Let $G$ be a group with identity $e$ and $R$ be a commutative $G$-graded ring with nonzero unity $1$. Graded semi-primary and graded $1$-absorbing primary ideals have been investigated and examined by several authors as generalizations of graded primary ideals. However, these three concepts are different. In this article, we characterize graded rings over which every graded semi-primary ideal is graded $1$-absorbing primary and graded rings over which every graded $1$-absorbing primary ideal is graded primary.

Let R be a commutative graded ring with unity, S be a multiplicative subset of homogeneous elements of R and P be a graded ideal of R such that P\bigcap S=\emptyset In this article, we introduce several results concerning graded S-prime ideals. Then we introduce the concept of graded weakly S-prime ideals which is a generalization of graded weakly prime ideals. We say that P is a graded weakly S-prime ideal of R if there exists s\in S such that for all x, y\in h(R), if 0\neq xy\in P, then sx\in P or sy\in P. We show that graded weakly S-prime ideals have many acquaintance properties to these of graded weakly prime ideals.

We propose a notion of $(q,\sigma,\tau)$-differential graded algebra, which generalizes the notions of $(\sigma,\tau)$-differential graded algebra and $q$-differential graded algebra. We construct two examples of $(q,\sigma,\tau)$-differential graded algebra, where the first one is constructed by means of generalized Clifford algebra with two generators (reduced quantum plane), where we use a $(\sigma,\tau)$-twisted graded $q$-commutator. In order to construct the second example, we introduce a notion of $(\sigma,\tau)$-pre-cosimplicial algebra.

In our study we investigated the additive manufacturing (AM) of ceramic-based Functionally Graded Materials (FGM) by the direct AM technology Thermoplastic 3D-Printing (T3DP). Zirconia components with a varying microstructure were additively manufactured by using thermoplastic suspensions with different contents of pore forming agents (PFA) and were co-sintered defect-free. Different materials were investigated concerning their suitability as PFA for the T3DP process. Different zirconia-based suspensions were prepared and used for AM of single- and multi-material test components. All samples were sintered defect-free and in the end we could realize a brick wall-like component consisting of dense (<1% porosity) and porous (approx. 5% porosity) zirconia areas to combine different properties in one component. The T3DP opens the door to AM of further ceramic-based 4D-components like multi-color or multi-material, especially multi-functional components.

The aim of this study was to clarify effects of 3-week work-matched high-intensity intermittent cycling training (HIICT) with different cadences on VO2max in university athletes. Eighteen university athletes performed HIICT with either 60 rpm (n = 9) or 120 rpm (n = 9). HIICT consisted of eight sets of 20-s exercise with a 10-s passive rest between each sets. The initial training intensity was set at 135% of VO2 max and was decreased by 5% every two sets. Athletes in both groups performed 9 sessions of HIICT during 3-week. The total work-load and achievement rate of the work load calculated before experiments in each group were used for analysis. VO2max was measured pre and post-training. After 3-week of training, no significant differences in the total work-load and achievement rate of the work load were found between the two groups. VO2max similarly increased in both groups from pre to post training (p = 0.016), with no significant differences between the groups (p = 0.680). These results suggest that cadence during HIICT is not training variable affecting effect of VO2max.

Directed energy deposition (DED) is an efficient method to fabricate functionally graded materials (FGMs) with gradient composition and complex structures, allowing for local tailoring of properties instead of the costly need for extraneous welds and joints. In this study, a FGM from stainless steel to Inconel alloy was successfully fabricated using the powder-based laser DED. A very refined grain structure has been observed in at the composition with 75 wt.% Inconel alloy content, which also exhibits the highest (entropy). For the first time, the post heat treatments, microstructure and aging precipitation behaviors of FGMs were systematically studied via experimental characterization and computation, to elucidate their effects on the gradient smoothing and mechanical properties. The diffusion and segregation of Ni, Nb and Ti elements underly the transformation mechanism between Laves, δ, γ’ and γ’’ phases during precipitation. Homogenization on FGMs not only eliminates the heterogeneity inherited from the AM process, but also provides a practical way to smoothen the gradient on composition and microstructure for the eventual good gradient properties. It has a direct influence on the following precipitation behaviors in the FGM, which highly relies on the diffusion degree of the elements in the matrix and grain boundaries. The high-throughput thermodynamic modeling and kinetic modeling were exploited to evaluate the experimental microstructure and address computational uncertainty using different thermodynamic conditions and databases, which enables an accelerated design through local tailoring of process-structure-property relationships to develop new functional materials.

Let N = N₀+ N₁+ N₂ be a Z₃-graded Novikov algebra. The main goal of the paper is to prove that over a field of characteristic not equal to 3 the algebra N is solvable if N₀ is solvable. We also show that a $Z_2$-graded Novikov algebra N=N₀+ N₂ over a field of characteristic not equal to 2 is solvable if N₀ is solvable. This implies that for every n of the form n=2^k3^l, any Z_n-graded Novikov algebra N over a field of characteristic not equal to 2,3 is solvable if N₀ is solvable.

Additive manufacturing has already been established as a highly versatile manufacturing technique with demonstrated potential to completely transform conventional manufacturing in the future. The objective of this paper is to review the latest progress and challenges associated with the fabrication of multi-material parts using additive manufacturing technologies. Various manufacturing processes and materials used to produce functional components were investigated and summarized. The latest applications of multi-material additive manufacturing (MMAM) in automotive, aerospace, biomedical and dentistry field were demonstrated. Investigation on the current challenges were also carried out to predict the future direction of MMAM processes. It is concluded that the further research and development needed in the design of multi-material interfaces, manufacturing processes and material compatibility of MMAM parts are necessary.

Solidification cracking is a major obstacle when joining dissimilar alloys using additive manufacturing. In this work, location-specific solidification cracking susceptibility has been investigated using an integrated computational materials engineering (ICME) approach for a graded alloy formed by mixing P91 steel and Inconel 740H superalloy. An alloy derived from a mixture of 26 wt.% P91 steel and 74 wt.% Inconel 740H, with high configurational and total entropy, was fabricated using wire-arc additive manufacturing. Microstructure characterization revealed intergranular solidification cracks, which increased in length along with the build height. With inputs from experiments, such as secondary dendrite arm spacing, the DICTRA (diffusion-controlled transformations) module within the Thermo-Calc software was used to model location-specific solidification cracking susceptibility. The top region, with the highest cooling rate, has the highest solidification cracking susceptibility and is in good agreement with the experimentally observed crack length. From Scheil simulations, it was deduced that pronounced segregation of Nb and Cu within the cracks increased the solidification range by suppressing the solidus temperature. The overall solidification cracking susceptibility and freezing range was highest for the 26 wt.% P91 alloy amongst the mixed compositions between P91 steel and 740H superalloy, proving that solidification characteristics play a major role in alloy design for additive manufacturing.

The paper describes the Field Boundary Element Method applied to the fracture analysis of a 2D rectangular plate made of Functionally Graded Material to calculate Mode I Stress Intensity Factor. The object of the Field Boundary Element Method is the transversely isotropic plane plate. Its material presents an exponential variation of the elasticity tensor depending on a scalar function of position, i.e., the elastic tensor results from multiplying a scalar function by a constant taken as a reference. Several examples using a parametric representation of the structural response show the suitability of the method that constitutes a sight of Stress Intensity Factor evaluation of Functionally Graded Materials plane plates even in the case of more complex geometries.

Construction and demolition waste (CDW) represents 1/3 of the weight of all-waste produced. Increasing their recycling and reutilization with recycled aggregates (RA) means closing the life cycle of construction materials. Research has been carried out on artificial aggregates from the exclusive crushing of structural concrete waste in selective demolitions (CDWRConc). This study analyses the use of recycled concrete as graded aggregate (GARConc) and in cement soil (CSRConc). The material complies with the requirements as a road base, although due to the low values of resistance to fragmentation these materials are adequate for use in sensitive road systems and other places such as urban roads and car parks. The sensitive road systems are infrastructures in places of great natural wealth and low traffic intensity, with an annual average of heavy vehicle traffic (AADTh) below 50 vhp/d. As soluble salt contents have been detected, additional waterproofing or drainage measures must be adopted to prevent water infiltration into the layers made up of CDWRHorm. Finally, the high initial values of UCS allow the temporary passage of light vehicles over CSRConc after 3 days.

This paper presents an approach to the vibration analysis of axially functionally graded non-prismatic Timoshenko beams (AFGNPTB) using the finite difference method (FDM). The characteristics (cross-sectional area, moment of inertia, elastic moduli, shear moduli, and mass density) of axially functionally graded beams vary along the longitudinal axis. The Timoshenko beam theory covers cases associated with small deflections based on shear deformation and rotary inertia considerations. The FDM is an approximate method for solving problems described with differential equations. It does not involve solving differential equations; equations are formulated with values at selected points of the structure. In addition, the boundary conditions and not the governing equations are applied at the beam’s ends. In this paper, differential equations were formulated with finite differences, and additional points were introduced at the beam’s ends and at positions of discontinuity (supports, hinges, springs, concentrated mass, spring-mass system, etc.). The introduction of additional points allowed us to apply the governing equations at the beam’s ends and to satisfy the boundary and continuity conditions. Moreover, grid points with variable spacing were also considered, the grid being uniform within beam segments. Vibration analysis of AFGNPTB was conducted with this model, and natural frequencies were determined. Finally, a direct time integration method (DTIM) was presented. The FDM-based DTIM enabled the analysis of forced vibration of AFGNPTB, considering the damping. The results obtained in this study showed good agreement with those of other studies, and the accuracy was always increased through a grid refinement.

This paper presents an approach to the vibration analysis of axially functionally graded (AFG) non-prismatic Euler-Bernoulli beams using the finite difference method (FDM). The characteristics (cross-sectional area, moment of inertia, elastic moduli, and mass density) of AFG beams vary along the longitudinal axis. The FDM is an approximate method for solving problems described with differential equations. It does not involve solving differential equations; equations are formulated with values at selected points of the structure. In addition, the boundary conditions and not the governing equations are applied at the beam’s ends. In this paper, differential equations were formulated with finite differences, and additional points were introduced at the beam’s ends and at positions of discontinuity (supports, hinges, springs, concentrated mass, spring-mass system, etc.). The introduction of additional points allowed us to apply the governing equations at the beam’s ends and to satisfy the boundary and continuity conditions. Moreover, grid points with variable spacing were also considered, the grid being uniform within beam segments. Vibration analysis of AFG non-prismatic Euler-Bernoulli beams was conducted with this model, and natural frequencies were determined. Finally, a direct time integration method (DTIM) was presented. The FDM-based DTIM enabled the analysis of forced vibration of AFG non-prismatic Euler-Bernoulli beams, considering the damping. The results obtained in this paper showed good agreement with those of other studies, and the accuracy was always increased through a grid refinement.