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The multi-objective optimization is to optimize several objective functions over a common feasible set. Because the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies multi-objective optimization problems that are given by polynomial functions. First, we study the geometry for (weakly) Pareto values and represent Pareto front as the boundary of a convex set. Linear scalarization problems (LSPs) and Chebyshev scalarization problems (CSPs) are typical approaches for getting (weakly) Pareto points. For LSPs, we show how to use tight relaxations to solve them and how to detect existence or nonexistence of proper weights. For CSPs, we show how to solve them by moment relaxations. Moreover, we show how to check whether a given point is a (weakly) Pareto point or not and how to detect existence or nonexistence of (weakly) Pareto points. We also study how to detect unboundedness of polynomial optimization, which is used to detect nonexistence of proper weights or (weakly) Pareto points. Funding: J. Nie is partially supported by the National Science Foundation [Grant DMS-2110780]. [ABSTRACT FROM AUTHOR]

Electrocardiogram (ECG) signals generate massive volume of digital data, so they need to be suitably compressed for efficient transmission and storage. Polynomial approximations and polynomial interpolation have been used for ECG data compression where the data signal is described by polynomial coefficients only. Here, we propose approximation using hermite polynomial interpolation with chebyshev nodes for compressing ECG signals that consequently denoises them too. Recommended algorithm is applied on various ECG signals taken from MIT-BIH arrhythmia database without any additional noise as the signals are already contaminated with noise. Performance of the proposed algorithm is evaluated using various performance metrics and compared with some recent compression techniques. Experimental results prove that the proposed method efficiently compresses the ECG signals while preserving the minute details of important morphological features of ECG signal required for clinical diagnosis. [ABSTRACT FROM AUTHOR]

In 1939 Turán raised the question about lower estimations of the maximum norm of the derivatives of a polynomial p of maximum norm 1 on the compact set K of the complex plain under the normalization condition that the zeroes of p in question all lie in K. Turán studied the problem for the interval I and the unit disk D and found that with n : = deg p tending to infinity, the precise growth order of the minimal possible derivative norm (oscillation order) is n for I and n for D. Erőd continued the work of Turán considering other domains. Finally, in 2006, Halász and Révész proved that the growth of the minimal possible maximal norm of the derivative is of order n for all compact convex domains. Although Turán himself gave comments about the above oscillation question in L q norms, till recently results were known only for D and I. Recently, we have found order n lower estimations for several general classes of compact convex domains, and proved that in L q norm the oscillation order is at least n / log n for all compact convex domains. In the present paper we prove that the oscillation order is not greater than n for all compact (not necessarily convex) domains K and L q norm with respect to any measure supported on more than two points on K. [ABSTRACT FROM AUTHOR]

AbstractAn attempt has been made to investigate the cracked composite medium with thermally conducting multiple cracks at its interface of the dissimilar orthotropic media subjected to thermal and mechanical loadings. The present article examines the governing equations, the associated differential constraints and boundary conditions those govern the temperature field and stress field. Fourier integral transforms, together with their corresponding inverses, have been employed to convert the singular integral equations into a set of linear equations by using the concept of orthogonality and completeness. The numerical technique, namely the Schmidt method, which employs a polynomial expansion of the unknown functions, is used to solve algebraic equations to determine the desired temperature and stress fields. The semi-analytical findings of the expressions for heat flux intensity factor (HFIF), stress intensity factor (SIF), and crack displacements have been mentioned in the article. Both mode-I and II types of cracks have been studied to investigate the effect of thermal conductivity. Detailed graphical representations effectively illustrate the numerical results and the interrelations between crack lengths, bonded strip width, and the partial conductivity coefficient of the crack surface. As the thermal conductivity coefficient increases, the temperature difference tends to zero. The results reveal that an increase in thermal conductivity decreases the SIFs. [ABSTRACT FROM AUTHOR]

Since all training data is interpolated, interpolating classifiers have zero training error. However, recent work provides compelling reasons to investigate these classifiers, including their significance for ensemble methods. Interpolation kernel machines, which belong to the class of interpolating classifiers, are capable of good generalization and have proven to be an effective substitute for support vector machines, particularly for graph classification. In this work, we further enhance their performance by studying multiple kernel learning. To this end, we propose a general scheme of polynomial combined kernel functions, employing both quadratic and cubic kernel combinations in our experimental work. Our findings demonstrate that this approach improves performance compared to individual graph kernels. Our work supports the use of interpolation kernel machines as an alternative to support vector machines, thereby contributing to greater methodological diversity. • Enhanced performance of interpolation kernel machines (a good alternative to SVMs) • General framework of polynomial combined kernel functions for performance enhancement • Experimental results demonstrate the performance improvement potential of our approach [ABSTRACT FROM AUTHOR]

Analysis of ECG for detecting different cardiovascular diseases requires real-time ECG signals which are acquired by attaching electrodes to the body. During the ECG signal acquisition, noise gets added to original signal, which might distort the morphological features, like amplitude, segment length and the interval aspects of the ECG leading to a false diagnosis and improper interpretation of cardiovascular disease. Therefore, ECG denoising is imperative. Here, we propose approximation using hermite polynomial interpolation with chebyshev nodes for denoising electrocardiogram signals that consequently compresses them too. Recommended algorithm is applied on twelve ECG signals taken from MIT-BIH arrhythmia database without any additional noise as the signals are already corrupted with noise. Performance of the proposed algorithm is evaluated using various performance metrics. Experimental results prove that the proposed method efficiently denoises electrocardiogram signals and gives quite encouraging results when compared with other existing denoising and compression algorithms. [ABSTRACT FROM AUTHOR]

In this research, we attempted to fit a trading system based on polynomial moving regression bands (MRB) to Nasdaq100 stocks from 2017 till the end of March 2024. Since stocks movement does not follow a linear behavior, we used multiple degree polynomial regression models to identify the stocks' trends and two standard deviations from the regression model to generate the trading signals. This way, the MRB was transformed into a momentum indicator designed to identify strong uptrends that can be used by a fully automated trading system. Our results indicate that the behavior of Nasdaq100 stocks can be tracked using all three examined polynomial models and can be traded profitably using fully automated systems based on those models. The best performing model was the model that used a four-degree polynomial MRB achieving the highest average net profit (USD 162.73). Regarding the risks involved, the third model has the lowest loss in dollar value (USD −95.52), and the highest minimum percent of profitable trades (41.51%) and profit factor (0.55) that indicates that this strategy is relatively less risky than the other two strategies. [ABSTRACT FROM AUTHOR]

We present some extensions of Chu's formulas and several striking generalizations of some well-known combinatorial identities. As applications, some new identities on binomial sums, harmonic numbers, and the generalized harmonic numbers are also derived.

In this study, a broader class of rational functions r(u(z)) of degree mn, where u(z) is a polynomial of degree m is taken into consideration and obtain certain sharp compact generalization of well-known inequalities for rational functions. [ABSTRACT FROM AUTHOR]

Motivated by the relationship between the area of the image of the unit disk under a holomorphic mapping h and that of zh, we study various L2 norms for Tϕ(h), where Tϕ is the Toeplitz operator with symbol ϕ. In Theorem 2.1, given polynomials p and q we find a symbol ϕ such that Tϕ(p) = q. We extend some of our results to the polydisc. [ABSTRACT FROM AUTHOR]

An analog of Smale's well-known mean value conjecture for complex polynomials is considered in the case of finite Blaschke products. [ABSTRACT FROM AUTHOR]

Sharing confidential information is a critical concern in today's world. Secret sharing schemes facilitate the sharing of secrets in a way that ensures only authorized participants (shareholders) can access the secret using their allocated shares. Hierarchical secret sharing schemes (HSSSs) build upon Shamir's scheme by organizing participants into different levels based on priority. Within HSSS, participants at each level can reconstruct the secret if a specified number, denoted as the threshold value (t), or more of them are present. Each level has a predetermined threshold value. If the number of participants falls below the threshold at any level, higher-level participants must be involved in reconstructing the secret at lower levels. Our paper proposes schemes that implement hierarchical access structures and enable the sharing of multiple secrets. Additionally, our proposed scheme includes share verification. We have analyzed potential attacks and demonstrated the scheme's resistance against them. Through security analysis and comparison with existing schemes, we highlight the novelty and superiority of our proposed approach, contributing to advancements in secure information-sharing practices. [ABSTRACT FROM AUTHOR]

Beijing is a city on the North China Plain with severe land subsidence. In recent years, Beijing has implemented effective measures to control land subsidence. Since this implementation, the development of time-series land subsidence in Beijing has slowed and has shown nonlinearity. Most previous studies have focused on the linear evolution of land subsidence; the nonlinear evolutionary patterns of land subsidence require further discussion. Therefore, we aimed to identify the evolution of land subsidence in Beijing, based on Envisat ASAR and Radarsat-2 images from 2003 to 2020, using permanent scatterer interferometric synthetic aperture radar (PS-InSAR) and cubic curve polynomial fitting methods. The dates of the extreme and inflection points were identified from the polynomial coefficients. From 2003 to 2020, the subsidence rate reached 138.55 mm/year, and the area with a subsidence rate > 15 mm/year reached 1688.81 km2. The cubic polynomials fit the time-series deformation well, with R2 ranging from 0.86 to 0.99 and the RMSE ranging from 1.97 to 60.28 mm. Furthermore, the subsidence rate at 96.64% of permanent scatterer (PS) points first increased and then decreased. The subsidence rate at 86.58% of the PS points began to decrease from 2010 to 2015; whereas the subsidence rate at 30.51% of the PS point reached a maximum between 2015 and 2019 and then decreased. The cumulative settlement continued to increase at 69.49% of the PS points. These findings imply that groundwater levels are highly correlated with the temporal evolution of subsidence in areas with pattern D (Vs+-, S+), with increasing and then decelerating rates and increasing amounts. In regions with a thickness of compressible clay layer over 210 m, subsidence follows pattern E (Vs+, S+), with increasing rates and amounts. Fractures such as the Gaoliying and Sunhe fractures significantly influence the spatial distribution of subsidence patterns, showing distinct differences on either side. Near the Global Resort Station, pattern E (Vs+, S+) intensifies in subsidence, potentially due to factors like land use changes and construction activities. [ABSTRACT FROM AUTHOR]

With the expansion of network bandwidth and the rise of social networks, image sharing on open networks has become a trend. The ensuing privacy leakage events have aroused widespread concerns. Therefore, image sharing that protects privacy is desired. Progressive Secret Image Sharing (PSIS), a multilevel privacy protection technology for images, offers a promising solution. However, the progressivity of the majority of PSIS schemes depends on the preprocessing of a secret image, which increases the calculation costs. In addition, a block-based PSIS may have information leakage security risks when processing highly confidential images. Many existing PSIS schemes use a single operation to share secret images, which makes the schemes inflexible and limits the application scenarios. Therefore, we propose a PSIS based on Boolean operations and Polynomial interpolations (PSIS-BP). The proposed scheme divides the bit-plane of the pixel into two parts. One part is utilized to perform the Boolean operation, and the other part is used to perform the polynomial interpolation. Different assignment strategies can produce different progressive reconstruction levels and expand the application scenarios of the scheme. Theoretical analyses and experimental results demonstrate that the proposed scheme is secure, low-cost, and flexible. [ABSTRACT FROM AUTHOR]

We consider polynomials f(x1, ..., xn) over a finite filed that satisfy the following condition: the set of solutions of the equation f(x1, ..., xn) = b, where b is some element of the field, coincides with the set of solutions of some system of linear equations over this field. Such polynomials are said to be multiaffine with the right-hand side b (or with respect to b). We describe a number of properties of multiaffine polynomials. Then on the basis of these properties we propose a polynomial algorithm that takes a polynomial over a finite field and an element of the field as an input and decides whether the polynomial is multiaffine with respect to this element. In case of the positive answer the algorithm also outputs a system of linear equations that corresponds to this polynomial. The complexity of the proposed algorithm is the smallest in comparison with other known algorithms that solve this problem. [ABSTRACT FROM AUTHOR]

As an anti-staling agent in bread, the desorption isotherm of polydextrose has not been studied due to a very long equilibrium time. The adsorption and desorption isotherms of five Chinese polydextrose products were measured in the range of 0.1–0.9 aw and 20–35 °C by a dynamic moisture sorption analyzer. The results show that the shape of adsorption and desorption isotherms was similar to that of amorphous lactose. In the range of 0.1–0.8 aw, the hysteresis between desorption and adsorption of polydextrose was significant. The sorption isotherms of polydextrose can be fitted by seven commonly used models, and our developed seven-parameter polynomial, the adsorption equations of generalized D'Arcy and Watt (GDW) and Ferro-Fontan, and desorption equations of polynomial and Peleg, performed well in the range of 0.1–0.9 aw. The hysteresis curves of polydextrose at four temperatures quickly decreased with aw increase at aw ˂ 0.5, andthereafter slowly decreased when aw ≥ 0.5. The polynomial fitting hysteresis curves of polydextrose were divided into three regions: ˂0.2, 0.2–0.7, and 0.71–0.9 aw. The addition of 0–10% polydextrose to rice starch decreased the surface adsorption and bulk absorption during the adsorption and desorption of rice starch, while it increased the water adsorption value at aw ≥ 0.7 due to polydextrose dissolution. DSC analysis showed that polydextrose as a gelling agent inhibited the retrogradation of rice starch, which could be used to maintain the quality of cooked rice. [ABSTRACT FROM AUTHOR]

The multi-degree-of-freedom (multi-DOF) follower may suffer from unwanted vibrations when the cam works at the high speed. The vibrations will cause significant problems of positioning accuracy, noise, wear, forces, and operating costs for the cam-follower mechanism. It is challenging to design high-speed cam profiles for multi-DOF followers because of the complicated dynamics. A novel method is presented to design the cam profile in this article. A polynomial profile filters through a continuous-piecewise smoother to produce the cam profile. While the profile and their derivatives are continuous, the profile provides good performance on the vibration reduction for multi-DOF followers. Simulated and experimental results from a flexible-link manipulator validate the effectiveness of the cam profiles created by the new method. [ABSTRACT FROM AUTHOR]

An analysis of the characteristics of automotive mass air flow sensors is made. A test system has been developed to study the sensors. The measurement data is processed with MATLAB using curve fitting. [ABSTRACT FROM AUTHOR]

If p(z) = Xn ν=0 aνz ν is a polynomial of degree n having all its zeros in |z| ≤ k, k ≥ 1, Jain [Bull. Math. Soc. Sci. Math. Roumania Tome, 59(2016), 339-347] proved max |z|=1 |p′ (z)| ≥ nAk max |z|=1 |p(z)|, where Ak = ( |a0| + |an|k n+1/ |ao|(1 + k n+1) + |an|(k n+1 + k 2n) ) . In this paper, we initially derive a generalized form that not only encompasses but also enhances the aforementioned inequality. Additionally, we extend this formulation to a more comprehensive result, thereby producing an improved outcome for certain established inequalities as a specific instance. [ABSTRACT FROM AUTHOR]

We show that, in general, the characteristic polynomial of a hypergraph is not determined by its "polynomial deck", the multiset of characteristic polynomials of its vertex-deleted subgraphs, thus settling the "polynomial reconstruction problem" for hypergraphs in the negative. The proof proceeds by showing that a construction due to Kocay of an infinite family of pairs of 3-uniform hypergraphs which are non-isomorphic but share the same hypergraph deck, in fact, have different characteristic polynomials. The question remains unresolved for ordinary graphs. [ABSTRACT FROM AUTHOR]

In the present paper we shall obtain the following result: Let n ≥ 2 and m ≥ 1 be integers. Let p (x 1 , ... , x m) be a polynomial with zero constant term in non-commutative variables over an algebraically closed field K. Suppose that 1 ≤ r ≤ n − 1 , where r is the order of p. Then p (T n (K)) is a dense subset of T n (K) (r − 1) (with respect to the Zariski topology). This is a solution of a problem presented by Gargate and de Mello and a supplement to a result obtained by Panja and Prasad in 2023. [ABSTRACT FROM AUTHOR]

We present some extensions of Chu's formulas and several striking generalizations of some well-known combinatorial identities. As applications, some new identities on binomial sums, harmonic numbers, and the generalized harmonic numbers are also derived. [ABSTRACT FROM AUTHOR]

We explicitly provide numbers d, e such that each irreducible factor of a polynomial f(x) with integer coefficients has a degree greater than or equal to d and f(x) can have at most e irreducible factors over the field of rational numbers. Moreover, we prove our result in a more general setup for polynomials with coefficients from the valuation ring of an arbitrary valued field. [ABSTRACT FROM AUTHOR]

Due to the high demands of data communication, the broadcasting system streams the data daily. This service not only sends out the message to the correct participant but also respects the security of the identity user. In addition, when delivered, all the information must be protected for the party who employs the broadcasting service. Currently, Attribute-Based Broadcast Encryption (ABBE) is useful to apply for the broadcasting service. (ABBE) is a combination of Attribute-Based Encryption (ABE) and Broadcast Encryption (BE), which allows a broadcaster (or encrypter) to broadcast an encrypted message, including a predefined user set and specified access policy to install the authorization mechanism. It is desirable to hide all the information when producing in the ciphertext, which has not been considered in the previous works of ABBE. Motivated by the above issue, we devise a solution to achieve anonymity for the ABBE scheme, which not only hides the access structures but also anonymizes the user's identity. In this work, we propose two schemes as Anonymous Key Policy (AKP)-ABBE and Anonymous Ciphertext Policy (ACP)-ABBE with supporting multiple access structures by using OR / AND gates. Specifically, we present the generic constructions of AKP/ACP-ABBE on the building block of the Inner Product Encryption (IPE ), which enables the hidden user's identity and complex OR / AND -Gate access structure. We show that our proposed schemes are secured under the standard models. [ABSTRACT FROM AUTHOR]

The widespread use of unmanned aerial vehicles (UAVs) of various classes in both the military and civilian spheres requires the development and production of high-precision on-board navigation systems of low cost, weight and dimensions. An important characteristic that determines the ability and quality of the UAV's flight task performance is the accuracy of its positioning. The basis of management of existing UAVs is the use of satellite navigation systems (SNS). In SNS of UAVs, increasing the accuracy of positioning is achieved by using various algorithms for processing received navigation data. A generalized analysis of the most common approaches to solving the problem of filtering navigation measurements showed that the task of synthesizing effective filtering algorithms remains relevant. A possible way to increase the accuracy of determining the navigation parameters is the joint processing of the results of measurements of the distance to the satellite and the radial velocity. The work describes the methodology of synthesis of complex filtering algorithms for range measurements in UAV satellite navigation systems. The methodology is based on a polynomial model of the filtering algorithm and input data. The described approach is based on the presentation of smoothing filters as dynamic systems described by discrete transfer functions. The theoretical basis for determining the transfer functions is the third form of the invariance conditions of the filter error with respect to the input influence model. The proposed approach allows: synthesizing effective complex filtering algorithms that have minimal computational complexity for their implementation; at the stage of synthesis, forming the properties of filters in relation to noise smoothing and exclusion of dynamic errors; in the synthesis process, determining the conditions under which the digital filter will be stable. The workability and efficiency of the synthesized algorithm was investigated by means of computer simulation. It is shown that the application of the synthesized filter allows reducing the dynamic range estimation error in the conditions of changing the mathematical model of the input data without deteriorating the quality of filtering of measurement errors.

In this paper, we establish inequalities concerning the growth of polynomials involving the polar derivative of the polynomials. [ABSTRACT FROM AUTHOR]

This study attempted to represent psychological development curves using polynomial equations. We utilized standardized data from the 2020 edition of the Kyoto Scale of Psychological Development to specify these equations. Using the least squares method, we calculated equations from the first to the sixth degrees. The results indicated no difference in the fit of the psychological development curve at the third degree and beyond in terms of coefficients of agreement. Further, specifying the psychological development curve as a third-degree equation was found to be favorable. Additionally, the study inferred that individualsʼ rate of development varies from birth to adulthood; however, the speed of development gradually decreases with increasing age. 【Research Impact】 The Kyoto Scale of Psychological Development is a standardized scale widely used in Japan. This study investigated the representation of the psychological development curve using polynomial equations based on standardized data from the 2020 edition of the scale. Notably, this scale exhibited social significance because it can serve as an index of psychological development. [ABSTRACT FROM AUTHOR]

In standard books on calculus the existence of primitive functions of continuous functions is proved, in one way or another, using Riemann sums. In this note we present a completely different self-contained, however probably folkloristic, proof of this existence. Our proof combines, on the one hand, the so-called Stone Weierstrass theorem on uniform approximation of continuous functions on the unit interval by polynomials, and, on the other hand, a classical result from calculus on the existence of limits of differentiated sequences of functions. The sought for primitive is then constructed as the limit of primitives of the polynomials approximating the original function. [ABSTRACT FROM AUTHOR]

This work extends the results for the Diophantine equation x² + 16 ∙ 7b = yn for n = 2r, where x,y, b,r ∈ Z+ . Earlier results classified the generators of solutions, which are the pair of integers (x,yr) into several categories and presented the general formula that determines the values of x and yr for the respective category. The lower bound for the number of non-negative integral solutions associated with each b is also provided. We now extend the results and prove the necessary and sufficient conditions required to obtain integral solutions x and y to the equation, by considering various scenarios based on the parity of b. We also determine the values of n for which integral solutions exist. [ABSTRACT FROM AUTHOR]

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Let P (z) = a n z n + ∑ j = μ n a n − j z n − j , 1 ≤ μ ≤ n , is a polynomial of degree n having all zeros in | z | ≤ k , k ≤ 1 , then for α , β ∈ C with | α | ≥ k μ , | β | ≤ 1 and for each p > 0 ; s > 1 ; t > 1 with 1 s + 1 t = 1 ; it was proved by (N. A. Rather et al., Some L r inequalities involving the polar derivative of a polynomial, Appl. Math. E-Notes 14 (2014) 116–122) n (| α | − k μ) ∫ 0 2 π P (e i ) + β m k n − μ p d 1 p ≤ ∫ 0 2 π | 1 + k μ e i | p s d 1 p s ∫ 0 2 π D α P (e i ) − m n k n − μ p t d 1 p t . In this paper, we establish some refinements and generalizations of above and some known polynomial inequalities concerning the polar derivative of a polynomial. [ABSTRACT FROM AUTHOR]

Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on extensions of finite fields, especially for the cases of quadratic and cubic extensions. Our achievements are obtained by investigating absolute irreducibility of some polynomials in two indeterminates. [ABSTRACT FROM AUTHOR]

Denote by τ k (n) , ω (n) and μ 2 (n) the number of representations of n as a product of k natural numbers, the number of distinct prime factors of n and the characteristic function of the square-free integers, respectively. Let [ t ] be the integral part of real number t. For f = ω , 2 ω , μ 2 , τ k , we prove that ∑ n ≤ x f x n = x ∑ d ≥ 1 f (d) d (d + 1) + O (x f + ) for x → ∞ , where ω = 5 3 1 1 0 , 2 ω = 9 1 9 , μ 2 = 2 5 , τ k = 5 k − 1 1 0 k − 1 and > 0 is an arbitrarily small positive number. These improve the corresponding results of Bordellès. [ABSTRACT FROM AUTHOR]

Electricity theft is a serious issue that many nations face, especially in developing areas where non-technical losses can make up a significant percentage of the overall losses sustained by utilities. Electricity theft detection (ETD) is a very challenging task because it frequently introduces irregularities in customer electricity consumption patterns. In recent times, machine learning (ML) techniques have been investigated as a potential solution for ETD. In this research, author propose electricity theft detection based on four kernel functions of support vector machines (SVM). The proposed method analyzes the electricity consumption patterns and then predicts the category of the user. The kernel functions utilized includes polynomial, sigmoid, radial basis function (RBF) and linear kernel function. For experimentation and model training, a dataset of Pakistani utility company is used, which contains the electricity consumption information. The results highlight SVM method works well for accurate ETD. The detection accuracy of the various kernel functions of SVM is 83%, 79%, 80%, and 76% for RBF, polynomial, sigmoid, and linear kernel functions, respectively, demonstrating the effectiveness of the proposed SVM-based method for theft detection. By leveraging these ML-based methods, utility companies can strengthen their ability to detect and prevent electricity theft, leading to improved revenue management and dependability of services. [ABSTRACT FROM AUTHOR]

For the polynomial of degree n having all its zeros in , , Jain in "On the derivative of a polynomial," Bull. Math. Soc. Sci. Math. Roumanie Tome 59, 339–347 (2016) proved that In this paper we strengthen the above inequality and other related results for the polynomials of degree . [ABSTRACT FROM AUTHOR]

In this paper, we establish some new polynomial inequalities involving various operators and their relationship with the existing results. All these inequalities have been proved under the assumption that the underlying polynomial is being constrained with respect to its zeros. [ABSTRACT FROM AUTHOR]

In this research, we attempted to fit a trading system based on polynomial moving regression bands (MRB) to Nasdaq100 stocks from 2017 till the end of March 2024. Since stocks movement does not follow a linear behavior, we used multiple degree polynomial regression models to identify the stocks’ trends and two standard deviations from the regression model to generate the trading signals. This way, the MRB was transformed into a momentum indicator designed to identify strong uptrends that can be used by a fully automated trading system. Our results indicate that the behavior of Nasdaq100 stocks can be tracked using all three examined polynomial models and can be traded profitably using fully automated systems based on those models. The best performing model was the model that used a four-degree polynomial MRB achieving the highest average net profit (USD 162.73). Regarding the risks involved, the third model has the lowest loss in dollar value (USD −95.52), and the highest minimum percent of profitable trades (41.51%) and profit factor (0.55) that indicates that this strategy is relatively less risky than the other two strategies.

The goal of this research is fit the best curve to the image histogram using polynomial (i.e., linear, quadratic, cubic, and quartic), Fourier and Gaussian with two different term numbers, and Bezier functions, and then compare their performance with nine automatic state-of-the-art thresholding methods: Shanbhag, Triangle, Huang, Intermode, IsoData, Li's, Maximum entropy, Moment, and Otsu. The visible bands of the Landsat-9, Landsat-8, and Sentinel 2 satellite images are averaged to create an index map, which was used to perform the cloud detection. Since many satellites system only has visible bands, the average index map was used. Three different images which include various cloud types were clipped from each satellite imaging. Thresholding methods were evaluated using statistical tools such as structural similarity index measure (SSIM), peak signal-to-noise ratio (PSNR), and universal image quality index (UIQI), accuracy, Cohen's kappa, precision, recall, F-Measure, and G-Mean. The histogram-based approaches that performed the best after Li's method were Bezier (96.71% accuracy and 99.83% SSIM), 2nd Gaussian (97.62% precision), Quartic (80.56% kappa, 16.16% PSNR, 82.45% F-Measure, and 89.52%), and 2nd Fourier (81.08% recall and 89.27% G-Mean), according to the average statistics of all images. Additionally, methods other than Shanbhag yielded favorable results (more than 90% accuracy). [ABSTRACT FROM AUTHOR]

This paper investigates a real-time process generator of wideband signals, which calculates waveforms in a field-programmable gate array (FPGA) using the high-level synthesis (HLS) method. To obtain high-resolution and wide-swath images, the generator must produce multiple modes of large time-bandwidth product (TBP) linear frequency modulation (LFM) signals. However, the conventional storage method is unrealistic as it requires huge storage resources to save pre-computed waveforms. Therefore, this paper proposes a novel processing approach that calculates waveforms in real-time based simply on parameters such as the sampling frequency, bandwidth, and time width. Additionally, this paper implements predistortion through the polynomial curve to approximate phase errors of the system. The parallelizing process in the FPGA is necessary to satisfy the high-speed requirement of a digital-to-analog converter (DAC); however, repeatedly multiplexing real-time calculation consumes extensive logic and DSP resources, potentially exceeding FPGA limitations. To address this, this paper proposes a piecewise linear algorithm to conserve resources, which processes the polynomial only once, acquires the difference in two adjacent values through the register and pipeline, and then adds this increment to facilitate parallel computations. The performance of this proposed generator is validated through simulation and implemented in experiments with an X-band airborne SAR system. [ABSTRACT FROM AUTHOR]

For B ∈ F q [ T ] of degree 2 n ≥ 2 , consider the number of ways of writing B = E 2 + γ F 2 , where γ ∈ F q ⁎ is fixed, and E , F ∈ F q [ T ] with deg E = n and deg F = m < n. We denote this restricted sum-of-squares function by S γ ; m (B). We obtain an exact formula for the variance of S γ ; m (B) over short intervals in F q [ T ] where q is an odd prime power. Interestingly, when m + 1 ≤ n ≤ 2 m , the variance vanishes on some (not all) short intervals, which is in contrast to the standard function that counts representations as a sum of two squares. We use the method of additive characters and Hankel matrices that we previously used for the variance and correlations of the divisor function. In Section 2, we give a short overview of our approach. Section 3 gives new results relating to values of quadratic forms, over F q , that are defined from Hankel matrices. [ABSTRACT FROM AUTHOR]

Finding the sharp estimate of max | z | = 1 | p ′ (z) | in terms of max | z | = 1 | p (z) | for the class of polynomials p(z) satisfying p (z) ≡ z n p (1 / z) has been a well-known open problem for a long time and many papers in this direction have appeared. The earliest result is due to Govil, Jain and Labelle [9] who proved that for polynomials p(z) satisfying p (z) ≡ z n p (1 / z) and having all the zeros either in left half or right half-plane, the inequality max | z | = 1 | p ′ (z) | ≤ n 2 max | z | = 1 | p (z) | holds. A question was posed whether this inequality is sharp. In this paper, we answer this question in the negative by obtaining a bound sharper than n 2 . We also conjecture that for such polynomials max | z | = 1 | p ′ (z) | ≤ ( n 2 - 2 - 1 4 (n - 2)) max | z | = 1 | p (z) | and provide evidence in support of this conjecture. [ABSTRACT FROM AUTHOR]