Unsteady state heat flow in epidermis and dermis of a human body

We investigate the unsteady state temperature distribution in human skin where subcutaneous tissues are not present. The mathematical model is employed for a onedimensional unsteady state case, taking the blood mass flow rate and metabolic heat generation variable with respect to the position in the dermis. The metabolic heat generation depends on the tissue temperature. The thermal conductivity is taken constant but different in two layers. The problem has been solved using Laplace transform and Bessel functions. Numerical results for a simple case are discussed.     

Some Connections Between the Classical Calogero–Moser Model and the Log-Gas

Journal of Statistical Physics - In this work we discuss connections between a one-dimensional system of N particles interacting with a repulsive inverse square potential and confined in a harmonic...     

Positive Solutions to Singular Boundary Value Problems with Sign Changing Nonlinearities on the Half-Line via Upper and Lower Solutions

This paper presents a lower and upper solution technique for singular second order boundary value problems on the half line.     

Study of inverse a.c. Josephson effect in Y–Ba–Cu–O and Y–8a–Sr–Cu–O

Microwave induced d.c. voltage due to inverse a.c. Josephson effect has been observed across bulk samples of Y-Ba-Cu-O and Y-Ba-Sr-Cu-O. The d.c. voltage is found to vary with microwave power, frequency and also with small external magnetic fields. Although the resistivity curve of Y-Ba-Cu-O does not show any appreciable resistance drop around 230 K, the microwave induced d.c. voltage due to the inverse a.c. Josephson effect has been found to exist upto 230 K. The resistivity behaviour of Y-Ba-Sr-Cu-O shows a sharp resistivity drop above 230 K. In this sample the inverse Josephson effect is found to exist upto +26 °C, indicating the presence of a phase having a superconducting onset around this temperature.     

Design and fabrication of fluid controlled dynamic optical lens system

A novel small fluid controlled optical lens system that is capable of displaying dynamic variation of its focal length and field-of-view (FOV) is designed and fabricated. In this active lens system, appropriate volume of the optical fluid can be pumped into or out of the lens chamber to provide double-convex (DCX) or double-concave (DCV) lens effect. Simple optical imaging experiments were performed using different sets of glass lenses with fixed focal lengths to determine the optimum lens configuration required for designing a dynamic optical lens system. The experimental results obtained from the glass lenses demonstrate that a combination of a single DCX lens with three DCV lenses provides a wider FOV. The flexible membranes for fluid controlled lenses were fabricated using polydimethylsiloxane polymer material, which has good optical transparency and elasticity. A simple fluid injection system is used to vary the radius of curvature of the lenses, and thereby to change the focal length. A dynamic optical lens system with a combination of one DCX and multiple variable focal length DCV lenses as designed here can image an object with a wide range of focal length and FOV. With this fluid controlled optical system, the FOV and focal length could be continuously varied and a maximum FOV of 118.3° could be achieved. The smallest f-number (f_/#) for this fluid controlled single lens system was found to be 1.3, which corresponds to the numerical aperture value of 0.35.     

Approximations of solutions to neutral functional differential equations with nonlocal history conditions

This work is concerned with a class of neutral functional differential equations with nonlocal history conditions in a Hilbert space. The approximation of solution to a class of such problems is studied. Moreover, the convergence of Faedo-Galerkin approximation of solution is shown. For illustration, an example is worked out.     

Linear and nonlinear nonlocal boundary value problems for differential-operator equations

This study focuses on nonlocal boundary value problems (BVPs) for linear and nonlinear elliptic differential-operator equations (DOEs) that are defined in Banach-valued function spaces. The considered domain is a region with varying bound and depends on a certain parameter. Some conditions that guarantee the maximal L_p -regularity and Fredholmness of linear BVPs, uniformly with respect to this parameter, are presented. This fact implies that the appropriate differential operator is a generator of an analytic semigroup. Then, by using these results, the existence, uniqueness and maximal smoothness of solutions of nonlocal BVPs for nonlinear DOEs are shown. These results are applied to nonlocal BVPs for regular elliptic partial differential equations, finite and infinite systems of differential equations on cylindrical domains, in order to obtain the algebraic conditions that guarantee the same properties.     

Fredholm boundary value problems for perturbed systems of dynamic equations on time scales

This paper offers conditions ensuring the existence of solutions of linear boundary value problems for systems of dynamic equations on time scales. Utilizing a method of Moore–Penrose pseudo‐inverse matrices leads to an analytical form of a criterion for the existence of solutions in a relevant space and, moreover, to the construction of a family of linearly independent solutions of such problems in a general case with the number of boundary conditions (defined by a linear vector functional) not coinciding with the number of unknowns of a system of dynamic equations. As an example of an application of the presented results, the problem of bifurcation of solutions of boundary value problems for systems of dynamic equations on time scales with a small parameter is considered.