Double Formula Research Articles

A Prime-Order Group with Complete Formulas from Even-Order Elliptic Curves

This paper describes a generic methodology for obtaining unified, and then complete formulas for a prime-order group abstraction homomorphic to a subgroup of an elliptic curve with even order. The method is applicable to any curve with even order, in finite fields of both even and odd characteristic; it is most efficient on curves with order equal to 2 modulo 4, dubbed "double-odd curves". In large characteristic fields, we obtain doubling formulas with cost as low as 1M + 5S, and the resulting group allows building schemes such as signatures that outperform existing fast solutions, e.g. Ed25519. In binary fields, the obtained formulas are not only complete but also faster than previously known incomplete formulas; we can sign and verify in as low as 18k and 27k cycles on x86 CPUs, respectively.

Degree of the 3-secant variety

In this paper, we present a formula for the degree of the 3-secant variety of a nonsingular projective variety embedded by a 5-very ample line bundle. The formula is provided in terms of Segre classes of the tangent bundle of a given variety. We use the generalized version of the double point formula to reduce the calculation into the case of the 2-secant variety. As a resolution of the 2-secant variety, we use secant bundle and compute powers of desired algebraic cycles.

Determinants of Depression among Adult Epileptic Patients, in Ayder Comprehensive Specialized Hospital and Mekelle General Hospital, Tigray, Ethiopia. Case Control Study

Background: Depression is one of the most prevalent psychiatric disorders occurring in patients with epilepsy. There are no studies that assessed the factors among epileptic people in Mekelle, Tigray, Ethiopia. Therefore, this study determined the factors of depression in people with epilepsy. Methods: Unmatched case control study was conducted from May 1 to 30, 2019 in Ayder Comprehensive Specialized Hospital and Mekelle General Hospital on 66 cases and 132 controls calculated using double population proportion formula. Study subjects were selected two controls after each case. Data were collected using a standardized and pretested questioner. Data was collected by four trained BSc nursing professionals under Psychiatric Nurse supervisor. Depression was measured by patient health questionnaire-nine using face to face interview techniques. Data were analyzed using SPSS 23. Result: This study revealed that being female (AOR=2.79, 95% CI: 1.08-7.18, P=0.03), living with relative (AOR=2.82,95% CI:1.12-7.18, P=0.03), seizure frequency four and above per month (AOR=6.00, 95% CI:1.39-25.86, P=0.02), age onset of epilepsy between 12-24 years of age (AOR=3.11, 95% CI: 1.06-9.18, P=0.04), poor social support (AOR=5.34, 95% CI: 2.13-13.41, P=0.00) were significantly associated with depression. Conclusion: Factor associated like gender (female), living status (with relative), poor social support, age onset of epilepsy (between 12 to 24 years) and seizure frequency are the factors associated with depression. Depression prevention efforts should be targeted towards these risk factors.

A quantitative study between HPGR and cone crusher aided ball mill grinding: mathematical modeling by evaluating the possible microfracture effect produced by HPGR technology and cone crusher

High Pressure Grinding Rolls (HPGR) have been used in the mining industry for decades. However, there are limited quantifications of the particle properties after comminution. Furthermore, the influence of microcracks in grinding provided by this technology has not been extensively quantified. In the recent work, there were two comminution paths tested: 1 (Jaw crusher + cone crusher + ball mill) and 2 (Jaw crusher + HPGR + ball mill). The possible weakening effect aiding ball mill grinding due to microcracks of HPGR path was shown via specific energy, fines generation and breakage rate measurements. To achieve a quantification about the impact of microcracks and the high rate of reduction rate of HPGR technology, first the product was reconstructed using Rosin Rammler's Weibull double formula and the similar particle size distribution was obtained by a conventional cone crusher. By this way the feed size distribution to the grinding stage remained constant regardless of the type of crushing process (HPGR or cone crusher). The results showed that the microfractures generated by the HPGR technology influence the specific energy consumption, fines generation and breakage rates. Ball mill after HPGR consumed 12.46 kWh/t of specific energy, however ball mill after cone crusher consumed 14.36 kWh/t of specific energy. The experimental methodology proposed in this paper maintains a consistent feed size range (-1500 to +41.31 µm) to show that the size reduction observed in the sample undergoing HPGR grinding is not the primary factor contributing to reduced energy consumption and increased fines generation. Instead, it is predominantly associated with the microfractures generated through the compression in HPGR technology; the energy reduction (optimization) of a grinding path is shown in the study.

Some basic theorems and formulas for building fractal nonlinear wave models

As a tool to deal with the phenomenon in layered or porous media, many theoretical problems need to be improved urgently. In this paper, the definitions of two kinds of fractal derivatives based on scale transformation are developed from the perspective of mathematics, and the four operation rules, chain rules, Rolle theorem, mean value theorem, Taylor formula, variable upper limit integral derivation rule, definite integral basic principle, partial integral formula and double partial integral formula of the fractal version are given. Better still, we derive the fractal Euler-Lagrangian equation by using the variational method, and demonstrate the steps and effectiveness of deriving the fractal nonlinear wave equation based on the fractal Euler-Lagrangian equation through the example of the functionally graded beam.

Determinants of Podoconiosis in Bensa District, Sidama Region, Ethiopia: A case control study.

Podoconiosis is one of the neglected tropical diseases (NTD) with the greatest potential for elimination. Despite its public health importance, podoconiosis is a poorly understood disease which led to a widespread misconception about its cause, prevention, and treatment. Even though the exact global burden is still to be measured, it is estimated that at least 4 million people are affected with podoconiosis worldwide, of which more than 1.5 million people are in Ethiopia. The objective of this study was to identify the determinants of podoconiosis in Bensa District, Sidama Regional State, Ethiopia. A community-based unmatched case-control study was used to identify the determinants of podoconiosis. The sample size was estimated using the double population proportion formula. An interviewer-administered structured questionnaire was used for data collection. Blood specimens collected from cases were tested by Filariasis Test Strip to exclude lymphatic filariasis. Data were checked for completeness, coded and entered into Epi-data Version 4.6, and exported to the SPSS version 22 software. Variables with a p<0.2 in the bivariate analysis were further analyzed using multivariable binary logistic regression. Multivariable logistic regression analysis was used to examine determinants that could be associated with podoconiosis with a 95% confidence interval. A total of 459 (153 cases and 306 controls) participants were included with a response rate of 100%. Factors such as the age of participant [AOR = 0.34, 95% CI (0.13-0.87)], being female [AOR = 2.90, 95% CI (1.40-6.10)], age at which shoe wearing started [AOR = 0.7, 95% CI (0.03-0.16)], not wearing shoe daily [AOR = 2.26, 95% CI (1.05-4.86)], wearing hard plastic shoe [AOR = 3.38, 95% CI (1.31-10.89)], and family history with a similar disease (leg swelling) [AOR = 10.2, 95% CI (3.97-26.37)] were significantly associated with the occurrence of podoconiosis. The age of the participants, gender, the age at which shoe wearing started, type of shoe the participants' wear, frequency of shoe wearing, traveling barefoot, and family history with similar disease (leg swelling) were significantly associated with the occurrence of podoconiosis. Sidama regional health bureau along with non-governmental organizations working on the neglected tropical disease should plan modalities on awareness creation and comprehensive health education on shoe wearing and foot hygiene.

Finite-time ℋ∞ filtering for Markov jump systems with uniform quantization

This paper is concerned with finite-time ℋ ∞ filtering for Markov jump systems with uniform quantization. The objective is to design quantized mode-dependent filters to ensure that the filtering error system is not only mean-square finite-time bounded but also has a prescribed finite-time ℋ ∞ performance. First, the case where the switching modes of the filter align with those of the MJS is considered. A numerically tractable filter design approach is proposed utilizing a mode-dependent Lyapunov function, Schur’s complement, and Dynkin’s formula. Then, the study is extended to a scenario where the switching modes of the filter can differ from those of the MJS. To address this situation, a mode-mismatched filter design approach is developed by leveraging a hidden Markov model to describe the asynchronous mode switching and the double expectation formula. Finally, a spring system model subject to a Markov chain is employed to validate the effectiveness of the quantized filter design approaches.

Bivariate Fractal Interpolation Functions on Triangular Domain for Numerical Integration and Approximation

The primary objectives of this paper are to present the construction of bivariate fractal interpolation functions over triangular interpolating domain using the concept of vertex coloring and to propose a double integration formula for the constructed interpolation functions. Unlike the conventional constructions, each vertex in the partition of the triangular region has been assigned a color such that the chromatic number of the partition is 3. A new method for the partitioning of the triangle is proposed with a result concerning the chromatic number of its graph. Following the construction, a formula determining the vertical scaling factor is provided such that the actual double integral coincides with the integral value calculated using fractal theory. Convergence of the proposed method to the actual integral value is proven with sufficient lemmas and theorems. Adequate examples are presented to illustrate the method of construction and to verify the value of double integration.

A Simplified Analytical Method for the Deformation of Pile Foundations Induced by Adjacent Excavation in Soft Clay

The development of foundation excavations in congested urban areas inevitably induces stress release and soil movements, resulting in additional lateral deflections in adjacent pile foundations, commonly referred to as passive loading piles. Prior research on pile deflection resulting from nearby excavations primarily focused on single-pile behavior and paid little attention to the characteristics of pile groups. This paper presents a two-step approach to predicting the behavior of pile deformation resulting from nearby excavation. Firstly, Mindlin solution in combination with the double Gauss-Legendre formula is employed to calculate the additional lateral stress acting on the centerline of the passive pile resulting from nearby excavations. Secondly, the equation governing the deflection of the passive pile is determined using the Pasternak foundation model and solved using the finite difference method. On the basis of the Mindlin equation, shielding influence among piles is developed and applied to the analysis of a laterally loaded passive pile group. Last but not least, the accuracy of the presented approach is validated by comparing the results from two published centrifuge model tests with single piles and pile groups, and good agreements are obtained. Generally, the recommended two-step approach presents effective insight into the interaction between the excavation, soil, and pile, taking into account the influence of the shielding effect between piles. It can be applied as an alternative method for the conservation evaluation of the deformation tendency of pile foundation deformation in the pre-design of nearby excavations.

Serological Evidence and Associated Factors of Hepatitis B Virus and Hepatitis C Virus Among Waste Handlers: A Cross-Sectional Study from Northeastern Ethiopia.

The World Health Organization (WHO) has identified viral hepatitis, caused by hepatitis B virus (HBV) and hepatitis C virus (HCV), as one of the main global public health issues. People who work in the collection of waste materials, from either household or medical environments, are at greatest risk. To determine the prevalence of and factors associated with HBV and HCV among medical and domestic waste handlers in Northeast Ethiopia. A comparative cross-sectional study was conducted from January to April 2021 at selected healthcare facilities and municipal settings in Dessie town, Northeast Ethiopia. The sample size was determined using a double population proportion formula, and a simple random sampling technique was employed to select 70 individuals in the medical waste handlers (MWHs) group and 206 in the domestic waste handlers (DWHs) group. Five milliliters of venous blood was collected from each participant and tested for HBV and HCV using an enzyme-linked immunosorbent assay. Data were analyzed using SPSS version 23; the prevalence was computed, Fisher's exact test was used, and logistic regression was applied. A total of 276 study participants were enrolled and the overall seroprevalence of hepatitis virus was 5.1%. The seroprevalence of HBV infection among MWHs and DWHs was 8.6% and 1.9%, respectively. The overall seroprevalence of HCV infections among MWHs and DWHs was 4.3% and 0.5%, respectively. Medical waste handling, having a history of needle stick injury, and not using personal protective equipment were factors significantly associated with HBV infection. The overall seroprevalence of viral hepatitis was high. The prevalence of HBV infection among MWHs was in line with the high endemicity classification of the WHO, and there was a significant difference in prevalence between DWHs and MWHs. Both groups of waste handlers should receive proper attention to protect them from HBV and HCV infection.

A novel method for calculating the mutual inductance between two perpendicular coils in wireless power transfer

SummaryThe perpendicular coil is increasingly applied in some wireless power transfer (WPT) systems where space position is limited. The existing method of calculating the mutual inductance between perpendicular coils is mainly applied to rectangular and circular coils. However, the practical rectangular coil often has rounded corners, so it unavoidably introduces systematic errors. Concerning this issue, this paper proposed an analytical method to calculate the mutual inductance between mutually perpendicular round‐corner rectangular (RCR) coils. The proposed method is based on a second‐order vector potential (SOVP) model where the mutual inductance between the coils is described as a double integral formula. In this formula, a novel shape and position function is introduced. This shape and position function describes not only RCR coils but also rectangular (including square), circular, and runway ones. A series of experiments were used to validate the proposed method. According to the consistency validation, the proposed method can be more generalized for calculating the mutual inductance of rectangular and circular coils. Through experimental comparison, the proposed method computes the mutual inductance between the perpendicular coil in excellent agreement with the measured ones. Therefore, the proposed method unifies the mutual inductance calculation of mutually perpendicular circular, rectangular (square), runway, and RCR coils and can provide an important basis for designing WPT systems using the above coils.

An advanced discrete‐time RNN for handling discrete time‐varying matrix inversion: Form model design to disturbance‐suppression analysis

AbstractTime‐varying matrix inversion is an important field of matrix research, and lots of research achievements have been obtained. In the process of solving time‐varying matrix inversion, disturbances inevitably exist, thus, a model that can suppress disturbance while solving the problem is required. In this paper, an advanced continuous‐time recurrent neural network (RNN) model based on a double integral RNN design formula is proposed for solving continuous time‐varying matrix inversion, which has incomparable disturbance‐suppression property. For digital hardware applications, the corresponding advanced discrete‐time RNN model is proposed based on the discretisation formulas. As a result of theoretical analysis, it is demonstrated that the advanced continuous‐time RNN model and the corresponding advanced discrete‐time RNN model have global and exponential convergence performance, and they are excellent for suppressing different disturbances. Finally, inspiring experiments, including two numerical experiments and a practical experiment, are presented to demonstrate the effectiveness and superiority of the advanced discrete‐time RNN model for solving discrete time‐varying matrix inversion with disturbance‐suppression.

A spinorial double copy for mathcal{N} = 0 supergravity

The Weyl double copy is a formula relating solutions of scalar, gauge and gravity theories, and is related to the BCJ double copy for scattering amplitudes. The latter relates Yang-Mills theory to mathcal{N} = 0 supergravity, where an axion and dilaton are present in addition to the graviton. However, the traditional Weyl double copy applies only to pure gravity solutions, such that it remains to be seen whether or not it can be extended to the full spectrum of mathcal{N} = 0 supergravity. We examine this question using recently developed twistor methods, showing that some sort of double copy formula for mathcal{N} = 0 supergravity is indeed possible for certain solutions. However, it differs both from the traditional Weyl double copy form, and recent conjectures aimed at generalising the Weyl double copy to non-vacuum solutions.

Kontribusi Sikap Belajar dan Motivasi Belajar Terhadap Hasil Perkuliahan Bahasa Indonesia Mahasiswa

The learning outcomes obtained by each student are different because the potential possessed by students is different, as well as how to develop their potential. How to develop their potential depends on the desires of each student. This is influenced by the motivation that each student has. Learning attitudes also affect student learning outcomes in Indonesian language learning. A person's attitude to something will be addressed through behavior. Students who are positive about and open to accepting learning will provide encouragement to students to achieve success. The objectives of this study are as follows. (1) Knowing the amount of significant contribution between learning attitudes towards student Learning Outcomes of Indonesian language lectures. (2) Knowing the amount of significant contribution of learning motivation to the learning outcomes of student Indonesian language lectures. (3) Knowing the amount of significant contribution between learning attitudes and motivation to learn together to the learning outcomes of student Indonesian language lectures. This type of research is quantitative with descriptive methods and uses correlation design. The population of this study is all FKIP students of Batanghari University. The sampling technique is carried out by random sampling, namely the sampling of sample members from the population which is carried out randomly. This research instrument is in the form of a questionnaire that has been tested for validity and reliability. The data were analyzed using the Pearson Product Moment (PPM) correlation test, double correlation test, t test, F test, and determinant coefficient formula to determine the magnitude of the contribution of free variables to bound variables, either individually or jointly.The results showed that learning attitudes and learning motivation contributed significantly to student lecture learning outcomes by 20.5%. Thus, these variables have a good influence on the learning outcomes of FKIP students at Batanghari University

Biased 2 times 2 periodic Aztec diamond and an elliptic curve

We study random domino tilings of the Aztec diamond with a biased 2 times 2 periodic weight function and associate a linear flow on an elliptic curve to this model. Our main result is a double integral formula for the correlation kernel, in which the integrand is expressed in terms of this flow. For special choices of parameters the flow is periodic, and this allows us to perform a saddle point analysis for the correlation kernel. In these cases we compute the local correlations in the smooth disordered (or gaseous) region. The special example in which the flow has period six is worked out in more detail, and we show that in that case the boundary of the rough disordered region is an algebraic curve of degree eight.

The Hodge bundle, the universal 0-section, and the log Chow ring of the moduli space of curves

We bound from below the complexity of the top Chern class $\lambda _g$ of the Hodge bundle in the Chow ring of the moduli space of curves: no formulas for $\lambda _g$ in terms of classes of degrees 1 and 2 can exist. As a consequence of the Torelli map, the 0-section over the second Voronoi compactification of the moduli of principally polarized abelian varieties also cannot be expressed in terms of classes of degree 1 and 2. Along the way, we establish new cases of Pixton's conjecture for tautological relations. In the log Chow ring of the moduli space of curves, however, we prove $\lambda _g$ lies in the subalgebra generated by logarithmic boundary divisors. The proof is effective and uses Pixton's double ramification cycle formula together with a foundational study of the tautological ring defined by a normal crossings divisor. The results open the door to the search for simpler formulas for $\lambda _g$ on the moduli of curves after log blow-ups.

Poly-Cauchy Numbers with Higher Level

In this article, mainly from the analytical aspect, we introduce poly-Cauchy numbers with higher levels (level s) as a kind of extensions of poly-Cauchy numbers with level 2 and the original poly-Cauchy numbers and investigate their properties. Such poly-Cauchy numbers with higher levels are yielded from the inverse relationship with an s-step function of the exponential function. We show such a function with recurrence relations and give the expressions of poly-Cauchy numbers with higher levels. Poly-Cauchy numbers with higher levels can be also expressed in terms of iterated integrals and a combinatorial summation. Poly-Cauchy numbers with higher levels for negative indices have a double summation formula. In addition, Cauchy numbers with higher levels can be also expressed in terms of determinants.

Adherence to iron and folate supplementation and associated factors among women attending antenatal care in public health facilities at Covid-19 pandemic in Ethiopia.

Adhesion is the degree to which a patient complies with treatment recommendations made by a health care professional. The majority of pregnant women worldwide don't get the recommended amounts of iron and folic acid (30 to 60 mg of iron and 400 g of folic acid/day for 6 months) pregnant women are more likely to develop iron- and folic acid deficiency anemia. For iron and folate supplementation programs to be effective in Ethiopia, adherence is a significant issue. So, this study aimed to evaluate the level and barriers preventing women receiving antenatal care from taking iron and folate supplements. A phenomenological qualitative study design was added to a facility-based cross-sectional study. The sample was established using a double population proportion formula. For the quantitative and qualitative study, 308 pregnant women and the focal points for the health facilities were chosen at random, using systematic random sampling and purposive sampling techniques. For the quantitative study, a face-to-face interviewer-guided, pre-tested structured questionnaire was used; for the qualitative study, a semi-structured questionnaire was used. Data was entered twice, cross-checked by comparing the two separate entries in Epi Data version 7.2.2.6, and exported to SPSS version 25 for analysis. COR and AOR with 95% CI are used to evaluate the relationship between variables and control for confounding factors. Statistical significance was declared at a p-value < 0.05. All, 308 (100%) participants were involved. 56.5% of pregnant women attending an ANC clinic (95% CI: 51%-62.2%) adhered to Iron and folate supplementation. Mothers with primary education], Urban residents mothers, Mother who had four or more ANC visits, mothers who had registered for their first ANC at early gestational age, mothers who had good awareness about birth defects were independent predictors of adherence to Iron and folate supplementation. In our study, adherence to iron and folate supplementation was low relative to previous research findings. Promoting early and frequent ANC visits and improving pregnant women's awareness of anemia and birth defects through education is necessary to increase the adherence status.

Does community-based health insurance reduce disparities in modern health service utilization among households in Ethiopia? A community-based comparative cross-sectional study.

Community-based health insurance (CBHI) is an emerging and promising concept to access affordable and effective healthcare by substantially pooling risks to improve health service utilization (HSU) and equity. While there have been improvements in healthcare coverage in Ethiopia, disparities in healthcare remain a challenge in the healthcare system. Hence, the study aimed to assess the effects of CBHI on the reduction of disparities in modern health service (MHS) utilization among households. A community-based comparative cross-sectional study was conducted between 1 February and 30 April 2022 among households in the Gida Ayana district, Ethiopia. The sample size of 356 was determined using the double population proportion formula, and participants were selected using multistage sampling. Data were entered into EpiData 4.6 and exported to SPSS 25 for analysis. Among 356 households, 321 (90.2%) reported that at least one member of their family fell ill in the previous 6 months; 153 (47.7%) and 168 (52.3%) households were among the insured and uninsured, respectively. Only 207 [64.5, 95% confidence interval (CI) = 59.0-69.7%] of them utilized health services. The level of MHS was 122 (79.7, 95% CI = 75.5-85.8%) and 85 (50.6, 95% CI = 42.8-58.4%) among insured and uninsured, respectively. Insured households were four times more likely to utilize MHS compared to uninsured households [adjusted odds ratio (AOR) = 4.27, 95% CI = 2.36-7.71]. Despite the households being insured, significant disparities in MHS utilization were observed across the place of residence (AOR = 14.98, 95% CI = 5.12-43.82) and education level (AOR = 0.20, 95% CI = 0.05-0.83). Overall, the CBHI scheme significantly improved the level of MHS and reduced disparities in utilization across wealth status and family size differences. However, despite households being insured, significant disparities in the odds of MHS utilization were observed across the place of residence and education level. Hence, strengthening the CBHI scheme and focusing on the place of residence and the education level of households are recommended to improve MHS utilization and reduce its disparities.

Differential addition on binary elliptic curves

This paper presents new and fast differential addition (i.e., the addition of two points with the known difference) and doubling formulas, as the core step in Montgomery scalar multiplication, for various forms of elliptic curves over binary fields. The formulas are provided for binary Edwards, binary Hessian and binary Huff elliptic curves with cost of 5M+4S+1D when the given difference point is in affine form. Here, M,S,D denote the costs of a field multiplication, a field squaring and a field multiplication by a constant, respectively. In this paper, we show that every ordinary elliptic curve E over binary field F2n has Lopez and Dahab differential addition and doubling formulas with suitable function. This paper also presents, new complete differential addition formulas for binary Edwards curves with cost of 5M+4S+2D. Also, new complete Montgomery ladder and scalar multiplication algorithms are presented using the complete differential addition formulas.