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People commonly use new technologies to promote a healthy lifestyle and help them lose weight through nutritional programs. This study evaluated the quality of individualized meal plans offered by dietary apps.Ten apps that offer personalized meal plans were selected for the study, weekly meal plans were generated, and the nutritional values of the diets were calculated. The Healthy Diet Indicator and the Diet Quality Index were estimated.Significant differences between apps were observed in the calculated energy values (p0.0001) and macronutrients (p0.05), the content of vitamins (vitamin A, E, K, B1, B3, B6, folates, C: p0.05) and minerals (potassium, calcium, phosphor, magnesium, iron, zinc, copper, manganese: p0.05), as well as diet quality (p0.05) and food group consumption (vegetables, fruits, grains, dairy products, vegan products, meat, nuts, fats, sweets, beverages: p0.05). Most diets covered the demand for the required nutrients, but the percentage of energy from fats, proteins and carbohydrates differed from the recommendations. Moreover, the nutritional values of the diets provided in the apps significantly differ from the values calculated using the nutritional databases.The meal plans from apps significantly differ in nutrients and food group intake. The quality of the diets offered in the app should be improved.

The paper deals with the thermoelastic problem of a multilayered pipe subjected to normal loadings on its inner surface and temperature differences on its internal and external surfaces. Two types of nonhomogeneous pipe materials of pipe are considered: (1) a ring-layered composite composed of two repeated thermoelastic solids with varying thickness and (2) a functionally graded ring layer. The ring-layered pipe with periodic structure is investigated by using the homogenized model with microlocal parameters. A homogenization approach is proposed for the modelling of the FGM pipe. The analysis of obtained circumferential, radial and axial stress is presented in the form of figures and discussed in detail. It was shown that the proposed approach to the homogenization allows us to correctly calculate the averaged characteristics in the representative cell (the macro-characteristics) and also the characteristics dependent on the choice of the component in the representative cell (the micro-characteristics) for both microperiodic composites and functionally graded materials.

The paper deals with the analysis of nonhomogeneous inner coatings for a homogeneous pipe with respect of heat loss from the outer pipe surface. Two kinds of the coatings in the form of ring layers are considered: (1º) with the thermal properties changing continuously along the coating thickness (called the coating A), (2º) multilayered coatings with piecewise continuous thermal properties (called the coatings B). The analysis is connected with the stationary heat conduction problems. Some special cases of the coatings A and B are investigated. The obtained analytical results and the comparison of the coatings are presented.

The quasi-stationary problem of heat conduction for a homogeneous half-space and composite layer being a coating is considered in the paper. Heat fluxes distributed in a strip and moving on the boundary plane of the considered body with a constant velocity are taken into consideration. The composite layer being the coating is assumed to be composed of four repeated periodical beams with rectangular cross sections. The homogenized model with microlocal parameters is used for the description of the composite layer. Some special cases of an influence of composite components and their locations on the temperature field are analysed.

The quasi-stationary three-dimensional problem of the heat conduction for a nonhomogeneous half-space heated by heat fluxes distributed at a circle and moving with constant speed is investigated. T...

We present a microscopic description of molecular magnets by the multi-orbital Hubbard model, which includes the correlated hopping term, i.e. the dependence of electron hopping amplitude between orbitals on the degree of their occupancy. In the limit of large Coulomb on-site interaction, we derived the spin Hamiltonian using the perturbation theory. The magnetic coupling constant between two ions we determined in two different ways: a)from the expression obtained in the perturbation calculus and b)from the analysis of distances between the lowest levels of the energy spectrum obtained by the diagonalization of the multi-orbital Hubbard model. The procedure we use can be applied to various nanomagnets, but the final calculations we performed for the molecular ring $Cr_8$. We showed that the correlated hopping can reduce the antiferromagnetic exchange between ions, what is essential for a proper description of $Cr_8$., Comment: 6 pages, 2 figures, to be published in Physical Review B

The paper deals with the nonstationary heat conduction problem of a homogeneous half-space with a multi-layered periodic coating subjected to the action of a moving heat source with constant velocity on its surface. The analysis is performed with the framework of two approaches: (1o) the first one is based on the exact description, (2o) the second one uses the homogenized model with microlocal parameters. Some special cases of the heat source and components of the stratified coating are investigated. The obtained results are compared for the determination of applicability of the homogenized model and the periodically layered coatings.

The article deals with a homogeneous isotropic thermoelastic half-space with an inhomogeneous gradient coating under thermal loadings over an elliptically shaped area. The shear modulus, th...

The paper deals with the problem of heat conduction in a nonhomogeneous rigid body which is a homogeneous conductive layer with a periodic composite coating. The coating layer is a composite in which every unit cell in general case is composed of four rigid beams with rectangular cross-sections. The assumed structure permits to analyse some special cases of coatings: laminated composites with layer parallel or perpendicular to the boundary, composites with periodically distributed inclusions with rectangular cross-section and a homogeneous layer. The distributions of temperature and heat flux distributions on the interface between the coating and the homogenous layer are investigated.

The paper deals with the axisymmetric problem of the thermoelastic half-space with temperature dependent properties. The thermal coefficients: heat conductivity and coefficient of linear expansion are assumed to be functions of temperature. The mechanical properties: Young modulus and Poisson ratio are taken into account as constants. Two cases of boundary conditions are considered: a normal heat flux acting on a circle with given radius and two variants of the boundary conditions on the outside of the heated region: (1) a thermal insulation, or (2) a constant temperature, taken as reference. The boundary is assumed to be free of mechanical loadings. The linear dependences of thermal properties on temperature is considered as a special case. The obtained exact results are presented in the forms of multiple integrals and the detailed analysis are derived for linear dependences of the thermal properties on temperature.

The paper deals with the modelling of heat conduction in periodically stratified composites with slant layering to boundaries. The relations of the homogenized model with microlocal parameters for the case of layering parallel to the boundary are transformed to conform to requirements of the composite geometry. The plane problem of periodically stratified half-space with slant layering heated by given boundary temperature is solved analytically. The obtained results are analyzed and compared with the solutions for special cases: (1) homogenized half-space, (2) half-space with parallel layering to the boundary, (3) half-space with vertical layering to the boundary.

The paper deals with the problem of SH harmonic wave propagation in an elastic layer with temperature dependent properties. The shear modulus and mass density are linearly dependent on temperature. The layer is rested on a rigid foundation and the upper boundary is free of loadings. The boundary planes are kept at different constant temperatures. The wave velocity and amplitude of stresses are analysed.

The paper deals with the two-dimensional stationary temperature distribution in a composite layer. The nonhomogenous body is assumed to be composed of periodically repeated two-layered laminae. The layering is inclined with an arbitrary angle to the boundary planes. The lower and upper boundary planes are assumed to be kept at given temperatures. The considered problem is solved within the framework of the homogenized model with microlocal parameters, where the continuity thermal conditions on interfaces are satisfied.

The paper deals with the stationary problems of diffusion in a homogeneous isotropic layer with a cylindrical hole. The hole is partially filled by diffusing substance. The considered problem is described within the framework of the Fick's law and the integral Weber–Orr transform method is applied to solve it. The obtained exact results expressed by integrals will be presented in the form of figures.

This paper is concerned with the axisymmetric elastostatic problem related to the rotation of a rigid punch which is bonded to the surface of a nonhomogeneous half-space. The half-space is composed of an isotropic homogeneous coating in the form of layer, which is attached to the functionally graded half-space. The shear modulus of the FGM is assumed to vary in the direction of axis Oz normal to the boundary as μ1(z) = μ0(1 + αz)β, where μ0, α, β are positive constants. The punch undergoes rotation due to the action of the internal loads. By using Hankel's integral transforms, the mixed boundary value problem is reduced to dual integral equations, and next, to a Fredholm's integral equation of the second kind, which is solved numerically for the case of β = 2. The final results show the effect of non-homogeneity on the shear stresses and an unknown moment of punch rotation.

The paper deals with a contact problem of a moving infinitely long punch on the boundary plane of vertically laminated half-space. The problem is solved within the homogenized model with microlocal parameters and under some physical assumptions. By using Fourier transforms the problem is reduced to a integral equation, which is solved numerically. The analysis of temperature and stress distributions and Barber’s contact parameter is presented.

The distributions of temperature and heat fluxes in a periodically laminated layer with a vertically located cylindrical hole are obtained approximately within the homogenized model with microlocal parameters. The method of solution is based on the Weber–Orr integral transforms. The effects of geometrical and mechanical parameters of the composite structure on the thermal fields are discussed and presented in graphical form.

The paper deals with the heat conduction in a semi-infinite laminated layer. The nonhomogeneous body is assumed to be composed of periodically repeated two-layered laminae. The boundary perpendicular to the layering is subjected to the acting of normal heat flux with parabolic distribution. The free exchange of heat with the surroundings is assumed on the remaining parts of the boundary. The problem is solved by using two approaches: (1°) the formulation basing on the classical model of heat conduction with the continuity conditions on interfaces, and (2°) the homogenized model with microlocal parameters (cf. Matysiak, Woźniak, Acta Mech. (1986)). The results obtained on both ways are compared and some adequate conclusions connected with the possibilities of applications of the homogenized model with microlocal parameters are presented.

The stress fields in an infinite elastic bimaterial layered system with an embedded rigid ribbon-like inclusion oriented in the normal direction to the layering and subjected to a far-field uniform tension loading are obtained approximately within the linear static elasticity with microlocal parameters. The solution method is based on the Fourier transform and dual integral equations. The effects of geometrical and mechanical parameters of the composite structure on the stress singularities near the inclusion tips are discussed and presented in graphical form.

We obtain the analytic solution of an antiplane problem of the theory of elasticity for a cracked layer made of a composite material whose cross section is formed by a periodic array of repeated rectangular elements. Each element, in turn, contains four rectangular cells of different types. A crack is located on one of the interfaces of materials of these cells. The distributions of displacements on the outer surfaces of the layer are regarded as given. The numerical analyses are performed for the stress intensity factors depending on the mechanical properties of materials and the sizes of the cells.

The paper deals with the plane problem of stress distribution near crack tips in an elastic periodically stratified space. The crack is normal to the layering in a two-constituent laminated composite. The lower and upper crack surfaces are loaded symmetrically by arbitrary normal loads. The problem is approximated using the homogenized model with micro-local parameters [C. Woźniak, A nonstandard method of modelling of thermoelastic periodic composites, Int. J. Eng. Sci. 25 (1987) 483–499; S.J. Matysiak, C. Woźniak, Micromorphic effects in a modeling of periodic multilayered elastic composites, Int. J. Eng. Sci. 25 (1987) 549–559]. The stress intensity factors are obtained and the influence of geometrical and mechanical parameters and the location of crack tips on the SIF’s values are investigated.

The paper deals with the problem of surface waves in a vertically layered elastic half-space. The transmitting medium is composed of periodically repeated two-constituent laminae, and its boundary is assumed to be normal to the layering. The problem is solved using an approximate model proposed by Woźniak (Int J Eng Sci 25:483–499, 1987) and Matysiak and Woźniak (Int J Eng Sci 25:549–559, 1987), which is referred to as the homogenized model with microlocal parameters. The velocity of the surface wave is obtained as a function of geometric and dynamic properties of the laminae. The variation of the surface wave velocity with respect to composite constituents is illustrated by numerical examples.

The paper deals with some mixed-in-time nonstationary problem of heat conduction for a rigid composite half-space. The body is composed of periodically repeated cells with rectangular cross-section, which consists of four rectangular structural elements. The half-space is assumed to be initially at zero temperature, the boundary plane is kept at a known temperature for time 0 ≤ t ≤t0 and is insulated for t > t0. The influence of composite microstructure on temperature distributions is investigated.

The paper deals with a mixed nonstationary problem of heat conduction for a microperiodic two-layered half-space. The body is assumed to be initially at zero temperature, the boundary plane is kept at a known temperature for time 0 ≤ t ≤ t0 and is insulated for t > t0. The half-space is composed of periodically repeated two-layered laminae with layering parallel to the boundary. The problem is solved within the framework of homogenized model with microlocal parameters [Cz. Woźniak, A nonstandard method of modelling of thermoelastic periodic composites, International Journal of Engineering Science 25, (1987), pp. 483–499, S.J. Matysiak Cz. Woźniak, On the modelling of heat conduction problem in laminated bodies, Acta Mechanica, 65, (1986), pp. 223–238.]. The influence of thermal and geometric properties of the composite components on the temperature distribution for some special case of the boundary condition is analyzed.

This paper deals with the plane contact problem of an infinite long cylinder pressured into an elastic laminated semi-space. The nonhomogeneous body is composed of periodically repeated two constituent laminae and its boundary is assumed to be normal to the layering. The homogenized model with microlocal parameters given by Woźniak [Woźniak C. A nonstandard method of modelling of thermoelastic periodic composites. Int J Eng Sci 1987;25:483–99]. Matysiak and Woźniak [Matysiak SJ, Woźniak C. Micromorphic effects in a modeling of periodic multilayered elastic composites. Int J Eng Sci 1987;25:549–59.] are applied to find an approximate solution to the problem. The problem is reduced to well-known dual integral equations and the stresses are obtained in the form of Fourier integrals. Numerical results, which show the influence of geometrical and mechanical properties of composite constituents on stress distributions, are presented in figures.

We construct fundamental solutions of the problem of antiplane deformation of an unbounded composite body with interface cut or a linear rigid inclusion subjected to the action of concentrated forces. The periodic cell of the composite contains four different elements with rectangular cross sections. The problem is studied by the method of homogenization with microlocal parameters. The formulas for the stress intensity factors are obtained in the analytic form and investigated.

The paper deals with the asymptotic analysis of stresses near interface crack tips in the periodically two-layered elastic composites. The problem is investigated for the plane state of strain within the framework of the homogenized model with microlocal parameters. The angular dependence of stresses at the crack tip is presented for different mechanical and geometrical properties of the composite.

We obtain the analytic solution of a nonstationary problem of heat conduction for a piecewise homogeneous body formed by a half space and a composite layer applied to its surface. The surface of the layer is heated by a heat flow whose intensity is equal to the specific power of friction in the process of braking. The dependences of the distributions of temperature on the geometric parameters and thermal properties of the composite material and the substrate are investigated.

This paper deals with some comparison results for displacements and stresses in a periodically stratified elastic semi-infinite layer determined within the framework of two approaches: (1) based on the homogenized model with microlocal parameters [Woźniak (1987) Int J Eng Sci 25: 483–499; Woźniak (1987) Bull Ac Pol Tech Sci 35: 143–151]; (2) obtained directly from the theory of elasticity. A body is assumed to be composed of n elastic two-component periodically repeated laminae. The perfect mechanical bonding between the layers is assumed. The normal displacements and zero shear stresses on the boundary being a cross-section of the composite component are taken into account. The lateral boundary surfaces are assumed to be rigid fixed. The obtained results from the two approaches are compared and presented in the form of figures.

The paper deals with some mixed nonstationary problem of heat conduction for a homogeneous rigid half-space. The body is assumed to be initially at zero temperature, the boundary plane is kept at a known temperature f ( t ) for time 0 ≤ t ≤ t 0 and is insulated for t > t 0 . The exact solution is obtained by using the integral Fourier method. Some special case is solved in details.

An approximate method for the determination of temperature and stress distributions in an elastic half-space heated by a laser impulse on its boundary is derived. The method is based on the solutions for two cases of laser time structure: sectionally constant and sectionally linear. Piecewise-constant and piecewise-linear finite functions are used for approximation of the temporal profile of analyzed laser impulses. Numerical results are presented for typical lasers found in engineering practice.

The paper deals with some comparison of results obtained within the framework of homogenized model with microlocal parameters [Cz. Woźniak, Int. J. Eng. Sci. 25 (1987) 483–499; S.J. Matysiak, Cz. Woźniak, Acta Mech. 63 (1986) 223–238; S.J. Matysiak, Acta Mech., 78 (1989) 95–108] and within the framework of classical heat conduction equations for a periodically two-layered half-space. The body is assumed to be heated by a constant heat flux on a boundary circle.

The paper deals with the heat conduction problem of a semi-infinite periodically stratified layer heated by a constant heat flux directed according to the layering, normal to the boundary being a cross-section of the composite components. The free heat exchange with surroundings is considered on the remaining parts of the boundary. The body is assumed to be composed of n periodically repeated two-layered, perfect bonding lamine. The problem is solved on two ways: (1) directly as heat conduction problem or (2) by using the homogenized model with microlocal parameters [R. Kulchytsky-Zhyhailo, S.J. Matysiak, On some heat conduction problem in a periodically two-layered body. Comparative results, Int. Commun. Heat Mass Transf., in press]. The obtained results are compared and presented in the form of figures.

This paper is devoted to the anti-plane static problem of an interface Griffith crack in a micro-periodic composite solid. The repeated unit cell of the body under consideration consists of four different elastic materials taking the shape of the fibers of infinite length with rectangular cross-sections. An approximate analysis is carried out within the homogenized model with microlocal parameters. The analytical results obtained may be used for the interface crack problems in micro-periodic fiber-reinforced composites as well as in solids with layered or chessboard periodic microstructures.

The paper presents a method for determination of effective absorption coefficient of irradiation during action of a pulsed laser. For this purpose the solution of some axisymmetrical boundary value problem of heat conduction for half-space and the experimentally obtained polymorphous zones of transformation in the exposed materials are applied. The verification of the methodology is given for St 45 steel and the monocrystal cobalt samples.

In present paper the effect of the correlation between spectral radiative characteristics of different lasers and absorptive characteristics of laser irradiated two-component elastic semitransparent material upon coupled thermal, diffusive and elastic processes in the layer is examined. Irradiated material is supposed to consist of elastic matrix and gaseous admixture. Investigations are carried out within the model applied early to the study of mentioned coupled processes in the layer subjected to thermal infrared radiation. Calculations were carried out for four different infrared lasers. Peculiarities of heat and admixture mass transfer caused by laser irradiation are established and discussed.

This paper deals with the study of thermal stresses due to a plane crack lying on an interface in a microperiodic two-layered composite under a uniform perpendicular heat flow. An approximate analysis is carried out within the framework of linear stationary thermoelasticity with microlocal parameters. Taking this approach, a general method of solving the resulting boundary-value problem is presented. Effective results have been achieved through the use of suitable potential solutions and reducing the thermal crack problem to its skew-symmetric isothermal mechanical counterpart. An illustrative example is given in the paper by considering an insulated stress-free penny-shaped crack. For this problem the solution is obtained in terms of elementary functions and discussed from the point of view of fracture theory.

In this paper coupled thermal, mechanical and diffusive processes in two-layer semitransparent composite subjected to thermal infrared radiation are examined. One of the layers is supposed to be multi-component consisting of deformable matrix and gaseous admixture. Effect of radiation upon a composite is taken into account by heat sources in composite and heat supply to admixture. Model equations are solved within iterative approach. On each step of iterative process radiation equations are solved analytically while for solving diffusion and thermal conductivity equations the finite difference method is applied. Numerical calculations suggested that the presence of the layer located closer to radiation source allows reduce thermal stresses in another layer of two-layer semitransparent elastic composite in both cases when materials of layers are the same and different. The layer located closer to radiation source and whose thickness is less than that of another layer is heated to lower temperatures, their distributions are more homogeneous and consequently, it undergoes weaker stress loading.

The paper deals with the analysis of diffusion process in homogeneous, isotropic half-space. The diffusing substance is located in an infinite long ditch with a constant width. Moreover, the constant concentration of diffusing substance or the constant gradient of diffusing substance in the ditch is assumed for each time t ≥ 0. The Ficks equation of diffusion is taken into account as a mathematical model. By using integral transform methods the concentration is found for arbitrary point of body and time.

The analytical model for the determination of contact temperature and wear on a working surface of friction brakes is presented. It is assumed that one of the friction element is composed of a periodic two-layered composite and the second element is a homogeneous half-space. In the frictional process, the wear coefficient is linearly dependent on the contact temperature. The influences of composite parameters as well as a parameter characterizing the changing of loading from zero to the nominal value on the distribution of contact temperature and wear during braking is considered.

The main goal of this study was to achieve a medico-economic comparison between four disposable laryngeal masks (LM) (LMA-Unique™, Ambu AuraOnce™, I-Gel™ and LMA-Suprême™).A prospective, randomized, monocentre study.In a center, using routinely LMA-Unique masks, scheduled breast surgery patients were allocated into four groups according to the LM model. After the induction, the modalities of use were collected, as well as the intraoperative events that required additional anesthetic equipment. The real cost of each model was calculated (cost of the mask+extra cost related to complications). Using the LMA-Unique as a reference, we performed a cost-efficacy analysis. We realized a cost-efficiency analysis putting in parallel the impact on the cost and the incidence of the events.A total of 178 patients were included. According to the cost-efficacy analysis, the dominant model was the Ambu AuraOnce™ (Δreal cost: -34.2%, Δevents: -30.6%). The LMA-Unique™ was dominated because of a high morbidity rate. The I-Gel™ and LMA-Suprême™ models were more efficient but more expensive (Δreal cost: +16% and +22.5% respectively). To compensate for additional costs, it would be necessary to apply a price reduction of at least 50%.Despite their better efficiency and safety, the latest generation laryngeal masks are still expensive in spite of a low rate of complication. These results do not take into account very rare and severe complications not met in this study in the limited size; then the economic and medical impact can influence the choice beyond the simple analysis cost-efficiency.

The paper deals with problems of modelling of diffusion processes in microperiodic two-layered elastic solids. By using the homogenization procedure with microlocal parameters and relations of the linear-coupled theory of diffusion in elastic homogeneous bodies a homogenized model accounting certain local effects of stresses, diffusion fluxes is derived. As an example illustrating the application of the presented model the stationary problem of diffusion in a microperiodic stratified elastic layer is considered.

The paper deals with the plane problem on frictional contact of stratified elastic half-spaces provided discontinuity of their direct touch. Imperfectness of contact of the bodies is assumed to be caused by surface unevenness of their surface layers. The problem is formulated within the framework of the homogenized model with microlocal parameters. Using the method of complex potentials in combination with the method of interface gaps the problem is reduced to a singular integral equation on the function of interface gap height. Copyright © 2001 John Wiley & Sons, Ltd.

The paper presents some numerical results of the problem on contact of stratified elastic half-spaces possessing unevenness of their surface layers. The approach of the Jacobi polynomials is used to reduce the singular integral equation of the problem to a system of linear algebraic equations. On the basis of the system's solution the dependence of gaps' geometric characteristics on external load and friction is investigated for two types of initial boundary disturbances, namely a local symmetric recess and a periodic set of recesses at a flat boundary. Numerical results are presented in figures for a few elastic and geometric parameters of joint components. The analysis shows that elastic properties and geometric structure of a laminated half-space have a significant influence on the shape of interface gaps and their location. Copyright © 2001 John Wiley & Sons, Ltd.