Conventional Formula Research Articles

Numerical Solution for Arbitrary Domain of Fractional Integro-differential Equation via the General Shifted Genocchi Polynomials

The Genocchi polynomial has been increasingly used as a convenient tool to solve some fractional calculus problems, due to their nice properties. However, like some other members in the Appell polynomials, the nice properties are always limited to the interval defined in 0 , 1 . In this paper, we extend the Genocchi polynomials to the general shifted Genocchi polynomials, S n a , b x , which are defined for interval a , b . New properties for this general shifted Genocchi polynomials will be introduced, including the determinant form. This general shifted Genocchi polynomials can overcome the conventional formula of finding the Genocchi coefficients of a function f x that involves f n − 1 x which may not be defined at x = 0 , 1 . Hence, we use the general shifted Genocchi polynomials to derive the operational matrix and hence to solve the Fredholm-type fractional integro-differential equations with arbitrary domain a , b .

삼각형의 내접 타원의 넓이에 대한 연구

This research introduces a new method to calculate the area of inellipse of triangle. This formula is derived using the coordinates in the complex plane, the geometrical property of the ellipse, and the Siebeck-Marden theorem rather than the projective transformation and Affine transformation used in the conventional formula derivation. Through this paper, the following results can be obtained. Firstly, we calculated the area of inellipse of triangle related to the ratio of a divided triangle edge determined by the tangency point. Secondly, we derived the area and the ratio of a divided triangle edge of various well-known inellipses of triangle. Thirdly, we reconfirmed that the Steiner inellipse has the maximum area among all inellipses of triangle. This research established the relationship between the area of inellipse of triangle and the Siebeck-Marden theorem, which gives the two foci of inellipse. The new approach could contribute to further research of inellipses.

Formulation Development And In Vitro- Assesment Of Herbal Anti-Bacterial Cream

Objectives of the study: To evaluate various formulation factors and the topical cream formulation of Cassia Siamea flower extract for antibacterial activity. Phytochemical screening and characterization of the topical formulation (cream) made from the alcoholic extract are done after the extraction of Cassia Siamea.
 Materials and Methods:A suitable procedure was used to gather and extract the plants. The yield of the extract was estimated after drying. The broth dilution method was used to determine the MIC. This made it easier to determine the formulation's yield quantity. This yield was used to create cream, after which evaluations were conducted to test the product's quality.
 Results and Discussions: Began with the extraction and was followed by confirmation of the phytochemical evaluation. According to the confirmatory study, the ethanolic extract was devoid of saponins and glycosides. Tannins, phenolics, flavonoids, and alkaloids were also discovered, but not these carbohydrates. In MIC testing, the Cassia Siamea flower extract shown good activity and effectively inhibited the growth of Propionibacterium acnes and Pseudomonas aeruginosa. The designed composition produced a very smooth cream. In accordance with I. P., evaluations were also discovered to be within the range of conventional formulas. Evaluations revealed that the overall formulation had good activity against microorganisms.
 Conclusion: This study reveals that a range of phytochemicals are present in Cassia siamea flowers as an active component, producing positive findings against antibacterial activity and showing great promise as an antibacterial agent. This study also comes to the conclusion that the extraction of Cassia Siamea flowers is essential for the development of better, safer, and more affordable drugs to treat different bacterial illnesses.

MP24-13 PROSTATE SHAPE AND INTRAVESICAL PROSTATIC PROTRUSION ASSESSED BY MAGNETIC RESONANCE IMAGING ARE RELATED TO URINARY SYMPTOMS

MP24-13 PROSTATE SHAPE AND INTRAVESICAL PROSTATIC PROTRUSION ASSESSED BY MAGNETIC RESONANCE IMAGING ARE RELATED TO URINARY SYMPTOMS

Ritual and modern “politeness” in the Romanian Principalities during the Phanariot period

Abstract The paper focusses on ritual “politeness” in the eighteenth- and early-nineteenth century Romanian Principalities of Wallachia and Moldavia from a historical sociopragmatic perspective. The analysis of ceremonial literature and memoirs aims to highlight the instrumental role that the performance of conventional gestures and the use of conventional formulae have in presenting the self/other image. The period under consideration attests to the prominence of the Ottoman cultural model in the Romanian Principalities; nevertheless, the conduct prompted by Western and Central European culture was also rapidly emerging in these borderlands at the same time. When Romanian participants shift their behaviour in intercultural interactions according to the Eastern or Western norms, the choices they make have profound implications (political, social, and cultural).

Interdigital Resonators in Wideband Ridged-Waveguide Filters

Abstract. An interdigital resonator approach for wideband filter applications in ridged-waveguide technology is presented. The interdigital arrangement of the ridged-waveguide resonators ensures stronger coupling between the resonators. As the coupling sections are consequently enlarged by the interdigital arrangement of the resonators, more feasible filter structures are possible at increasing frequencies. The approach itself can be easily implemented with conventional filter synthesis formulas, which is demonstrated by two 20 GHz examples with a bandwidth of 2 GHz and 100 MHz, respectively. The designed filters are subsequently compared to the standard implementation of ridged-waveguide filters.

Force Computation for Dielectrics Using Shape Calculus

Abstract We are concerned with the numerical computation of electrostatic forces/torques in only piece-wise homogeneous materials using the boundary element method (BEM). Conventional force formulas based on the Maxwell stress tensor yield functionals that fail to be continuous on natural trace spaces. Thus their use in conjunction with BEM incurs slow convergence and low accuracy. We employ the remedy discovered in [P. Panchal and R. Hiptmair, Electrostatic force computation with boundary element methods, SMAI J. Comput. Math. 8 (2022), 49–74]. Motivated by the virtual work principle which is interpreted using techniques of shape calculus, and using the adjoint method from shape optimization, we derive stable interface-based force functionals suitable for use with BEM. This is done in the framework of single-trace direct boundary integral equations for second-order transmission problems. Numerical tests confirm the fast asymptotic convergence and superior accuracy of the new formulas for the computation of total forces and torques.

A parametric study on shear deflection performance of open web steel joist

This paper focuses on doing a parametric analysis to ascertain the shear deflection of an open web steel joist under non-uniform bending utilizing theoretical and numerical studies. The goal of this work is to determine the significance of taking shear deflection into account when dealing with open web steel joists as well as how it interacts with changes in beam parameter variations. Using ABAQUS software, a total of forty finite element models were created. The differences between these models may be seen in the flange and web slenderness ratios, which are derived from the three standard steel design codes. Theoretical shear deflection was calculated using Timoshenko and Gere's equations, and flexural deflection for the point load case was calculated using conventional formulae. Since theoretical equations up to the elastic limit are known, the elastic behaviour of the joists is the focus of the whole research. The result compares the load to the maximum elastic deflection obtained by theoretical and finite element analysis and demonstrates strong collaboration, validating the numerical investigation. Additionally, a plot of load versus deflections was made for fewer models, with and without taking into account shear deflection, demonstrating the significance of this factor. Finally, the variance in shear deflection was shown by plotting the total elastic deflections versus the load for all the models with various values. The study's findings suggest that it is significant to take the impact of shear and determine the shear deflection in the case of structural components such open web steel joists. The analysis further reveals that an open web steel joist's shear deflection is greatly impacted by the parametric variation.

Isotropic cosmic birefringence from early dark energy

A tantalizing hint of isotropic cosmic birefringence has been found in the $E B$ cross-power spectrum of the cosmic microwave background (CMB) polarization data with a statistical significance of $3\sigma$. A pseudoscalar field coupled to the CMB photons via the Chern-Simons term can explain this observation. The same field may also be responsible for early dark energy (EDE), which alleviates the so-called Hubble tension. Since the EDE field evolves significantly during the recombination epoch, the conventional formula that relates $E B$ to the difference between the $E$- and $B$-mode auto-power spectra is no longer valid. Solving the Boltzmann equation for polarized photons and the dynamics of the EDE field consistently, we find that currently favored parameter space of the EDE model yields a variety of shapes of the $EB$ spectrum, which can be tested by CMB experiments.

The utility of sonographic signs to diagnose simple and complicated appendicitis in children

BackgroundAcute appendicitis is classified into simple (SA) and complicated (CA). Ultrasound scans (USS) can be useful in clinically equivocal cases, by visualising primary and secondary signs. This study explores the utility of sonographic signs to diagnose and differentiate appendicitis in children.MethodsSingle-centre retrospective cohort study over a 2-year period. Consecutive USS for suspected appendicitis were included; sonographic signs were extracted from standardised institutional worksheets. USS results were compared with pre-defined intraoperative criteria for SA and CA, confirmed with histological analysis. Data are reported as median [interquartile range], percentages (number), area under the curve (AUC), conventional diagnostic formulae and adjusted odds ratios following multiple logistic regression (p < 0.05 considered significant).ResultsA total of 934 USS were included, with median age 10.7 [8.0–13.4] years, majority were female (54%). One quarter (n = 226) had SA, 12% (n = 113) had CA, 61% (n = 571) had no appendectomy and 3% (n = 24) had negative appendicectomy. Appendix visualisation rate on USS was 61% (n = 569), with 62% (n = 580) having a conclusive report. Sonographic signs suggesting appendicitis included an appendiceal diameter > 7 mm (AUC 0.92, [95% CI: 0.90–0.94]), an appendicolith (p = 0.003), hyperaemia (p = 0.001), non-compressibility (p = 0.029) and no luminal gas (p = 0.004). Secondary sonographic signs included probe tenderness (p < 0.001) and peri-appendiceal echogenic fat (p < 0.001). Sonographic signs suggesting CA over SA comprised a diameter > 10.1 mm (AUC 0.63, [95% CI: 0.57–0.69]), an appendicolith (p = 0.003) and peri-appendiceal fluid (p = 0.004).ConclusionPresence of specific sonographic signs can aid diagnosis and differentiation of simple and complicated appendicitis in children.

Explicit Linear Left-and-Right 5-Step Formulas With Zeroing Neural Network for Time-Varying Applications.

In this article, being different from conventional time-discretization (simply called discretization) formulas, explicit linear left-and-right 5-step (ELLR5S) formulas with sixth-order precision are proposed. The general sixth-order ELLR5S formula with four variable parameters is developed first, and constraints of these four parameters are displayed to guarantee the zero stability, consistence, and convergence of the formula. Then, by choosing specific parameter values within constraints, eight specific sixth-order ELLR5S formulas are developed. The general sixth-order ELLR5S formula is further utilized to generate discrete zeroing neural network (DZNN) models for solving time-varying linear and nonlinear systems. For comparison, three conventional discretization formulas are also utilized. Theoretical analyses are presented to show the performance of ELLR5S formulas and DZNN models. Furthermore, abundant experiments, including three practical applications, that is, angle-of-arrival (AoA) localization and two redundant manipulators (PUMA560 manipulator and Kinova manipulator) control, are conducted. The synthesized results substantiate the efficacy and superiority of sixth-order ELLR5S formulas as well as the corresponding DZNN models.

Experimental investigations on effects of gas pressure on mechanical behaviors and failure characteristic of coals

The mechanical behavior of coal is the key factor affecting underground coal mining and coalbed methane extraction. In this study, triaxial compression and seepage tests were carried out on coal at different gas pressures. The mechanical properties and failure process of coal were studied, as well as the acoustic emission (AE) and strain energy. The influence of gas pressure on the mechanical parameters of this coal was analyzed. Based on the conventional energy calculation formula, the pore pressure was introduced through the effective stress formula, and each energy component of coal containing gas was refined innovatively. The contribution of gas pressure to the total energy input and dissipation during loading was quantitatively described. Finally, the influence of gas pressure on coal strength was theoretically analyzed from the perspectives of Mohr–Coulomb criterion and fracture mechanics. The results show that the total absorbed energy comprises the absorbed energy in the axial pressure direction (positive) and in the confining pressure direction (negative), as well as that induced by the pore pressure (initially negative and then positive). The absorbed energy in the axial pressure direction accounts for the main proportion of the total energy absorbed by coal. The quiet period of AE in the initial stage shortens, and AE activity increases during the pre-peak stage under high gas pressure. The fractal characteristics of AE in three stages are studied using the correlation dimension. The AE process has different forms of self-similarity in various deformation stages.

Development of Room Acoustic Prediction and Evaluation Tools for Designers

We develop room acoustic prediction and evaluation tools for designers to be used in halls and conference areas where the design of acoustical performance is essential. The designers, with no specialized knowledge of acoustics, are able to examine the tools at an early stage of the project. The interface tool consists of the 3D CAD software-Rhinoceros, and its plug-in tool-Grasshopper. The designers first build a room model on Rhinoceros and locate the sound source and the receiver points in the model. They then set the calculation conditions via Grasshopper, such as room use and type of interior finishes. Next, room sound propagation is calculated using the ray tracing method in the external python programs. Then, acoustic indices, such as the average sound absorption coefficient and clarity, are predicted. These indices are automatically evaluated according to the room use, and the evaluated results are visualized in the room model on Rhinoceros. This paper outlines these tools and exhibits the agreement of predicted and measured indices in a small hall. These tools are applied to a lecture room with complicated ceiling ribs, and an office with a stairwell, which are difficult to examine by the conventional reverberation formula.

A new method to estimate children's weight accurately in emergency settings using foot length and mid-upper arm circumference

BackgroundIn emergency settings, medication dosages are primarily determined based on the child's weight; however, the healthcare personnel sometimes may have to make the first intervention without knowing the patient's weight, which may result in an underdose or overdose of the medication. We aimed to find a reliable method to estimate children's bodyweight, including the obese and malnourished. MethodsWe conducted the study with children between the ages of 3 and 17 years. We measured the children's bodyweight, right foot length, and mid-upper arm circumference in centimeters during their examination. We created a concise formula through regression analysis to estimate the patients' weight based on the right foot length and mid-upper arm circumference. Finally, we compared this formula to other conventional formulae. ResultsThe study included 741 patients whose average age was 8.4±3.9 (3–17) years. A high correlation was found between the patients' foot length, arm circumference, and bodyweight (R: 0.866, p<0.001 and R: 0.910, p<0.001, respectively). A single formula was created by regression analysis based on foot length and the mid-upper arm circumference without including sex and age in the calculation to make a more straightforward and faster calculation in emergency cases. ConclusionThe formula created may be advantageous for reliably and easily estimating the weight of children aged 3–17 of any sex and body habitus in emergency settings without special equipment. This newly developed formula may enable a low-cost optimal level of weight estimation without the need for special equipment.

Multi-gene GP and GA-FIS Models to Deal with Scaling Problem in the ANFIS model for Estimating Roughness Coefficient in Erodible Channels

Estimation of the roughness coefficient is important for reliable hydraulic design in erodible channels. In this paper, the capability of multi-gene Genetic Programming (GP), a combined Genetic Algorithm and Fuzzy Inference System (GA-FIS) model, and Multi Regression (MR) methods are employed to estimate the roughness coefficient. These methods try to extract either an explicit or an implicit relationship between the roughness coefficient and input variables. In addition, traditional GP, widely used by researchers, and conventional empirical formulas are implemented to evaluate the models. Results show that the employed methods are more accurate than empirical methods. In addition, the effects of some other parameters, such as non-dimensional water depth and shear Reynolds number, are highlighted over the roughness coefficient while previously ignored in the empirical methods. Also, findings prove that the GA is a helpful tool to optimize a FIS compared with gradient-based models like ANFIS, while the scale of input variables is not in the same order. The R2 for multi-gene GP and GA-FIS are 0.8504 and 0.8842, respectively, while this value for the most accurate empirical method (Yalin, 1992) is 0.6286.

Профилактика пищевой аллергии: современные тенденции

An elimination diet is one of the main measures to prevent flares of different food allergies. Primary prophylaxis of food allergies aims to form tolerance and prevent sensitization to food allergens in infants prone to allergies. Pediatric recommendations for the prevention of food allergies based on elimination diets with conventional formulas replaced by hydrolyzed formulas have been revised in the last decade. Currently, the exclusion of food allergens from the mother's diet, as well as administration of vitamins, prebiotics, probiotics, or synbiotics during pregnancy and breastfeeding are not recommended to prevent food allergies in infants. The age between 4 and 6 months is believed to be optimal for introducing complementary foods. It is still not recommended to use soy formula in infants under 6 months of age and use cow milk-based formulas in infants with a risk of allergy during their first week of life. There are no recommendations on any specific formulas to prevent allergy: it is possible to use both hydrolyzed and conventional formulas. Among the latter, goat milk-based formulas have a number of advantages. The assessment of the preventive effect of goat milk-based formulas, and particularly those containing the 2'-FL oligosaccharide, is undoubtedly promising. Key words: infants, allergy, allergy prevention, food allergy, goat milk, 2'-FL oligosaccharide

Novel T1 Analysis Method to Address Reduced Measurement Accuracy Due to Irregular Heart Rate Variability in Myocardial T1 Mapping Using Polarity-corrected Inversion Time Preparation.

Polarity-corrected inversion time preparation (PCTIP), a myocardial T1 mapping technique, is expected to reduce measurement underestimation in the modified Look-Locker inversion recover method. However, measurement precision is reduced, especially for heart rate variability. We devised an analysis using a recurrence formula to overcome this problem and showed that it improved the measurement accuracy, especially at high heart rates. Therefore, this study aimed to determine the effect of this analysis on the accuracy and precision of T1 measurements for irregular heart rate variability. A PCTIP scan using a 3T MRI scanner was performed in phantom experiment. We generated the simulated R-waves required for electrocardiogram (ECG)-gated acquisition using a signal generator set to 30 combinations. T1 map was generated using the signal train of the PCTIP images by nonlinear curve fitting using conventional and recurrence formulas. Accuracy against reference T1 and precision of heart rate variability were evaluated. To evaluate the fitting accuracy of both analyses, the relative fitting error was calculated. For the longer T1, the fitting error was larger than the short T1, with the conventional analysis showing 10.1±2.0%. The recurrence formula analysis showed a small fitting error less than 1%, which was consistent for all heart rate variability patterns. In the conventional analysis, the accuracy, especially for longer T1, showed a large underestimation of the measurements and poor linearity. However, in the recurrence formula analysis, the accuracy improved at a long T1, and linearity also improved. The Bland-Altman plot showed that it varied greatly depending on the heart rate variability pattern for the longer T1 in the conventional analysis, whereas the recurrence formula analysis suppressed this variation. T1 analysis of PCTIP using the recurrence formula analysis achieved accurate and precise T1 measurements, even for irregular heart rate variability.

A novel metric to improve mismatched primer selection and quantification accuracy in amplifying DNA repeats for quantitative polymerase chain reactions.

In quantitative polymerase chain reaction (qPCR) experiments, primers containing mismatches with respect to the template are widely used in measuring repetitive DNA elements. Primer-template mismatches may lead to underestimation of the input sample quantity due to inefficient annealing and amplification. But how primer-template mismatches affect quantification accuracy has not been rigorously investigated. In this study, we performed a series of qPCR experiments in which we tested three pairs of mismatched telomere primers (tel1/tel2, tel1b/tel2b and telg/telc) and two pairs of perfect-match reference gene primers (36B4-F/-R and IFNB1-F/-R) at three different primer concentrations under four cycling conditions. Templates used were genomic DNA from two human cell lines and oligo duplexes which contained telomere sequences, reference gene sequences, or both. We demonstrated that the underestimation of input sample quantity from reactions containing mismatched primers was not due to lower amplification efficiency (E), but due to ineffective usage of the input sample. We defined a novel concept of amplification efficacy (f) which quantifies the effectiveness of input sample amplification by primers. We have modified the conventional qPCR kinetic formula to include f, which corrects the effects of primer mismatches. We demonstrated that reactions containing mismatched telomere primer pairs had similar efficiency (E), but varying degrees of reduced efficacy (f) in comparison to those with the perfect-match gene primer pairs. Using the quantitative parameter f, underestimation of initial target by telomere primers can be adjusted to provide a more accurate measurement. Additionally, we found that the tel1b/tel2b primer set at concentration of 500 nM and 900 nM exhibited the best amplification efficacy f. This study provides a novel way to incorporate an evaluation of amplification efficacy into qPCR analysis. In turn, it improves mismatched primer selection and quantification accuracy in amplifying DNA repeats using qPCR methods.

„Wziąwszy Testamenty obadwa do ręku”. Wiersze religijne z „Pocztu herbów” Wacława Potockiego (przyczynek do rehabilitacji materii i dalszych badań)

The aim of this article is to present selected poems from Poczet herbów by Wacław Potocki – those concerning religious issues. They are unappreciated by the modern researchers but can be perceived differently: as the perfect examples of rejuvenation conventional formula of a stemma. The article focuses on such aspects of these texts as their connection with the tradition of the baroque conceptism, allegorical interpretation of the Bible, and the concept of the Book of Nature.

Refined prediction of crosswind forces on rectangular tall buildings with different side ratios

The crosswind responses of tall buildings are complicated due to numerous influencing factors. However, the relevant codes for estimating the crosswind responses have a limited application scope and the corresponding empirical formulas may cause inaccurate assessment of structural responses due to the fitting errors. This study aims to achieve more accurate and flexible predictions of the crosswind forces and wind-induced responses of rectangular tall buildings in comparison with using the conventional empirical formulas. A series of high-frequency force balance (HFFB) tests was conducted on rectangular tall buildings with side ratios from 0.2 to 5 to investigate the crosswind force spectra and the root mean square (RMS) base moment coefficients in two terrain categories. The crosswind force spectra and the crosswind responses of the structure were predicted by using the new proposed formulas and genetic algorithm-backpropagation (GA-BP) neural network, respectively. The results showed that the RMS crosswind base moment coefficients of rectangular tall buildings generally increase with the increase in the side ratio, and can be expressed as piecewise functions related to the side ratio. The proposed formulas can effectively predict the crosswind force spectra of rectangular tall buildings with different side ratios. Compared with the traditional nonlinear fitting method, the GA-BP neural network has higher fitting accuracy and stronger ability for extrapolation prediction. Combined with the random vibration theory, the GA-BP neural network can accurately predict the crosswind responses of rectangular tall buildings. By comparing with the relevant codes, it shows that the crosswind responses of rectangular tall buildings under different side ratios are overestimated to different degrees by GB 50009-2012.