We develop the theory of twisted L-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on H(M, R) and they generalize the standard notions. A new feature of the twisted L-cohomology theory is that in addition to satisfying the standard L Morse inequalities, they also satisfy certain asymptotic L Morse inequalities. These...

Morse theory could be very well be called critical point theory. The idea is that by understanding the critical points of a smooth function on your manifold, you can recover the topology of your space. This basic idea has blossomed into many Morse theories. For instance, Robin Forman developed a combinatorial adaptation called discrete morse theory. We also have Morse-Bott theory, where we cons...

The scattering phase shifts for n-p have been modeled using various two term exponential type potentials such as Malfliet-Tjon, Manning-Rosen and Morse to study the in S-channels. As a first step, model arameters each of are determined by obtaining binding energy deuteron matrix methods vis-a-vis Variational Monte-Carlo (VMC) technique minimize percentage error w.r.t. experimental value. Then, ...

The increasing popularity of automated tools for software and hardware verification puts ever increasing demands on the underlying decision procedures. This paper presents a framework for distributed decision procedures (for first-order problems) based on Craig interpolation. Formulas are distributed in a lazy fashion, i.e., without the use of costly decomposition algorithms. Potential models w...

Scalar-valued functions are ubiquitous in scientific research. Analysis and visualization of scalar functions defined on low-dimensional and simple domains is a well-understood problem, but complications arise when the domain is high-dimensional or topologically complex. Topological analysis and Morse theory provide tools that are effective in distilling useful information from such difficult s...

some preliminaries about the integrable families of riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional schrodinger equation with the kerr law nonlinearity. finally by using of this method and solutions of ri...

Let f be a Morse function on a closed manifold M , and v be a Riemannian gradient of f satisfying the transversality condition. The classical construction (due to Morse, Smale, Thom, Witten), based on the counting of flow lines joining critical points of the function f associates to these data the Morse complex M * (f, v). In the present paper we introduce a new class of vector fields (f-gradie...

We propose a new ternary infinite (even full-infinite) square-free sequence. The sequence is defined both by an iterative method and by a direct definition. Both definitions are analogous to those of the Thue-Morse sequence. The direct definition is given by a deterministic finite automaton with output. In short, the sequence is automatic.