Batra [1] used a linear relationship between the second Piola-Kirchhoff stress tensor S and the Green-St. Venant strain tensor E to study finite simple shearing and finite simple extension deformations of an elastic body. In each case he found that the tangent modulus (i.e. the slope of the shear stress vs. the shear strain curve or the slope of the axial stress vs. the axial stretch curve) is ...

An effective action describing N=1, 2d-induced supergravity in the chi-ral gauge is obtained on the supertorus and on a compact SRS without boundary of arbitrary genus. This action integrates the superconformal Ward identity for the superdiffeomorphism anomaly; it yields the last step in the extension to more complicated topologies of the action initially obtained by A.M. Polyakov on the ordina...

This paper presents some explicit results concerning an extension of the mechanical quadrature technique, namely, the Gauss-Jacobi numerical integration scheme, to the class of integrals whose kernels exhibit second order of singularity (i.e., one degree more singular than Cauchy). In order to ascribe numerical values to these integrals they must be understood in Hadamard's finite-part sense. T...

The Cauchy problem for a quasilinear system of hyperbolic-parabolic equations is addressed with the method linearization and fixed point. Coupling between hyperbolic parabolic variables allowed in we do not assume Friedrich's symmetrizability system. This coupling results linear energy estimates that prevent application Banach's contraction principle. A metric point theorem developed order to c...

Convergence with respect to a valuation is discussed as convergence of a Cauchy sequence. Cauchy sequences of polynomials are defined. They are used to formalize Hensel’s lemma.

The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...

This paper concerns the three-dimensional Cauchy problem of compressible isentropic magneto-micropolar fluid equations with initial density containing vacuum states. Based on energy method and structural characteristics model, we show global existence classical solutions provided that $ \big[(\gamma-1)^\frac{1}{9}+\nu^{-\frac{1}{4}}\big]E_0 is suitably small, where \gamma, \nu $, E_0 represent ...

In this paper we show that sufficiently smooth coefficients of the elliptic operator ∇x · σ(x)∇x − c(x′), x ∈ R, x′ ∈ R can be uniquely determined from the Cauchy data given on a strip in the plane {x3 = 0}. This is an extension of Tikhonov’s formulation of the one-dimensional inverse problem of electric prospecting to two dimensions. In this formulation, the number of variables in the Cauchy d...

We generalize the Davenport transform to prove that, for A = (A,+) a cancellative unital semigroup and X,Y subsets of A such that the smallest subsemigroup generated by Y is commutative, one has that |X + Y | ≥ Ω(X,Y ) := min ( |X|+ |Y | − 1, sup y0∈Y× min y∈Y \{y0} ord(y − y0) ) if 2 ≤ |X|, |Y | < ∞. While extending the Cauchy-Davenport theorem to the broader and abstract setting of (possibly ...