In this paper the single cycle T-functions are studied. Making use of the explicit formulas of sum and product of 2-adic integers, we present the necessary and sufficient conditions on the generalized polynomial p̃(x) = a0⊕a1x + ⊕ · · · + ⊕adx d(mod2n) being a single cycle T-function. Furthermore, for any given generalized polynomial, we can deduce some expressions about its coefficients by whic...

with a continuous function a and a subcritical growth function g. This type of equation includes the Makutuma equation, when a(|x|) = 1/(1 + |x|2) and g(s) = |s|p−1s, with 1 < p < 2∗ − 1 = (N + 2)/(N − 2), which appears in astrophysics and scalar curvature equations on RN (see, e.g., [15, 17, 18]) In [16] Munyamarere and Willem obtained a result of multiplicity of nodal solutions for these equa...

The stretched-spiral vortex model is used to calculate the velocity-scalar cross spectrum for homogeneous, isotropic turbulence in the presence of a mean scalar gradient. The only nonzero component of the cospectrum is that contributed by the velocity component in the direction of the imposed scalar gradient while the quadrature spectrum is identically zero, in agreement with experiment. For th...

The stretched-spiral vortex model is used to calculate the velocity-scalar cross spectrum for homogeneous, isotropic turbulence in the presence of a mean scalar gradient. The only nonzero component of the cospectrum is that contributed by the velocity component in the direction of the imposed scalar gradient while the quadrature spectrum is identically zero, in agreement with experiment. For th...

The Yamabe invariant Y(M) of a smooth compact manifold is roughly the supremum of the scalar curvatures of unit-volume constant-scalar-curvature Riemannian metrics g on M . (To be precise, one only considers those constant-scalar-curvature metrics which are Yamabe minimizers, but this technicality does not, e.g. affect the sign of the answer.) In this article, it is shown that many 4-manifolds ...

The Yamabe invariant Y(M) of a smooth compact manifold is roughly the supremum of the scalar curvatures of unit-volume constant-scalarcurvature Riemannian metrics g on M . (To be precise, one only considers those constant-scalar-curvature metrics which are Yamabe minimizers, but this technicality does not, e.g., affect the sign of the answer.) In this article, it is shown that many 4-manifolds ...

One of the actual problems for theory and practice control dynamic objects is development methods research synthesis systems multidimensional objects. The paper proposes a universal approach to construct Lyapunov vector functions directly from equation state system new gradient-speed method study aperiodic robust stability linear with m inputs n outputs. automatic based on construction systems....

‎Given a compact space $X$ and a commutative Banach algebra‎ ‎$A$‎, ‎the character spaces of $A$-valued function algebras on $X$ are‎ ‎investigated‎. ‎The class of natural $A$-valued function algebras‎, ‎those whose characters can be described by means of characters of $A$ and‎ ‎point evaluation homomorphisms‎, ‎is introduced and studied‎. ‎For an‎ ‎admissible Banach $A$-valued function algebra...