This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the e...

We consider the problem of minimizing relative perimeter under a volume constraint in an unbounded convex body C ⊂ ...

The writhing number of a curve in Euclidean 3-space, introduced by Călugăreanu (1959-61) and named by Fuller (1971), is the standard measure of the extent to which the curve wraps and coils around itself; it has proved its importance for molecular biologists in the study of knotted duplex DNA and of the enzymes which affect it. The helicity of a vector field defined on a domain in Euclidean 3-s...

We study the relation between the growth of a subharmonic function in the half space R + and the size of its asymptotic set. In particular, we prove that for any n ≥ 1 and 0 < α ≤ n, there exists a subharmonic function u in the R + satisfying the growth condition of order α : u(x) ≤ x−α n+1 for 0 < xn+1 < 1, such that the Hausdorff dimension of the asymptotic set ⋃ λ6=−∞ A(λ) is exactly n−α. He...

In this paper concerns the third-order boundary-value problem u′′′(t) + f(t, u(t), u′(t), u′′(t)) = 0, 0 < t < 1, r1u(0)− r2u(0) = r3u(1) + r4u(1) = u′′(0) = 0. By placing certain restrictions on the nonlinear term f , we prove the existence of at least one solution to the boundary-value problem with the use of lower and upper solution method and of Schauder fixed-point theorem. The constructio...

Synthetic floats are released in an ocean general circulation model to study fluid pathways followed by the upper limb of the meridional overturning circulation from the subtropical South Atlantic to the subtropical North Atlantic. The floats are designed to track this fundamentally three-dimensional, nonisentropic flow while sampling water properties and all terms of the equation governing the...

An upper elemental compositional boundary for fossil hydrocarbons has previously been established as double-bond equivalents (i.e., DBE = rings plus double bonds) not exceeding 90% of the number of carbons. For heteroatom-containing fossil compounds, the 90% rule still applies if each N atom is counted as a C atom. The 90% rule eliminates more than 10% of the possible elemental compositions at ...

We consider a free boundary problem for a system of partial differential equations, which arises in a model of tumor growth with a necrotic core. For any positive number R there exists a radially symmetric stationary solution with free boundary r = R and interior boundary r = ρ.The system depends on a positive parameter μ, and for a sequence of values μ2 < μ3 < · · · there also exist branches o...

In minimal non-critical string theory we show that the principal (r,s) ZZ brane can be viewed as the basic (1,1) ZZ boundary state tensored with the (r,s) Cardy boundary state. In this sense there exists only one ZZ boundary state, the basic (1,1) boundary state.

This paper is concerned with Kolmogorov's two-equation model for turbulence in R 3 $\mathbb {R}^3$ involving the mean velocity u, pressure p, an average frequency ω > 0 $\omega >0$ , and a turbulent kinetic energy k. We consider system space-periodic boundary conditions cube Ω = ( ] [ ) $\Omega =({]0,a[}){}^3$ which good choice studying decay of free motion sufficiently far away from boundaries...