Related papers: E_\infty-structure and differentials of the Adams …
In this study, a formula for regularized sums of eigenvalues of a Sturm-Liouville problem with retarded argument at the point of discontinuity is obtained. Moreover, oscillation properties of the related problem is investigated.
We address the novel structures arising in quantum and string integrable theories, as well as construct methods to obtain them and provide further analysis. Specifically, we implement the automorphic symmetries on periodic lattice systems…
We compute the 5-local cohomology of a 5-local analogue of the Weierstrass Hopf algebroid used to compute $tmf$ homology. We compute the Adams-Novikov differentials in the cohomology, giving the homotopy, V(0)-homology, and V(1)-homology of…
We construct the Atiyah-Hirzebruch spectral sequence (AHSS) for twisted differential generalized cohomology theories. This generalizes to the twisted setting the authors' corresponding earlier construction for differential cohomology…
We study the spectral sequence that one obtains by applying mod 2 homology to the Goodwillie tower which sends a spectrum X to the suspension spectrum of its 0th space X_0. This converges strongly to H_*(X_0) when X is 0-connected. The E^1…
In the paper, Sturm--Liouville differential operators on time scales consisting of a finite number of isolated points and segments are considered. Such operators unify differential and difference operators. We obtain properties of their…
This work surveys classical and recent advances around the existence of exotic differentiable structures on spheres and its connection to stable homotopy theory.
In 1981, Andr\'e Joyal provided a combinatorial interpretation of the algebra of formal power series, a central gadget in the toolkit of enumerative combinatorics. In Joyal's theory of species of structures, combinatorial species (like…
We consider a hierarchy of graph invariants that naturally extends the spectral invariants defined by F\"urer (Lin. Alg. Appl. 2010) based on the angles formed by the set of standard basis vectors and their projections onto eigenspaces of…
We present an algorithm for constructing numerical solutions to one--dimensional nonlinear, variable coefficient boundary value problems. This scheme is based upon applying the Homotopy Analysis Method (HAM) to decompose a nonlinear…
We explain how the approach of Andre and Quillen to defining cohomology and homology as suitable derived functors extends to generalized (co)homology theories, and how this identification may be used to study the relationship between them.…
Quantum sphere is introduced as a quotient of the so-called Reflection Equation Algebra. This enables us to construct some line bundles on it by means of the Cayley-Hamilton identity whose a quantum version was discovered in \cite{PS},…
Working in a generic derived algebro-geometric context, we lay the foundations for the general study of affineness and local descendability. When applied to $\mathbf{E}_\infty$ rings equipped with the fpqc topology, these foundations give…
The enumerative theory of simplicial subdivisions (triangulations) of simplicial complexes was developed by Stanley in order to understand the effect of such subdivisions on the $h$-vector of a simplicial complex. A key role there is played…
We employ the Goodwillie spectral sequence for the iterated loop space functor in order to provide realizability conditions on certain unstable modules over the Steenrod algebra at an odd prime.
Using techniques in motivic homotopy theory, especially the theorem of Gheorghe, the second and the third author on the isomorphism between motivic Adams spectral sequence for $C{\tau}$ and the algebraic Novikov spectral sequence for…
We present a spectral sequence which efficiently computes Betti numbers of a closed semi-algebraic subset of RP^n defined by a system of quadratic inequalities and the image of the homology homomorphism induced by the inclusion of this…
The multifrequency electrical impedance tomography consists in retrieving the conductivity distribution of a sample by injecting a finite number of currents with multiple frequencies. In this paper we consider the case where the…
The idea of the principle of nested intervals or the concept of convergent sequences which is equivalent to this idea dates back to the ancient world. Archimedes calculated the unknown in excess and deficiency, approximating with two sets…
A semiclassical approach to the universal ergodic spectral statistics in quantum star graphs is presented for all known ten symmetry classes of quantum systems. The approach is based on periodic orbit theory, the exact semiclassical trace…