Related papers: On identity theorem for real functions
Density functional theory is usually formulated in terms of the density in configuration space. Functionals of the momentum-space density have also been studied, and yet other densities could be considered. We offer a unified view from a…
Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic…
This overview of integrated information theory (IIT) emphasizes IIT's "consciousness-first" approach to what exists. Consciousness demonstrates to each of us that something exists--experience--and reveals its essential properties--the…
The notion of analyticity is studied in the context of hypercomplex numbers. A critical review of the problems arising from the conventional approach is given. We describe a local analyticity condition which yields the desired type of…
In this paper, we employ the theory of normal families in several complex variables to obtain some uniqueness theorems for entire functions. These results extend the related works of Li and Yi [11], and Lu et al. [18] to the setting of…
Uniqueness quantification ($\exists !$) is a quantifier in first-order logic where one requires that exactly one element exists satisfying a given property. In this paper we investigate the strength of uniqueness quantification when it is…
P. V. Chung showed that there are many multiplicative functions $f$ which satisfy $f(m^2+n^2) = f(m^2)+f(n^2)$ for all positive integers $m$ and $n$. In this article, we show that if more than $2$ squares in the additive condition are…
We prove an interesting identity for the sum of determinants, which is a generalization of the sum of a geometric progression. The proof is quite long and a number of other identities are proved along the way. Some of the more elementary…
In this paper we give simple extension and uniqueness theorems for restricted additive and logarithmic functional equations.
This work establishes a strong uniqueness property for a class of planar locally integrable vector fields. A result on pointwise convergence to the boundary value is also proved for bounded solutions.
In this paper, based on results of exact learning and test theory, we study arbitrary infinite binary information systems each of which consists of an infinite set of elements and an infinite set of two-valued functions (attributes) defined…
Conceiving of premises as collected into sets or multisets, instead of sequences, may lead to triviality for classical and intuitionistic logic in general proof theory, where we investigate identity of deductions. Any two deductions with…
We prove in this paper the uniqueness theorem for a certain class of harmonic functions defined in unbounded domain lying in a band.
This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…
We consider the space of real-valued continuously differentiable functions on a compact subset of a euclidean space. We characterize the completeness of this space and prove that the space of restrictions of continuously differentiable…
We obtain a criterion for an analytic subset of a Euclidean space to contain points of differentiability of a typical Lipschitz function, namely, that it cannot be covered by countably many sets, each of which is closed and purely…
Integrated information theory (IIT) starts from consciousness itself and identifies a set of properties (axioms) that are true of every conceivable experience. The axioms are translated into a set of postulates about the substrate of…
A rigorous mathematical proof is given of a class of vector identities that provide a way to separate an arbitrary vector field (over a linear space) into the sum of a radial (i.e., pointing toward the radial unit vector) vector field,…
For a function defined on an arbitrary subset of a Riemann surface, we give conditions which allow the function to be extended conformally. One folkloric consequence is that two common definitions of an analytic arc in ${\mathbb C}$ are…
Density functional theory (DFT) is a powerful theoretical tool widely used in such diverse fields as computational condensed matter physics, atomic physics, and quantum chemistry. DFT establishes that a system of $N$ interacting electrons…