The local Solow growth model

growth models

Development of the mathematical model of the electric resistance baking process

Received: March 23rd, 2021 ; Accepted: May 25th, 2021 ; Published: June 16th, 2021 ; Correspondence: [email protected] work is dedicated to the development of the mathematical model of the electric resistance baking process for the purpose of predicting temperature changes during baking of dough pieces of arbitrary sizes. The equation for the non-stationary thermal regime of a body with an internal heat source was used with a number of assumptions. The dynamics of the dough temperature changes was determined by numerical solution of the equation in Comsol Multiphysics. Due to the complexity of the dough baking process and the impossibility of solving the equation by analytical method only, a number of values included in the energy balance of ER baking were determined experimentally. A dough piece with dimensions of 100×50×80 mm was baked during the experiment. After the adjustment, the adequacy of the model was checked by comparing the data on the dough temperature changes during baking dough pieces of the same recipe, but of different sizes (150×49×80, 80×62×80, and 65×75×80). Statistical analysis using Fisher's criterion confirmed the adequacy of the model

Shape of a magnetic resonance line in a thin film on the surface of anisotropic superconductor with irregularly distributed Abrikosov's vortices

The form of an electron paramagnetic resonance (EPR) in a thin paramagnetic film (λ/10, λ-London's depth of magnetic field penetration into superconductor) overlying the surface of an anisotropic superconductor is calculated taking into account the local magnetic field non-uniformity of an irregular Abrikosov's vortex lattice. It is shown that the form of EPR is noticeably varied with the degree of irregularity of the superconductor vortex lattice. It is suggested that an inclusion of this circumstance into consideration may essentially change the conclusions made on the lattice type and parameters of this superconductor, which are typically derived from the analysis of the EPR form. © Springer Science+Business Media, Inc. 2007

Distribution of a Local Magnetic Field in Superconductors with an Uncorrelated Random Lattice of Abrikosov Vortices

The distribution of a local magnetic field near the surface of a uniaxial anisotropic type-II superconductor is determined in the framework of the London model in the case when the Abrikosov vortices are randomly distributed in the superconductor. The distribution of a local magnetic field is obtained as a function of the distance from the surface of the superconductor. It is demonstrated that the shape of the distribution of the local magnetic field near the surface differs substantially from that in the bulk of the superconductor. This difference should be taken into account in interpreting experimental data on the local magnetic field in the surface region of the superconductor and in thin superconducting films (with a thickness of less than or equal to λ, where λ is the depth of penetration of the magnetic field into the superconductor). It is shown that, as in the case of a regular lattice of vortices, the value of λ, can be determined from observations of the distribution of the local magnetic field in type-II superconductors with an uncorrelated random lattice of vortices. © 2004 MAIK "Nauka/ Interperiodica"

Shape of the nuclear magnetic resonance line in anisotropic superconductors with an irregular vortex lattice

The NMR line shape in type-II superconductors has been constructed with allowance for a change in the nonuniform magnetic field of an irregular vortex lattice near the surface of a superconductor. The NMR line shape is shown to change as a function of the irregularity of the vortex lattice rather that being simply broadened. This change is related to a lowering of the local symmetry of the irregular vortex lattice in the superconductor. This circumstance can substantially change the conclusions regarding the vortex-lattice type and the superconductor parameters that are usually drawn from the NMR line shape. © Pleiades Publishing, Inc., 2006

Divided Differences & Restriction Operator on Paley-Wiener Spaces PWtaupPW_{tau}^{p} for N−N-Carleson Sequences

For a sequence of complex numbers $\Lambda$ we consider the restriction operator $R_{\Lambda}$ defined on Paley-Wiener spaces $PW_{\tau}^{p}$ ($1<p<\infty$). Lyubarskii and Seip gave necessary and sufficient conditions on $\Lambda$ for $R_{\Lambda}$ to be an isomorphism between $PW_{\tau}^{p}$ and a certain weighted $l^{p}$ space. The Carleson condition appears to be necessary. We extend their result to $N-$Carleson sequences (finite unions of $N$ disjoint Carleson sequences). More precisely, we give necessary and sufficient conditions for $R_{\Lambda}$ to be an isomorphism between $PW_{\tau}^{p}$ and an appropriate sequence space involving divided differences

Normal Pressure Hydrocephalus as an Unusual Presentation of Supratentorial Extraventricular Space-Occupying Processes: Report on Two Cases

Normal pressure hydrocephalus (NPH) is a clinical and radiographic syndrome characterized by ventriculomegaly, abnormal gait, urinary incontinence, and dementia. The condition may occur due to a variety of secondary causes but may be idiopathic in approximately 50% of patients. Secondary causes may include head injury, subarachnoid hemorrhage, meningitis, and central nervous system tumor. Here, we describe two extremely rare cases of supratentorial extraventricular space-occupying processes: meningioma and glioblastoma multiforme, which initially presented with NPH