Search Results (155)

This work aims to analyze the effect of pore size on the catalytic reaction of 316L stainless steel electrodes. Porous compacts were fabricated using the space holder technique and sintering at low temperatures. The fabricated porous compacts were characterized using computed tomography and the hydrogen evolution reaction was evaluated under 0.5 M and 1.5 M NaOH. Results indicate that porosity is well controlled by the pore formers, which allows different pore size distributions of pores with similar relative density values to be obtained. The pores are fully interconnected, allowing the passing of fluid throughout the compacts. Permeability is sensitive to the pore size, increasing as the pore size does. The catalytic activity of hydrogen evolution reaction HER is improved as the pore volume and pore size increase concerning the compact fabricated without pore formers. The compact that showed higher C_dl and R_f values was fabricated with S100 pore formers, which means a higher active area that favors the HER. It can be concluded that porosity enhances HER reactivity. However, larger pores are not beneficial due to a more significant permeability value. Full article

Biometals used for the replacement of damaged bones are required to have a Young’s modulus comparable with that of the surrounding bones, in addition to having no toxicity, high corrosion resistance, and high strength. The Young’s modulus of natural bones is much lower than those of common biometals. Porous biometals have been widely studied to achieve a lower Young’s modulus. However, these materials commonly exhibit low strength because the pores tend to behave as microscopic defects. In this study, porous titanium, a promising biometal, was reinforced with short titanium fibers. The porous structure and fiber reinforcement provided a low Young’s modulus and relatively high strength, respectively. The short-titanium-fiber-reinforced porous titanium was fabricated using the space holder method with spark plasma sintering. The porosity of the matrix (uniform porous titanium), volume fraction of the fibers, and aspect ratio were set to 60%, 30%, and 8 to 64, respectively. A bending test revealed that the Young’s modulus was low and almost constant, irrespective of the aspect ratio, and that the strength increased with an increased aspect ratio. A high strength, which is difficult to obtain with uniform porous titanium, and a low Young’s modulus were achieved by applying fiber reinforcement. The results demonstrate that short-titanium-fiber-reinforced porous titanium is a candidate biometal for the replacement of damaged bones. Full article

We explore the existence and uniqueness of solutions to nonlinear fractional differential equations (FDEs), defined in the sense of RL-fractional derivatives of order $\eta \in (1,2)$. The nonlinear term is assumed to have a discontinuity at zero. By employing techniques from Lebesgue spaces, including Holder’s inequality, we establish uniqueness theorems for this problem, analogous to Nagumo, Krasnoselskii–Krein, and Osgood-type results. These findings provide a fundamental framework for understanding the properties of solutions to nonlinear FDEs with discontinuous nonlinearities. Full article

The problem of equivalence between differential and integral problems is absolutely crucial when applying solution methods based on operators and their properties in function spaces. In this paper, we complement the solution of this important problem by considering the case of general derivatives and integrals of fractional order for vector functions for weak topology. Even if a Caputo differential fractional order problem has a right-hand side that is weakly continuous, the equivalence between the differential and integral forms may be affected. In this paper, we present a complete solution to this problem using fractional order Pettis integrals and suitably defined pseudo-derivatives, taking care to construct appropriate Hölder-type spaces on which the operators under study are mutually inverse. In this paper, we prove, in a number of cases, the equivalence of differential and integral problems in Hölder spaces and, by means of appropriate counter-examples, investigate cases where this property of the problems is absent. Full article

We study fixed-point theorems of contractive mappings in b-metric space, cone b-metric space, and the newly introduced extended b-metric space. To generalize an existence and uniqueness result for the so-called ${\mathsf{\Phi }}_s$ functions in the b-metric space to the extended b-metric space and the cone b-metric space, we introduce the class of ${\mathsf{\Phi }}_M$ functions and apply the Hölder continuous condition in the extended b-metric space. The obtained results are applied to prove the existence and uniqueness of solutions and positive solutions for nonlinear integral equations and fractional boundary value problems. Examples and numerical simulation are given to illustrate the applications. Full article

In this paper, we study the problem of the uniqueness of fixed points for operators defined on subspaces of the space of continuous functions $C[a,b]$ equipped with norms stronger than the supremum norm. We are particularly interested in Hölder spaces since they are natural ranges of integral operators of fractional order. Our goal is to preserve the expected regularity of the fixed points (solutions of the equations) when investigating their uniqueness, without assuming a contraction condition on the space under study. We claim some symmetry between the case of the obtained results and the case of the classical Banach fixed-point theorem in such spaces, even for operators which are not necessarily contractions in the sense of the norm of these subspaces. This result is of particular interest for the study of quadratic integral equations, and as an application example we prove the uniqueness theorem for such a kind equations with general fractional order integral operators, which are not necessarily contractions, in a suitably constructed generalized Hölder space. Full article

Highly porous titanium foams are great candidates for replacing bone structures with a low elastic modulus owing to their ability to avoid the stress shielding effect. However, the production of highly porous foams (>70 vol.%) with well-distributed, stable, and predictable porous architectures using powder compaction and space holders is challenging. In this study, pure titanium powder and mechanically alloyed Ti-13Ta-6Sn were mixed with 50, 70, and 80 vol.% KCl powders as a space holder, cold-compacted, and sintered in a plasma-assisted sintering reactor to produce highly porous foams. The space holder was completely removed using heat and plasma species collisions prior to sintering. A Ti-13Ta-6Sn alloy powder with α, β, and metastable FCC-γ phases was synthesized. The characteristics of the alloyed powder, mixing step, and the resulting sintered samples were compared to those of CP-Ti. After sintering, the alloy exhibited α and β phases and a reduced elastic modulus. Foams with an elastic modulus in the range of the cortical and trabecular bones were obtained. The results showed the effects of the space holder volume fractions on the volume fraction, size, distribution, interconnectivity, and shape of the pores. The Ti-13Ta-6Sn foams exhibited a uniform open-celled porous architecture, lower elastic modulus, higher yield strength, and higher passivation resistance than CP-Ti. Ti-13Ta-6Sn exhibited a nontoxic effect for the mouse fibroblast cell line. Full article

An infinite homogeneous tree is a special type of graph that has a completely symmetrical structure in all directions. For an infinite homogeneous tree $T=(\mathcal{V},\mathcal{E})$ with the natural distance d defined on graphs and a weighted measure $\mu$ of exponential growth, the authors introduce the variable Lebesgue space $L^{p(·)}\left(\mu \right)$ over $(\mathcal{V},d,\mu )$ and investigate it under the global Hölder continuity condition for $p(·)$. As an application, the strong and weak boundedness of the maximal operator relevant to admissible trapezoids on $L^{p(·)}\left(\mu \right)$ is obtained, and an unbounded example is presented. Full article

Capillary pressure and permeability of porous media are important for heat transfer devices, including loop heat pipes. In general, smaller pore sizes enhance capillary pressure but decrease permeability. Introducing a bi-porous structure is promising for solving this trade-off relation. In this study, the bi-porous aluminum was fabricated by the space holder method using two different-sized NaCl particles (approximately 400 and 40 μm). The capillary pressure and permeability of the bi-porous Al were evaluated and compared with those of mono-porous Al fabricated by the space holder method. Increasing the porosity of the mono-porous Al improved the permeability but reduced the capillary pressure because of better-connected pores and increased effective pore size. The fraction of large and small pores in the bi-porous Al was successfully controlled under a constant porosity of 70%. The capillary pressure of the bi-porous Al with 40% large and 30% small pores was higher than the mono-porous Al with 70% porosity without sacrificing the permeability. However, the bi-porous Al with other fractions of large and small pores did not exhibit properties superior to the mono-porous Al. Thus, accurately controlling the fractions of large and small pores is required to enhance the capillary performance by introducing the bi-porous structure. Full article

Alleged practices of magical assault and vampirism are a recurrent feature of popular explanations of misfortune in Tuva, South Siberia. Based on a field study of healing practices in an “Association of Shamans”, this article analyses rituals of redressing curse afflictions in the context of Russian political domination. A central purpose of this discussion is to foreground the centrality of kinds of parasitical worship and occult threat to structures of political power in—and beyond—the territory of Tuva. Focusing on a “cursescape”, which develops from the combative practices of shamans, occult specialists, and office-holders, the article probes a repertoire of shamanic healing symbols. It is argued that healing efficacy is constructed in the process of engaging with hunting symbols and animal spirits, which appear in Indigenous Siberian cosmologies. The analysis shows that ideas of ritual risk underpin the process of symbolic resolution. Whereas shamanic practices provide refuge to spirits evicted from their natural landscapes, Tibetan Buddhism—the unifying religion of Tuva—offers an alternative path of healing the effects of the shamans’ propagation of spirits. The article highlights indigenous perceptions of a “cursed” landscape as a space where the agencies of “darkness” and their political sponsors are confronted with an emancipating religious modality emerging from local Buddhist rituals. The analysis displays the unsolved drama of itinerant spirits and shamanic ancestral souls, whose agency is revealed through successive—yet inauspicious—forms of reincarnation. Full article

In this paper, we offer Ostrowski-type inequalities that extend the findings that have been proven for functions of one variable with values in Banach spaces, conducted in a remarkable study by Dragomir, to functions of two variables containing values in the product Banach spaces. Our findings are also an extension of several previous findings that have been established for functions of two variable functions. Prior studies on Ostrowski-type inequalities incriminated functions that have values in Banach spaces or Hilbert spaces. This study is unique and significant in the field of mathematical inequalities, and specifically in the study of Ostrowski-type inequalities, because they have been established for functions having values in a product of two Banach spaces. Full article

As claimed in many papers, the equivalence between the Caputo-type fractional differential problem and the corresponding integral forms may fail outside the spaces of absolutely continuous functions, even in Hölder spaces. To avoid such an equivalence problem, we define a “new” appropriate fractional integral operator, which is the right inverse of the Caputo derivative on some Hölder spaces of critical orders less than 1. A series of illustrative examples and counter-examples substantiate the necessity of our research. As an application, we use our method to discuss the BVP for the Langevin fractional differential equation $\frac{d_{\psi }^{\beta ,\mu }}{d{t}^{\beta }}\left(\frac{d_{\psi }^{\alpha ,\mu }}{d{t}^{\alpha }}+\lambda \right)x\left(t\right)=f(t,x\left(t\right)),t\in [a,b],\lambda \in \mathbb{R}$, for $f\in C\left([a,b]\times \mathbb{R}\right)$ and some critical orders $\beta ,\alpha \in (0,1)$, combined with appropriate initial or boundary conditions, and with general classes of $\psi$-tempered Hilfer problems with $\psi$-tempered fractional derivatives. The BVP for fractional differential problems of the Bagley–Torvik type was also studied. Full article

The microstructure, elastoplastic properties, and corrosive response of induced porous Ti-TiH₂ materials reinforced with TiB₂ particles were investigated. Samples were fabricated using CP-Ti Grade1, Titanium Hydride (TiH₂), TiB₂ powders (0, 3, 10, and 30 vol.%), and ammonium bicarbonate salt (40 vol.%) as a space holder. Composites were fabricated using the Powder Metallurgy technique under high-vacuum conditions (HVS) at 1100 °C. Scanning electron microscopy, X-ray diffraction, nanoindentation tests, and electrochemical assays were used to investigate the pore formation, pore distribution, phase formation, elastoplastic properties, and electrochemical behavior of the compounds, respectively. With a mean pore diameter of 50–900 µm and Young’s modulus of less than 100 GPa, which is close to the properties of human bone, the pore structures of the compounds processed here are shown to be a potential biomaterial for osseointegration. In addition, their $H/E_r$ and $H^3/{E_r}^2$ ratios for the reinforced samples are higher than those of the unreinforced sample (1.5 and 4 times higher than the unreinforced sample, respectively), suggesting a better wear resistance of the Ti-TiH₂/xTiB₂ composites. Electrochemical experiments demonstrated that the Ti-TiH₂/xTiB₂ composites exhibited superior passivation properties compared to the Ti-TiH₂ sample. Additionally, the corrosion rates exhibited by the 3 and 10 vol.% of TiB₂ samples were found to be within an acceptable range for potential biomedical applications (29.26 and 185.82 E-3 mm·y⁻¹). The elastoplastic properties combined with the electrochemical behavior place the Ti-TiH₂/3-10TiB₂ composites as potential candidates for the biomedical application of CP-Ti. Full article

Although introducing high porosity in biomedical Ti alloys can reduce their elastic modulus and promote new bone ingrowth, relieving the stress–shielding effect and implant failure, this also causes a decline in the alloys’ mechanical strength. In this work, a new preparation method for the high–strength and high–porosity Ti₆₅Nb_23.33Zr₅Ta_1.67Fe₅ (TNZTF, at.%) alloy was suggested by sintering nanocomposite powder precursor in combination with the use of a space holder technique, in which NH₄HCO₃ is adopted to achieve a porous structure. The highly porous TNZTF alloy possesses a homogeneous fine–grained microstructure consisting of equiaxed α–Ti and a small amount of FeTi_2, the latter of which is distributed in the β–Ti matrix. Through adjusting the mass fraction of NH₄HCO₃, a novel high–porosity, and high–strength TNZTF alloy with a low modulus was successfully prepared. The porous alloy with the addition of 30 wt.% NH₄HCO₃ exhibits a porosity of 50.3 ± 0.2%, a maximum strength of 327.3 ± 2.1 MPa, and an elastic modulus of 12.2 ± 0.3 GPa. The strength enhancement is mainly attributed to the unique fine–grained microstructure, which is obtained by the crystallization of the amorphous phase and the ductile–brittle mixed fracture mechanism. The prepared porous TNZTF alloy possesses higher mechanical strength and well–matched elastic modulus, showing great potential as an implant material. Full article

This study presents research into the unique method of depositing carbon layers onto processed surfaces, during finishing with abrasive films, on a global basis. The authors of this article are holders of the patent for this method. What makes this technology outstanding is that it integrates processes, whereby micro-finishing and the deposition of a carbon layer onto freshly exposed surface fragments is achieved simultaneously, in a single process. Among the main advantages accruable from this process is the reduction of surface irregularities, while the deposition of a carbon layer is achieved simultaneously. Ultrathin graphite layers can be widely used in conditions where other methods of reducing the coefficient of friction are not possible, such as in regard to micromechanisms. This article illustrates the application of carbon coating, end on, on a surface processed with abrasive film, containing intergranular spaces, saturated with graphite. Thin carbon layers were obtained on two substrates that did not contain carbon in their initial composition: soda–lime glass and a tin–bronze alloy. It was performed through microscopic examinations of the produced surface, roughness analyses of these surfaces, and analysis of the chemical compositions determined by two methods, namely EDS and GDOES, proving the existence of the coatings. The aim of this paper is to prove the possibility and efficiency of using graphite-impregnated lapping films in the deposition process of carbon films, with improved surface smoothness, durability, and wear resistance. The produced coatings will be tested in regard to their operational properties in further research. The authors underline the potential of this method to revolutionize surface treatment processes, due to the significant advantages it offers across various industries. Full article