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In the paper, in view of two monotonicity rules for the ratios of two functions and of two Maclaurin power series expansions, the authors establish several sharp inequalities involving (hyperbolic) tangent, tanc, cosine, and their reciprocals. [ABSTRACT FROM AUTHOR]

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In this article, the authors introduce Qi’s normalized remainder of the Maclaurin series expansion of Qi’s normalized remainder for the cosine function. By virtue of a monotonicity rule for the quotient of two series and with the aid of an increasing monotonicity of a sequence involving the quotient of two consecutive non-zero Bernoulli numbers, they prove the logarithmic convexity of Qi’s normalized remainder. In view of a higher order derivative formula for the quotient of two functions, they expand the logarithm of Qi’s normalized remainder into a Maclaurin series whose coefficients are expressed in terms of determinants of a class of specific Hessenberg matrices. In light of a monotonicity rule for the quotient of two series, they present the monotonicity of the ratio between two normalized remainders. Finally, the authors connect two of their main results with the generalized hypergeometric functions.

The influence of night shift work on circadian heart-rate rhythm was examined in nurses engaged in shift work using a Holter electrocardiogram, continuously measured for two weeks, and cosine periodic regression analysis. We enrolled 11 nurses who were engaged in a two-shift system. The R² value in the cosine regression curve of heart-rate rhythm (concordance rate), indicating the concordance rate between the actual heart rate over 24 h and the cosine regression curve approximated by the least-squares procedure, was significantly lower in the night shift (0.40 ± 0.15) than in the day shift (0.66 ± 0.19; p<0.001). Moreover, the amplitude was significantly lower and the acrophase was significantly delayed in the night shift. Thus, the circadian heart-rate rhythm was disrupted by the night shift work. Although the heart-rate acrophase recovered during the day and two days after the night shift, the concordance rate and amplitude did not recover, indicating that the influence of night shift work on circadian heart-rate rhythm might persist even two days after the night shift. Based on these results, adequate clinical attention should be paid to how to spend the day and two days after the night shift to correct the circadian heart-rate rhythm disruption caused by night shift work. [ABSTRACT FROM AUTHOR]

In this paper, algorithms for different types of trigonometric power sums are developed and presented. Although interesting in their own right, these trigonometric power sums arise during the creation of an algorithm for the four types of twisted trigonometric power sums defined in the introduction. The primary aim in evaluating these sums is to obtain exact results in a rational form, as opposed to standard or direct evaluation, which often results in machine-dependent decimal values that can be affected by round-off errors. Moreover, since the variable, m, appearing in the denominators of the arguments of the trigonometric functions in these sums, can remain algebraic in the algorithms/codes, one can also obtain polynomial solutions in powers of m and the variable r that appears in the cosine factor accompanying the trigonometric power. The degrees of these polynomials are found to be dependent upon v, the value of the trigonometric power in the sum, which must always be specified. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish the monotonicity results of the ratios between normalized tails of the Maclaurin power series expansions of the sine and cosine functions and restate them in terms of the generalized hypergeometric functions. [ABSTRACT FROM AUTHOR]

This paper presents the design and implementation of an efficient multiparametric recommender engine for low-power applications with incremental post-processor optimizations. The need for this work arises from the increasing demand for energy-efficient recommender systems that can provide accurate recommendations with low energy consumption and delay levels. To address this need, we propose a novel approach that combines the use of Fourier, Cosine, LSTM, GRU, Wavelet, and Gabor features for the representation of collected network datasets& samples. These features are processed using low-power recurrent neural networks (LP RNN) to reduce energy consumption and delay levels. To further improve the accuracy and efficiency of the recommender engine, we apply an augmented post-evaluation Q-learning process. Our proposed method is compared with existing models, and we demonstrate its superior performance in terms of accuracy, precision, recall, energy consumption, and delay levels. Experimental results on multiple datasets and samples show that our proposed approach achieves an accuracy of 98.9%, precision of 97.5%, and recall of 98.3% while consuming less energy and incurring lower delay compared to existing models. Overall, our proposed multiparametric recommender engine provides an efficient and effective solution for low-power applications that require accurate recommendations for data patterns. [ABSTRACT FROM AUTHOR]

In the paper, the authors intrinsically observe that Hoffman’s combinatorial identity discovered in 1992 and Genčev’s combinatorial identities extended in 2024 can be reformulated in terms of complete Bell polynomials. They provide alternative proofs and offer some elementary generalizations of these combinatorial identities. [ABSTRACT FROM AUTHOR]

The superconductivity of CaC6 as a function of pressure and Ca isotopic composition was revisited using DFT calculations on a 2c–double hexagonal superlattice. The introduction of superlattices was motivated by previous synchrotron absorption and Raman spectroscopy results on other superconductors that showed evidence of superlattice vibrations at low (THz) frequencies. For CaC6, superlattices have previously been invoked to explain the ARPES data. A superlattice along the hexagonal c-axis direction is also illustrative of atomic orbital symmetry and periodicity, including bonding and antibonding s-orbital character implied by cosine-modulated electronic bands. Inspection of the cosine band revealed that the cosine function has a small (meV) energy difference between the bonding and antibonding regions, relative to a midpoint non-bonding energy. Fermi surface nesting was apparent in an appropriately folded Fermi surface using a superlattice construct. Nesting relationships identified phonon vectors for the conservation of energy and for phase coherency between coupled electrons at opposite sides of the Fermi surface. A detailed analysis of this Fermi surface nesting provided accurate estimates of the superconducting gaps for CaC6 with the change in applied pressure. The recognition of superlattices within a rhombohedral or hexagonal representation provides consistent mechanistic insight on superconductivity and electron−phonon coupling in CaC6. [ABSTRACT FROM AUTHOR]

In this paper, in view of a determinantal formula for higher order derivatives of the ratio of two differentiable functions, we expand the logarithm of the normalized tail of the power series expansion of the cosine function into a Maclaurin power series expansion whose coefficients are expressed in terms of specific Hessenberg determinants, present the decreasing property and concavity of the normalized tail of the Maclaurin power series expansion of the cosine function, deduce a new determinantal expression of the Bernoulli numbers, and verify the decreasing property for the ratio of the logarithms of the first two normalized tails of the Maclaurin power series expansion of the cosine function. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce two notions, the normalized remainders, or say, the normalized tails, of the Maclaurin power series expansions of the sine and cosine functions, derive two integral representations of the normalized tails, prove the nonnegativity, positivity, decreasing property, and concavity of the normalized tails, compute several special values of the Young function, the Lommel function, and a generalized hypergeometric function, recover two inequalities for the tails of the Maclaurin power series expansions of the sine and cosine functions, propose three open problems about the nonnegativity, positivity, decreasing property, and concavity of a newly introduced function which is a generalization of the normalized tails of the Maclaurin power series expansions of the sine and cosine functions. These results are related to the Riemann–Liouville fractional integrals. [ABSTRACT FROM AUTHOR]

In this paper, in view of a determinantal formula for higher order derivatives of the ratio of two differentiable functions, we expand the logarithm of the normalized tail of the power series expansion of the cosine function into a Maclaurin power series expansion whose coefficients are expressed in terms of specific Hessenberg determinants, present the decreasing property and concavity of the normalized tail of the Maclaurin power series expansion of the cosine function, deduce a new determinantal expression of the Bernoulli numbers, and verify the decreasing property for the ratio of the logarithms of the first two normalized tails of the Maclaurin power series expansion of the cosine function.

In current epilepsy disease research, accurate identification of epilepsy electroencephalogram (EEG) signals is crucial for improving diagnostic efficiency and developing personalized treatment plans. This study proposes an innovative epilepsy recognition model, MAC, which combines the unique advantages of a multilayer perceptron (MLP), a self-attention mechanism and the cosine distance. This model uses a MLP as the basic model and effectively reduces individual differences among epilepsy patients through its superior linear fitting ability. To more accurately measure the difference between two EEG signals, we introduced the cosine distance as a new feature metric. This metric enhances the performance of epilepsy EEG classification by using the cosine value of the angle in vector space to precisely assess the difference between two individuals. In addition, we introduced a self-attention mechanism into the model to enhance the impact of various factors on the final EEG data. Our experiments employed the EEG database of the Epilepsy Research Center of the University of Bonn. Through comparative experiments, it was proven that the proposed MAC model achieved significant improvement in performance on the epilepsy EEG signal recognition task. This study fills the existing research gap in the field of epilepsy identification and provides a powerful tool for the accurate diagnosis of epilepsy diseases in the future. We believe that the introduction of the MAC model will promote new breakthroughs in epilepsy EEG signal recognition and lay a solid foundation for the development of related fields. This research provides an important theoretical and practical reference for advancing the field of epilepsy identification. [ABSTRACT FROM AUTHOR]

In the paper, the author presents lower and upper bounds for norms of the sine and cosine functions along a circle on the complex plane. [ABSTRACT FROM AUTHOR]

Breast cancer diagnosis from mammographic scans is a complex challenge, demanding accurate and efficient methodologies. Existing approaches often rely on time-consuming manual feature extraction or lack scalability when employed with diverse clinical image sets. To address these limitations, this paper presents an innovative solution: the MPC2EL (Multiple Phased Convolution model for Pre-emption of Breast Cancer via Extensive Learning Operations). The core problem tackled by this research is the need for improved breast cancer detection, especially concerning scalability, accuracy, and practicality. To achieve this, MPC2EL leverages extensive learning operations and multiple phased convolutions to process extensive clinical datasets containing both cancerous and benign images. Our novel approach begins with the conversion of these images into multimodal feature sets, encompassing frequency, cosine, wavelet, and Gabor domains. These feature sets enable enhanced classification of images into different cancer stages. The proposed methodology lies in a Dual 1D Convolutional Neural Network (D1D CNN) architecture, capable of categorizing images initially into malignant and benign types and subsequently refining classification for malignant images. Experimental results reveal a substantial 5.9% increase in classification accuracy and a 4.5% improvement in recall compared to conventional deep learning methods. Moreover, the model demonstrates lower processing delay and higher precision, making it a promising candidate for real-world clinical deployment. [ABSTRACT FROM AUTHOR]

This work focuses on determining semantically close words and using semantic similarity in general in order to improve performance in information retrieval tasks. The semantic similarity of words is an important task with many applications from information retrieval to spell checking or even document clustering and classification. Although, in languages with rich linguistic resources, the methods and tools for this task are well established, some languages do not have such tools. The first step in our experiment is to represent the words in a collection in a vector form and then define the semantic similarity of the terms using a vector similarity method. In order to tame the complexity of the task, which relies on the number of word (and, consequently, of the vector) pairs that have to be combined in order to define the semantically closest word pairs, A distributed method that runs on Apache Spark is designed to reduce the calculation time by running comparison tasks in parallel. Three alternative implementations are proposed and tested using a list of target words and seeking the most semantically similar words from a lexicon for each one of them. In a second step, we employ pre-trained multilingual sentence transformers to capture the content semantics at a sentence level and a vector-based semantic index to accelerate the searches. The code is written in MapReduce, and the experiments and results show that the proposed methods can provide an interesting solution for finding similar words or texts in the Kazakh language. [ABSTRACT FROM AUTHOR]

Propagation properties of Cosine‑hyperbolic Vortex Gaussian Beams propagating in turbulent atmosphere are investigated. In this context, the effect of topological charges and decentred parameters on the beam size and the kurtosis parameter is evaluated. It is obtained that, beams with bigger topological charges face additional beam spreading, as well as a decrease in the kurtosis parameter. On the other hand, as the decentred parameter increases, beams spread less in long communication links. Inversely, Kurtosis parameters increase especially as the decentred parameters is greater than 1.5. Up to this end, the presented results are critical for both the design and the performance improvement of the free-space optical communication systems. [ABSTRACT FROM AUTHOR]

In our analysis, we approximate the sine and cosine trigonometric functions within the interval [0, π/2]. This examination yields two distinct formulas for approximating sine and cosine. Initially, we endeavor to derive the formula that involves a square root, and then we develop an alternative formula that does not require any use of a square root. However, even after establishing the square root-free procedure, we seek to enhance its accuracy and subsequently derive yet another formula for more precise approximations of trigonometric functions within the interval [ 0, π/2]. Thus, our analysis presents two primary procedures. One is utilizing square roots, and the other abstaining from them. Our focus extends to ensuring the accuracy of these trigonometric functions specifically within the interval [ 0, π/2]. This precision assessment is visually represented through graphs, illustrating the disparity between the values generated by the formulated functions and the exact values of these functions. Consequently, these graphs serve as indicators of the error within the interval [ 0, π/2]. Finally, we conduct a comparative analysis between our approximation and the 7th-century Indian mathematician Bhaskara I's approximation formula. [ABSTRACT FROM AUTHOR]

A new method for solving ordinary differential equations is suggested. As it is shown the deferential equation can be solved not only by means integration of its differentiation as well. It is shown that the differential equation can be solved not only by integration, but also by differentiation. The developed method is applied for consideration of corresponding equations for the exponential function and trigonometric functions. In the framework of the developed method the simple approach for derivation of Taylor series of a function is demonstrated. Based imminently on the geometric definition the connections between trigonometric functions and their derivatives are obtained as well. The well-known Euler formula is also produced, which establishes a connection between trigonometric functions and exponential function. [ABSTRACT FROM AUTHOR]

Mathematical functions that establish a relationship between the angles of a right triangle and the lengths of its sides are known as trigonometric functions. In this project, we will explore two of the six trigonometric functions and their properties using the trigonometric circle. Initially, trigonometric functions were defined only for acute angles related to right triangles. To extend the sine and cosine functions to functions whose domain is the entire real line, geometric definitions using the unit circle with radius 1 are often used. Then, the domain of the other trigonometric functions is the real line with some isolated points removed. Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows the extension of the definition of sine and cosine functions to the entire complex plane and the definition of other trigonometric functions on the complex plane with some isolated points removed. This project discusses the use of GeoGebra in studying trigonometric functions, the Law of Sine, and Law of Cosine. GeoGebra is a powerful mathematical software that allows for the visualization and exploration of trigonometric functions. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to generate fractals of sine and cosine functions for a complex polynomial z k + c via Picard–Mann iterations. To generate Mandelbrot and Julia sets, escape criteria are established and proven for sin z k + c and cos z k + c for Picard–Mann iterations. Various input parameters for different k are used to compare images between sine and cosine. generation time and average number of iterations of the generated Mandelbrot and Julia sets are presented. [ABSTRACT FROM AUTHOR]

We present methods to write Tn(x), Chebyshev polynomials of the first kind, as a product of minimal polynomials of cos(2π/m) over integers, Ψm(x), and to write Ψm(x) as ratios of expressions in Tn(x). We also prove the relation Ψm(Tn(x)) = Ψn(Tm(x)) for m, n having the same prime divisors and use it to express Ψm(x) as a linear combination of Tn(x) for certain values of m. [ABSTRACT FROM AUTHOR]

Introduction of the World Wide Web (WWW) and progressions in the field of multimedia and computer technology have enlarged the amount of image collections and databases including art galleries, digital libraries, and medical imageries that extend to millions of images. From these large-scale datasets, the retrieval procedure of images is carried out by classical approaches like chi square distance, colour histogram and text-based image retrieval, which however requires more time for getting the desired images. Thus, there is a need of proposing an effective retrieval system for images by handling these large numbers of images. For this reason, a new ContentBased Image Retrieval (CBIR) system has been implemented in this paper for retrieving the desired images of users from the collected images. Initially, different kinds of images like medical images, texture images, and environmental images etc., are collected from the standard image database. The deep feature extraction using Visual Geometry Group network (VGG-16), Inception v3, and Xception are used to get the features of all the images in the database. The parameters in these three deep learning techniques are tuned with an enhanced optimization algorithm of Modified Bypass-Rider Optimization Algorithm (MB-ROA). The features from VGG16, Inception and Xception are used for optimal weighted fused feature selection using enhanced ROA under training phase. During testing with query images, it undergoes deep feature extraction with the same set of techniques and, then fed into the optimal weighted fused feature selection to get the features of query image. Then, the multi-similarity function considering the cosine, Euclidean and Jaccard similarity are checked between the optimal features of database images and query image. The database images with the minimum similarity with the query image are retrieved from the database. The overall precision and recall to retrieve the top ten images related to the provided query image from the Corel dataset are 77.25% and 76.89%, respectively, while 70.15% and 70.26%, respectively from the VisTex dataset. The experimental findings show that the recommended model is effective at retrieving images from the database. [ABSTRACT FROM AUTHOR]

This work focuses on determining semantically close words and using semantic similarity in general in order to improve performance in information retrieval tasks. The semantic similarity of words is an important task with many applications from information retrieval to spell checking or even document clustering and classification. Although, in languages with rich linguistic resources, the methods and tools for this task are well established, some languages do not have such tools. The first step in our experiment is to represent the words in a collection in a vector form and then define the semantic similarity of the terms using a vector similarity method. In order to tame the complexity of the task, which relies on the number of word (and, consequently, of the vector) pairs that have to be combined in order to define the semantically closest word pairs, A distributed method that runs on Apache Spark is designed to reduce the calculation time by running comparison tasks in parallel. Three alternative implementations are proposed and tested using a list of target words and seeking the most semantically similar words from a lexicon for each one of them. In a second step, we employ pre-trained multilingual sentence transformers to capture the content semantics at a sentence level and a vector-based semantic index to accelerate the searches. The code is written in MapReduce, and the experiments and results show that the proposed methods can provide an interesting solution for finding similar words or texts in the Kazakh language.

The drainage gates have been controlled for desalination under normal conditions and flood defense in Saemangeum basin, Korea. Recently, it became an issue that the gates have been opened not to deteriorate water quality in the lake. It is, thus, necessary to precisely estimate the changes of water quality characteristics, especially DO, phosphate and nitrate, in the lake according to various gate operations. In this study, Semi-implicit Cross-scale Hydroscience Integrated System Model and Carbon, Silicate, Nitrogen Ecosystem model (SCHISM-CoSiNE) which is cable to simulate dynamic exchange such as gate operation conditions was utilized to obtain reliable and reasonable results including hydrodyanamic and environmental variables. For the verification, the measured data at 6 locations in Saemangeum basin was used to compare incluidng temperatue and salintiy from 2016 and each relative error became small enough to show high accurary. Also, under various scenarios by changing the designated water surface elevation on flood seasons, this model has been applied to present the best designated water surface elevation in terms of both water quality and water supply in the Saemangeum basin. It becomes possbile to show reliable guidance for dynamic operations and environmental changes with this model as requested in near future.

Web information retrieval (WIR) faces the challenges in finding more relevant information due to unstructured characteristic of the data and the tremendous growth in the size of the information. As a result, the users in search of information face difficulties in obtaining specific information on the web. The similarity measures play significant role in serving the machines to deal with the natural language. Various similarity functions used in the context of WIR to match between query and the documents. In this study, a new version of similarity measure for documents retrieval (SMDR) has been proposed. The experiments are conducted on various queries over CACM and RCV1 document collections to evaluate and analyse the performance of SMDR. The standard particle swarm optimization algorithm is used to optimize the entire WIR process. The comparative study is carried out considering the three important similarity measures in the context of WIR such as Cosine, Dice and Jaccord. The results show that significant improvement in the performance of the proposed similarity measure in retrieving the set of relevant documents. [ABSTRACT FROM AUTHOR]

Let (C(t))t∈ℝ be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – cosh λt is semi-Fredholm (resp. semi-Browder, Drazin inversible, left essentially Drazin and right essentially Drazin invertible) operator and λt ∉ iπℤ, then A – λ2 is also. We show by counterexample that the converse is false in general.

Let (C(t))t∈𝕉 be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – coshλt is Saphar (resp. quasi-Fredholm) operator and λt /∉iπ𝕑, then A – λ2 is also Saphar (resp. quasi-Fredholm) operator. We show by counter-example that the converse is false in general.

Cosine and cotangent similarity measurements are critical in applications for determining degrees of difference and similarity between objects. In the literature, numerous similarity measures for various extensions of fuzzy set, soft set, Intuitionistic Fuzzy Sets (IFSs), Pythagorean Fuzzy Sets (PFSs) and HyperSoft Sets (HSSs) have been explored. Neutrosophic HyperSoft Sets (NHSSs), on the other hand, has fewer cosine and cotangent similarity measures. In this paper, we propose the trigonometric similarity measures of NHSSs. We further investigate the basic operators, theorems, and propositions for the proposed similarity measures. We know that global warming causes environmental problems. One of applications for solving global warming is the concept of renewable energy. To show the effectiveness of the proposed similarity measures, we apply them to renewable energy source selection problems. The study reveals the best geographical area to install the energy production units, under some technical attributive factors. To check the validity and superiority of the proposed work, it is compared with some existing techniques which reveal that, decision-making problems with further bifurcated attributes, have more accurate and precise results and can only be solved with this technique. In the future, the proposed techniques can be applied to case studies, in which attributes are more than one and further bifurcated along with more than one decision-maker. Also, this proposed work can be extended for several existing hybrids of hypersoft sets, intuitionistic hypersoft, neutrosophic hypersoft set, bi-polar hypersoft, m-polar hypersoft sets, and Pythagorean hypersoft set to solve Multi-Criteria Decision Making (MCDM) problems.

The South China Sea (SCS) is the largest semi-enclosed marginal sea in the western Pacific. The alternation of East Asian monsoon causes a significant seasonal pattern of chlorophyll, primary productivity, and export flux of sinking particles. However, the source and sink of dissolved organic carbon (DOC) pools with different bioavailability are less studied. Here we evaluated the seasonal production of DOC in labile, semi-labile and refractory forms using a coupled physical-biogeochemical model. This study aims to understand the dynamics and budgets of organic matters in the SCS. Model results show that the production of labile, semi-labile and refractory DOC is highly correlated with the net primary productivity (NPP) which is higher in winter and lower in summer, reflecting a dependence of DOC on the NPP. The seasonal variation in Pearl River discharge dominates the DOC production in the northern coastal region. In the northeast, the Kuroshio intrusion associated frontal system is attributed to cause high winter production. The DOC production in the southwest is controlled by both winter mixing and summer upwelling. The production of refractory DOC with the least bioavailability favors carbon sequestration. Its annual mean production is 1.8±0.5 mg C m−2 d−1, equivalent to 26% of the export flux of particulate organic carbon at 1000 m. [ABSTRACT FROM AUTHOR]

Sosyal ağlar günümüzde oldukça popüler bir konumda bulunmaktadır. İnsanlar tarafından yoğun olarak kullanılan bir platform halini almıştır. Bu durum yüksek miktarda veri üretimine neden olmaktadır. Bu verilerin anlamlı ve faydalı bir forma dönüştürebilmek için birçok yöntem geliştirilmiştir. Bu yöntemler arasında veri madenciliği teknikleri ilk sıralarda yer almaktadır. Bu çalışmada veri madenciliği ve sosyal ağ yöntemleri kullanılarak yazarların yayınlarında belirtmiş oldukları anahtar kelimelere göre ilgili yazarlar arasındaki çalışma alanı benzerlikleri tespit edilmiştir. Veri seti olarak IDAP 2018(International Conference on Artificial Intelligence and Data Processing ) sempozyumunun yayın verileri kullanılmıştır. 536 yazar ve 1188 anahtar kelimeden oluşan veri setine Jaccard, Euclidean, Cosine benzerlik yöntemleri uygulanmıştır ve çalışmalarına göre yazarların yayınları arasındaki benzerlikler analiz edilerek karşılaştırılmıştır. Yazarların sonraki yayınlarında birbirleri ile çalışma yapabilmeleri açısından yönlendirici sonuçlar elde edilmiştir. Verilerin analize uygun forma getirilmesi için SQL Server kullanılırken, analiz ve görsel öğelerin oluşturulması için ise, R dili ve R Studio IDE kullanılmıştır.