Efficient Formula Research Articles

Design of polarization-independent multilayer dielectric gratings: a reflection-phase threaded approach

We present a method to design polarization-independent multilayer dielectric gratings. In this method the reflection phases in TE and TM polarizations of the multilayer stack thread surface-relief grating at the top and the multilayer stack at the bottom together, allowing the two parts first to be designed separately and efficiently, and then to be combined to achieve simultaneously high diffraction efficiency and large fabrication tolerance. We find numerically that in general a periodic stack is unable to provide the top-grating-demanded phase difference between TM and TE polarizations; adequate aperiodic layers atop of a periodic stack are needed. The analytic diffraction efficiency formula of a recent work [J. Opt. Soc. Am. A 41, 252 (2024)] is used at various places of the presented optimization algorithm to save computation time. An example grating with rectangular surface-relief profile and another with trapezoidal profile were successfully designed, validating the effectiveness of this design method.

The heat engine of magnetic black holes in AdS space with rational nonlinear electrodynamics

The heat engine of magnetic black holes in Einstein-AdS gravity coupled to rational nonlinear electrodynamics, as the working substance, is studied. The dynamical negative cosmological constant is considered as a thermodynamic pressure. We investigate the efficiency of black hole heat engines in extended space thermodynamics for rectangle closed path in the P−V plane and the maximally efficient Carnot cycles. The exact efficiency formula which is written in terms of the mass of the black hole is obtained. It was demonstrated that the black hole efficiency decreases when the nonlinear electrodynamics coupling increases and the black hole efficiency increases if the magnetic charge increases. The relation between the efficiency, event horizon radiuses (entropy) and pressure is obtained. We study an efficiency of the holographic heat engine of a cycle in the vicinity of a critical point. Thus, the heat engine of our model can produce work.

Correcting for Observation Bias in Cancer Progression Modeling.

Tumor progression is driven by the accumulation of genetic alterations, including both point mutations and copy number changes. Understanding the temporal sequence of these events is crucial for comprehending the disease but is not directly discernible from cross-sectional genomic data. Cancer progression models, including Mutual Hazard Networks (MHNs), aim to reconstruct the dynamics of tumor progression by learning the causal interactions between genetic events based on their co-occurrence patterns in cross-sectional data. Here, we highlight a commonly overlooked bias in cross-sectional datasets that can distort progression modeling. Tumors become clinically detectable when they cause symptoms or are identified through imaging or tests. Detection factors, such as size, inflammation (fever, fatigue), and elevated biochemical markers, are influenced by genomic alterations. Ignoring these effects leads to "conditioning on a collider" bias, where events making the tumor more observable appear anticorrelated, creating false suppressive effects or masking promoting effects among genetic events. We enhance MHNs by incorporating the effects of genetic progression events on the inclusion of a tumor in a dataset, thus correcting for collider bias. We derive an efficient tensor formula for the likelihood function and apply it to two datasets from the MSK-IMPACT study. In colon adenocarcinoma, we observe a significantly higher rate of clinical detection for TP53-positive tumors, while in lung adenocarcinoma, the same is true for EGFR-positive tumors. Compared to classical MHNs, this approach eliminates several spurious suppressive interactions and uncovers multiple promoting effects.

Surfaceology for colored Yukawa theory

Arkani-Hamed and collaborators have recently shown that scattering amplitudes for colored theories can be expressed as integrals over combinatorial objects simply constructed from surfaces decorated by kinematic data. In this paper we extend the curve integral formalism to theories with colored fermionic matter and present a compact formula for the all-loop, all-genus, all-multiplicity amplitude integrand of a colored Yukawa theory. The curve integral formalism makes certain properties of the amplitudes manifest and repackages non-trivial numerators into a single combinatorial object. We also present an efficient formula for L-loop integrated amplitudes in terms of a sum over 2L combinatorial determinants.

What sizes of droplets contribute to long-range airborne transmission?

The size range of respiratory droplets contributing to long-range airborne transmission of infections determines the targeted intervention methods. However, the exact size range remains unknown, and the influencing parameters are also undetermined. Here, we investigated the size-resolved transport and fate of respiratory droplets in four reported venues of COVID-19 outbreaks. We utilised a transient number balance model, a set of expired droplet size distributions, existing formulas for size-resolved settling rates and filtration efficiencies, and a deposition model from the International Commission on Radiological Protection. This enabled us to obtain the size-resolved concentrations of exhaled droplets in indoor air, the size-resolved number of droplet nuclei in the inhaled air, and the number of droplets deposited throughout the respiratory tract. The newly defined airborne transmission size range of expired droplets depends on the effective dilution flow rate of the infection venue under consideration. Three criteria were proposed for determining the sizes of droplets involved in long-range airborne transmission. The airborne transmission droplets typically featured an initial diameter of 0.1–4–6 µm, with an hourly volume generation rate of 0.38–0.42 nL/h per index case in the four venues. This newly estimated volume of airborne transmission droplets provides an essential input into the viral load method for estimating the infectious quanta generation rate. Practical significanceOur size-resolved estimation reveals that only a tiny fraction of expired infectious droplets within an airborne transmission size range survives after the removal effects of ventilation, settling, deactivation, and filtration, as well as the transient dilution effect. These droplets remain in indoor air, potentially contributing to long-range airborne transmission. The airborne transmission size range depends on the size-dependent dilution capacity of a room.

An extended group decision-making algorithm with intuitionistic fuzzy set information distance measures and their applications

The intuitionistic fuzzy set is a generalization of the fuzzy set that performs noticeably better in expressing and managing uncertainty. The amount that one intuitionistic fuzzy set differs from the others is given by the distance measure. Certain distance measures that have been suggested by the various researchers do not satisfy the axioms of distance measures and also be counter-intuitive circumstances. In this paper we present a novel distance measure for intuitionistic fuzzy sets that is based on the difference between the cross-evaluation factor’s minimum and maximum, the membership degree and non-membership degree, respectively. The proposed measure satisfies all the axiomatic properties and also resolves the counter-intuitive cases. Consequently, this study provides an efficient symmetric distance formula for determining the distance between the information contained by intuitionistic fuzzy sets. By using numerical examples, it is shown that the new measurement is reliable. Also, we provide pattern recognition algorithms and employ them to solve diagnostic-related problems in medicine.

A comprehensive method for error separation in hydrological modelling

AbstractEvaluation metrics play a pivotal role in the calibration process of hydrological models, serving as objective functions that directly influence the final values of model parameters and significantly affect users' perceptions of model performance. However, the choice and interpretation of evaluation metrics are subjective; therefore, this study provides a more objective framework for assessing model performance. This paper initially explored the applicability of various commonly used evaluation metrics, providing an overview of their limitations. Following this, we decomposed errors by analysing their physical significance and geometric representation in scatter plots, categorizing them into systematic and unsystematic errors. Through the decomposition and derivation of the Nash–Sutcliffe efficiency (NSE) formula, we established the quantitative relationship among various evaluation metrics. The soil and water assessment tool (SWAT) model was utilized to simulate monthly runoff in the Baishan basin (China), for the period 1994–2017, with NSE serving as the objective function for calibration. Our findings are consistent with previous studies, indicating that the model tends to slightly underestimate high flows while significantly overestimating low flows. Further analysis through error decomposition and the examination of relationships among various evaluation metrics revealed that unsystematic errors were dominant during the spring snowmelt runoff period, while systematic errors prevailed in the dry season. By evaluating the runoff series based on the magnitude of runoff or by categorizing it according to seasons and months, a more stringent assessment of the model's performance was achieved. These findings not only highlight the necessity for careful selection of evaluation metrics but also underscore the significance of our methodological advancements in enhancing hydrological model precision and reliability.

Experimental study on interceptor performance of bridge rainwater inlet

ABSTRACT Rainwater inlets are important for bridge drainage, and this paper carries out modeling tests on the interception performance of bridge rainwater inlets in the Daxinganling region of China. The effects of slope, different inlet methods, and grate opening forms on the interception efficiency of rainwater inlets are mainly investigated. The results show: (1) Rainwater inlet interception efficiency increases with increasing cross slope and decreases with increasing longitudinal slope. (2) The innovatively proposed inlet method of spraying above the flume, which is less efficient than the rainwater inlet interception of the diffuse flow method at the front of the flume, the inlet method is more in line with the actual situation. (3) Combined with the weir flow formula to fit the interception efficiency formula, the relative error between the predicted and measured values of the interception efficiency of the formula is less than 5%, indicating the applicability of the formula. (4) Comparing the interception efficiency of grates with different opening forms, it is concluded that the longitudinal curved opening is the best, followed by the longitudinal linear opening, and the transverse opening is the worst. In the transverse opening grates, the fewer longitudinal bars, the better the interception efficiency.

Changes in composition, yield, antimicrobial and antioxidant activities of the Ocimum tenuiflorum L. essential oils as affected by fertilizers

The purpose of this study is to evaluate the impact of multifunctional microbial fertilizer and inorganic macronutrient fertilizers N, P, K on plant biomass, essential oil yield, chemical composition, antimicrobial and antioxidant activities of tulsi (Ocimum tenuiflorum L.) grown in Hanoi, Vietnam. Among the four formulas tested, F2 emerged as the most favourable, comprising a basal fertilization of 10 tons of decomposed manure, 15 kg of multifunctional microbial fertilizer, 150 kg of P fertilizer, and 75 kg of K fertilizer, together with top dressing of 200 kg of N fertilizer and 75 kg of K fertilizer per hectare. This formula yielded the highest tulsi dry biomass (4.73 ton/ha), essential oil yield (0.831%), and essential oil production (39.29 L/ha), which were significantly different (p < 0.001) from those of the remaining formulas. In addition, the concentration of the essential oil main compound - eugenol (63.1%) of tulsi in F2 was also the highest, which may be the cause of the strongest antibacterial activity against Bacillus subtilis, Escherichia coli (IC50 of 320, 273 µg/mL, respectively), and antifungal activity against Candida albicans (IC50 of 400 µg/mL), as well as antioxidant activity (IC50 of 0.165 µg/mL) compared to the other formulas tested. The results suggested the role of both multifunctional microbial fertilizer and inorganic macronutrient fertilizers N, P, K on growth and essential oil biosynthesis in tulsi. These findings are important in identifying the most efficient fertilization formula for cultivating tulsi, serving the needs of the cosmetic and medicinal industries.

Asymptotics of solutions to systems of (pseudo)differential equations with localized right-hand sides

Abstract The article describes a method for constructing semiclassical asymptotic solutions of multidimensional (pseudo)differential partial differential equations with localized right-hand sides. The method is based on the asymptotic reduction of vector problems (under certain additional conditions) to scalar (pseudo)differential problems, for which efficient asymptotic formulas have recently been constructed. The method is based on the Feynman–Maslov operator calculus. Even if the original problems are stated for differential equations, the operators in reduced problems, as a rule, turn out to be pseudodifferential. Further, nontrivial problems of calculating operator symbols in the reduced scalar problems arise in the reduction process. We discuss approaches to the transformation of these symbols so as to enable their effective use when solving real problems. The method is illustrated by several physical examples.

Marketing Efficiency of Banana in Yenagoa Metropolis, Bayelsa State, Nigeria

The study examines the marketing efficiency of bananas in Yenagoa Metropolis of Bayelsa State, Nigeria. The objectives were to describe the socio-economic characteristics of banana marketers; determine the marketing margin and efficiency of banana marketers; identify marketing channels of bananas; and identify the constraints associated with banana marketers in the study area. Ninety (90) questionnaires were retrieved and used for the analysis out of the one hundred and four (104) questionnaires distributed to the banana marketers selected through a multistage random sampling technique from eight (8) markets in Yenagoa Metropolis of Bayelsa State using a structured questionnaire. Descriptive Statistics and marketing margin and efficiency formulas were used to analyse the data. The result showed that banana marketers were predominantly female. Budgetary analysis showed marketing efficiency greater than one which indicated profitability of the market. The Likert type showed the constraints, which significantly affect banana marketing as high perishability (3.88), high cost of transportation (2.98), inadequate market information (2.85) and heavy imposition of tax/levies (2.63). The study, therefore, recommends that Marketers should be encouraged to have market informants that will inform them of the increase or decrease in the prices of bananas in different markets in the study area.

Collection efficiencies of cylindrical and plane parallel ionization chambers: analytical and numerical results and implications for experimentally determined correction factors

Objectives. To derive a collection efficiency formula, fGauss , for cylindrical ionization chambers in pulsed radiation beams from a volume recombination model of Boag et al (1996 Phys. Med. Biol. 41 885–97) including free electrons. To validate fGauss and a parallel plate chamber formula fexp using an ion transport code and calculate changes in collection efficiencies caused by electric field charge screening at 0.1–100 mGy doses-per-pulse. And to determine collection efficiencies CE∞ predicted at infinite voltage in the absence of avalanche effects by fitting scaled formulae to efficiencies computed for 100–400 V chamber voltages and 10 and 100 mGy doses-per-pulse. Approach. Calculations were performed for an idealized parallel plate chamber with 2 mm electrode separation d , and for an idealized cylindrical chamber with 0.5 and 2.333 mm inner and electrode radii rin and rout . Main results. fGauss and fexp predict the same collection efficiencies for cylindrical and parallel plate chambers satisfying d2=(rout2−rin2)ln(rout/rin)/2 , an equivalence condition met by the chambers studied. Without charge screening, efficiencies computed using the code equalled fGauss and fexp . With screening, efficiencies changed by ⩽0.03%, ⩽1.1% and ⩽21.3% at 1, 10 and 100 mGy doses-per-pulse, and differed between the chambers by ⩽0.9% and ⩽19.6% at ⩽10 and 100 mGy dose-per-pulse. For fits of fexp and fGauss , CE∞ values were ⩽1.2% and ⩽17.6% from unity at 10 and 100 mGy per pulse respectively, closer than for other formulae tested. Significance. Allowing for screening, fGauss and fexp described computed collection efficiencies to within 0.03%, 1.1% and 21.3% at doses-per-pulse ⩽1, 10 and 100 mGy. Equivalence of the two chambers broke down at 100 mGy per pulse. Departures of CE∞ values from unity suggest that collection efficiencies determined experimentally by fitting fGauss or fexp to readings made at multiple voltages will be accurate to within 1.2% and 17.6% at 10 and 100 mGy per pulse respectively.

New Data-Driven Models of Mass Flow Rate and Isentropic Efficiency of Dynamic Compressors

Dynamic compressors are widely used in many industrial sectors, such as air, land, and marine vehicle engines, aircraft environmental control systems (ECS), air-conditioning and refrigeration, gas turbines, gas compression and injection, etc. The data-driven formulas of mass flow rate and isentropic efficiency of dynamic compressors are required for the design, energy analysis, performance simulation, and control- and/or diagnosis-oriented dynamic simulation of such compressors and the related systems. This work develops data-driven models for predicting the performance of dynamic compressors, including empirical models for mass flow rate and isentropic efficiency, which have high prediction accuracy and broad application range. The performance maps of two multi-stage axial compressors of an aero engine and a centrifugal compressor of an aircraft ECS were chosen for evaluation of the existing empirical formulas and testing of the new models. There are 16 empirical models of mass flow rate and 14 empirical models of isentropic efficiency evaluated, and the results show that it is necessary to develop highly accurate empirical formulas both for mass flow rate and isentropic efficiency. With the data-driven method, two empirical models for mass flow rate and one for isentropic efficiency are developed. They are in general form, with some terms removable to make them simple while enhancing their applicability and prediction accuracy. The new models have much higher prediction accuracy than the best existing counterparts. The new mass flow rate models predict for the three compressors a mean absolute relative deviation (MAD) not greater than 1.3%, while the best existing models all have MAD > 2.0%. The new efficiency model predicts for the three compressors an MAD of 1.0%, 0.4%, and 1.9%, respectively, while the best existing model predicts for the three compressors an MAD of 1.8%, 0.8%, and 3.2%, respectively.

Efektivitas dan Efisiensi Pengelolaan Keuangan Dana Desa pada Dalu Sepuluh A Tanjung Morawa

Purpose: To evaluate the effectiveness and efficiency of financial management of village funds in Dalu Sepuluh A Village, Tanjung Morawa. Research Methodology: Comparative analysis using effectiveness and efficiency formulas. Document analysis of financial reports and budget plans. Interviews with village officials. Results: Village fund budget management in Dalu Sepuluh A Village did not meet efficiency standards. The effectiveness ratio is 100%. Improvements include better budget planning and increased transparency in financial reporting. Limitations: The study focused on a single village for one fiscal year, limiting its generalizability. Reliance on self-reported data from village officials. Contribution: The findings will contribute to local government financial management, rural development studies, and public administration. This study provides insights for policymakers on village fund management in Indonesia.

Market, Fertility, and Perfection of Agriculture: Conceptual Synthesis in a Single Formula of Efficiency

Market, Fertility, and Perfection of Agriculture: Conceptual Synthesis in a Single Formula of Efficiency

Design and Evaluation of Face Mask Filtration: Mechanisms, Formulas, and Fluid Dynamics Simulations

The global adoption of face masks as a preventive measure against the spread of the SARS-CoV-2 virus (COVID-19) has spurred extensive research into their filtration efficacy. This study begins by elucidating various mechanisms of particle penetration and comparing filtration efficiency formulas with experimental data from prior studies. This is compared to the filtration efficiency experimental measurement developed in our previous study. Moreover, it delves into fluid dynamics simulations to examine different turbulent airflow models. Specifically, it contrasts the airflow velocity distribution of the k-ω and k-ε turbulent flow models with that of a quadrant-based average velocity model developed within this research. Furthermore, the study conducts fluid dynamic simulations to assess airflow profiles for six distinct medical and non-medical face masks. The results underscore substantial disparities among the simulations, emphasising the criticality of employing accurate fluid dynamics models for evaluating airflow patterns during diverse respiratory activities such as breathing, coughing, or sneezing, thereby enhancing environmental health in the realm of infectious disease prevention.

Effects of strengthening prospective nursing practice on sleep quality, anxiety, and depression of awake patients in intensive care unit.

The intensive care unit (ICU) is a specialized hospital department. Awake patients in the ICU frequently encounter adverse psychological states, such as anxiety and fear, often accompanied by poor sleep quality. This situation has garnered significant attention within the medical community. To investigate the impact of prospective nursing intervention strategies on the sleep quality and negative emotional state of conscious ICU patients. One hundred and twenty ICU awake patients admitted to our hospital were selected and randomly divided into control (n = 60) and observation (n = 60) groups. Patients in the control group were cared for using the conventional nursing model, while patients in the observation group were cared for using the prospective nursing model. Sleep improvement was assessed using the International Standardized Sleep Efficiency Formula and Pittsburgh Sleep Quality Index (PSQI). The PSQI, Generalized Anxiety Disorder 7-item (GAD-7) scale, Self-Depression Scale (SDS), and satisfaction before and after treatment were used to assess the negative emotional states of patients under the two care models. Patient satisfaction in the observation group was significantly higher than in the control group. The GAD-7 and SDS scores in the observation group were significantly lower than those in the control group, and the total effective rate of sleep improvement in the observation group was significantly higher than in the control group. After treatment, the PSQI scores of the two groups significantly decreased (P < 0.05). The decrease in the observation group was more significant than that in the control group, and the difference between the two groups was statistically significant. Prospective nursing interventions can improve sleep quality and psychological levels and significantly affect conscious patients in the ICU, which is worthy of clinical application.

Stiffness of Loaded Face of Steel Rectangular Hollow Section Columns with and without Concrete Infill in Beam-column Endplate Connections

This paper presents a new analytical approach for calculating the stiffness of the loaded face of a rectangular hollow section RHS column in beam-column connections with and without concrete infill, as well as with flush and extended endplates, to determine the behavior curve of these types of connections. The approach, based on Eurocode 03's component method, offers efficient analytical formulas for accurately determining the loaded face's stiffness. A comparison with existing methods demonstrates its remarkable simplicity and efficiency, allowing a simple beam model to represent the RHS column's behavior with all relevant parameters considered. Comparison of the new approach to existing ones from the literature demonstrates their reliability and efficiency. Furthermore, when compared to 32 experimental tests presenting nearly the entire range of probable connection configurations, as well as attachment techniques commonly used in construction practice, the margin of error does not exceed 12 percent on average and a maximum of less than 25 percent.

Wound healing potential of a formula based on Populus nigra L. flower buds extract with anti-inflammatory activity

Ethnopharmacological relevanceWound healing is a complex and dysnamic process supported by a myriad of cellular events that are tightly coordinated to repair efficiently damaged tissue. Populus nigra L. (Salicaceae) flower buds are traditionally used in the treatment of dermatitis, upper respiratory tract infections, rheumatism and wounds. Aim of the studyThe aim of this study was to assess the wound healing potential of black poplar ointment containing 10 or 20 % of Populus nigra ethanolic flower buds extract using the excision model in rats. Materials and methodsTwo ointments (10 and 20 %) were prepared from Populus nigra flower buds ethanolic extract and topically applied on the area of excised skin of the rats for either 14 or 20 days. Morphological, macroscopic, histological and biochemical parameters were evaluated. ResultsThe results showed that the extract contained high amounts of total phenols (89.5 ± 7.7 mg caffeic acid equivalent/g of extract) and hydrolysable tannins (142.05 ± 2.55 mg tannic acid equivalent/g of extract), in correlation with strong DPPH (2,2-diphenyl-1-picrylhydrazyl) radical scavenging activity and beta-carotene bleaching with values of 96.31 ± 3.42 and 85.27 ± 1.79 %, respectively. Anti-inflammatory potential was illustrated by lipoxygenase and cyclooxygenase inhibition (52.80 ± 0.2 and 53.88 ± 2.55 %, respectively). Treatment with Populus nigra ointment (10 and 20 %) promoted wound contraction of 97.37 ± 1.19 and 97.28 ± 0.91 %, respectively. The antioxidant marker enzymes, catalase (0.10 ± 0.001; 0.08 ± 0.003 U/mg protein) and superoxide dismutase (363.34 ± 24.37; 317.82 ± 53.83 U/mg protein) activities in the granulation tissues were upgraded with respective treatments of 10 or 20 % ointment. Concurrently, the myeloperoxidase activity (2.21 ± 1.01; 2.13 ± 0.75 U/mg protein) was repressed, indicating anti-inflammatory potential, when compared to untreated, standard and excipient groups. Moreover, a significant increase in respective levels of hydroxyproline (p < 0.001) (28.05 ± 1.20; 25.29 ± 1.17 μg/mg tissue) and hexosamine (p < 0.05) (20.18 ± 1.21; 18.95 ± 1.98 μg/mg tissue) was triggered, reflecting a high regeneration of collagen in the scarred tissue. Histological examination of treated skin tissue revealed higher rates of re-epithelialization, lower neutrophils infiltration and re-vascularization in comparison to the control group. ConclusionGiven that the 10 % ointment was the optimal concentration, our findings offer an efficient drug formula for wound healing.

Parameterization of Secondary Ionization Rates and Photoelectron Heating Rates of Venus and Mars

AbstractAs a fundamental physical process in the ionosphere, photoionization and the associated photoelectrons play vital roles in determining the ionospheric electron density and temperature for Earth and other planets with atmospheres such as Mars and Venus. The production and transport of ionospheric photoelectrons have been widely examined on Earth, but relatively less studied for other terrestrial planets, such as Mars and Venus. In this study, a two‐stream photoelectron transport model for Mars and Venus is constructed, in which the photoelectron fluxes, photoelectron heating rates, primary and secondary ionization rates are calculated. The simulated photoelectron fluxes agree with Mars Atmosphere and Volatile Evolution (MAVEN) observations at various altitudes, with the input of solar spectrum irradiance, electron density and temperature, neutral density and temperature observed by MAVEN. Moreover, by parametrically fitting the simulation results for various solar zenith angles and solar activities, we obtain empirical parameterized formulas for ionization and heating efficiencies which can potentially be adapted to planetary ionospheric models for the community.