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We provide a new characterization of the equality of two positive-definite matrices A and B, and we use this to propose several new computationally convenient statistical tests for the equality of two unknown positive-definite matrices. Our primary focus is on testing the information matrix equality (e.g. White, 1982, 1994). We characterize the asymptotic behavior of our new trace-determinant information matrix test statistics under the null and the alternative and investigate their finite-sample performance for a variety of models: linear regression, exponential duration, probit, and Tobit. The parametric bootstrap suggested by Horowitz (1994) delivers critical values that provide admirable level behavior, even in samples as small as n = 50. Our new tests often have better power than the parametric-bootstrap version of the traditional IMT; when they do not, they nevertheless perform respectably.

The present randomised controlled trial aimed to assess the effects of 8-week supplementation of n-3 long-chain polyunsaturated fatty acids (n-3 LCPUFA) on the n-3 index and performance of professional male football players.

A total of 27 professional male football players were randomly assigned into 2 groups: placebo (n = 14) and n-3 LCPUFA (n = 13). n-3 LCPUFA supplements containing 1.5 g eicosapentaenoic acid (EPA) and 600 mg docosahexaenoic acid (DHA) were administered as 6 capsules (four in the morning and two in the evening, 30 min after a meal). Anthropometry, body composition, dried-blood spot n-3 LCPUFA levels, exercise performance and dietary intake of football players were measured at week 0, week 4 and week 8.

n-3 LCPUFA supplementation improved blood levels of EPA and DHA levels, omega-3 index vs placebo (p time*group = 0.010, 0.041 and 0.018, respectively). n-3 LCPUFA supplemented group had significantly higher aerobic capacity than placebo participants, at week 8 (p group = 0.021).

This study shows the effect of n-3 LCPUFA supplementation in Malaysian professional male football players involved in team sports having low dietary intakes of n-3 LCPUFA.

This chapter develops an asymptotic theory for a general transformation model with a time trend, stationary regressors, and unit root nonstationary regressors. This model extends that of Han (1987) to incorporate time trend and nonstationary regressors. When the transformation is specified as an identity function, the model reduces to the conventional cointegrating regression, possibly with a time trend and other stationary regressors, which has been studied in Phillips and Durlauf (1986) and Park and Phillips (1988, 1989). The limiting distributions of the extremum estimator of the transformation parameter and the plug-in estimators of other model parameters are found to critically depend upon the transformation function and the order of the time trend. Simulations demonstrate that the estimators perform well in finite samples.

The purpose of this paper is to determine the structure of nilpotent (n+6)-dimensional n-Lie algebras of class 2 when n≥4.

By dividing a nilpotent (n+6)-dimensional n-Lie algebra of class 2 by a central element, the authors arrive to a nilpotent (n+5) dimensional n-Lie algebra of class 2. Given that the authors have the structure of nilpotent (n+5)-dimensional n-Lie algebras of class 2, the authors have access to the structure of the desired algebras.

In this paper, for each n≥4, the authors have found 24 nilpotent (n+6) dimensional n-Lie algebras of class 2. Of these, 15 are non-split algebras and the nine remaining algebras are written as direct additions of n-Lie algebras of low-dimension and abelian n-Lie algebras.

This classification of n-Lie algebras provides a complete understanding of these algebras that are used in algebraic studies.

The purpose of the study is to perform elastic stress and deformation analysis of a functionally graded hollow disk under different conditions (rotation, gravity, internal pressure, temperature with variable heat generation) and their combinations.

The classical method of solution, Navier's equation, is used to solve the governing equation. The analysis considers thermal and mechanical boundary conditions and takes into account the variation of material properties according to a power law function of the radius of the disk and grading parameter.

The findings of the study reveal distinct trends and behaviors based on different grading parameters. The influence of gravity is found to be negligible, resulting in similar patterns to the pure rotation case. Variable heat generation introduces non-linear temperature profiles and higher displacements, with stress values influenced by grading parameters.

The study provides valuable insights into the behavior of displacement and stresses in hollow disks, offering a deeper understanding of their mechanical response under varying conditions. These insights can be useful in the design and analysis of functionally graded hollow disks in various engineering applications.

The originality and value of this study lies in the consideration of various loading combinations of rotation, gravity, internal pressure and temperature with variable heat generation. Furthermore, the study of effect of various angular rotations, temperatures and pressures expands the understanding of the mechanical behavior of such structures, contributing to the existing body of knowledge in the field.

The purpose of this paper is to analyse the appropriateness of the analytical hierarchy process (AHP) to measure consumers’ acceptance and preference for eggs enriched with omega-3 (n-3) fatty acids as a health claim and to compare its results with the traditional nine-point hedonic scale.

The AHP was used as a multi-criteria decision analysis. Data were obtained from a face-to-face questionnaire completed by 122 consumers in a controlled environment in Cataluña (Spain).

Results showed the capacity of the AHP to analyse consumers’ acceptance and preferences. An agreement between the AHP and the nine-point scale was found showing that n-3 enriched eggs had lower flavour acceptance, conventional eggs had higher yolk colour acceptance, and conventional and the free-range eggs had similar and higher odour acceptance than the other egg types. The most important attributes that determine preferences for egg purchase were the type and the egg price followed by the origin and the egg size.

The AHP approach seems to be a reliable tool to evaluate consumers’ hedonic preferences. However, further testing on other food products with larger sample size is needed.

The AHP methodology has been widely used in many fields in the last decades, but to the knowledge, not in the sensory field. In the Spanish market, studies that analyse consumers’ preferences and acceptance of eggs are scarce, and new insights are needed particularly regarding n-3 enriched eggs.

A unified framework for solving the bending, buckling and vibration problems of rectangular thin plates (RTPs) with four free edges (FFFF), including isotropic RTPs, orthotropic rectangular thin plates (ORTPs) and nano-rectangular plates, is established by using the symplectic superposition method (SSM).

The original fourth-order partial differential equation is first rewritten into Hamiltonian system. The class of boundary value problems of the original equation is decomposed into three subproblems, and each subproblem is given the corresponding symplectic eigenvalues and symplectic eigenvectors by using the separation variable method in Hamiltonian system. The symplectic orthogonality and completeness of symplectic eigen-vectors are proved. Then, the symplectic eigenvector expansion method is applied to solve the each subproblem. Then, the symplectic superposition solution of the boundary value problem of the original fourth-order partial differential equation is given through superposing analytical solutions of three foundation plates.

The bending, vibration and buckling problems of the rectangular nano-plate/isotropic rectangular thin plate/orthotropic rectangular thin plate with FFFF can be solved by the unified symplectic superposition solution respectively.

The symplectic superposition solution obtained is a reference solution to verify the feasibility of other methods. At the same time, it can be used for parameter analysis to deeply understand the mechanical behavior of related RTPs. The advantages of this method are as follows: (1) It provides a systematic framework for solving the boundary value problem of a class of fourth-order partial differential equations. It is expected to solve more complicated boundary value problems of partial differential equations. (2) SSM uses series expansion of symplectic eigenvectors to accurately describe the solution. Moreover, symplectic eigenvectors are orthogonal and directly reflect the orthogonal relationship of vibration modes. (3) The SSM can be carried to bending, buckling and free vibration problems of the same plate with other boundary conditions.

The objective of this study is to assess whether pro-health herbal probiotics, ascorbic acid and allicin added to the finishing diets of hybrid pig influenced the intramuscular fat (IMF) content in longissimus lumborum (LL) muscle, the fatty acid profile and lipid quality indices, as it has an impact on human health.

After 80 days of equal fattening, the pigs were divided into the control group (CT, n = 30 received commercially allowed and applicable antibiotics) and the experimental group (EX, n = 30), which until 95 days of rearing were supplied with fermented herbs extract (FHE Multikraft® Austria) with probiotics Saccharomyces cerevisiae, Lactobacillus casei, Lactobacillus plantarum, L-ascorbic acid and extract of garlic (10% allicin). After slaughter, crude fat content and fatty acid profile were determined in LL muscle samples, and on that basis lipid indices were calculated.

Supplementation with FHE, probiotics, L-ascorbic acid and allicin has significantly impacted the crude fat content in the meat and the percentage of fatty acids content: tricosanoic (C23:0), heptadecanoid (C17:1 n-7), eicosanic (C22:1 11cis n-9) and eicosatrienoic (C20:3 11cis n-3), in comparison to CT group. Amongst lipid quality indices, IMF in LL of pigs from EX group, the C18:2 n-6/C18:3 n-3 ratio is characterised by a significantly higher value and thus is more beneficial to the health of the consumer.

The authors have indicated that using FHE, probiotic supplements with ascorbic acid and allicin in commercial fattening of pigs, as an alternative for antibiotic growth promoters (AGP), improves the fatty acid profile of the meat.

The purpose of this paper is to assess the application of graph coloring and domination to solve the airline-scheduling problem. Graph coloring and domination in graphs have plenty of applications in computer, communication, biological, social, air traffic flow network and airline scheduling.

The process of merging the concept of graph node coloring and domination is called the dominator coloring or the χ_d coloring of a graph, which is defined as a proper coloring of nodes in which each node of the graph dominates all nodes of at least one-color class.

The smallest number of colors used in dominator coloring of a graph is called the dominator coloring number of the graph. The dominator coloring of line graph, central graph, middle graph and total graph of some generalized Petersen graph P_(n ,1) is obtained and the relation between them is established.

The dominator coloring number of certain graph is obtained and the association between the dominator coloring number and domination number of it is established in this paper.

Looks at the evidence and summarizes the reasons behind the encouragements to consume more oil‐rich fish in relation to its benefits in coronary heart disease and other diseases, together with early development. The type of fatty acids, the long chain n‐3 polyunsaturate fatty acids, almost exclusively found in oil‐rich fish, show beneficial effects on the metabolism of biologically active substances called eicosanoids which regulate many processes in the human body. This is the most likely mechanism for the positive effects of oil‐rich fish on various disease processes.