. The main purpose of this package is to correct for measurement error effects in continuous or binary random variables and develop the corrected control charts based on the EWMA statistic. In addition, the corrected control charts can detect out-of-control process accurately. The package contains a function to generate synthetic data and includes functions to determine the reasonable coefficient of control limit as well as estimate average run length. Moreover, for the visualization, we also provide the control charts to show the monitoring of in-control and out-of-control process. Finally, the functions in this package are clearly demonstrated, and numerical studies show the validity of the package. [ABSTRACT FROM AUTHOR]

Many papers have been recently devoted to the study of the radial behavior as z → 1 − of transcendental r-Mahler functions holomorphic in the open unit disk. In particular, Bell and Coons showed in 2017 that, in a generic sense, r-Mahler functions behave like (1 + o (1)) C (z) / (1 − z) ρ for some ρ ∈ ℂ and C (z) is a real analytic function of z ∈ (0 , 1) such that C (z) = C (z r). They did not provide a formula for C (z) which was made explicit only in a few examples of r-Mahler functions of orders 1 and 2, and for specific values of r. In this paper, we first provide an explicit expression of C (z) as an exponential of a Fourier series in the variable log log (1 / z) / log (r) for every r-Mahler function of order 1. Then, extending to a large setting a method introduced by Brent–Coons–Zudilin in 2016 to compute C (z) associated to the Dilcher–Stolarsky function (a 4-Mahler function of order 2 in ℚ [ [ z ] ]), we provide an explicit expression of C (z) for every r-Mahler function of order 2 under mild assumptions on the coefficients in ℝ (z) of the underlying r-Mahler equations. This applies in particular to the generating function of the Baum–Sweet sequence. We do the same for r-Mahler functions solutions of inhomogeneous Mahler equations of order 1. [ABSTRACT FROM AUTHOR]

The causal shift-invariant convolution is studied from the point of view of inversion. Abel's algorithm, used in the tautochrone problem, is considered and Sonin's existence condition is deduced. To generate pairs of functions verifying Sonin's condition, the class of Mittag-Leffler type functions is used. In particular, functions that are impulse responses of ARMA(N,N) systems serve as a basis. The possible use of Abel's procedure as a support for introducing generalized fractional derivatives is evaluated. [ABSTRACT FROM AUTHOR]

AbstractInversion sequences of length n are positive integer sequences e1 e2 …en such that 1 ≤ ei ≤ i for all 1 ≤ i ≤ n. These sequences are in bijection with the permutations of [n]. This paper focuses on the polyomino or barpgraph representation of the inversion sequences. More precisely, we study the distribution of lattice points on these polyominoes. We find the generating functions respect to the length, the number of interior vertices, corners, and vertices of a given degree. We also give simple explicit formulas for the total values of these parameters over all polyominoes of inversion sequences of length n. Throughout this work, we use symbolic computer algebra to facilitate the computations. [ABSTRACT FROM AUTHOR]