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In this paper, we develop a novel method to construct Goethals–Seidel (GS) sequences with special structures. In the existing methods, utilizing Turyn sequences is an effective and convenient approach; however, this method cannot cover all GS sequences. Motivated by this, we are devoted to designing some sequences that can potentially construct all GS sequences. Firstly, it is proven that a quad of ± 1 polynomials can be considered a linear combination of eight polynomials with coefficients uniquely belonging to { 0 , ± 1 } . Based on this fact, we change the construction of a quad of Goethals–Seidel sequences to find eight sequences consisting of 0 and ± 1 . One more motivation is to obtain these sequences more efficiently. To this end, we make use of the k-block, of which some properties of (anti) symmetry are discussed. After this, we can then look for the sequences with the help of computers since the symmetry properties facilitate reducing the search range. Moreover, we find that one of the eight blocks, which we utilize to construct GS sequences directly, can also be combined with Williamson sequences to generate GS sequences with more order. Several examples are provided to verify the theoretical results. The main contribution of this work is in building a bridge linking the GS sequences and eight polynomials, and the paper also provides a novel insight through which to consider the existence of GS sequences. [ABSTRACT FROM AUTHOR]

Compared to fixed orthodontic appliances with brackets, thermoplastic invisible orthodontic aligners offer several advantages, such as high aesthetic performance, good comfort, and convenient oral health maintenance, and are widely used in orthodontic fields. However, prolonged use of thermoplastic invisible aligners may lead to demineralization and even caries in most patients' teeth, as they enclose the tooth surface for an extended period. To address this issue, we have created PETG composites that contain piezoelectric barium titanate nanoparticles (BaTiO3NPs) to obtain antibacterial properties. First, we prepared piezoelectric composites by incorporating varying amounts of BaTiO3NPs into PETG matrix material. The composites were then characterized using techniques such as SEM, XRD, and Raman spectroscopy, which confirmed the successful synthesis of the composites. We cultivated biofilms of Streptococcus mutans (S. mutans) on the surface of the nanocomposites under both polarized and unpolarized conditions. We then activated piezoelectric charges by subjecting the nanocomposites to 10 Hz cyclic mechanical vibration. The interactions between the biofilms and materials were evaluated by measuring the biofilm biomass. The addition of piezoelectric nanoparticles had a noticeable antibacterial effect on both the unpolarized and polarized conditions. Under polarized conditions, nanocomposites demonstrated a greater antibacterial effect than under unpolarized conditions. Additionally, as the concentration of BaTiO3NPs increased, the antibacterial rate also increased, with the surface antibacterial rate reaching 67.39% (30 wt% BaTiO3NPs). These findings have the potential for application in wearable, invisible appliances to improve clinical services and reduce the need for cleaning methods. [ABSTRACT FROM AUTHOR]

In this paper, we are devoted to finding Goethals–Seidel sequences by using k-partition, and based on the finite Parseval relation, the construction of Goethals–Seidel sequences could be transformed to the construction of the associated polynomials. Three different structures of Goethals–Seidel sequences will be presented. We first propose a method based on T-matrices directly to obtain a quad of Goethals–Seidel sequences. Next, by introducing the k-partition, we utilize two classes of 8-partitions to obtain a new class of polynomials still remaining the same (anti)symmetrical properties, with which a quad of Goethals–Seidel sequences could be constructed. Moreover, an adoption of the 4-partition together with a quad of four symmetrical sequences can also lead to a quad of Goethals–Seidel sequences. [ABSTRACT FROM AUTHOR]

In this paper, we provide the left and right Parseval relations over the quaternions. Moreover, we construct a new infinite family of sequences almost over $Q_{8} $ with period $p$ by a generalization of Legendre mapping, where $p\equiv 1 \pmod {8}$ is prime and the sequences have ideal autocorrelation. The sequences are symmetric when $p\equiv 1 \pmod {16}$ , and antisymmetric when $p\equiv 9 \pmod {16} $. [ABSTRACT FROM AUTHOR]

Objectives: Evidence on cardiovascular-related and all-cause mortality risks in a wide range of cancer survivors is scarce but needed to inform prevention and management. Methods: We performed a nationwide prospective cohort study using information from the Continuous National Health and Nutrition Examination Survey (NHANES) in the United States and the linked mortality follow-up files, available for public access. A propensity score-matched analysis with a 1:1 ratio was conducted to reduce the baseline differences between participants with and without cancer. The relationship between cancer status and the cardiovascular-related and all-cause mortality risk was examined using weighted Cox proportional hazards regression. Independent stratification analysis and cancer-specific analyses were also performed. Results: The study sample included 44,342 participants, aged 20-85, interviewed between 1999 and 2018. Of these, 4,149 participants had cancer. All-cause death occurred in 6,655 participants, of whom 2,053 died from cardiovascular causes. Propensity-score matching identified 4,149 matched pairs of patients. A fully adjusted Cox proportional hazards regression showed that cancer was linked to an elevated risk of cardiovascular-related and all-cause mortality both before and after propensity score matching. Stratification analysis and cancer-specific analyses confirmed robustness of results. Conclusion: Our study confirmed that cancer was strongly linked to cardiovascular-related and all-cause mortality, even after adjusting for other factors that could impact a risk, including the American Heart Association (AHA)'s Life's Simple 7 cardiovascular health score, age, sex, ethnicity, marital status, income, and education level., Competing Interests: The authors declare that they do not have any conflicts of interest., (Copyright © 2023 Shen, Wang, Wang, Tian, Guo, Shen, Liu and Zou.)

Background: Prior research on women who had hysterectomies has shown mixed results on whether or not hysterectomies increased the incidence of stroke and cause-specific or all-cause mortality., Methods: Using information from the Continuous National Health and Nutrition Examination Survey (NHANES) in the United States, including linked mortality follow-up files available for public access, a multicycle cross-sectional design mortality linkage study was performed., Results: Conducted during the years 2005-2018, the study sample included 14,214 female participants ranging in age from 20 to 85 years. The relationship between the hysterectomy status and the risk of stroke and cause-specific and all-cause mortality was examined using a series of weighted logistic regressions and Cox proportional hazards regressions, respectively. The presence of a hysterectomy was consistently linked to an elevated risk of stroke using weighted logistic regression models. The hysterectomy status, however, consistently showed no effect on survival by adjusted weighted Cox regression analysis., Conclusion: Our study found a significant association between hysterectomy and stroke, even after adjusting for other factors that could impact risk, such as the American Heart Association (AHA)'s Life's Simple 7 cardiovascular health score and variables of age, ethnicity, marital status, income, education, and depression severity., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Shen, Wang, Tian, Wang, Guo, Shen, Liu and Zou.)

Background: Morbidity and mortality of arteriosclerotic cardiovascular disease (ASCVD) varied according to socioeconomic status (SES), and evidence on the association between SES and ASCVD risk, and cause-specific and all-cause mortality was nevertheless lacking in large-scale or population-based studies., Methods: A multicycle cross-sectional design and mortality linkage study was conducted using data from Continuous National Health and Nutrition Examination Survey (NHANES) in the United States, including public use linked mortality follow-up files through December 31, 2019. Poverty income ratio (PIR) served as a SES index. A series of weighted Logistic regressions and Cox proportional hazards regressions were used to investigate the association between the SES and the risk of ASCVD and mortality, respectively., Results: The study sample was comprised of 30,040 participants aged 20-85 years old during the 2005-2018 period. Weighted Logistic regression models consistently indicated significant relationship between people experiencing poverty and increased risk of ASCVD, and linear trend tests were all statistically significant (all P for trend < 0.001). Additionally, weighted Cox regression analysis consistently demonstrated that the hazards of cause-specific and all-cause mortality increased, with the decrease of each additional income level, and trend analyses indicated similar results (all P for trend < 0.001)., Conclusions: Our study confirmed that the SES was strongly linked to living with ASCVD, and cause-specific and all-cause mortality, even after adjusting for other factors that could impact risk, such as the American Heart Association (AHA)'s Life's Simple 7 cardiovascular health score and variables of age, sex, marital status, education, and depression severity., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Shen, Zhao, Wang, Guo, Shen, Liu, Liu and Zou.)

Consensus about the universality of the power law feature in complex networks is experiencing widespread challenges. In this paper, we propose a generic theoretical framework in order to examine the power law property. First, we study a class of birth-and-death networks that are more common than BA networks in the real world, and then we calculate their degree distributions; the results show that the tails of their degree distributions exhibit a distinct power law feature. Second, we suggest that in the real world two important factors-network size and node disappearance probability-will affect the analysis of power law characteristics in observation networks. Finally, we suggest that an effective way of detecting the power law property is to observe the asymptotic (limiting) behavior of the degree distribution within its effective intervals.

Research on the association between level of depression and coronary heart disease (CHD), stroke risk, and all-cause and cardiovascular mortality is lacking in large-scale or population-based studies incorporating cardiovascular disease (CVD) endpoints. We aim to assess the relationship between the level of a person's depression and their risk of CHD, stroke, and all-cause and cardiovascular mortality. Utilizing data from the United States National Health and Nutrition Examination Survey (NHANES), multicycle cross-sectional design and mortality linkage studies were conducted. The study sample included 30918 participants aged 20-85 years old during the 2005-2018 period. Depression was assessed using the nine-item Patient Health Questionnaire (PHQ-9), with scores of 5, 10, 15, and 20 being the cut-off points for mild, moderate, moderately severe, and severe depression, respectively. A series of weighted logistic regression analyses and Cox proportional hazards models were utilized to examine the relationship between the level of depression with the risk of CHD, stroke, all-cause, and cardiovascular mortality. Trend analyses were conducted by entering the level of depression as a continuous variable and rerunning the corresponding regression models. Weighted logistic regression models consistently indicated a statistically significant association between the level of depression and increased risk of CHD and stroke, and those linear trend tests were statistically significant (P for trend < 0.001). Furthermore, weighted Cox regression analyses consistently indicated that participants who had a more severe degree of depression were at a higher risk of all-cause death, and trend analyses suggested similar results (P for trend < 0.001). Another weighted Cox regression analysis also consistently indicated that except for severe depression, the hazard of cardiovascular death was increased with each additional level increase of depression. Our study confirmed that the level of depression was strongly associated with CHD, stroke, and all-cause and cardiovascular mortality, even after accounting for other factors that could impact risk, including variables of age, gender, ethnicity, income, education, body mass index (BMI), marital, and smoking status., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Shen, Zhao, Wang, Guo, Shen, Liu and Zou.)