Multiple Formula Research Articles

Multi-Static Radar System Deployment Within a Non-Connected Region Utilising Particle Swarm Optimization

This paper is mainly devoted to studying the deployment problem of a multi-static radar system (MSRS) within a non-connected deployment region using multi-objective particle swarm optimization (MOPSO). By modeling and reformulating the problem, it can be represented as a multi-objective mixed integer programming (MOMIP), which eliminates the need for additional constraints. To enhance the algorithm performance, integer variables and continuous ones are treated separately employing multiple velocity formulas. The velocity formulas for integer variables are modified using the sigmoid function and genetic operation, leading to the proposal of two MSRS deployment algorithms, namely MOPSO-Sigmoid and MOPSO-Gene. To evaluate the performance of the proposed algorithms, they are compared with two existing MOPSO-based algorithms. The first algorithm is the MSRS deployment algorithm for the non-connected deployment region that addresses the additional constraint problem model. The second algorithm is based on an existing conventional MOPSO algorithm and addresses the equivalent MOMIP problem model. A numerical study demonstrates that MOPSO-Sigmoid and MOPSO-Gene exhibit promising efficiency and effectiveness.

Multiple integral formulas for weighted zeta moments: the case of the sixth moment

Multiple integral formulas for weighted zeta moments: the case of the sixth moment

An explicit multiple case-deletion formula for a linear regression model with correlated errors and a resulting property of the BLUP of a multivariate predictand

An explicit multiple case-deletion formula for a linear regression model with correlated errors and a resulting property of the BLUP of a multivariate predictand

A Novel Method to Optimize Personal IOL Constants

ObjectiveTo describe a novel method called ‘three variable optimization’ that entails a process of doing just one calculation to zero out the mean prediction error of an entire dataset (regardless of size), using only 3 variables: 1) the constant used, 2) the average intraocular lens (IOL) power and 3) the average PE. DesignDevelopment, evaluation, and testing of a method to optimize personal IOL constants. MethodsA dataset of 876 eyes was used as a training set, and another dataset of 1,079 eyes was used to test the method. The Barrett Universal II, Cooke K6, Haigis, RBF 3.0, Hoffer Q, Holladay 1, Holladay 2, SRK/T and T2 were analyzed. The same dataset was also divided into 3 subgroups (short, medium and long eyes). The three variable optimization process was applied to each dataset and subset, and the obtained optimized constants were then used to obtain the mean PE of each dataset. We then compared those results with those obtained by zeroing out the mean PE in the classical method. ResultsThe three variable optimization showed similar results to classical optimization with less data needed to optimize and no clinically significant difference. Dividing the dataset into subsets of short, medium and long eyes, also shows that the method is useful even in those situations. Finally, the method was tested in multiple formulas and it was able to reduce the PE with no clinical significant difference from classical optimization. ConclusionThis method could then be applied by surgeons to optimize their constants by reducing the mean prediction error to zero without prior technical knowledge and it is available online for free at http://wwww.ioloptimization.com.

Quantifying higher-order epistasis: beware the chimera.

Epistasis, or interactions in which alleles at one locus modify the fitness effects of alleles at other loci, plays a fundamental role in genetics, protein evolution, and many other areas of biology. Epistasis is typically quantified by computing the deviation from the expected fitness under an additive or multiplicative model using one of several formulae. However, these formulae are not all equivalent. Importantly, one widely used formula - which we call the chimeric formula - measures deviations from a multiplicative fitness model on an additive scale, thus mixing two measurement scales. We show that for pairwise interactions, the chimeric formula yields a different magnitude, but the same sign (synergistic vs. antagonistic) of epistasis compared to the multiplicative formula that measures both fitness and deviations on a multiplicative scale. However, for higher-order interactions, we show that the chimeric formula can have both different magnitude and sign compared to the multiplicative formula - thus confusing negative epistatic interactions with positive interactions, and vice versa. We resolve these inconsistencies by deriving fundamental connections between the different epistasis formulae and the parameters of the multivariate Bernoulli distribution . Our results demonstrate that the additive and multiplicative epistasis formulae are more mathematically sound than the chimeric formula. Moreover, we demonstrate that the mathematical issues with the chimeric epistasis formula lead to markedly different biological interpretations of real data. Analyzing multi-gene knockout data in yeast, multi-way drug interactions in E. coli , and deep mutational scanning (DMS) of several proteins, we find that 10 - 60% of higher-order interactions have a change in sign with the multiplicative or additive epistasis formula. These sign changes result in qualitatively different findings on functional divergence in the yeast genome, synergistic vs. antagonistic drug interactions, and and epistasis between protein mutations. In particular, in the yeast data, the more appropriate multiplicative formula identifies nearly 500 additional negative three-way interactions, thus extending the trigenic interaction network by 25%.

The Influence Of Education, Coaching, Work Culture And Employee Attitudes On The Work Performance Of Employees Of Puskesmas Tanjung Raya Muara Enim

The research was conducted by the author with the aim of knowing and analyzing the influence of education, coaching, work culture and employee attitudes individually and collectively on the work performance of Tanjung Raya Muara Enim Health Center employees. The research method used in this research is a quantitative method using questionnaires distributed to respondents. Test data quality using validity tests, reliability tests, normality tests. The analysis used is descriptive analysis and inferential analysis using statistical calculations with multiple regression formulas, partial simultaneous tests and coefficient of determination. The research results showed that education, coaching, work culture and employee attitudes had a significant influence individually and collectively on the work performance of Tanjung Raya Muara Enim Community Health Center employees

The Influence Of Work Skills, Communication, Supervision, Work Quality, Support Facilities And Work Load On The Work Achievement Of Employees In The Protocol And Communication Section Of Lahat Regional Secretary Leaders

The research was carried out by the author with the aim of knowing and analyzing the influence of work skills, communication, supervision, work quality, supporting facilities and workload individually and collectively on the work performance of employees of the Protocol and Communication Section of the Lahat Regional Secretary. The research method used in this research is a quantitative method using questionnaires distributed to respondents. Test data quality using validity tests, reliability tests, normality tests. The analysis used is descriptive analysis and inferential analysis using statistical calculations with multiple regression formulas, partial simultaneous tests and coefficient of determination. The research results showed that work skills, communication, supervision, work quality, supporting facilities and workload had a significant effect individually and collectively on the work performance of employees of the Protocol and Communication Section of the Lahat Regional Secretary.

Dilemmas in Elderly Diabetes and Clinical Practice Involving Traditional Chinese Medicine.

Diabetes is a widespread chronic disease that occurs mainly in the elderly population. Due to the difference in pathophysiology between elderly and young patients, the current clinical practice to treat elderly patients with anti-diabetes medications still faces some challenges and dilemmas, such as the urgent need for early diagnosis and prevention, and an imbalance between restricted dietary intake and the risk of undernutrition. Traditional Chinese medicine (TCM) offers various treatment regimens that are actively utilized in the field of diabetes management. Through multiple targets and multiple pathways, TCM formulas, medicinal herbs, and active natural products enhance the efficacy of diabetes prevention and diabetes control measures, simplify complex medication management, and improve common symptoms and common diabetic complications in elderly people. Historically, natural products have played a key role in material composition analysis of TCM and mechanism interpretation to enable drug discovery. However, there have been few conclusions on this topic. This review summarizes the development of TCM for the prevention and management of diabetes in elderly people, existing evidence-based clinical practices, and prospects for future development.

Prosedur Kerja, Hubungan Antar Manusia, Kesejahteraan Kerja dan Disiplin Kerja terhadap Prestasi Kerja Pegawai Dinas Perdagangan Lahat

This research aims to determine the influence of work procedures, human relations, work welfare and work discipline both partially and simultaneously on the work performance of Lahat Trade Service employees. The research method used in this research is a quantitative method using questionnaires distributed to respondents. Test data quality using validity tests, reliability tests, normality tests. The analysis used is descriptive analysis and inferential analysis using statistical calculations with multiple regression formulas, partial tests and coefficients of determination. Work procedures have a significant effect on the work performance of Lahat Trade Service employees. Human Relations Have a Significant Influence on the Work Performance of Lahat Trade Service Employees. Work Welfare Has a Significant Influence on the Work Performance of Lahat Trade Service Employees. Work Discipline Has a Significant Influence on the Work Performance of Lahat Trade Service Employees. Work Procedures, Human Relations, Work Welfare and Work Discipline Have a Significant Influence Together on the Work Performance of Lahat Trade Service Employees. Keywords: Work Discipline, Human Relations, Work Welfare, Work Performance, Work Procedures

Income of Kijang City Village: Impact of Working Capital, Technology, Experience, and Selling Price

The purpose of this research is to determine the influence of working capital, technology, experience, and selling prices on the income of fishermen in the Kijang Kota Village. This study utilizes both primary and secondary data. The research method employed is a quantitative descriptive method. The primary data consists of questionnaires, while secondary data includes records and data from the Central Statistics Agency (BPS). Data collection techniques include questionnaires, documentation, and literature review, with 77 respondents answering a questionnaire containing 53 statements. The data analysis technique involves testing data validity and reliability, classical assumption tests, multiple linear regression tests, and hypothesis testing. The multiple linear regression formula obtained from this research is Y = (0.585) + 0.303X1 + 0.392X2 – 0.144X3 + 0.304X4 + e. The t-test results show calculated t-values of 2.287 for working capital, 5.067 for technology, -1.348 for experience, and 3.244 for selling prices, while the tabulated t-value is 1.993. The F-test results indicate a calculated F-value of 85.191 and a tabulated F-value of 2.73. The coefficient of determination is 0.816, as seen from the Adjusted R Square value. Based on the data analysis results, it can be concluded that working capital, technology, experience, and selling prices, both individually and simultaneously, have an impact on the income of fishermen in the Kijang Kota Village. The influence of these four variables results in an 81.6% increase in the income of fishermen in the Kijang Kota Village, with the remaining percentage being influenced by variables not included in this study.

Determinants of Trust in Cash Waqf Linked Sukuk (CWLS) Stakeholder Institutions: Evidence from A Survey of Indonesian Muslims

This study aims to identify and analyze the influence of the implementation of Good Corporate Governance (GCG), which consists of indicators of transparency, accountability, responsibility, independence, and fairness in three CWLS stakeholder institutions, namely Bank Syariah Indonesia (BSI), Badan Wakaf Indonesia (BWI), and the Indonesian Ministry of Finance. This research falls under quantitative research because the approach used for research proposals, processes, hypotheses, fieldwork, data analysis, and data conclusions up to the writing uses aspects of measurement, calculation, formulas, and certainty of numerical data. The research subjects were Muslim communities who had become CWLS investors and those who had the potential to become investors. In this study, the population and sample were all Muslim community investors and prospective CWLS investors, which collected 261 people. Data were analyzed using multiple linear regression formula. The results of the study show that partially the implementation of GCG in the three CWLS stakeholder institutions, namely BSI, BWI, and MoF, has a significant effect on the level of public trust. Simultaneously, these three institutions also significantly affect the level of public trust in the CWLS management institution.

Metal‐organic frameworks‐assisted electrochemical sensing toward magnesium in medicinal and edible homologous for pharmacological evaluation.

AbstractGiven the importance of Magnesium (Mg) assay for efficacy evaluation of medicinal and edible homologous (MEH), an electrochemical sensor is designed by exploiting the cooperative properties of metal–organic frameworks (MOFs) and gold nanoparticles (AuNPs). To be specific, the constructed bimetallic MOFs ((FeZr)MOF) are designed by using Zr(IV) and Fe(III) clusters as metal sources, which provide a large platform for AuNPs attachment to design signal probes. Benefitting from the catalytic properties of (FeZr)MOF toward hydroxylamine, electrochemical signal is attained for Mg2+ analysis with the detection limit to be 3 μM (corresponding to 0.072 μg g−1). Relying on DNAzymes as recognition elements, good anti‐jamming is achieved for Mg2+ analysis against the coexisting ions in Puerarin, Chinese wolfberry, hawthorn and dangshen. With the superiority of rapid response, acceptable sensitivity and specificity, the electrochemical sensor provides a useful pattern for assessing the pharmacological effects of MEH substances, pointing to reasonable selection and combination of multiple health function dietary therapy formulas.

Radiographic Alignment Parameters for Lumbosacral Reconstruction in Patients With Altered S1 Morphology.

Retrospective quantitative analysis study. Pelvic incidence has been established as central radiographic marker which determines patient-specific correction goals during surgery for adult spinal deformity. In cases with sacral doming or sacral osteotomy where the PI cannot be calculated, reliable radiographic parameters need to be established to determine surgical goals. We aim to determine multiple radiographic parameters and formulas that can be utilized when the S1 superior endplate is obscured. Retrospective analysis was performed on 68 healthy volunteers without prior spine surgery with full-length radiographs. Pelvic incidence, sacral slope, and pelvic tilt were calculated for each patient. Additional measurements such as L4, L5, and S2 incidence, tilt, and slope were collected. A new radiographic parameter defined as the L4-Sciatic notch angle was measured. Regression analysis was performed on each value to determine its relationship with S1 based incidence, tilt, and slope. Mean values for L5 incidence, L4 incidence, and L4 sciatic notch angle were 21.8° ± 8.9, 4.4° ± 8.1, and 44.4° ± 12, respectively. The linear regression analysis produced the following formulas which can be utilized to determine deformity correction goals when pelvic incidence can be calculated pre-operatively: L5i = .65*S1i-11.4, L4i = .44*S1i-18.6, and L4SNA = -.34*S1i + 66.5. In settings where pelvic incidence cannot be calculated, the following formulas can be utilized: L5i = .66*S2i-32.3 and L4SNA = -.02*S2i2 + 1.1*S2i + 63.5. P-values for all regression analyses were <.001. This study provides target radiographic alignment values that can be utilized for patients with either pre-operative altered S1 endplates or in cases with intraoperative alteration of S1 (sacral osteotomy).

Absorption by a Layered Microbolometer Pixel’s Active Element

Microbolometer arrays, i.e., arrays of micro-scale pixels sensing temperature via resistance changes, have proven to be an effective basis for real-time imaging instrumentation in infrared as well as terahertz frequencies. In previous work, a design of THz and IR absorbing nano-laminates of dielectric and metal layers was studied. It was shown via numerical modeling that absorption may be maximized by appropriate choices of thickness, permittivity and conductivity. In this work, an analytical approach to the problem is formulated based on the standard recursive multiple reflection formulas for multi-layered planar structures. The results fully confirm and extend previous numerical work. A previous relationship between wavelength and silicon thickness for maximum absorption, derived numerically for specific parameter combinations, is now generalized in a parametric closed form. The method can be extended to include multiple lossy dielectric layers and may serve as a tool for optimizing the absorption characteristics of more complex layered absorbing structures. This could enhance the sensitivity of the detection scheme of interest, providing benefits in terms of cost, efficiency, precision, and adjustability.

Visualizing the support of Kostant’s weight multiplicity formula for the rank-2 Lie algebras

Visualizing the support of Kostant’s weight multiplicity formula for the rank-2 Lie algebras

Pengaruh Leverage, Likuiditas, Profitabilitas, Umur Perusahaan dan Ukuran Perusahaan Terhadap Kualitas Laporan Keuangan (Study Empiris pada Perusahaan Manufaktur Sektor Makanan &amp; Minuman Yang Terdaftar di Bursa Efek Indonesia Periode 2018 – 2021)

This study aims to examine the effect of Leverage, Liquidity, Profitability, Company Size and Company Age on the Quality of Financial Statements in manufacturing companies listed on the Indonesia Stock Exchange (IDX) for the 2018-2021 period. The population of this study consisted of 32 manufacturing companies listed on the Stock Exchange and the sampling method was carried out by purposive sampling. With this method, a sample of 15 companies was obtained with an observation period of 4 years (2018-2021) so that the number of observations was 60. The annual report data is accessed through the Indonesia Stock Exchange website (www.idx.co.id).Variable Quality of Financial Statements is measured by the Multiple Linear Regression Formula measured by the total Variable x, Variable x Leverage is measured by DAR = Total Debt: Total Assets, Liquidity is measured using the formula Current Ratio = Current Assets: Current Liabilities, Profitability is measured using the formula ROA = Net income after tax: Total assets, company size is measured using the formula Company Size = Ln Total assets, company age is measured using the formula Company age = Research year. The data used in this research is quantitative data. The data collection technique used in this research is the proportional sampling method. The data analysis technique used multiple linear regression analysis.The results showed that: 1) Leverage had a partial effect on the quality of financial statements, 2) Liquidity had a partial effect on the quality of financial statements, 3) Profitability had a partial effect on the quality of financial statements, 4) Company size had a partial effect on the quality of financial statements, 5) Age The company partially influences the quality of financial statements, and Leverage, Liquidity, Profitability, Company size and company age Simultaneously influence the quality of financial statements

Accuracy of the Majority Voting Method with Multiple IOL Power Formulae.

This study aimed to evaluate the efficacy of a majority decision algorithm that integrates intraoperative aberrometry (IA) and two intraocular lens (IOL) frequency formulas. The primary objective was to compare the accuracy of three formulas (IA; Sanders, Retzlaff, and Kraff/Theoretical (SRK/T); and Barrett Universal II (BUII)), in achieving emmetropia in eyes implanted with TFNT lenses (Alcon). A total of 145 eyes of 145 patients were included in the evaluation. Preoperative data were obtained from IOLMaster 700, while intraoperative data were collected from ORA SYSTEMTM. Visual acuity ≥0.8 at the 3-month post-surgery mark was confirmed. We assessed refractive prediction error (RPE), which is the difference between predicted refraction (PR) and postoperative subjective refraction. This evaluation aimed to identify the optimal IOL power with the implemented algorithm. Among the 145 eyes evaluated, 55.9%, 78.7%, and 97.2% achieved postoperative subjective refraction within ±0.13 Diopters (D), ±0.25 D, and ±0.50 D, respectively. The percentages of eyes within ±0.25 D of PR varied by formula type, with values of 57%, 57%, and 54% for IA, BUII, and SRK/T, respectively. For eyes with short to medium axial length (AL<26.00 mm), the percentages within ±0.25 D of RPE were 52%, 58%, and 58% for IA, SRK/T, and BUII, respectively. In contrast, for eyes with long axial length (≥26.00 mm) the percentages were 68%, 52%, and 45% for IA, BUII, and SRK/T, respectively. The proposed majority decision algorithm incorporating IA and two IOL frequency formulas was effective in reducing postoperative refractive error. IA was particularly beneficial for eyes with long axial length. These findings suggest the algorithm has potential to optimize IOL power selection to improve quality of life of patients and clinical practice outcomes.

Excess properties and intermolecular interactions of 2-methoxyethanol + ethylenediamine binary system: Density, viscosity, spectral analyses, computational chemistry, and CO2 absorption property

To examine the fundamental physicochemical properties as well as intermolecular interactions for the 2-methoxyethanol (EGME) (1) + ethylenediamine (EDA) (2) binary system, this work systemically measured the density (ρ) and viscosity (η) values of the binary system with various mole ratios at P = 100.5 kPa and T = (298.15–318.15) K with the growth gap of 5 K. The as-measured values of the pure substances were compared with literature data. Multiple semi-empirical formulas were used to fit ρ and η values, and the absolute average deviations (AAD%) were calculated. After that, the excess molar volume (VmE), partial molar volume (V¯), apparent molar volume (Vφ), viscosity deviation (Δη), excess activation of Gibbs free energy (ΔG∗E), and several thermodynamic properties of the binary system were systemically analyzed. According to analysis results, it has been proven that the interaction exists between EGME and EDA molecules. And then, excess properties were fitted to the Redlich-Kister equation using multi-parametric nonlinear regression analyses, and standard deviations (σ) were calculated. In addition, based on various characterization methods including Raman, ultraviolet (UV), and nuclear magnetic resonance hydrogen (1H NMR) spectral analyses and density functional theory (DFT) calculation results, it is demonstrated that there is intermolecular hydrogen bonds in EGME (1) + EDA (2) binary system as the form of –OH⋯NH2–, which was consistent with the existence forms of intermolecular hydrogen bonds in different alcohol-amine systems from references. Finally, CO2 absorption capacity by pure EDA, pure EGME, and the EGME (1) + EDA (2) binary system were severally determined.

Structural reliability analysis under stochastic seismic excitations and multidimensional limit state based on gamma mixture model and copula function

A novel method for analyzing the reliability of structures under non-stationary stochastic seismic excitations, considering the combined effect of multiple structural demand extreme values, is proposed. The spectral representation method is employed to establish a non-stationary stochastic seismic excitation model, and based on the theory of first-passage probability, multiple integral formulas for seismic reliability under multidimensional limit states are derived. The extreme value distribution is established using the Gamma mixture model (GMM). The equations for estimating the model parameters are derived based on both fractional moments and moment-generating functions, while the determination of the number of gamma distribution components is guided by the probability distribution and statistical characteristics of the samples. The joint probability density function (JPDF) for multiple demand extreme values is established by incorporating copula functions to account for correlation, and the fitting accuracy of different copula functions is assessed. The proposed method is illustrated using reinforced concrete (RC) frame structures. The results demonstrate that the fitting accuracy of extreme value distribution can be enhanced by adjusting the number of gamma distribution components in the GMM, which exhibits high accuracy in fitting both the main and tail regions. The presence of correlation can induce variations in the JPDF, thereby exerting an influence on the failure probability. Consequently, disregarding correlation is not conducive to reliability analysis.

The Koszul Complex and a Certain Induced Module for a Quantum group

Abstract We give a description of a certain induced module for a quantum group of type $A$. Together with our previous results this gives a proof of Lusztig’s conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra of type $A_{n}$ at the $\ell $-th root of unity, where $\ell $ is an odd integer satisfying $(\ell ,n+1)=1$ and $\ell&amp;gt; n+1$.