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The present work has been able to relate the magnetic field produced to the basic physical ionization process and derive a general expression for the same starting from the fundamental retarded scalar and vector potentials (Leinard-Weichert potentials).

The general expression is derived for the diffusiophoretic velocity of a large spherical colloidal particle of radius a in a concentration gradient of general electrolytes of Debye-Huckel parameter κ. On the basis of this expression, simple approximate analytic expressions for the diffusiophoretic velocity correct to the order of (1/κa)0 are derived, which can be applied for large particles with κa ≥ 50 at arbitrary values of the particle zeta potential with negligible errors.

The analysis and design of concrete columns wrapped with fiber-reinforced polymer (FRP) composites require the mathematical equation of stress–strain relationship and the ultimate conditions (i.e., stress and strain) corresponding to the failure of FRP-confined concrete. The ultimate conditions of FRP-confined concrete were mostly developed using empirical methods based on regression analysis of test data obtained from the literature. There is a lack of mechanics-based formulations of the ultimate condition. In addition, from a practical design perspective, despite new advancements in the field of FRP confinement and the availability of sophisticated analysis-oriented and data-driven models, design guidelines and practicing engineers mainly need a single equation for the stress–strain relationship of confined concrete. Thus, in this study, a five-parameter William-Warnke plasticity model was utilized to find a new mechanics-based prediction of the ultimate condition of FRP-confined concrete using an updated database of 788 test data. Moreover, a new optimized stress–strain relationship based on the general expression of the Richard and Abbott equation was developed using 200 complete experimental stress–strain curves from 16 different independent studies. The proposed stress–strain relationship was presented in a single equation for the ease of application and its performance was verified against the experimental curves.

In this article, we introduce a q-analogue of the operators defined by Usta and Betus (Linear Multilinear Algebra, DOI: 10.1080/03081087.2020.1791033 (2020)) and find a general expression of moment...

In this paper, we apply the semi-tensor product of matrices and the real vector representation of quaternion matrix to solve quaternion matrix equations for the first time. We derive the expressions of the least squares Hermitian, Persymmetric and Bisymmetric solution for the quaternion matrix equation $$AXB=C$$ , respectively. Furthermore, we also put forward the equivalent conditions of existence and general expression of the Hermitian, Persymmetric and Bisymmetric solution to the quaternion matrix equation $$AXB=C$$ , respectively. Finally, the validity of our method is verified by numerical experiments with different dimensions.

We investigate the critical transitions in the ensemble of nonlinear oscillators interacting with the dynamical environment based on a threshold. The threshold is encoded by the amplitude of individual oscillators present in the network. The key idea is that whenever the oscillator’s amplitude is above the threshold, that node will be coupled to the environment with particular interaction strength. This consideration mimics the mechanism of quorum sensing by which many biological and chemical systems attain collective behavior when the population density reaches the threshold. We found the emergence of first-order discontinuous transition to steady states when the threshold is less than the maximum amplitude. We also deduced the general expression to obtain critical points in the chosen models.

In the paper, the authors establish Maclaurin's series expansions and series identities for positive integer powers of the inverse sine function, for positive integer powers of the inverse hyperbolic sine function, for the composite of incomplete gamma functions with the inverse hyperbolic sine function, for positive integer powers of the inverse tangent function, and for positive integer powers of the inverse hyperbolic tangent function, in terms of the first kind Stirling numbers and binomial coefficients, apply the newly established Maclaurin's series expansion for positive integer powers of the inverse sine function to derive a closed-form formula for specific values of partial Bell polynomials and to derive a series representation of the generalized logsine function, and deduce several combinatorial identities involving the first kind Stirling numbers. Some of these results simplify and unify some known ones. All of these newly established Maclaurin's series expansions of positive integer powers of the inverse (hyperbolic) sine and tangent functions can be used to derive infinite series representations of the circular constant Pi and of positive integer powers of Pi.

Հոդվածը նվիրված է ընտանեկան հոգեբանության ու հոգեթերա- պիայի առանցքային երեւույթներից մեկին՝ ընտանեկան միֆերին: Աշխա- տանքում տեսական վերլուծության են ենթարկվում մասնագիտական գրականությանը հայտնի մի շարք դրույթներ, մոտեցումներ ու տեսա- կետներ, որոնք, ըստ էության, բացահայտում են ընտանեկան միֆերի տեսակները, ձեւավորման առանձնահատկությունները, նրանց գործառույթ- ները, ազդեցության ձեւերը ընտանեկան հարաբերությունների վրա եւ այլն: Փորձ է արվել ընտանեկան միֆերը ուսումնասիրել եւ վերլուծել սոցիալ- հոգեբանական մոտեցումներով: Կազմակերպված հետազոտության նպա- տակն է եղել բացահայտել ընտանեկան միֆերի կապը ընտանիքի սոցիալ- հոգեբանական առանձնահատկությունների՝ հարմարման եւ համախմբման հետ: Ստացված արդյունքները ցույց են տալիս, որ ընտանեկան սոցիալ-հոգեբանական առանձնահատկությունները առավելապես պայմանա- վորված են ոչ թե միֆոլոգիականության ընդհանուր արտահայտվածության աստիճանով, այլ ընտանեկան միֆի բնույթով, բովանդակությամբ: Հետազոտության արդյունքները կարող են օգտակար լինել ընտանիքների հետ տարվող թերապեւտիկ աշխատանքներում, ինչպես նաեւ կարող են հիմք հանդիսանալ երիտասարդ ընտանիքների հիմնախնդիրները ուսումնասիրել ընտանեկան միֆերի տեսանկյունից։

In this work, a theoretical model is developed to address the effect of primary creep on the relationship between indentation and uniaxial creep tests. By considering the expansion of a spherical cavity in the materials following the primary creeping law, a general expression of the conversion factor is deduced during the primary creep stage. For creep tests with spherical and flat punch indenters, a closed-form formula is specified for the conversion factor that is determined by the stress exponent and hardening exponent. By further considering the difference of the critical time at the onset of steady-state creep deformation between uniaxial and indentation creep tests, it becomes available to convert the indentation creep data into uniaxial creep results during the steady-state creep stage. The rationality and accuracy of the proposed model are verified by comparing with the experimental data of Sn37Pb solder, AZ31 Mg alloy and Succinonitrile. Furthermore, the comparison with previous theoretical models indicates that the ignoring of primary creep effect could lead to the deviation of converted indentation creep data from uniaxial creep results.

In the article, they analyze the concepts of innovation and entrepreneurship in the transformation of universities into entrepreneurial institutions, understanding university institutions as organizations that, in a macro concept of their management is represented in its most general expression; that is the production and application of knowledge. In this sense, the characteristic features of commercial, academic activities in innovative and entrepreneurial universities are analyzed, and the optimal organizational and economic mechanisms for the development of this model are studied, in order to use even more positive experience in systems of higher education in countries with less innovative-entrepreneurial development.

Purpose The consolidation behavior of prefabricated vertical drain (PVD)-installed soft deposits mainly depends on the PVD performance. The purpose of this study is to propose a numerical solution for the consolidation of PVD-installed soft soil using the large-strain theory, in which the reduction of discharge capacity of PVD according to depth and time is simultaneously considered. Design/methodology/approach The proposed solution also takes into account the general constitute relationship of soft soil. Subsequently, the proposed solution is applied to analyze and compare with the monitoring data of two cases, one is the experimental test and another is the test embankment in Saga airport. Findings The results show that the reduction of PVD discharge capacity according to depth and time increased the duration required to achieve a certain degree of consolidation. The consolidation rate is more sensitive to the reduction of PVD discharge capacity according to time than that according to the depth. The effects of the reduction of PVD discharge capacity according to depth are more evident when PVD discharge capacity decreases. The predicted results using the proposed numerical solution were validated well with the monitoring data for both cases in verification. Research limitations/implications In this study, the variation of PVD discharge capacity is only considered in one-dimensional consolidation. However, it is challenging to implement a general expression for discharge capacity variation according to time in the two-dimensional numerical solution (two-dimensional plane strain model). This is the motivation for further study. Practical implications A geotechnical engineer could use the proposed numerical solution to predict the consolidation behavior of the drainage-improved soft deposit considering the PVD discharge capacity variation. Originality/value The large-strain consolidation of PVD-installed soft deposits could be predicted well by using the proposed numerical solution considering the PVD discharge capacity variations according to depth and time.

A general expression is obtained for retarded potentials for a system of equations of macroscopic electrodynamics with fractional Caputo derivatives with respect to time. An analog of the Lienard–Wiechert potentials is obtained. All expressions contain a nonlocal (time-distributed) delay, which takes the temporal dispersion in the system into account.

A theory of the dynamic electrophoresis of a spherical colloidal particle with a slip surface in an oscillating electric field is developed. The slipping length on the particle surface, which is the measure of the degree of the particle surface hydrophobicity, is introduced. The general expression of the particle electrophoretic mobility and its approximate analytic expressions for a particle carrying a low zeta potential are derived.

A general expression to estimate the measurement uncertainty of double-flank gear rolling tests, according to the uncertainty budget method outlined in the GUM, is presented in this paper. This method is more precise than the comparator method and it allows us to know the individual contributions of each error source. Therefore, it is often applied in secondary calibration laboratories or industrial facilities that require a better understanding of their measurement process capability. Furthermore, the proposed expression can be adapted to estimate the measurement uncertainty of any gear tester configuration that works under rolling principles. The paper describes a case study where the uncertainty budget developed is applied to a double-flank worm gear rolling tester. Using experimental values of calibration and characterization of the gear tester, the expanded uncertainties of the rolling parameters Fi”, Fr” and fi” were calculated. Finally, an optimized uncertainty budget is proposed where the main detected error sources are minimized improving therefore the measurement capacities of the tester.

Nair, Sankaran and John (Metron 76 (2018) 133–153) have defined and studied the properties of reliability functions in terms of copulas. In the present paper, we investigate the utility of such functions in inferring the time-dependent association of bivariate distributions. We consider the Clayton measure of association for the study. A general expression for this measure in terms of the generator of Archimedean copulas is given, and a method of finding nature of association using the generators is provided. We derive the relationship of the association measure with the ageing property of the distribution, associated with the generator. We analyze how the hazard rate of survival copulas can be utilized in studying the association between two random variables. Applications of the results in real life situations are discussed.

This study presents a novel expression for the tendon force associated with residual stresses produced during welding of large, thin sections. A general engineering equation is presented as the combination of a closed-form expression, based on idealized treatment, and correction factors to account for the effects of temperature-dependent thermal and mechanical material properties. The closed-form expression corresponds to the assumption of constant material properties. A rigorous mathematical treatment is utilized to derive explicit, exact expressions for the temperature-dependent correction factors without the need for empirical correlations. The temperature-dependent behavior of materials is captured accurately using four dimensionless groups. The analysis was validated through numerical simulations with common structural grades of low-carbon steel, stainless steel, aluminum, and titanium. The idealized treatment resulted in predictions with a mean difference of 18%, which was reduced to 7% by incorporating the correction factors. The remaining error is a systematic overestimate, which can be attributed to compliance effects of the finite plate used in the simulations, and is the focus of ongoing research. The utility of applying the novel tendon force equation to problems in fabrication procedure design is demonstrated with an example predicting distortion during manufacturing of hollow structural sections.

The general expression is derived for the diffusiophoretic velocity of a spherical colloidal particle of radius a in a concentration gradient of symmetrical electrolyte. On the basis of this expression, simple approximate analytic expressions for the diffusiophoretic velocity correct up to the order of 1/κa is derived, where κ is the Debye-Huckel parameter. It is found that the approximate expression correct to order unity can be applied for κa ≥ 50 with negligible errors, while the approximate expression correct to order 1/κa can be applied for κa ≥ 20 with negligible errors.

The Environmental burden of disease (EBD) quantitatively evaluates the health impacts of pathogens by using the disability-adjusted life year (DALY) method. The life loss due to morbidity is a general expression for the EBD outcome and, thus, morbidity analysis is indispensable. Considering the deficiency of previous morbidity analysis methods, the objective of this study was to construct a linear morbidity model by using a generalized linear model (GLM) as a template and introducing exposure dose, pathogen toxicity and human immunity as impact variables. Human experimental data were collected for model fitting, and the results indicated a good fit of the majority of the pathogen data. Consequently, two practical cases of water reuse in Xi'an Siyuan University (Case 1) and Lake Cui, Kunming (Case 2) were selected for model validation. Results for case 1 indicated the major EBD to be attributed to rotaviruses (5.57 × 10−7 DALYs, 95% confidence interval (CI): 4.46 × 10−7-1.72 × 10−4 DALYs) and sprinkling irrigation (5.12 × 10−7 DALYs, 95% CI: 1.95 × 10−7-1.47 × 101 DALYs). Conversely, that for case 2 is mainly attributed to noroviruses (1.42 × 10−7 DALYs, 95% CI: 7.51 × 10−11-2.67 × 10−4 DALYs) and road flushing (1.62 × 10−7 DALYs, 95% CI: 1.16 × 10−7-2.67 × 10−4 DALYs). However, comparison with the suggested threshold of 10−6 DALYs indicated the EBDs for both cases are acceptable and, thus, water reuse is confirmed to be safe. The methodology for morbidity modelling proposed in this research can effectively compensate for missing data in DALY calculation and, thereby, help to optimize the process for EBD evaluation.

An alternative method for the standardless quantitative x-ray diffraction analysis of mixtures of inorganic crystalline phases proposed in the literature several years ago is presented. Our method requires only previously calculated μ*i values from tabulated data for all phases present in the mixtures. It does not require either the determination of calibration constants or the use of external standards, but it does require that the number of analyzed mixtures is larger than or equal to the number of phases present in them, and that the chemical composition of the mixtures are significantly different from each other. The integrated intensities of the chemically pure phases are estimated by a least-squares procedure from XRD data obtained from the mixtures. The method was tested against data published in the literature, with good results. Finally, a general expression for the “Normalized Height Law” proposed on an empirical basis by other researchers, has been theoretically derived.

This paper is dedicated to the solidification of a water drop impacting a cold solid surface. In a first part, we establish a 1D solidification model, derived from the Stefan problem, that aims at predicting the freezing dynamic of a liquid on a cold substrate, taking into account the thermal properties of this substrate. This model is then experimentally validated through a 1D solidification setup, using different liquids and substrates. In a second part, we show that during the actual drop spreading, a thin layer of ice develops between the water and the substrate, and pins the contact line at its edge when the drop reaches its maximal diameter. The liquid film then remains still on its ice and keeps freezing. This configuration lasts until the contact line eventually depins and the liquid film retracts on the ice. We measure and interpret this crucial time of freezing during which the main ice layer is built. Finally, we compare our 1D model prediction to the thickness of this ice pancake and we find a very good agreement. This allows us to provide a general expression for the frozen drop main thickness, using the drop impact and liquid parameters., 17 pages, 6 figures

In this paper, we investigate the modulational instability (MI) in an elliptical birefringent positive-negative index coupler. Also, we derive the general expression for instability gain by taking into account cross-phase modulation (XPM), self-steepening (SS) and intrapulse Raman scattering. The instability gain is attained. Using standard linear stability analysis, particularly, we study different configurations of the birefringence with self-steepening or intrapulse Raman scattering effects on MI for both normal and anomalous group velocity dispersion regimes. We observe that the instability gain exhibits significant changes due to the effects of the cross-phase modulation. Finally, we show that efficient control of the MI can be realized by adjusting the self-steepening and intrapulse Raman scattering term, even in the presence of different configurations of the birefringence.

In this paper, when A and B are {1;1}-quasiseparable matrices, we consider the structured generalized relative eigenvalue condition numbers of the pair $$(A, \, B)$$ with respect to relative perturbations of the parameters defining A and B in the quasiseparable and the Givens-vector representations of these matrices. A general expression is derived for the condition number of the generalized eigenvalue problems of the pair $$(A,\, B)$$ , where A and B are any differentiable function of a vector of parameters with respect to perturbations of such parameters. Moreover, the explicit expressions of the corresponding structured condition numbers with respect to the quasiseparable and Givens-vector representation via tangents for $$\{1; 1\}$$ -quasiseparable matrices are derived. Our proposed condition numbers can be computed efficiently by utilizing the recursive structure of quasiseparable matrices. We investigate relationships between various condition numbers of structured generalized eigenvalue problem when A and B are {1;1}-quasiseparable matrices. Numerical results show that there are situations in which the unstructured condition number can be much larger than the structured ones.

The radial consolidation rate of prefabricated vertical drain (PVD)-installed soft deposits is known to be closely related to the PVD discharge capacity, which usually decreases during consolidation. Conventional solutions for radial consolidation of PVD-installed deposits have been developed to consider discharge capacity reduction using small-strain theory, in which the volume compressibility coefficient and soil permeability were assumed to be constant. This paper formulates a general expression for discharge capacity reduction with time in numerical analysis based on large-strain theory. Soil disturbance effects caused by PVD installation, such as a nonlinear distribution for radial hydraulic conductivity, are captured in the proposed solution. The proposed solution was applied to field data from a test embankment at Saga Airport. The proposed solution provides a good result which is close to the measured data.

We provide a general mathematical framework based on the theory of graphical models to study admixture graphs. Admixture graphs are used to describe the ancestral relationships between past and present populations, allowing for population merges and migration events, by means of gene flow. We give various mathematical properties of admixture graphs with particular focus on properties of the so-called F-statistics. Also the Wright–Fisher model is studied and a general expression for the loss of heterozygosity is derived.

The real symmetric matrix is widely applied in various fields, transforming non-symmetric matrix to symmetric matrix becomes very important for solving the problems associated with the original matrix. In this paper, we consider the constrained inverse eigenvalue problem for symmetrizable matrices, and obtain the solvability conditions and the general expression of the solutions. Moreover, we consider the corresponding optimal approximation problem, obtain the explicit expressions of the optimal approximation solution and the minimum norm solution, and give the algorithm and corresponding computational example.

Despite the extensive literature on model fitting to estimate volume in different tree species and regions of Argentina, the references related to volume equations for Populus spp. in irrigated plantations in the Province of Mendoza are scarce. This information is essential for silvicultural management. The objectives of this study were: 1) to calculate and compare the artificial form factors for Populus x canadensis ‘Conti 12’ and ‘Guardi’ clones growing in irrigated plantations in Uco Valley, Mendoza, 2) to fit and compare different equations of stem volume with bark for these two clones and 3) to evaluate the possibility of using a single function to estimate this parameter in both clones. Seven models previously used on Populus in Argentina were fitted to estimate the total stem volume per tree. The form factors for ‘Conti 12’ and ‘Guardi’ were different between them (0.44 and 0.38, respectively). For both, ‘Conti 12’ and ‘Guardi’, the adjustment of the seven models allowed estimating the total stem volume with bark with a very high and similar degree of precision, although in both situations two models (Schumacher-Hall and a variant of the standard function with constant form factor) highlighted over the rest. The statistics of self-validation, homoscedasticity and parsimony criteria allow favoring the decision for the Schumacher-Hall model adjusted individually for each clone and not as a general expression.

In this paper, analytical and numerical solutions are presented for computing the displacements and stresses in a FGM thick-walled cylinder under a uniform internal and external pressure. An analytical and a finite element (FE) model of the pressurized vessel were constructed, where the radial continuous varying of elastic modulus along the thickness was assumed and implemented in a FE code. It has been assumed that the elastic modulus is varying through thickness of the FGM material according to a nonlinear general expression. The analytical solutions of distribution of displacements and stresses were obtained and illustrated in radial direction for pressurized FGM cylinder. The results are checked with FE results. Thus, the inhomogeneity in material properties can be exploited to optimize stress distribution.

Aggregation and deposition of misfolded amyloid-β (Aβ) peptide in the brain is central to Alzheimer's disease (AD). Oligomeric, protofibrillar, and fibrillar forms of Aβ are believed to be neurotoxic and cause neurodegeneration in AD, but the toxicity mechanisms are not well understood and may involve Aβ-interacting molecular partners. In a previous study, we identified potential Aβ42 protofibrillar-binding proteins in serum and cerebrospinal fluid (CSF) using an engineered version of Aβ42 (Aβ42CC) that forms protofibrils, but not fibrils. Here we studied binding of proteins to Aβ42 fibrils in AD and non-AD CSF and compared these with protofibrillar Aβ42CC-binding partners. Aβ42 fibrils sequestered 2.4-fold more proteins than Aβ42CC protofibrils. Proteins with selective binding to fibrillar aggregates with low nanomolar affinity were identified. We also found that protofibrillar and fibrillar Aβ-binding proteins represent distinct functional categories. Aβ42CC protofibrils triggered interactions with proteins involved in catalytic activities, like transferases and oxidoreductases, while Aβ42 fibrils were more likely involved in binding to proteoglycans, growth factors and neuron-associated proteins, e.g., neurexin-1, -2, and -3. Interestingly, 10 brain-enriched proteins were identified among the fibril-binding proteins, while protofibril-extracted proteins had more general expression patterns. Both types of Aβ aggregates bound several extracellular proteins. Additionally, we list a set of CSF proteins that might have potential to discriminate between AD and non-AD CSF samples. The results may be of relevance both for biomarker studies and for studies of Aβ-related toxicity mechanisms.

The performance analysis of the improved proportionate affine projection (IPAP) algorithm is performed in this brief. Based on the energy-conservation arguments, the steady-state analysis of the IPAP algorithm is performed, which provides a general expression of steady-state excess mean-square error for the proportionate-type affine projection algorithms. The tracking behavior is also studied and the step size that optimizes the tracking performance is provided. Simulation results confirm the accuracy of the proposed expressions under different operating scenarios.

Central nervous system (CNS) lymphoma is a rare and aggressive non-Hodgkin lymphoma that might arise in the CNS (primary CNS lymphoma, PCNSL) or disseminates from a systemic lymphoma to the CNS (secondary CNS lymphoma, SCNSL). Dysregulated expression of microRNAs (miRNAs) is associated with various pathological processes and miRNA expression patterns may have diagnostic, prognostic and therapeutic implications. However, miRNA expression is understudied in CNS lymphomas. Here, we performed expression analysis of 798 miRNAs in 73 CNS lymphoma samples using the NanoString platform, followed by a detailed statistical analysis to identify potential novel biomarkers characterizing subgroups and to examine differences based on their primary and secondary nature, molecular subtype, mutational patterns and survival. We describe the general expression patterns of miRNAs across CNS lymphoma samples and identified 31 differentially expressed miRNAs between primary and secondary groups. Additionally, we identified 7 more miRNAs associated with a molecular subtype and 25 associated with mutation status. Using unsupervised clustering methods, we defined a small but distinct primary CNS lymphoma subgroup, with characteristically different expression patterns compared to the rest of the cases. Finally, we identified differentially regulated pathways in the above comparisons and assessed the utility of miRNA expression patterns in predicting survival. Our study identifies a novel CNS lymphoma subgroup defined by distinct miRNAs, proves the importance of specific miRNAs and pathways in their pathogenesis, and provides the basis for future research.

International audience; The electrical and thermal contact resistances are key parameters for obtaining an accurate electro-thermal model of the spark plasma sintering (SPS) process. However, due to the lack of a general expression, these parameters are usually determined empirically. Thus, they are only valid for a specific material and SPS configuration.A simple method based on a limited amount of experiments as well as a new formulation of the electrical and thermal contact resistances are developed. First, the evolution of those resistances is optimized on simple shapes (pellets) experiments. They are then transferred into the electro-thermal simulation of complex shapes configurations, which showed a good agreement between the experimental and computed data.

A vibrational model of heat transfer in simple liquids with soft pairwise interatomic interactions is discussed. A general expression is derived, which involves an averaging over the liquid collective mode excitation spectrum. The model is applied to quantify heat transfer in a dense Lennard-Jones liquid and a strongly coupled one-component plasma. Remarkable agreement with the available numerical results is documented. A similar picture does not apply to the momentum transfer and shear viscosity of liquids., 8 pages, 5 figures

The process of leaf elongation in grasses is characterized by the creation and transformation of distinct cell zones. The prevailing turgor pressure within these cells is one of the key drivers for the rate at which these cells divide, expand and differentiate, processes that are heavily impacted by drought stress. In this article, a turgor-driven growth model for grass leaf elongation is presented, which combines mechanistic growth from the basis of turgor pressure with the ontogeny of the leaf. Drought-induced reductions in leaf turgor pressure result in a simultaneous inhibition of both cell expansion and differentiation, lowering elongation rate but increasing elongation duration due to the slower transitioning of cells from the dividing and elongating zone to mature cells. Leaf elongation is, therefore, governed by the magnitude of, and time spent under, growth-enabling turgor pressure, a metric which we introduce as turgor-time. Turgor-time is able to normalize growth patterns in terms of varying water availability, similar to how thermal time is used to do so under varying temperatures. Moreover, additional inclusion of temperature dependencies within our model pioneers a novel concept enabling the general expression of growth regardless of water availability or temperature.

Since its proposal, the simplified Spb method has been successfully applied to the fracture toughness evaluation of metallic and polymer materials. However, some points of this methodology remain unclear, like the applicability on standardized geometries in which ηpl depends on the a/W ratio. In order to discuss this and other aspects, theoretical analyses of the Spb method were made and some experimental tests were performed. The theoretical analysis revealed that considerable differences in C(T) and SE(T) geometries could be present when the same ηpl factor for both blunt notched and pre-cracked specimens is used. To minimize these differences, the use of the most general expression of the Spb method in addition to ηpl factors provided by the standards for geometries where ηpl change with a/W is proposed. The proposed experimental methodology, based on the load separation and on ηpl factors provided by the standards, proved to be suitable for C(T) geometry, whereas for SE(T) geometry the results indicate that more research is still needed.

One of the experimental methods to determine the coefficient of surface diffusion of species migrating in a porous material uses the measurement of the time lag. It represents the time required for the species to spend their life within the material when permeating through it. Describing the mass transport by a suitable transport model, the time lag can be expressed in terms of integrals whose evaluation depends on the adsorption isotherm of the studied species in the material. For porous building materials, the BET (Brunauer-Emmett-Teller) and BSB (Brunauer-Skalny-Bodor) model isotherms are usually very good approximations to the measured isotherms at low and medium concentrations. In this paper we derive a formula for the time lag for both these model isotherms. The formula can be readily applied in the analysis of experimental data, whereas the general expression involving integrals is much less straightforward to employ, being usually evaluated numerically for fixed values of parameters. The sensitivity of the time lag formula to the surface diffusivity is illustrated for an example of a porous brick with a water adsorption isotherm known from previous experiments.

Understanding the interactions of viruses with cell membranes is important for the proposal of vaccines and treatments for diseases caused by this type of contamination. An example of this is the case of the pandemic caused by the new Covid-19, which in 2020 placed was responsible for a third of the world under virus quarantine, causing huge economic losses and thousand of deaths across the planet. In this context, this research proposes to build a mathematical model for the interaction of a virus with the plasma membrane in a mammalian cell, which leads to a mathematical problem with boundary conditions. Using Green’s functions, the model was able to answer what is the general expression for potential electrostatic energy of this interaction in terms of Bessel functions and Wigner coefficients. It is reasonable to speculate, based on the results presented by the model, that a virus has to present an effective charge resulting in a solution with a pH value of about 7 to approach the cell membrane, while an electrically neutral virus should not have the ability to interact and enter membranes. The values ?for the interaction energy and the force between the membrane and the cluster offer the order of magnitude of the distances over which such interaction is effective. O entendimento das interações dos vírus com as membranas celulares é de fundamental importância para a proposta de vacinas e tratamentos de doenças causadas por esse tipo de contaminação. A exemplo disso, cita-se o caso da pandemia causada pelo novo coronavírus causador da Covid-19, que no ano de 2020 colocou um terço do mundo em situação de quarentena, causando milhares de mortes e prejuízos econômicos em todo o planeta. Nesse contexto, o presente estudo propõe-se a construir um modelo matemático para a interação de um vírus com a membrana plasmática da célula de um mamífero, que conduz a um problema matemático com condições de contorno. Fazendo uso das funções de Green, o modelo foi capaz de responder qual é a expressão geral para energia potencial eletrostática desta interação em termos das funções de Bessel e os coeficientes de Wigner. Pode-se especular, ancorado nos resultados apresentados pelo modelo, que um vírus tem que apresentar uma carga efetiva resultante em solução com pH da ordem de 7 para se aproximar da membrana celular, enquanto um vírus eletricamente neutro não deve apresentar a capacidade de interagir e adentrar em membranas. Os valores para a energia de interação e para a força entre a membrana e o aglomerado oferecem a ordem de grandeza das distâncias em que tal interação é efetiva.

In the article analyzes the issues of ensuring the safety of the most stressed and critical components and parts and the theoretical aspects of diagnostics using electromagnetic-acoustic wave phenomena, provides a general expression for the instantaneous mechanical stress $\sigma\mathrm{m}$ acting on the surface of a layered medium, a complex of diagnostic parameters for determining the technical condition of metal elements of power equipment; algorithms for determining the technical condition of metal elements of power equipment; methods for assessing the safe operation resource of technological equipment by signal parameter values.

We present a theoretical study of optomechanical systems in which the mechanical resonator modulates both the resonant frequency (dispersive coupling) and the decay rates (dissipative coupling) of the optical cavity. We extend the generic dispersive framework to a more general case in which the dissipative coupling is split between its external and intrinsic contribution. We report a complete analysis of the influence of each kind of optical losses (intrinsic and external) on the three coupling mechanisms and highlight the interest of each external decay rate regime. The basic tools to experimentally identify the three couplings and their relative influence on the optical response are presented. We demonstrate the general expression of the optical spring effect and optomechanical damping. Comparison between experimental measurements in photonic crystal systems from the literature and our theoretical modal yields good agreement., Comment: 12 pages, 6 figures

Repeated measurements in quantum mechanics can freeze (the quantum Zeno effect) or enhance (the quantum anti-Zeno effect) the time-evolution of a quantum system. In this paper, we present a general treatment of the quantum Zeno and anti-Zeno effects for arbitrary driven open quantum systems, assuming only that the system-environment coupling is weak. In particular, we obtain a general expression for the effective decay rate of a two-level system subjected to arbitrary driving fields as well as periodic measurements. We demonstrate that the driving fields change the decay rate, and hence the quantum Zeno and anti-Zeno behavior, both qualitatively and quantitatively. We also extend our results to systems consisting of more than one two-level system, as well as a two-level system strongly coupled to an environment of harmonic oscillators, to further illustrate the non-trivial effect of the driving fields on the quantum Zeno and anti-Zeno effects., 18 pages, comments most welcome

Self-accelerating beams are fascinating solutions of the Schr\"odinger equation. Thanks to their particular phase engineering, they can accelerate without the need of external potentials or applied forces. Finite-energy approximations of these beams have led to many applications, spanning from particle manipulation to robust in vivo imaging. The most studied and emblematic beam, the Airy beam, has been recently investigated in the context of the fractional Schr\"odinger equation. It was notably found that the packet acceleration would decrease with the reduction of the fractional order. Here, I study the case of a general nth-order self-accelerating caustic beam in the fractional Schr\"odinger equation. Using a Madelung decomposition combined with the wavelet transform, I derive the analytical expression of the beam's acceleration. I show that the non-accelerating limit is reached for infinite phase order or when the fractional order is reduced to 1. This work provides a quantitative description of self-accelerating caustic beams' properties., Comment: 8 pages, 4 figures

We investigate quantum teleportation in the two-copy setting based on GHZ measurement and propose the detailed protocol. The output state after the teleportation is analyzed, and the protocol is proved to be trace preserving. The general expression of the optimal teleportation fidelity is derived. The optimal teleportation fidelity is shown to be a linear function of two-copy fully entangled fraction, which is invariant under local unitary transformations. At last, we show two-copy teleportation based on GHZ measurement can be better than one-copy teleportation by an explicit example, which is amenable to demonstration in experiments. Our study is significant for improving the fidelity of teleportation for some limited resource which cannot be significantly distilled. Moreover, it can inspire us to find many other more efficient protocols for teleportation.