Search Results (38)

In order to test within-group homogeneity for numerical or ordinal variable groupings, we have introduced a family of discrete probability distributions, related to the Gini mean difference, that we now study in a deeper way. A member of such a family is the law of a statistic that operates on the ranks of the values of the random variables by considering the sums of the inter-subgroups ranks of the variable grouping. Being so, a law of the family depends on several parameters such as the cardinal of the group of variables, the number of subgroups of the grouping of variables, and the cardinals of the subgroups of the grouping. The exact distribution of a law of the family faces computational challenges even for moderate values of the cardinal of the whole set of variables. Motivated by this challenge, we show that an asymptotic result allowing approximate quantile values is not possible based on the hypothesis observed in particular cases. Consequently, we propose two methodologies to deal with finite approximations for large values of the parameters. We address, in some particular cases, the quality of the distributional approximation provided by a possible finite approximation. With the purpose of illustrating the usefulness of the grouping laws, we present an application to an example of within-group homogeneity grouping analysis to a grouping originated from a clustering technique applied to cocoa breeding experiment data. The analysis brings to light the homogeneity of production output variables in one specific type of soil. Full article

We give some characterizations of dual Toeplitz operators acting on the orthogonal complement of the Bergman space over bounded symmetric domains. Our main result characterizes those finite sums of products of Toeplitz operators that are themselves dual Toeplitz operators. Furthermore, we obtain a necessary condition for such finite sums of dual Toeplitz products to be compact. As an application of our main result, we derive a sufficient and necessary condition for when the (semi-)commutators of dual Toeplitz operators is zero. Notably, we find that a dual Toeplitz operator is compact if and only if it is the zero operator. Full article

This paper presents a novel Q-value-based formability assessment for optimizing deep drawing processes. The Q-value, derived from thinning limit diagrams (TLDs), uses offset thinning and wrinkling limit curves to define severity levels. It is calculated by summing the product of Pascal’s triangle weighting factors and normalized element counts within each severity level. The effectiveness of this Q-value assessment was demonstrated using experimentally validated finite element analysis (FEA) to optimize blank size, tool geometry, and drawbead design (male bead height and contra-bead radius) for a deep-drawn AA5754-O automotive fuel tank. Validation of FEA results with experimental thickness measurements showed that the Barlat and Lian 1989 yield criterion provided higher accuracy than Hill’s 1948 model. An optimal condition, determined using the Q-value, consists of a 430 mm × 525 mm blank formed by a redesigned tool cooperated with optimized semi-circular drawbead geometries, achieving experimental significant formability improvements by minimizing wrinkling and thinning. During optimization, this study revealed a significant interaction between blank width and length, which influenced formability. Side-wall wrinkles were attributed to insufficient tool support for the blank during forming and were relieved through tool redesign. Furthermore, increasing the male drawbead height effectively reduced wrinkling but led to increased thinning, whereas increasing the contra-bead radius had the opposite effect. Full article

The reliance on soil acidity correctives and mineral fertilizers poses a threat to food production due to the finite nature of these resources and their susceptibility to price volatility from importation. Soil remineralizers have emerged as a sustainable alternative. This study assessed silicate agrominerals as soil remineralizers to replace limestone, gypsum, and conventional fertilizers in a no-tillage system. Conducted in a tropical climate on sandy/medium-textured Ultisol, twelve treatments (combinations of liming, gypsum, mineral fertilization, and remineralizer) were tested for their effects on soybean and sorghum agronomic traits. Applying a remineralizer at 2500 kg ha⁻¹ enhanced soybean productivity by 15% and sorghum by 35% in succession, along with increases in P, S, Ca, Mg, sum of bases (SB), cation exchange capacity (CEC), base saturation (V%) in the 0–0.20 m layer and organic matter in the 0–0.40 m layer, benefiting soil microbiological parameters, with the treatment combining all four products improving soil fertility; however, for better crop productivity, split applications appear to be an alternative to avoid nutrient imbalance. Due to the finer particle size of the remineralizer, which allows faster nutrient release, further research is recommended to investigate the long-term impacts on soil microbiota dynamics, optimal doses and combinations, and economic viability across various soil types and climates. Full article

Relaxation time and frequency spectra are not directly available by measurement. To determine them, an ill-posed inverse problem must be solved based on relaxation stress or oscillatory shear relaxation data. Therefore, the quality of spectra models has only been assessed indirectly by examining the fit of the experiment data to the relaxation modulus or dynamic moduli models. As the measures of data fitting, the mean sum of the moduli square errors were usually used, the minimization of which was an essential step of the identification algorithms. The aim of this paper was to determine a relaxation spectrum model that best approximates the real unknown spectrum in a direct manner. It was assumed that discrete-time noise-corrupted measurements of a relaxation modulus obtained in the stress relaxation experiment are available for identification. A modified relaxation frequency spectrum was defined as a quotient of the real relaxation spectrum and relaxation frequency and expanded into a series of linearly independent exponential functions that are known to constitute a basis of the space of square-integrable functions. The spectrum model, given by a finite series of these basis functions, was assumed. An integral-square error between the real unknown modified spectrum and the spectrum model was taken as a measure of the model quality. This index was proved to be expressed in terms of the measurable relaxation modulus at uniquely defined sampling instants. Next, an empirical identification index was introduced in which the values of the real relaxation modulus are replaced by their noisy measurements. The identification consists of determining the spectrum model that minimizes this empirical index. Tikhonov regularization was applied to guarantee model smoothness and noise robustness. A simple analytical formula was derived to calculate the optimal model parameters and expressed in terms of the singular value decomposition. A complete identification algorithm was developed. The analysis of the model smoothness and model accuracy for noisy measurements was carried out. The equivalence of the direct identification of the relaxation frequency and time spectra has been demonstrated when the time spectrum is modeled by a series of functions given by the product of the relaxation frequency and its exponential function. The direct identification concept can be applied to both viscoelastic fluids and solids; however, some limitations to its applicability have been pointed out. Numerical studies have shown that the proposed identification algorithm can be successfully used to identify Gaussian-like and Kohlrausch–Williams–Watt relaxation spectra. The applicability of this approach to determining other commonly used classes of relaxation spectra was also examined. Full article

Mainstream economics describes virtual wealth with theory that is at odds with the physical laws that govern a nation’s physical resources. This confusion fundamentally prevents the realization of “sustainable” economies. The relation between debt and the metabolism of a country (measured by GDP or power consumption) appears to follow a diffusion relationship, in which debt encodes the temporal evolution of an economic potential. Debt enables the production of resources and the realization of a country’s economic wealth potential (the sum of its environmental, geological, and societal endowments, among others). Any economic scheme dependent on finite stocks of free energy for growth must eventually collapse, and as such cannot be considered sustainable. Our simple debt–diffusion model is shown to closely match the trajectories of 44 different economies. Full article

Finite impulse response (FIR) filters are explicitly used in decisive applications such as communication and signal processing areas. Advancement in the latest technologies necessitates specific designs with optimal characteristics. This research work proposes the realization of an efficient distributed arithmetic adaptive FIR filter (DAAFA) architecture using radix-4 and radix-8 computation. Distributed arithmetic (DA) is extensively used to calculate the sum of products without involving a multiplier. The proposed fixed-point realization of a single multiply and accumulate (MAC) FIR adaptive filter is implemented with minimum complex design. The total longest-way computation time is a combination of the delay that occurred in the error calculation module and the delay involved in updating the filter weights. The longest-way computation time of the filter structure is higher, which results in increased latency. In addition, the approximate design of the radix DA multiplier structure is constructed using Booth recoding, partial product formation block and shifting-based accumulation block. Further, the approximate design of DA offers a reduction in complexity and area with respect to the number of slices and enhances the operating speed. The partial product is created using shifters and efficient adders, which further enhances the performance of the realization. This work is implemented in Xilinx and Altera devices and is compared with the present literature. From the synthesis results, it is observed that the propounded design outperforms in terms of complexity, slice delay product and ultimate speed of exertion. The suggested architecture was found to be decisive in terms of area, delay and complexity abatement. The results indicate that the propounded design achieves area reduction (slices) of about 92.03% compared to the existing design. Also, a speed enhancement of about 90.7% is accomplished for the proposed architecture. Nonetheless, the devised architecture utilizes the least means square approach, which enhances the convergence rate notably. Full article

The determination of the distributions of the eigenvalues associated with matrix-variate gamma and beta random variables of either type proves to be a challenging problem. Several of the approaches utilized so far yield unwieldy representations that, for instance, are expressed in terms of multiple integrals, functions of skew symmetric matrices, ratios of determinants, solutions of differential equations, zonal polynomials, and products of incomplete gamma or beta functions. In the present paper, representations of the density functions of the smallest, largest and $j^{\mathrm{th}}$ largest eigenvalues of matrix-variate gamma and each type of beta random variables are explicitly provided as finite sums when certain parameters are integers and, as explicit series, in the general situations. In each instance, both the real and complex cases are considered. The derivations initially involve an orthonormal or unitary transformation whereby the wedge products of the differential elements of the eigenvalues can be worked out from those of the original matrix-variate random variables. Some of these results also address the distribution of the eigenvalues of a central Wishart matrix as well as eigenvalue problems arising in connection with the analysis of variance procedure and certain tests of hypotheses in multivariate analysis. Additionally, three numerical examples are provided for illustration purposes. Full article

In this study, finite element (FE) simulation by the software Abaqus was relied on to investigate the roll forming process of a wheel rim made of an innovative dual-phase steel, i.e., DP590, after flash butt welding (FBW). In the simulation, an FE model was generated, including the design of the dies for flaring, three-roll forming, and expansion, and detailed key processing parameters based on practical production of the selected DP590. Combined with the microstructures and properties of the weld zone (WZ) and heat-affected zones (HAZs) after FBW, the distribution of stress/strain and the change in thickness of the base metal (BM), WZ and HAZs were analyzed, and compared in the important stages of roll forming. Theoretically, the variation in the microstructure and the corresponding stress–strain behaviors of the BM, WZ, and HAZs after FBW have led to the thickness reduction of DP590 that originated from softening behaviors occurring at the region of subcritical HAZs (SCHAZs), and a small amount of tempered martensite has evidently reduced the hardness and strength of the SCHAZ. Meanwhile, the distribution of stress/strain has been influenced to some extent. Further, the study includes the influence of the friction coefficient on the forming quality of the wheel rim to guarantee the simulation accuracy in practical applications. In sum, the dual-phase steel has to be carefully applied to the wheel rim, which needs to experience the processes of FBW and roll forming, focusing on the performance of SCHAZs. Full article

Ni-based superalloys are widely used in aerospace applications. However, traditional constitutive equations often lack the necessary accuracy to predict their high-temperature behavior. A novel constitutive model, utilizing Taylor series expansions and partial derivatives, is proposed to predict the high-temperature flow behavior of a nickel-based superalloy. Hot compression tests were conducted at various strain rates (0.01 s⁻¹, 0.1 s⁻¹, 1 s⁻¹, and 10 s⁻¹) and temperatures (850 °C to 1200 °C) to gather comprehensive experimental data. The performance of the new model was evaluated against classical models, specifically the Arrhenius and Hensel–Spittel (HS) models, using metrics such as the correlation coefficient (R), root mean square error (RMSE), sum of squared errors (SSE), and sum of absolute errors (SAE). The key findings reveal that the new model achieves superior prediction accuracy with an R value of 0.9948 and significantly lower RMSE (22.5), SSE (16,356), and SAE (5561 MPa) compared to the Arrhenius and HS models. Additionally, the stability of the first-order partial derivative of logarithmic stress with respect to temperature ($\partial \mathrm{l}\mathrm{n}\sigma /\partial T$) indicates that the logarithmic stress–temperature relationship can be approximated by a linear function with minimal curvature, which is effectively described by a second-degree polynomial. Furthermore, the relationship between logarithmic stress and logarithmic strain rate ($\partial \mathrm{l}\mathrm{n}\sigma /\partial \mathrm{l}\mathrm{n}\dot{\epsilon }$) is more precisely captured using a third-degree polynomial. The accuracy of the new model provides an analytical basis for finite element simulation software. This helps better control and optimize processes, thus improving manufacturing efficiency and product quality. This study enables the optimization of high-temperature forming processes for current superalloy products, especially in aerospace engineering and materials science. It also provides a reference for future research on constitutive models and high-temperature material behavior in various industrial applications. Full article

The concept of symmetry has played a major role in Hilbert space setting owing to the structure of a complete inner product space. Subsequently, different studies pertaining to symmetry, including symmetric operators, have investigated real Hilbert spaces. In this paper, we study the solutions to multiple-set split feasibility problems for a pair of finite families of $\beta$-enriched, strictly pseudocontractive mappings in the setup of a real Hilbert space. In view of this, we constructed an iterative scheme that properly included these two mappings into the formula. Under this iterative scheme, an appropriate condition for the existence of solutions and strong and weak convergent results are presented. No sum condition is imposed on the countably finite family of the iteration parameters in obtaining our results unlike for several other results in this direction. In addition, we prove that a slight modification of our iterative scheme could be applied in studying hierarchical variational inequality problems in a real Hilbert space. Our results improve, extend and generalize several results currently existing in the literature. Full article

We characterize the boundedness and compactness of dual Toeplitz operators on the orthogonal complement of the generalized Fock space. We study the problem when the finite sum of the dual Toeplitz products is compact. Additionally, we also consider when the sum of the dual Toeplitz operators is equal to another dual Toeplitz operator. Full article

Lauricella, G. in 1893 defined four multidimensional hypergeometric functions $F_A$, $F_B$, $F_C$ and $F_D$. These functions depended on three variables but were later generalized to many variables. Lauricella’s functions are infinite sums of products of variables and corresponding parameters, each of them has its own parameters. In the present work for Lauricella’s function $F_A^{\left(n\right)}$, the limit formulas are established, some expansion formulas are obtained that are used to write recurrence relations, and new integral representations and a number of differentiation formulas are obtained that are used to obtain the finite and infinite sums. In the presentation and proof of the obtained formulas, already known expansions and integral representations of the considered $F_A^{\left(n\right)}$ function, definitions of gamma and beta functions, and the Gaussian hypergeometric function of one variable are used. Full article

The urgent need to reduce industrial electricity consumption due to diminishing fossil fuels and environmental concerns drives the pursuit of energy-efficient production processes. This study addresses this challenge by investigating the Smoothed Particle Method (SPH) for simulating dry ice compaction, an intricate process poorly addressed by conventional methods. The Finite Element Method (FEM) and SPH have been dealt with by researchers, yet a gap persists regarding SPH mesh parameters’ influence on the empirical curve fit. This research systematically explores Particle Packing Density (PPD) and Mass Scaling (MS) effects on the agreement between simulation and experimental outputs. The Sum of Squared Errors (SSE) method was used for this assessment. By comparing the obtained FEM and SPH results under diverse PPD and MS settings, this study sheds light on the SPH method’s potential in optimizing the dry ice compaction process’s efficiency. The SSE based analyses showed that the goodness of fit did not vary considerably for PDD values of 4 and up. In the case of MS, a better fit was obtained for its lower values. In turn, for the ultimate compression force F_C, an empirical curve fit was obtained for PDD values of 4 and up. That said, the value of MS had no significant bearing on the ultimate compression force F_C. The insights gleaned from this research can largely improve the existing sustainability practices and process design in various energy-conscious industries. Full article

Currently, fossil fuels are used to produce fuels and electricity, which are finite sources and have a negative impact on the natural environment. An excellent alternative to these fuels is biofuels, such as bioethanol from waste forest biomass. Pine needles are one of the most important available forest biomass materials with s significant impact on local understory vegetation. Forest waste biomass, which is a rich source of lignocellulose, can be used in various ways, such as for the eco-economical production of bioethanol. The aim of this study was to analyze the possibilities of bioethanol production from pine needle biomass obtained from forest land following different soil preparations and logging residue management. The pine needle dry matter yield, chemical components of pine needle biomass (cellulose, hemicellulose, lignin), and the amount of ethanol yield per hectare were evaluated. The highest average yield pine needle equal to 6.17 Mg∙ha⁻¹ was observed. Bioethanol yield per hectare from this biomass was the highest for plowing with the LPZ-75 plow and was 1.08 m³∙ha⁻¹. The discussed results were confirmed by detailed statistical analysis. To sum up, the researched pine needle biomass turned out to be an interesting raw material with the potential for bioethanol production. Full article